The Rule of 72 is a shortcut to the Compound Interest — definition">compound interest formula. Here's why it works.
When money grows at a constant annual rate $r$, the formula for doubling is:
$$2 = (1 + r)^t$$
Taking the natural logarithm of both sides:
$$\ln(2) = t \times \ln(1 + r)$$
$$t = \frac{\ln(2)}{\ln(1 + r)}$$
For small rates of return (which financial returns typically are), $\ln(1 + r) \approx r$ (this is a Taylor series approximation). So:
$$t \approx \frac{\ln(2)}{r} = \frac{0.693}{r}$$
Multiply numerator and denominator by 100 to convert to percentages:
$$t \approx \frac{69.3}{r(\%)} \approx \frac{72}{r(\%)}$$
72 is chosen because it's close to 69.3 and has more factors — making mental math easier.
The approximation breaks down at very high rates (>20%), but for typical investment and debt scenarios, it's reliable within 3–5% error.
[1]The Rule of 72 also works in reverse for liabilities: credit card debt at 18% doubles every 4 years if unpaid.