Compound Interest Calculator

Benjamin Franklin's two thousand pounds

In 1790, Benjamin Franklin left £1,000 each to the cities of Boston and Philadelphia in his will, with instructions that the money be loaned to young tradesmen and the interest collected. Half the fund could be spent after a hundred years; the other half had to keep compounding for another century. When the trusts were finally wound down in 1990, Boston's share had grown to roughly $5 million; Philadelphia's, to about $2 million. Franklin's bequest sat for 200 years at compound interest and turned a few thousand colonial pounds into a small fortune.

That is the entire intuition behind compound interest, told in a story instead of a formula. Interest earned in year one earns its own interest in year two. By year fifty, the money you are growing is mostly money the original deposit has already earned, not the original deposit. The calculator above runs this for you with whichever rate and horizon you specify.

The formula, derived in two steps

Start with simple growth: after one year at rate r, an amount P becomes P(1 + r). After two years, that whole amount grows again: P(1 + r)². After t years, with interest applied once a year, the answer is P(1 + r)^t.

If interest compounds n times per year, each compounding period gets a smaller rate (r/n) but happens more often (nt times). Substitute those into the expression above and you have the full compound-interest formula: A = P · (1 + r/n)^nt. That is the equation behind every number this calculator produces. A is the future value; A − P is the interest earned.

How much compounding frequency actually matters

Less than most marketing copy suggests. Consider $10,000 at 5% for ten years:

• Annual compounding: $16,288.95
• Monthly compounding: $16,470.09 (+$181)
• Daily compounding: $16,486.65 (+$197)
• Continuous compounding (the theoretical limit, using Pe^rt): $16,487.21 (+$198)

The jump from annual to monthly is meaningful; the jump from monthly to daily, almost nothing. Daily-compounding marketing is mostly a tiebreaker between otherwise-identical accounts, not a real differentiator. For long horizons and large balances, monthly is functionally equivalent to daily.

What this calculator assumes — and what it does not

The math above models a static rate and a single lump-sum deposit held untouched for the full term. Three real-world frictions are not in the formula:

• Rates change. Savings accounts and CDs adjust. The compound formula assumes a constant r; in practice, the rate floats.
• Taxes. Interest in a taxable account is generally taxed each year as ordinary income. The compounding above is on the pre-tax balance. After-tax growth is materially lower unless the money is in a tax-advantaged account.
• Inflation. A 7% nominal return during 4% inflation is a 3% real return. Use a real-return rate (nominal minus expected inflation) for purchasing-power projections.

To layer in regular contributions on top of a starting balance, use the investment calculator. For a retirement-specific projection that handles withdrawals and inflation, the retirement calculator and 401(k) calculator are better tools.

The Rule of 72, briefly

A useful shortcut: at rate r% annually, your money roughly doubles in 72 / r years. At 6%, that's 12 years; at 8%, 9 years; at 4%, 18 years. The rule is exact only at a specific rate (around 8%) and slightly off elsewhere, but it gets you within a year or two for any rate between 4% and 12%, which is most of the realistic range.