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.

Common mistakes

1. Using a nominal return for a long-term goal. Historical stock returns of roughly 10% nominal are closer to 7% after inflation; entering the higher number overstates what a distant balance will actually buy.
2. Assuming a smooth year-by-year path. The calculator projects a constant rate, but real markets rise and fall unevenly — treat the output as a long-run average, not a promise for any single year.
3. Approximating a mismatched contribution and compounding schedule by hand. Manually estimating “monthly deposits into an account that compounds daily” introduces error the calculator’s exact conversion avoids — let it handle any combination instead of eyeballing an average rate.
4. Forgetting taxes on a regular, non-tax-advantaged account. Interest and gains outside retirement accounts are typically taxable in the year earned, which the projection doesn’t subtract.

Practical tips

1. 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.
2. 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.
3. 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.
4. 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.