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NOTES - CHAPTER 2 SOLUTIONS
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FOLLOWING ARE SOME THOUGHTS ABOUT THE PROBLEMS AND SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS.
THIS IS, PERHAPS, THE MOST CRITICAL CHAPTER IN THE BOOK IN THAT IT DEALS WITH THE "TIME VALUE OF MONEY (TVM)," A FUNDAMENTAL CONCEPT USED THROUGHOUT THE REST OF THE BOOK.
THERE ARE 180 BASE PROBLEMS, MANY WITH MULTIPLE PARTS, AND MULTIPLE SOLUTIONS FOR MANY OF THOSE PARTS ARE PRESENTED IN THIS SOLUTION MANUAL
THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS. THEY INCLUDE USE OF (1) SIMPLE AND COMPOUND INTEREST FORMULAS, (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEM 5 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" AND "GOAL SEEK" TOOLS, AND (5) BRUTE FORCE TABULAR APPROACHES
THE COMPOUND INTEREST FORMULAS ARE OFTEN THE MOST ONEROUS TO USE, GIVEN THAT THEY REPRESENT THE FUNDAMENTAL MATHEMATICS OF TVM.
THE INTEREST TABLES REPRESENT THE MOST COMMON APPROACH USED HERETOFORE IN "ENGINEERING ECONOMY" COURSES; THEY USUALLY VASTLY SIMPLIFY THE MATHEMATICS INVOLVED BY INCORPORATING ONE OR MORE COMPOUND INTEREST FORMULAS INTO A SINGLE TABULATED "FACTOR" AVAILABLE IN APPENDICES A AND B. SINCE THE INTEREST TABLES ARE FOR ONLY A FINITE (ALTHOUGH VERY LARGE) SET OF INTEREST RATES (i AND j) AND TIME HORIZONS (n), THEY MAY NOT BE AVAILABLE FOR A SPECIFIC SET OF i, j, OR n NEEDED. "ELECTRONIC" INTEREST TABLES ARE AVAILABLE, AND HAVE BEEN USED WHEN UNAVAILABLE TABULATED VALUES OF i, j, AND/OR n HAVE BEEN NEEDED.
PROBLEMS 25, 63, 92, 123, AND 146 ASK FOR THE DEVELOPMENT OF CERTAIN INTEREST FACTORS SUCH AS ARE PRESENTED IN THE INTEREST TABLES. THESE SERVE TO CONVINCE THE STUDENT THAT THERE IS NO "MAGIC" INVOLVED IN THE INTEREST TABLES. IN ADDITION, THE FORMULAS USED IN DEVELOPING THE INTEREST FACTORS HAVE BEEN VERY USEFUL TO THE AUTHORS IN "COPY AND PASTE" OPERATIONS IN THE DEVELOPMENT OF THE CHAPTER 2 SOLUTIONS.
THE EXCEL FUNCTIONS HAVE NOT TRADITIONALLY BEEN WIDELY USED IN TEACHING "ENGINEERING ECONOMY." THEY HAVE, HOWEVER, BEEN USED IN THE WORLD OF FINANCE. THE EXCEL FUNCTIONS ARE WELL DESIGNED, AND PROVIDE A VERY PRECISE TOOL FOR USE IN SOLVING A WIDE ARRAY OF PROBLEMS INVOLVING TVM. BEWARE! FOR THE NOVICE, THESE EXCEL FUNCTIONS MAY APPEAR CONFUSING, COMPLEX, AND NOT WORTH THE TIME TO LEARN. THEY ARE, HOWEVER, QUITE STRAIGHTFORWARD AND CONSISTENT, ONCE ONE GETS PAST THE INITIAL TRIALS OF LEARNING SOMETHING NEW. THEY ARE LIKELY TO BE YOUR FAVORITE METHOD OF PROBLEM SOLUTION IF YOU USE THEM TO SOLVE OR CHECK YOUR SOLUTIONS IN THIS CHAPTER.
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SOMETIMES, YOU WILL NEED TO SOLVE FOR A MONETARY VALUE, AN INTEREST RATE, A TIME INTERVAL, A GRADIENT, OR WHATEVER, NEEDED TO MATCH OTHER PARAMETERS OF A PROBLEM (E.G., WHAT INTEREST RATE MAKES AN INVESTMENT OF $100 WORTH $150 IN THREE YEARS). WHILE IT IS OFTEN POSSIBLE AND CONVENIENT TO USE ANALYTICAL APPROACHES (E.G., ALGEBRA), SOMETIMES THESE SOLUTIONS ARE DIFFICULT AND CUMBERSOME (ANALYTICALLY INTRACTABLE OR NEARLY SO). SEARCH PROCEDURES CAN BE VERY HANDY IN THESE CASES. EXCEL PROVIDES "SOLVER" AND "GOAL SEEK," BOTH OF WHICH RECEIVE SOME USE IN THE SOLUTIONS FOR CHAPTER 2. THE AUTHORS HAVE FOUND SOLVER TO BE QUITE ROBUST AND ACCURATE FOR THE PROBLEMS OF CHAPTER 2. GOAL SEEK, ALTHOUGH CLOSE, IS NOT QUITE AS CONSISTENT. BOTH ARE EASY TO USE.
THE "BRUTE FORCE" TABULAR APPROACH CAN BE VERY USEFUL WHEN A PROBLEM IS VERY COMPLEX AND DIFFICULT TO KEEP IN MIND WHILE ATTEMPTING TO USE AN INTEREST TABLE APPROACH OR AN EXCEL FUNCTION APPROACH. IN THESE INSTANCES, IT IS OFTEN USEFUL TO SIMPLY LIST THE ENTIRE SET OF CASH FLOWS, PERIOD BY PERIOD. THEN, OFTEN AN NPV FUNCTION OR AN FV-PLUS-NPV FUNCTION OR A PMT-PLUS-NPV FUNCTION CAN BE EASILY USED ON THE TABLE. THE BRUTE FORCE TABULAR APPROACH ALSO HAS THE ADVANTAGE THAT THE ENTIRE PATTERN OF CASH FLOWS CAN BE SEEN AND UNDERSTOOD. BE CAREFUL! ACTUALLY, MOST PROBLEMS CAN BE SOLVED USING THE BRUTE FORCE APPROACH - IN FACT, IT IS QUITE COMMONLY USED IN INDUSTRY! FOR NOW, WHILE LEARNING THIS MATERIAL, USE THE BRUTE FORCE APPROACH ONLY AS A LAST RESORT OR AS A PROBLEM CHECK AS HAS BEEN DONE IN THESE SOLUTIONS. TO USE THE BRUTE FORCE APPROACH ALONE IN CHAPTER 2 IS TO NOT LEARN THE OTHER APPROACHES.
IN THIS CHAPTER, WITH MULTIPLE APPROACHES USED IN SOLVING MANY PROBLEMS, THERE ARE OFTEN SLIGHTLY DIFFERENT SOLUTIONS ACHIEVED. THESE ARE NOT WRONG! USUALLY, IF NOT ALWAYS, THE INTEREST FORMULA APPROACH AND THE EXCEL FUNCTION APPROACH WILL BE PRECISELY THE SAME BECAUSE THERE IS VIRTUALLY NO ROUND OFF ERROR WITHIN THE COMPUTER. THE INTEREST TABLE APPROACH WILL BE SLIGHTLY DIFFERENT, DUE TO THE PRESENTATION OF INTEREST FACTORS TO FIVE PLACES AFTER THE DECIMAL IN MOST CASES. MANY TABLES USE ONLY FOUR PLACES. EVEN WITH FIVE PLACES, THERE WILL BE SOME MINOR DISCREPANCIES WHEN COMPARED TO THE EVEN MORE PRECISE APPROACHES. NOTE THAT SUCH DIFFERENCES ARE ALMOST ALWAYS INCONSEQUENTIAL BECAUSE THE ESTIMATES REQUIRED IN ECONOMIC EVALUATIONS ARE USUALLY ONLY APPROXIMATIONS ANYWAY.
EVEN THOUGH MANY PROBLEMS HAVE MULTIPLE PARTS, IT IS NOT INTENDED THAT ALL PARTS OF A PROBLEM NECESSARILY BE ASSIGNED AND WORKED. IN MANY CASES, THE LEARNING THAT TAKES PLACE CAN BE ACHIEVED BY WORKING ONLY ONE OR TWO PARTS. SEE, FOR EXAMPLE, PROBLEM 79.
WHILE MULTIPLE APPROACHES ARE OFTEN USED HEREIN TO SOLVE A PROBLEM, KEEP IN MIND THAT THERE ARE AN INFINITE (LITERALLY) NUMBER OF WAYS A TVM PROBLEM CAN BE SET UP AND SOLVED. TRANSLATION - THE SOLUTIONS PRESENTED HEREIN ARE QUITE DIRECT IN THEIR APPROACH, BUT NOT THE ONLY APPROACH.
PROBLEM 2.1
DCF STANDS FOR "DISCOUNTED CASH FLOW."
THE MOVEMENT OF MONEY FORWARD OR BACKWARD IN TIMEAN EXPLICIT METHOD FOR CONSIDERING THE TIME VALUE OF MONEY
A B123456
PROBLEM 2.2A
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FOUR DCF RULES:
1. MONEY HAS A TIME VALUE
2. MONEY CANNOT BE ADDED OR SUBTRACTED UNLESS IT OCCURS AT THE SAME POINT(S) IN TIME
3. TO MOVE MONEY FORWARD ONE TIME UNIT, MULTIPLY TIMES ONE PLUS THE DISCOUNT OR INTEREST RATE
4. TO MOVE MONEY BACKWARD ONE TIME UNIT, DIVIDE BY ONE PLUS THE DISCOUNT OR INTEREST RATE
B12345
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PROBLEM 2.3A
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456789
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THE WORTH OF THE DEAL RIGHT NOW IS $200 + $100/(1+0.05) = $295.24THE WORTH OF THE DEAL 1 YEAR FROM NOW IS $200*(1+0.05) + $100 = $310.00OR $295.24*(1+0.05) = $310.00
THE WORTH OF THE BUYER'S OFFER RIGHT NOW IS $300/(1+0.05) = $285.71THE WORTH OF THE BUYER'S OFFER 1 YEAR FROM NOW IS $300.00
THE OFFER IS NOT FAIR AND EQUITABLE BECAUSE THE BUYER IS VIOLATING THE DCF RULES. SPECIFICALLY, THE BUYER IS ADDING AND SUBTRACTING MONEY AT DIFFERENT POINTS IN TIME.
B12
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456789
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PROBLEM 2.4
a FAIR AMOUNT NOW = $500 + $500/(1+0.06) = $971.70
b FAIR AMOUNT 1 YEAR FROM NOW = $500*(1+0.06) + $500 = $1030.00OR $971.70*(1+0.06) = $1030.00
A B123456
PROBLEM 2.5
CFD FROM BANK'S PERSPECTIVE
NOT NECESSARILY TO SCALE
(+) $X $X $X $X
0 1 2 3 4
(-)
$2,000
A B C D E F G123456789
101112131415
PROBLEM 2.6
CFD FROM YOUR PERSPECTIVE
NOT NECESSARILY TO SCALE
$10,000
$4,000
(+)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
(-)$2,880 $2,880 $2,880 $2,880 $2,880
$2,880 $2,880 $2,880 $2,880 $2,880
A B C D E F G H I J K L M N O123456789
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P123456789
10111213141516171819202122
PROBLEM 2.7
FROM KAELYN'S GRANDFATHER'S PERSPECTIVE$X+6000
NOT NECESSARILY TO SCALE $X+4500$X+3000
$X+1500(+) $X
$2,000
0 1 2 3 4 5 6 7 8 9 10 11
(-)
$30,000
A B C D E F G H I J K L M N123456789
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PROBLEM 2.8
CFD FROM DAVID'S PERSPECTIVE
NOT NECESSARILY TO SCALE
$150,000
(+)
0 1 2 3 4 5 6 7 8
(-) $20,000 $20,000 $X
$X+8000$X+16,000
$X+24,000
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$X+24,000
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PROBLEM 2.9
CFD OF MERCRUISER CNC MACHINE
NOT NECESSARILY TO SCALE
(+) $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000
0 1 2 3 4 5 6 7 8 9 10$1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000
(-) $1000+5000
SINCE PLANNING HORIZON IS 10 YEARS,WOULD NOT SHOW UPGRADE AT YEAR 10
$50,000
A B C D E F G H I J K L M123456789
1011121314151617181920212223
PROBLEM 2.10
CFD OF APARTMENT RENT
NOT NECESSARILY TO SCALE $450
(+)
0 1 2 3 4 5 6 7 8 9 10 11 12
(-) $150
$550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150
$550+450
A B C D E F G H I J K L M N123456789
101112131415161718192021
O123456789
101112131415161718192021
PROBLEM 2.11
USA DENIM (TWO MACHINES)
NOT NECESSARILY TO SCALE
0 1 2 3 4 5 6 7
(-)
$12,000 $14,000
$16,000 $18,000
$20,000
$30,000
$38,000
$30,000+24,000
A B C D E F G H I123456789
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$22,000
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PROBLEM 2.12
LASER CUTTING MACHINE CFD
NOT NECESSARILY TO SCALE
$14,000 $14,000 $14,000 $14,000 $14,000 $14,000
(+)
0 1 2 3 4 5 6$2,000
(-) $3,000 $4,000 $5,000
$23,000
A B C D E F G H I123456789
101112131415161718192021222324252627
PROBLEM 2.13
CFD OF SYNTHETIC RUBBER BLENDING MACHINE
NOT NECESSARILY TO SCALE$24,000-4000+8000-1600
$24,000-4000 $24,000-4000 $24,000-4000$18,000-1600 $24,000-4000 $24,000-4000 $24,000-4000
$12,000-1200$10,000-800
(+)
0 1 2 3 4 5 6 7 8 9 10
(-)
$62,000+8000
A B C D E F G H I J K L M123456789
1011121314151617181920212223242526272829303132
PROBLEM 2.14
i= 5.00%n= 12F= $8,000
a P= $5,000 USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+0.05*12)
b P= $4,454.70 USING COMPOUND INTEREST FORMULA THIS IS =8000/(1+0.05)^12
P= $4,454.72 USING THE INTEREST TABLES THIS IS=$8,000*(P|F 5%,12)
P= $4,454.70 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,12,,-8000)
A B C D E F G123456789
1011121314
PROBLEM 2.15
ACCT
1 i= 5.50% SIMPLE INTERESTn= 5P= $10,000.00
F= $12,750.00 USING SIMPLE INTEREST FORMULA THIS IS =10000*(1+0.055*5)
2 i= 5.00% COMPOUNDED ANNUALLYn= 5P= $10,000.00
F= $12,762.82 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.05)^5
F= $12,762.80 USING THE INTEREST TABLES THIS IS $10,000*(F|P 5%,5)
F= $12,762.82 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,5,,-10000)
3 i= 6.50% SIMPLE INTERESTn= 5P= $10,000.00
F= $13,250.00 USING SIMPLE INTEREST FORMULA THIS IS =10000*(1+0.065*5)
4 i= 6.00% COMPOUNDED ANNUALLYn= 5P= $10,000.00
F= $13,382.26 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.06)^5
F= $13,382.30 USING THE INTEREST TABLES THIS IS= $10,000*(F|P 6%,5)
F= $13,382.26 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,5,,-10000)
ACCOUNT 1 2 3 4AMOUNT $12,750.00 $12,762.82 $13,250.00 $13,382.26
ACCOUNT 4 IS PREFERRED SINCE IT GIVES THE HIGHEST FUTURE VALUE
A B C D E F G123456789
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PROBLEM 2.16
a i= 8.00% SIMPLE INTERESTn= 3P= $1,000.00
F= $1,240.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.08*3)
TOTAL INTEREST $240.00 THIS IS THE FUTURE VALUE OF $1,240 MINUSTHE PRESENT VALUE OF $1,000
b i= 8.00% COMPOUNDED ANNUALLYn= 3P= $1,000.00
F= $1,259.71 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^3
F= $1,259.71 USING INTEREST TABLES THIS IS= $1,000*(F|P 8%,3)
F= $1,259.71 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,3,,-1000)
TOTAL INTEREST $259.71 THIS IS THE FUTURE VALUE OF $1,259.71 MINUSTHE PRESENT VALUE OF $1,000.
A B C D E F G123456789
10111213141516171819202122232425
USING COMPOUND INTEREST FORMULAS THIS IS
H123456789
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PROBLEM 2.17
a i= 12.00% SIMPLE INTERESTn= 5P= $3,000.00
F= $4,800.00 USING SIMPLE INTEREST FORMULA THIS IS =3000*(1+.012*5)
b i= 12.00% COMPOUNDED ANNUALLYn= 5P= $3,000.00
F= $5,287.03 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.12)^5
F= $5,287.02 USING INTEREST TABLES THIS IS=$3,000*(F|P 12%,5)
F= $5,287.03 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,5,,-3000)
A B C D E F G H123456789
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PROBLEM 2.18
a i= 5.00%n= 3P= $1,000.00
F= $1,150.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.05*3)
b TOTAL INTEREST $150.00
c i= 5.00%n= 3P= $1,000.00
F= $1,157.63 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.05)^3
F= $1,157.63 USING INTEREST TABLES THIS IS=$1,000*(F|P 5%,3)
F= $1,157.63 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,3,,-1000)
d TOTAL INTEREST $157.63 THIS IS THE FUTURE VALUE OF $1,157.63 MINUSTHE PRESENT VALUE OF $1,000.
