Engineering Economic Analysis

Uniform Series Compound Interest Formulas 89

Jim Hayes read that out west, a parcel of land could be purchased for $1000 cash. Jim decided

to save a uniform amount at the end of eacn month.sothat he would have the required $1000 at

the end of one year. The local credit union pays 6% interest, compounded monthly. How much

would Jim have to deposit each month?

In this example,

F= $1000 n= 12 A= unknown

A= 1000(AjF, 1/2%,12)= 1000(0.0811) = $81.10

=

Jim would have to deposit $81.10 each month.

If we use the sinking fund formula (Equation 4-6) and substitute for F the single payment

compound amount formula (Equation 3-3), we obtain

[

i

]

n

[

i

]

A-F -PI i

• (1 +i)n- 1 - (+) (1 +i)n- 1

[

i(I+i)n

]

.

A=P. =P(AjP,I%,n)

(1 +l)n- 1

(4-7)

We now have an equation for determiningthe value of a series of end-of-period payments-

or disbursements-A when the present sumPis known.

The portion inside the brackets

[

i(1 +i)n

(1 +i)n- 1]

is called the uniform.series capital recovery factor and has the notation(Aj P, i, n).

Consider a situation in which you borrow $5000. You will repay the loan in five equal end-of-
the-year payments. The first payment is due one year after you receive the loan. Interest on the
loan is 8%. What is the size of each of the five payments?

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