compound interest

With simple interest, you earn money only on your original deposit. With compound interest, you also earn interest on the interest you have already collected — your earnings start earning. Because each period's interest joins the pile that grows next period, the balance climbs faster and faster, the very signature of exponential growth.

The standard formula is A = P · (1 + r/n)^(n·t), where P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years. More frequent compounding (bigger n) earns a little more. As n grows without bound, the formula approaches the continuous case A = P · e^(r·t).

Compounding is the engine behind long-term investing and the trap behind unpaid debt. Two practical handles: the more often interest compounds, the higher the effective yearly rate, and to find how long money takes to reach a goal you solve for t with a logarithm. A quick mental estimate is the Rule of 72: years to double ≈ 72 / (interest rate in percent).