What Is Compound Interest?

Compound interest is interest calculated on both an original amount of money and all the interest that amount has already earned — so growth accelerates over time instead of staying flat. Contrast that with simple interest, which is calculated only on the original principal, every period, no matter how much has accumulated.

The mechanics, with a plain example

Say you invest $1,000 at a 10% annual rate.

With simple interest, you earn $100 every year, forever, because the calculation always uses the original $1,000. After three years: $1,300.

With compound interest, year one earns $100 on $1,000, bringing the balance to $1,100. Year two earns 10% on $1,100 — $110, not $100 — bringing the balance to $1,210. Year three earns 10% on $1,210, or $121, bringing the total to $1,331. Same rate, same principal, but $31 more than simple interest after just three years — and the gap widens every year after that, because each year’s interest is calculated on a larger base than the year before.

Why the compounding frequency matters

The formula for compound interest is:

A = P × (1 + r/n)^(n×t)

Where P is the principal, r is the annual interest rate, n is the number of times interest compounds per year, and t is the number of years. The n term is easy to overlook but meaningfully changes the outcome: interest that compounds monthly grows faster than the same nominal rate compounded annually, because each month’s interest starts earning its own interest eleven months sooner than it would under annual compounding. This is why a savings account’s advertised rate is sometimes quoted as both a nominal rate and an “annual percentage yield” that already accounts for compounding frequency — the two numbers can differ even though they describe the same underlying rate.

Where compounding works for you — and against you

Compounding is the core mechanic behind long-horizon investing. It’s also the entire argument behind dollar-cost averaging: contributing steadily over time means each contribution has a different amount of time left to compound, and the earliest contributions — the ones that get the most compounding periods — end up mattering the most to the final total. Time in the market, not the size of any single contribution, is what compounding rewards.

The same math runs in reverse on debt. Credit card balances and many loans compound interest on unpaid balances, which is why debt that isn’t paid down can grow faster than intuition suggests — the interest owed becomes part of the balance that next period’s interest is calculated on, the same acceleration that makes compounding a powerful ally in savings makes it a serious liability in debt.

Compounding also underlies how bonds and interest-bearing instruments are priced and compared, and it’s part of why a mutual fund’s or ETF’s long-run returns depend heavily on reinvesting dividends and gains rather than withdrawing them — money that’s withdrawn stops compounding, full stop.

Compound interest vs. simple interest

	Compound interest	Simple interest
Calculated on	Principal plus all prior interest	Principal only
Growth pattern	Accelerates over time	Constant, linear
Common in	Savings accounts, investments, many loans	Some short-term or fixed-installment loans
Effect of time horizon	Strongly favors longer horizons	Time horizon matters, but linearly
Effect of compounding frequency	More frequent compounding grows the total faster	Not applicable — no compounding involved

A note on real returns

Compound interest describes how a rate of return accumulates, but it doesn’t say anything about what rate you’ll actually get, or whether that rate beats inflation. A guaranteed 10% compounding rate exists only in textbook examples — real investments carry risk, and their returns vary year to year. The math of compounding is the same regardless of the underlying instrument, whether it’s a savings account, a bond ladder, or equity holdings vested through something like restricted stock units that grow in value over a vesting schedule — but the reliability of the rate itself is a separate question from the mechanics of compounding.

The takeaway

Compound interest earns returns on returns, which is why its growth curve bends upward over time instead of climbing in a straight line. The two levers that matter most are time — because the earliest periods get the most compounding cycles — and compounding frequency, since more frequent compounding lets interest start earning its own interest sooner. The same mechanism that builds wealth quietly in a long-term investment is exactly what makes unpaid debt so costly to carry: it’s the same math, just pointed in the direction you didn’t want.