Compound Interest Calculator

What this calculator does

Compound interest is the mechanism behind almost every long-term financial outcome — retirement balances, savings growth, and (in reverse) debt spirals. This calculator projects an account forward from a starting amount, with regular contributions on any schedule and interest compounding at any frequency. You get the final balance, the split between what you contributed and what interest earned, and a chart showing both curves — the moment they diverge is compounding becoming visible.

How the math works

Interest that compounds gets added to the balance, so the next period’s interest is calculated on a bigger number. For a lump sum:

FV = P(1 + r/m)^(m·t)

where P is the starting amount, r the annual rate, m the compounding periods per year, and t the years. Regular contributions add an annuity term. When your deposit schedule differs from the compounding schedule, the calculator converts the rate exactly:

rate per contribution period = (1 + r/m)^(m/p) − 1

with p contributions per year — no approximation, whatever combination you pick.

A worked example

Two scenarios, both verified against the formula:

Lump sum: $10,000 at 5%, compounded annually, left alone for 10 years: 10,000 × 1.05¹⁰ = $16,288.95. You did nothing after year zero; compounding added 63% to the pile.

Contributions only: $0 starting, $100 every month at 6% compounded monthly for 10 years: the annuity formula gives $16,387.93 on deposits of just $12,000 — interest contributed $4,388, about 27% of the final balance. Stretch the same $100 monthly habit to 30 years and the balance passes $100,450, of which only $36,000 is your money. Time, not the deposit size, does the heavy lifting.

Practical tips

Start before you optimize. The variable with the most leverage is years invested. Starting five years earlier typically beats a full percentage point of extra return over a working lifetime — you can verify that comparison in about ten seconds with this calculator.
Compare APY, not APR, on savings products. APY already includes the effect of compounding frequency, so two accounts’ APYs are directly comparable regardless of how often each compounds. Banks are required to publish it.
Automate the contribution. The formula assumes perfect monthly consistency, and automation is the only reliable way humans achieve that. An automatic transfer on payday turns the projection on this page into a plan.
Mind the gap between nominal and real. At 2.5% inflation, prices roughly double in 28 years — a projected $100,000 three decades out buys about what $48,000 buys today. For long horizons, mentally halve distant balances or use an inflation-adjusted return (historical stock returns minus inflation ≈ 7%).

The rule of 72

For quick mental math, divide 72 by the annual return to estimate how many years money takes to double: at 6%, about 12 years; at 8%, about 9. It’s an approximation of the exact logarithmic answer, accurate within a few months for rates between 4% and 12%. Use it to sanity-check any projection — including this calculator’s: $10,000 at 6% monthly compounding shows roughly $18,194 after 10 years, right on schedule for a 12-year double.

Frequently asked questions

What's the difference between compounding frequency and contribution frequency?

Compounding frequency is how often the bank or fund credits interest (daily, monthly, annually). Contribution frequency is how often you add money. They're independent — a savings account might compound daily while you deposit monthly. This calculator handles any combination exactly, converting the rate mathematically instead of approximating.

How much does compounding frequency actually matter?

Less than most people expect. $10,000 at 5% for 10 years grows to $16,289 with annual compounding and $16,486 with daily compounding — about 1.2% more over a decade. The rate, the time horizon, and your contributions dominate; frequency is a rounding-level effect at typical rates.

Are contributions assumed at the beginning or end of each period?

End of period, which is the standard "ordinary annuity" convention and matches how most people actually save (depositing after payday). Beginning-of-period contributions would earn one extra period of interest each — a small upward shift you can approximate by adding one extra contribution to the starting amount.

What rate of return should I enter?

For a savings account or CD, use the published APY. For long-term stock investments, the S&P 500 has historically averaged around 10% per year before inflation, roughly 7% after — but past returns don't guarantee future ones, and real portfolios experience volatility, not a smooth average. Run a conservative and an optimistic scenario to bracket the range.

Does the calculator account for taxes or inflation?

No. Interest in a regular account is taxable in the year it's earned, and inflation erodes what the final balance buys. In tax-advantaged accounts (401(k), IRA) the compounding runs tax-free or tax-deferred, which is exactly why those accounts are powerful. Treat the result as a pre-tax, nominal figure.

Growth over time