About the Rule of 78 Calculator
This Rule of 78 calculator shows how much interest you get back — the rebate of unearned finance charges — when you pay off a precomputed loan early. Enter the amount financed, the total finance charge from your contract, the number of monthly payments and how many you have made to see the interest earned so far, the rebate and the payoff amount.
Precomputed loans add the whole finance charge to the balance on day one. When you repay early, the lender must refund the unearned part. Under the Rule of 78 (the “sum of the digits” method) far more interest is assigned to the early months than under simple-interest (actuarial) amortization, so your rebate is smaller. The calculator also estimates the actuarial payoff so you can see what the Rule of 78 costs you.
In the US, federal law bans the Rule of 78 on precomputed consumer loans with terms longer than 61 months, and many states restrict it further, so it now appears mainly on shorter auto, furniture and installment loans. Check your contract for the rebate method and any prepayment charges.
With the default inputs, the interest rebate (rule of 78) is $810.81. Change any value above to recalculate instantly.
How to use the rule of 78 calculator
- 1Find the amount financed and the finance charge on your Truth in Lending disclosure.
- 2Enter the number of monthly payments in the contract.
- 3Enter how many payments you have made (or will have made at payoff).
- 4Read the rebate and payoff amount, then compare with the actuarial payoff.
Formula and method
The Rule of 78 splits the finance charge F across the months in proportion to the digits n, n−1, … 1, where n is the number of payments. The digits add up to S = n(n+1)/2 — 78 for a 12-month loan, which gives the rule its name. Month 1 is charged n/S of the interest, month 2 (n−1)/S and so on, so interest is heavily front-loaded.
After k payments, the unearned interest is the share belonging to the remaining months: F × (sum of 1 to n−k) ÷ S. The payoff is the remaining scheduled payments minus that rebate. For comparison, the actuarial method finds the APR that the level payment implies and charges simple interest on the declining balance; its payoff is the present value of the remaining payments at that APR.
- F
- Total finance charge
- n
- Total number of monthly payments
- k
- Payments already made
- S
- Sum of the digits 1…n
- PMT
- Level monthly payment = (amount financed + F) ÷ n
Worked examples
$10,000 loan, $1,800 finance charge, paid off after 12 of 36 months
The digits 1–36 sum to 666. The remaining 24 months account for 300 of those digits, so the rebate is $1,800 × 300 ÷ 666 = $810.81. Twenty-four payments of $327.78 total $7,866.67; subtracting the rebate gives a payoff of $7,055.86.
12-month loan paid off after 3 months
For 12 months the digits sum to 78. The 9 remaining months hold 45 of them, so the rebate is $390 × 45 ÷ 78 = $225 and $165 counts as earned. Nine payments of $282.50 ($2,542.50) minus the $225 rebate gives a $2,317.50 payoff.
Frequently asked questions
What is the Rule of 78?+
It is a method for allocating the finance charge on a precomputed loan using the sum of the months’ digits. For a 12-month loan the digits add to 78, and month 1 is charged 12/78 of the interest, month 2 11/78, and so on.
Is the Rule of 78 legal?+
US federal law (15 U.S.C. § 1615) prohibits it on precomputed consumer credit with a term longer than 61 months, and requires a prompt refund of unearned interest. Many states ban or restrict it on shorter loans too.
Does the Rule of 78 penalize early payoff?+
Yes, compared with simple interest. Because more interest is assigned to early months, paying off early leaves a smaller rebate than the actuarial method would give. The penalty is largest when you pay off in the first third of the term.
How do I know if my loan uses the Rule of 78?+
Look in your contract for terms such as “precomputed”, “sum of the digits” or “Rule of 78” in the prepayment or rebate section. Simple-interest loans instead charge interest daily on the outstanding balance.
Should I pay off a Rule of 78 loan early?+
You still save the rebated interest, just less than on a simple-interest loan. Late in the term most of the interest has already been earned, so the savings from paying off early are small.
Results are estimates for educational purposes and are not financial advice. Rates, fees and terms vary — confirm with your lender or a licensed advisor before making decisions.