Compound interest is interest calculated on the principal and on the interest already added to it. Each time interest is added, the balance gets bigger, so the next round of interest is bigger too. That snowball effect is why compound interest is so powerful for savers and so expensive for borrowers who do not pay down their debt.
Interest on interest, year by year
Suppose you invest $1,000 at 10% per year, compounded annually.
| Year | Balance at start | Interest (10%) | Balance at end |
|---|---|---|---|
| 1 | $1,000.00 | $100.00 | $1,100.00 |
| 2 | $1,100.00 | $110.00 | $1,210.00 |
| 3 | $1,210.00 | $121.00 | $1,331.00 |
In year 2 you earn $10 more than in year 1 — that $10 is interest on the first year’s interest. With simple interest you would earn exactly $100 every year.
The compound interest formula
A = P × (1 + r/n)n × t
- A — final amount
- P — starting principal
- r — annual interest rate as a decimal (10% = 0.10)
- n — how many times interest is added per year
- t — number of years
The interest earned is A − P. For the example above, 1,000 × 1.103 = $1,331.
What “compounding frequency” means
Interest can be added annually, quarterly, monthly or daily. The more often it is added, the sooner each piece of interest starts earning interest of its own. At 5% on $10,000 for 10 years, annual compounding gives $16,288.95 and monthly compounding gives $16,470.09. The difference is real but modest; we compare them in detail in Daily vs Monthly vs Annual Compounding.
Why time matters most
Because growth builds on itself, the later years contribute far more than the early ones. Take $10,000 at 6% compounded annually:
- After 10 years: $17,908.48
- After 20 years: $32,071.35
- After 30 years: $57,434.91
The balance grows by about $7,900 in the first decade but by about $25,400 in the third — with no extra money added. The single most effective thing a saver can do is give compounding more time.
Compound interest on debt
The same maths works against you on debt. Unpaid credit card interest is added to the balance and then charged interest itself. A $3,000 balance at 22% APR compounded monthly grows to $3,730.79 in a year if nothing is paid — an effective rate of about 24.4%. This is why paying more than the minimum on high-interest debt is usually one of the best “returns” available.
Effective annual rate (APY)
Because of compounding, a stated rate of 5% compounded monthly actually grows money by 5.12% in a year. That true yearly figure is called the effective annual rate or annual percentage yield (APY). Always compare savings accounts by APY.
Key takeaways
- Compound interest is interest on principal plus previously earned interest.
- The longer the time, the more dramatic the effect.
- More frequent compounding helps a little; the rate and the time help a lot.
- Compounding works against you on unpaid debt.
See the effect on your own numbers with the Compound Interest Calculator, or learn the method in How to Calculate Compound Interest.