Answer
$19.2818=t$
The investment would take approximately 19 years.
Work Step by Step
The future value of a general compound rate can be described with the following function:
$A(t)=P*(1+\frac{r}{m})^{mt}$, where $P$ is the amount of investment at $t=0$, $r$ is the compound rate and $t$ is the number of years since the investment and $m$ is the number of compounding times within a year.
In this exercise:
$A(t)=20,000$
$P=10,400$
$r=0.034$
$m=12$
Therefore the question is to calculate $t$, such as:
$20,000=10,400*(1+\frac{0.034}{12})^{12t}$
$\frac{20,000}{10,400}=1.923=(1.00283^{12t})$
$\log_{1.00283}1.923=231.382=12t$
$19.2818=t$
The investment would take approximately 19 years.
