You lent a friend 10,000 and they paid back 12,000 three years later. What interest rate did you earn?
Or the other way round: you know the rate and the time, and want to know how much interest you’ll get. Both questions come up constantly, and the answers depend on whether the interest is simple or compound. This interest rate calculator handles all three cases and shows the rate in the forms people actually quote it.
How to use the Interest Rate Calculator#
- Choose what to find. Pick the interest rate, simple interest or compound interest.
- Enter the starting amount. This is the principal.
- Enter the final amount, or the rate. Use the final amount to find the rate. Use the rate to find the interest.
- Enter the time. Choose years or months.
- Choose the compounding. For compound interest and the compounded rate, pick how often interest is added.
Simple interest#
With simple interest you earn the same amount every year, because it’s only ever calculated on the original sum.
10,000 at 5 percent for 5 years earns 10,000 × 0.05 × 5 = 2,500. You finish with 12,500. Simple interest is common on short loans and some bonds.
Compound interest#
With compound interest, each payment of interest joins the balance and starts earning interest itself.
The more often interest is added, the more you end up with. Here’s 10,000 at 5 percent for five years:
| Interest type | Final amount |
|---|---|
| Simple | 12,500.00 |
| Compounded yearly | 12,762.82 |
| Compounded monthly | 12,833.59 |
| Compounded daily | 12,840.03 |
Finding the rate from two amounts#
Now the loan to your friend. You lent 10,000 and received 12,000 after three years. The calculator gives you three versions of the answer:
- Equivalent simple rate: 6.67 percent a year. That’s 2,000 of interest, spread evenly over three years.
- Compounded monthly: 6.09 percent a year. The nominal rate that, added monthly, reaches 12,000.
- Effective annual rate: 6.27 percent. What you really earned each year, with compounding counted.
The three figures describe the same deal. Which one you quote depends on who you’re talking to. Banks tend to say the nominal rate, savers should compare the effective one. If you want to turn a rate into an annual yield, the APY calculator does that directly.
A quick mental shortcut#
The rule of 72 estimates how long it takes money to double: divide 72 by the annual rate. At 5 percent that’s 14.4 years. The exact figure is 14.2 years, so the shortcut is close. It works best for rates between about 4 and 12 percent.
A few cautions#
- Check the compounding. A “5 percent” account that compounds daily isn’t the same as one that pays once a year.
- Monthly rate. To get a monthly rate from a yearly one, a rough method is to divide by 12. A 6 percent rate becomes 0.5 percent a month. Strictly, the effective monthly rate is a touch lower.
- Fees and tax. The calculator ignores both, and they can change the real return a lot.
For fixed-term deposits, the CD calculator shows the balance at maturity.
Finding the rate: a worked example#
You lend 10,000 and get back 12,000 after three years. The simple rate is (12,000 − 10,000) ÷ 10,000 ÷ 3 = 6.67 percent a year. If the interest was compounded annually, the rate is (1.2)^(1/3) − 1 = 6.27 percent a year. The compound rate is lower, because it assumes interest earned in earlier years also earned interest. The calculator gives both, together with the effective annual rate.
Monthly rates and loan apps#
Always check whether a rate is quoted per month or per year. A loan advertised at 10 percent a month is 120 percent a year on a simple basis, and 214 percent if the interest compounds monthly. A rate of 3 percent a month is 36 percent simple and 42.6 percent compounded. Short loans with fees can have an annual cost far above what the headline suggests. Ask for the total amount to repay and compare it with the amount you borrow. For the repayments on a standard loan, use the loan payment calculator.
Frequently asked questions#
Divide the final amount by the starting amount, raise it to the power of 1 over the years, subtract 1 and multiply by 100. For 10,000 growing to 12,000 over 3 years that’s an effective 6.27 percent a year.
Simple interest is earned only on the original amount. Compound interest is earned on the original amount and on the interest already added.
Multiply the principal by the rate and the time in years. 10,000 at 5 percent for 5 years earns 2,500.
More frequent compounding earns slightly more. On 10,000 at 5 percent over five years, monthly compounding earns about 70 more than yearly.
Divide 72 by the annual rate. At 5 percent it takes about 14.4 years, and the exact figure is 14.2 years.