Compound Interest & Investment Growth Calculator

What compounding actually does

Simple interest pays only on the original amount. Compound interest pays on the original amount plus everything already earned, so each period's interest starts earning interest of its own. The effect is easy to underestimate because it is invisible for years and then dominates.

The practical consequence is that time in the market matters more than the size of any single contribution. A contribution made in year one compounds for the whole horizon; the same amount contributed in the final year compounds once. This is why projections of long horizons produce numbers that look implausible until you check the arithmetic.

The maths this page uses

Contributions are treated as monthly — that is what people actually mean when they save — so the annual rate is first converted to an effective monthly rate for the compounding frequency you choose:

• Effective monthly rate = (1 + annual rate ÷ n)^(n ÷ 12) − 1, where n is the compounding periods per year
• Each month = balance × (1 + monthly rate) + contribution
• Total contributed = initial lump sum + (monthly contribution × months)
• Interest earned = final balance − total contributed
• Exact doubling time = ln(2) ÷ ln(1 + effective annual rate)

Why the rate is converted rather than the deposit schedule

Converting the rate rather than the contribution schedule keeps the two frequencies independent. Raising n increases the effective annual rate slightly — the difference between annual and daily compounding on the same nominal rate is real, but small, typically a fraction of a percentage point per year.

Contributions stay monthly because that is how people actually save. Adjusting the rate instead means the compounding frequency you select changes the growth on the opening balance without silently rewriting your deposit schedule into something you did not ask for.

Reading the result honestly

The calculator applies one constant rate for the whole period. Real markets do not do that. Returns arrive unevenly, some years are negative, and the order in which gains and losses occur changes the outcome for anyone contributing as they go.

A constant-rate projection is therefore a planning tool, not a forecast. It answers questions like 'what does this monthly amount become over twenty years if the rate behaves roughly as assumed', which is useful for comparing options. It does not tell you what will happen.

Three specific cautions. Past returns are not a reliable guide to future returns, whatever figure you enter. Inflation is not modelled, so the number is in nominal terms — at 3% annual inflation, money twenty years out buys roughly half what it does today. And tax on gains, platform fees and fund charges all reduce the realised figure, often substantially over long horizons; fees of 1% a year compound against you exactly the way returns compound for you.

What the Rule of 72 gets you

Divide 72 by the annual rate and you get a rough doubling time: at 8%, about nine years. It is a mental-arithmetic approximation that is reasonably accurate in the 6% to 10% range and drifts at extremes.

This page shows the exact figure alongside it, calculated from the logarithms. The approximation is worth knowing because you can do it in your head mid-conversation; the exact value is worth having because it accounts for the compounding frequency you selected.

Where compounding works against you

The same mathematics that grows a portfolio also grows a balance owed. Credit-card debt, unsecured loans and buy-now-pay-later arrangements compound at rates far higher than any plausible investment return, which is why clearing expensive debt before investing is usually the better financial decision — the certainty of avoiding a 20% charge beats the hope of an 8% return.

The mirror image is that compounding rewards not touching the money. Withdrawals early in the period remove the contributions that would have compounded for longest, so an interruption in a twenty-year plan costs more than the same amount removed at the end.

Not advice

This is an arithmetic tool. It is not financial, investment or tax advice, it does not know your circumstances, and it cannot tell you whether a given assumed rate is realistic for you. If a decision matters, take it to someone qualified who can see your full position.