Answer
$12.127=t$
The investment would take approximately 12 years.
Work Step by Step
The future value of an annual compound rate can be described with the following function:
$A(t)=P*(1+r)^t$, 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.
In this exercise:
$A(t)=15,000$
$P=10,000$
$r=0.034$
Also, we can transform our function as:
Therefore the question is to calculate $t$, such as:
$15,000=10,000*(1+0.034)^t$
$\frac{15,000}{10,000}=1.5=(1.034^t)$
$\log_{1.034}1.5=12.127=t$
$12.127=t$
The investment would take approximately 12 years.