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McGraw-Hill Ryerson©
6 - 1Simple
Interest
Simple
Interest 66 66
Chapter
6McGraw-Hill Ryerson©
IISS imple nterest
McGraw-Hill Ryerson©
6 - 2Simple
Interest
Simple
Interest 66 66
Calculate
Learning ObjectivesLearning
ObjectivesAfter completing this chapter, you will be able to:
… interest, maturity value,
future value, and present value
in a simple interest environment
… details of the amount and timing of payments in a time
diagram
… the equivalent value on any date of a single
payment or a stream of payments, and
Present
LO-1LO-1
LO-2LO-2
McGraw-Hill Ryerson©
6 - 3Simple
Interest
Simple
Interest 66 66
Borrower
Example: LoanExample: Loan
Lender
PartiesParties
Lends the PrincipalLends the Principal Borrower OWES (Debt) to Lender
Borrower OWES (Debt) to Lender
LO-1LO-1
McGraw-Hill Ryerson©
6 - 4Simple
Interest
Simple
Interest 66 66
BorrowerLender
Earns (Income) from Borrower
i.e. Interest on the Principal
Earns (Income) from Borrower
i.e. Interest on the PrincipalBorrower pays
Interest to Lender
Borrower pays Interest to Lender
Rate of Interest: Simple Interest …Calculated on an ANNUAL or
per annum (pa) basis
Simple Interest …Calculated on an ANNUAL or
per annum (pa) basis
Example: LoanExample: Loan
McGraw-Hill Ryerson©
6 - 5Simple
Interest
Simple
Interest 66 66ExamplesExamples
Invest $1000 at 10% simple interest for one year.
Interest earned is?
Principal X Interest Rate $1000 *10% = $100
Invest $1000 at 10% simple interest for six months.
Interest earned is?
Principal X Interest Rate $1000 * 10% $50/2 =
=
=
McGraw-Hill Ryerson©
6 - 6Simple
Interest
Simple
Interest 66 66
Invest $1000 at 10% simple interest for three months
Interest earned is?Principal X Interest Rate = $1000 X 10% $25
Invest $1000 at 10% simple interest for one month.
Interest earned is?
Principal X Interest Rate = $1000 X 10% $8.33/12 =
/4 =
ExamplesExamples
McGraw-Hill Ryerson©
6 - 7Simple
Interest
Simple
Interest 66 66
Up to this point we have taken months to represent 1/12th of a year, i.e. each month is treated as having the same number of days!
Would it not be more accurate to calculate the interest due or payable based on the actual number of days
in each month?
McGraw-Hill Ryerson©
6 - 8Simple
Interest
Simple
Interest 66 66 Yes, it would! In fact, interest continues
to accumulate as each day passes!
Invest $1000 at 10% simple interest for 30 days!
Interest earned is?
ExampleExample
Principal x Interest Rate = $1000 *10% * 30
Year = 365 days or 366 in a Leap YearYear = 365 days or 366 in a Leap Year
$8.22=365
McGraw-Hill Ryerson©
6 - 9Simple
Interest
Simple
Interest 66 66
trPI
“What is the formula that can be used to calculate SI?”
Principal Interest Rate Time
Four Elements are involved …Four Elements are involved …
Interest
Formula Formula
Principal Amount (loan or
investment)
Principal Amount (loan or
investment)
Annual Rateof SI
Annual Rateof SI
Amount (paid or received)
Amount (paid or received)
Time period …expressed as a fraction or a multiple
of a year
Time period …expressed as a fraction or a multiple
of a yearI = Prt
McGraw-Hill Ryerson©
6 - 10Simple
Interest
Simple
Interest 66 66
Calculate the Interest earned on $5000
invested at 4% for 7 months.
Formula Formula I = Prt
I = P * r * t $5000 *
.04 * 7 /12
I = $116.67I = $116.67
McGraw-Hill Ryerson©
6 - 11Simple
Interest
Simple
Interest 66 66
“I may need to invest or need a loan for a number
of days rather than a complete
month.”
“How do I calculate the
time between the
starting date and the ending date?”
McGraw-Hill Ryerson©
6 - 12Simple
Interest
Simple
Interest 66 66
Add up the days according to the days covered by the specific months.Include either
the FIRST date or the LAST
date when doing this calculation!
Include either the FIRST date
or the LAST date when doing this calculation!
