What Is Compound Interest? A Simple Guide
The one-sentence definition
Compound interest is interest earned on both your original money and on the interest you have already earned. Each period, your balance grows; the next period's interest is calculated on the new, larger balance. That feedback loop is why growth starts slow and then accelerates — the classic "snowball" effect.
Contrast this with simple interest, which is calculated only on the original principal. A 5% simple return on $10,000 earns you $500 every year, forever. A 5% compound return earns $500 the first year, $525 the second, $551.25 the third — and keeps climbing.
A real example with numbers
Imagine you invest $10,000 at a 7% annual return, compounded yearly, and add $200 per month:
- After 10 years: about $48,000 (you contributed $34,000)
- After 20 years: about $118,000 (you contributed $58,000)
- After 30 years: about $264,000 (you contributed $82,000)
Notice the pattern: your contributions roughly double from year 10 to year 30, but your balance grows more than fivefold. That gap is compounding doing the heavy lifting. Try your own numbers in our Compound Interest Calculator.
The formula (and what each part means)
A = P × (1 + r/n)nt
- A — the future value (what you end up with)
- P — the principal (what you start with)
- r — the annual interest rate as a decimal (7% = 0.07)
- n — compounding periods per year (12 = monthly)
- t — time in years
The most important variable is t. Because time sits in the exponent, starting ten years earlier matters far more than earning one extra percentage point of return.
APR vs. APY: the number that actually matters
Banks quote two different rates, and mixing them up costs people money:
- APR (Annual Percentage Rate) is the nominal rate before compounding.
- APY (Annual Percentage Yield) includes compounding — it is what your money actually earns in a year.
For the same APR, more frequent compounding gives a higher APY. When comparing savings accounts, always compare APY to APY.
How to make compounding work for you
- Start early, even with small amounts. $100/month from age 25 beats $300/month from age 40 at the same return.
- Automate contributions. Money you never see is money you never miss — and every deposit starts compounding immediately.
- Reinvest earnings. Compounding only works if interest and dividends stay invested instead of being withdrawn.
- Keep fees low. A 1% annual fee does not sound like much, but over 30 years it can erase roughly a quarter of your gains. Fees compound too — against you.
- Do not interrupt the snowball. Every withdrawal resets part of the compounding clock.
One caution: compounding works in both directions. Credit card debt at 24% APR compounds against you just as relentlessly — paying down high-interest debt is often the best "investment" available.
FAQ
How long does it take money to double?
Use the Rule of 72: divide 72 by your annual rate. At 7%, money doubles in roughly 10.3 years (72 ÷ 7). At 10%, about 7.2 years.
Is compound interest the same as investment returns?
Not exactly. Compound interest describes the math of growth on growth. Stock market returns compound in a similar way over long periods, but unlike a savings account, they are volatile — some years are negative. The calculator's smooth curve is an average, not a promise.
Does compounding frequency matter much?
Only a little. Daily vs. monthly compounding on the same APR changes the outcome by a fraction of a percent per year. The interest rate and the time horizon matter far more.