What is compound interest?
Compound interest means each period's interest is added to your balance, so the next period's interest is calculated on the bigger amount. Unlike simple interest, which only pays on the original principal, compounding earns "interest on interest," and the gap widens over time (Brealey et al., 2020).
How do you calculate compound interest?
Future value is FV = PV × (1 + r)ⁿ, where PV is the principal, r the rate per period and n the number of periods. Put $1,000 away at 5% a year for 30 years and simple interest gets you $2,500, while compounding gets you about $4,322.
| Years | Simple (5%) | Compound (5%) |
|---|---|---|
| 10 | $1,500 | About $1,629 |
| 20 | $2,000 | About $2,653 |
| 30 | $2,500 | About $4,322 |
The Rule of 72 estimates how long it takes to double your money: divide 72 by the annual rate. At 6%, that's about 12 years. The more often interest compounds, the higher the real yield, which banks report as APY (annual percentage yield).
What should you watch out for?
Compounding works on debt too, so high-rate credit card balances snowball quickly. Research also finds that people tend to see exponential growth as a straight line—exponential growth bias—which is linked to saving less and borrowing more (Stango & Zinman, 2009). For long-term returns, think in real terms after subtracting inflation.
FAQ
- How much difference does monthly compounding make?
- At 5% a year, monthly compounding gives an APY of about 5.12%. The gap grows slowly over longer periods.
- Is APR the same as APY?
- No. APR is the simple annual rate; APY includes the effect of compounding, so it's higher when interest compounds more than once a year.
Sources reviewed: 2026-10-25
See also: Bonds
References
- Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments (12th ed.). McGraw-Hill Education.
- Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of corporate finance (13th ed.). McGraw-Hill Education.
- Stango, V., & Zinman, J. (2009). Exponential growth bias and household finance. Journal of Finance, 64(6), 2807–2849.