A B C D E F G123456789
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USING COMPOUND INTEREST FORMULAS THIS IS
H123456789
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PROBLEM 2.19
UNCLE ESWARi= 8.00% COMPOUNDED ANNUALLYn= 5P= $5,000.00
F= $7,346.64 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.08)^5
F= $7,346.65 USING INTEREST TABLES THIS IS =$5,000*(F|P 8%,5)
F= $7,346.64 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,5,,-5000)
UNCLE SHANKARi= 9.00% SIMPLE INTERESTn= 5P= $5,000.00
F= $7,250.00 USING SIMPLE INTEREST FORMULA THIS IS =5000*(1+0.09*5)
GO WITH UNCLE SHANKAR'S LOAN
A B C D E F G123456789
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PROBLEM 2.20
a i= 8.00%n= 10F= $8,000.00
P= $3,705.55 USING COMPOUND INTEREST FORMULAS THIS IS =8000/(1+0.08)^10
P= $3,705.52 USING INTEREST TABLES THIS IS =$8,000*(P|F 8%,10)
P= $3,705.55 USING EXCEL'S PV FUNCTION THIS IS=PV(8%,10,,-8000)
b i= 11.59% USING SIMPLE INTEREST FORMULA THIS IS =(8000-3705.52)/(3705.52*10)
OR, CAN USE SOLVER TO FIND VALUE OF i
i= 11.59% <--SOLVER CHANGED CELLn= 10F= $8,000.00
P= $3,705.55 <--SOLVER TARGET CELLUSING SIMPLE INTEREST FORMULA THIS IS =8000/(1+i*10)
A B C D E F123456789
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PROBLEM 2.21
a i= 6.00%n= 4P= $12,000.00
F= $15,149.72 USING COMPOUND INTEREST FORMULAS THIS IS =12000*(1+0.06)^4
F= $15,149.76 USING INTEREST TABLES THIS IS =$12,000*(F|P 6%,4)
F= $15,149.72 USING EXCEL'S FV FUNCTION THIS IS=FV(6%,4,,-12000)
b i= 6.56% USING SIMPLE INTEREST FORMULA THIS IS =(15149.72-12000)/(12000*4)
OR, CAN USE SOLVER TO FIND VALUE OF i
i= 6.56% <--SOLVER CHANGED CELLn= 4P= $12,000.00
F= $15,149.72 <--SOLVER TARGET CELLUSING SIMPLE INTEREST FORMULA THIS IS =12000*(1+i*4)
A B C D E F123456789
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PROBLEM 2.22
i= 7.00%n= 5P= $11,000.00
F= $15,428.07 USING COMPOUND INTEREST FORMULAS THIS IS =11000*(1+0.07)^5
F= $15,428.08 USING INTEREST TABLES THIS IS =$11,000*(F|P 7%,5)
F= $15,428.07 USING EXCEL'S FV FUNCTION THIS IS=FV(7%,5,,-11000)
PRINCIPAL $11,000.00 FINAL AMT $15,428.07 INTEREST $4,428.07 =15428.07-11000.00
A B C D E F G H123456789
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PROBLEM 2.23
i= 8.00%n= 4P= $2,500.00
AT THE END OF 4 YEARS AT 8% SIMPLE INTEREST THE MAN HAS:F= $3,300.00 USING SIMPLE INTEREST FORMULA THIS IS
=2500*(1+0.08*4)
NOW, REINVESTING THE $3,300.00 FOR 9 YEARS RESULTS INi= 6.00%n= 9P= $3,300.00
AT THE END OF 9 MORE YEARS AT 6% COMPOUND INTEREST THE MAN HAS:F= $5,575.28 USING COMPOUND INTEREST FORMULAS THIS IS
=3300*(1+0.06)^9F= $5,575.28 USING INTEREST TABLES THIS IS
=$3,300*(F|P 6%,9)F= $5,575.28 USING EXCEL'S FV FUNCTION THIS IS
=FV(6%,9,,-3300)
A B C D E F G H I123456789
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PROBLEM 2.24
ACCOUNT1 i= 7.00%
n= 4P= $10,000.00
F= $13,107.96 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.07)^4
F= $13,108.00 USING INTER10,000*(F|P 7%,4)=$10,000*(F|P 7%,4)
F= $13,107.96 USING EXCEL'S FV FUNCTION THIS IS=FV(7%,4,,-10000)
2 i= 7.50%n= 4P= $10,000.00
F= $13,000.00 USING SIMPLE INTEREST FORMULA THIS IS =10000*(1+0.075*4)
3 i= 7.50%n= 4P= $10,000.00
F= $13,354.69 USING COMPOUND INTEREST FORMULAS THIS IS $13,354.69
F= $13,354.70 USING INTEREST TABLES (USER TAB) THIS IS =$10,000*(F|P 7.5%,4)
F= $13,354.69 USING EXCEL'S FV FUNCTION THIS IS=FV(7.5%,4,,-10000)
4 i= 8.25%n= 4P= $10,000.00
F= $13,300.00 USING SIMPLE INTEREST FORMULA THIS IS =10000*(1+0.0825*4)
ACCOUNT 1 2 3AMOUNT OWED $13,107.96 $13,000.00 $13,354.69
PREFER LOAN 2
A B C D E F G123456789
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USING COMPOUND INTEREST FORMULAS THIS IS
USING SIMPLE INTEREST FORMULA THIS IS
USING COMPOUND INTEREST FORMULAS THIS IS
USING INTEREST TABLES (USER TAB) THIS IS
USING SIMPLE INTEREST FORMULA THIS IS
4$13,300.00
H123456789
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PROBLEM 2.25
F|P
i= 8.00%n= 3
(F|P i%,n) = 1.25971 USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.08)^3
P|F
i= 10.00%n= 20
(P|F i%,n) = 0.14864 USING COMPOUND INTEREST FORMULAS THIS IS =1/(1+0.1)^20
CHECKS OK WITH APPENDIX A
A B C D E F G H123456789
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PROBLEM 2.26
i= 8.00%n= 5P= $25,000.00
F= $36,733.20 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.08)^5
F= $36,733.25 USING INTEREST TABLES THIS IS =$25,000*(F|P 8%,5)
F= $36,733.20 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,5,,-25000)
A B C D E F G H123456789
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PROBLEM 2.27
i= 4.00%n= 10F= $100,000.00
P= $67,556.42 USING COMPOUND INTEREST FORMULAS THIS IS =100000/(1+0.04)^10
P= $67,556.00 USING INTEREST TABLES THIS IS =$100,000*(P|F 4%,10)
P= $67,556.42 USING EXCEL'S PV FUNCTION THIS IS=PV(4%,10,,-100000)
A B C D E F G123456789
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PROBLEM 2.28
i= 7.00%n= 10P= $25,000.00
F= $49,178.78 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.07)^10
F= $49,178.75 USING INTER25,000*(F|P 7%,10)=$25,000*(F|P 7%,10)
F= $49,178.78 USING EXCEL'S FV FUNCTION THIS IS=FV(7%,10,,-25000)
A B C D E F G123456789
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PROBLEM 2.29
i= 5.00%n= 25F= $150,000.00
P= $44,295.42 USING COMPOUND INTEREST FORMULAS THIS IS =150000/(1+0.05)^25
P= $44,295.00 USING INTEREST TABLES THIS IS =$150,000*(P|F 5%,25)
P= $44,295.42 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,25,,-150000)
A B C D E F G123456789
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PROBLEM 2.30
P= $0.04n= 49F= $0.41
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 4.8641% =(0.41/0.04)^(1/49)-1
OR, CAN USE RATE FUNCTIONP= $0.04n= 49F= $0.41
i= 4.8641% =RATE(49,,-0.04,0.41)
OR, CAN USE SOLVERP= $0.04 n= 49i= 4.8641% <--SOLVER CHANGED CELL
F= $0.41 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$0.04*(1+i)^49
F= $0.41 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,49,,-0.04)
A B C D E F G H123456789
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PROBLEM 2.31
a i= 8.00% COMPOUNDED ANNUALLYn= 10P= $1,000.00
F= $2,158.92 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^10
F= $2,158.92 USING INTEREST TABLES THIS IS $1,000*(F|P 8%,10)
F= $2,158.92 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,10,,-1000)
b i= 11.00%n= 4P= $5,000.00
F= $7,590.35 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.11)^4
F= $7,590.35 USING INTEREST TABLES THIS IS $5,000*(F|P 11%,4)
F= $7,590.35 USING EXCEL'S FV FUNCTION THIS IS=FV(11%,4,,-5000)
c i= 9.00% COMPOUNDED ANNUALLYn= 7P= $13,000.00
F= $23,764.51 USING COMPOUND INTEREST FORMULAS THIS IS =13000*(1+0.09)^7
F= $23,764.52 USING INTEREST TABLES THIS IS $13,000*(F|P 9%,7)
F= $23,764.51 USING EXCEL'S FV FUNCTION THIS IS =FV(9%,7,,-13000)
d i= 10.00% COMPOUNDED ANNUALLYn= 3P= $25,000.00
F= $33,275.00 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.1)^3
F= $33,275.00 USING INTEREST TABLES THIS IS $25,000*(F|P 10%,3)
F= $33,275.00 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,3,,-25000)
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PROBLEM 2.32
a i= 5.00%n= 6F= $10,000.00
P= $7,462.15 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.05)^6
P= $7,462.20 USING INTEREST TABLES THIS IS =$10,000*(P|F 5%,6)
P= $7,462.15 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,6,,-10000)
b i= 8.00%n= 4F= $6,500.00
P= $4,777.69 USING COMPOUND INTEREST FORMULAS THIS IS =6500/(1+0.08)^4
P= $4,777.70 USING INTEREST TABLES THIS IS =$6,500*(P|F 8%,4)
P= $4,777.69 USING EXCEL'S PV FUNCTION THIS IS=PV(8%,4,,-6500)
c i= 6.00%n= 12F= $3,400.00
P= $1,689.70 USING COMPOUND INTEREST FORMULAS THIS IS =3400/(1+0.06)^12
P= $1,689.70 USING INTEREST TABLES THIS IS =$3,400*(P|F 6%,12)
P= $1,689.70 USING EXCEL'S PV FUNCTION THIS IS=PV(6%,12,,-3400)
d i= 10.00%n= 5F= $13,500.00
P= $8,382.44 USING COMPOUND INTEREST FORMULAS THIS IS =13500/(1+0.1)^5
P= $8,382.42 USING INTEREST TABLES THIS IS =$13,500*(P|F 10%,5)
P= $8,382.44 USING EXCEL'S PV FUNCTION THIS IS=PV(10%,5,,-13500)
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PROBLEM 2.33
a i= 14.00% COMPOUNDED ANNUALLYn= 7P= $3,000.00
F= $7,506.81 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.14)^7
F= $7,506.81 USING ELECTRONIC INTEREST TABLES THIS IS =$3,000*(F|P 14%,7)
F= $7,506.81 USING EXCEL'S FV FUNCTION THIS IS =FV(14%,7,,-3000)
b i= 12.00%n= 17P= $1,600.00
F= $10,985.67 USING COMPOUND INTEREST FORMULAS THIS IS =1600*(1+0.12)^17
F= $10,985.66 USING INTEREST TABLES THIS IS =$1,600*(F|P 12%,17)
F= $10,985.67 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,17,,-1600)
c i= 16.00% COMPOUNDED ANNUALLYn= 38P= $20,000.00
F= $5,629,030.30 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.16)^38
F= $5,629,030.20 USING ELECTRONIC INTEREST TABLES THIS IS =$20,000*(F|P 16%,38)
F= $5,629,030.30 USING EXCEL'S FV FUNCTION THIS IS =FV(16%,38,,-20000)
d i= 8.00% COMPOUNDED ANNUALLYn= 71P= $3,500.00
F= $826,332.21 USING COMPOUND INTEREST FORMULAS THIS IS =3500*(1+0.08)^71
F= $826,332.22 USING ELECTRONIC INTEREST TABLES THIS IS =$3,500*(F|P 8%,71)
F= $826,332.21 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,71,,-3500)
e i= 11.50% COMPOUNDED ANNUALLYn= 34P= $5,000.00
F= $202,448.93 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.115)^34
F= $202,448.95 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 11.5%,34)
F= $202,448.93 USING EXCEL'S FV FUNCTION THIS IS
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=FV(11.5%,34,,-5000)A B C D E F G H
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PROBLEM 2.34
a i= 9.00%n= 5F= $19,000.00
P= $12,348.70 USING COMPOUND INTEREST FORMULAS THIS IS =19000/(1+0.09)^5
P= $12,348.67 USING INTEREST TABLES THIS IS =$19,000*(P|F 9%,5)
P= $12,348.70 USING EXCEL'S PV FUNCTION THIS IS=PV(9%,5,,-19000)
b i= 15.00%n= 12F= $8,300.00
P= $1,551.33 USING COMPOUND INTEREST FORMULAS THIS IS =8300/(1+0.15)^12
P= $1,551.35 USING INTEREST TABLES THIS IS =$8,300*(P|F 15%,12)
P= $1,551.33 USING EXCEL'S PV FUNCTION THIS IS=PV(15%,12,,-8300)
c i= 12.00%n= 53F= $6,200.00
P= $15.27 USING COMPOUND INTEREST FORMULAS THIS IS =6200/(1+0.12)^53
P= $15.27 USING ELECTRONIC INTEREST TABLES THIS IS =$6,200*(P|F 12%,53)
P= $15.27 USING EXCEL'S PV FUNCTION THIS IS=PV(12%,53,,-6200)
d i= 19.20%n= 18F= $13,000.00
P= $550.77 USING COMPOUND INTEREST FORMULAS THIS IS =13000/(1+0.192)^18
P= $550.81 USING ELECTRONIC INTEREST TABLES THIS IS =$13,000*(P|F 19.2%,18)
P= $550.77 USING EXCEL'S PV FUNCTION THIS IS=PV(19.2%,18,,-13000)
e i= 8.00%n= 10F= $5,000.00
P= $2,315.97 USING COMPOUND INTEREST FORMULAS THIS IS =5000/(1+0.08)^10
P= $2,315.95 USING INTEREST TABLES THIS IS =$5,000*(P|F 8%,10)
P= $2,315.97 USING EXCEL'S PV FUNCTION THIS IS
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=PV(8%,10,,-5000)A B C D E F G H
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PROBLEM 2.35
a P= $10,000.00n= 10F= $23,674.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 9.0002% =(23674/10000)^(1/10)-1
OR, CAN USE RATE FUNCTIONP= $10,000.00n= 10F= $23,674.00
i= 9.0002% =RATE(10,,-10000,23674)
OR, CAN USE SOLVERP= $10,000.00 n= 10
i= 9.0002% <--SOLVER CHANGED CELL
F= $23,674.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$10,000*(1+i)^10
F= $23,674.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,10,,-10000)
b P= $2,000.00n= 18F= $15,380.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 12.0000% =(15380/2000)^(1/18)-1
OR, CAN USE RATE FUNCTIONP= $2,000.00n= 18F= $15,380.00
i= 12.0000% =RATE(18,,-2000,15380)
OR, CAN USE SOLVER
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P= $2,000.00 n= 18
i= 12.0000% <--SOLVER CHANGED CELL
F= $15,380.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2000*(1+i)^18
F= $15,380.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,18,,-2000)
c P= $2,500.00n= 5F= $4,212.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 10.9966% =(4212/2500)^(1/5)-1
OR, CAN USE RATE FUNCTIONP= $2,500.00n= 5F= $4,212.00
i= 10.9966% =RATE(5,,-2500,4212)
OR, CAN USE SOLVERP= $2,500.00 n= 5
i= 10.9966% <--SOLVER CHANGED CELL
F= $4,212.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2500*(1+i)^5
F= $4,212.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,5,,2500)
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PROBLEM 2.36
i= 11.00%n= 9F= $15,000.00
a P= $5,863.80 USING INTEREST TABLES THIS IS =$15,000*(P|F 11%,9)
b P= $5,863.87 USING COMPOUND INTEREST FORMULAS THIS IS =15000/(1+0.11)^9
c P= $5,863.87 USING EXCEL'S PV FUNCTION THIS IS=PV(11%,9,,-15000)
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PROBLEM 2.37
i= 8.00%
CHOICE 1: TAKE TODAYP= $1,000.00 ALREADY AT TIME 0
CHOICE 2: WAIT 3 YEARS AND TAKEF= $1,500.00 n= 3
P= $1,190.75 USING COMPOUND INTEREST FORMULAS THIS IS =1500/(1+0.08)^3
P= $1,190.75 USING INTEREST TABLES THIS IS =$1,500*(P|F 8%,3)
P= $1,190.75 USING EXCEL'S PV FUNCTION THIS IS=PV(8%,3,,-1500)
CHOICE 3: WAIT 5 YEARS AND TAKEF= 3000n= 5
P= $2,041.75 USING COMPOUND INTEREST FORMULAS THIS IS =3000/(1+0.08)^5
P= $2,041.74 USING INTEREST TABLES THIS IS =$3,000*(P|F 8%,5)
P= $2,041.75 USING EXCEL'S PV FUNCTION THIS IS=PV(8%,5,,-3000)
FOR EACH OF THE 3 CHOICES, DETERMINE THE VALUE AT THE SAME POINT IN TIME. BELOW, THE POINT IN TIME WILL BE THE PRESENT (TIME 0)
THE HIGHEST PRESENT VALUE IS ACHIEVED BY TAKING THE $3,000 AFTER 5 YEARS
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PROBLEM 2.38
i= 10.00%n= 7F= $23,384.61
TO FIND HOW MUCH HE BORROWED, FIND THE PW OF THE LOAN PAYOFF
P= $12,000.00 USING COMPOUND INTEREST FORMULAS THIS IS =23384.61/(1+0.1)^7
P= $12,000.05 USING INTEREST TABLES THIS IS =$23,384.61*(P|F 10%,7)
P= $12,000.00 USING EXCEL'S PV FUNCTION THIS IS=PV(10%,7,,-23384.61)
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PROBLEM 2.39
i= 11.50%n= 37SET THE FUTURE WORTH AT $1.00F= $1.00
THE (P|F 11.5%,37) FACTOR IS
P= 0.0178168 USING COMPOUND INTEREST FORMULAS THIS IS =1/(1+0.115)^37
P= 0.0178168 USING EXCEL'S PV FUNCTION THIS IS=PV(11.5%,37,,-1)
BOTH RESULTS ARE IDENTICAL
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PROBLEM 2.40
i= 12.00%n= 7F= $6,000.00
a P= $2,714.10 USING INTEREST TABLES THIS IS =$6,000*(P|F 12%,7)
b P= $2,714.10 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^7
c P= $2,714.10 USING EXCEL'S PV FUNCTION THIS IS=PV(12%,7,,-6000)
TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE WITHDRAWAL
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TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE
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PROBLEM 2.41
P= $5,000.00n= 10F= $8,955.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 6.0009% =(8955/5000)^(1/10)-1
OR, CAN USE RATE FUNCTIONP= $5,000.00n= 10F= $8,955.00
i= 6.0009% =RATE(10,,-5000,8955)
OR, CAN USE SOLVERP= $5,000.00 n= 10
i= 6.0009% <--SOLVER CHANGED CELL
F= $8,955.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$5,000*(1+i)^10
F= $8,955.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,10,,-5000)
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PROBLEM 2.42
P= $1,500.00n= 3F= $2,500.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 18.5631% =(2500/1500)^(1/3)-1
OR, CAN USE RATE FUNCTIONP= $1,500.00n= 3F= $2,500.00
i= 18.5631% =RATE(3,,-1500,2500)
OR, CAN USE SOLVERP= $1,500.00 n= 3
i= 18.5631% <--SOLVER CHANGED CELL
F= $2,500.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1,500*(1+i)^3
F= $2,500.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,3,,-1500)
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PROBLEM 2.43
P= $2,500.00i= 5.00%F= $4,430.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 11.73 =LN(4430/2500)/LN(1+0.05)USE 12 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $2,500.00i= 5.00%F= $4,430.00
n= 11.73 =NPER(5%,,-2500,4430)USE 12 YEARS
OR, CAN USE SOLVERP= $2,500.00 i= 5.00%
n= 11.73 <--SOLVER CHANGED CELLUSE 12 YEARS
F= $4,430.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n
F= $4,430.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(5%,n,,-2500)
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PROBLEM 2.44
a P= $1.00n= 10F= $2.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 7.1773% =(2/1)^(1/10)-1
OR, CAN USE RATE FUNCTIONP= $1.00n= 10F= $2.00
i= 7.1773% =RATE(10,,-1.00,2.00)
b P= $1.00n= 10F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 11.6123% =(3/1)^(1/10)-1
OR, CAN USE RATE FUNCTIONP= $1.00n= 10F= $3.00
i= 11.6123% =RATE(10,,-1.00,3.00)
c P= $1.00n= 10F= $4.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 14.8698% =(4/1)^(1/10)-1
OR, CAN USE RATE FUNCTIONP= $1.00n= 10F= $4.00
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i= 14.8698% =RATE(10,,-1,4)
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PROBLEM 2.45
P= $1.00i= 9.00%F= $2.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 8.04 =LN(2/1)/LN(1+0.09)USE 9 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 9.00%F= $2.00
n= 8.04 =NPER(5%,,-2500,4430)USE 9 YEARS
OR, CAN USE SOLVERP= $1.00 i= 9.00%
n= 8.04 <--SOLVER CHANGED CELLUSE 9 YEARS
F= $2.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n
F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(5%,n,,-2500)
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PROBLEM 2.46
P= $1.00i= 6.00%F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 18.85 =LN(3/1)/LN(1+0.06)USE 19 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 6.00%F= $3.00
n= 18.85 =NPER(6%,,-1.00,3.00)USE 19 YEARS
OR, CAN USE SOLVERP= $1.00 i= 6.00%
n= 18.85 <--SOLVER CHANGED CELLUSE 19 YEARS
F= $3.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n
F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(6%,n,,-1.00)
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PROBLEM 2.47
P= $1.00n= 10F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 11.6123% =(3/1)^(1/10)-1USE 12%
OR, CAN USE RATE FUNCTIONP= $1.00n= 10F= $3.00
i= 11.6123% =RATE(10,,-1,3)USE 12%
OR, CAN USE SOLVERP= $1.00 n= 10
i= 11.6123% <--SOLVER CHANGED CELLUSE 12%
F= $3.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+i)^10
F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,10,,-1)
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PROBLEM 2.48
a P= $1.00i= 6.00%F= $2.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 11.90 =LN(2/1)/LN(1+0.06)USE 12 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 6.00%F= $2.00
n= 11.90 =NPER(6%,,-1.00,2.00)USE 12 YEARS
OR, CAN USE SOLVERP= $1.00 i= 6.00%
n= 11.90 <--SOLVER CHANGED CELLUSE 12 YEARS
F= $2.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n
F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(6%,n,,-1.00)
b P= $1.00i= 6.00%F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 18.85 =LN(3/1)/LN(1+0.06)USE 19 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 6.00%F= $3.00
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n= 18.85 =NPER(6%,,-1.00,3.00)USE 19 YEARS
OR, CAN USE SOLVERP= $1.00 i= 6.00%
n= 18.85 <--SOLVER CHANGED CELLUSE 19 YEARS
F= $3.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n
F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(6%,n,,-1.00)
c P= $1.00i= 6.00%F= $4.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)
n= 23.79 =LN(4/1)/LN(1+0.06)USE 24 YEARS
OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 6.00%F= $4.00
n= 23.79 =NPER(6%,,-1.00,4.00)USE 24 YEARS
OR, CAN USE SOLVERP= $1.00 i= 6.00%
n= 23.79 <--SOLVER CHANGED CELLUSE 24 YEARS
F= $4.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n
F= $4.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS
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PROBLEM 2.49
a i= 5.00%
APPR 1 APPR 2 APPR 314.40000 F|P 5%,14 1.97993 14.20670
=72/(100*0.05) F|P 5%,15 2.07893 =LOG(2)/LOG(1+0.05)INTERPOLATING 14.20273=14+(2-1.97993)/(2.07893-1.97993)
APPR 4 APPR 514.20670 n= 14.20670 <--SOLVER CHANGED CELL
=NPER(5%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(5%,n,,-1)
APPR 6n= 14.20658 <--GOAL SEEK CHANGED CELLF= $2.00 <--GOAL SEEK SET CELL
=FV(5%,n,,-1)
b i= 7.00%
APPR 1 APPR 2 APPR 310.28571 F|P 7%,10 1.96715 10.24477
=72/(100*0.07) F|P 7%,11 2.10485 =LOG(2)/LOG(1+0.07)INTERPOLATING 10.23856=10+(2-1.96715)/(2.10485-1.96715)
APPR 4 APPR 510.24477 n= 10.24477 <--SOLVER CHANGED CELL
=NPER(7%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(7%,n,,-1)
APPR 6n= 10.24499 <--GOAL SEEK CHANGED CELLF= $2.00 <--GOAL SEEK SET CELL
=FV(5%,n,,-1)
c i= 10.00%
APPR 1 APPR 2 APPR 37.20000 F|P 10%,7 1.94872 7.27254
=72/(100*0.10) F|P 10%,8 2.14359 =LOG(2)/LOG(1+0.10)INTERPOLATING 7.26315=7+(2-1.94872)/(2.14359-1.94872)
APPR 4 APPR 57.27254 n= 7.27254 <--SOLVER CHANGED CELL
=NPER(10%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(10%,n,,-1)
APPR 6n= 7.27432 <--GOAL SEEK CHANGED CELL
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F= $2.00 <--GOAL SEEK SET CELL=FV(5%,n,,-1)
d i= 15.00%
