The compound-interest formula for a lump sum is A = P(1 + r/n)^(nt). P is the starting amount, r is the annual rate written as a decimal (8% is 0.08), n is how many times a year interest compounds, and t is the number of years. For example, 10,000 at 8% compounded monthly for 10 years grows to about 22,196. When you also save a fixed amount regularly, each contribution compounds for the rest of the term, so AnyTool adds those period by period rather than with the lump-sum formula alone, and recomputes live as you type.

The more often interest compounds, the sooner earned interest starts earning its own interest, so daily compounding beats monthly, which beats annual — but with sharply diminishing returns. At 5% on 10,000 over 10 years, annual compounding yields about 16,289 while daily yields about 16,487, a difference of roughly 198. The effective annual yield captures this: it is (1 + r/n)ⁿ − 1, so for the same nominal rate a higher n gives a marginally higher APY. AnyTool lets you switch between daily, monthly, quarterly, half-yearly and annual compounding and shows the effective annual yield for each.

If a contribution lands at the beginning of each period it starts earning interest immediately, whereas an end-of-period deposit only begins earning from the next period. Over many years this small head start compounds into a noticeable difference, which is why an annuity-due (begin) finishes ahead of an ordinary annuity (end) at the same rate. AnyTool lets you choose either timing, places each deposit exactly on its period in a month-by-month loop, and updates the future value and the year-by-year table immediately.

The calculator assumes the same fixed rate every year and that contributions arrive on time, which real markets and savings rates do not guarantee — actual returns vary and can be negative. The figures are nominal and do not subtract taxes on interest or gains, account fees, or the effect of inflation on buying power, so treat them as a what-if illustration of compounding rather than a promise. AnyTool Compound Interest Calculator runs entirely in your browser, so your amounts are never sent to a server and the page works offline.