## Compound Interest

Continuously compounding accounts are best modeled using an exponential function. If the amount invested is P at the r per year which is being compounded continuously, the amount accumulated after t years will be:

$$A=Pe^{rt}$$

The amount invested is {eq}P=\$9000 {/eq} and the amount accumulated is {eq}A=2*\$9000=\\$18000 {/eq}. The rate of interest is {eq}r=0.07 {/eq} compounded continuously. Now, the time can be found as follows.

\begin{align} 9000e^{0.07t}&=18000\\ e^{0.07t}&=2\\ 0.07t&=\ln 2\\ t&\approx 9.90\text{ years} \end{align}