How long will it take to double your money?
The Rule of 72 estimates how many years it takes money to double: divide 72 by the growth rate. At 8%, that works out to 9 years.
It is a rounded stand-in for the exact formula, years equals ln(2) divided by ln(1 plus the rate), which comes out to about 0.693 divided by the rate for small rates. 72 sits close enough to 0.693 as a percentage, and unlike 69.3, it divides evenly by small numbers such as 2, 3, 4, 6, 8, 9 and 12, which is the entire point of a mental-math shortcut.
Closest in the middle of the range most people use it for, and it drifts at the edges. At 6% it estimates 12 years against an exact 11.90, off by 0.9%. At 10% it estimates 7.2 against an exact 7.27, off by 1.0%.
At 2% it estimates 36 years against an exact 35.00, off by 2.8%, and at 20% it estimates 3.6 against an exact 3.80, off by 5.3%. The calculator above shows the estimate and the exact figure together so the size of the gap is visible at whatever rate you enter.
The Rule of 72 is a mental-math shortcut for estimating how many years it takes an investment to double at a given annual growth rate: divide 72 by the interest rate. At 8% annual growth, for example, 72 ÷ 8 = 9 years to double.
The number 72 comes from approximating the exact doubling-time formula, years = ln(2) / ln(1 + r). Since ln(2) ≈ 0.693, and ln(1+r) ≈ r for small rates, doubling time is approximately 0.693/r, and 0.693 rounds conveniently to 72 (as 72/rate%), because 72 has many small integer divisors (2, 3, 4, 6, 8, 9, 12...) that make the mental math easy.
The approximation holds well for rates roughly between 6% and 10%, but drifts at the extremes. Use the exact logarithmic calculation, years = ln(2)/ln(1+r), when you need precision at very low rates (under ~3%) or very high rates (above ~20%), where the Rule of 72's rounding error becomes more noticeable.