Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

20.5 Present Worth of a Future Amount

Let us now consider the following situation. You would like to have $2000 available to you for

a down payment on a car when you graduate from college in, say, five years. How much money

do you need to put in a certificate of deposit (CD) with an interest rate of 6.5% (compounding

annually) today? The relationship between the future and present value was developed earlier

and is given by Equation (20.2). Rearranging Equation (20.2), we have

(20.5)

and substituting in Equation (20.5) for the future valueF, the interest ratei, and the periodn,

we have

This may be a relatively large sum to put aside all at once, especially for a first-year engineering

student. A more realistic option would be to put aside some money each year. Then the ques-

tion becomes, how much money do you need to put aside every year for the next five years at

the given interest rate to have that $2000 available to you at the end of the fifth year? To answer

this question, we need to develop the formula that deals with a series of payments or series of

deposits. This situation is discussed next.

20.6 Present Worth of Series Payment or Annuity

In this section, we will first formulate the relationship between a present lump sum,P, and future

uniform series payments,A, and then from that relationship we will develop the formula that

relates the uniform series paymentsAto a future lump sumF. This approach is much easier to fol-

low as you will see. To derive these relationships, let us first consider a situation where we have bor-

rowed some money, denoted byP, at an annual interest rateifrom a bank, and we are planning

to pay the loan yearly, in equal amountsA,innyears, as shown in Figure 20.4.

P

2000

11 0.065 2

5

$1459.76

P

F

11 i 2

n

20.6 Present Worth of Series Payment or Annuity 663

■Figure 20.4

The cash flow diagram for a

borrowed sum of money and its

equivalent series payments.

P

A

0

1 2 3 4 n  3 n  2 n  1 n

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