Rule of 72: drag the rate

Money doubles when $(1 + r/100)^{t} = 2$. The exact wait is $\ln 2 / \ln(1 + r/100)$. The rule of 72 replaces that with $72 / r$.

72 is a convenience near $100 \times \ln 2 \approx 69.3$, nudged up so that it divides cleanly by 6, 8, 9 and 12. At 8 percent the shortcut is 9 years and the logarithm is 9.0065. At 7 percent it runs about 15 days long. At 20 percent it runs about 74 days short.

How the rule of 72 works is the long form, with the rule of 72 calculator under the answer.

Nobody knows a future growth rate to four decimals, so at 7 or 8 percent the approximation costs nothing you could act on. At high rates, the kind that turn up on card debt, take the logs.

The rule assumes a constant compound interest rate. A return that jumps around compounds at less than its average, which is a different page: volatility drag. The compound interest explorer is the balance at that wait: drag the years toward the doubling time and read what the curve has done.