A $10,000 debt is repaid by payments of $800 at the end of each quarter for five years. What quarterly-annually compounded nominal interest rate was charged on the loan?

Question

Quizplus · Accepted Answer

The correct answer is found by using the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PV is the present value (or initial loan amount), PMT is the payment amount per period, r is the interest rate per period, and n is the total number of payments. Rearranging to solve for r when PV = $10,000, PMT = $800, and n = 20 (5 years of quarterly payments), we find that the interest rate that fits these conditions is approximately 4.96% per quarter, compounded quarterly.

A $10,000 Debt Is Repaid by Payments of $800 at the End