Compound Interest Calculator
Calculate how much an investment grows over time with compound interest, at any compounding frequency — instantly.
Future value
$1,628.89
Total interest earned: $628.89
- Free — No signup required
- Instant — Results update as you type
- Private — Processed in your browser
Simple interest grows in a straight line; compound interest grows on what it already earned. Over a couple of years the difference is a rounding error. Over thirty it is most of the money. The calculator above shows where a principal ends up, and how much of the total is interest rather than the amount you put in.
How it works
Enter the principal, the annual interest rate, how often interest is compounded — annually, semi-annually, quarterly, monthly or daily — and the number of years. Two figures come back: the future value, and the total interest earned on top of the principal.
The formula is the standard one:
A = P × (1 + r/n)^(n × t)P is the principal, r the annual rate as a decimal, n the number of compounding periods per year, and t the time in years. Daily compounding uses 365 periods and ignores leap days, which is the ordinary convention and changes the answer by a fraction of a percent at most.
Inputs are validated: a principal or term of zero or less, and a negative rate, are rejected rather than producing a misleading figure. Everything is rounded to two decimals at the end. The currency symbol in the summary is decorative — the arithmetic is unit-free.
One limitation to be clear about: this models a single lump sum. It does not handle regular contributions, so it is not a savings-plan projection. For a monthly deposit plan you need the future value of an annuity, which is a different formula.
What the numbers actually show
Compounding frequency matters less than people expect. 1,000 at 5% for 10 years gives 1,628.89 compounded annually and 1,648.66 compounded daily — about 1.2% apart. The gap narrows with every step up in frequency because the sequence converges on the continuous limit, P × e^(rt). Frequency is a detail; the rate and the time are the substance.
Time is the dominant variable. Doubling the rate roughly doubles the interest earned; doubling the term does far more, because the exponent is where the term lives. The familiar shortcut is the rule of 72: divide 72 by the annual percentage rate to get the approximate doubling time. At 6% that is 12 years, and the exact figure is 11.9 — close enough for a mental check, and reliable for rates between about 4% and 12%.
Nominal and effective rates are different numbers. 12% compounded monthly is an effective annual rate of 12.68%, because each month's interest earns interest for the rest of the year. When comparing products, compare effective rates (AER or APY); a headline nominal rate with a high compounding frequency flatters itself.
Inflation is not modelled. A balance that grows 5% a year in an economy running 3% inflation has real growth of about 2%, not 5%. If the question is purchasing power, subtract the inflation rate from the interest rate before entering it — the result is then in today's money.
Where compounding shows up
Compounding is the mechanism behind bond yields, reinvested dividends, discount rates and every present-value calculation used to price a future cash flow. It also runs in reverse: credit card balances compound against you at rates that make the doubling time alarmingly short. Introduction to financial markets covers yields and the time value of money; capital markets fundamentals shows how those discount rates are used to value instruments.
Related tools
To price borrowing rather than saving, the loan calculator and mortgage calculator run the same exponential from the lender's side. To measure a return that already happened rather than project one, use the ROI calculator.
FAQ
- What's the difference between compound and simple interest?
- Simple interest is earned only on the original principal. Compound interest is earned on the principal plus all previously accumulated interest, so growth accelerates over time.
- Why does compounding frequency matter?
- More frequent compounding (daily vs. annually, for example) earns slightly more, because interest starts earning its own interest sooner. The difference is small for short time periods but grows meaningfully over many years.
- Does this include regular deposits or contributions?
- No — this calculates growth of a single lump-sum principal only, without additional monthly or annual contributions.