How Compound Interest Works (with Real Numbers)

Compound interest is the reason a small amount of money you save today can turn into a much bigger pile decades from now. The basic idea: you earn interest on the money you put in, and then you also earn interest on the interest. Over time, the second part starts to matter more than the first.

This is a plain-English explainer with real numbers. The Securities and Exchange Commission's beginner site, Investor.gov, has a free compound interest calculator at investor.gov. For more on the underlying ideas, see interest rate and compound interest in our glossary.

Simple interest first

Pretend you put $1,000 in an account that pays 5% simple interest per year. Simple interest only earns on the original amount — what banks call the principal.

• Year 1: $1,000 + $50 = $1,050
• Year 2: $1,000 + $50 + $50 = $1,100
• Year 3: $1,150
• After 10 years: $1,500
• After 30 years: $2,500

Your money grew, but in a straight line. Each year added the same $50.

Now turn on compounding

Same $1,000, same 5% rate, but the interest stays in the account and earns interest itself.

• Year 1: $1,000 grows to $1,050.
• Year 2: $1,050 grows to $1,102.50 (the extra $2.50 is interest on last year's interest).
• Year 5: about $1,276.
• Year 10: about $1,629.
• Year 20: about $2,653.
• Year 30: about $4,322.

Same starting deposit. Same rate. Almost double the simple-interest result over 30 years. That is compounding doing the work in the background.

The "Rule of 72"

A rough shortcut Investor.gov teaches: divide 72 by the interest rate to estimate how many years it takes for money to roughly double.

• At 4%: 72 ÷ 4 = about 18 years to double.
• At 6%: 72 ÷ 6 = about 12 years.
• At 8%: 72 ÷ 8 = about 9 years.
• At 12%: 72 ÷ 12 = about 6 years.

It is not exact, but it is close enough for a back-of-the-napkin feel. The Federal Reserve's free education site at federalreserveeducation.org uses the same shortcut.

Time matters more than amount

This is the part that surprises people. Compare two savers who both put money into an account earning 7% per year on average.

• Saver A starts at age 22, puts in $200 per month, and stops at age 32. Total contributed: $24,000.
• Saver B starts at age 32, puts in $200 per month, and keeps going until age 62. Total contributed: $72,000.

By age 62, Saver A is often ahead even though they put in only one-third the cash. The extra ten years of compounding does the heavy lifting.

You can run the same scenario for yourself with the free Investor.gov compound interest calculator.

APR vs APY

Two terms that look almost the same:

• APR (Annual Percentage Rate) — the yearly interest rate before compounding is added in. Loans are usually quoted in APR.
• APY (Annual Percentage Yield) — the yearly rate after compounding. Savings accounts are usually quoted in APY because it shows the real return.

When you compare two savings accounts, line up the APYs. When you compare two loans, line up the APRs. The Consumer Financial Protection Bureau (CFPB) requires both numbers to be calculated the same way at every bank, which is why they are useful.

Compounding works in reverse on debt

The math that helps you save also hurts you when you owe. A credit card with a 24% APR that you pay only the minimum on can take decades to pay off, with the total cost ending up two to three times what you charged. The CFPB has a free credit card payoff calculator that shows exactly this at consumerfinance.gov.

This is why personal finance educators talk about high-interest debt as one of the most expensive problems to leave alone. See Debt Snowball vs. Debt Avalanche for two common ways to attack it.

How to make it work for you

You do not need to be an investing expert to put compounding to work. The basic steps:

1. Start somewhere. Even $25 a month invested early matters more than $200 a month invested ten years later.
2. Pick a tax-advantaged account when you can. Workplace 401(k)s, IRAs, and 529 plans all let earnings compound without yearly tax bills. See Roth vs. Traditional IRA.
3. Reinvest dividends. If you own mutual funds or ETFs, set them to reinvest automatically.
4. Leave it alone. The math only works if you do not interrupt it. That is also why you keep an emergency fund somewhere else — see Emergency Funds.
5. Watch fees. A 1% annual fee may not sound like much, but compounded over 30 years it can eat a meaningful chunk of your final balance. Investor.gov has a fee impact calculator.

A note for younger savers

If you are a teenager working a part-time job, a custodial Roth IRA is one of the longest-running compounding head starts you can give yourself. The IRS lets a parent open one in your name as long as you have earned income (a paycheck or self-employment). Talk to a trusted adult or a qualified tax pro before opening one — the rules are simple but worth getting right.

A note on the numbers

Real-world rates change. Stock returns are bumpy from year to year, even when the long-term average looks smooth. The 5%, 7%, and 8% numbers above are example assumptions, not promises. Investor.gov's calculator lets you change the rate to see how sensitive the result is.

Numbers and rules in this article change every year — always check the latest from the IRS, CFPB, and your bank.