Compound Interest Calculator

How compound interest works

FV = P · (1 + r/m)^(m·t)

P is the starting amount, r the annual rate, m the number of times interest compounds per year, and t the number of years. Because each period's interest itself earns interest, the balance grows faster the more frequently it compounds.

APY = (1 + r/m)^m − 1

The effective annual rate (APY) is the real yearly growth once compounding is accounted for — useful for comparing accounts with different compounding frequencies. This calculator models a single lump sum with no further deposits or withdrawals.

Why frequency matters

Compounding is interest earning interest. Each period the balance grows, and the next period's interest is calculated on that larger balance, so growth accelerates over time. Compounding more often nudges the total up because interest starts earning sooner — but the effect is smaller than people expect. On a 5% rate, moving from annual to monthly compounding only lifts the effective yearly return from 5.00% to about 5.12%. The rate and the time horizon dominate; compounding frequency is a minor tweak on top.

Worked example

Put £1,000 in at 5% compounded monthly for 10 years. That's FV = 1000 × (1 + 0.05/12)^(12×10) ≈ £1,647 — about £647 of interest. Roughly £150 of that is interest-on-interest thatsimple interest would have missed. Stretch the term to 20 years and it more than doubles to about £2,712, showing how the curve steepens the longer money stays invested.

A note on assumptions

This models a single deposit left untouched. Real accounts often add regular contributions, deduct fees or tax, or change rates over time, all of which shift the outcome. For borrowing rather than saving, the same compounding maths drives what you owe — see theloan calculator for monthly payments and total interest.

What this projection leaves out

Three things are absent unless you account for them separately. Taxon the interest reduces what you keep, and because it removes money that would otherwise have compounded, the effect grows over time. Feesdo the same. And inflation means a balance projected decades out is stated in today's money but will not buy today's basket — 5% nominal growth against 3% inflation is under 2% in real terms. The calculation also assumes a constant rate and uninterrupted contributions, which few real accounts deliver. See the guide tosimple and compound interest for the rate conventions that catch people out.