Use a Number of Days TABLE
Use the TI BAII Plus calculator!
There are three methods that can be used to
calculate the number of days:
McGraw-Hill Ryerson©
6 - 13Simple
Interest
Simple
Interest 66 66
Method 1.Method 1.
What is the interest earned on $5000 invested from Oct. 11th to Dec.
29th at 4.5%?
Calculating the Number of Days
Oct 11th to end of month = 20
Days
Nov Total month =
30
Dec From 1st to 29th
of month = 29 79 79 Includes the last date
McGraw-Hill Ryerson©
6 - 14Simple
Interest
Simple
Interest 66 66
JanMar
MayJuly
FebAprJun
Spaces are ALL 30 days except for February which can be either
28 or 29 days in a Leap year!
Aug Oct Dec
Nov
Sept
The “Hand Calculator!”The “Hand Calculator!”
Knuckles are ALL 31 days
McGraw-Hill Ryerson©
6 - 15Simple
Interest
Simple
Interest 66 66
Thirty days has September,April, June and November.
All the rest have 31,
but February with just 28 days clear
plus one more in each leap year!
McGraw-Hill Ryerson©
6 - 16Simple
Interest
Simple
Interest 66 66Day of Month
TABLE 6.2The Serial Number of Each Day of the YearJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365
12345678910111213141516171819202122232425262728293031
363
284Oct 11
Dec 29
= 79 Days= 79 DaysMethod 2.Method 2.
54
McGraw-Hill Ryerson©
6 - 17Simple
Interest
Simple
Interest 66 66
12.2902
Using… Texas Instruments BAII PLUS
i
Days Between DatesDays Between Dates
2nd
CPT
Enter
Method 3.Method 3.
Example 1.Example 1.
Calculate… the interest
earned on $5000
invested from Oct. 11th
to Dec. 29th, 02 at 4.5%.
Start
DBD = 79 Date
10.1102 Enter
McGraw-Hill Ryerson©
6 - 18Simple
Interest
Simple
Interest 66 66
Formula Formula I = Prt
Calculate the Interest earned on $5000 invested
at 4.5%
for ? .
79 Days
I =$5000*.045 * 79/365
I = $48.70I = $48.70
McGraw-Hill Ryerson©
6 - 19Simple
Interest
Simple
Interest 66 66
Method 1.Method 1.
What is the interest earned on $5000 invested from Nov 30th, 02 to Jan
6th, 03 at 4.5%?
Nov 30th to end of month = 0
Days
Dec Total month =
31
Jan From 1st to 6th
of month = 6 37 37
Includes the last date
Calculating the Number of Days
McGraw-Hill Ryerson©
6 - 20Simple
Interest
Simple
Interest 66 66Day of Month
TABLE 6.2The Serial Number of Each Day of the YearJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365
12345678910111213141516171819202122232425262728293031
54 6
365334
Jan 6
= 37 Days= 37 Days
Method 2.Method 2.Nov 30
Dec 31
= 31 Days= 31 Days
McGraw-Hill Ryerson©
6 - 21Simple
Interest
Simple
Interest 66 66
01.0603
Using… Texas Instruments BAII PLUS
i
Days Between DatesDays Between Dates
2nd
CPT
Enter
Method 3.Method 3.
Example 1.Example 1.
Calculate… the interest
earned on $5000
invested from
Nov. 30th,, 02 to Jan
6th. 03 at 4.5%.
Start
DBD = 37 Date
11.3002 Enter
McGraw-Hill Ryerson©
6 - 22Simple
Interest
Simple
Interest 66 66
Formula Formula I = Prt
I =$5000*.045 * 37/365
I = $22.81I = $22.81
Calculate the Interest earned on $5000 invested
at 4.5%
for ? .
37 Days
McGraw-Hill Ryerson©
6 - 23Simple
Interest
Simple
Interest 66 66
Method 1.Method 1.
What is the interest earned on $5000 invested from Oct 11th , 02 to Mar
11th, 03 at 4.0%?
