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Lecture No.11
Chapter 4
Contemporary Engineering Economics
Copyright 2010
Contemporary Engineering Economics, 5th edition, 2010
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Equivalence Calculations using Effective
Interest RatesStep 1: Identify the payment period (e.g., annual,
quarter, month, week, etc)
Step 2: Identify the interest period (e.g., annually,
quarterly, monthly, etc)
Step 3: Find the effective interest rate that covers thepayment period.
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Case I: When Payment Period is Equal to
Compounding Period
Step 1: Identify the number of compounding periods (M) per
year
Step 2: Compute the effective interest rate per payment
period (i)
Step 3: Determine the total number of payment periods (N)
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Example 4.4:
Calculating Auto
Loan PaymentsGiven:
MSRP = $20,870
Discounts & Rebates =
$2,443
Net sale price = $18,427
Down payment = $3,427
Dealers interest rate =
6.25% APR
Length of financing = 72
months
Find: the monthly payment
(A)
Solution:
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Dollars Down
in the DrainSuppose you drink a cupof coffee ($3.00 a cup) on
the way to work every
morning for 30 years. If you
put the money in the bank
for the same period, howmuch would you have,
assuming your accounts
earns a 5% interest
compounded daily.
NOTE: Assume you drink a
cup of coffee every day
including weekends.
Solution:
Payment period = daily
Compounding period = daily
Contemporary Engineering Economics, 5th edition, 2010
5%0.0137% per day
365
30 365 10,950 days
$3( / ,0.0137%,10950)
$76,246
i
N
F F A
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Case II: When Payment Periods Differ from
Compounding Periods Step 1: Identify the following parameters.
M = No. of compounding periods
K= No. of payment periods per year
C= No. of interest periods per payment period Step 2: Compute the effective interest rate per payment
period.
For discrete compounding
For continuous compounding
Step 3: Find the total no. of payment periods.
N= K(no. of years)
Step 4: Use iand Nin the appropriate equivalence formula.
Contemporary Engineering Economics, 5th edition, 2010
[1 / ] 1Ci r CK
/ 1r Ki e
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Example 4.5 Compounding
Occurs More Frequently than
Payments are Made (Discrete
Case)Given:A = $1,500 per quarter, r= 6% per year, M = 12compounding periods per year,and N= 2 years
Find: F
Step 1:M = 12 compoundingperiods/year K= 4 paymentperiods/year C= 3 interest periodsper quarter
Step 2:
Step 3: N= 4(2) = 8
Solution:
F= $1,500 (F/A, 1.5075%, 8)= $14,216.24
Contemporary Engineering Economics, 5th edition, 2010
30.06
1 112
1.5075% per quarter
i
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Example 4.6
Compounding is Less
Frequent than
Payments
Given:A = $500 per month, r=10% per year, M = 4 quarterlycompounding periods per year, andN= 10 years
Find: F
Step 1:
M = 4 compoundingperiods/year K= 12 paymentperiods/year C= 1/3 interest periodper quarter
Step 2:
Step 3: N= 4(2) = 8
Solution:
F= $500 (F/A, 0.826%, 120)= $101,907.89
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0.101 14
0.826%
i
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A Decision Flow Chart on How to Compute the
Effective Interest Rate per Payment Period
Contemporary Engineering Economics, 5th edition, 2010
7/27/2019 Chapter 4-2 Equivalence Analysis Using Effective Interest Rates (1)
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Key Points
Financial institutions often quote interest rate
based on an APR.
In all financial analysis, we need to convert the APR
into an appropriate effective interest rate based ona payment period.
When payment period and interest period differ,
calculate an effective interest rate that covers the
payment period. Then use the appropriate interest
formulas to determine the equivalent values