Short answer: on a simple interest loan, interest is charged on the balance you still owe, so paying early saves the interest you have not yet been charged. On a precomputed loan, the interest for the whole term is added to the loan up front, and if you pay early you get back only a rebate of the unearned part. The Rule of 78s is one way to compute that rebate, and it gives back less than the actuarial method. Federal law requires a refund of unearned interest when you prepay in full, and bans the Rule of 78s on precomputed loans longer than 61 months (15 U.S.C. 1615).
Simple interest vs precomputed interest
| Simple interest | Precomputed interest | |
|---|---|---|
| How interest is charged | Each period, on the unpaid balance | For the whole term, added to the loan when you sign |
| What you owe at any time | The unpaid balance plus interest since the last payment | The remaining scheduled payments, less any rebate if you pay off |
| If you pay off early | You pay the balance; later interest is never charged | You get a rebate of unearned interest; the method sets how much |
| What the disclosure says | Whether a penalty may be charged for paying early | Whether you get a rebate if you pay early |
The last row comes from Regulation Z, which has the lender state on the Truth in Lending disclosure whether a prepayment penalty may be charged or a rebate given. That rule and the other early payoff questions are in our prepayment penalty guide; to find the box on your own papers see how to read a loan disclosure.
How the Rule of 78s works
On a 12-month loan, number the months 12, 11, 10 and so on down to 1. They add up to 78, which gives the rule its name. The lender treats month 1 as earning 12/78 of the total interest, month 2 as earning 11/78, and so on. If you pay off early, the rebate is the share of the interest for the months left: add up their numbers and divide by 78. For other terms the total changes: n x (n + 1) / 2, so 1,176 for 48 months. Because the early months carry the biggest numbers, the lender keeps more of the interest early in the loan than it would under the actuarial method.
The actuarial method is the one an amortizing loan uses: each payment pays the interest due on the balance first and the rest reduces the balance (15 U.S.C. 1615(d)(1)). Paying off under it costs the same as paying off a simple interest loan with the same rate and payments made on time.
Worked example: a 12-month loan paid off after 6 payments
Assumptions: $3,000 at 30% APR for 12 months, a payment of $292.46. These are examples, not quotes. Total of payments: 12 x $292.46 = $3,509.52, so the precomputed interest is $509.52. You pay off after 6 payments, with 6 payments, $1,754.76, still scheduled.
| Step | Rule of 78s | Actuarial method |
|---|---|---|
| Share of the interest rebated | 6 + 5 + 4 + 3 + 2 + 1 = 21, so 21/78 | The interest in the remaining payments |
| Rebate | 21/78 x $509.52 = $137.18 | $143.84 |
| Payoff amount | $1,754.76 - $137.18 = $1,617.58 | $1,754.76 - $143.84 = $1,610.92 |
On this short loan the Rule of 78s costs $6.66 more to pay off. The gap grows with the term.
The same comparison on a 48-month loan
Assumptions: $5,000 at 30% APR for 48 months, a payment of $180.03, precomputed interest $3,641.44. Again, examples, not quotes.
| Paid off | Scheduled payments left | Rule of 78s share | Rule of 78s rebate | Actuarial rebate | Extra cost under the Rule of 78s |
|---|---|---|---|---|---|
| After 6 payments | $7,561.26 | 903/1176 | $2,796.11 | $2,912.78 | $116.67 |
| After 12 payments | $6,481.08 | 666/1176 | $2,062.24 | $2,240.25 | $178.01 |
| After 24 payments | $4,320.72 | 300/1176 | $928.94 | $1,100.89 | $171.95 |
Monthly payment: P x r / (1 - (1 + r)-n), with r = APR / 12, rounded to the cent. Actuarial payoff = the balance after the payments made, with payments on time. A 48-month loan is under the 61-month line, so the federal ban does not reach it; check the contract and your state's law for how a rebate is figured.
What federal law requires
- If you prepay a consumer credit transaction in full, the lender must promptly refund any unearned portion of the interest charge; no refund is required if it would be less than $1 (15 U.S.C. 1615(a)).
- This applies however the loan is paid off, including a refinancing or consolidation, and when the lender accelerates the loan (15 U.S.C. 1615(a)(3)).
- For a precomputed loan with a term over 61 months, made after September 30, 1993, the refund must be figured by a method at least as favorable to you as the actuarial method (15 U.S.C. 1615(b)).
- On a precomputed account you can ask for the amount needed to pay it off and the rebate included; the lender must answer within 5 days, in writing if you asked in writing, with one statement a year free (15 U.S.C. 1615(c)).
Before you sign
- Ask whether interest is simple interest on the unpaid balance or precomputed.
- If precomputed, ask how the rebate is figured if you pay early: the Rule of 78s, the actuarial method, or something else.
- If you plan to refinance, consolidate or pay off early, ask for a payoff figure in writing first and compare it with the balance.
- Compare offers by APR and total of payments, as shown on the disclosure.
Thinking of replacing a loan? See refinancing a personal loan.
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Disclosure: Modern Lending Solutions is not a lender, loan broker or agent for any lender or loan broker, and does not make credit decisions. Any compensation we receive is paid by participating lenders, only for advertising services. This guide is general information, not financial or legal advice.