Doubling time and the rule of 70

Money grows at a continuously compounded rate of $r$ percent per year. Explain why it takes roughly $70/r$ years to double.

Because $\ln2\approx0.693$. Doubling requires $e^{(r/100)T}=2$, so $T=\tfrac{100\ln2}{r}\approx\tfrac{69.3}{r}$, which is rounded to $70/r$ (with annual compounding, $\ln(1+r)<r$ makes the rule slightly optimistic, hence people sometimes use $72$).