APPR 1 APPR 2 APPR 34.80000 F|P 15%,4 1.74901 4.95948
=72/(100*0.15) F|P 15%,5 2.01136 =LOG(2)/LOG(1+0.15)INTERPOLATING 4.95670=4+(2-1.74901)/(2.01136-1.74901)
APPR 4 APPR 54.95948 n= 4.95948 <--SOLVER CHANGED CELL
=NPER(15%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(15%,n,,-1)
APPR 6n= 4.96242 <--GOAL SEEK CHANGED CELLF= $2.00 <--GOAL SEEK SET CELL
=FV(5%,n,,-1)
e i= 20.00%
APPR 1 APPR 2 APPR 33.60000 F|P 20%,3 1.72800 3.80178
=72/(100*0.20) F|P 20%,4 2.07360 =LOG(2)/LOG(1+0.20)INTERPOLATING 3.78704=3+(2-1.728)/(2.0736-1.728)
APPR 4 APPR 53.80178 n= 3.80178 <--SOLVER CHANGED CELL
=NPER(20%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(20%,n,,-1)
APPR 6n= 3.80304 <--GOAL SEEK CHANGED CELLF= $2.00 <--GOAL SEEK SET CELL
=FV(5%,n,,-1)
A B C D E F G H56575859606162636465666768697071727374757677787980818283848586878889909192939495
PROBLEM 2.50
P= $176,000.00n= 9F= $525,000.00
USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1
i= 12.9116% =(525000/176000)^(1/9)-1
OR, CAN USE RATE FUNCTIONP= $176,000.00n= 9F= $525,000.00
i= 12.9116% =RATE(9,,-176000,525000)
OR, CAN USE SOLVERP= $176,000.00 n= 9
i= 12.9116% <--SOLVER CHANGED CELL
F= $525,000.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$176000.00*(1+i)^9
F= $525,000.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,9,,-176000)
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PROBLEM 2.51
i= 8.50%n= 10-4= 6P= $5,000.00
FINDING FW AT END OF YEAR 10 OF DEPOSIT AT END OF YEAR 4
F= $8,157.35 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 8.5%,6)
F= $8,157.34 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.085)^6
F= $8,157.34 USING EXCEL'S FV FUNCTION THIS IS=FV(8.5%,6,,-5000)
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PROBLEM 2.52
i= 12.00%n= 40F= $15,000,000.00
P= $161,201.97 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^40
P= $161,250.00 USING INTEREST TABLES THIS IS =$15,000,000*(P|F 12%,40)
P= $161,201.97 USING EXCEL'S PV FUNCTION THIS IS=PV(12%,40,,-15000000)
TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE DESIRED FUTURE AMOUNT
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PROBLEM 2.53
i= 7.50% COMPOUNDED ANNUALLYn= 10
EOY DEPOSIT0 $5,000.001 $1,000.002 $1,000.00
FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*(1+0.075)^10+1000*(1+0.075)^9+1000*(1+0.075)^8
FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING ELECTRONIC INTEREST TABLES THIS IS
=$5,000*(F|P 7.5%,10)+$1,000*(F|P 7.5%,9)+$1,000*(F|P 7.5%,8)
FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING EXCEL'S FV FUNCTION THIS IS
=FV(7.5%,10,,-5000)+FV(7.5%,9,,-1000)+FV(7.5%,8,,-1000)
SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FWF= $14,005.87 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
=FV(7.5%,10,,-(NPV(7.5%,1000,1000)+5000))
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PROBLEM 2.54
i= 6.00% COMPOUNDED ANNUALLYn= 15
EOY DEPOSIT0 $2,000.001 $0.002 $3,000.003 $0.004 $0.005 $4,000.006 $0.007 $1,000.00
FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.14 USING COMPOUND INTEREST FORMULAS THIS IS
=2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8
FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.16 USING INTEREST TABLES THIS IS
=$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6%,8)
FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.14 USING EXCEL'S FV FUNCTION THIS IS
=FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000)
SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FWF= $19,949.14 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
=FV(6%,15,,-(NPV(6%,0,3000,0,0,4000,0,1000)+2000))
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=2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8
=$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6%,8)
=FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000)
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PROBLEM 2.55
i= 7.00% COMPOUNDED ANNUALLYn= 11
EOY 0 1 2 3 4 5 6 7 8DEP/WDL $2,000.00 $0.00 $0.00 -$1,000.00 $0.00 $3,000.00 $0.00 $0.00 $1,500.00
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.27 USING COMPOUND INTEREST FORMULAS THIS IS
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.26 USING INTEREST TABLES THIS IS
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.27 USING EXCEL'S FV FUNCTION THIS IS
SUM THE PW OF EACH DEPOSIT OR WITHDRAWAL AND THEN FIND ITS FWF= $4,209.70 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
=FV(7%,11,,-(NPV(7%,0,0,-1000,0,3000,0,0,1500)+2000))
=2000*(1+0.07)^11-1000*(1+0.07)^8+3000*(1+0.07)^6+1500*(1+0.07)^3
=$2,000*(F|P 7%,11)-$1,000*(F|P 7%,8)+$3,000*(F|P 7%,6)+$1,500*(F|P 7%,3)
=FV(7%,11,,-2000)+FV(7%,8,,1000)+FV(7%,6,,-3000)+FV(7%,3,,-1500)
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PROBLEM 2.56
i= 6.50%n= 7
EOY 0 1 2 3 4 5 6 7NCF $0.00 -$500.00 $200.00 $400.00 -$300.00 $500.00 -$200.00 $100.00
a F= $150.76 USING EXCEL'S FV FUNCTION THIS IS
$150.77 USING ELECTRONIC INTEREST TABLES THIS IS
b P= $97.02 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6.5%,-500,200,400,-300,500,-200,100)+0
$97.02 USING ELECTRONIC INTEREST TABLES THIS IS
c P= $97.02 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION=PV(6.5%,7,,-150.76)
$97.02 USING ELECTRONIC INTEREST TABLES THIS IS =$150.76*(P|F 6.5%,7)
=FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,-400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100
=-$500*(F|P 6.5%,6)+$200*(F|P 6.5%,5)+$400*(F|P 6.5%,4)-300*(F|P 6.5%,3)+500*(F|P 6.5%,2)-200*(F|P 6.5%,1)+100
=-$500*(P|F 6.5%,1)+$200*(P|F 6.5%,2)+$400*(P|F 6.5%,3)-$300*(P|F 6.5%,4)+$500*(P|F 6.5%,5)-$200*(P|F 6.5%,6)+$100*(P|F 6.5%,7)
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PROBLEM 2.57
i= 8.00%n= 6
EOY 0 1 2 3 4 5 6NCF $0.00 $500.00 -$200.00 $600.00 $300.00 -$100.00 $200.00
a P= $1,046.28 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6.5%,-500,200,400,-300,500,-200,100)+0
$1,046.28 USING INTEREST TABLES THIS IS
b F= $1,660.31 USING EXCEL'S FV FUNCTION THIS IS
$1,660.31 USING INTEREST TABLES THIS IS
c P= $1,046.28 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION=PV(8%,6,,-1660.31)
$1,046.28 USING INTEREST TABLES THIS IS =$1,660.31*(P|F 8%,6)
d FIND THE WORTH AT EOY 4F4= $1,423.45 USING EXCEL'S PV AND FV FUNCTIONS THIS IS
$1,423.45 USING INTEREST TABLES THIS IS
e CONVERT THE WORTH AT EOY 4 TO PRESENTP= $1,046.28 USING EXCEL'S PV FUNCTION THIS IS
=PV(8%,4,,-1423.45)$1,046.28 USING INTEREST TABLES THIS IS
=$1,423.45*(P|F 8%,4)
=$500*(P|F 8%,1)-$200*(P|F 8%,2)+$600*(P|F 8%,3)+$300*(P|F 8%,4)-$100*(P|F 8%,5)+$200*(P|F 8%,6)
=FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,-400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100
=$500*(F|P 8%,5)-$200*(F|P 8%,4)+$600*(F|P 8%,3)+$300*(F|P 8%,2)-$100*(F|P 8%,1)+$200
=FV(8%,3,,-500)+FV(8%,2,,200)+FV(8%,1,,-600)+300+PV(8%,1,,100)+PV(8%,2,,-200)
=$500*(F|P 8%,3)-200*(F|P 8%,2)+600*(F|P 8%,1)+$300-$100*(P|F 8%,1)+$200*(P|F 8%,2)
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PROBLEM 2.58
i= 6.00%
a $8,000
0 1 2 3 4 5 6 7 8
$X $X+100 $X+400
$2X
b
X= $2,272.61 <--SOLVER CHANGED CELL
P= $8,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV AND NPV FUNCTIONS THIS IS=PV(6%,4,,-NPV(6%,X,X+100,X+400,2*X))
CAN ALSO SOLVE USING INTEREST TABLES.
P= $8,000 USING INTEREST TABLES THIS IS =$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8)=$X*(0.74726)+($X+$100)*(0.70496)+($X+$400)*(0.66506)+$2X*(0.62741)=3.37210*X+$336.52
X= $2,272.61 =(8000-336.52)/3.3721
c EOY PAYMENT5 $2,272.61 $X6 $2,372.61 $X+1007 $2,672.61 $X+4008 $4,545.23 $2X
TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF RENALDO'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $8,000.
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=$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8)
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PROBLEM 2.59i= 5.50%
$5X
a $4X
$3X
$2X
$X
0 1 2 3 4 5 6 7 8
-$20,000.00
b
X= $1,900.97 <--SOLVER CHANGED CELL
P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV AND NPV FUNCTIONS THIS IS=PV(5.5%,3,,-NPV(5.5%,X,2*X,3*X,4*X,5*X))
CAN ALSO SOLVE USING INTEREST TABLES.
P= $20,000 USING ELECTRONIC INTEREST TABLES THIS IS
TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $20,000.
=$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 5.5%,6)+$4*X*(P|F 5.5%,7)+$5*X*(P|F 5.5%,8)
A B C D E F G H I J123456789
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=10.52099*XX= $1,900.96 =20000/10.52099
c EOY PAYMENT4 $1,900.97 5 $3,801.93 6 $5,702.90 7 $7,603.87 8 $9,504.83
d SUM $28,514.50 INTEREST $8,514.50 =28,514.50-20,000.00
AMOUNT OF KEN'S CHECK
=$X*(0.80722)+$2*X*(0.76513)+$3*X*(0.72525)+$4*X*(0.68744)+$5*X*(0.65160)
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TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE
=$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 5.5%,6)+
K123456789
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=$X*(0.80722)+$2*X*(0.76513)+$3*X*(0.72525)+$4*X*(0.68744)+
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PROBLEM 2.60
i= 8.00%n= 8
EOY 0 1 2 3 4 5 6 7 8NCF $300.00 $300.00 $600.00 -$500.00 -$300.00 $0.00 $800.00 $700.00 $600.00
a P= $1,711.50 USING EXCEL'S NPV FUNCTION THIS IS=NPV(8%,300,600,-500,-300,0,800,700,600)+300
$1,711.50 USING INTEREST TABLES THIS IS
b F= $3,167.86 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,C4,,-C9)
F= $3,167.86 USING INTEREST TABLES THIS IS =$1,711.50*(F|P 8%,8)
c F2= $1,996.29 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,2,,-1711.5)
F2= $1,996.29 USING INTEREST TABLES THIS IS =$1,711.50*(F|P 8%,2)
=$300+$300*(P|F 8%,1)+$600*(P|F 8%,2)-$500*(P|F 8%,3)-$300*(P|F 8%,4)+$800*(P|F 8%,6)+$700*(P|F 8%,7)+$600*(P|F 8%,8)
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PROBLEM 2.61
i= 5.00%n= 8
EOY 0 1 2 3 4 5 6 7 8NCF $150.00 $300.00 $450.00 $0.00 -$500.00 $0.00 $600.00 $700.00 $800.00
a P= $1,919.20 USING COMPOUND INTEREST FORMULAS THIS IS
P= $1,919.21 USING INTEREST TABLES THIS IS
P= $1,919.20 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,300,450,0,-500,0,600,700,800)+150
b F= $2,835.54 USING COMPOUND INTEREST FORMULAS THIS IS
F= $2,835.55 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,8)
F= $2,835.54 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,8,,-1919.20)
c F6= $2,571.92 USING COMPOUND INTEREST FORMULAS THIS IS
F6= $2,571.93 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,6)
F6= $2,571.92 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,6,,-1919.20)
=150+300*(1+0.05)^-1+450*(1+0.05)^-2-500*(1+0.05)^-4+600*(1+0.05)^-6+700*(1+0.05)^-7+800*(1+0.05)^-8
=$150+$300*(P|F 5%,1)+$450*(P|F 5%,2)-$500*(P|F 5%,4)-$600*(P|F 5%,6)+$700*(P|F 5%,7)+$800*(P|F 5%,8)
=150*(1+0.05)^8+300*(1+0.05)^7+450*(1+0.05)^6-500*(1+0.05)^4+600*(1+0.05)^2+700*(1+0.05)^1+800
=150*(1+0.05)^6+300*(1+0.05)^5+450*(1+0.05)^4-500*(1+0.05)^2+600+700*(1+0.05)^-1+800*(1+0.05)^-2
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PROBLEM 2.62
i= 12.00%COST $30,000.00
PAYMENT METHOD 1GET CASH DISCOUNT= 3.00%
PW= $29,100.00 =30000*(1-0.03)
PAYMENT METHOD 2PAY ACCORDING TO THE FOLLOWING SCHEDULEEOY 0 1 2 3 4 5CF $5,000.00 $8,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00
PW= $28,414.37 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,8000,6000,6000,6000,6000)+5000
PW= $28,414.40 USING INTEREST TABLES THIS IS
USE PAYMENT METHOD 2 - LOWER PW
=$5,000+$8,000*(P|F 12%,1)+$6,000*(P|F 12%,2)+$6,000*(P|F 12%,3)+$6,000*(P|F 12%,4)+$6,000*(P|F 12%,5)
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PROBLEM 2.63
P|A FACTOR
i= 8.00% USING 8% FOR EXAMPLE CALCn= 8 USING 8 FOR EXAMPLE CALC
(P|A i%,n)= 5.74664 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.08)^8-1)/(0.08*(1+0.08)^8)
A|P FACTOR
i= 3.00% USING 3% FOR EXAMPLE CALCn= 5 USING 5 FOR EXAMPLE CALC
(A|P i%,n)= 0.21835 USING COMPOUND INTEREST FORMULAS THIS IS =(0.03*(1+0.03)^5)/((1+0.03)^5-1)
F|A FACTOR
i= 10.00% USING 10% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC
(F|A i%,n)= 15.93742 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.1)^10-1)/0.1
A|F FACTOR
i= 3.00% USING 3% FOR EXAMPLE CALCn= 5 USING 5 FOR EXAMPLE CALC
(A|F i%,n)= 0.18835 USING COMPOUND INTEREST FORMULAS THIS IS =0.03/((1+0.03)^5-1)
ALL CHECK OK WITH APPENDIX A
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PROBLEM 2.64
i= 9.00%n= 7P= $40,000.00
A= $7,947.62 USING COMPOUND INTEREST FORMULAS THIS IS =40000*(0.09*(1+0.09)^7)/((1+0.09)^7-1)
A= $7,947.60 USING INTEREST TABLES THIS IS 40,000*(A|P 9%,7)
A= $7,947.62 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.09,7,-40000)
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PROBLEM 2.65
i= 4.00%n= 10A= $5,000.00
F= $60,030.54 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.04)^10-1)/0.04
F= $60,030.55 USING INTEREST TABLES THIS IS =$5,000*(F|A 4%,10)
F= $60,030.54 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,10,-5000)
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PROBLEM 2.66
i= 6.00%n= 8A= $7,500.00
P= $46,573.45 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.06)^8-1)/(0.06*(1+0.06)^8)
P= $46,573.43 USING INTEREST TABLES THIS IS =$7,500*(P|A 6%,8)
P= $46,573.45 USING EXCEL'S PV FUNCTION THIS IS=PV(6%,8,-7500)
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PROBLEM 2.67
i= 7.00%n= 35F= $2,000,000.00
A= $14,467.92 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*0.07/((1+0.07)^35-1)
A= $14,468.00 USING ELECTRONIC INTEREST TABLES THIS IS =$2,000,000*(A|F 7%,35)
A= $14,467.92 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.07,35,,-2000000)
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PROBLEM 2.68
i= 7.00%n= 5P= $25,000.00
A= $6,097.27 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(0.07*(1+0.07)^5)/((1+0.07)^5-1)
A= $6,097.25 USING INTEREST TABLES THIS IS =$25,000*(A|P 7%,5)
A= $6,097.27 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.07,5,-25000)
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PROBLEM 2.69
a i= 4.00%n= 20A= $7,500.00
F= $223,335.59 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04
F= $223,335.60 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,20)
F= $223,335.59 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,20,-7500)
i= 4.00%n= 25A= $7,500.00
F= $312,344.31 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^25-1)/0.04
F= $312,344.33 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,25)
F= $312,344.31 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,25,-7500)
i= 4.00%n= 30A= $7,500.00
F= $420,637.03 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^30-1)/0.04
F= $420,637.05 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,30)
F= $420,637.03 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,30,-7500)
b i= 5.00%n= 20A= $7,500.00
F= $247,994.66 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^20-1)/0.05
F= $247,994.63 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,20)
F= $247,994.66 USING EXCEL'S FV FUNCTION THIS IS=FV(0.05,20,-7500)
i= 5.00%n= 25
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A= $7,500.00
F= $357,953.24 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^25-1)/0.05
F= $357,953.25 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,25)
F= $357,953.24 USING EXCEL'S FV FUNCTION THIS IS=FV(0.05,25,-7500)
i= 5.00%n= 30A= $7,500.00
F= $498,291.36 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^30-1)/0.05
F= $498,291.38 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,30)
F= $498,291.36 USING EXCEL'S FV FUNCTION THIS IS=FV(0.05,30,-7500)
c PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 4%=39.85% =(312344.31-223335.59)/223335.59
PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 4%=88.34% =(420637.03-223335.59)/223335.59
PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 5%=44.34% =(357953.24-247994.66)/247994.66
PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 5%=100.93% =(498291.36-247994.66)/247994.66
PERCENTAGE INCREASE FROM 4% TO 5% FOR 20 YEARS=11.04% =(247994.66-223335.59)/223335.59
PERCENTAGE INCREASE FROM 4% TO 5% FOR 25 YEARS=14.60% =(357953.24-312344.31)/312344.31
PERCENTAGE INCREASE FROM 4% TO 5% FOR 30 YEARS=18.46% =(498291.36-420637.03)/420637.03
AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AND 88.34%, RESPECTIVELYAT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% AND 100.93%, RESPECTIVELYA 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%, AND 18.46%, RESPECTIVELY, FOR 20, 25, AND 30 YEARS
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AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AND 88.34%, RESPECTIVELYAT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% AND 100.93%, RESPECTIVELYA 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%, AND 18.46%, RESPECTIVELY, FOR 20, 25, AND 30 YEARS
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PROBLEM 2.70
a i= 7.00%n= 5P= $50,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 1A= $12,194.53 USING COMPOUND INTEREST FORMULAS THIS IS
=50000*(0.07*(1+0.07)^5)/((1+0.07)^5-1)A= $12,194.50 USING INTEREST TABLES THIS IS
=$50,000*(A|P 7%,5)A= $12,194.53 USING EXCEL'S PMT FUNCTION THIS IS
=PMT(0.07,5,-50000)
b i= 7.00%n= 5 PAYMENTSt= 4 WITH FIRST PAYMENT AT EOY 4P= $50,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 4FIND VALUE OF $50,000 AT EOY 3, THEN FIND AMOUNT OF 5 ANNUAL PAYMENTS
A= $14,938.83 USING COMPOUND INTEREST FORMULAS THIS IS =50000*((1+0.07)^(4-1))*(0.07*(1+0.07)^5)/((1+0.07)^5-1)
A= $14,938.75 USING INTEREST TABLES THIS IS =$50,000*(F|P 7%,3)*(A|P 7%,5)
A= $14,938.83 USING EXCEL'S PMT AND FV FUNCTIONS THIS IS=PMT(7%,5,-FV(7%,4-1,,-50000))
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PROBLEM 2.71
a i= 5.00%n= 10A= $5,000.00
WITH THE FIRST WITHDRAWAL AT THE END OF YEAR 1P= $38,608.67 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)P= $38,608.65 USING INTEREST TABLES THIS IS
=$5,000*(P|A 5%,10)P= $38,608.67 USING EXCEL'S PV FUNCTION THIS IS
=PV(5%,10,-5000)
b i= 5.00%n= 10 WITHDRAWALSt= 3 WITH FIRST WITHDRAWAL AT EOY 3A= $5,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 3FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH
P= $35,019.21 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1))
P= $35,019.20 USING INTEREST TABLES THIS IS $5,000*(P|F 5%,2)*(P|A 5%,10)
P= $35,019.21 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,3-1,,-PV(5%,10,-5000))
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USING COMPOUND INTEREST FORMULAS THIS IS
FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH
USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1))
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PROBLEM 2.72
LET'S CONSIDER INTEREST RATES FROM 0% TO 20%A= $10,000.00 $5,000.00 n= 5 10
PV OF PV OFINTEREST 10K FOR 5 YR 5K FOR 10 YR
0.00% $50,000.00 =PV(0%,5,-10000) $50,000.00 =PV(0%,10,-5000)1.00% $48,534.31 $47,356.52 2.00% $47,134.60 $44,912.93 3.00% $45,797.07 =PV(3%,5,-10000) $42,651.01 =PV(3%,10,-5000)4.00% $44,518.22 $40,554.48 5.00% $43,294.77 $38,608.67 6.00% $42,123.64 $36,800.44 7.00% $41,001.97 $35,117.91 8.00% $39,927.10 $33,550.41 9.00% $38,896.51 $32,088.29
10.00% $37,907.87 $30,722.84 11.00% $36,958.97 $29,446.16 12.00% $36,047.76 $28,251.12 13.00% $35,172.31 $27,131.22 14.00% $34,330.81 $26,080.58 15.00% $33,521.55 $25,093.84 16.00% $32,742.94 $24,166.14 17.00% $31,993.46 $23,293.02 18.00% $31,271.71 $22,470.43 19.00% $30,576.35 $21,694.67 20.00% $29,906.12 =PV(20%,5,-10000) $20,962.36 =PV(20%,10,-5000)
PREFER TO RECEIVE YOUR MONEY QUICKER AT $10K FOR EACH OF 5 YEARS
PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS
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PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS
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PROBLEM 2.73
a i= 6.00%n= 8
A(3 TO 10)= $10,000.00DISPLACED n= 2
A(1 TO 8)= $8,899.96 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.06)^2
A(1 TO 8)= $8,900.00 USING INTEREST TABLES THIS IS =$10,000*(P|F 6%,2)
A(1 TO 8)= $8,899.96 USING EXCEL'S PV FUNCTION THIS IS=PV(6%,2,,-10000)
A(1 TO 8)= $8,900.22 USING INTEREST TABLES THIS IS =$10,000*(P|A 6%,8)*(P|F 6%,2)*(A|P 6%,8)
A(1 TO 8)= $8,899.96 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(6%,8,-PV(6%,2,,-PV(6%,8,-10000)))
b i= 10.00%n= 8
A(3 TO 10)= $10,000.00DISPLACED n= 2
A(1 TO 8)= $8,264.46 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.10)^2
A(1 TO 8)= $8,264.50 USING INTEREST TABLES THIS IS =$10,000*(P|F 10%,2)
A(1 TO 8)= $8,264.46 USING EXCEL'S PV FUNCTION THIS IS=PV(10%,2,,-10000)
A(1 TO 8)= $8,264.46 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(10%,8,-PV(10%,2,,-PV(10%,8,-10000)))
A(1 TO 8)= $8,264.33 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,8)*(P|F 10%,2)*(A|P 10%,8)
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER
OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8.
