Solve the problem using the rule of 78s.
-Jamal has a 60-month fixed installment loan, with a monthly payment of $318.50. The amount he Borrowed was $12,250. Instead of making his 37th payment, Jamal is paying the remaining balance On the loan. How much interest will Jamal save?
A) $980.55
B) $1189.82
C) $1034.62
D) $931.16

Question

Quizplus · Accepted Answer

The rule of 78s is a method of calculating the interest rebate a borrower would receive if they pay off a fixed installment loan early. The total interest saved by Jamal can be calculated by first determining the sum of the digits for the total loan term (60 months in this case), which is the sum of numbers from 1 to 60. This sum is 1830 (the 60th triangular number). The interest for each month is weighted more heavily at the beginning of the loan period. After 36 payments, Jamal has 24 months left. The sum of the digits for the remaining months (37 to 60) is 1176 (the sum of the numbers from 37 to 60). The proportion of interest Jamal saves by paying off early is the sum of the digits for the months he won't be paying (1176) divided by the total sum of digits (1830). The total interest Jamal would have paid without early payoff can be calculated by subtracting the principal ($12,250) from the total payments (60 months * $318.50 = $19,110), which equals $6,860 in total interest. The interest Jamal saves is then a proportion of this total interest, calculated as $6,860 * (1176/1830) = $4,403.01 in interest he would have paid for the remaining months. Subtracting this from the total interest he would have paid without early payoff gives the interest saved, which is approximately $1034.62.

Solve the Problem Using the Rule of 78s