Oct 11th to end of month = 20Days
Total = 61 Total = 59
151 151
Jan & Feb
Mar To 11th of month = 11
Nov & Dec30 31
2831
Includes the last date
Calculating the Number of Days
McGraw-Hill Ryerson©
6 - 24Simple
Interest
Simple
Interest 66 66Day of Month
TABLE 6.2The Serial Number of Each Day of the YearJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 3418 39 67 98 128 159 189 220 251 281 312 3429 40 68 99 129 160 190 221 252 282 313 34310 41 69 100 130 161 191 222 253 283 314 34411 42 70 101 131 162 192 223 254 284 315 34512 43 71 102 132 163 193 224 255 285 316 34613 44 72 103 133 164 194 225 256 286 317 34714 45 73 104 134 165 195 226 257 287 318 34815 46 74 105 135 166 196 227 258 288 319 34916 47 75 106 136 167 197 228 259 289 320 35017 48 76 107 137 168 198 229 260 290 321 35118 49 77 108 138 169 199 230 261 291 322 35219 50 78 109 139 170 200 231 262 292 323 35320 51 79 110 140 171 201 232 263 293 324 35421 52 80 111 141 172 202 233 264 294 325 35522 53 81 112 142 173 203 234 265 295 326 35623 82 113 143 174 204 235 266 296 327 35724 55 83 114 144 175 205 236 267 297 328 35825 56 84 115 145 176 206 237 268 298 329 35926 57 85 116 146 177 207 238 269 299 330 36027 58 86 117 147 178 208 239 270 300 331 36128 59 87 118 148 179 209 240 271 301 332 36229 88 119 149 180 210 241 272 302 333 36330 89 120 150 181 211 242 273 303 334 36431 90 151 212 243 304 365
12345678910111213141516171819202122232425262728293031
54
Oct 11Dec 31 365
284 = 81 Days= 81 Days
Mar 11 70 = 70 Days= 70 Days
=151 Days=151 Days
Method 2.Method 2.
McGraw-Hill Ryerson©
6 - 25Simple
Interest
Simple
Interest 66 66
03.1103
Using… Texas Instruments BAII PLUS
i
Days Between DatesDays Between Dates
2nd
CPT
Enter
Method 3.Method 3.
Example 1.Example 1.
Calculate… the interest
earned on $5000
invested from
Oct. 11th,, 02 to Mar
11th. 03 at 4.0%.
Start
DBD = 151 Date
10.1102 Enter
McGraw-Hill Ryerson©
6 - 26Simple
Interest
Simple
Interest 66 66
Formula Formula I = Prt
I =$5000* .04 * 151/365
I = $82.74I = $82.74
Calculate the Interest earned on $5000 invested
at 4.0%
for ? .
151 Days
McGraw-Hill Ryerson©
6 - 27Simple
Interest
Simple
Interest 66 66
Formula Formula I = Prt
We can ‘reorganize’ the formula to also get each of the following separately:
PrincipalRateRateTimeTime
Shortcut Tool!Shortcut Tool!
McGraw-Hill Ryerson©
6 - 28Simple
Interest
Simple
Interest 66 66
IPrt
Formula Formula I = PrtTo help remember this…
we can place the formula into a triangle as follows…
The Triangle …another useful non-calculator!
Where variables are BESIDE EACH OTHER this
means to MULTIPLY!
Using this tool!Using this tool!
P*r*tP*r*t
IPrt
Where a variable is ABOVE ANOTHER this means to
DIVIDE!
McGraw-Hill Ryerson©
6 - 29Simple
Interest
Simple
Interest 66 66
If you want to find P then I /rt
If you want to find r
then I /Pr
then I /Pt
If you want to find t
Using this tool!Using this tool!
IPrt
The Triangle …another useful non-calculator!
McGraw-Hill Ryerson©
6 - 30Simple
Interest
Simple
Interest 66 66
What is a Time Line?
A Time Line is, as the name suggests, a line that shows the various points of time along
which a loan or investment travels to maturity.
It is used for diagramming problems involving multiple payments or investments.
Two BenefitsTwo Benefits…Helps organize data…Helps organize data
…Indicates the steps needed to implement the solution
…Indicates the steps needed to implement the solution
Using a Time LineTime Line
McGraw-Hill Ryerson©
6 - 31Simple
Interest
Simple
Interest 66 66
Calculate the interest earned at 4% on $5000 invested from Oct. 11th to March 11th
Calculate the interest earned at 4% on $5000 invested from Oct. 11th to March 11th
Draw a line for the entire period
Step 1Step 1
Oct 11 March 11
$5000
Start Finish
Enter the key dates on the line
Step 2Step 2Dec 31
Enter the number of days
between each date and
add
Step 4Step 4
81 days70 days
151 days
Enter the Investment
Step 3Step 3
The calculation can now be restated as follows…
284 365 70
Look up
Using a Time LineTime Line
McGraw-Hill Ryerson©
6 - 32Simple
Interest
Simple
Interest 66 66
Calculate the interest earned at 4% on $5000 invested for 151 days.
