Compound interest is interest that earns interest on itself. Each period the interest is added to the balance, and the next period’s interest is calculated on the bigger amount. It is why $10,000 left alone at 5% for 20 years becomes about $27,000, and why an unpaid credit card balance doubles in a few years.
What is compound interest?
Compound interest is interest that earns interest. Each period, the interest you earned is added to your balance, and the next period’s interest is calculated on the new, larger balance. Simple interest only ever pays on the original amount.
That difference sounds small for one year and becomes enormous over thirty. It is the single most important mechanic in saving and investing, and it is the reason a 1% difference in a fee or a rate can cost you a five-figure sum by retirement.
The compound interest formula
The standard formula is:
A = P (1 + r / n)nt
- A = the final amount, including interest
- P = the principal, the amount you started with
- r = the annual interest rate, written as a decimal (5% = 0.05)
- n = how many times interest is compounded per year
- t = the number of years
If you only want to know how much interest you earned, subtract the principal: interest = A − P.
A worked example with real numbers
You deposit $10,000 at 5% annual interest, compounded monthly, and leave it alone for 20 years.
Here r = 0.05, n = 12, and t = 20, so r / n = 0.0041667 and nt = 240.
A = 10,000 × (1 + 0.0041667)240 = $27,126
You contributed $10,000 and earned $17,126 in interest. With simple interest — 5% of $10,000 every year for 20 years — you would have earned $10,000 and finished with $20,000. Compounding added roughly $7,000 on the same principal at the same rate.
Why the last years matter more than the first
Compounding is not linear. In the example above, the balance grows by about $500 in year one and about $1,290 in year twenty. The money you add early does more work than the money you add late, because early money has more years to compound.
| Years invested | Balance at 5% monthly compounding |
|---|---|
| 5 | $12,833 |
| 10 | $16,470 |
| 20 | $27,126 |
| 30 | $44,677 |
Doubling the time from 5 to 10 years does not double the balance — it multiplies the interest portion by roughly 2.5×. Going from 10 to 20 years multiplies it again.
Compounding frequency: does it matter?
More frequent compounding pays slightly more at the same stated rate, but the effect is small once you get past monthly. At 5%:
- Annually: 5.000% effective
- Monthly: 5.116% effective
- Daily: 5.127% effective
That is why banks quote an APY (annual percentage yield) instead of a nominal rate: APY already includes the compounding, so you can compare accounts directly. A 5.00% APY account always beats a 5.00% nominal rate that compounds monthly.
Compounding works against you too
The same math applies to debt. A credit card at 24% APR, compounded monthly, roughly doubles an unpaid balance in about three and a half years. Minimum payments mostly cover interest, which is why balances feel stuck.
This is the practical rule: compounding is a tool you either use or pay for. Earning 5% and paying 24% at the same time is a losing trade, which is why paying down high-interest debt usually beats investing.
Common mistakes
- Using simple interest by accident. “5% a year for 20 years” is not 100% growth; with compounding it is 165%.
- Ignoring fees. A 1% annual fee compounds exactly like a 1% lower return. Over 30 years it can remove a quarter of the final balance.
- Comparing a nominal rate with an APY. Always compare APY to APY, and APR to APR.
- Forgetting inflation. A 5% return with 3% inflation is a 2% real return. See what inflation does to savings.
How to use this in a decision
- Compare on the same basis. Convert every option to APY before comparing.
- Check the time horizon. Under two years, compounding barely helps; fees and risk dominate instead.
- Price your debt. If a balance costs 20% and an investment might return 7%, pay the debt first.
- Start the clock. The main variable you control is how long the money compounds.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus interest already earned, so the base grows each period.
What is the rule of 72?
Divide 72 by the annual return to estimate the years needed to double your money. At 6%, 72 ÷ 6 = 12 years. It is an approximation, accurate to within a few months for rates between 4% and 12%.
Is compound interest monthly or yearly?
It depends on the account. Savings accounts usually compound daily or monthly and quote APY. Loans usually quote APR, which may compound monthly. The compounding period is stated in the account terms.
Does compound interest beat inflation?
Only if the after-tax return is higher than inflation. If you earn 4% and inflation is 3%, your real return is about 1% before tax.
Reviewed 22 October 2026. This article is educational and is not financial advice. See our disclaimer.