Simple Interest

Simple interest is interest computed on the original principal for the whole period, without adding earned interest back to the balance. The formula is principal multiplied by the annual rate multiplied by the number of years, so a sum earning or costing simple interest grows in a straight line rather than accelerating. The contrast is with compound interest, where each period's interest joins the balance and earns in its turn.

The phrase carries a second, more consequential meaning that a reader is far more likely to meet on paper. In auto and personal lending, a simple-interest loan means a loan that is not precomputed. Interest accrues on the principal you still owe, day by day, and stops accruing when the principal is gone. On a precomputed loan the total interest for the whole scheduled term is calculated at the outset and written into the amount you promise to pay, so paying the loan off early does not make that interest disappear by itself; it has to be refunded to you.

Both senses are genuinely called simple interest, and neither is wrong. The first is a way of calculating an amount. The second is a way of structuring a contract, and it is named that way because interest is charged on the balance outstanding rather than compounded on unpaid interest.

Simple-interest accrual and amortization are not competing descriptions, and almost every consumer installment loan is both. Simple interest describes how interest accrues, which is against the balance you owe. Amortization describes how each level payment is split, which is interest first and the remainder against principal. A conventional car loan or personal loan accrues simple interest and amortizes, and asking which one it is misunderstands the question.

The reader-facing consequence of the distinction is the payment date. On a simple-interest loan, interest is accruing every day on the outstanding balance, so a payment that arrives on the first of the month stops fewer days of accrual than one that arrives on the fifteenth. More of the earlier payment therefore reaches principal, and the effect repeats for the life of the loan. On a precomputed loan the same early payment changes nothing about the interest charge, because that charge was fixed when the note was signed. This is why "does paying early save me money" has two correct answers depending on a word in the contract.

Prepaying in full is a federal right on either structure, and the amounts differ. 15 USC 1615(a)(1) provides that "if a consumer prepays in full the financed amount under any consumer credit transaction, the creditor shall promptly refund any unearned portion of the interest charge to the consumer," with a de minimis exception at (a)(2) where the refund would come to less than a dollar. Subsection (a)(3) is the under-known limb: the right applies "without regard to the manner or the reason for the prepayment," and it names two situations expressly, a prepayment made in connection with refinancing, consolidation or restructuring the transaction, and a prepayment resulting from the creditor accelerating the debt. So consolidating a precomputed loan into a new one triggers the refund on the old one, and so does the lender calling it in.

The Rule of 78s is restricted rather than abolished, and the boundary is the term. The Rule of 78s is a method of deciding how much of a precomputed interest charge has been "earned" at any point, and it front-loads: it treats the earliest payments as containing far more interest than a straight-line or actuarial calculation would, so a borrower who prepays halfway through gets back much less than half. Congress restricted it in 1992, and the restriction is narrower than its popular summary. 15 USC 1615(b) provides that for any refund required under subsection (a) "for any precomputed consumer credit transaction of a term exceeding 61 months which is consummated after September 30, 1993, the creditor shall compute the refund based on a method which is at least as favorable to the consumer as the actuarial method," and (d)(1) defines the actuarial method as applying each payment "first to the accumulated finance charge and any remainder" to the unpaid balance. Two limits follow directly. It reaches only precomputed transactions, so it says nothing about an ordinary simple-interest loan. And it reaches only terms exceeding 61 months, which leaves the 48-month and 60-month contracts common in auto lending outside it.

The precomputed payoff statement is a separate right and it is free once a year. 15 USC 1615(c) requires a creditor or assignee, within five days of an oral or written request, to give the consumer a statement of the amount needed to prepay a precomputed consumer credit account in full, together with the amount of any refund included in that figure, in writing if the request was in writing. One such statement per year is free, and a reasonable disclosed fee may be charged for further ones. The right is limited to precomputed accounts, which is a reason to know which kind of loan you have before asking for a payoff quote.

A note on the phrase you will meet in banking rather than lending. Federal deposit regulation uses "seven days' simple interest" as a term of art: it is the minimum early-withdrawal penalty that makes a deposit a time deposit at all, and it applies only to money taken out in the first six days. That is this same arithmetic, applied to a handful of days, rather than a separate concept, and the material on certificates of deposit covers what it does and does not limit.

For the arithmetic, multiply the principal by the annual rate by the time in years. $8,000 at 6% for three years produces $1,440 of simple interest ($8,000 × 0.06 × 3), for $9,440 repaid. The same sum compounded annually would produce more, because each year's interest would join the balance, and the material on compound interest works that comparison.

For the lending sense, the mechanics are daily. Divide the annual rate by the number of days in the year to get a daily rate, apply it to the balance outstanding, and add the result each day until a payment arrives. On a $20,000 balance at 9%, one day of interest is about $4.93 ($20,000 × 0.09 ÷ 365). Paying fourteen days earlier therefore stops about $69.04 of accrual on that balance, and the whole of that $69.04 goes to principal instead.

A hypothetical example of why the structure matters on prepayment. Two borrowers each take a 48-month loan carrying $3,600 of interest, and each pays it off after exactly 24 payments. One contract is precomputed and computes the refund on a straight-line basis; the other is precomputed and computes it by the Rule of 78s.

Straight-line treats half the term as half the interest, so $1,800 is unearned and refunded ($3,600 × 24 ÷ 48).

The Rule of 78s weights each payment by the number of payments then remaining. Over 48 payments those weights total 1,176 (48 × 49 ÷ 2). The first 24 payments carry the weights 48 down to 25, which sum to 876, so $2,681.63 counts as earned ($3,600 × 876 ÷ 1,176) and only $918.37 is refunded ($3,600 × 300 ÷ 1,176). The two figures add back to $3,600.

The gap is $881.63 on identical loans prepaid at the identical moment, and because the term is 48 months rather than more than 61, 15 USC 1615(b) does not require the more favorable calculation. A borrower on a simple-interest contract never reaches this question at all, because there was no precomputed interest charge to divide up; they owe the principal still outstanding plus the interest accrued to the day they pay.

Pros of a simple-interest loan structure, from the borrower's side

• Interest stops when the principal does, so paying the loan off early always reduces total interest.
• Every extra dollar of principal reduces the interest that accrues from that day forward, so overpaying works exactly as intuition suggests.
• Paying earlier within the month reduces the accrual on that balance, which is a saving available at no cost.
• The payoff figure is arithmetic on the balance rather than the output of a refund formula, so it is easier to check.

Cons and limits

• Interest accrues daily, so a late payment costs more than the late fee alone. More of the payment is consumed by accrued interest and less reduces principal.
• Paying only interest, or paying late repeatedly, can leave the balance barely moving even though every payment was made.
• On the arithmetic sense, simple interest understates the cost or the growth of anything held for a long period, because real accounts and real balances compound.
• A precomputed contract is the alternative structure and it is not always obvious from the paperwork. The refund method is what to look for.
• The Rule of 78s remains lawful on a precomputed transaction of 61 months or less, which covers many auto contracts.