The compound interest formula
With no extra deposits, money compounding n times a year at annual rate r for t years grows to:
A = P × (1 + r/n)n·t
Put 5,000 at 5% compounded monthly for 10 years: A = 5,000 × (1 + 0.05/12)¹²⁰ ≈ 8,235. Add a monthly deposit and each contribution starts its own compounding clock — the calculator simulates every month so contributions, timing and frequency are all handled exactly.
Interest on interest: why the curve bends
Simple interest pays only on your original deposit. Compound interest pays on the deposit plus every bit of interest already earned, so growth accelerates. In year one of the example above you earn about 256; by year ten the same money earns about 401 a year — 57% more, without you adding anything. Over long horizons this bend in the curve is where most of the final balance comes from, which is why starting five years earlier routinely beats contributing more later.
Does compounding frequency matter much?
Less than people think. 5% compounded yearly yields exactly 5.00%; monthly, 5.12%; daily, 5.13%. The jump from yearly to monthly is worth having, but daily vs monthly is pennies. The number that captures it is the effective annual rate (APY) — shown in your results — and it's the only fair way to compare accounts with different compounding schedules.
The rule of 72 (and the exact answer)
Divide 72 by the interest rate to estimate doubling time: at 5%, 72 ÷ 5 ≈ 14.4 years. The exact math (ln 2 ÷ ln(1 + APY)) gives 13.9 years at 5% monthly compounding — the rule of 72 is a good mental shortcut between about 4% and 12%. Your exact doubling time is computed in the results panel.
Don't skip the inflation field
A balance of 21,000 in ten years won't buy what 21,000 buys today. Enter an inflation estimate (central banks target ~2%, long-run averages run 2–4% in most developed economies, higher elsewhere) and the calculator shows the real value — your future balance expressed in today's buying power. If your interest rate is below inflation, your money is compounding backwards in real terms, which is the strongest argument for not leaving long-term savings in a zero-interest account.
Contribution timing: start vs end of month
Depositing at the start of each month gives every contribution one extra month of growth. On 100/month at 5% for 10 years it's worth about 65 extra — small, but free. The toggle lets you match how your account actually credits deposits.