How compound interest actually works
Simple interest pays you on your principal only. Compound interest pays you on your principal and on every unit of interest you've already earned. Each month, this calculator multiplies your current balance by the monthly rate (annual rate ÷ 12), adds that interest to the balance, then adds your monthly contribution. Next month's interest is calculated on the new, larger balance — that feedback loop is the entire secret.
For a lump sum with no contributions, the closed-form formula is:
A = P · (1 + r/n)^(n·t)
where P is the principal, r the annual rate as a decimal, n the number of compounding periods per year (12 here), and t the number of years. With monthly contributions the future value of the contribution stream is added on top; this tool computes both by direct month-by-month simulation, so the numbers are exact.
Why time matters more than rate
In the exponent of the formula, time and rate multiply each other — but in practice you control time far more reliably than you control returns. Doubling your time horizon roughly squares your growth factor, while chasing a couple of extra percentage points of return usually means taking on real risk. Run the calculator with 10 years versus 25 years at the same rate and watch the "interest share of balance" line: in long horizons, the majority of your final balance is often money the market gave you, not money you deposited.
The rule of 72
A useful mental shortcut: divide 72 by your annual return to estimate how many years your money takes to double. At 7%, that's about 10.3 years; at 4%, about 18. It's an approximation, but it's accurate enough to sanity-check any long-term projection — including the table above.
Frequently asked questions
Does this account for inflation?
No — results are in nominal terms. To think in today's purchasing power, subtract an expected inflation rate (historically around 2–3% in the US) from your annual return and re-run the calculation. 7% nominal with 3% inflation ≈ 4% real.
Does this account for taxes or fees?
No. Taxes on interest, dividends, or capital gains, and any fund or account fees, will reduce real-world results. Tax-advantaged accounts (401(k), IRA, ISA, etc.) can defer or eliminate some of that drag.
Are contributions added at the start or end of the month?
At the end of each month, after interest is credited. This is the conservative convention; start-of-month contributions would produce a slightly higher final balance.