A precomputed car loan: $15,000 at 18% for 60 months.

You ask for a payoff quote and the number is not the balance you expected. Either the statement balance looks like the total of all your remaining payments, or the payoff comes in higher than the principal you thought you owed. Both are signs of a precomputed loan, also called precomputed interest or add-on interest. It is common on car loans from dealers and finance companies, on furniture and appliance financing, and on small personal loans from consumer finance companies. Banks and credit unions mostly use simple interest instead.

Two ways to charge interest

Simple interest. Interest is worked out each month on what you still owe. Pay early and there is less balance to charge on, so you pay less interest. The payoff is the principal owed plus a few days of interest.

Precomputed interest. The lender works out the finance charge for the full term on day one and adds it to the amount financed. The payment and the total interest are the same as a simple-interest loan at the same rate would charge over the full term, so nothing looks different while you pay on schedule. The difference appears when you pay off early: you are owed a rebate of the interest not yet earned, and the method your contract uses to work out that rebate decides your payoff.

The two rebate methods

Actuarial. The rebate brings your payoff down to what a simple-interest loan would owe at that point. Fair, and the same figure the other tools on this site would show.

Rule of 78s. Also called the sum of the digits. The finance charge is split across the months in proportion to the digits counting down: on a 12-month loan, 12/78 of it counts as earned in month one and 1/78 in the last month, because 1 + 2 + … + 12 = 78. More of the interest is treated as earned early, so the rebate is smaller and the payoff higher than under simple interest. Federal law prohibits it for calculating the prepayment refund on covered precomputed consumer loans with terms exceeding 61 months made after 30 September 1993, and some states restrict it on shorter loans, but it is still written into many contracts under five years.

A worked example

A used-car loan: $15,000.00 financed at 18% for 60 months. The payment is $380.90 and the finance charge for the full term is $7,854.08. After 18 payments, 42 remain.

After 18 of 60 payments	Rule of 78s	Actuarial (simple interest)
Remaining scheduled payments	$15,997.86	$15,997.86
Rebate of unearned interest	$3,875.54	$4,192.18
Payoff today	$12,122.32	$11,805.68

The statement may show $15,997.86 as the balance, which is simply the 42 payments left. The payoff is that figure minus the rebate. Under the Rule of 78s the lender keeps $316.64 more of the finance charge than a simple-interest loan would have charged by now. The gap is widest about a third of the way through the term and closes to zero at the end.

How to tell which kind you have

• The contract’s prepayment section says “precomputed”, “add-on”, “Rule of 78”, “sum of the digits” or “actuarial”.
• The statement balance equals the number of payments left multiplied by the payment.
• An extra payment does not lower next month’s interest; it prepays the next instalment.
• The payoff quote is below the statement balance by a “rebate” or “unearned finance charge” line.

Questions to ask your lender

1. Is this a simple-interest or a precomputed loan?
2. If precomputed, is the rebate of unearned interest calculated by the Rule of 78s or the actuarial method?
3. What is my payoff amount today, through what date is it good, and what does it include?
4. Does the balance on my statement show the remaining payments or the principal owed?
5. If I pay extra without paying off, does it shorten the loan and earn a rebate?

See it with your own numbers

Enter the amount financed, the contract rate, the term and the payments you have made in What is my payoff on a precomputed loan?. It shows the payoff under both rebate methods, the rebate, how much interest the lender keeps, and a month-by-month chart of the gap. If you are weighing a refinance, carry that payoff into Does refinancing help? as the balance today.

Related: Precomputed interest and the Rule of 78s shows the formulas. Glossary: precomputed interest, Rule of 78s, payoff amount.

Educational tool, not advice. Your lender’s payoff quote is the authoritative figure.