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

20.3 Future Worth of a Present Amount 659

■Figure 20.3

The cash flow diagram for future

worth of a deposit made in the

bank today.

TABLE 20.2 The Relationship Between Present ValuePand the Future ValueF

Balance at the

Beginning of Interest for Balance at the End of the Year,

Year the Year the Year Including the Interest

1 P (P)(i) P(P)(i) P(1 i)

2 P(1 i) P(1 i)(i) P(1 i) P(1 i)(i) P(1 i)

2

3 P(1 i)

2

P(1 i)

2

(i) P(1 i)

2

P(1 i)

2

(i) P(1 i)

3

4 P(1 i)

3

P(1 i)

3

(i) P(1 i)

3

P(1 i)

3

(i) P(1 i)

4

5 P(1 i)

4

P(1 i)

4

(i) P(1 i)

4

P(1 i)

4

(i) P(1 i)

5

. ...... ... ...... ... ...... ...... ...... ..
nP(1 i)
n 1
P(1 i)
n 1
(i) P(1 i)
n 1
P(1 i)
n 1
(i) P(1 i)
n

P

0 n

F

1 2 3 4 n  2 n  1

theP(1i) amount that we started with in the second year, we will have a total amount ofP(1i)

P(1i)i.Factoring out theP(1i) term, we will haveP(1i)

2

dollars at the end of the second

year. Now by following Table 20.2 you can see how the interest earned and the total amount are com-

puted for the third, fourth, fifth,... , and thenth year. Consequently, you can see that the relation-

ship between the present worthPand the future valueFof an amount collectingi% interest

compounding annually afternyears is given by

FP 11 i 2 (20.2)

n

Example 20.3 Compute the future value of a $1500 deposit made today, after eight years, in an account that

pays an interest rate of 7% that compounds annually. How much interest will be paid to this

account?

The future value of the $1500 deposit is computed by substituting in Equation (20.2) for

P,i,andn, which results in the amount that follows:

The total interest earned during the eight-year life of this account is determined by calculating

the difference between the future value and the present deposit value.

interest$2577.27$1500$1077.27

FP 11 i 2

n

 150011 .07 2

8

$2577.27

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