Calculate the interest earned at 4% on $5000 invested for 151 days.
I = 5000 *
Using this tool!Using this tool!
IPrt = $82.74
I = Prt
.04 * 151/365
Using a Time LineTime Line
McGraw-Hill Ryerson©
6 - 33Simple
Interest
Simple
Interest 66 66 You can now use this tool!You can now use this tool!
IPrt
In the next few examples you have to…(a) First identify which variable you are being asked to solve for, and
In the next few examples you have to…(a) First identify which variable you are being asked to solve for, and
(b) Reorganize the formula in order to meet the requirement in (a).
(b) Reorganize the formula in order to meet the requirement in (a).
McGraw-Hill Ryerson©
6 - 34Simple
Interest
Simple
Interest 66 66 Calculating the
PrincipalPrincipal
Formula Formula I rtP=
P = $195 .0525 *(150/365)
P = $195
P = $9,038.10
.0121575342
$195 interest is earned on a 150 day GIC at 5.25%.
Find the initial investment .
McGraw-Hill Ryerson©
6 - 35Simple
Interest
Simple
Interest 66 66
.0525
*150/
365=/
195
=
$9038.10$9038.101/x1/x
9038.10
P = $195 .0525 *(150/365)
McGraw-Hill Ryerson©
6 - 36Simple
Interest
Simple
Interest 66 66 Calculating the RateCalculating the Rate
What Rate of Interest is needed to earn $200 on a
$5000 investment invested for 180 days?
What Rate of Interest is needed to earn $200 on a
$5000 investment invested for 180 days?
r =
Formula Formula r = I Pt
/($5000*180/365)$200
$200
0.081111 or 8.11% /2465.75 r =
r =
McGraw-Hill Ryerson©
6 - 37Simple
Interest
Simple
Interest 66 66
5000
*180/
365=/
200
=
8.11%8.11%1/x1/x
0.08111
/($5000*180/365) r = $200
McGraw-Hill Ryerson©
6 - 38Simple
Interest
Simple
Interest 66 66 Calculating the TimeCalculating the Time
What is the length of Time required for $2000 to grow to
$2100 when invested at 5.6%?
What is the length of Time required for $2000 to grow to
$2100 when invested at 5.6%?
Formula Formula t I P= r
Step 1Step 1 Find the amount of InterestFind the amount of Interest
$2100
PP
= $100
More
- $2000
IIP + I = SumP + I = SumI
McGraw-Hill Ryerson©
6 - 39Simple
Interest
Simple
Interest 66 66
What is the length of Time required for $2000 to grow to $2100 when invested at 5.6%?
What is the length of Time required for $2000 to grow to $2100 when invested at 5.6%?
t = / ($2000*.056)/ ($2000*.056)t =
$100$100/ 112
t = 0.8928 Years
t = 326 days
Step 2Calculate
Step 2Calculate
Calculating the TimeCalculating the Time
Formula Formula t I P= r
*365 days*365 days
McGraw-Hill Ryerson©
6 - 40Simple
Interest
Simple
Interest 66 66
100
2000/
0.056=
365=
326 days326 days
325.89
/ ($2000*.056)/ ($2000*.056)$100t =
/
0.8928 Years*
McGraw-Hill Ryerson©
6 - 41Simple
Interest
Simple
Interest 66 66
McGraw-Hill Ryerson©
6 - 42Simple
Interest
Simple
Interest 66 66
Formula Formula I = Prt
P + ISum =
Up to this point we have used two formulae:
Now, we substitute for INow, we substitute for I
withwith PrtStep 1Step 1
P +Sum =
Collecting like termsCollecting like terms
Formula Future ValueFuture Value Sum =P(1+rt)
Step 2Step 2
& Sum = P + IWe can combine them as follows:
McGraw-Hill Ryerson©
6 - 43Simple
Interest
Simple
Interest 66 66
Sum = P(1+rt)
I place $17000 in a 150 day
term deposit on Jan. 6 paying
6.5%.
