Interest that does not snowball
With simple interest, interest is only ever calculated on the original amount. It never earns interest of its own. That makes it easy to compute and predictable, and it is still used for short-term loans, many auto loans, Treasury bills, bonds’ coupon payments, late payment charges and loans between family members.
The formula
I = P × r × t
- P: the principal, the amount borrowed or invested
- r: the annual interest rate as a decimal
- t: the time in years
The total repaid or received is A = P × (1 + r × t). For periods in months, t = months ÷ 12. For periods in days, t = days ÷ 365 (Actual/365) or days ÷ 360 (Actual/360, used by many banks and for T-bills and commercial loans).
Worked example: $10,000 at 5% for 3 years
- Interest per year: 10,000 × 0.05 = $500.
- Interest over 3 years: 500 × 3 = $1,500.
- Total: 10,000 + 1,500 = $11,500.
- With annual compounding instead, you would earn $1,576.25, which is $76.25 more.
Day counts matter for short loans
A 90-day loan of $10,000 at 5%:
- Actual/365: 10,000 × 0.05 × 90 ÷ 365 = $123.29
- Actual/360: 10,000 × 0.05 × 90 ÷ 360 = $125.00
The 360-day convention charges slightly more for the same quoted rate, which is why it is worth asking which basis a lender uses.
Simple vs compound over time
| Years | Simple interest | Total | Extra with annual compounding |
|---|---|---|---|
| 1 | $500 | $10,500 | $0 |
| 2 | $1,000 | $11,000 | $25.00 |
| 3 | $1,500 | $11,500 | $76.25 |
| 5 | $2,500 | $12,500 | $262.82 |
| 10 | $5,000 | $15,000 | $1,288.95 |
| 20 | $10,000 | $20,000 | $6,532.98 |
Over a year or less, the two methods give almost the same result. Over decades, compounding pulls far ahead. When you invest, compounding works for you; when you borrow, a simple-interest loan is the cheaper structure for the same rate.
Simple-interest auto loans
Most US auto loans charge simple interest on the outstanding balance, calculated daily. Each payment first covers the interest accrued since the last payment, then reduces principal. Paying a few days early, or adding a little to each payment, reduces the interest you owe, while a late payment increases it. The total interest still follows the I = P × r × t logic, applied to a balance that shrinks every month.
Checking a loan offer
Ask for the annual percentage rate (APR), the day-count basis, and whether interest is simple or precomputed. A precomputed loan fixes the total interest upfront, so paying it off early saves less than a simple-interest loan would.