What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and on the interest that has accumulated over time. Unlike simple interest, which is always calculated only on the original amount, compound interest lets your money grow on top of itself — and this exponential effect is what makes compounding so powerful over long periods.
Albert Einstein reportedly called compound interest the "eighth wonder of the world". Whether or not he actually said it, the effect is dramatic. A $10,000 investment at 7% annually grows to $19,671 in 10 years and to $76,123 in 30 years — more than 7.5× the original, all from a fixed 7% rate.
The compound interest formula
For a lump sum with no additional contributions:
A = P × (1 + r/n)^(n × t)
| Variable | Meaning |
|---|---|
| A | Final balance |
| P | Initial principal |
| r | Annual interest rate (as a decimal, e.g. 0.07 for 7%) |
| n | Compounds per year (365 daily, 12 monthly, 4 quarterly, 1 annually) |
| t | Time in years |
When there are also regular contributions, the formula adds a second term:
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]
Compound vs simple interest
| Year | Simple (7%) | Compound (7%) |
|---|---|---|
| 1 | $10,700 | $10,700 |
| 5 | $13,500 | $14,026 |
| 10 | $17,000 | $19,671 |
| 20 | $24,000 | $38,697 |
| 30 | $31,000 | $76,123 |
After 30 years, the compound investment is worth 2.5× more than the simple one, despite both earning 7% on the same $10,000 start. The difference is entirely due to compounding — interest on interest.
How compounding frequency affects growth
The more often interest is compounded, the higher the effective annual return. The difference is small but grows with the rate.
| Frequency | Effective rate at 7% nominal | Balance after 10y on $10k |
|---|---|---|
| Annually | 7.000% | $19,671.51 |
| Semi-annually | 7.123% | $19,897.88 |
| Quarterly | 7.186% | $20,015.97 |
| Monthly | 7.229% | $20,096.61 |
| Daily | 7.250% | $20,136.17 |
The Effective Annual Rate (EAR) — also called APY — captures this difference in a single number: EAR = (1 + r/n)^n − 1. This calculator shows the EAR for your inputs so you can compare investments fairly.
The Rule of 72
A famous rule of thumb: divide 72 by your annual rate to estimate how many years it takes your money to double. At 6% it takes about 12 years; at 8% about 9 years; at 12% about 6 years. The rule is approximate but remarkably accurate for rates between 4% and 15%.
Common use cases
Savings Accounts
Project bank savings growth with monthly compounding.
Investment Planning
Model stock market returns over decades.
Retirement
See how monthly contributions build a retirement fund.
Education Funds
Plan savings for a child's future education costs.
Down Payment
Save toward a house down payment with regular deposits.
Compare Investments
Compare different rates and frequencies on equal terms.
Privacy and accuracy
This compound interest calculator runs entirely in your browser. All calculations happen locally using a month-by-month amortization to model compound growth precisely. Nothing is uploaded, stored or logged.