The Rule of 78's is a computing used method of computing the amount of interest when the balance of a is repaid in advance.
Adding the numbers representing 12 months gives
1 + 2 + 3 + 4 + 5 + . . . + 11 + 12 = 78
If a 12-month loan is repaid at the end of one month, for example, the interest the borrower would be charged is 12/78 of the year's interest. If the loan is repaid at the end of 2 months, the total interest charged would be (12+ 11)/78, or 23/78 of the year's interest. After 11 months the interest charge would therefore be 77/78 of the total year's interest.
Helen Reddy borrowed $10,000 on January 1 at 9% annual interest, compounded monthly. The loan was to be repaid in 12 equal end-of-period payments. Helen made the first two payments and then decided to repay the balance of the loan when she pays the third payment. Thus she will pay the third payment plus an additional sum.
You are to calculate the amount of this additional sum
(a) Based on the rule of 78s.
(b) Based on exact economic analysis methods.