How Compound Interest Actually Works

Simple interest pays you on your original money only. Compound interest pays you on your original money and on the interest it has already earned — interest on interest. That one recursive step is the entire secret, and it's why long time horizons produce numbers that feel wrong the first time you see them.

The formula

A = P(1 + r/n)^nt, where P is the principal (your starting amount), r is the annual interest rate as a decimal, n is how many times per year interest compounds, t is the number of years, and A is the final amount. Each compounding period, the balance is multiplied by (1 + r/n); over t years there are n×t such multiplications.

Worked example: $10,000 at 5% APR for 10 years. Compounded annually: 10,000 × 1.05¹⁰ = $16,288.95. Compounded monthly: 10,000 × (1 + 0.05/12)¹²⁰ = $16,470.09. Notice the interest earned ($6,470) is far more than the simple-interest answer of $5,000 — the extra $1,470 is interest earned on interest.

What compounding frequency really changes

More frequent compounding helps, but less than people expect: in the example above, going from annual to monthly compounding added $181 over ten years — about 1% of the final amount. Frequency mostly matters for comparing offers, which is what APY (annual percentage yield) is for: it folds the compounding frequency into a single comparable number. A 5% APR compounded monthly is a 5.12% APY. When comparing savings accounts, compare APYs and the frequency question disappears.

The Rule of 72

A useful mental shortcut: divide 72 by the interest rate to estimate the years to double your money. At 5%, 72 ÷ 5 ≈ 14.4 years (the exact answer with monthly compounding is 13.9 — the rule is an approximation, best between about 4% and 12%). It also runs in reverse for costs: inflation at 3% halves money's purchasing power in roughly 24 years, and a 24% APR credit-card balance doubles in about 3 — compounding works exactly as hard against you as for you.

Contributions: where compounding gets dramatic

The formula above covers a lump sum, but regular contributions are how most people actually save, and each contribution starts its own compounding clock. Take the same $10,000 at 5% compounded monthly, and add $200 at the end of every month: after 10 years you'd have about $47,527. You contributed $24,000 along the way on top of the original $10,000 — so roughly $13,527 of the final balance is growth. Stretch the same plan to 30 years and the growth dwarfs the deposits, which is the whole argument for starting early: time is the exponent in the formula, and it's the one input you can't buy back later.

You can verify every number in this guide with the Compound Interest Calculator, which shows the formula, supports contributions, and charts the balance year by year. The U.S. SEC's Investor.gov runs a well-known compound interest calculator too, if you want a second opinion from a government source. Informational only — not financial advice.

Try it yourself

This guide pairs with the free Compound Interest Calculator — no sign-up, runs in your browser, and shows its formula.