With a typical installment loan, you are asked to sign a contract stating the te

Question

With a typical installment loan, you are asked to sign a contract stating the terms of repayment. If you pay off the loan early, you are entitled to an interest rebate. For example, if you finance $500 and are charged $90 interest (APR 8.46%), the total to be repaid is $590 with 24 monthly payments of $24.59. After 1 year, you decide to pay off the loan, so you figure that the rebate should be $45 (half of the interest for 2 years), but instead you are told the interest rebate is only $23.40. What happened? Look at the fine print on the contract. It says interest will be refunded according to the Rule of 78. The formula for the rebate is as follows: INTEREST REBATEk+1) x FINANCE CHARGE n(n 1) where k is the number of payments remaining and n is the total number of payments. Determine the interest rebate on the following. (Round your answers to the nearest cent.) (a) $1,056 interest on an 18-month loan; pay off loan after 12 months (b) $390 interest on a 2-year loan with 10 payments remaining (c) $10,500 borrowed at 11% on a 4-year loan with 36 months remaining (d) $52,000 borrowed at 10% on a 5-year loan with 18 payments remaining

Explanation / Answer

k k+1 n n+1 k(k+1) n(n+1) k(k+1)/n(n+1) charge rebate 12 13 24 25 156 600 0.26 90 23.4 12 13 18 19 156 342 0.456140351 1056 481.6842 10 11 24 25 110 600 0.183333333 390 71.5 12 13 48 49 156 2352 0.066326531 4620 306.4286 18 19 60 61 342 3660 0.093442623 26000 2429.508

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