Abstract The article presents a heuristic approach to effective rates of interest being charged on loans repaid in equal installments. For instance, a situation is considered in which a one-year loan to be repaid in 12 equal monthly installments and a 6% interest rate quoted on the original unpaid balance is calculated. Figuring the average amount of outstanding principal for the year and dividing that amount into the interest charge to compute the effective rate would compute the effective rate of interest charged. A short-cut computation is available to convert from a quoted rate to an effective rate but noting that it is only necessary to multiply the quoted rate by the ratio of the original principal to the average principal outstanding. Still, a further shortcut is to note that the average principal outstanding is equal to the average of the sum of first schedule balance and last schedule balance. Assuming a 36-month loan to be repaid in equal monthly installments and a 6% annual interest rate quoted on the original unpaid balance effective rate is calculated. The result suggests that the effective rate could approach but not exceed twice the quoted rate.
Robert M. Jennings (Fri,) studied this question.