What Is Compound Interest?
Compound interest means you earn interest on your interest. Each period, the interest earned is added to the balance, and the next period's interest is calculated on that larger amount. Albert Einstein allegedly called it the eighth wonder of the world — apocryphal or not, the math is real: growth accelerates over time.
A = P × (1 + r/n)n·t
P is your starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the time in years.
Worked Example
$10,000 at 7 % compounded monthly for 20 years grows to about $40,387 — quadrupling without a single additional deposit. Compounded only yearly it reaches $38,697; the extra $1,690 is purely from more frequent compounding.
The Rule of 72
To estimate doubling time, divide 72 by the annual rate. At 7 %, money doubles roughly every 72 ÷ 7 ≈ 10.3 years. It's an approximation, but a remarkably good one for rates under ~15 %.
Compounding Frequency and APY
| Compounding | Effective APY at 7 % nominal |
|---|---|
| Yearly | 7.00 % |
| Quarterly | 7.19 % |
| Monthly | 7.23 % |
| Daily | 7.25 % |
More frequent compounding always helps, but the gains shrink quickly — the jump from yearly to monthly matters far more than monthly to daily.