Calculate a Rule of 78 loan payoff: enter the amount financed, finance charge, term and payments made to get the payoff and finance-charge rebate.
Rule of 78 Formula
The sum of the monthly digits for an N-month contract is:
S = N(N + 1) / 2
If m payments remain, the unearned finance-charge rebate is:
U = F * [m(m + 1)] / [N(N + 1)] Payoff = m * Payment - U
Variables:
- N is the original number of monthly payments
- m is the number of payments remaining
- F is the original precomputed finance charge
- U is the unearned finance charge
The method assigns larger finance-charge weights to early months and smaller weights to later months. This model uses equal, unrounded monthly installments and estimates the payoff immediately after complete, on-time payments. Enter whole payment counts and USD amounts with at most two decimals. Each displayed amount rounds independently to cents. Target-rebate mode solves the continuous quadratic, then rounds its payment count to the nearest whole payment; an exact half-payment tie chooses the later payment. It does not minimize the dollar difference from the target.
Rule of 78 Payoff Reference
The method front-loads the earning of a precomputed finance charge. That makes timing especially important for an early payoff.
| Payment timing | Remaining-month weights | Unearned-charge pattern | Borrower effect |
|---|---|---|---|
| Very early | Large | Large rebate, but much finance charge is already front-loaded | Payoff can exceed a simple-interest balance |
| Middle of term | Moderate | Rebate declines rapidly | Difference narrows |
| Near maturity | Small | Little unearned charge remains | Payoff approaches scheduled balance |
| At maturity | Zero | No rebate remains | Scheduled contract is complete |
Example Problems
Example 1: Estimate a payoff after 12 payments.
A 36-month contract finances $12,000 and includes a $2,400 precomputed finance charge. The installment is ($12,000 + $2,400) ÷ 36 = $400. After 12 payments, 24 remain. The unearned charge is $2,400 × [24 × 25] ÷ [36 × 37]. Subtract that rebate from the remaining scheduled payments to estimate the payoff.
Example 2: Find the month associated with a rebate.
Enter the same contract and a target rebate from $0 through the original finance charge. The calculator solves m(m + 1) from the rebate ratio, converts remaining months into payments made, and rounds that count to the nearest whole payment, with exact half-payment ties choosing the later payment. If the finance charge and target rebate are both zero, every payment count qualifies; the target cannot identify one payoff month.
Frequently Asked Questions
Is the Rule of 78 the same as simple interest?
No. Simple interest is based on the outstanding principal over time. The Rule of 78 allocates a precomputed finance charge using declining monthly weights, which earns more of the charge early.
Can every lender use this method?
Rules depend on the loan and jurisdiction. For covered U.S. precomputed consumer-credit transactions with terms exceeding 61 months that were consummated after September 30, 1993, 15 U.S.C. 1615(b) requires a refund method at least as favorable to the consumer as the actuarial method. A shorter term does not establish that the Rule of 78 is permitted. Confirm the contract and applicable law; this calculator does not determine legal eligibility.
Why can the official payoff differ?
The lender may use exact dates, additional fees, late charges, insurance refunds, or a legally required rebate method. Request a dated payoff statement before sending funds.