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER
OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8.
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PROBLEM 2.74
a i= 6.00%n= 10
A(3 TO 10)= $10,000.00DISPLACED n= 10
A(11 TO 20)= $17,908.48 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.06)^2
A(11 TO 20)= $17,908.50 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)
A(11 TO 20)= $17,908.48 USING EXCEL'S FV FUNCTION THIS IS=FV(6%,10,,-10000)
A(11 TO 20)= $17,908.74 USING INTEREST TABLES THIS IS =$10,000*(F|A 6%,10)*(A|P 6%,10)
A(11 TO 20)= $17,908.48 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(6%,10,-FV(6%,10,,-PV(6%,10,-10000)))
b i= 10.00%n= 10
A(3 TO 10)= $10,000.00DISPLACED n= 10
A(11 TO 20)= $25,937.42 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.10)^2
A(11 TO 20)= $25,937.40 USING INTEREST TABLES THIS IS =$10,000*(F|P 10%,10)
A(11 TO 20)= $25,937.42 USING EXCEL'S FV FUNCTION THIS IS=FV(10%,10,,-10000)
A(11 TO 20)= $25,938.15 USING INTEREST TABLES THIS IS =$10,000*(F|A 10%,10)*(A|P 10%,10)
A(11 TO 20)= $25,937.42 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(10%,10,-FV(10%,10,,-PV(10%,10,-10000)))
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER
OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 11-20.
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER
OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AT EOY 10, AND THEN USE THAT AMOUNT AS A PW TO DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES OVER YEARS 11-20.
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PROBLEM 2.75
i= 5.00%n= 10A= $1,000.00
F= $12,577.89 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04
F= $12,577.89 USING INTEREST TABLES THIS IS =$1,000*(F|A 5%,10)
F= $12,577.89 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,20,-7500)
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PROBLEM 2.76
a i= 8.00%n= 8A= $1,000.00
FINDING THE PW AT EOY 0P= $5,746.64 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*((1+0.08)^8-1)/(0.08*(1+0.08)^8)P= $5,746.64 USING INTEREST TABLES THIS IS
=$1,000*(P|A 8%,8)P= $5,746.64 USING EXCEL'S PV FUNCTION THIS IS
=PV(8%,8,-1000)
b i= 8.00%n= 8A= $1,000.00
FINDING THE FW AT EOY 8F= $10,636.63 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*((1+0.08)^8-1)/0.08F= $10,636.63 USING INTEREST TABLES THIS IS
=$1,000*(F|A 8%,8)F= $10,636.63 USING EXCEL'S FV FUNCTION THIS IS
=FV(0.08,8,-1000)
c i= 8.00%n= 8A= $1,000.00t= 11 THREE YEARS AFTER LAST DEPOSIT
FINDING THE FW AT EOY 11F= $13,399.09 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*(((1+0.08)^8-1)/0.08)*(1+0.08)^3F= $13,399.07 USING INTEREST TABLES THIS IS
=$1,000*(F|A 8%,8)*F|P(8%,3)F= $13,399.09 USING EXCEL'S FV FUNCTION THIS IS
=FV(8%,11,,PV(8%,8,1000))
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PROBLEM 2.77
a A= $60,000.00 i= 10.00%
n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWALn(withdrawal)= 10 NUMBER OF WITHDRAWALS
P= $60,281.15 USING COMPOUND INTEREST FORMULAS THIS IS=60000*((1+0.1)^10-1)/(0.1*(1+0.1)^10)*(1+0.1)^-19
P= $60,281.92 USING INTEREST TABLES THIS IS $60,000*(P|A 10%,10)*(P|F 10%,19)
P= $60,281.15 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,20,,-PV(10%,10,-60000))
b A= $60,000.00 i= 15.00%
n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWALn(withdrawal)= 10 NUMBER OF WITHDRAWALS
P= $21,158.72 USING COMPOUND INTEREST FORMULAS THIS IS=60000*((1+0.15)^10-1)/(0.15*(1+0.15)^10)*(1+0.15)^-19
P= $21,160.14 USING INTEREST TABLES THIS IS $60,000*(P|A 15%,10)*(P|F 15%,19)
P= $21,158.72 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,20,,-PV(15%,10,-60000))
FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0.
FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0.
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PROBLEM 2.78
i= 7.00%n= 12P= $200,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 1A= $25,180.40 USING COMPOUND INTEREST FORMULAS THIS IS
=200000*(0.07*(1+0.07)^12)/((1+0.07)^12-1)A= $25,180.00 USING INTEREST TABLES THIS IS
=$200,000*(A|P 7%,12)A= $25,180.40 USING EXCEL'S PMT FUNCTION THIS IS
=PMT(0.07,12,-200000)
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PROBLEM 2.79
a A= $4,000.00 5.00%
3
8.00%
5
F= $18,528.23 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(((1+5%)^3-1)/5%)*(1+8%)^5
F= $18,528.25 USING INTEREST TABLES THIS IS =$4,000*(F|A 5%,3)*(F|P 8%,5)
F= $18,528.23 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,5,,-FV(5%,3,-4000))
b A= $12,000.00 10.00%
10
5.00%
3
F= $221,394.73 USING COMPOUND INTEREST FORMULAS THIS IS=12000*(((1+10%)^10-1)/10%)*(1+5%)^3
F= $221,395.63 USING INTEREST TABLES THIS IS =$12,000*(F|A 10%,10)*(F|P 5%,5)
F= $221,394.73 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,3,,-FV(10%,10,-12000))
c A= $18,000.00 9.00%
5
7.00%
8
F= $185,091.25 USING COMPOUND INTEREST FORMULAS THIS IS=18000*(((1+9%)^5-1)/9%)*(1+7%)^8
F= $185,091.64 USING INTEREST TABLES THIS IS =$18,000*(F|A 9%,5)*(F|P 7%,8)
F= $185,091.25 USING EXCEL'S FV FUNCTION THIS IS=FV(7%,8,,-FV(9%,5,-18000))
i1=
n1=
i2=
n2=
FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD.
i1=
n1=
i2=
n2=
FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD.
i1=
n1=
i2=
n2=
FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD.
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PROBLEM 2.80
a A= $2,000.00 i= 5.00%n= 15
F= $43,157.13 USING COMPOUND INTEREST FORMULAS THIS IS =2000*((1+0.05)^15-1)/0.05
F= $43,157.12 USING INTEREST TABLES THIS IS =$2,000*(F|A 5%,15)
F= $43,157.13 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,15,-2000)
b A= $3,000.00 i= 8.00%
n(deposits=) 10n(more years) 5
F= $63,856.54 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(((1+0.08)^10-1)/0.08)*(1+0.08)^5
F= $63,856.61 USING INTEREST TABLES THIS IS =$3,000*(F|A 8%,10)*(F|P 8%,5)
F= $63,856.54 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,5,,-FV(8%,10,-3000))
ci= 8.00%
A(1st)= $2,000.00 n(1st)= 5A(2nd)= $4,000.00 n(2nd) 5A(3rd)= $6,000.00 n(3rd)= 5
F= $95,010.53 TABLES
F= $95,010.55 EXCEL
=$2,000*(F|A 8%,5)*(F|P 8%,10)+$4,000*(F|A 8%,5)*(F|P 8%,5)+$6,000*(F|A 8%,5)
=FV(8%,5,-6000)+FV(8%,5,,-FV(8%,5,-4000))+FV(8%,5+5,,-FV(8%,5,-2000))
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PROBLEM 2.81
i= 5.00%
$1,200.00 YEARS 1-5
5 DEPOSITS YEARS 1-5
-$700.00 YEARS 4-7
4 WITHDRAWALS YEARS 4-7
4 START TIME OF WITHDRAWALS
P= $3,051.18 USING INTEREST TABLES THIS IS =$1,200*(P|A 5%,5)-$700*(P|A 5%,4)*(P|F 5%,3)
P= $3,051.18 USING EXCEL'S FV FUNCTION THIS IS=PV(5%,5,-1200)-PV(5%,3,,-PV(5%,4,-700))
A1=
n1=
A2=
n2=
t2=
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PROBLEM 2.82
aP= $1.00 i= 7.000%A= $0.20 20% OF P
n= 6.367 USING EXCEL'S NPER FUNCTION THIS IS=NPER(7%,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE n
n= 6.367 <--SOLVER CHANGED CELL
P= $1.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(7%,n,-0.2)
b P= $1.00 n= 7A= $0.20
i= 9.196% USING EXCEL'S RATE FUNCTION THIS IS=RATE(7,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE i
i= 9.196% <--SOLVER CHANGED CELL
P= $1.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(i%,7,-0.2)
SINCE THE AMOUNT PAID IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $1.00 IS SELECTED HERE
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PROBLEM 2.83
P= $6.00 n= 7A= $1.00
i= 4.009% USING EXCEL'S RATE FUNCTION THIS IS=RATE(7,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE i
i= 4.009% <--SOLVER CHANGED CELL
P= $6.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(i,7,-C6)
SINCE THE AMOUNT OF THE LOAN IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $6.00 IS SELECTED HERE.
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PROBLEM 2.84
i= 9.00%n1= 25 NUMBER OF DEPOSITSA= $4,000.00t= 28 TIME OF FIRST WITHDRAWAL
n2= 30 NUMBER OF WITHDRAWALS
a
F27= $402,532.54 USING COMPOUND INTEREST FORMULAS THIS IS =4000*(((1+0.09)^25-1)/0.09)*(1+0.09)^2
F27= $402,532.56 USING INTEREST TABLES THIS IS =$4,000*(F|A 9%,25)*(F|P 9%,2)
F27= $402,532.54 USING EXCEL'S FV FUNCTION THIS IS=FV(9%,28-25-1,,-FV(9%,25,-4000))
b
A= $39,181.05 USING COMPOUND INTEREST FORMULAS THIS IS =402532.54*(0.09*(1+0.09)^30)/((1+0.09)^30-1)
A= $39,182.52 USING INTEREST TABLES THIS IS =$402,532.54*(A|P 9%,30)
A= $39,181.05 USING EXCEL'S PMT FUNCTION THIS IS=PMT(9%,30,-402532.54)
c FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN
A= $36,227.93 =402532.54*0.09
FIRST, DETERMINE THE AMOUNT IN THE ACCOUNT RIGHT AFTER THE LAST DEPOSIT AT EOY 25. THEN, FIND THE FW OF THAT AMOUNT ONE YEAR BEFORE THE FIRST WITHDRAWAL AT EOY 27
USING THE ANSWER TO PART a, FIND THE PAYMENT AMOUNT OVER THE WITHDRAWAL PERIOD
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PROBLEM 2.85
i= 12.00%n DEPOSITS= 30
A= $7,500.00 ($5,000 FROM YOU + $2,500 FROM EMPLOYER)n WITHDRAWALS= 30
a F= $1,809,995.13 USING COMPOUND INTEREST FORMULAS THIS IS =7500*(((1+0.12)^30-1)/0.12)
F= $1,809,995.10 USING INTEREST TABLES THIS IS =$7,500*(F|A 12%,30)
F= $1,809,995.13 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,30,-7500)
b SUM(YOU)= $150,000.00 =5000*30
c SUM(EMPLOYER)= $75,000.00 =2500*30
d EARNINGS= $1,584,995.13 $1,584,995.13
e
A= $224,699.42 USING COMPOUND INTEREST FORMULAS THIS IS =1809995.13*(0.12*(1+0.12)^30)/((1+0.12)^30-1)
A= $224,692.80 USING INTEREST TABLES THIS IS =$1,809,995.13*(A|P 12%,30)
A= $224,699.42 USING EXCEL'S PMT FUNCTION THIS IS=PMT(12%,30,-1809995.13)
f FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWNINTEREST ONLY= $217,199.42 =1809995.13*0.12
USING THE ANSWER TO PART a, FIND THE YEARLY AMOUNT OVER THE WITHDRAWAL PERIOD
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PROBLEM 2.86
i= 6.00%P= $10,000.00 DEPOSIT AT EOY 0A= -$1,000.00 WITHDRAWALS AT EOY 3-7
10 YEARS FROM DEPOSIT TO FINAL WITHDRAWAL
5 YEARS OF WITHDRAWALS (3, 4, 5, 6, 7)
3 YEARS FROM 5TH WITHDRAWAL TO FINAL WITHDRAWAL
FIND THE FW AT EOY 10 OF THE INITIAL DEPOSIT AND THE FIVE WITHDRAWALS
F= $11,194.61 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)-$1,000*(F|A 6%,5)*(F|P 6%,3)
F= $11,194.61 USING EXCEL'S FV FUNCTION THIS IS=FV(6%,10,,-10000)+FV(6%,3,,-FV(6%,5,-(-1000)))
n1=
n2=
n3=
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PROBLEM 2.87
i= 12.00%
P= $15,000.00 LOAN VALUE AT EOY 0A= $3,000.00 PAYMENTS AT EOY 1, 2, 3, 4
4 YEARS UNTIL FINAL A=$3,000 PAYMENT
1 ADDITIONAL YEARS UNTIL FINAL PAYMENT
F= $10,376.58 USING COMPOUND INTEREST FORMULAS THIS IS =15000*(1+0.12)^(4+1)-(3000*(((1+0.12)^4-1)/0.12))*(1+0.12)^1
F= $10,376.55 USING INTEREST TABLES THIS IS =$15,000*(F|P 12%,5)-$3,000*(F|A 12%,4)*(F|P 12%,1)
F= $10,376.58 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,4+1,,-15000)+FV(12%,1,,-FV(12%,4,3000))
F= $10,376.58 IS THE AMOUNT OF THE YEAR 5 PAYMENT
n1=
n2=
FIND THE LOAN VALUE AT EOY 5 AND SUBTRACT OFF THE PAYMENT VALUES AT EOY 5. WHAT'S LEFT IS THE FINAL LOAN PAYMENT AT EOY 5.
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PROBLEM 2.88
i= 9.00%n1= 10 YEARS OF WITHDRAWALS
5 WITHDRAWALS REMAINING AT EOY 45AMT45= $32,801.60 AMOUNT LEFT IN ACCT AT EOY 45
THE FOLLOWING WILL BE NEEDED IN THE LAST STEPS OF THE PROBLEM
15 YEARS FROM DEPOSIT 1 TO EOY 40
10 YEARS FROM DEPOSIT 2 TO EOY 40
5 YEARS FROM DEPOSIT 3 TO EOY 40
FIRST, DETERMINE THE AMOUNT OF THE ANNUAL WITHDRAWALSA= $8,432.96 USING INTEREST TABLES THIS IS
=$32,801.60*(A|P 9%,5)A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS
=PMT(9%,5,-32801.6)
AMT40= $54,120.41 USING INTEREST TABLES THIS IS =$8433.04*(P|A 9%,10)
AMT40= $54,120.39 USING EXCEL'S PV FUNCTION THIS IS=PV(9%,10,-8433.04)
AMT40= =7.54846 USING INTEREST TABLES THIS IS TIMES X =(F|P 9%,15)+(F|P 9%,10)+(F|P 9%,5)
=(3.64248+2.36736+1.53862)=7.54846
X= $7,169.73 =$54,120.41/7.54846
AMT40= 7.54847 USING EXCEL'S FV FUNCTION THIS ISTIMES X =(FV(9%,15,,-1)+(FV(9%,10,,-1)+(FV(9%,5,,-1))))
X= $7,169.72 =54120.39/7.54847******************************************************THIS PROBLEM MAY BETTER BE ANSWERED USING SOLVER
X= $7,169.73 <--SOLVER CHANGED CELL
SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40AMT40= $54,120.44 USING INTEREST TABLES THIS IS
X*(F|P 9%,15)+X*(F|P 9%,10)+X*(F|P 9%,5)NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50
A= $8,433.05 =$54,120.84*(A|P 9%,10)=$54,120.84*0.15582
NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45AMT45= $32,801.60 <--SOLVER TARGET CELL
=$8,433.11*(P|A 9%,5)
n2=
n3=
n4=
n5=
NOW KNOWING THE ANNUAL WITHDRAWAL, DETERMINE THE AMOUNT IN THE ACCOUNT AT EOY 40
NOW, DETERMINE THE VALUE AT EOY 40 OF THE THREE "$X" DEPOSITS AT EOY 25, 30, AND 35 AND SOLVE FOR X
LET X BE ANY VALUE AT THIS POINT. SET UP ALL FOLLOWING EQUATIONS AS IF THE VALUE OF X IS RIGHT. SOLVER WILL LATER BE USED TO CORRECTLY SEARCH FOR AND SET THE VALUE OF X
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X= $7,169.72 <--SOLVER CHANGED CELL
SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40AMT40= $54,120.39 USING EXCEL'S FV FUNCTION THIS IS
=(FV(9%,15,,-X)+FV(9%,10,,-X)+(FV(9%,5,,-X))NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50
A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS=PMT(9%,10,-54120.91)
NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45AMT45= $32,801.60 <--SOLVER TARGET CELL
USING EXCEL'S PV FUNCTION THIS IS=PV(9%,5,-8433.12)
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TIMES XTIMES XTIMES X
TIMES X
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PROBLEM 2.89
P= $20,000.00 AT EOY 30i= 5% YEARS 31-40i= 6% YEARS 41-50i= 7% YEARS 51 AND BEYOND
10 YEARS AT 5%
10 YEARS AT 6%
10 YEARS AT 7%
10 YEARS OF WITHDRAWALS
5 YEARS OF WITHDRAWALS REMAINING AT EOY 65
a FIRST, SOLVE FOR THE AMOUNT AVAILABLE AT EOY 60AMT60= $114,767.37 USING INTEREST TABLES THIS IS
=$20,000*(F|P 5%,10)*(F|P 6%,10)*(F|P 7%,10)A= $16,340.58 USING INTEREST TABLES THIS IS
=$114,767.37*(A|P 7%,10)AMT60= $114,767.63 USING EXCEL'S FV FUNCTION THIS IS
=FV(7%,10,,-FV(6%,10,,-FV(5%,10,,-20000)))A= $16,340.33 USING EXCEL'S PMT FUNCTION THIS IS
=PMT(7%,10,-114767.63)
b
WDL65= $83,340.22 USING INTEREST TABLES THIS IS =$16,340.58*(P|A 7%,5)+$16,340.58
WDL65= $83,338.90 USING EXCEL'S PV FUNCTION THIS IS=PV(7%,5,-16340.33)+16340.33
n1=
n2=
n3=
n4=
n5=
SOLVE FOR THE PW OF THE 5 REMAINING WITHDRAWALS AT EOY 66-70 PLUS THE WITHDRAWAL DUE AT EOY 65
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PROBLEM 2.90
i= 10.00%n= 8
EOY 0 1 2 3 4 5 6 7 8CF -$2,500.00 $3,000.00 $4,500.00 $0.00 -$5,000.00 $0.00 -$1,000.00 $7,000.00 $3,000.00
P= $4,958.42 USING INTEREST TABLES THIS IS
A= $929.41 USING INTEREST TABLES THIS IS =$4,958.43*(A|P 10%,8)
P= $4,958.37 USING EXCEL'S NPV FUNCTION THIS IS=NPV(10%,3000,4500,0,-5000,0,-1000,7000,3000)-2500
A= $929.42 USING EXCEL'S PMT FUNCTION THIS IS=PMT(C3,C4,-C10)
FIRST, FIND THE PW OF THIS CASH FLOW SERIES. THEN FIND THE EQUIVALENT VALUE OF "A"
=$2,500+$3,000*(P|F 10%,1)+$4,500*(P|F 10%,2)-$5,000*(P|F 10%,4)-$1,000*(P|F 10%,6)+$7,000*(P|F 10%,7)+$3,000*(P|F 10%,8)
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PROBLEM 2.91
a F= B*(F|P i%,1)*(F|A i%,n)
b F= B*(1+i)*((1+i)^n-1)/i
c B= $1,000.00n= 5i= 10.00%
USING (a) F= $6,715.61 USING INTEREST TABLES THIS IS =$1,000*(F|P 10%,1)*(F|P 10%,5)
USING (b) F= $6,715.61 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.1)*((1+0.1)^5-1)/0.1
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PROBLEM 2.92
P|G FACTOR
i= 8.00% USING 8% FOR EXAMPLE CALCn= 3 USING 3 FOR EXAMPLE CALC
P|G= 2.44500 USING COMPOUND INTEREST FORMULAS THIS IS =(1-(1+3*0.08)*(1+0.08)^(-3))/(0.08^2)
F|G FACTOR NOT TABULATED IN APPENDIX A
i= 12.00% USING 12% FOR EXAMPLE CALCn= 25 USING 25 FOR EXAMPLE CALC
F|G= 902.78225 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.12)^25-(1+25*0.12))/(0.12^2)
A|G FACTOR
i= 10.00% USING 10% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC
A|G= 3.72546 USING COMPOUND INTEREST FORMULAS THIS IS =(1/0.10)-(10/0.10)*(0.10/((1+0.10)^10-1))
P|G AND A|G CHECK OK WITH APPENDIX A
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PROBLEM 2.93
i= 5.00%n= 5
$800.00 G= $100.00
P= $4,287.28 USING INTEREST TABLES THIS IS =$800*(P|A 5%,5)+$100*(P|G 5%,5)
P= $4,287.27 USING EXCEL'S NPV FUNCTION=NPV(5%,800,900,1000,1100,1200)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.00 1 $800.00 2 $900.00 3 $1,000.00 4 $1,100.00 5 $1,200.00
P= $4,287.27 =NPV(5%,800,900,1000,1100,1200)+0
A1=
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PROBLEM 2.94
i= 6.00%n= 7
$5,000.00 G= $1,000.00
FV= $65,199.79 USING INTEREST TABLES THIS IS =($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7
FV= $65,199.82 USING EXCEL'S FV AND NPV FUNCTIONS=FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000))
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.00 1 $5,000.00 2 $6,000.00 3 $7,000.00 4 $8,000.00 5 $9,000.00 6 $10,000.00 7 $11,000.00
FV= $65,199.82 =FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))
A1=
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=($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7
=FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000))
