We have the following:
The formula in this case is the following:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]solving for t:
replacing
A is 8000, P is 5000, n is 12 and r is 6% (0.06)
[tex]\begin{gathered} 8000=5000(1+\frac{0.06}{12})^{12t} \\ \frac{8000}{5000}=1.005^{12t} \\ \ln (\frac{8}{5})=12\cdot t\ln (1.005)_{} \\ t=\frac{\ln (\frac{8}{5})}{12\ln (1.005)} \\ t=7.85 \end{gathered}[/tex]therefore, the answer is 7.9 years
