Rule of 78: worked example
| Amount financed | $20,000 |
|---|---|
| APR | 8.0% |
| Loan term (months) | 48 |
| Month you pay off the loan | 12 |
| Interest earned by the lender (Rule of 78) | $1,490 |
| Interest refunded | $1,946 |
| Monthly payment | $488 |
Rule of 78: changing APR
| APR | Interest earned by the lender (Rule of 78) | Interest refunded | Monthly payment |
|---|---|---|---|
| 4.0% | $727 | $949 | $452 |
| 6.0% | $1,104 | $1,442 | $470 |
| 8.0% (example) | $1,490 | $1,946 | $488 |
| 10.0% | $1,886 | $2,462 | $507 |
| 12.0% | $2,290 | $2,990 | $527 |
Rule of 78: compare input ranges
| Input | Tested from | To | Interest earned by the lender (Rule of 78): low input | Interest earned by the lender (Rule of 78): high input | Swing |
|---|---|---|---|---|---|
| APR | 6.0% | 10.0% | $1,104 | $1,886 | $782 (52%) |
| Amount financed | $18,000 | $22,000 | $1,341 | $1,639 | $298 (20%) |
| Month you pay off the loan | 11 | 13 | $1,382 | $1,595 | $213 (14%) |
| Loan term (months) | 43 | 53 | $1,460 | $1,516 | $56 (3.8%) |
Rule of 78: individual input comparisons
| Input | Value | Interest earned by the lender (Rule of 78) | Interest refunded | Monthly payment |
|---|---|---|---|---|
| Amount financed | $16,000 | $1,192 | $1,557 | $391 |
| $18,000 | $1,341 | $1,752 | $439 | |
| $20,000 | $1,490 | $1,946 | $488 | |
| $22,000 | $1,639 | $2,141 | $537 | |
| $24,000 | $1,788 | $2,335 | $586 | |
| APR | 4.0% | $727 | $949 | $452 |
| 6.0% | $1,104 | $1,442 | $470 | |
| 8.0% | $1,490 | $1,946 | $488 | |
| 10.0% | $1,886 | $2,462 | $507 | |
| 12.0% | $2,290 | $2,990 | $527 | |
| Loan term (months) | 38 | $1,424 | $1,282 | $598 |
| 43 | $1,460 | $1,609 | $537 | |
| 48 | $1,490 | $1,946 | $488 | |
| 53 | $1,516 | $2,291 | $449 | |
| 58 | $1,539 | $2,642 | $417 | |
| Month you pay off the loan | 10 | $1,271 | $2,165 | $488 |
| 11 | $1,382 | $2,054 | $488 | |
| 12 | $1,490 | $1,946 | $488 | |
| 13 | $1,595 | $1,841 | $488 | |
| 14 | $1,698 | $1,739 | $488 |
Rule of 78: combined input changes
| APR / Amount financed | $16,000 | $20,000 | $24,000 |
|---|---|---|---|
| 4.0% | $581 | $727 | $872 |
| 6.0% | $883 | $1,104 | $1,325 |
| 8.0% | $1,192 | $1,490 | $1,788 |
| 10.0% | $1,509 | $1,886 | $2,263 |
| 12.0% | $1,832 | $2,290 | $2,748 |
Rule of 78: which assumptions move the result?
Rule of 78: values and definitions
| Quantity and definition | Value used |
|---|---|
| Amount financed | $20,000 |
| APR | 8.0% |
| Loan term (months) | 48 |
| Month you pay off the loan — Payoff after this many monthly payments have been made. | 12 |
| Interest earned by the lender (Rule of 78) | $1,490 |
| Interest refunded | $1,946 |
| Monthly payment | $488 |
Rule of 78: half and double APR
| APR | Interest earned by the lender (Rule of 78) |
|---|---|
| 4.0% | $727 |
| 8.0% | $1,490 |
| 16.0% | $3,125 |
Rule of 78: formula
Common error: Assuming an early payoff saves the interest left on a normal amortization schedule. Under this rule the refund is smaller, because the early months keep the biggest share of interest.
Federal law bans the rule of 78 for consumer loans longer than 61 months, and many states restrict or prohibit it for others, so it now mainly appears on short loans and some subprime or older contracts. Most auto and personal loans use simple interest, where paying early saves the full interest not yet accrued. Fees and insurance refunds are separate.
Amount financed is the loan principal, APR is the rate, the loan term is in months, and the month you pay off the loan is when you plan to repay in full. The rule of 78 is a method of allocating interest on a precomputed loan that front-loads it, so early payoff saves less than a standard method would. The contract determines whether the loan uses Rule of 78 or simple-interest payoff treatment.
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The Rule of 78 is a way to split a precomputed loan's interest across the months so that early payments carry more of it. On $20,000 at 8 percent over 48 months, the total interest is $3,436.41. Paying off after month 12 leaves the lender with $1,490.28 under this rule and refunds $1,946.13, less than a level-interest schedule would.
The payoff method determines how unearned interest is refunded. The federal Rule of 78 restriction covers consumer loans with terms over 61 months; state restrictions can differ.
Compare with a standard payoff on the loan payoff and auto loan payoff calculators, and see the loan prepayment penalty page. The loan payment and amortization calculators show simple-interest schedules. If your loan uses this rule, weigh the smaller savings before paying it off early.
What is the rule of 78?
A way of dividing the total interest of a precomputed loan across the months so that early months carry more interest, using the sum-of-the-digits method.
Is the rule of 78 legal?
It is banned for consumer loans longer than 61 months and restricted or prohibited in many states, but it can still appear in some short-term contracts.
How do I know if my loan uses it?
The loan’s refund-of-unearned-interest provision determines the Rule of 78 payoff treatment. If it mentions the sum of digits, or the rule of 78, it applies.