Simple interest formula
- P = principal, the amount lent or borrowed
- R = interest rate per year, in per cent
- T = time in years. For months, use months ÷ 12; for days, use days ÷ 365.
The rate is always per year, so a monthly rate must be multiplied by 12 first: 1% a month is 12% a year. Rearranging the formula lets you find any one value from the other three:
| To find | Formula |
|---|---|
| Interest | SI = P × R × T ÷ 100 |
| Principal | P = SI × 100 ÷ (R × T) |
| Rate | R = SI × 100 ÷ (P × T) |
| Time | T = SI × 100 ÷ (P × R) |
Worked example
You lend 50,000 at 8% a year for 3 years.
- SI = 50,000 × 8 × 3 ÷ 100 = 12,000, so the total repaid is 62,000.
- For 18 months: T = 18 ÷ 12 = 1.5 years, so SI = 50,000 × 8 × 1.5 ÷ 100 = 6,000.
- For 100 days: T = 100 ÷ 365, so SI = 50,000 × 8 × 100 ÷ 36,500 = 1,095.89.
- Working backwards: if 50,000 earned 12,000 in 3 years, R = 12,000 × 100 ÷ (50,000 × 3) = 8%.
With yearly compounding, the same 50,000 at 8% for 3 years grows to 50,000 × 1.08³ = 62,985.60. That's 12,985.60 of interest, 985.60 more than simple interest, because each year's interest also earns interest. The gap widens quickly over longer periods; see the compound interest calculator for monthly or quarterly compounding.
Where simple interest is used
- Flat-rate loans. Some personal loans and car loans quote a "flat" rate, worked out as simple interest on the full amount for the whole term, even though you repay part of it every month.
- Bond coupons. A bond pays a fixed coupon on its face value each period. The coupon itself doesn't compound unless you reinvest it.
- Short-term lending. Loans between people, trade credit and many short deposits calculate interest by days on the original amount.
- Interest paid out. A deposit that pays interest out to your bank account each quarter, instead of adding it to the balance, effectively earns simple interest.
Why a flat rate costs more than it looks
Take a 5,00,000 car loan at a 9% flat rate for 5 years. The interest is 5,00,000 × 9 × 5 ÷ 100 = 2,25,000, so you pay 7,25,000 over 60 months: 12,083.33 a month. Because the interest is charged on the full amount even after you've repaid most of it, the same EMI on a normal reducing-balance loan works out at about 15.7% a year, not 9%. Use the EMI calculator to compare offers on a reducing-balance basis.
Frequently asked questions
What is the formula for simple interest?
How do I calculate simple interest for months or days?
What is the difference between simple and compound interest?
How do I find the rate of interest?
Do banks use simple interest?
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