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
=FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))
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PROBLEM 2.95
i= 8.00%n= 6
$12,000.00G= -$2,000.00
P= $34,428.02 USING INTEREST TABLES THIS IS =$12,000*(P|A 8%,6)-$2,000*(P|G 8%,6)
P= $34,428.01 USING EXCEL'S NPV FUNCTION=NPV(8%,12000,10000,8000,6000,4000,2000)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.00 1 $12,000.00 2 $10,000.00 3 $8,000.00 4 $6,000.00 5 $4,000.00 6 $2,000.00
P= $34,428.01 =NPV(8%,12000,10000,8000,6000,4000,2000)+0
A1=
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SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
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PROBLEM 2.96
i= 10.00%n= 4
$2,000.00G= $500.00
a P= $8,528.80 USING INTEREST TABLES THIS IS =$2,000*(P|A 10%,4)+$500*(P|G 10%,4)
P= $8,528.79 USING EXCEL'S NPV FUNCTION=NPV(10%,2000,2500,3000,3500)
b A= $2,690.58 USING INTEREST TABLES THIS IS =$8,528.80*(A|P 10%,4)
A= $2,690.59 USING INTEREST TABLES THIS IS =$2,000+$500*(A|G 10%,4)
A= $2,690.58 USING EXCEL'S PMT FUNCTION=PMT(10%,4,-8528.79)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.00 1 $2,000.00 2 $2,500.00 3 $3,000.00 4 $3,500.00
P= $8,528.79 =NPV(10%,2000,2500,3000,3500)+0
A= $2,690.58 =PMT(10%,4,-8528.79)
A1=
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SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
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PROBLEM 2.97
i= 12.00%n= 6
-$2,000.00G= $1,000.00
P= $707.35 USING INTEREST TABLES THIS IS -$2,000*(P|A 12%,6)+$1,000*(P|G 12%,6)
P= $707.36 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,-2000,-1000,0,1000,2000,3000)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.001 -$2,000.002 -$1,000.003 $0.004 $1,000.005 $2,000.006 $3,000.00
P= $707.36 =NPV(12%,-2000,-1000,0,1000,2000,3000)+0
A1=
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PROBLEM 2.98
a i= 6.00%n= 8
INITIAL CF= -$75,000.00
$3,000.00G= $3,000.00
P= $3,154.11 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 6%,8)+3,000*(P|G 6%,8)
P= $3,154.12 USING EXCEL'S NPV FUNCTION THIS IS
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWEREOY CF
0 -$75,000.001 $3,000.002 $6,000.003 $9,000.004 $12,000.005 $15,000.006 $18,000.007 $21,000.008 $24,000.00
P= $3,154.12
b i= 7.00%n= 8
INITIAL CF= -$75,000.00
$3,000.00G= $3,000.00
P= -$719.28 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 7%,8)+3,000*(P|G 7%,8)
P= -$719.29 USING EXCEL'S NPV FUNCTION THIS IS
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWEREOY CF
0 -$75,000.001 $3,000.002 $6,000.003 $9,000.004 $12,000.005 $15,000.006 $18,000.007 $21,000.008 $24,000.00
A1=
=NPV(6%,3000,3000+3000,3000+2*3000,3000+3*3000,3000+4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000
=NPV(6%,3000,6000,9000,12000,15000,18000,21000,24000)-75000
A1=
=NPV(7%,3000,3000+3000,3000+2*3000,3000+3*3000,3000+4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000
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P= -$719.29 =NPV(7%,3000,6000,9000,12000,15000,18000,21000,24000)-75000
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PROBLEM 2.99
a i= 5.00%n= 35
INITIAL CF= $0.00
$7,500.00G= $1,000.00
FW= $1,783,809.42 USING ELECTRONIC INTEREST TABLES THIS IS $0+$7,500*(F|A 5%,35)+$1,000*(P|G 5%,35)*(F|P 5%,35)
b i= 6.00%n= 35
INITIAL CF= $0.00
$7,500.00G= $1,000.00
FW= $2,109,674.39 USING ELECTRONIC INTEREST TABLES THIS IS $0+$7,500*(F|A 6%,35)+$1,000*(P|G 6%,35)*(F|P 6%,35)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
a FOR 5% b FOR 6%EOY CF EOY CF
0 $0.00 0 $0.001 $7,500.00 1 $7,500.002 $8,500.00 2 $8,500.003 $9,500.00 3 $9,500.004 $10,500.00 4 $10,500.005 $11,500.00 5 $11,500.006 $12,500.00 6 $12,500.007 $13,500.00 7 $13,500.008 $14,500.00 8 $14,500.009 $15,500.00 9 $15,500.00
10 $16,500.00 10 $16,500.0011 $17,500.00 11 $17,500.0012 $18,500.00 12 $18,500.0013 $19,500.00 13 $19,500.0014 $20,500.00 14 $20,500.00
A1=
A1=
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15 $21,500.00 15 $21,500.0016 $22,500.00 16 $22,500.0017 $23,500.00 17 $23,500.0018 $24,500.00 18 $24,500.0019 $25,500.00 19 $25,500.0020 $26,500.00 20 $26,500.0021 $27,500.00 21 $27,500.0022 $28,500.00 22 $28,500.0023 $29,500.00 23 $29,500.0024 $30,500.00 24 $30,500.0025 $31,500.00 25 $31,500.0026 $32,500.00 26 $32,500.0027 $33,500.00 27 $33,500.0028 $34,500.00 28 $34,500.0029 $35,500.00 29 $35,500.0030 $36,500.00 30 $36,500.0031 $37,500.00 31 $37,500.0032 $38,500.00 32 $38,500.0033 $39,500.00 33 $39,500.0034 $40,500.00 34 $40,500.0035 $41,500.00 35 $41,500.00
FW= $1,783,808.45 FW= $2,109,673.85 =FV(5%,35,,-NPV(5%,CF YR 1:CF YR 35)+0) =FV(6%,35,,-NPV(6%,CF YR 1:CF YR 35)+0)
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PROBLEM 2.100
i= 5.00%n= 5
INITIAL CF= -$90,000.00
$30,000.00G= -$3,000.00
PW= $15,173.64 USING INTEREST TABLES THIS IS =-$90,000+$30,000*(P|A 5%,5)-$3,000*(P|G 5%,5)
PW= $15,173.55 USING EXCEL'S NPV FUNCTION THIS IS
A1=
=NPV(5%,30000,30000-3000,30000-2*3000,30000-3*3000,30000-4*3000)-90000
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PROBLEM 2.101
a i= 6.00%n= 7
INITIAL CF= $0.00
$7,000.00G= -$1,000.00
EQ(t=5)= $31,618.32 USING INTEREST TABLES THIS IS =($7,000*(P|A 6%,7)-$1,000*(P|G 6%,7))*(F|P 6%,5)
b i= 10.00%n= 7
INITIAL CF= $0.00
$7,000.00G= -$1,000.00
EQ(t=5)= $34,329.34 USING INTEREST TABLES THIS IS =($7,000*(P|A 10%,7)-$1,000*(P|G 10%,7))*(F|P 10%,5)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
a EOY CF b EOY CF0 $0.00 0 $0.001 $7,000.00 1 $7,000.002 $6,000.00 2 $6,000.003 $5,000.00 3 $5,000.004 $4,000.00 4 $4,000.005 $3,000.00 5 $3,000.006 $2,000.00 6 $2,000.007 $1,000.00 7 $1,000.00
EQ(t=5)= $31,618.22 EQ(t=5)= $34,329.33
A1=
A1=
=FV(6%,5,,-NPV(6%,CF YR 1:CF YR 7)+0)
=FV(10%,5,,-NPV(10%,CF YR 1:CF YR 7)+0)
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PROBLEM 2.102
i= 12.00%n= 8
INITIAL CF= -$50,000.00
$13,000.00G= -$1,000.00
PW= $107.87 USING INTEREST TABLES THIS IS =-$50,000+$13,000*(P|A 12%,8)-$1,000*(P|G 12%,8)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00
PW= $107.87 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,CF YR 1:CF YR 8)-50000
A1=
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PROBLEM 2.103
i= 10.00%n= 8
INITIAL CF= -$50,000.00
$13,000.00G= -$1,000.00
A= $623.52 USING INTEREST TABLES THIS IS =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00
A= $623.32 USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS=PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))
A1=
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USING INTEREST TABLES THIS IS =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS=PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))
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PROBLEM 2.104
i= 8.00%n= 8
INITIAL CF= -$50,000.00
$13,000.00G= -$1,000.00
FW= $12,771.82 USING INTEREST TABLES THIS IS =(-$50,000+$13,000*(P|A 8%,8)-$1,000*(P|G 8%,8))*(F|P 8%,8)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00
FW= $12,771.80 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(8%,8,,-(NPV(8%,CF YR 1:CF YR 8)-50000))
A1=
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PROBLEM 2.105
i= 6.00%n= 8
INITIAL CF= -$50,000.00
$13,000.00G= -$1,000.00
FIRST, DETERMINE THE PW OF THE CASH FLOW SERIESPW= $10,885.69 USING INTEREST TABLES THIS IS
=-$50,000+$13,000*(P|A 6%,8)-$1,000*(P|G 6%,8)NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X
PW= $10,885.69 =X*(P|A 6%,8)+X*(P|G 6%,8)$10,885.69 =X*(6.20979+19.84158)$10,885.69 =26.05137*X
X= $417.85
THIS CAN ALSO BE WELL APPROACHED USING SOLVER AS FOLLOWS
X= $417.86 <--SOLVER CHANGED CELL
EOY CF EOY CF0 -$50,000.00 0 01 $13,000.00 1 $417.862 $12,000.00 2 $835.713 $11,000.00 3 $1,253.574 $10,000.00 4 $1,671.435 $9,000.00 5 $2,089.286 $8,000.00 6 $2,507.147 $7,000.00 7 $2,925.008 $6,000.00 8 $3,342.85
PW= $10,885.74 PW= $10,885.74 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION USING EXCEL'S NPV FUNCTION=NPV(6%,CF YR 1:CF YR 8)-50000 =NPV(6%,CF YR 1:CF YR 8)+0
A1=
FIRST, DETERMINE THE PW OF THE ORIGINAL CASH FLOW SERIES. THEN, LET X BE ANY VALUE AND SET UP A TABLE OVER 8 YEARS ASSUMING THE VALUE OF X IS CORRECT. DETERMINE THE PW OF THE CASH FLOWS IN THE TABLE USING THE CELL WHERE YOUR VALUE OF X IS STORED. THEN, USE SOLVER TO DETERMINE THE VALUE OF X THAT MAKES THE PW OF THE CASH FLOWS EQUAL TO THE PW VALUE OF THE ORIGINAL CASH FLOW SERIES
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NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X
<--SOLVER CHANGED CELL
<--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION
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PROBLEM 2.106
i= 6.00%n= 8
INITIAL CF= -$45,000.00
$12,000.00G= -$1,000.00
PW= $9,675.90 USING INTEREST TABLES THIS IS =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
AMT6= $13,725.46 USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,6)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00
PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS
AMT6= $13,725.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
A1=
=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000
=FV(6%,6,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))
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PROBLEM 2.107
i= 6.00%
8 YEARS IN ORIGINAL GRADIENT SERIESINITIAL CF= -$45,000.00
$12,000.00G= -$1,000.00t= 3 YEAR BEFORE ANNUAL SERIES FROM 4 TO 7
4 YEARS IN UNIFORM ANNUAL SERIES
PW= $9,675.90 USING INTEREST TABLES THIS IS =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
AMT3= $11,524.19 USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,3)
A(4-7)= $3,325.77 USING INTEREST TABLES THIS IS =$11,524.19*(A|P 6%,4)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00
PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000
AMT3= $11,524.21 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))
A(4-7)= $3,325.79 USING EXCEL'S PMT FUNCTION THIS IS=PMT(6%,4,-11524.21)
n1=
A1=
n2=
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YEARS IN ORIGINAL GRADIENT SERIES
YEAR BEFORE ANNUAL SERIES FROM 4 TO 7
YEARS IN UNIFORM ANNUAL SERIES
USING INTEREST TABLES THIS IS =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,3)USING INTEREST TABLES THIS IS =$11,524.19*(A|P 6%,4)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
USING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))USING EXCEL'S PMT FUNCTION THIS IS=PMT(6%,4,-11524.21)
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PROBLEM 2.108
FROM PROBLEM 2.106:i= 6.00%n= 8
INITIAL CF= -$45,000.00
$12,000.00G= -$1,000.00
PW= $9,675.90 USING INTEREST TABLES THIS IS =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
PW= $9,675.90 USING INTEREST TABLES THIS IS
WE KNOW $10,000
WE KNOW $10,000-7*GPW= $9,675.90 =-$45,000+($10,000-7*G)*(P|A 6%,8)+G*(P|G 6%,8)
=-$45,000+($10,000-7*G)*6.20979+G*19.84158=$17,097.90-23.62695*G
G= $314.13
THEREFORE
$10,000.00 GIVEN IN PROBLEM
$7,801.07 =10000-7*314.13G= $314.13
THIS IS EASIER DONE USING SOLVER AS FOLLOWSFIRST, FIND THE PW OF THE ORIGINAL GRADIENT SERIES
EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00
PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS
G= $314.13 <--SOLVER CHANGED CELL
A1=
NOW, SET UP A NEW GRADIENT SERIES THAT HAS THE SAME PW AS THE ORIGINAL SERIES
=A1*(P|A 6%,8)+G*(P|G 6%,8)
A8=
A1=
A8=
A1=
=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000
NOW, SET THE GRADIENT AMOUNT "G" TO ANY VALUE AND GO FORWARD AS IF IT IS THE CORRECT VALUE
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$10,000.00 GIVEN IN PROBLEM
EOY CF0 -$45,000.001 $7,801.082 $8,115.213 $8,429.344 $8,743.475 $9,057.606 $9,371.747 $9,685.878 $10,000.00
PW= $9,675.95 <--SOLVER TARGET CELL=NPV(6%,CF YR 1:CF YR 8)-45000
NOW, SET UP ANOTHER TABLE OF CASH FLOWS USING THE FACT THAT A8=$10,000, A1=$10,000-7*G, AND A0=-$45,000. THEN, USE SOLVER TO FIND THE PW OF THE SERIES EQUAL TO THAT OF THE ORIGINAL SERIES WHILE CHANGING THE VALUE OF G
A8=
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PROBLEM 2.109
i= 8.00%n= 5
$500.00 G= $100.00
a P= $2,733.60 USING INTEREST TABLES THIS IS =$500*(P|A 8%,5)+$100*(P|G 8%,5)
P= $2,733.60 USING EXCEL'S NPV FUNCTION THIS IS=NPV(C3,500,600,700,800,900)
b A= $684.65 USING INTEREST TABLES THIS IS =$500+$100*(A|G 8%,5)
A= $684.65 USING EXCEL'S PMT FUNCTION THIS IS=PMT(8%,5,-2733.60)
A1=
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PROBLEM 2.110
i= 12.00%n= 25
$1,000.00G= $200.00
a P= $18,464.07 USING INTEREST TABLES THIS IS =$1,000*(P|A 12%,25)+$200*(P|G 12%,25)
F= $313,890.26 USING INTEREST TABLES THIS IS =$18,464.07*(F|P 12%,25)
F= $313,890.35 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,25,,-18464.07)
b A= $2,354.17 USING INTEREST TABLES THIS IS =$1,000+$200*(A|G 12%,25)
A= $2,354.18 USING INTEREST TABLES THIS IS =$313,890.35*(A|F 12%,25)
A= $2,354.17 USING EXCEL'S PMT FUNCTION THIS IS=PMT(12%,25,,-313890.35)
A1=
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PROBLEM 2.111
i= 10.00%n= 10
$7,000.00G= -$300.00
a P= $36,144.59 USING INTEREST TABLES THIS IS =$7,000*(P|A 10%,10)-$300*(P|G 10%,10)
F= $93,749.66 USING INTEREST TABLES THIS IS =$36,144.59*(F|P 10%,10)
F= $93,749.75 USING EXCEL'S FV FUNCTION THIS IS=FV(10%,10,,-36144.59)
b A= $2,354.17 USING INTEREST TABLES THIS IS =$7,000-$300*(A|G 10%,10)
A= $5,882.80 USING INTEREST TABLES THIS IS =$93,749.66*(A|F 10%,10)
A= $5,882.37 USING EXCEL'S PMT FUNCTION THIS IS=PMT(10%,10,,-93749.75)
A1=
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PROBLEM 2.112
i= 8.00%n= 6P= $140,000.00
$11,000.00X= G
a
PW= USING INTEREST TABLES THIS IS =$11,000*(P|A 8%,6)+G*(P|G 8%,6)=$11,000*4.62288+G*10.52327
SO $140,000.00 =$50,851.68+G*10.52327G=X $8,471.54 =(140000-50851.68)/10.52327
G=X $8,471.54 <--SOLVER CHANGED CELL
EOY CF01 $11,000.002 $19,471.543 $27,943.084 $36,414.625 $44,886.166 $53,357.69
P= $140,000.00 <--SOLVER TARGET CELL=NPV(8%,CF YR 1:CF YR 6)+0
b LAST PAYMENT $53,357.69 =11000+5*8471.54
c i= 8.00%n= 6P= $140,000.00
G=X -$7,500.00
PW= $140,000.00 USING INTEREST TABLES THIS IS
$140,000.00
$140,000.00
A1=
THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G.
THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G.
THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE GRADIENT IS KNOWN, SOLVE FOR THE FIRST PAYMENT A1.
=A1*(P|A 8%,6)-$7,500*(P|G 8%,6)
=A1*4.62288-$7,500*10.52327
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SO $140,000.00
$47,356.74 =(140000+78924.53)/4.62288
$47,356.75 <--SOLVER CHANGED CELL
EOY CF01 $47,356.752 $39,856.753 $32,356.754 $24,856.755 $17,356.756 $9,856.75
P= $140,000.00 <--SOLVER TARGET CELL=NPV(8%,CF YR 1:CF YR 6)+0
=A1*4.62288-$78,924.53
A1=
THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "A1" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF A1 TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF A1.
A1=
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PROBLEM 2.113
i= 10.00%n= 9P= $170,000.00A= $10,000.00 YEARS 1, 2, 3, 4
$11,000.00 YEAR 5X= G
a
PW= USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,9)+G*(P|G 10%,6)*(P|F 10%,3)=$10,000*5.75902+G*9.68417*0.75131
SO $170,000.00 =$57590.20+G*7.27581G=X= $15,449.80 $15,449.80
G=X= $15,449.68 <--SOLVER CHANGED CELL
EOY CF01 $10,000.002 $10,000.003 $10,000.004 $10,000.005 $25,449.686 $40,899.377 $56,349.058 $71,798.749 $87,248.42
P= $170,000.00 <--SOLVER TARGET CELL=NPV(10%,CF YR 1:CF YR 9)+0
bLAST PAYMENT=
$87,248.42 =10000+5*15449.68
c TOTAL INTEREST PAID=$151,745.27 =SUM(CF YR 0:CF YR 9)-170000
A1=
THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G.
THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G.
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PROBLEM 2.114
i= 10.00%n= 5
$10,000.00G= -$1,000.00
P= $31,046.10 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,5)-$1,000*(P|G 10%,5)
AMT3= $41,322.36 USING INTEREST TABLES THIS IS $31,046.10*(F|P 10%,3)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF0 $0.001 $10,000.002 $9,000.003 $8,000.004 $7,000.005 $6,000.00
AMT3= $41,322.31 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS
A1=
=NPV(10%,7000,6000)+FV(10%,2,,-10000)+FV(10%,1,,-9000)+8000
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PROBLEM 2.115
a n= 4
-$10,000.00
$3,000.00G= $1,000.00
i= 24.8883% <--SOLVER CHANGED CELL
PW= $0.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =-10000+3000*((1+i)^4-1)/(i*(1+i)^4)+1000*(1-(1+4*i)*(1+i)^(-4))/(i^2)
i= 24.8883% <--SOLVER CHANGED CELL
EOY CF0 -$10,000.001 $3,000.002 $4,000.003 $5,000.004 $6,000.00
P= $0.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(i%,3000,4000,5000,6000)-10000
b i= 24.8883%
A= $4,226.00 <--SOLVER CHANGED CELL
P= $0.00 <--SOLVER TARGET CELLFORMULAS=-10000+A*((1+0.2489)^4-1)/(0.2489*(1+0.2489)^4)
A0=
A1=
THIS PROBLEM, IN WHICH THE VALUE OF THE INTEREST RATE IS TO BE FOUND, IS BEST APPROACHED USING SOLVER. THIS IS DUE TO THE DIFFICULTY OF TRYING TO SOLVE ANALYTICALLY FOR THE INTEREST RATE USING FORMULAS OR INTERPOLATION.
