Simple interest formula
The simple interest formula is I = P × r × t: interest equals the principal times the annual rate (as a decimal) times the time in years. The amount owed or saved at the end is A = P + I = P(1 + rt).[1]
Worked example: $5,000 × 0.04 × 3 = $600. Over 3 years that is $200 a year, the same every year, because the base never changes.
Rearranging the formula
Any one of the four values can be found from the other three:
| To find | Formula | Example |
|---|---|---|
| Interest | I = P × r × t | 5,000 × 0.04 × 3 = $600 |
| Principal | P = I ÷ (r × t) | 600 ÷ (0.04 × 3) = $5,000 |
| Rate | r = I ÷ (P × t) | 600 ÷ (5,000 × 3) = 0.04 = 4% |
| Time | t = I ÷ (P × r) | 600 ÷ (5,000 × 0.04) = 3 years |
Simple interest for days or months: 360 vs 365
For periods shorter than a year, divide the days by the number of days in the year. "Exact" interest uses 365 days; "ordinary" or banker's interest uses 360, which gives a slightly larger result. $10,000 at 5% for 90 days is $123.29 on a 365-day year and $125.00 on a 360-day year.
Both conventions appear in practice. Treasury bill prices are computed on a 360-day year, while their investment rate uses 365 or 366 days, which is why the two rates differ; the T-bill calculator shows both.[3] Federal rules also lean on simple interest: a time deposit withdrawn within six days of being made must carry a penalty of at least seven days' simple interest.[2]
Where simple interest is used
- Short loans and notes, where interest is calculated on the original principal for the term.
- CD early-withdrawal penalties, usually stated as a number of days or months of simple interest; see the CD calculator.
- Bonds and Treasury bills, whose discount or coupon is quoted as a simple annual rate.
- Accrued interest between payment dates.
Savings grow faster than thisSavings accounts and CDs compound, so over more than a year they earn more than simple interest at the same rate. Use the compound interest calculator for them.
Simple interest vs compound interest
Compound interest overtakes simple interest after the first compounding period. At 4% for 3 years the $5,000 example earns $600 simple or $624.32 compounded once a year. The interest calculator lists every compounding method side by side.
Interest is generally taxable as ordinary income in the year you receive it.[4]
Related calculators
- Interest calculatorInterest earned on a sum, simple or compound, every method side by side
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- CD calculatorValue at maturity from APY or rate, any term
Frequently asked questions
What is the simple interest formula?
I = P × r × t, where P is the principal, r the annual rate as a decimal and t the time in years. The total is P + I.
How do you calculate simple interest for months?
Divide the months by 12 to get years. $5,000 at 4% for 18 months: 5,000 × 0.04 × 1.5 = $300.
How do you calculate simple interest for days?
Divide the days by 365 (or 360 for ordinary interest). $10,000 at 5% for 90 days = 10,000 × 0.05 × 90/365 = $123.29.
How do you find the rate in simple interest?
Divide the interest by principal × time: r = I ÷ (P × t). $300 of interest on $2,000 over 2 years is 300 ÷ 4,000 = 7.5% a year.