What is the Rule of 72?
The Rule of 72 is a mental-math shortcut: divide 72 by an annual growth rate to estimate how many years it takes to double. At 6%, money doubles in about 12 years; at 9%, about 8. It works because 72 is close to the true doubling constant (100 × ln 2 ≈ 69.3) and divides evenly by 2, 3, 4, 6, 8, 9 and 12.
- It’s most accurate around 8%. Below about 5% it slightly overestimates the time; above about 12% it underestimates it. The table in the results shows the exact gap.
- It works for anything that compounds. At 3% inflation prices double in about 24 years. A credit card at 24% APR doubles an unpaid balance in about 3 years.
- Other multiples follow the same idea. Tripling uses roughly 114 ÷ rate, quadrupling 144 ÷ rate.
The exact formula
years = ln(multiple) ÷ ln(1 + rate)
For doubling at 8%, that’s ln 2 ÷ ln 1.08 = 9.01 years, versus the Rule of 72’s 9.0. Solving for the rate flips it around: rate = multiple1/years − 1. See the methodology for compounding variations.