Chapter 10.4, Problem 40E

Repayment Comparisons Christine took a world cruise that had a cash price of $23,000 by paying 10% down and financing the balance with a 48-month fixed installment loan. The APR on the loan was 6.0%. Before making the 12th payment, Christine decides to pay off the loan.

1. a. Determine the original finance charge on the 48-month loan.
2. b. Determine Christine’s monthly payment.
3. c. If the actuarial method is used, determine the amount of interest Christine will save by paying the loan off early.
4. d. If the rule of 78s (see Exercise 39) is used, determine the amount of interest Christine will save by paying the loan off early.

1. e. Which method, the actuarial method or the rule of 78s, is more advantageous to the consumer?

39. Rule of 78s When an installment loan is repaid early, there is a second method for calculating unearned interest called the rule of 78s. Although rarely used today, the following formula can be used to calculate unearned interest.

$u=\frac{f\cdot k\left(k+1\right)}{n\left(n+1\right)}$

where u is the unearned interest, f is the original finance charge, k is the number of remaining monthly payments (excluding the current payment), and n is the original number of payments. Joscelyn obtained a new sport utility vehicle that had a cash price of $35,000 by paying 15% down and financing the balance with a 60-month fixed installment loan. The APR on the loan was 8.5%. Before making the 24th payment, Joscelyn decides to pay off the loan.

1. a. Determine the original finance charge on the 60-month loan.
2. b. Determine Joscelyn’s monthly payment.
3. c. If the actuarial method is used, determine the amount of interest Joscelyn will save by paying the loan off early.
4. d. If the rule of 78s is used, determine the amount of interest Joscelyn will save by paying the loan off early.
5. e. Which method, the actuarial method or the rule of 78s, is more advantageous to the consumer?