No compounding. Used in short-term loans, T-bills, and many auto loans. Always compare to the equivalent compound rate.
| Year | Simple interest | Compound interest | Gap |
|---|
Simple interest computes only on the original principal — the base never grows. Each period earns the same dollar amount, the total scales linearly with time. It's the math used by short-term consumer loans, T-bills, daily-simple-interest auto loans, and most short-tenor money-market instruments. The simplicity is the feature: no compounding to track, no exponents in the formula.
I — total interestP — principalr — annual rate (decimal)t — time in yearsA — accumulated amount at maturity| Instrument | Method | Day-count |
|---|---|---|
| US Treasury bills | Simple, bank discount yield | Actual/360 |
| Most US auto loans | Daily simple interest (DSI) | Actual/365 |
| Short-term personal loans | Simple amortization | Actual/365 |
| Commercial paper, money market | Simple discount | Actual/360 |
| Corporate bonds (accrual within coupon) | Simple accrual | 30/360 |
| Payday loans | Flat fee, equivalent simple APR | Actual/365 |
| Mortgages | "Simple-interest amortizing" | Actual/365 (close to monthly compounding in practice) |
A 90-day product yielding 1.25% simple sounds modest until you annualize: 1.25% × (365 ÷ 90) = 5.07% APR. Conversely, a payday loan's "$15 fee on $100 for 14 days" is 391% APR (15 ÷ 100 ÷ 0.0384). Reg Z (12 CFR 1026.18) requires APR disclosure precisely to make these comparisons honest.
Most US auto loans use Daily Simple Interest. Sending the payment 5-7 days before the due date can save $2-5/month on a typical $25,000 loan because interest accrues against a smaller balance for fewer days. Mortgages don't have this property — payment date within the month doesn't change the cycle's interest charge.
Rule of 78s allocates total scheduled interest to each month using sum-of-digits weighting (1+2+...+12 = 78), front-loading more aggressively than standard simple-interest amortization. Federal law banned it on consumer loans >61 months in 1992 (15 USC 1615), but it still appears on subprime auto and short-term consumer loans. Always check the loan disclosure for "precomputed" language.
Sources: TreasuryDirect bank discount yield methodology; Federal Reserve H.15 daily yield publication; Reg Z (12 CFR 1026.18) APR disclosure for consumer credit; 15 USC 1615 prohibition of Rule of 78s >61 months; ISDA 2006 Definitions for day-count conventions in derivatives and bond markets.
Interest computed only on original principal: I = P × r × t. Each period earns the same dollar amount because the base never grows. Total amount at maturity = P × (1 + rt). Opposite of compound interest, where interest is added to principal each period and starts earning interest itself.
Most US auto loans (DSI), short-term personal loans, US Treasury bills (bank discount yield), corporate bonds during accrual within a coupon, payday and pawn-shop lending. Mortgages are "simple-interest amortizing" but math is closer to monthly compounding. Long-term savings, CDs, money markets, investments use compound.
Small at short horizons, enormous at long. $10k at 5%: 1 yr — simple $500, compound $511 (2% gap); 5 yr — $2,500 vs $2,834 (13%); 30 yr — $15,000 vs $34,885 (132%). Compound earns interest-on-interest while simple earns flat each period. This is why long-term wealth uses compound but short-term loans use simple.
DSI computes interest each day: daily interest = balance × (APR ÷ 365). Most US auto loans use DSI, so paying early in the billing cycle reduces accrual days. On $25,000 / 5-yr / 7%, paying 5 days before due date saves ~$2-5/month. Mortgages use monthly accrual — day-of-month payment doesn't affect cycle interest.
Neither, exactly. T-bills issued at discount, pay face at maturity — difference is the return. Quoted as bank discount yield (BDY) using simplified simple-interest: BDY = (face − price) ÷ face × (360 ÷ days). Treasury also publishes bond equivalent yield (BEY) for cross-instrument comparison. Both are simple-interest concepts because T-bills mature in under a year.
The rule a security uses to count days. Common: Actual/365 (Treasuries, most consumer products); Actual/360 (commercial loans, money market — slightly inflates daily rates); 30/360 (US corporate bonds — assumes 30-day months). Matters most in money-market math where small per-day differences scale to millions for institutional volumes.
Sum-of-digits precomputed-interest method (1+2+...+12 = 78 for 12-mo loan). Front-loads more aggressively than standard simple-interest amortization, penalizing early payoff. Federal law banned on consumer loans >61 months in 1992 (15 USC 1615). Some short-term subprime auto and personal loans still use it. Technically a precomputed variant, neither pure simple nor pure compound.
For 1-year, simple = APY when interest paid at year-end (no compounding effect). Sub-year: multiply simple by (365 ÷ days) to annualize, then convert: APY = (1 + simple ÷ n)n − 1. Example: 90-day at 1.25% simple annualizes to 5.07% (1.25 × 365/90); APY ≈ 5.16% if compounded quarterly.
Lenders quote a flat fee, not APR. $15 fee on $100 for 14 days: I=$15, P=$100, t=14/365=0.0384, r=15/100/0.0384 = 391% APR. Reg Z (12 CFR 1026.18) requires APR disclosure — that's how the 391-400% range became visible. Several states cap APRs at 36%, effectively ending payday lending; others permit without caps.
"Simple-interest monthly amortization" — each month, interest = balance × monthly rate, added to upcoming payment. Computationally similar to monthly compounding, but the formula doesn't add interest to principal — it allocates payment between interest charge and principal reduction. Net effect over 30 years is very close to monthly compounding, which is why amortization tables look exponential late in the schedule.