Engineering Economic Analysis

Nominal and Effective Interest 113

F =P(1 +i)n=50(1 + 0.20)52

=$655,200

With a nominal interest rate of 1040%per year and effectiveinterest rate of 1,310,400%per year,

ifhe started with $50, the loan shark would have $655,200 at the end of one year.

When the varioustime periods in a problem match, we generally can solve the problem

using simple calculations. Thus in Example 4-3, where we had $5000 in an account pay-

ing 8% interest, compounded annually, the five equal end-of-year withdrawals are simply

computed as follows:

A=P(Aj P, 8%, 5)=5000(0.2505) =$1252

Consider how this simple problem becomes more difficult if the compounding period is

changed so that it no longer match the annual withdrawals.

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On January 1, a woman deposits $5000 in a' credit union that pays 8% nominal annual interest,

compoundedquarterly.She wishes to withdrawall the money in fiveequal yearly sums, beginning

December 31 of the first year. How much should she withdraw each year?

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Since the 8% nominal annual interest rateris compounded quarterly, we know that the effective

interest rate per interest period,i,is 2%; and there are a total of 4 x 5=20 interest periods in

5 years. For the equation A =P (A j P, i, n)to be used, there must be as many periodic withdrawals

as there'are interest periods,n.In this example we have 5 withdrawalsand 20 interest periods.

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j =2% per quarter

n=20 quarters

$5000

To solve the problem, we must adjust it so that it is in one of the standard forms for which we

== = have compound interest factors.This means we must first comp;pt~either an equivalent~;;:. - :;: ~ C! ~ ~ ;; = = a~ -.- - A.{oreach.. _

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