Compound interest calculator

What is compound interest?

Compound interest is interest that earns interest. Once a period's interest is added to the balance, the next period's interest is calculated on the larger amount, so growth accelerates rather than staying flat. That is the whole mechanism, and it is why a small difference in rate or term turns into a large difference in money given enough time.

The part people underestimate is that a stated rate does not by itself determine an answer. Interest has to be added at some interval — yearly, quarterly, monthly, daily — and the same 7% produces a different balance for each. Interest also has to be added either before or after any money you pay in that period. Neither of those is implied by the rate, and neither is usually shown.

This calculator does the arithmetic exactly, using whole-number fractions rather than decimals that drift, and rounds once at the end. More usefully, it refuses to make the compounding choice silently: every answer is shown at all five frequencies at once, so you can see the size of the assumption you are relying on.

How to use the compound interest calculator

1. Enter the starting amount, the rate and the term. The rate is the stated, nominal annual rate — the number an account advertises before compounding is taken into account. Results update as you type, with no button to press. Amounts carry no currency, so read them in whatever you typed.
2. Choose how often interest compounds. Yearly, every six months, quarterly, monthly or daily. Whichever you pick is highlighted in the comparison table below the results, so the alternatives stay visible rather than disappearing behind your choice.
3. Add regular contributions if you make them. Enter the total you add each year; it is paid in equal instalments, one per compounding period. Choose whether instalments land at the start or the end of each period — the start is worth exactly one period of extra growth, which the results quantify for your own figures.

One rate, five legitimate answers

Take $10,000 at a stated 7% for 30 years and add nothing to it. Compounded once a year it becomes 76,122.55. Compounded daily it becomes 81,645.26. Those are both correct answers to the same question, and they differ by 5,522.71 — 7.26% of the smaller one, on an account where nothing about the advertised rate changed.

This is the single largest effect on the page, and it is a convention rather than a calculation. That is why the comparison table is not an optional extra here: a calculator that quietly picks monthly and prints one number has answered a question you did not know you were being asked, and the number it printed could be thousands out.

The same gap explains the two rates every account quotes. A nominal 7% compounded monthly has an effective annual rate — the APY, defined in Regulation DD as the annualised relationship between interest earned and principal — of 7.229008%. If you take the stated 7% and treat it as though it were the effective rate, you land 6.2126% below the balance you would actually have after 30 years. The tool shows both figures side by side so the two can never be confused.

Honest limitations

It is worth knowing how the sources of error here rank, because the ordering is not intuitive. On that same $10,000 at 7% over 30 years: the compounding frequency is worth up to 7.26%; reading the nominal rate as effective is worth 6.21%; paying contributions at the start of each period rather than the end is worth 0.58%; rounding the balance to the cent every period instead of once at the end moves it by between 22 cents and 84 cents; and using ordinary floating-point arithmetic instead of exact fractions is worth about seven cents on a forty-billion balance. The thing people worry about is last by a factor of roughly a hundred billion.

Exact arithmetic is still what this page uses, but for a different reason than accuracy: it makes rounding a decidable question rather than an assumption. A fraction has a terminating decimal only when its denominator's sole prime factors are 2 and 5, and a monthly rate of 7% divides by 1200, which carries a factor of 3. Compound balances are therefore repeating decimals essentially always — every calculator rounds, and the only real question is how many times. This one rounds once.

Daily compounding here uses 365 days. Real institutions vary: some use 360, some count actual days including leap years, and the difference is small but genuine. The calculator also assumes the rate never changes, which no real savings account or investment guarantees, and it models neither tax, fees nor inflation — a balance thirty years out buys less than the same figure today. Treat the output as arithmetic on the assumptions you entered, not as a forecast.

The engine is checked against an independent implementation that computes each case by adding one period at a time in exact fractions, over 272 generated cases spanning every frequency and both contribution timings; all 272 agree exactly, not approximately. Forty-four assertions in total pin that and the published figures above.

Why is it free?

The calculation is arithmetic, and it runs in your browser as you type. Nothing about your savings, your rate or your balance is sent anywhere, which matters more here than on most pages — financial figures are exactly what people are reluctant to type into someone else's server.

That also means no account, no capped number of projections, and no premium tier holding the comparison table hostage.