I place $17000 in a 150 day
term deposit on Jan. 6 paying
6.5%.How much will the bank pay me on the
maturity date?
How much will the bank pay me on the
maturity date?
S = $17454.11
S = $17000(1.0267123)
S = $17000 1+ .065(150)365
McGraw-Hill Ryerson©
6 - 44Simple
Interest
Simple
Interest 66 66
.065
Date of Maturity
*150/
365=+1=
$17454.11$17454.11
*17000
S = $17000 1+ .065(150)365
17454.11
=
McGraw-Hill Ryerson©
6 - 45Simple
Interest
Simple
Interest 66 66
Day of Month
TABLE 6.2The Serial Number of Each Day of the YearJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1 32 60 91 121 152 182 213 244 274 305 3352 33 61 92 122 153 183 214 245 275 306 3363 34 62 93 123 154 184 215 246 276 307 3374 35 63 94 124 155 185 216 247 277 308 3385 36 64 95 125 156 186 217 248 278 309 3396 37 65 96 126 157 187 218 249 279 310 3407 38 66 97 127 158 188 219 250 280 311 341
1234567
Determine the Maturity DateDetermine the Maturity Date
I place $17000 in a 150 day term deposit on Jan. 6 paying 6.5% pa.I place $17000 in a 150 day term deposit on Jan. 6 paying 6.5% pa.
= 6 days +150 = 156 days
Find 156
Find 156 The Term Deposit will mature on June 5th.
Look up
McGraw-Hill Ryerson©
6 - 46Simple
Interest
Simple
Interest 66 66
5,000
8,000
10,000
During the year, I invested the following funds at a constant 4% p.a.
Feb 14th $5,000
Mar 17th $3,000
July 1st $2,000
What Total amount will I have on December 29th?What Total amount will I have on December 29th?
(The second and third amounts were added to the Feb 14th amount.)
McGraw-Hill Ryerson©
6 - 47Simple
Interest
Simple
Interest 66 66
Step 1
Three Steps are required to solve this problem:
Draw a time line, including the dates and dollar amounts.
Step 2
Determine the time between each of the
dates
Step 3
Calculate the interest amounts,
and add together.
McGraw-Hill Ryerson©
6 - 48Simple
Interest
Simple
Interest 66 66
Step 1
Draw a time line
Feb 14 March 17 July 1 Dec 29
45 76 182 363
$5000
$3000
$2000
363 – 45 = 318 Days
363 – 76 = 287 DaysStep 2
Determine the Time
363 – 182 = 181 Days
Look up
McGraw-Hill Ryerson©
6 - 49Simple
Interest
Simple
Interest 66 66
S = $10308.28Total Amount
S = $10308.28Total Amount
Step 3
Calculate the
Interest amounts, and
add togethe
r.
Calculate the
Interest amounts, and
add togethe
r.
Formula Formula I = Prt
I1 = 5000 *.04 *318/365 $174.25
I2 = 3000 *.04 *287/365
I3 = 2000 *.04 *182/365
94.36
39.67
$308.28
$10000 +$10000 + $308.28
$308.28
McGraw-Hill Ryerson©
6 - 50Simple
Interest
Simple
Interest 66 66
“During the year I made an investment that had changes in
the rate of interest.How do I determine the total
interest earned during the period under review?”
Every time the interest rate changes,you must stop and
make a calculation up to that point.
McGraw-Hill Ryerson©
6 - 51Simple
Interest
Simple
Interest 66 66
I invest $1,000 on Feb. 14th at 6%.The changes in interest rates to July 4th
are as follows:
Investment Date rate
$1,000 Feb 14th 6%
April 20th 6.8%
May 18th 7.1%
How much Interest did I earn up to July 4th ?How much Interest did I earn up to July 4th ?
McGraw-Hill Ryerson©
6 - 52Simple
Interest
Simple
Interest 66 66
Look up
for Days
… by finding the number of days between each rate change!
