Compound interest is the mechanism that makes your money grow exponentially over time. Unlike simple interest (calculated only on the principal), compound interest earns interest on previously earned interest.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
Where: A = final amount, P = principal, r = annual rate, n = compounding frequency per year, t = years.
Example
$10,000 at 7% compounded monthly for 10 years: A = $10,000 × (1 + 0.07/12)^(12×10) = $20,096.61. You earned $10,096.61 — more than doubling your money.
The Rule of 72
Divide 72 by your interest rate to estimate how many years it takes to double your money. At 7%, your money doubles in roughly 72 ÷ 7 ≈ 10.3 years.
Compound vs. Simple Interest
Simple interest only ever applies to the original principal, so it grows in a straight line: Interest = P × r × t. Compound interest applies to principal plus all previously earned interest, so it grows exponentially. On $10,000 at 7% for 30 years, simple interest earns $21,000 total; compound interest (annual) earns over $66,000 — more than 3× as much from the same rate and principal.
Compounding Frequency Matters
More frequent compounding periods (n in the formula) produce slightly higher returns for the same nominal rate: annual, monthly, and daily compounding on the same 7% rate over 20 years differ by a few hundred dollars on a $10,000 balance. The effect is real but smaller than most people expect — the rate and time horizon matter far more than compounding frequency.