Rule of 72

Example

The yearly return rate of an investment is 9%, your asset will double in approximate 72/9=8 years.

The yearly return rate of an investment is 6%, your asset will double in approximate 72/6=12 years.

Mathematical Proof

(1)
\begin{align} {(\frac{1}{1+r})}^{t}{x}_{0}=2{x}_{0} \end{align}
(2)
\begin{align} {(\frac{1}{1+r})}^{t}\approx{e}^{rt} \end{align}
(3)
\begin{equation} {e}^{rt}{x}_{0}=2{x}_{0} \end{equation}
(4)
\begin{equation} {e}^{rt}=2 \end{equation}
(5)
\begin{align} rt=\log(2)\approx0.72 \end{align}
(6)
\begin{align} t\approx\frac{0.72}{r} \end{align}
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