Engineering Economic Analysis

Uniform Series Compound Interest Formulas 87

Looking at Figure 4-1, we see that if an amountAis investedat the end of each year for

4 years, the total amountFat the end of 4 years will be the sum of the compound amounts

of the individual investments.

A A A A A A A A

+ + + + + ..q'-- -+ + +

0-1-2-3-4=0-1-2-3-4+0-1-2-3-4+0-1-2-3-4+0-1-2-3-4

1 1 ~ t

F A(l +i)3 + A(l +i)2 + A(l +i) + A

In the general case fornyears,

F=A(1+i)n-l+ ... +A(1+i)3+A(1+i)2+A(1+i)+A (4-1)

Multiplying Equation (4-1) by (1 +i),we have.

(1 +i)F =A(1+i)n+... +A(1+i)4

• A(1+i)3+A(1+i)2+A(1+i) (4-2)

Factoring outAand subtracting Equation 4-1 gives

(4-3)

(4-4)

Solving Equation 4-4 forFgives

[

(1 +i)n- 1

]

.

F=A i =A(F/A,z%,n)

(4-5)

Thus we have an equation forFwhenAis known. The term inside the brackets

is called theuniformseriescompound amount factorand has the notation(F/A, i,n).

A man deposits $500 in a credit union at the end of each yearfot5 years. The credit union pays
5% interest, compounded annually.At the end of 5 years, immediately after the fifth deposit, how
much does the man have in his account?