Engineering Economic Analysis

Summary 81

earn more interest each year, indicating that we can begin with asmaller Pand still accumulate

enough money for the subsequent cash flows. The computation is:

P 400(P/F,i5'%,3) +600(P/F,15%,5)

=400(0.6575) +600(0.4972)

=$561.32

The value ofPis smaller at 15% than at 12% interest.

.-.

Summary

This chapter describes cash flow tables, the time value of money, and equivalence. The

single payment compound interest formulas were derived. It is essential that these concepts

and the use of the interest formulas be carefully understood, since the remainder of this

book and the practice of engineering economy are based on them.

Time value of money:The continuing offer of banks to pay interest for the temporary

use of other people's money is ample proof that there is a time value of money.

Thus, we would always choose to receive $100 today rather than the promise of

$100 to be paid at a future date.

Equivalence:What sum would a person be willing to accept a year hence instead

of $100 today? If a 9% interest rate is considered to be appropriate, he would

require $109 a year hence. If $100 today and $109 a year hence are considered

equally desirable, we say the two sums of money are equivalent.But, if on further

consideration, we decided that a 12% interest rate is applicable, then $109 a year

hence would no longer be equivalentto $100 today.This illustratesthat equivalence

is dependent on the interest rate.

Single Payment Formulas

Theseformulasare for compoundinterest,whichis used in engineeringeconomy.

Compound amount

Present worth

F= P(l +i)n= P(F/P, i, n)

P=F(1+i)-n = F (P/F, i, n)

wherei =interest rate per interest period (stated as a decimal)

n =number of interest periods

P=a present sum of money

F=a future sum of money; the future sumFis an amount,ninterest periods from

the present, that is equivalenttoPwith interest ratei

This chapter also defined simple interest, where interest does not carry over and become

part of the principal in subsequent periods. Unless otherwise specified, all interest rates in

this text are compound rates.