Understanding compound interest
Interest earning interest.
The single most important idea in personal finance, and the most under-appreciated one too.
The mechanic.
Simple interest pays you a percent of the original principal each period. Compound interest pays you a percent of the running balance — including the interest you've already earned. After enough periods, the running balance dwarfs the original principal, and the growth is exponential, not linear.
FV = P × (1 + r/n)ⁿᵗ
The rule of 72.
Divide 72 by the annual rate (in percent) to get roughly how many years it takes for money to double. At 6%, your balance doubles every 12 years; at 9%, every 8; at 12%, every 6. The approximation is good enough that you can do it in your head, and it's the fastest way to internalise why time in the market beats timing the market.
doubling time ≈ 72 ÷ rate
Compounding frequency.
The more often interest compounds, the more you earn — but the difference shrinks fast. Going from yearly to monthly compounding on a 7% rate adds about 0.23 percentage points to the effective rate. Going from monthly to daily adds another 0.01. Beyond that, you're fighting for noise. Continuous compounding is the theoretical limit and is captured by e^(rt).
Why starting early matters.
A 25-year-old who invests $10,000 once and never adds another penny will have more at 65 than a 35-year-old who invests the same $10,000 — assuming the same return. The early decade of compounding does most of the work. Time is the asymmetric ingredient; rate of return is the linear one.
Inflation eats some of it.
Compound interest pays you nominal dollars; inflation erodes their purchasing power. If your investment earns 7% and inflation runs at 3%, your real return is around 4%. To gauge buying power, subtract inflation before celebrating.