Rule of 78S Calculator
Paying a loan off early should save you interest, but not under the Rule of 78s. This old lender method, also called the sum-of-the-digits method, front-loads the interest: you pay a big share of the total interest in the first months and almost none at the end. This calculator shows both sides of that deal: the interest charged in any single month, and the early-payoff picture of interest paid, interest remaining and the payoff amount. It models the lender’s precomputed-interest method, not simple interest: do not mix it up with the simple-interest payoff tools on this site.
The payoff figure is the remaining principal: remaining installments less the unearned (remaining) interest, assuming equal monthly installments of (principal + total interest) ÷ term. It credits the principal you have already repaid, so it matches a lender-style payoff; always confirm against the lender’s actual payoff statement before settling.
Quick Answer
Borrow $10,000 for 12 months with $1,200 of precomputed interest and settle after month 6: the sum of digits is 78, month 3 carries $153.85 (12.8%), you have paid $876.92 with $323.08 remaining, and the payoff is $5,276.92. Halfway through, 73.1% of the interest is already gone: read the payoff section for the full accounting.
Key takeaways
- Month 1 of a 12-month loan takes 15.4% of the total interest; month 12 takes 1.3%. The weights run 12 down to 1.
- Settling halfway through a 12-month loan saves only about 27% of the finance charge, not half. That is the whole point of the method: it protects the lender's interest when you leave early.
- The calculator's payoff equals the remaining principal: remaining installments of $5,600.00 less the $323.08 of unearned interest. The old figure (original principal plus remaining interest, $10,323.08) double-counted principal already repaid and is no longer used.
- Federal law bars the Rule of 78s rebate on precomputed loans longer than 61 months. It survives mainly in short-term consumer and auto loans.
- Quick Answer
- How to use the Rule of 78s calculator
- The Rule of 78s formula
- Worked example: $10,000, 12 months, settle after month 6
- The front-loading curve, month by month
- Reading the payoff figure honestly
- Rule of 78s vs the alternatives
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the Rule of 78s calculator
Enter your loan details once, then read two panels: the interest in any single month, and the early-payoff breakdown. Results stay hidden until you click Calculate, and Reset restores the worked example.
- Enter the loan principal, the amount you borrowed, and the loan term in months (12, 24, 36 and similar).
- Enter the total interest over the full loan life, in dollars, from your loan agreement: the precomputed finance charge, not an APR.
- Enter the month to inspect to see that single month's interest allocation. It must not exceed the term.
- Enter months already paid for the payoff picture: interest paid, interest remaining, payoff amount. It must not exceed the term either.
- Click Calculate and read the color-coded analysis line: red means you are still in the heavy-interest part of the loan.
This tool only makes sense for precomputed-interest loans. If your loan charges simple interest on the declining balance, the amortization schedule calculator is the right page: extra payments there genuinely reduce the interest, which is the opposite of how precomputed loans behave.
The Rule of 78s formula
Each month gets a weight counting down from n to 1, and the weights sum to n × (n + 1) ÷ 2. For a 12-month loan that sum is 78, which is where the name comes from.
Interest in month k = Total interest × (n − k + 1) ÷ Sum of digits
Interest paid after m months = Total interest × [m × (2n − m + 1) ÷ 2] ÷ Sum of digits
Payoff amount = Remaining installments − Unearned (remaining) interest = Remaining principal
The third line is just the first m weights added up: for months 1 to 6 of a 12-month loan, 12 + 11 + 10 + 9 + 8 + 7 = 57, and 57 ÷ 78 of the interest is earned by month 6. The fourth line is the lender payoff: it credits the principal already repaid through your installments and rebates the unearned interest. Some same-keyword tools still show principal plus remaining interest instead; the payoff section below shows why that figure double-counts.
Worked example: $10,000, 12 months, settle after month 6
The calculator is pre-filled with this example. Every figure below is a real run of the tool.