Investment Date rate
$1,000 Feb 14th 6%
April 20th 6.8%
May 18th 7.1%
July 4th
McGraw-Hill Ryerson©
6 - 53Simple
Interest
Simple
Interest 66 66
= 45= 110 = 65 Days
= 28 Days
Number of Days
Number of Days
Table reading
Table reading
Look up
for Days
Feb 14th
April 20th
May 18th
July 4th = 47 Days
Interest EarnedInterest Earned
= 138
= 185
McGraw-Hill Ryerson©
6 - 54Simple
Interest
Simple
Interest 66 66
Feb 14th
April 20th65 Days
Formula Formula I = Prt
I1 = 1000 * .06 * 65/365 = $10.68
May 18th
28 DaysI2 = 1000 * .068 * 28/365
I3 = 1000 * .071 * 47/365
= 5.22
July 4th47 Days
= 9.14
$25.04$25.04
Interest EarnedInterest Earned
McGraw-Hill Ryerson©
6 - 55Simple
Interest
Simple
Interest 66 66
McGraw-Hill Ryerson©
6 - 56Simple
Interest
Simple
Interest 66 66
What are we being asked to provide?
“How much must I invest…
to grow…”
“How much must I invest…
to grow…”
…this suggests finding the
Principal
How much must I invest in order for it to grow to $5000 within 6 months @ 4.4% simple interest?
McGraw-Hill Ryerson©
6 - 57Simple
Interest
Simple
Interest 66 66
What data do we need?
We need the appropriate data to be
able to use the appropriate formula…We need the appropriate data to be
able to use the appropriate formula…
Formulae Formulae I = Prt & Sum = P(1+rt)
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
McGraw-Hill Ryerson©
6 - 58Simple
Interest
Simple
Interest 66 66
r = 4.4% t = 6 months = .5Sum = $5000
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
What data do we have?
Formulae Formulae I = Prt & Sum = P(1+rt)
McGraw-Hill Ryerson©
6 - 59Simple
Interest
Simple
Interest 66 66
As we know the Sum, the formula now becomes…
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
Formulae Formulae I = Prt & Sum = P(1+rt)
Using Sum = P(1+rt)
P = Sum/(1+rt)
McGraw-Hill Ryerson©
6 - 60Simple
Interest
Simple
Interest 66 66
P =5000/ 1 + 0.044(.5)
P = $4892.37P = $4892.37
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
How much must I invest in order for it to grow to $5000 within 6 months, @ 4.4% simple interest?
FormulaFormula P = Sum/(1+rt)
McGraw-Hill Ryerson©
6 - 61Simple
Interest
Simple
Interest 66 66
LO-2LO-2
Simple
Interest
Simple
Interest 66 66
McGraw-Hill Ryerson©
6 - 62Simple
Interest
Simple
Interest 66 66
Future
Value
What is the equivalent value on September 15 of a $2000 payment on July
4, if money is worth 6% pa?
What is the equivalent value on September 15 of a $2000 payment on July
4, if money is worth 6% pa?
Step 1
Step 2
Draw a Timeline
July 4 September 15
$2000
2000[1+.06(69/365)]
= $2022.68= $2022.68
Sum =
69 Days
Sum = P(1+rt)
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Present Value
What is the equivalent value on May 18th of a $2000 payment due on the following December 15th if money can earn 5.2%?
What is the equivalent value on May 18th of a $2000 payment due on the following December 15th if money can earn 5.2%?
Step 1
Step 2
Draw a Timeline
May 18 December 15
$2000
= 2000/[1+.052(211/365)]
211 Days
= $1941.63= $1941.63
P = Sum/(1+rt)
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Heather owes Mark $3000 payable on April 27.
If money can earn 4%, what amount should Mark accept in
settlement of the debt:A) 30 days before the scheduled
payment?B) 90 days before the scheduled
payment?
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Simple
Interest 66 66
Step 1
Draw a Timeline
April 27
Present Value30 days
90 days
$3000
Step 2 P = Sum/(1+rt)
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AA P = 3000/[1+.04(30/365)]
P = $2990.17P = $2990.17
BB P = 3000/[1+.04(90/365)]
P = $2970.17P = $2970.17
P = Sum/(1+rt)
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You can prepay $1234 tuition for a course or delay payment for 3 months and pay
$1432.
If you can earn 6% on your money, which option should you choose?
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Data
$1234 = Present Value = P1
$1432 = Future Value = S2
P2 = 1432/[1+.06(.25)]
Tip:Find the PV of the
future payment!
Tip:Find the PV of the
future payment! P2 = $1410.84
Money saved ($176.84) by paying now!
Which formula should
you use?
Which formula should
you use? $1234.00
P = Sum/(1+rt)P = Sum/(1+rt)3
months = 1/4
3 months = 1/4
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This completes Chapter 6This completes Chapter 6