Answer
$5.6294=t$
The investment would take approximately 6 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:
$\frac{A(t)}{P}=2$
$r=0.127$
$m=2$ (every 6 months is twice a year)
Also we can transform the function as:
$A(t)=P*(1+\frac{r}{m})^{mt}$
$\frac{A(t)}{P}=(1+\frac{r}{m})^{mt}$
Therefore the question is to calculate $t$, such as:
$2=(1+\frac{0.127}{2})^{2t}$
$2=(1.0635^{2t})$
$\log_{1.0635}2=11.2587=2t$
$5.6294=t$
The investment would take approximately 6 years.
