How Compound Interest Works (The Formula, the Rule of 72 & Examples)
Compound interest is interest earning interest. Over long periods it's the difference between linear and exponential growth — and time matters more than rate.
Compound interest grows an amount by A = P × (1 + r/n)^(n·t), where P is the principal, r the annual rate, n the number of compounding periods per year and t the years. Unlike simple interest, each period's interest is added to the balance and earns interest itself.
Simple vs. compound
Simple interest pays a fixed amount each period on the original principal only: $1,000 at 10% for 5 years earns $500. Compound interest pays interest on the growing balance: the same deposit becomes $1,610.51 — the extra $110.51 is interest that itself earned interest.
The formula
A = P × (1 + r/n)^(n·t)
- P
- — Principal — the starting amount
- r
- — Annual interest rate (as a decimal)
- n
- — Compounding periods per year (12 = monthly, 365 = daily)
- t
- — Time in years
$10,000 at 8% for 10 years, compounded monthly
A lump sum left to grow with no further deposits.
- Rate per period = 8% ÷ 12
- 0.6667%
- Periods = 12 × 10
- 120
- Growth factor = (1.006667)^120
- ≈ 2.2196
- Final amount
- $22,196
Grows to about $22,196 — $12,196 of interest, more than the original deposit.
Compounding frequency
| Compounding | $10,000 at 8% for 10 years |
|---|---|
| Annually | $21,589 |
| Monthly | $22,196 |
| Daily | $22,253 |
More frequent compounding helps, but the effect is small compared with the rate and the time horizon. Going from annual to daily adds about $664 over a decade here.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate. At 8%, money doubles in about 72 ÷ 8 = 9 years. At 6% it's 12 years; at 12%, 6 years. It's a mental-maths shortcut, accurate to within a few months for rates between about 4% and 15%.
Why starting early beats saving more
Because growth is exponential, the earliest contributions do the most work — they have the most time to compound. Someone who invests for 10 years then stops often ends up ahead of someone who starts 10 years later and never stops.
Common mistakes
- Comparing a nominal rate to an effective annual rate — 12% compounded monthly is an effective 12.68%
- Ignoring inflation — a 7% return with 3% inflation is really about 4% in purchasing power
- Forgetting that debt compounds too — an unpaid credit-card balance grows the same way
Run your own numbers
Enter a principal, rate, time and compounding frequency to see the final amount, total interest and doubling time.
Open the Compound Interest calculator