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

660 Chapter 20 Engineering Economics

Many financial institutions pay interest that compounds more than once a year. For

example, a bank may pay you an interest rate that compounds semiannually (twice a year), or

quarterly (four times a year), or monthly (12 periods a year). If the principalPis deposited for

a duration ofnyears and the interest given is compoundedmperiods (ormtimes) per year, then

the future valueFof the principalPis determined from

(20.3)

Example 20.4 Compute the future value of a $1500 deposit, after eight years, in an account that pays an

interest rate of 7% that compounds monthly. How much interest will be paid to this

account?

To determine the future value of the $1500 deposit, we substitute in Equation (20.3) for

P,i,mandn.The substitution results in the future value shown next.

And the total interest is

The results of Examples 20.2, 20.3, and 20.4 are compared and summarized in

Table 20.3. Note the effects of simple interest, interest compounding annually, and interest

compounding monthly on the total future value of the $1500 deposit.

interest$2621.73$1500$1121.73

F 1500 a 1 

0.07

12

b

182 1122

 1500 a 1 

0.07

12

b

96

$2621.73

FP a 1 

i

m

b

n m

TABLE 20.3 Comparison of Results for Examples 20.2, 20.3, and 20.4

Future Interest

Value Earned

Example Principal Duration (dollars (dollars

Number (dollars) Interest Rate (years) and cents) and cents)

Example 20.2 1500 7% simple 8 2340.00 840.00

Example 20.3 1500 7% compounding 8 2577.27 1077.27

annually

Example 20.4 1500 7% compounding 8 2621.73 1121.73

monthly

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