The Rule of 78s

Also known as the sum-of-the-digits method, the Rule of 78s is a term used in lending that refers to a method of yearly interest calculation. The name comes from the total number of months’ interest that is being calculated in a year (the first month is 1 month’s interest, whereas the second month contains 2 months’ interest, etc.). This is an accurate interest model only based on the assumption that the lessee pays only the amount due each month. If the lessee pays off the loan early, this method maximizes the amount paid by applying funds to interest before principal.

A simple fraction (as with 12/78) consists of a numerator (the top number, 12 in the example) and a denominator (the bottom number, 78s in the example). The denominator of a Rule of 78s’ loan is the sum of the digits, the sum of the number of monthly payments in the loan. For a 12 month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 + . . . +12 = 78). For a 24 month loan, the denominator is 300. The sum of the numbers from 1 to n is given by the equation n (n+1) / 2. If n were 24, the sum of the numbers from 1 to 24 is 24 (24+1) / 2 = 12 x 25 = 300, which is the loan’s denominator, D.

For a 12 month loan, 12/78s of the finance charge is assessed as the first month’s portion of the finance charge, 11/78s of the finance charge is assessed as the second month’s portion of the finance charge and so on until the 12th month at which time 1/78s of the finance charge is assessed as that month’s portion of the finance charge. Following the same pattern, 24/300 of the finance charge is assessed as the first month’s portion of a 24 month precomputed loan.
Formula for calculating the unearned interest:

u = f X k(k+1)/n(n+1) u = unearned interest; f = total agreed finance charges; k = number of months paying off early; n = total term of loan in months

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