In more detail
The formula is A = P(1 + r/n)^(nt), where P is the principal, r the annual rate, n the compounding periods per year and t the years. Each period's interest is added to the balance and earns interest itself, so growth accelerates over time. More frequent compounding raises the result slightly; the APY captures that as a single yearly figure. See How Compound Interest Works.
Why it matters
Over long periods the effect is large, which rewards starting to save early and punishes carrying high-interest debt: an unpaid card balance at 2% a month grows by 26.82% in a year. Small differences in rate or fees compound into large differences in the final amount.
Example
$10,000 at 5% for 10 years:
| Method | Final amount |
|---|---|
| Simple interest | $15,000.00 |
| Compounded yearly | $16,288.95 |
| Compounded monthly | $16,470.09 |
| Compounded continuously | $16,487.21 |
Adding $200 at the end of every month (monthly compounding) brings the total to $47,526.55, of which $34,000 is money paid in.
Common confusion
Simple interest is paid only on the original principal, so it grows in a straight line instead of a curve.