Engineering Economic Analysis

74 INTERESTAND EQUIVALENCE

This may be rearranged by factoringP(1+i), which gives us

P(1+ i)(l +i)

or

If the process is continued for a third year, the end-of-the-third-year total amount will be

P(1+i)3;at the end ofnyears, we will haveP(l +i)n.The progression looks like this:

Year

1

2

3

Amount at Beginning of

Interest Period

P

P(1+i)

P(1+i)2

P(l +i)n-l

+ Interest for

Period

+iP

+iP(l+i)

+iP(1+i)2

+ i P(1+i)n-l

= Amount at End of

Interest Period

=P(1+i)

= P(1 +i)2

= P(1+i)3

n = P(1 +i)n

In other words, a present sumPincreases innperiods toP(1 + i)n.We therefore have a

relationship between a present sumPand its equivalentfuture sum,F.

Future sum=(Present sum) (1 +i)n

F= P(1+i)n (3-3)

This is the single payment compound amount formula and is written in functional nota-

tion as

F=P(FjP,i,n) (3-4)

The notation in parentheses(F j P, i, n)can be read as follows:

To find a future sumF,given a present sum,P,at an interest rateiper interest period,

andninterest periods hence..

Functional notation is designed so that the compound interest factors may be written in

an equation in an algebraically correct form. In Equation 3-4, for example, the functional

notation is interpreted as

which is dimensionallycorrect. Without proceeding further,we can see that when we derive.

a compound interest factor to find a present sumP,given a future sumF,the factor will

be(P j F, i, n);so, the resulting equation would be

P=F(PjF,i,n)

which is dimensionally correct.