The formula
- n
- Total number of scheduled periods
- m
- Periods remaining
- F
- Total precomputed finance charge
- R
- Unearned-interest rebate
Worked example: 12-month contract paid after 5 months
For 12 months, total weight is 12 × 13 ÷ 2 = 78. After 5 periods, 7 periods remain, so remaining weight is 7 × 8 ÷ 2 = 28.
If the original precomputed finance charge were $780, the unearned portion would be $280 under this simplified month-based example.
Why it is called the Rule of 78
The sum of the integers 1 through 12 is 78. A 12-month contract assigns weights 12, 11, 10, and so on down to 1. Longer contracts use the same sum-of-digits concept even though the denominator is no longer 78.
How to calculate the remaining weight
If m whole periods remain, the remaining weight is m(m + 1) ÷ 2. Divide that by the total weight and multiply by the precomputed finance charge to estimate the unearned portion.
Legal and contract limitations
The Rule of 78 is not permitted for every loan or jurisdiction, and contracts can specify additional payoff rules. Use the formula for mathematical analysis and verify the applicable contract and law for an actual payoff.
Check the math with a calculator
Enter your own numbers in the matching Power of Interest calculator. The calculator performs the arithmetic while this page explains the formula and assumptions behind it.