BEGIN BY SETTING A CELL TO HOUSE THE INTEREST RATE. SELECT ANY INTEREST RATE FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.
NOW, DEVELOP A FORMULA FOR THE OVERALL PW AS A FUNCTION OF THE INTEREST RATE. THEN, USE SOLVER TO SET THE PW VALUE EQUAL TO 0 BY CHANGING THE INTEREST RATE i.
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE INTEREST RATE FOUND USING SOLVER BELOW IS THE SAME VALUE FOUND ABOVE.
BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE EQUAL ANNUAL INCOMES, "A." SELECT ANY VALUE FOR "A" IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.
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A= $4,226.00 <--SOLVER CHANGED CELL
EOY CF0 -$10,000.001 $4,226.002 $4,226.003 $4,226.004 $4,226.00
P= $0.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(24.8883%,4226,4226,4226,4226)-10000
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE EQUAL ANNUAL INCOME "A" FOUND BELOW IS THE SAME VALUE FOUND ABOVE.
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PROBLEM 2.116
a P= INR 20,000,000.00i= 5.00%n= 10
INR 2,000,000.00X= G
P= INR 20,000,000.00 USING INTEREST TABLES THIS IS INR 20,000,000.00 =INR 2,000,000*(P|A 5%,10)+G*(P|G 5%,10)INR 20,000,000.00 =INR 2,000,000*7.72173+G*31.65205INR 20,000,000.00 =INR 15,443,460+G*31.65205
G=X= INR 143,957.18 =(20000000-15443460)/31.65205
G=X= INR 143,956.88 <--SOLVER CHANGED CELL
EOY CF0 INR 0.001 INR 2,000,000.002 INR 2,143,956.883 INR 2,287,913.774 INR 2,431,870.655 INR 2,575,827.536 INR 2,719,784.417 INR 2,863,741.308 INR 3,007,698.189 INR 3,151,655.06
10 INR 3,295,611.94
P= INR 20,000,000.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 10)+0
b AMT5= INR 12,960,976.54 USING INTEREST TABLES THIS IS
AMT5= INR 12,961,013.55 USING INTEREST TABLES THIS IS
AMT5= INR 12,961,004.03 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 6:CF YR 10)
A1=
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF G=X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.
=INR 20,000,000*(F|P 5%,5)-2,000,000(F|A 5%,5)-143,957.18(P|G 5%,5)(F|P 5%,5)
=INR 2,719,784.41*(P|A 5%,5)+INR 143,956.88*(P|G 5%,5)
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PROBLEM 2.117
i= 7.00%
EOY -1 0 1 2 3 4 5 6 7 8 9 10CF $1,200 $1,000 $800 $500 $500 $500 $500 $0 -$800 -$800 $0 $1,500
TO FIND THE VALUE OF AMT5,
AMT5= $6,189.74 USING INTEREST TABLES THIS IS
CHECK THIS USING EXCEL'S NPV AND FV FUNCTIONS
AMT5= $6,189.73 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS=NPV(7%,CF YR 6:CF YR 10)+FV(7%,7,,-NPV(7%,CF YR -1:CF YR 5))
=(($1,200-$200*(A|G 7%,3))*(F|A 7%,3)*(P|F 7%,2)+$500*(P|A 7%,4)*(P|F 7%,2)-$800*(F|A 7%,2)*(P|F 7%,9)+$1,500*(P|F 7%,11))*(F|P 7%,6)
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PROBLEM 2.118
i= 8.00%n= 40
$2,000.00
$1,000.00
20
$21,000.00
-$1,000.00
20
FIRST, FIND THE PW OF THE CASH FLOW PROFILE.
P= $118,139.04 USING INTEREST TABLES THIS IS
G= $500.00
P= $118,139.04 USING INTEREST TABLES THIS IS $118,139.04 =X*(P|A 8%,40)+$500*(P|G 8%,40)$118,139.04 =X*11.92461+$500*126.04220$118,139.04 =11.92461*X+$63,021.10
X= $4,622.20 =(118139.04-63021.1)/11.92461**********OR, RATHER THAN PERFORM THE ABOVE CALCULATIONS, CAN USE SOLVER
X= $4,622.20 <--SOLVER CHANGED CELL
G= $500.00
P= $118,139.04 <--SOLVER TARGET CELLUSING INTEREST TABLES THIS IS =X*(P|A 8%,40)+$500*(P|G 8%,40)
**********
A11=
G1=
n1=
A12=
G2=
n2=
=$2,000*(P|A 8%,20)+$1,000*(P|G 8%,20)+($21,000*(P|A 8%,20)-$1,000*(P|G 8%,20))*(P|F 8%,20)
NOW, LET X EQUAL THE FIRST OF 40 AMOUNTS IN A GRADIENT SERIES WITH GRADIENT G=$500. SOLVE FOR THE PW OF THIS GRADIENT SERIES.
BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.
NOW, DEVELOP A FORMULA FOR THE PW AS A FUNCTION OF X. THEN, USE SOLVER TO SET THE PW VALUE TO ITS TARGET VALUE BY CHANGING THE VALUE OF X.
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.
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X= $4,622.18 <--SOLVER CHANGED CELL
ORIGINAL NEWEOY CF CF
0 $0.00 $0.001 $2,000.00 $4,622.182 $3,000.00 $5,122.183 $4,000.00 $5,622.184 $5,000.00 $6,122.185 $6,000.00 $6,622.186 $7,000.00 $7,122.187 $8,000.00 $7,622.188 $9,000.00 $8,122.189 $10,000.00 $8,622.18
10 $11,000.00 $9,122.1811 $12,000.00 $9,622.1812 $13,000.00 $10,122.1813 $14,000.00 $10,622.1814 $15,000.00 $11,122.1815 $16,000.00 $11,622.1816 $17,000.00 $12,122.1817 $18,000.00 $12,622.1818 $19,000.00 $13,122.1819 $20,000.00 $13,622.1820 $21,000.00 $14,122.1821 $21,000.00 $14,622.1822 $20,000.00 $15,122.1823 $19,000.00 $15,622.1824 $18,000.00 $16,122.1825 $17,000.00 $16,622.1826 $16,000.00 $17,122.1827 $15,000.00 $17,622.1828 $14,000.00 $18,122.1829 $13,000.00 $18,622.1830 $12,000.00 $19,122.1831 $11,000.00 $19,622.1832 $10,000.00 $20,122.1833 $9,000.00 $20,622.1834 $8,000.00 $21,122.1835 $7,000.00 $21,622.1836 $6,000.00 $22,122.1837 $5,000.00 $22,622.1838 $4,000.00 $23,122.1839 $3,000.00 $23,622.1840 $2,000.00 $24,122.18
BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.
FIRST SOLVE FOR THE PW OF THE ORIGINAL GRADIENT SERIES. THEN, ADJUST THE PW OF THE NEW GRADIENT SERIES WITH FIRST AMOUNT X AND GRADIENT G=500 TO THE PW OF THE ORIGINAL SERIES BY ADJUSTING THE VALUE OF X. NOTE THAT THE VALUE OF X BELOW IS ESSENTIALLY THE SAME AS THE VALUE FOUND ABOVE.
A B C D E F G H I
44
454647
48
4950515253545556575859606162636465666768697071727374757677787980818283848586878889909192
P= $118,138.78 $118,138.78 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(8%,NEW CF YR 1: NEW CF YR 40)+CF YR 0
A B C D E F G H I93949596
PROBLEM 2.119
EOY 0 1 2 3 4 5 6 7 8 9 10CF $100 $80 $60 $40 $20 $0 -$20 -$40 -$60 -$80 -$100
i= 18.00%n= 11
$100.00 G= -$20.00
PW= $172.48 USING INTEREST TABLES THIS IS =($100*(P|A 18%,11)-$20*(P|G 18%,11))*(F|P18%,1)
PW= $172.48 USING EXCEL'S FV FUNCTION THIS IS=FV(18%,1,,-NPV(18%,100,80,60,40,20,0,-20,-40,-60,-80,-100))
A1=
A B C D E F G H I J K L M N1234567
8
9101112131415
PROBLEM 2.120
TOTALEOY CF1 CF2 CF3 CF4 CF
0 $800.00 $800.001 $950.00 $0.00 $950.002 $950.00 -$450.00 $500.003 $950.00 -$900.00 $50.004 $950.00 -$1,350.00 -$400.005 -$600.00 -$600.006 -$600.00 -$600.007 -$600.00 -$600.00
A B C D E F G123456789
101112
PROBLEM 2.121
EOY CF1 CF2 CF3 CF0 -$7,000.00 -$7,000.001 $0.002 $0.003 $0.004 $0.005 $1,850.00 $0.00 $1,850.006 $1,850.00 $200.00 $2,050.007 $1,850.00 $400.00 $2,250.008 $1,850.00 $600.00 $2,450.009 $1,850.00 $800.00 $2,650.00
10 $1,850.00 $1,000.00 $2,850.00
A B C D E F123456789
1011121314
PROBLEM 2.122
a (F|G i%,n)=(P|G i%,n)*(F|P i%,n)
b (F|G i%,n)= ((1+i)^n-(1+n*i))/(i^2)
c i= 10.00%n= 5
$0.00G= $1,000.00
USING THE METHOD OF PART a
(F|G i%,n)=(P|G i%,n)*(F|P i%,n)(P|G 10%,5)= 6.8618(F|P 10%,5)= 1.61051
F= $11,051.00 USING INTEREST TABLES THIS IS $1,000*(P|G 10%,5)*(F|P 10%,5)
USING THE METHOD OF PART b
(F|G i%,n)= 11.05100 =((1+0.1)^5-(1+5*0.1))/(0.1^2)
F= $11,051.00 =$1,000.00*11.05100
A1=
A B C D E F12345678
9
101112131415161718192021222324
USING INTEREST TABLES THIS IS
G12345678
9
101112131415161718192021222324
PROBLEM 2.123
FACTOR
i= 7.00%USING 7% FOR EXAMPLE CALCj= 5.00%USING 5% FOR EXAMPLE CALCn= 10USING 10 FOR EXAMPLE CALC
8.59763CHECKS WITH GEOMETRIC SERIES-PRESENT WORTH TABLE
FACTOR
i= 7.00% USING 7% FOR EXAMPLE CALCj= 5.00% USING 5% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC
16.91284 CHECKS WITH GEOMETRIC SERIES-FUTURE WORTH TABLE
FACTOR
i= 7.00% USING 7% FOR EXAMPLE CALCj= 5.00% USING 5% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC
1.22411 NOT TABULATED IN APPENDIX A
NOW, COMPLETING THE PROBLEM:
$1,000.00i= 7.00%j= 5.00%
A= $1,224.11=$1,000*1.22411
A= $1,224.13
=$1,000*8.59763*0.14238
A= $1,224.15
=$1,000*16.91284*0.07238
P|A1
P|A1=
F|A1
F|A1=
A|A1
A|A1=
A1=
USING A|A1 FACTOR
USING P|A1 FACTOR * A|P FACTOR
=$1,000*(P|A1 7%,5%,10)*(A|P 7%,10)
USING F|A1 FACTOR * A|F FACTOR
=$1,000*(F|A1 7%,5%,10)*(A|F 7%,10)
A B C D E F G H I12
3
4567
8
910
11
12131415
16
1718
19
20212223
24
252627
28
293031
32
3334
35
36
3738
39
40
41
PROBLEM 2.124
i= 5.00%n= 30
$7,500.00j= 5.00%
F= $926,130.53 USING INTEREST TABLES THIS IS
**********
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF01 $7,500.00 =$7,500*(1+0.05)^(1-1)2 $7,875.00 =$7,500*(1+0.05)^(2-1)3 $8,268.754 $8,682.195 $9,116.306 $9,572.117 $10,050.728 $10,553.259 $11,080.92
10 $11,634.9611 $12,216.7112 $12,827.5513 $13,468.9214 $14,142.3715 $14,849.4916 $15,591.9617 $16,371.5618 $17,190.1419 $18,049.6420 $18,952.1321 $19,899.7322 $20,894.7223 $21,939.4624 $23,036.4325 $24,188.2526 $25,397.6627 $26,667.5528 $28,000.9229 $29,400.9730 $30,871.02 =$7,500*(1+0.05)^(30-1)
F= $926,130.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(5%,30,,-NPV(5%,CF YR 1:CF YR 30)+0)
A1=
=$7,500*(F|A1 5%,5%,30)
A B C D E F G1234
5
678
9
101112131415161718192021222324252627282930313233343536373839404142434445464748
PROBLEM 2.125
i= 6.00%n= 30
$7,500.00j= 6.00%
F= $1,219,137.30 USING INTEREST TABLES THIS IS
**********
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF01 $7,500.00 =$7,500*(1+0.06)^(1-1)2 $7,950.00 =$7,500*(1+0.06)^(2-1)3 $8,427.004 $8,932.625 $9,468.586 $10,036.697 $10,638.898 $11,277.239 $11,953.86
10 $12,671.0911 $13,431.3612 $14,237.2413 $15,091.4714 $15,996.9615 $16,956.7816 $17,974.1917 $19,052.6418 $20,195.8019 $21,407.5420 $22,692.0021 $24,053.5222 $25,496.7323 $27,026.5324 $28,648.1225 $30,367.0126 $32,189.0327 $34,120.3728 $36,167.5929 $38,337.6530 $40,637.91 =$7,500*(1+0.06)^(30-1)
F= $1,219,137.28 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,30,,-NPV(6%,CF YR 1:CF YR 30)+0)
A1=
=$7,500*(F|A1 6%,6%,30)
A B C D E F G1234
5
678
9
101112131415161718192021222324252627282930313233343536373839404142434445464748
PROBLEM 2.126
i= 5.00%n= 35
$7,500.00j= 8.00%
F= $2,317,332.22 USING ELECTRONIC INTEREST TABLES THIS IS
**********
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
AGE EOY CF25 026 1 $7,500.00 =$7,500*(1+0.08)^(1-1)27 2 $8,100.00 =$7,500*(1+0.08)^(2-1)28 3 $8,748.0029 4 $9,447.8430 5 $10,203.6731 6 $11,019.9632 7 $11,901.5633 8 $12,853.6834 9 $13,881.9835 10 $14,992.5336 11 $16,191.9437 12 $17,487.2938 13 $18,886.2839 14 $20,397.1840 15 $22,028.9541 16 $23,791.2742 17 $25,694.5743 18 $27,750.1444 19 $29,970.1545 20 $32,367.7646 21 $34,957.1847 22 $37,753.7548 23 $40,774.0549 24 $44,035.9850 25 $47,558.8651 26 $51,363.5652 27 $55,472.6553 28 $59,910.4654 29 $64,703.3055 30 $69,879.5656 31 $75,469.9357 32 $81,507.5258 33 $88,028.1259 34 $95,070.3760 35 $102,676.00 =$7,500*(1+0.08)^(35-1)
F= $2,317,332.23
A1=
=$7,500*(F|A1 5%,8%,35)
USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
A B C D E F1234
5
678
9
101112131415161718192021222324252627282930313233343536373839404142434445464748495051
52
=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)
A B C D E F
53
PROBLEM 2.127
FIRST, REVIEW THE ORIGINAL PROBLEM 2.126
i= 5.00%n= 35
$7,500.00j= 8.00%
F= $2,317,332.22 USING ELECTRONIC INTEREST TABLES THIS IS
F= $2,317,332.22 USING ELECTRONIC INTEREST TABLES THIS IS
$2,317,332.22
$2,317,332.22
$20,080.69 =2317332.23/115.40101**********
$20,080.17 SOLVER CHANGED CELLORIGINAL NEW
AGE EOY CF AGE EOY CF25 0 25 026 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 26 1 $0.0027 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 27 2 $0.0028 3 $8,748.00 28 3 $0.0029 4 $9,447.84 29 4 $0.0030 5 $10,203.67 30 5 $0.0031 6 $11,019.96 31 6 $0.0032 7 $11,901.56 32 7 $0.0033 8 $12,853.68 33 8 $0.0034 9 $13,881.98 34 9 $0.0035 10 $14,992.53 35 10 $0.0036 11 $16,191.94 36 11 $20,080.1737 12 $17,487.29 37 12 $21,686.5838 13 $18,886.28 38 13 $23,421.5139 14 $20,397.18 39 14 $25,295.2340 15 $22,028.95 40 15 $27,318.8541 16 $23,791.27 41 16 $29,504.3642 17 $25,694.57 42 17 $31,864.7143 18 $27,750.14 43 18 $34,413.8844 19 $29,970.15 44 19 $37,167.0045 20 $32,367.76 45 20 $40,140.3546 21 $34,957.18 46 21 $43,351.5847 22 $37,753.75 47 22 $46,819.7148 23 $40,774.05 48 23 $50,565.2949 24 $44,035.98 49 24 $54,610.51
A1=
=$7,500*(F|A1 5%,8%,35)
NOW, SOLVE FOR THE FIRST INVESTMENT ON HIS 36TH BIRTHDAY TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A1 BE THE VALUE OF THE FIRST INVESTMENT AT EOY 36.
=A1*(F|A1 5%,8%,25)
=A1*115.40101
A1=
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF A1 FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.
A1=
50 25 $47,558.86 50 25 $58,979.3551 26 $51,363.56 51 26 $63,697.7052 27 $55,472.65 52 27 $68,793.5153 28 $59,910.46 53 28 $74,297.0054 29 $64,703.30 54 29 $80,240.7655 30 $69,879.56 55 30 $86,660.0256 31 $75,469.93 56 31 $93,592.8257 32 $81,507.52 57 32 $101,080.2458 33 $88,028.12 58 33 $109,166.6659 34 $95,070.37 59 34 $117,899.9960 35 $102,676.00 =$7,500*(1+0.08)^(35-1) 60 35 $127,331.99
F= $2,317,332.23 F= $2,317,332.23
SOLVER TARGET CELL
USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)
=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)
PROBLEM 2.128
FIRST, REVIEW THE ORIGINAL PROBLEM 2.126
i= 5.00%j= 8.00%n= 35
$7,500.00
F= $2,317,332.22 USING ELECTRONIC INTEREST TABLES THIS IS
F= $2,317,332.23 USING COMPOUND INTEREST FORMULAS THIS IS=7500*(((1+0.05)^35-(1+0.08)^35))/(0.05-0.08)
A= $25,656.82 USING COMPOUND INTEREST FORMULAS THIS IS=2317332.23*(0.05/((1+0.05)^35-1))
A= $25,652.87 USING INTEREST TABLES THIS IS =$2,317,332.23*(A|F 5%,35)
A= $25,656.82 USING EXCEL'S PMT FUNCTION THIS IS=PMT(5%,35,,-2317332.23)
A= $25,656.82
ORIGINAL CHECK NEWAGE EOY CF AGE EOY CF25 0 25 026 1 $7,500.00 26 1 $25,656.8227 2 $8,100.00 27 2 $25,656.8228 3 $8,748.00 28 3 $25,656.8229 4 $9,447.84 29 4 $25,656.8230 5 $10,203.67 30 5 $25,656.8231 6 $11,019.96 31 6 $25,656.8232 7 $11,901.56 32 7 $25,656.8233 8 $12,853.68 33 8 $25,656.8234 9 $13,881.98 34 9 $25,656.8235 10 $14,992.53 35 10 $25,656.8236 11 $16,191.94 36 11 $25,656.8237 12 $17,487.29 37 12 $25,656.8238 13 $18,886.28 38 13 $25,656.8239 14 $20,397.18 39 14 $25,656.8240 15 $22,028.95 40 15 $25,656.8241 16 $23,791.27 41 16 $25,656.82
A1=
=$7,500*(F|A1 5%,8%,35)
NOW, SOLVE FOR THE UNIFORM ANNUAL INVESTMENT TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A BE THE VALUE OF THE ANNUAL INVESTMENT.
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF "A" FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.
A B C D E F G H I1234567
8
910
11
12
13
14151617181920212223242526
27
28293031323334353637383940414243444546474849
42 17 $25,694.57 42 17 $25,656.8243 18 $27,750.14 43 18 $25,656.8244 19 $29,970.15 44 19 $25,656.8245 20 $32,367.76 45 20 $25,656.8246 21 $34,957.18 46 21 $25,656.8247 22 $37,753.75 47 22 $25,656.8248 23 $40,774.05 48 23 $25,656.8249 24 $44,035.98 49 24 $25,656.8250 25 $47,558.86 50 25 $25,656.8251 26 $51,363.56 51 26 $25,656.8252 27 $55,472.65 52 27 $25,656.8253 28 $59,910.46 53 28 $25,656.8254 29 $64,703.30 54 29 $25,656.8255 30 $69,879.56 55 30 $25,656.8256 31 $75,469.93 56 31 $25,656.8257 32 $81,507.52 57 32 $25,656.8258 33 $88,028.12 58 33 $25,656.8259 34 $95,070.37 59 34 $25,656.8260 35 $102,676.00 60 35 $25,656.82
F= $2,317,332.23 F= $2,317,332.23
SOLVER TARGET CELL
USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+CF YR 0)
=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+CF YR 0)
A B C D E F G H I50515253545556575859606162636465666768697071
72
73
74
EXCELJ K L M N O
50515253545556575859606162636465666768697071
72
73
74
PROBLEM 2.129
P= -$90,000.00i= 5.00%j= -10.00%n= 5
$30,000.00
PW= $17,467.13 USING COMPOUND INTEREST FORMULAS THIS IS=30000*((1-(1-0.1)^5*(1+0.05)^-5)/(0.05+0.1))-90000
PW= $17,467.20 USING INTEREST TABLES THIS IS
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER.