Month 3 is flagged "Early period" in red because month 3 of 12 sits in the first quarter of the term. The $876.92 interest-paid line is 73.1% of the $1,200 total: that single percentage is the front-loading penalty in plain numbers.
| Loan | Month inspected | Interest paid | Payoff figure |
|---|---|---|---|
| $5,000, 36 mo, $1,462.36 interest, paid 18 | Month 1: $79.05 (5.4%) | $1,086.89 | $2,855.71 |
| $8,000, 12 mo, $960 interest, paid 3 | Month 1: $147.69 (15.4%) | $406.15 | $6,166.15 |
| $25,000, 24 mo, $3,000 interest, paid 24 | Month 24: $10.00 (0.3%) | $3,000.00 | $0.00 |
| $999.99, 7 mo, $111.11 interest, paid 7 | Month 5: $11.90 (10.7%) | $111.11 | $0.00 |
The front-loading curve, month by month
On a 12-month loan the weights run 12 down to 1, so the interest share collapses as the loan ages. Month 1 takes 15.4% of the total interest; month 12 takes 1.3%.
The colors match the calculator's own analysis bands: red for the early quarter, orange for early-middle, amber for late-middle, green for the final quarter. The first month interest calculator isolates that heaviest first month for any loan, and the front-loaded interest calculator models the same early-heavy pattern in a general form.
Reading the payoff figure honestly
The calculator now defines payoff as the lender does: remaining principal after crediting what you have already repaid. Some same-keyword tools still show the old figure, original principal plus remaining interest ($10,000 + $323.08 = $10,323.08 here); that figure double-counts principal already repaid, and the gap matters.
A lender's payoff credits the principal you have already repaid through your installments and rebates the unearned interest. Walk the worked example through that accounting, assuming equal monthly installments of $933.33 ($11,200 ÷ 12):
- Paid so far: 6 × $933.33 = $5,600.00
- Interest earned by the lender: $876.92 (the calculator's own figure)
- Principal already repaid: $5,600.00 − $876.92 = $4,723.08
- Remaining principal: $10,000.00 − $4,723.08 = $5,276.92
- Lender-style payoff: $5,276.92 of remaining principal, with the $323.08 of unearned interest rebated
The old figure showed $10,323.08 because it added the untouched original principal to the remaining interest instead of subtracting the $4,723.08 of principal already repaid. The interest lines (paid, remaining, per-month) were always correct; the payoff line now agrees with them, and it still pays to confirm against the lender’s statement. Always get the lender's actual payoff statement before refinancing or settling: federal law entitles you to one free statement a year, and it must show your interest refund.
Rule of 78s vs the alternatives
Three methods allocate precomputed interest, and the borrower's refund shrinks as you move down the list.
| Method | How the refund is computed | Borrower outcome |
|---|---|---|
| Actuarial (simple interest) | Interest accrues on the declining balance; the refund is the interest that would have accrued over the remaining months | Largest refund; federally required for precomputed loans over 61 months |
| Rule of 78s | Unearned interest = remaining digit-weights ÷ sum of digits | Smaller refund than actuarial; on a $5,000/36-month/17.5% loan settled after 6 months, roughly $28 less than the simple-interest refund |
| No rebate | Full precomputed interest is owed regardless | Worst case; the Truth in Lending disclosure must state whether a rebate applies |
The 61-month federal line comes from Public Law 102-550 (1992): beyond it, the refund method must be at least as favorable to the consumer as the actuarial method. State rules add their own restrictions, which is why the Rule of 78s survives mainly on short auto and personal loans. If you are planning the exit itself, the early debt payoff calculator models payoff strategy on the simple-interest side.
What competing calculators miss
Rule of 78s tools divide into camps, and none of them tells the whole story:
- Same-keyword tools (BraveCalculator): the closest match on the per-month math, but it still defines payoff as original principal plus remaining interest ($10,323.08 on this page's example), which double-counts principal already repaid; this page now credits it ($5,276.92). Gap: no per-month interest figure, so the front-loading curve itself stays invisible.
- Single-month tools (WayCalculator and similar): show one period's interest but no payoff panel, so the early-settlement question goes unanswered.
- Rebate-angle tools (SavvyCalculator and similar): cover the unearned-interest rebate but bury the per-period math.
- Explainers without tools (TimeBusinessNews and similar): explain the concept well, with nothing to type your own loan into.
- The gap this page fills: both panels in one place, the arithmetic step by step, the front-loading curve drawn, and the disclosure no competitor makes: what the payoff figure does and does not include, in dollars.
