Calculate the Annuity Value, Knowing the Present Value.

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?

SOLUTION

The annual loan payment is $1252.

In Example 4-3, with interest at 8%, a present sum of $5000 is equivalent to five equal end-of-period disbursements of $1252. This is anotherway of stating Plan 3 of Table 3-1.



The method for determining the annual payment that would repay $5000 in 5 years with 8% interest has now been explained. The calculation is simply



If the capital recovery formula (Equation 4-7) is solved for the present sum P, we obtain the uniform seriespresent worth formula

which is the uniform series present worth factor.