A bank is negotiating a loan. The loan can either be paid off as a lump sum of $100,000 at the end of five years, or as equal annual payments at the end of each of the next five years. If the interest rate on the loan is 10%, what annual payments should be made so that both forms of payment are equivalent?

Question

Quizplus · Accepted Answer

The present value of the lump sum payment is $100,000/(1.10)^5 = $62,092.10. The present value of the annual payments is $X/(1.10) + $X/(1.10)^2 + $X/(1.10)^3 + $X/(1.10)^4 + $X/(1.10)^5 = $X(1 - 1/(1.10)^5)/0.10 = $X(4.1002)/0.10 = $41,002.20. Setting this equal to the present value of the lump sum payment, we get $X = $41,002.20/$4.1002 = $10,000. Therefore, the annual payments should be $10,000.

A Bank Is Negotiating a Loan