Rule of 78 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:

\[\text { INTEREST REBATE }=\frac{k(k+1)}{n(n+1)} \times \text { FINANCE CHARGE }\]

where \(k\) is the number of payments remaining and \(n\) is the total number of payments. Determine the interest rebate on the following:

a. \(\$1,026\) interest on an 18-month loan; pay off loan after 12 months.

b. \(\$ 350\) interest on a 2 -year loan with 10 payments remaining.

c. \(\$ 10,200\) borrowed at \(11 \%\) on a 4 -year loan with 36 months remaining.

d. \(\$ 51,000\) borrowed at \(10 \%\) on a 5 -year loan with 18 payments remaining.