What is compound interest?
Compound interest is interest calculated on both the original amount and the interest already added to it. Each time interest compounds, it's added to the balance, so the next period's interest is a little larger. Over long periods this makes growth accelerate, which is why the time money is left invested matters so much.
For a plain-language explanation from a regulator, see the U.S. Securities and Exchange Commission's Investor.gov glossary entry on compound interest.
The formula this calculator uses
A = P × (1 + r/n)^(n × t)
- P is the principal, the amount you start with.
- r is the annual interest rate as a decimal (8% = 0.08).
- n is the number of times interest compounds per year: 1 (annually), 2 (semi-annually), 4 (quarterly), 12 (monthly) or 365 (daily).
- t is the time in years. Decimals such as 2.5 are allowed.
The calculator reports the future value A and the total interest earned, A − P, both rounded to two decimal places. It doesn't deduct tax on interest, fees or inflation, and it assumes the rate stays the same for the whole period.
Worked example
10,000 invested at an example rate of 8% a year for 10 years, compounded annually:
- Rate per period: 0.08 ÷ 1 = 0.08.
- Number of periods: 1 × 10 = 10.
- Growth factor: 1.08^10 = 2.158925.
- Future value: 10,000 × 2.158925 = 21,589.25.
- Interest earned: 21,589.25 − 10,000 = 11,589.25.
Switch the frequency to monthly and the rate per period becomes 0.08 ÷ 12, applied 120 times, giving 22,196.40.
How compounding frequency changes the result
The same 10,000 at 8% for 10 years, calculated with this tool:
| Compounding | Future value | Interest earned | Effective annual rate |
|---|---|---|---|
| Annually | 21,589.25 | 11,589.25 | 8.00% |
| Semi-annually | 21,911.23 | 11,911.23 | 8.16% |
| Quarterly | 22,080.40 | 12,080.40 | 8.24% |
| Monthly | 22,196.40 | 12,196.40 | 8.30% |
| Daily | 22,253.46 | 12,253.46 | 8.33% |
The effective annual rate, (1 + r/n)^n − 1, is the single yearly rate that would give the same result with annual compounding. It's the fairest way to compare two offers that compound at different frequencies. Banks may publish it as the APY (annual percentage yield) or AER.
More frequent compounding always earns a bit more, but the gain shrinks quickly: going from monthly to daily adds only 57.06 over ten years here.
Estimating doubling time
The rule of 72, described on Investor.gov, is a quick way to estimate how long compounding takes to double your money: divide 72 by the annual rate. At 8% that's about 9 years, and the exact answer with annual compounding is 9.01 years. At 4% it gives roughly 18 years.
How to use the calculator
- Enter the principal.
- Enter the annual interest rate as a percentage.
- Enter the number of years (decimals allowed).
- Pick the compounding frequency. If you're unsure, the account or deposit terms will say how often interest is compounded.
- Click Calculate to see the future value and total interest.
SEC's Investor.gov also has a compound interest calculator that adds monthly deposits, if you want to cross-check.
Related calculators
- SIP calculator: growth of a fixed monthly investment instead of one lump sum.
- FD & RD calculator: bank deposits with quarterly compounding.
- Retirement calculator: a lump sum plus monthly contributions over many years.
- ROI calculator: the overall return on an investment you've already made.
Results are estimates for illustration and aren't financial advice; actual returns depend on the product's terms and may differ.
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