Precomputed interest and the Rule of 78s

What "precomputed" means

On a simple-interest loan, interest is charged each month on what you still owe. On a precomputed loan the lender works out the finance charge for the whole term at signing and adds it to the amount financed. The contract's payment and finance charge are the same level-payment figures a simple-interest loan at the contract rate would produce, which is why the disclosed APR matches the contract rate. The difference appears only when you pay early.

payment        = amount × r × (1+r)^n ÷ ((1+r)^n − 1)     r = contract rate ÷ 12
finance charge = n × payment − amount financed                fixed at signing
statement balance is often   = remaining payments × payment

Paying early earns a rebate

Because the finance charge was added up front, paying off early means the lender returns the part not yet earned. The payoff is the remaining scheduled payments minus that rebate. Two methods decide how much is "earned" so far.

Actuarial. The rebate brings the payoff down to the balance a simple-interest loan at the contract rate would still owe. That is the amortization schedule's balance after the payments made, and it is the fairer of the two.

Rule of 78s. Also called the sum of the digits. The finance charge is spread across the term in proportion to the digits counting down: for a 12-month loan, 12/78 of it belongs to month 1, 11/78 to month 2, down to 1/78 in the last month (1 + 2 + … + 12 = 78, which gives the rule its name). More of the charge counts as earned early, so the rebate is smaller and the payoff higher.

m = payments remaining
rebate (Rule of 78s) = finance charge × m(m+1) ÷ n(n+1)
rebate (actuarial)   = remaining payments − schedule balance after k payments
payoff               = remaining payments − rebate

Worked example

$15,000.00 financed at 18% for 60 months, 18 payments made.

payment              = $380.90
finance charge       = 60 × payment − $15,000.00 = $7,854.08
remaining payments   = 42 × payment = $15,997.86

Rule of 78s: sum of digits 1830, remaining digits 903
  rebate             = $7,854.08 × 903 ÷ 1830 = $3,875.54
  payoff             = $15,997.86 − $3,875.54 = $12,122.32

Actuarial
  schedule balance   = $11,805.68
  rebate             = $15,997.86 − $11,805.68 = $4,192.18

difference           = $316.64 more under the Rule of 78s

Your payoff is about $12,122.32 under the Rule of 78s. After 18 of 60 payments, $15,997.86 remains on the schedule. Paying off now earns a rebate of $3,875.54 under the Rule of 78s, or $4,192.18 under the actuarial method, a difference of $316.64.

Where the gap is widest

At signing both methods give the amount financed, and at the last payment both give zero. In between, the Rule of 78s payoff sits above the actuarial one, with the gap widest around a third of the way through the term. The higher the rate and the longer the term, the bigger the gap in dollars.

What the method does not cover

• Contracts that state a finance charge different from the level-payment figure. The formulas still apply to the stated charge; the tool's finance charge would differ.
• Acquisition charges, minimum earned charges, late fees and prepayment penalties. Some contracts add these on top of the payoff.
• The law that applies to you. Federal law prohibits the Rule of 78s for calculating the prepayment refund on covered precomputed consumer loans with terms exceeding 61 months made after 30 September 1993 (15 U.S.C. 1615), and some states restrict or prohibit it on shorter loans. The lender's payoff letter is the authoritative figure.

Reviewed 5 September 2026. No corrections since. Any change to this method is dated here and in the corrections log.