Frequently asked questions
The digits 1 through 12 add up to 78, the sum of digits for a 12-month loan. They become the interest weights: month 1 gets weight 12, month 12 gets weight 1.
Yes in many places, but restricted for longer loans: federal law requires precomputed consumer loans over 61 months to use a refund method at least as favorable as the actuarial method, and several states restrict it further. Check your loan agreement and local law.
No. Mortgages use amortized simple interest. The Rule of 78s shows up mainly in short-term consumer loans: auto loans, personal loans, and some equipment financing.
Your loan agreement must state the interest method: look for "sum of the digits", "precomputed interest", or "Rule of 78s" in the Truth in Lending disclosure, which must also say whether a prepayment rebate applies and by what method.
Barely. The interest for each period is precomputed, so extra payments do not earn the interest savings a simple-interest loan would give you. Interest comes back only as a rebate of the unearned portion when you pay the loan off in full.
It is the remaining principal: remaining installments less the unearned (remaining) interest, assuming equal monthly installments of (principal + total interest) ÷ term. On the $10,000 example settled after 6 months, that is $5,600.00 of remaining installments less $323.08 of unearned interest = $5,276.92. Always get the lender's payoff statement before settling.
The actuarial method accrues interest on the declining balance, so its prepayment refund equals the interest that would actually have accrued over the remaining months. The Rule of 78s refund uses the digit weights instead and is always less favorable to the borrower: on a sample $5,000, 36-month loan at 17.5% settled after 6 months, roughly $28 less.
Often yes, with a comparable-rate simple-interest loan. Compare the lender's actual payoff statement, not this calculator's payoff figure, against the new loan's cost, and check your agreement for a prepayment penalty.
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References
- U.S. Statutes at Large, Vol. 106 (Public Law 102-550, 1992). Housing and Community Development Act: Rule of 78s refund restriction for precomputed loans over 61 months (refund must be at least as favorable as the actuarial method). Accessed October 23, 2026.
- Federal Deposit Insurance Corporation (archived consumer publication). Repaying a Loan Early May Be More Costly Than You Think (precomputed interest, unearned finance charge, and why the early-payoff balance surprises borrowers). Accessed October 23, 2026.
- St. Louis Fed FRASER archive. Federal Reserve Bank of New York Circulars: Regulation Z - Truth in Lending (rebate of precomputed interest computed under the Rule of 78s; prepayment disclosure requirements). Accessed October 23, 2026.
- New Mexico Regulation and Licensing Department, Financial Institutions Division. Rule of 78s Guidelines (regulator-published refund tables comparing Rule of 78s vs simple-interest refunds month by month). Accessed October 23, 2026.
- Dentons Consumer Finance Report. Back to Basics, Continued: Revisiting Prepayment and Refinancing (precomputed vs simple-interest finance charges; Rule of 78s as the precomputed refund methodology). Accessed October 23, 2026.
- Collect! (industry how-to). How to Use the Rule of 78 Interest (early payout amount = original principal + total interest - interest saved - principal paid - interest paid; remaining-weight rebate formula). Accessed October 23, 2026.
- SGCarMart. Calculate Your Car Loan Interest for Early Settlement Using Rule of 78 (worked early-redemption example: loan amount + total interest - installments paid - unpaid-interest rebate). Accessed October 23, 2026.
- Goldpoint Systems. Amortization Deep Dive: The Rule of 78s (origins in 1935 Indiana legislation; month-by-month weight allocation on a sample loan). Accessed October 23, 2026.
- LegalClarity. What Is the Rule of 78 and How Does It Affect Loans? (Rule of 78s vs actuarial refund comparison; Regulation Z 1026.18 prepayment disclosure). Accessed October 23, 2026.
- MoneyCrashers. Extra Car Loan Payments Save Little Unless the Loan Charges Simple Interest (precomputed loans: extra payments barely dent interest; federal free annual payoff statement). Accessed October 23, 2026.
- Knowledge Mentors (auto finance). How Precomputed Interest Loans Make Early Auto Refinancing Less Beneficial for Borrowers (unearned-interest refund mechanics and why refinancing precomputed loans disappoints). Accessed October 23, 2026.