How to use the simple interest calculator
The calculator starts with an example: $10,000 at 5% a year for 3 years. Replace the numbers with your own.
- Principal. The amount borrowed or deposited. Simple interest is always calculated on this figure, never on interest already earned.
- Annual interest rate. The yearly rate stated in the loan or note. Type 5 for 5%.
- Time unit and time. Choose years, months or days, then enter the length of the term. Fractions work: 2.5 years is fine.
- Day-count basis, when you measure in days. Use Actual/365 unless the contract says otherwise; many bank loans, commercial paper and money market instruments use Actual/360.
The chart compares simple interest with annual compounding at the same rate. For terms under five years it runs to 30 years, so you can see where the two methods part ways.
The simple interest formula
A = P + I = P × (1 + r × t)I is the interest, A the total amount, P the principal, r the annual rate as a decimal and t the time in years. For months, t = months ÷ 12; for days, t = days ÷ 365 or days ÷ 360.
Daily interest is P × r divided by the days in the year. On a loan that accrues daily, every day you hold the balance costs that amount.
A worked example
You lend $10,000 at 5% simple interest for 3 years.
Each year earns the same $500.00, so the interest is $1,500.00 and the borrower repays $11,500.00. That works out to $1.37 a day, or $41.67 a month.
Had the interest compounded annually, the balance would reach $11,576.25, a difference of $76.25. Put another way, the simple-interest deal is equivalent to an annually compounded rate of 4.77%.
Simple versus compound interest over time
Over short periods the two methods give almost the same answer. Over long periods compound interest pulls far ahead, because it earns interest on interest. With $10,000 at 5%:
| Term | Simple interest total | Compounded annually |
|---|---|---|
| 1 year | $10,500.00 | $10,500.00 |
| 3 years | $11,500.00 | $11,576.25 |
| 10 years | $15,000.00 | $16,288.95 |
| 30 years | $25,000.00 | $43,219.42 |
Simple interest grows in a straight line; compound interest curves upward. For terms under a year, simple interest actually pays slightly more than annual compounding, which adds nothing until the year is complete. For long-term savings, use the compound interest calculator.
Where simple interest is actually used
Simple interest is less common than textbooks suggest, but it does appear in a few places:
- Some auto and personal loans. On a “simple interest loan”, interest accrues daily on the outstanding principal and each payment covers that interest first. The loan still amortizes (the auto loan calculator gives the payment), but interest is never added to the balance.
- Short-term notes and money market instruments. Promissory notes, bank loans and commercial paper often charge simple interest for a stated number of days, frequently on an Actual/360 basis.
- Treasury bills. T-bills pay no interest; they are sold at a discount to face value. The discount is quoted as a simple annual rate on a 360-day year, so T-bill pricing uses simple-interest arithmetic; see the Treasury bill calculator.
- Bond accrued interest. When a bond changes hands between coupon dates, the buyer pays the seller the coupon earned so far, calculated as simple interest for the days elapsed.
The 360-day year
On an Actual/360 basis, the rate is divided by 360 but interest is charged for every calendar day, so a full year earns 365/360 of the stated rate: about 1.4% more interest than Actual/365. For 90 days on $10,000 at 5%, that is $125.00 instead of $123.29. Check which basis a contract uses.
What this calculator does not include
- Payments during the term. The principal is assumed to stay outstanding for the whole period. For a loan repaid in installments, use the loan calculator.
- Fees. Origination fees and other charges raise the true cost of borrowing above the stated rate.
- Other day-count conventions. Bonds may use 30/360 or Actual/Actual; this calculator offers Actual/365 and Actual/360.
- Taxes on interest received, which reduce what a lender keeps.