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Rule of 78 Calculator

Enter the total finance charge, total payments and payments remaining to find your interest rebate.

How it is calculated

The refund is the share of the finance charge that belongs to the months still to come. With n total payments and k payments remaining: fraction = k × (k + 1) / (n × (n + 1)), rebate = total finance charge × fraction, earned interest = total − rebate. The denominator n(n + 1) is twice the sum 1 + 2 + … + n, and the numerator is twice the sum of the last k months' weights. Payments are rounded to whole numbers, k cannot exceed n, and n must be above zero. The finance charge is in dollars. Only the interest rebate is calculated; any payoff fee, fees already paid or the principal balance are not included.

Worked example

A loan has a total finance charge of 1800 over 36 payments, and you pay it off with 12 payments remaining. Fraction = 12 × 13 / (36 × 37) = 156 / 1332 = 11.71%. Rebate = 1800 × 0.1171 = $210.81. Earned interest kept by the lender = 1800 − 210.81 = $1,589.19. With a straight pro-rata split you would expect 12/36 of the charge, which is 600, so the sum-of-digits method refunds far less.

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Common mistakes

  • Entering payments already made in the remaining field. The last field is payments still to be made, so for a 36-payment loan with 24 paid it is 12.
  • Expecting a simple pro-rata refund. Under this method early months carry the most interest, so the rebate is much smaller than the share of remaining months suggests.
  • Entering the loan principal instead of the total finance charge. The first field is the total interest and fees charged over the full term, not the amount borrowed.
  • Treating the rebate as the amount that clears the loan. It is only the unearned interest; you still owe the remaining principal and any payoff fee.
  • Entering decimal payment counts. The numbers are rounded to whole payments, so 12.4 is treated as 12.

Sources

About this calculator

The Rule of 78 (also called the sum-of-digits method) is an old way of front-loading interest on fixed-term installment loans, so that early payments cover much more interest and less principal than a simple straight-line split would suggest. For a loan of n months, the digits 1 through n are summed (for 12 months that is 1+2+…+12 = 78, which gives the method its name), and each month’s share of the total finance charge is weighted by its position in that countdown — month 1 carries the largest weight, the final month the smallest.

If the loan is paid off early, the lender only earns the weighted share of interest for months already elapsed and must rebate the rest — the unearned interest. Because early months are weighted so heavily, that rebate is smaller than a borrower expecting simple pro-rata interest would assume, which is why the method has been restricted or banned on longer consumer loans in many places.

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Comments (1)

  • Editorial team

    The rebate depends heavily on when you settle. On a 36-payment loan with a 1,200 finance charge, paying off with 24 payments left refunds 540.54, with 12 left refunds 140.54 and with only 6 left refunds just 37.84. Early payoffs return far more than late ones, and the refund is never the full interest of the remaining months. Ask your lender for the payoff figure in writing and compare. Which stage of your loan are you considering paying off?

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