The Math Behind 72

Compound growth follows exponential math. After n years at rate r, money multiplies by (1 + r)ⁿ. To double, (1 + r)ⁿ = 2. Take the natural log: n = ln(2) / ln(1 + r). Since ln(2) ≈ 0.693 and ln(1 + r) ≈ r for small r, the doubling time is about 0.693 / r — or, in percent terms, 69.3 divided by the rate.

Bankers rounded 69.3 up to 72 because it divides cleanly by 1, 2, 3, 4, 6, 8, 9, and 12 — close enough to be accurate, far easier to do in your head.