EOY CF0 -$90,000.001 $30,000.002 $27,000.003 $24,300.004 $21,870.005 $19,683.00
PW= $17,467.13 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 5)-90000
A1=
=$30,000*(P|A1 5%,-10%,5)-$90,000
A B C D E F123456
7
89
101112
13
14151617181920212223242526
PROBLEM 2.130
FIRST, FIND THE PW OF THE GIVEN CF PROFILE
i= 6.00%n= 8
INIT INV= $45,000.00
$12,000.00G= -$1,000.00
P= $9,675.90 USING INTEREST TABLES THIS IS -$45,000+$12,000(P|A 6%,8)-$1,000(P|G 6%,8)
P= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS
AT THIS POINT, WE KNOW THE PW OF THE CF PROFILE.
i= 6.00%n= 8
INIT INV= $45,000
$10,000
j= -4.04% <--SOLVER CHANGED CELL
P= $9,675.90 <--SOLVER TARGET CELLUSING INTEREST TABLES THIS IS
j= -4.04% <--SOLVER CHANGED CELL
EOY CF0 -$45,000.001 $10,000.002 $9,596.293 $9,208.874 $8,837.105 $8,480.336 $8,137.97
A1=
=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000
TO SOLVE FOR THE VALUE OF j, IT IS MUCH EASIER TO USE SOLVER RATHER THAN TO TRY INTERPOLATION OR AN ANALYTICAL SOLUTION
A1=
BEGIN BY SETTING THE VALUE OF "j" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF j TO DEVELOP THE CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO EQUAL THE PW OF THE ORIGINAL CF SERIES BY CHANGING j.
-$45,000+$10,000*(P|A1 6%,j%,8)
SEE BELOW FOR TABULATED CASH FLOWS WITH SOLVER USED TO CONFIRM THE ABOVE ANSWER. NOTE THAT THE VALUE OF j FOUND IS EQUAL TO THAT FOUND ABOVE.
A B C D E F G H1234567
8
91011121314
15
161718
19
20212223
24
25
26
2728293031
32
33
34
3536373839404142434445
7 $7,809.438 $7,494.15
PW= $9,675.95 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,CF YR 1:CF YR 8)-45000
A B C D E F G H464748495051
PROBLEM 2.131
i= 5.00%j= 10.00%n= 18
$2,000.00
PW= $52,410.42 USING COMPOUND INTEREST FORMULA THIS IS
PW= $52,410.42 USING INTEREST TABLES THIS IS
FW= $126,131.92 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,18,,-52410.42)
SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER.
EOY CF01 $2,000.002 $2,200.003 $2,420.004 $2,662.005 $2,928.206 $3,221.027 $3,543.128 $3,897.439 $4,287.18
10 $4,715.9011 $5,187.4812 $5,706.2313 $6,276.8614 $6,904.5415 $7,595.0016 $8,354.5017 $9,189.9518 $10,108.94
PW= $52,410.42 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 18)+0
FW= $126,131.96 USING INTEREST TABLES THIS IS =$52,410*(F|P 5%,18)
A1=
=$2,000*(P|A1 5%,10%,18)
=$2,000*(P|A1 5%,10%,18)
A B C D E F G H12345
6
78
9
1011
12
1314151617181920212223242526272829303132333435363738394041424344
PROBLEM 2.132
i= 12.00%j= 15.00%n= 6
$50,000.00
PW= $286,447.62 USING COMPOUND INTEREST FORMULAS THIS IS =50000*((1-(1+0.15)^6*(1+0.12)^-6)/(0.12-0.15))
PW= $286,447.50 USING ELECTRONIC INTEREST TABLES THIS IS
SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER.
EOY CF01 $50,000.002 $57,500.003 $66,125.004 $76,043.755 $87,450.316 $100,567.86
PW= $286,447.62 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,CF YR 1:CF YR 6)+0
A1=
=$50,000*(P|A1 12%,15%,6)
A B C D E F G12345
6
789
1011
12
1314151617181920212223242526
SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER.
H12345
6
789
1011
12
1314151617181920212223242526
PROBLEM 2.133
i= 7.00% COMPOUNDED ANNUALLYj= -40.00% COMPOUNDED ANNUALLYn= 4
$60,000.00
PW= $115,038.00 USING INTEREST TABLES THIS IS
PW= $115,037.72 USING FORMULAS THIS IS =60000*((1-(1-0.4)^4*(1+0.07)^-4)/(0.07-(-0.4)))
SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER.
EOY CF0 $0.001 $60,000.002 $36,000.003 $21,600.004 $12,960.00
PW= $115,037.72 USING EXCEL'S NPV FUNCTION THIS IS =NPV(7%,60000,36000,21600,12960)+0
A1=
=$60,000*(P|A1 7%,-40%,4)
A B C D E F12345
6
78
9
101112131415161718192021222324
PROBLEM 2.134
i= 15.00%j= 6.00%n= 20
$1,000.00
PW= $8,933.81 TABLES FROM APPENDIX A
PW= $8,933.81 TABLES FROM PROBLEM 2.123
USING TABULATED CASH FLOWS
EOY CF0 $0.001 $1,000.002 $1,060.003 $1,123.604 $1,191.025 $1,262.486 $1,338.237 $1,418.528 $1,503.639 $1,593.85
10 $1,689.4811 $1,790.8512 $1,898.3013 $2,012.2014 $2,132.9315 $2,260.9016 $2,396.5617 $2,540.3518 $2,692.7719 $2,854.3420 $3,025.60
PW= $8,933.81 USING EXCEL'S NPV FUNCTION THIS IS=NPV(15%,CF YR 1:CF YR 20)+0
A1=
=$1,000*(P|A1 15%,6%,20)
=$1,000*(P|A1 15%,6%,20)
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PROBLEM 2.135
i= 5.00%j= 10.00%n= 5
$1,000.00
PW= $5,237.53 USING INTEREST TABLES THIS IS
PW= $5,237.53 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)
A1=
=$1,000*(P|A1 5%,10%,5)
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=NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)
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PROBLEM 2.136
i= 5.00%j= 15.00%n= 7
$4,000.00
F= $50,116.76 USING INTEREST TABLES THIS IS
F= $50,116.78 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS
A1=
=$4,000*(F|A1 5%,15%,7)
=FV(5%,7,,-NPV(5%,4000,4000*1.15,4000*1.15^2,4000*1.15^3,4000*1.15^4,4000*1.15^5,4000*1.15^6))
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PROBLEM 2.137
i= 10.00%j= 5.00%n= 6
$9,000.00
PW= $43,839.18 USING INTEREST TABLES THIS IS
PW= $43,839.17 USING EXCEL'S NPV FUNCTION THIS IS
A1=
=$9,000*(P|A1 10%,5%,6)
=NPV(10%,9000,9000*1.05,9000*1.05^2,9000*1.05^3,9000*1.05^4,9000*1.05^5)
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PROBLEM 2.138
i= 10.00%j= 15.00%n= 4
$2,000.00
a PW= $7,783.80 USING INTEREST TABLES THIS IS
PW= $7,783.79 USING EXCEL'S NPV FUNCTION THIS IS=NPV(10%,2000,2000*1.15,2000*1.15^2,2000*1.15^3)
b A= $2,455.56 USING INTEREST TABLES THIS IS =$7,783.80*(A|P 10%,4)
A= $2,455.56 USING EXCEL'S PMT FUNCTION THIS IS=PMT(10%,4,-7783.79)
A1=
=$2,000*(P|A1 10%,15%,4)
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PROBLEM 2.139
i= 15.00%j= 10.00%n= 5
$14,000.00
a PW= $55,801.76 USING INTEREST TABLES THIS IS
PW= $55,801.73 USING EXCEL'S NPV FUNCTION THIS IS
b A= $16,646.78 USING INTEREST TABLES THIS IS =$55,801.76*(A|P 15%,5)
A= $16,646.52 USING EXCEL'S PMT FUNCTION THIS IS=PMT(15%,5,-55801.73)
A1=
=$14,000*(P|A1 15%,10%,5)
=NPV(15%,14000,14000*1.1,14000*1.1^2,14000*1.1^3,14000*1.1^4)
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PROBLEM 2.140
i= 6.00%j= 15.00%n= 18
$1,500.00 AT BEGINNING OF YEAR 1
FW= $168,206.35 USING INTEREST TABLES THIS IS
FW= $168,206.35 USING INTEREST TABLES FROM PROBLEM 2.123
USING TABULATED CASH FLOWS
EOY CF0 $1,500.001 $1,725.002 $1,983.753 $2,281.314 $2,623.515 $3,017.046 $3,469.597 $3,990.038 $4,588.539 $5,276.81
10 $6,068.3411 $6,978.5912 $8,025.3813 $9,229.1814 $10,613.5615 $12,205.5916 $14,036.4317 $16,141.9018 $0.00
FW= $168,206.36 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,18+1,,-NPV(6%,CF YR 0:CF YR 18))
NOTE THAT THE WORDING OF THIS PROBLEM IMPLIES THE 18 DEPOSITS START AT BIRTH (BEGINNING OF YEAR 1) AND CONTINUE THROUGH BEGINNING OF YEAR 18. THEN, THE AMOUNT AT THE END OF YEAR 18 IS REQUESTED.
A1=
=$1,500*(F|A1 6%,15%,18)*(F|P 6%,1)
=$1,500*(F|A1 6%,15%,18)*(F|P 6%,1)
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PROBLEM 2.141
i= 15.00%j= 10.00%n= 5
$140,000.00
PW= $558,017.60 USING INTEREST TABLES THIS IS
PW= $558,017.60 USING INTEREST TABLES FROM PROBLEM 2.123
USING TABULATED CASH FLOWS
EOY CF0 $0.001 $140,000.002 $154,000.003 $169,400.004 $186,340.005 $204,974.00
PW= $558,017.31 USING EXCEL'S NPV FUNCTION THIS IS=NPV(15%,CF YR 1:CF YR 5)+0
A1=
=$140,000*(P|A1 15%,10%,5)
=$140,000*(P|A1 15%,10%,5)
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PROBLEM 2.142
i= 11.00%
a LABOR MATERIAL OVERHEAD TOTALj= -5.00% 4.00% 8.00%
$2,000,000.00 $3,000,000.00 $1,600,000.00EOY
0 $0.00 $0.00 $0.00 $0.001 $2,000,000.00 $3,000,000.00 $1,600,000.00 $6,600,000.002 $1,900,000.00 $3,120,000.00 $1,728,000.00 $6,748,000.003 $1,805,000.00 $3,244,800.00 $1,866,240.00 $6,916,040.004 $1,714,750.00 $3,374,592.00 $2,015,539.20 $7,104,881.205 $1,629,012.50 $3,509,575.68 $2,176,782.34 $7,315,370.526 $1,547,561.87 $3,649,958.71 $2,350,924.92 $7,548,445.517 $1,470,183.78 $3,795,957.06 $2,538,998.92 $7,805,139.75
b P= $8,295,499.60 $15,693,016.73 $9,307,846.73 $33,296,363.05 USING EXCEL'S NPV FUNCTION, EACH COLUMN IS=NPV(11%,CF YR 1:CF YR 7)+0
P= $8,295,500.00 $15,693,030.00 $9,307,840.00 $33,296,370.00USING INTEREST TABLES FROM PROBLEM 2.123
c A= $7,065,996.66 USING EXCEL'S PMT FUNCTION THIS IS=PMT(11%,7,-33296363.05)
A= $7,066,155.64 USING INTEREST TABLES THIS IS =$33,296,370.00*(A|P 11%,7)
NOTE! TABLES DO NOT SUPPORT THIS LEVEL OF PRECISION
IN THIS PROBLEM, IT IS MUCH EASIER TO USE A SPREADSHEET AND TO KEEP LABOR, MATERIAL, AND OVERHEAD SEPARATE UNTIL COMBINED.
A1=
=$2,000,000.00*(P|A1 11%,-5%,7)
=$3,000,000.00*(P|A1 11%,4%,7)
=$1,600,000.00*(P|A1 11%,8%,7)
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PROBLEM 2.143
i= 8.00%j= 5.00%n= 10
SALARY $70,000.00% DEPOSITED 10.00%
$7,000.00
FW= $123,673.76 USING INTEREST TABLES THIS IS
FW= $123,673.76 TABLES FROM PROBLEM 2.123
USING TABULATED CASH FLOWS
EOY CF0 $0.001 $7,000.002 $7,350.003 $7,717.504 $8,103.385 $8,508.546 $8,933.977 $9,380.678 $9,849.709 $10,342.19
10 $10,859.30
FW= $123,673.75 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(8%,10,,-NPV(8%,CF YR 1:CF YR 10)+0)
A1=
=$7,000*(F|A1 8%,5%,10)
=$7,000*(F|A1 8%,5%,10)
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PROBLEM 2.144
i= 15.00%j= 10.00%n= 5P= $50,000.00
P= $50,000.00 USING INTEREST TABLES THIS IS
$12,544.41 =50000/3.98584
a SMALLEST PAYMENT $0.00
b LARGEST PAYMENT $18,366.27 =12544.41*(1+0.1)^4
$12,544.41 SOLVER CHANGED CELL
EOY CF0
a 1 $12,544.412 $13,798.863 $15,178.744 $16,696.61
b 5 $18,366.28
P= $50,000.00 SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(15%,CF YR 1:CF YR 5)+0
=A1*(P|A1 15%,10%,5)
A1=
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. WILL USE SOLVER TO FIND VALUE OF A1.
BEGIN BY DEDICATING A CELL FOR A1 AND LET IT TAKE ON ANY VALUE AS IF IT WERE CORRECT. IT WILL BE CHANGED TO THE CORRECT VALUE WHEN SOLVER IS USED.
A1=
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PROBLEM 2.145
i= 6.00%j= 4.00%n= 5
$15,000.00
FW= $91,179.45 TABLES FROM APPENDIX A
USING TABULATED CASH FLOWS
EOY CF0 $0.001 $15,000.002 $15,600.003 $16,224.004 $16,872.965 $17,547.88
FW= $91,179.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,5,,-NPV(6%,CF YR 1:CF YR 5)+0)
A1=
=$15,000*(F|A1 6%,4%,5)
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PROBLEM 2.146
TO GO FROM NOMINAL ANNUAL TO EFFECTIVE ANNUAL
NOMINAL ANNUAL INTEREST RATE r= 10.000% USED r=10% FOR EXAMPLE(E.G., 10.000%)COMPOUNDING PERIODS PER YEAR m= 4 USED m=4 FOR EXAMPLE(E.G., 4 FOR QUARTERLY)
EFFECTIVE ANNUAL INTEREST RATE 10.381%
=(1+0.1/4)^4-1
EFFECTIVE ANNUAL INTEREST RATE 10.381%
=EFFECT(10%,4)
TO GO FROM EFFECTIVE ANNUAL TO NOMINAL ANNUAL
EFFECTIVE ANNUAL INTEREST RATE 10.381%(E.G., 10.381%)COMPOUNDING PERIODS PER YEAR m= 4 USED m=4 FOR EXAMPLE(E.G., 4 FOR QUARTERLY)
NOMINAL ANNUAL INTEREST RATE r= 10.000% USED r=10% FOR EXAMPLE
=4*((1+0.10381)^(1/4)-1)
ieff=
USING COMPOUND INTEREST FORMULAS THIS IS
ieff=
USING EXCEL'S EFFECT FUNCTION THIS IS
ieff=
USING COMPOUND INTEREST FORMULAS THIS IS
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PROBLEM 2.147
i= 0.75% PER MONTHn= 480 MONTHSF= $2,000,000.00
A= $427.23 USING COMPOUND INTEREST FORMULAS THIS IS=2000000*(0.0075/((1+0.0075)^480-1))
A= $427.22 USING INTEREST TABLES THIS IS =$2,000,000*(A|F 0.75%,480)
A= $427.23 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.75%,480,,-2000000)
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PROBLEM 2.148
P= $12,000.00i= 0.75% PER MONTHA= $400.00 PER MONTH
n= 34.1129207 MONTHS USE 35 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.75%,-400,12000)
CAN ALSO USE SOLVER TO FIND n
n= 34.1129208 <--SOLVER CHANGED CELL USE 35 MONTHS
A= $400.00 <--SOLVER TARGET CELLUSING EXCEL'S PMT FUNCTION THIS IS=PMT(0.75%,n,-12000)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER.
EOY CF PW
01 $400.00 $397.02 2 $400.00 $791.09 3 $400.00 $1,182.22 4 $400.00 $1,570.44 5 $400.00 $1,955.78 6 $400.00 $2,338.24 7 $400.00 $2,717.86 8 $400.00 $3,094.65 9 $400.00 $3,468.63
10 $400.00 $3,839.83 11 $400.00 $4,208.27 12 $400.00 $4,573.97 13 $400.00 $4,936.94 14 $400.00 $5,297.21 15 $400.00 $5,654.80 16 $400.00 $6,009.73 17 $400.00 $6,362.01 18 $400.00 $6,711.67 19 $400.00 $7,058.73 20 $400.00 $7,403.21 21 $400.00 $7,745.12 22 $400.00 $8,084.49 23 $400.00 $8,421.33 24 $400.00 $8,755.66 25 $400.00 $9,087.50 26 $400.00 $9,416.88 27 $400.00 $9,743.80 28 $400.00 $10,068.28 29 $400.00 $10,390.36 30 $400.00 $10,710.03 31 $400.00 $11,027.33 32 $400.00 $11,342.26
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33 $400.00 $11,654.85 34 $400.00 $11,965.11 35 $400.00 $12,273.06 FIRST PW OF >= $12,00036 $400.00 $12,578.72 37 $400.00 $12,882.11 38 $400.00 $13,183.23 39 $400.00 $13,482.12 40 $400.00 $13,778.78
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SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER.
