Compound interest means earning interest on your interest. Each period's earnings are added to your balance, so the next period's earnings are calculated on a larger amount. Over long periods, that snowball effect does more of the work than your own contributions.
The formula
For a single lump sum, the future value is:
A = P × (1 + r/n)n×t
- P is the starting principal
- r is the annual interest rate as a decimal (7% = 0.07)
- n is the number of compounding periods per year (12 for monthly)
- t is the number of years
$10,000 at 7% compounded annually for 30 years grows to $10,000 × 1.07³⁰ ≈ $76,123. With simple interest (interest on the original $10,000 only), it would be $10,000 + 30 × $700 = $31,000.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate. At 6% it takes about 12 years. At 9% it takes about 8. This shortcut makes it easy to compare options in your head.
Why starting early matters
Compare two savers who each earn 7% a year, compounded monthly:
| Saver A | Saver B | |
|---|---|---|
| Saves $300/month | Ages 25–35 (10 years) | Ages 35–65 (30 years) |
| Total contributed | $36,000 | $108,000 |
| Balance at 65 | ≈ $421,000 | ≈ $366,000 |
Saver A stops contributing at 35 and still ends up ahead, because the early deposits get 30 extra years to compound. Time in the market is the biggest lever most people have.
Compounding frequency
More frequent compounding helps, but less than you might expect. $10,000 at 5% for 10 years grows to $16,289 compounded annually, $16,470 monthly, and $16,487 daily. The rate and the time horizon matter far more than the frequency. When comparing savings accounts, look at the APY, which already includes the effect of compounding.
Compounding works against you too
Credit-card balances compound as well, often at 20–30% APR. A $5,000 balance at 24% that you only make minimum payments on can take well over a decade to clear and cost thousands in interest. Paying off high-interest debt is effectively a guaranteed return at that rate.
Key takeaways
- Compound growth accelerates over time, so start as early as you can, even with small amounts.
- The rate of return and the number of years matter more than how often interest compounds.
- Fees and inflation compound too. A 1% annual fee can take a large share of long-run returns.
Examples are illustrative. Investment returns are not guaranteed, and past performance does not predict future results.