# rule of 78s

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## Rule of 78

## rule of 78s

A method for computing the refund due when a borrower wants to pay off an add-on interest loan at an earlier time than the maturity date. The reason there would be any refund at all is because all the interest is calculated up front, for the entire loan, and then paid in equal monthly installments. If the loan is repaid early, some portion of the interest has not been earned, but it has already been paid. Use of the rule of 78s results in the lender “earning” more of the interest than one might otherwise think. To calculate, you need to use a fraction that changes every month. For the first month,the numerator (top number) is the number of months remaining in the loan. The denominator (bottom number) is the sum of the digits for the number of months of the original loan.If the loan is for 1 year, then you add 1+ 2 + 3 + 4 + … + 11 + 12 = 78. For the first month, with 12 months remaining in the loan, the fraction is 12/78. According to the method,^{ 12}/78 of the interest has been earned in the first month, or 15.38 percent.You might think that only 1/12 of the interest—8.33 percent—has been earned,since only one month has passed,but that's the way the rule of 78s works— to the lender's advantage. The next month, you change the numerator by adding the number of remaining months (11) to last month's numerator of 12.The numerator is then 11 + 12 = 23, so 23/78 of the interest has been earned, or 29.48 percent. For month 3, the numerator is 10 + 23, and so on.