What it means
Borrowers assume a year's loan paid off at six months should cost half the interest. Under the Rule of 78, the lender has already collected most of it, and the payoff quote proves it.
The name is arithmetic: for a 12-month loan, the months' digits 1 through 12 sum to 78, and month one earns 12/78 of the interest, month two 11/78, and so on down. The method front-loads interest relative to simple amortisation, so a borrower prepaying mid-term has already paid more interest than the elapsed time would suggest.
Congress addressed the practice in the Truth in Lending framework: 15 USC 1615 prohibits refund calculations less favourable than the actuarial method for precomputed consumer loans, with the Rule of 78 restricted to shorter terms. The federal line sits at 61 months: precomputed loans longer than that must rebate interest by the actuarial method, which allocates by time, not by the declining digits.
The method survives where permitted: some short-term auto and personal loans, and certain state-regulated contexts, still compute rebates by the digits. The borrower's defence is a question: ask whether the loan is precomputed, and if so, how an early payoff rebate is calculated, before signing rather than after.
For a non-finance reader, the Rule of 78 is the fine print that makes early repayment disappointing: the interest was not accruing evenly, it was being taken at the front. The method's defenders make a risk argument: lenders face the highest default risk early in a loan's life, and front-loaded interest, they say, matches income to the period of greatest exposure.
The borrower's counter is arithmetic: whatever the risk theory, the practical effect is a hidden prepayment penalty, and transparency rules exist precisely because the effect is hidden.
In practice
Real-world examples.
Example
A borrower paying off a 36-month precomputed loan at month 18 has already been charged about 74% of the total interest, even though only half the term has elapsed.
Example
A 12-month loan allocates 12/78 of its interest to month one, declining each month thereafter. The digits decided the order, not the calendar.
Example
A borrower switches to a simple-interest loan after learning how the Rule of 78 rebate was computed, and asks the rebate question before signing anything precomputed.
Formula
Calculation
Each month's interest share = remaining months / digit sum. For a 12-month loan the digit sum is 78, so month one takes 12/78 of the total precomputed interest and month two takes 11/78. For an n-month loan the digit sum is n x (n + 1) / 2, and the rebate on early payoff equals the unearned fraction by the same declining digits.
Worked example: a 36-month loan has a digit sum of 36 x 37 / 2 = 666. With total precomputed interest of $2,700, month one carries 36/666 x $2,700 = $145.95 and month 18 carries 19/666 x $2,700 = $77.03. After 18 months, the interest earned by the lender is (36 + 35 + ... + 19) / 666 = 495/666 of the total, or about 74.3%.
That is 495/666 x $2,700 = $2,006.76 of interest after only half the term, against $1,350 if interest were spread evenly. The early-payoff rebate is therefore only $2,700 - $2,006.76 = $693.24, roughly $657 less than an even spread would suggest.Case study
Seen in the real world.
This case study is fictional and illustrative. A made-up car buyer finances $15,000 over three years through a dealer-arranged precomputed loan and receives a bonus at month eighteen, deciding to pay the loan off. The payoff quote stuns her: despite being halfway through the term, she owes far more than half the original interest. The lender's breakdown shows the machine: under the Rule of 78, month one of a 36-month loan carried 36/666 of the total interest and month eighteen still carries 19/666, so the first half of the schedule consumed well over half the interest.
Her state permits the method on loans of this term, the contract she signed disclosed it in the box she skimmed, and the payoff stands, costing her several hundred dollars more than actuarial allocation would have. The experience rewrites her borrowing habits: her next loan is simple-interest, she asks the rebate question before signing anything precomputed, and she gives her brother the lecture when he finances his truck, complete with the digit-sum maths on a napkin. The napkin ends with the sentence she wishes the dealer had said plainly: on this kind of loan, finishing early saves you least when you need the saving most.
Watch out
Common mistakes.
- Assuming interest accrues evenly; the Rule of 78 front-loads it, so time elapsed overstates the interest already earned in the borrower's intuition.
- Believing it is banned outright; federal law restricts it for precomputed loans over 61 months, but shorter terms and state rules still allow it.
- Skipping the rebate question; whether a loan is precomputed and how payoff rebates are calculated is a signing-day question, not a payoff-day discovery.
Questions
People also ask.
What is the Rule of 78?
A precomputed-loan interest method allocating interest by declining month digits, front-loading charges and reducing the savings from early payoff.
Why is it called 78?
The digits 1 through 12 sum to 78, and a 12-month loan allocates interest in twelfths of 78: 12/78 in month one, 11/78 in month two, and so on.
Is it still legal?
Yes, with limits: US federal law bars it for precomputed consumer loans over 61 months, requiring actuarial rebates, but shorter loans may still use it where states permit.
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