Question

A $400 loan is to be paid off in 66 monthly payments of $11.62. The borrower decides to pay off the loan after 18 payments. Use the rule of 78s to find the amount of interest saved

Answer 1

To calculate the amount of interest attributable to each payment under the Rule of 78's, first, add up all the digits for the number of payments scheduled to be made. For a 12-month loan this would be 1 + 2 + 3 + 4+ ... + 12 = 78. In the first month, before making any payments, you have the use of the entire amount borrowed. You thus pay 12/78 of the total interest in the first payment. In the second month, you pay 11/78; in the third, 10/78; and so on down to the last payment, 1/78. Likewise, the sum of the digits for a four-year (48 month) loan would be 1 + 2 + 3 +...... + 47 + 48 = 1, 176, and you would pay 48/1,176 of the total interest in the first payment, 47/1,176 in the second month, and so on.

To calculate how much interest will be saved by prepayment, you merely sum the digits for the remaining payments and multiply the fraction by the total amount of interest that must be paid on the loan.

66 x 11.62=766.92
766.92-400=366.92
366.92= interest

366.92*(66/2211)+366.92(65/2211)+....
............366.92(49/2211)=

171.76

366.92-171.76=$195.16

Answer 2

Do You Get It ??