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}

page revision: 2, last edited: 16 Apr 2009 19:58