How to Calculate Compound Interest (Formula + Examples)

Compound interest is interest earned on both your initial amount and the interest already added. The formula is A = P × (1 + r/n)^(n × t): 10,000 at 5% a year, compounded yearly for 10 years, grows to 16,288.95.

The formula explained

A = P × (1 + r/n)^(n × t)

• A: the final amount
• P: the initial amount (principal)
• r: the annual interest rate as a decimal (5% = 0.05)
• n: the number of times interest is added per year (1 = yearly, 4 = quarterly, 12 = monthly, 365 = daily)
• t: the number of years

The interest earned is simply A − P.

The difference from simple interest is that simple interest is always calculated on the original amount: 10,000 at 5% for 10 years earns 500 a year, so 5,000 in total and a final amount of 15,000. With yearly compounding, the same money reaches 16,288.95, because each year's interest also earns interest.

Worked examples

1. Yearly compounding

P = 10,000, r = 0.05, n = 1, t = 10 A = 10,000 × 1.05^10 = 10,000 × 1.628895 ≈ 16,288.95 Interest: 6,288.95

2. Monthly compounding

Same amount and rate, but n = 12: A = 10,000 × (1 + 0.05/12)^120 = 16,470.09

More frequent compounding gives a little more: 5% compounded monthly is equivalent to about 5.12% a year. Quarterly gives 16,436.19 and daily 16,486.65, so the gains from compounding more often get smaller and smaller.

3. Adding monthly contributions

Start with 10,000 at 5% compounded monthly, and add 200 at the end of every month for 10 years:

• Total invested: 10,000 + 200 × 120 = 34,000
• Final amount: 47,526.55
• Interest earned: 13,526.55

Regular contributions often matter more than the rate itself, because every deposit starts compounding as soon as it is made. The formula above only covers a single deposit; with contributions, a calculator that works month by month is the easiest route.

The rule of 72 (an approximation)

To estimate how many years it takes to double your money, divide 72 by the annual rate in percent:

• at 6%: 72 ÷ 6 = about 12 years (the exact answer is 11.9)
• at 8%: 72 ÷ 8 = about 9 years (exact: 9.0)

It is a mental shortcut, not an exact result, and it works best for rates between roughly 4% and 12%.

Don't forget inflation

A future amount is not worth the same as today's money. If prices rise 2% a year, they rise by about 22% over 10 years (1.02^10 = 1.219). The 16,470.09 from example 2 would then buy roughly what 13,511 buys today. As an approximation, your real return is (1 + rate) ÷ (1 + inflation) − 1: here 1.05 ÷ 1.02 − 1 ≈ 2.94% a year. The Inflation calculator shows how purchasing power changes over time.

Quick method with our tools

1. Open the Compound interest calculator.
2. Enter the initial amount, the annual rate and the number of years.
3. Choose the compounding frequency: yearly, quarterly, monthly or daily.
4. Add a monthly contribution if you plan to save regularly (or leave it at 0).
5. Read the final amount, the total invested and the interest earned, then check the year-by-year table.

To project regular investing with an expected return and see the result in today's money, use the Investment calculator. For interest on money you borrow, see how loan interest works.

Common mistakes

• Using 5 instead of 0.05 for the rate in the formula.
• Mixing up the periods: with monthly compounding, divide the rate by 12 and multiply the years by 12.
• Treating a return as guaranteed. A savings account may pay a fixed rate, but investment returns vary from year to year and can be negative. These calculations assume a constant rate.
• Ignoring fees and taxes, which reduce the rate you actually earn. The results here are before both.