How long to double your money?

Why Rule of 72 is an approximation

• The exact doubling time at annual rate r is ln(2) / ln(1 + r). Rule of 72 approximates this as 72 / (r × 100) because 72 has lots of small divisors (1, 2, 3, 4, 6, 8, 9, 12...), making the mental math easy — not because 72 is derived from anything special.
• The approximation is closest around 6–10% annual returns (within a couple hundredths of a year at 8%), and drifts further off at the extremes — at 2% it overshoots by about 1 year, and at 30% it undershoots by about a quarter of a year. The exact figure is always shown alongside it here.
• Some use Rule of 70 (marginally better below ~5%) or Rule of 69.3 (exact for continuous compounding) instead — 72 remains the most common because of how easily it divides.