Week 4 Day 1: The Simplest Shortcut in Finance

At 7% return: 72 / 7 = about 10.3 years to double. At 10%: 72 / 10 = 7.2 years. At 2% (savings account): 72 / 2 = 36 years. This one shortcut lets you estimate any investment's doubling time in your head, no calculator needed.

The Rule of 72 is not perfectly precise -- it is an approximation. But it is close enough to be incredibly useful for quick mental math. Here is how to use it in real life: your coworker says their portfolio returned 12% last year. You instantly know: 72 / 12 = 6 years to double. Your bank offers a 4.5% CD. 72 / 4.5 = 16 years to double. Your credit card charges 24% interest. 72 / 24 = 3 years for your debt to double if unpaid. That last one is the scary version -- the Rule of 72 works against you on debt just as powerfully as it works for you on investments.

The Rule of 72 is derived from the natural logarithm function: the exact doubling time is ln(2) / ln(1 + r), which equals 0.693 / r. Multiplying by 100 gives 69.3 / rate%. The number 72 is used instead of 69.3 because it is more divisible (by 2, 3, 4, 6, 8, 9, 12) and the rounding error is negligible for rates between 2-15%. For rates below 2%, the Rule of 69.3 is more accurate. For rates above 20%, the Rule of 76 works better. The rule was first described by Luca Pacioli in 'Summa de Arithmetica' in 1494 -- the same book that formalized double-entry bookkeeping. It has been a tool of financial thinking for over 500 years.