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PROBLEM 2.149
a r= 10.00%m= 2
ieff= 10.2500% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.1/2)^2-1
ieff= 10.2500% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,2)
b r= 10.00%m= 3
ieff= 10.3370% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.1/3)^3-1
ieff= 10.3370% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,3)
c r= 10.00%m= 4
ieff= 10.3813% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.1/4)^4-1
ieff= 10.3813% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,4)
d r= 10.00%m= 6
ieff= 10.4260% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.1/6)^6-1
ieff= 10.4260% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,6)
e r= 10.00%m= 12
ieff= 10.4713% USING COMPOUND INTEREST FORMULAS THIS IS10.4713%
ieff= 10.4713% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,12)
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PROBLEM 2.150
a r= 5.00%m= 2
ieff= 5.0625% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/2)^2-1
ieff= 5.0625% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,2)
b r= 5.00%m= 3
ieff= 5.0838% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/3)^3-1
ieff= 5.0838% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,3)
c r= 5.00%m= 4
ieff= 5.0945% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/4)^4-1
ieff= 5.0945% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,4)
d r= 5.00%m= 6
ieff= 5.1053% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/6)^6-1
ieff= 5.1053% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,6)
e r= 5.00%m= 12
ieff= 5.1162% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/12)^12-1
ieff= 5.1162% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,12)
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PROBLEM 2.151
r= 6.00% PER YEARm= 12i= 0.50% PER MONTHn= 60 MONTHSP= $50,000.00
A= $966.50 USING INTEREST TABLES THIS IS =$50,000*(A|P 0.50%,60)
A= $966.64 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.5%,60,-50000)
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PROBLEM 2.152
a i= 0.50% PER MONTHn= 30 MONTHLY PAYMENTSP= $500.00
A= $17.99 USING INTEREST TABLES THIS IS =$500*(A|P 0.50%,30)
A= $17.99 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.50%,30,-500)
b i= 0.50% PER MONTHn= 30 MONTHLY PAYMENTSP= $500.00
DELAY= 12 MONTHS
AMT12MO= $530.84 USING INTEREST TABLES THIS IS =$500.00*(F|P 0.5%,12)
A= $19.10 USING INTEREST TABLES THIS IS =$530.84*(A|P 0.50%,30)
AMT12MO= $530.84 USING EXCEL'S FV FUNCTION THIS IS=FV(0.5%,12,,-C16)
A= $19.10 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.5%,30,-530.84)
FIRST, DETERMINE THE FUTURE WORTH OF THE ORIGINAL $500 AFTER 12 MONTHS. THEN, DETERMINE THE MONTHLY PAYMENT
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PROBLEM 2.153
r= 6.000%m= 2
YRS= 10P= $4,000.00
FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(1+0.06/2)^(2*10)
FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS=FV(0.06/2,2*10,,-4000)
OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS
6.090% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(6%,2)
FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(1+0.0609)^10
FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS=FV(6.09%,10,,-4000)
ieff=
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PROBLEM 2.154
r= 5.000%m= 4
YRS= 4F= $10,000.00
P= $8,197.50 USING INTEREST TABLES THIS IS=$10,000*(P|F 1.25%,16)
P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS=PV(0.05/4,4*4,,-10000)
OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS
5.09453% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/4)^4-1
P= $8,197.46 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.0509453)^-4
P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS=PV(5.09453%,4,,-10000)
ieff=
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PROBLEM 2.155
a ANNUALLYr= 7.000%m= 1
YRS= 5P= $10,000.00
F= $14,025.52 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.07/1)^(1*5)
F= $14,025.50 USING INTEREST TABLES THIS IS=$10,000*(F|P 7%,5)
F= $14,025.52 USING EXCEL'S FV FUNCTION THIS IS=FV(0.07/1,1*5,,-10000)
b QUARTERLYr= 7.000%m= 4
YRS= 5P= $10,000.00
F= $14,147.78 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.07/4)^(4*5)
F= $14,147.80 USING INTEREST TABLES THIS IS=$10,000*(F|P 1.75%,20)
F= $14,147.78 USING EXCEL'S FV FUNCTION THIS IS=FV(0.07/4,4*5,,-10000)
c MONTHLYr= 7.000%m= 12
YRS= 5P= $10,000.00
F= $14,176.25 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.07/12)^(12*5)
F= $14,176.00 USING ELECTRONIC INTEREST TABLES THIS IS=$10,000*(F|P 7/12%,60)
F= $14,176.25 USING EXCEL'S FV FUNCTION THIS IS=FV(0.07/12,12*5,,-10000)
d DAILYr= 7.000%m= 365
YRS= 5P= $10,000.00
F= $14,190.20 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.07/365)^(365*5)
F= $14,190.00 USING ELECTRONIC INTEREST TABLES THIS IS=$10,000*(F|P 7/365%,1825)
F= $14,190.20 USING EXCEL'S FV FUNCTION THIS IS=FV(0.07/365,365*5,,-10000)
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PROBLEM 2.156
a ANNUALLYr= 6.000%m= 1
YRS= 8F= $20,000.00
P= $12,548.25 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/1)^(-1*8)
P= $12,548.20 USING INTEREST TABLES THIS IS=$20,000*(P|F 6%,8)
P= $12,548.25 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/1,1*8,,-20000)
b SEMI-ANNUALLYr= 6.000%m= 2
YRS= 8F= $20,000.00
P= $12,463.34 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/2)^(-2*8)
P= $12,463.40 USING INTEREST TABLES THIS IS=$20,000*(P|F 3%,16)
P= $12,463.34 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/2,2*8,,-20000)
c QUARTERLYr= 6.000%m= 4
YRS= 8F= $20,000.00
P= $12,419.86 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/4)^(-4*8)
P= $12,419.80 USING INTEREST TABLES THIS IS=$20,000*(P|F 1.5%,32)
P= $12,419.86 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/4,4*8,,-20000)
d MONTHLYr= 6.000%m= 12
YRS= 8F= $20,000.00
P= $12,390.48 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/12)^(-12*8)
P= $12,390.40 USING INTEREST TABLES THIS IS=$20,000*(P|F 0.5%,96)
P= $12,390.48 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/12,12*8,,-20000)
e WEEKLY
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r= 6.000%m= 52
YRS= 8F= $20,000.00
P= $12,379.09 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/52)^(-52*8)
P= $12,379.00 USING INTEREST TABLES THIS IS=$20,000*(P|F 0.6/52%,416)
P= $12,379.09 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/52,52*8,,-20000)
f DAILYr= 6.000%m= 365
YRS= 8F= $20,000.00
P= $12,376.16 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/365)^(-365*8)
P= $12,376.16 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/365,365*8,,-20000)
g HOURLYr= 6.000%m= 8760
YRS= 8F= $20,000.00
P= $12,375.69 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/8760)^(-8760*8)
P= $12,375.69 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/8760,8760*8,,-20000)
h MINUTELYr= 6.000%m= 525600
YRS= 8F= $20,000.00
P= $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/525600)^(-525600*8)
P= $12,375.67 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/525600,525600*8,,-20000)
i SECONDLYr= 6.000%m= 31536000
YRS= 8F= $20,000.00
P= $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/31536000)^(-31536000*8)
P= $12,375.67 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/31536000,31536000*8,,-20000)
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PROBLEM 2.157
BUILDING THE ACCOUNTr= 8.000% COMPOUNDED MONTHLYm= 12 MONTHS PER YEAR
YRS= 20A= $400.00 PER MONTH
DETERMINE AMOUNT IN ACCOUNT AT END OF 20 YEARS, END OF MONTH 240F(240)= $235,608.00 USING INTEREST TABLES THIS IS
$400*(F|A 8/12%,240)F(240)= $235,608.17 USING EXCEL'S FV FUNCTION THIS IS
=FV(0.08/12,12*20,-400)
DETERMINE AMOUNT IN ACCOUNT AT END OF MONTH 251, ONE MONTH BEFORE 1ST WITHDRAWAL AT END OF MONTH 252
1ST WDL 252 MONTH 252 IS FIRST WITHDRAWALr= 8.000% COMPOUNDED MONTHLYm= 12 MONTHS PER YEAR
YRS= 15
F(251)= $253,474.15 USING INTEREST TABLES THIS IS=$235608.00*(F|P 8/12%,11)
F(251)= $253,473.70 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,11,,-235608.17)
a A= $2,423.21 USING INTEREST TABLES THIS IS=$253,474.15*(A|P 8/12%,12*15)
A= $2,422.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.08/12,12*15,-253473.7)
b A= $1,689.82 CALCULATING MONTHLY INTEREST ONLY=(0.08/12)*253473.7
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PROBLEM 2.158
a BUILDING THE ACCOUNT FOR 30 YEARSr= 8.000%m= 12 MONTHS PER YEAR
YRS= 30A= $300.00 PER MONTH
AMT360= $447,120.00 USING INTEREST TABLES THIS IS=$300*(F|A 8/12%,360)
AMT360= $447,107.83 USING EXCEL'S FV FUNCTION THIS IS=FV(8%/12,12*30,-300)
b LETTING THE ACCOUNT BUILD FOR 7 MORE QUARTERSr= 12.000%m= 4 QTRS/YEAR
YRS= 15
AMT7QTR= $549,899.47 USING INTEREST TABLES THIS IS=$447,120*(F|P 3%,7)
AMT7QTR= $549,886.24 USING EXCEL'S FV FUNCTION THIS IS=FV(12%/4,7,,-C13)
c WITHDRAWING FROM THE ACCOUNTSTARTING 2 YEARS AFTER LAST DEPOSIT
A= $19,867.87 USING INTEREST TABLES THIS IS=$549,899.47*(A|P 3%,60)
A= $19,869.02 USING EXCEL'S PMT FUNCTION THIS IS=PMT(12%/4,4*15,-549886.24)
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PROBLEM 2.159
MONTHLY RATE= 2.50%m= 12P= $2,000.00
YRS= 2
a NOM ANN RATE= 30.000% =2.5%*12
b EFF ANN RATE= 34.4889% USING COMPOUND INTEREST FORMULAS THIS IS=(1+30%/12)^12-1
EFF ANN RATE= 34.4889% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(30%,12)
c F= $3,617.46 USING INTEREST TABLES THIS IS=$2,000*(F|P 2.5%,24)
F= $3,617.45 USING EXCEL'S FV FUNCTION THIS IS=FV(2.5%,12*2,,-2000)
d F= $3,617.46 USING ELECTRONIC INTEREST TABLES THIS IS=$2,000*(F|P 34.4889%,2)
F= $3,617.45 USING EXCEL'S FV FUNCTION THIS IS=FV(34.4889%,2,,-2000)
e INTEREST= $1,617.45 =3617.45-2000.00
f A= $111.82 USING INTEREST TABLES THIS IS=$2,000*(A|P 2.5%,24)
A= $111.83 USING EXCEL'S PMT FUNCTION THIS IS=PMT(2.5%,12*2,-2000)
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PROBLEM 2.160
m= 12 MONTHS PER YEARn= 40 MONTHSA= $250.00 PER MONTHF= $12,000.00
r= 10.932% <--SOLVER CHANGED CELL
F= $12,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(r%/12,40,-250)
NOW, KNOWING r, PROCEED WITH THE PROBLEM
a 0.911% =10.932%/12
b r= 10.932% FOUND USING SOLVER ABOVE
c 11.497% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.10932/12)^12-1
11.497% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10.932%,12)
SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.
BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE.
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PROBLEM 2.161
m= 12YRS= 5
A= $501.49P= $20,000.00
r= 17.412% <--SOLVER CHANGED CELL
P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(r/12,12*5,-20000)
NOW, KNOWING r, PROCEED WITH THE PROBLEM
a 1.451% =17.412%/12
b r= 17.412% FOUND USING SOLVER ABOVE
c 18.871% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.17412/12)^12-1
18.871% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(17.412%,12)
SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.
BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE.
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PROBLEM 2.162
a REFUND= $1,000.00INT RATE= 3.000% PER WEEKINT PAID= $30.00 =1000*0.03
m= 52 WEEKS/YR
CASH RCVD= $970.00 =1000-30
b WEEKLY INT= 3.093% =30/970
c r= 160.825% =3.093%*52
d 387.382% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.03093)^52-1
387.382% USING EXCEL'S EFFECT FUNCTION387.384%
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PROBLEM 2.163
PLAN 1 PLAN 2
r= 7.000% r= 6.625%m= 12 m= 12
YRS= 30 YRS= 15P= $600,000.00 P= $600,000.00
a A= $3,990.00 USING INTEREST TABLES THIS IS=$600,000*(A|P 7/12%,360)
A= $3,991.81 USING EXCEL'S PMT FUNCTION THIS IS=PMT(7%/12,12*30,-600000)
b A= $5,268.00 USING INTEREST TABLES THIS IS=$600,000*(A|P 6.625/12%,180)
A= $5,267.96 USING EXCEL'S PMT FUNCTION THIS IS=PMT(6.625%/12,12*15,-600000)
c 7.229% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.07/12)^12-1
7.229% USING EXCEL'S EFFECT FUNCTION=EFFECT(7%,12)
d 6.830% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06625/12)^12-1
6.830% USING EXCEL'S EFFECT FUNCTION=EFFECT(6.625%,12)
e INT PAID= $837,053.39 =3991.81*12*30-600000
f INT PAID= $348,233.27 =5267.96*12*15-600000
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USING COMPOUND INTEREST FORMULAS THIS IS
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PROBLEM 2.164
r= 6.00% PER YEARm= 4 CMPDGS PER YEARn= 60 MONTHSk= 12 PAYMENTS PER YEARP= $50,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)
i= 0.49752063% PER MONTHUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/4)^(4/12)-1
NOW, PROCEED WITH THE REST OF THE PROBLEM
A= $965.95 USING COMPOUND INTEREST FORMULAS THIS IS=50000*(0.0049752063*(1+0.0049752063)^60)/((1+0.0049752063)^60-1)
A= $966.00 USING INTEREST TABLES THIS IS=$50,000*(A|P 0.49752063%,60)
A= $965.95 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.49752063%,60,-50000)
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PROBLEM 2.165
NOTE! IF YOU HAVE THE FIRST PRINTING, SEE PROBLEM 2.167 FOR SOLUTION
FOLLOWING IS THE SOLUTION TO PROBLEM 2.165 IN LATER PRINTINGS
r= 6.000%m= 4 QUARTERS PER YEARk= 12 DEPOSITS PER YEARA= $150.00 PER MONTHF= $20,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)
i= 0.49752063% PER MONTHUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/4)^(4/12)-1
NOW, PROCEED WITH THE REST OF THE PROBLEM
n= 102.5293974279 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.4975206%,150,,-20000)
OR COULD USE SOLVER AS FOLLOWS
n= 102.52939742562 <--SOLVER CHANGED CELL
F= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(0.4975206,n,-150)
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NOTE! IF YOU HAVE THE FIRST PRINTING, SEE PROBLEM 2.167 FOR SOLUTION
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)
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PROBLEM 2.166
r= 7.000% PER YEARm= 12 MONTHS PER YEARk= 4 DEPOSITS PER YEARA= $300.00 PER QUARTERF= $15,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER)
i= 1.760% PER QUARTERUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.07/12)^(12/4)-1
NOW, PROCEED WITH THE REST OF THE PROBLEM
n= 36.18126076 QUARTERSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(1.760%,300,,-15000)
OR COULD USE SOLVER AS FOLLOWS
n= 36.18126076 <--SOLVER CHANGED CELLQUARTERS
F= $15,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(1.760%,n,-300)
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PROBLEM 2.167 (ALSO PROBLEM 2.165 IN FIRST PRINTING)
r= 7.000%m= 4 QUARTERS PER YEARk= 12 DEPOSITS PER YEARA= $100.00 PER MONTHF= $15,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)
i= 0.5799633% PER MONTHUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.07/4)^(4/12)-1
NOW, PROCEED WITH THE REST OF THE PROBLEM
n= 108.23482720625 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.57996326%,100,,-15000)
OR COULD USE SOLVER AS FOLLOWS
n= 108.23482720226 <--SOLVER CHANGED CELL
F= $15,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(0.57996326,n,-100)
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PROBLEM 2.168
r= 6.000% PER YEARm= 12 MONTHS PER YEARk= 4 WITHDRAWALS PER QTRA= $1,200.00 PER QUARTERP= $20,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER)
i= 1.508% PER QUARTERUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/12)^(12/4)-1
NOW, PROCEED WITH THE REST OF THE PROBLEM
n= 19.33837953 QUARTERSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(1.508%,1200,-20000)
OR COULD USE SOLVER AS FOLLOWS
n= 19.33837953 <--SOLVER CHANGED CELL QUARTERS
P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=FV(1.508%,n,-1200)
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PROBLEM 2.169
r= 6.000% PER YEARm= 4 QUARTERSk= 12 MONTHSA= $400.00 PER MONTHP= $20,000.00
FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)
i= 0.4975206% PER MONTHUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/4)^(4/12)-1
n= 57.6340855 USING EXCEL'S NPER FUNCTION THIS IS =NPER(0.004975206,400,-20000)OR 57 WHOLE MONTHS
OR, COULD USE SOLVER TO FIND n
n= 57.6340855 <--SOLVER CHANGED CELLMONTHS
P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS =PV(0.004975206,n,-400)
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PROBLEM 2.170
FOR n PERIODS FROM EQ 2.9
FOR m PERIODS FROM EQ 2.9
FOR m PERIODS FROM EQ 2.8
a FOR n+m PERIODS FROM EQ 2.9
(P|F i%,n)*(P|F i%,m) EQ 2.53 - QED
b FOR n-m PERIODS FROM EQ 2.9
(P|F i%,n)*(F|P i%,m) EQ 2.54 - QED
c FOR nm PERIODS FROM EQ 2.9
EQ 2.55 - QED
d FOR nm PERIODS FROM EQ 2.9
EQ 2.56 - QED
(P|F i%,n)=(1+i)-n
(P|F i%,m)=(1+i)-m
(F|P i%,m)=(1+i)m
(P|F i%,n+m)=(1+i)-(n+m)
(P|F i%,n+m)=(1+i)-(n+m)= (1+i)-n*(1+i)-m=
(P|F i%,n+m)=(1+i)-(n+m)=
(P|F i%,n-m)=(1+i)-(n-m)
(P|F i%,n-m)=(1+i)-(n-m)= (1+i)-n*(1+i)m=
(P|F i%,n-m)=(1+i)-(n-m)=
(P|F i%,nm)=(1+i)-nm
(P|F i%,nm)=(1+i)-(nm)= ((1+i)-n)m=
(P|F i%,nm)=(1+i)-(nm)= (P|F i%,n)m
(P|F i%,nm)=(1+i)-nm
(P|F i%,nm)=(1+i)-(nm)= ((1+i)-m)n=
(P|F i%,nm)=(1+i)-(nm)= (P|F i%,m)n
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PROBLEM 2.171
2.57 a $0 0 1
P=$0
b (P|G i%,n)=
(P|G i%,1)=
2.58 a $0 0 1
A=$0
b (A|G i%,n)=
(A|G i%,1)=
2.59 a $A=$P*(1+i)$F=$P*(1+i)
0 1
$P
b (A|P i%,n)=
(A|P i%,1)=
(F|P i%,n)=
(F|P i%,1)=
2.6 a $F
0 1
$A
b (A|F i%,n)=
(A|F i%,1)=
(F|A i%,n)=
(F|A i%,1)=
(1-(1+n*i)*(1+i)-n)/(i2)
(1-(1+i)*(1+i)-1)/(i2)=0
(1/i)-(n/i)*(i/((1+i)n-1))
(1/i)-(1/i)*(i/((1+i)1-1))=0
(i*(1+i)n)/((1+i)n-1)
(i*(1+i)1)/((1+i)1-1)=1+i
(1+i)n
(1+i)1=1+i
i/((1+i)n-1)
i/((1+i)1-1)=1
((1+i)n-1)/i
((1+i)1-1)/i=1
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FIRST YEAR OF A GRADIENT SERIES IS $0
FIRST YEAR OF A GRADIENT SERIES IS $0
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PROBLEM 2.172
a r= 5.000%m= 1
5.000% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/1)^1-1
5.000% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,1)
b r= 5.000%m= 365
5.127% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/365)^365-1
5.127% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(5%,365)
c r= 5.000%m= INFINITE 10000000 USING A VERY LARGE NUMBER
5.127% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/10000000)^10000000-1
5.127% USING EXCEL'S EFFECT FUNCTION THIS ISASSUME VERY LARGE m=EFFECT(5%,10000000)
5.127% USING EQUATION 2.A.1
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PROBLEM 2.173
a r= 10.000%m= 1
10.000% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.10/1)^1-1
10.000% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,1)
b r= 10.000%m= 365
10.516% USING COMPOUND INTEREST FORMULAS THIS IS10.516%
10.516% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,365)
c r= 10.000%m= INFINITE 10000000 USING A VERY LARGE NUMBER
10.517% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.10/10000000)^10000000-1
10.517% USING EXCEL'S EFFECT FUNCTION THIS ISASSUME VERY LARGE m=EFFECT(10%,10000000)
10.517% USING EQUATION 2.A.1
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PROBLEM 2.174
r= 10.000% COMPOUNDED CONTINUOUSLYYRS= 5
P= $10,000.00m= 10,000,000 LARGE NUMBER OF CPDG PERIODS PER YEAR
F= $16,487.21 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=C5*EXP(C3*C4)
F= $16,487.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
F= $16,487.21 USING EXCEL'S FV FUNCTION THIS ISASSUME VERY LARGE m=FV(10%/10000000,5*10000000,,-10000)
=$10,000*(F|P 10%,5)∞
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USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
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PROBLEM 2.175
r= 15.000% COMPOUNDED CONTINUOUSLYYRS= 4
F= $15,000.00m= 10000000 LARGE NUMBER OF CPDG PERIODS PER YEAR
P= $8,232.17 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=15000*EXP(-15%*4)
P= $8,232.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
P= $8,232.17 USING EXCEL'S PV FUNCTION THIS ISASSUME VERY LARGE m=PV(15%/10000000,4*10000000,,-15000)
=$15,000*(P|F 15%,4)∞
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PROBLEM 2.176
r= 5.000% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHS
a F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS$9,886.20
F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
b P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=500*(EXP(5%*14)-1)/(EXP(5%*14)*(EXP(5%)-1))
P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
c P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=9886.2*EXP(-5%*14)
P= $4,909.39 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD
=$500*(F|A 5%,14)∞
=$500*(P|A 5%,14)∞
=$9,886.2*(P|F 5%,14)∞
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USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
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PROBLEM 2.177
r= 5.000% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHSG= $100.00 PER 6 MONTHS
a F= $21,144.77
=$500*19.7724+$100*55.90849*2.01375
b P= $10,500.19
=$500*9.81868+$100*55.90849
P= $10,500.28
=$21,144.77*0.49659
c A= $1,069.50
=$21,144.77*0.05058
TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b
PERIOD PYT FW PW01 $500.00 $957.77 $475.612 $600.00 $1,093.27 $542.903 $700.00 $1,213.28 $602.504 $800.00 $1,318.98 $654.985 $900.00 $1,411.48 $700.926 $1,000.00 $1,491.82 $740.827 $1,100.00 $1,560.97 $775.168 $1,200.00 $1,619.83 $804.389 $1,300.00 $1,669.23 $828.92
10 $1,400.00 $1,709.96 $849.1411 $1,500.00 $1,742.75 $865.4212 $1,600.00 $1,768.27 $878.1013 $1,700.00 $1,787.16 $887.4814 $1,800.00 $1,800.00 $893.85
FOR PERIOD 8 =1200*EXP(0.05*(14-8))=1200*EXP(-0.05*8)
SUM $21,144.79 $10,500.19
NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
=$500*(F|A 5%,14)∞+$100*(P|G 5%,14)∞*(F|P 5%,14)∞
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
=$500*(P|A 5%,14)∞+$100*(P|G 5%,14)∞
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
=$21,144.77*(P|F 5%,14)∞
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
=$21,144.77*(A|F 5%,14)∞
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PROBLEM 2.178
r= 5.00% PER 6 MONTHSc= 20.00% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHS
a F= $42,410.96
=500*(EXP(5%*14)-EXP(20%*14))/(EXP(5%)-EXP(20%))
b P= $21,060.66
=500*(1-EXP((20%-5%)*14))/(EXP(5%)-EXP(20%))P= $21,060.86 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
c A= $2,145.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b
PERIOD PYT FW PW01 $500.00 $957.77 $475.612 $610.70 $1,112.77 $552.593 $745.91 $1,292.85 $642.014 $911.06 $1,502.08 $745.915 $1,112.77 $1,745.17 $866.636 $1,359.14 $2,027.60 $1,006.887 $1,660.06 $2,355.74 $1,169.828 $2,027.60 $2,736.97 $1,359.149 $2,476.52 $3,179.91 $1,579.10
10 $3,024.82 $3,694.53 $1,834.6511 $3,694.53 $4,292.43 $2,131.5612 $4,512.51 $4,987.09 $2,476.5213 $5,511.59 $5,794.17 $2,877.3014 $6,731.87 $6,731.87 $3,342.95
14 =500*EXP(20%*(14-1))14 =6731.87*EXP(5%*(14-14))14 =6731.87*EXP(-5%*14)
SUM $42,410.96 $21,060.66
NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r AND c MUST MATCH THE PERIOD
NOTE! PAYMENTS ARE INCREASING AT A CONTINUOUSLY COMPOUNDED 20%, NOT JUST 20%.
USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS
=$42,410.96*(P|F 5%,14)∞
=$42,410.96*(A|F 5%,14)∞
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USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
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PROBLEM 2.179
r= 10.000% PER YEAR COMPOUNDED CONTINUOUSLYYRS= 7
= $1,000.00 PER YEAR CONTINUOUS FLOW
a F= $10,137.53
=1000*(EXP(10%*7)-1)/10%F= $10,137.53
=$1,000*(F| 10%,7)
b P= $5,034.15
=1000*((EXP(10%*7)-1)/(10%*EXP(10%*7)))P= $5,034.15
=$1,000*(P| 10%,7)
P= $5,034.20
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST TABLES THIS IS
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST TABLES THIS IS
USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS
=$10,137.53*(P|F 10%,7)∞
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PROBLEM 2.180
r= 10.000% PER YEARYRS= 7
P= $20,000.00
$3,972.87
=20000*10%*EXP(10%*7)/(EXP(10%*7)-1)
$3,972.80
=$20,000*( |P 10%,7)
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST FORMULAS THIS IS
USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST TABLES THIS ISA
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