Finance
Compound interest calculator
Compounding is easy to state and hard to feel. Seeing the deposits and the interest listed separately is usually what makes it land.
The formula, and what each part does
The left term grows your opening balance. The right term is the future value of an annuity — it handles the stream of monthly deposits, each of which compounds for a different length of time. The deposit you make in month one compounds for the whole period; the one you make in the final month earns nothing.
The variable that does the heavy lifting is the exponent. Doubling the rate roughly doubles the interest in the short run, but doubling the time does far more than double it, because the growth applies to a base that is itself growing.
Nominal rate versus effective rate
A rate quoted as 7% compounded monthly does not return 7% over a year. Each month adds 0.5833%, and those additions themselves earn interest, so the effective annual yield is 7.229%. The more often interest is applied, the wider that gap gets — though it converges quickly. Daily compounding at 7% gives 7.250%, and continuous compounding, the theoretical limit, gives 7.251%.
This is why savings products are advertised as APY rather than a nominal rate: APY has the compounding already folded in, so two accounts can be compared directly.
The rule of 72
Divide 72 by the annual return to estimate how many years a balance takes to double. At 6% it is 12 years, at 8% it is nine, at 12% it is six. The approximation holds well between about 5% and 15% and is close enough for mental arithmetic.
Run it backwards and it becomes a useful check on unrealistic claims. An investment promising to double your money in two years is claiming a 36% annual return.
Inflation quietly removes part of the answer
Every figure here is nominal. If the balance grows at 7% while prices rise at 3%, your real return is closer to 3.9% — the exact calculation is (1.07 ÷ 1.03) − 1, not simple subtraction. Over 30 years, that difference turns a projected balance into something that buys roughly a third of what the headline number suggests.
One practical approach is to enter your expected return minus expected inflation. The result then comes out in today's money, which is far easier to reason about than a large nominal figure decades away.
Common questions
What return should I assume?
For a broad stock index over long periods, historical averages have run near 10% nominal and around 7% after inflation, but with severe variation — including decade-long stretches of near-zero real return. For cash and bonds, use the actual quoted rate. Whatever you pick, the projection is a scenario, not a forecast.
Does it matter whether I deposit at the start or the end of the month?
Slightly. Depositing at the start gives each contribution one extra month of growth, which raises the final balance by roughly the monthly rate — about 0.58% at a 7% annual return. This calculator uses end-of-month, the more conservative convention.
Why does a small fee cost so much over time?
Because it compounds too. A 1% annual fee on a portfolio returning 7% leaves you with 6%. Over 30 years on a $300 monthly contribution, that single percentage point costs roughly a fifth of the final balance — the fee is charged on the whole balance every year, not just on your deposits.
Is interest taxed?
In most countries, yes, unless the money sits in a tax-sheltered account. Taxable interest is usually charged in the year it is earned, which drags on compounding because the tax leaves the account instead of growing. This calculator ignores tax entirely.