Answer
$10.2$ years
Work Step by Step
The model for compounding n times a year is:
$A=P(1+\displaystyle \frac{r}{n})^{nt}$
We are given:
$\left\{\begin{array}{l}
A=3000,\\
P=2000,\\
r=0.04,\\
n=12
\end{array}\right.\qquad t=?$
We solve for $t$ as follows:
$3000=2000(1+\displaystyle \frac{0.04}{12})^{12t}$
$\displaystyle \frac{3000}{2000}=(1+\frac{0.04}{12})^{12t}$
$1.5=(1+\displaystyle \frac{0.01}{3})^{12t}$
$\displaystyle \ln 1.5=12t\cdot\ln(1+\frac{0.01}{3})$
$t=\displaystyle \frac{\ln 1.5}{12\ln(1+\frac{0.01}{3})}\approx 10.151351\approx 10.2$ years
