Rule of 78 Calculator
Calculate the payoff of a precomputed loan under the Rule of 78 (sum of the digits): the interest rebate, the interest charged so far and how much more you pay than with the actuarial (simple interest) method.
How it works
Finance charge I = payment × n − amount · interest in month j = I × (n − j + 1) ÷ [n(n + 1) ÷ 2] · rebate after k payments = I × m(m + 1) ÷ [n(n + 1)], m = n − k · payoff = m × payment − rebate · actuarial payoff = remaining balance at the contract rate
The Rule of 78 (sum-of-the-digits method) front-loads the interest of a precomputed loan: for a 12-month loan the first month carries 12/78 of the total interest, the second 11/78, and so on. If you pay off early, the lender rebates only the unearned interest by that schedule, which is less than you would save under the actuarial method, where interest is charged on the balance actually outstanding. The penalty is largest for long loans paid off about a third of the way through. The method is banned in the US for consumer loans longer than 61 months and restricted in many countries, but still appears in some car, furniture and consumer-finance contracts.
Worked example
A 10,000 precomputed loan at 12% for 24 months has payments of 470.73 and a finance charge of 1,297.63. Paying it off after 12 payments, the Rule of 78 rebates 1,297.63 × 12 × 13 ÷ (24 × 25) = 337.38 of interest, so the payoff is 12 × 470.73 − 337.38 = 5,311.43. The actuarial balance would be 5,298.16, so the Rule of 78 costs 13.28 more.
Sources: Investopedia — Rule of 78 · Wikipedia — Rule of 78
Frequently asked questions
Why is it called the Rule of 78?
For a 12-month loan the digits 1 through 12 add up to 78. Each month’s share of the interest is its digit over 78, starting with 12/78.
Does the Rule of 78 cost more if I never prepay?
No. If you make every payment to the end, the total interest is the same as the actuarial method. It only costs more when you pay off early.
How do I know if my loan uses the Rule of 78?
Look in the contract for “precomputed”, “sum of the digits”, “Rule of 78” or a rebate clause. Simple-interest loans say interest is charged on the unpaid balance.
Is the Rule of 78 legal?
In the US it is prohibited for consumer loans over 61 months, and many states and countries restrict it further. Check your local consumer-credit law.
Related calculators
Estimates for education and planning, not financial advice. Lenders’ contracts, fees, day-count and rounding rules differ — check the official cost disclosure (APR / TAE / CAT) in your loan or card agreement before deciding.