Rule of 78 Calculator (Early Loan Payoff Interest Refund)
How much of a precomputed loan's interest is refunded when you settle early under the Rule of 78, and how much more the lender keeps than with an even spread.
Results
The dashed line marks the value you entered.
What this tool does
The Rule of 78 spreads a loan's total interest over its instalments in proportion to the digits n, n−1, … 1 (for 12 months they add up to 78, hence the name), so the first payments carry the most interest. It front-loads the interest more than the real balance would, which means a borrower who settles early gets back less than with an even split. Some places restrict or forbid it, and the amounts are decided by your contract, so use this to understand and compare quotes, not as the figure you will be charged.
Formula
S = n(n+1) ÷ 2 · interest in instalment j = interest × (n − j + 1) ÷ S · refund = interest × (n − k)(n − k + 1) ÷ [n(n+1)]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ti | Total interest charged on the loan | — |
n | Number of monthly instalments | — |
k | Instalments already paid | — |
RB | Interest refunded on early payoff (Rule of 78) | — |
IP | Interest you have paid so far (Rule of 78) | — |
IK | Interest inside the last instalment paid | — |
RE | Refund if the interest were spread evenly | — |
XC | Extra interest kept by the lender versus an even spread | — |
Worked example
- Total interest charged on the loan1200
- Number of monthly instalments36
- Instalments already paid12
- Interest refunded on early payoff (Rule of 78)540.54
- Interest you have paid so far (Rule of 78)659.46
- Interest inside the last instalment paid45.05
- Refund if the interest were spread evenly800.00
- Extra interest kept by the lender versus an even spread259.46
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.