Answer
$0.231=r$
The compound rate should be 23.1%
Work Step by Step
The future value of a continuous compound rate can be described with the following function:
$A(t)=P*e^{rt}$, where $P$ is the amount of investment at $t=0$, $r$ is the compound rate and $t$ is the time since the investment.
In this exercise:
$\frac{A(t)}{P}=2$
$t=3$
Also, we can transform our function as:
$A(t)=P*e^{rt}$
$\frac{A(t)}{P}=e^{rt}$
Therefore the question is to calculate $r$, such as:
$2=e^{r*3}$
$\log_{e}2=\ln2=0.6932=3*r$
$0.231=r$
The compound rate should be 23.1%
