Simple Interest Formula: How It Works With Examples
The simple interest formula, worked examples in years, months and days, and how simple interest compares with compound interest on the same numbers.
In this article
Simple interest is the easiest kind of interest to work out. It is calculated only on the money you started with, so the interest is the same every year. This guide gives the formula, works through examples in years, months and days, and compares simple interest with compound interest using the same numbers.
What simple interest means
The St. Louis Fed lesson defines simple interest as an annual payment based on a percentage of the amount you save, and calls the original amount deposited or invested, leaving out any interest, the principal. The percentage is the annual interest rate. Unlike compound interest, earlier interest is never added to the amount that earns the next interest.
The formula
SI = P × R × T / 100- SI is the simple interest.
- P is the principal.
- R is the yearly rate in percent.
- T is the time in years.
The total amount is the principal plus the interest. The lesson's own example is 100 saved at 8%: the interest for one year is 100 × 0.08 = 8, so you have 108 after a year. Another from the same lesson: 60 at 10% for one year earns 6 and becomes 66.
Finding the rate, the time or the principal
The formula can be turned around when one of the other numbers is the unknown. Rearranged, it gives R = SI × 100 / (P × T), T = SI × 100 / (P × R) and P = SI × 100 / (R × T). Each one is just the same relationship solved for a different letter.
- Rate: ₹50,000 earns ₹6,000 in 2 years. R = 6,000 × 100 / (50,000 × 2) = 6% a year.
- Time: ₹80,000 at 5% earns ₹10,000. T = 10,000 × 100 / (80,000 × 5) = 2.5 years.
- Principal: ₹3,000 of interest in 3 years at 5%. P = 3,000 × 100 / (5 × 3) = ₹20,000.
The calculator works forward from principal, rate and time. Use these rearranged forms to check a figure a lender or a bank quotes you, or to work out which number is missing.
Months and days
The formula wants years, so a shorter period has to be turned into a fraction of a year. Our simple interest calculator counts a month as 1/12 of a year and a day as 1/365. Some lenders use other conventions, such as a 360-day year, so their figure can differ by a small amount. Check the terms of your loan or deposit.
- ₹1,00,000 at 8% for 3 years: interest ₹24,000, total ₹1,24,000.
- ₹1,00,000 at 8% for 6 months: interest ₹4,000, total ₹1,04,000.
- ₹50,000 at 9% for 90 days: interest about ₹1,109.59, total about ₹51,109.59.
Simple versus compound with the same numbers
Take ₹1,00,000 at 8% a year. With simple interest you earn ₹8,000 every year. With compound interest, interest added once a year, the first year is the same, but the second year's interest is worked out on ₹1,08,000.
- After 3 years: simple interest is ₹24,000. Compound interest is about ₹25,971.
- After 10 years: simple gives a total of ₹1,80,000. Compound gives about ₹2,15,892.
- After 20 years: simple gives ₹2,60,000. Compound gives about ₹4,66,096.
For one year the two are identical. The gap opens slowly and then quickly. This is also why the CFPB describes compound interest as earning interest on interest as well as on the money you saved, and simple interest has no such second layer.
When you meet simple interest
Short loans and some deposits are quoted with simple interest, and school and exam problems use it constantly. Whether a particular product uses simple or compound interest is stated in its terms, so ask. If it compounds, use the compound interest calculator instead.
Common mistakes
- Using months or days as if they were years. 6 months is 0.5 years, not 6.
- Forgetting to add the interest to the principal when you want the total amount.
- Using simple interest on something that compounds, which understates the result, especially over long periods.
How to use the calculator
Enter the principal, the yearly rate, the time and the unit. The calculator shows the interest and the total amount. To compare with compound interest, enter the same numbers in the compound interest calculator.
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