The Solution.
For the initial deposit of $3,000 to double it, means the amount will become $6,000.
Semi-annually implies 2 periods in a year.
The given formula is
[tex]nt=\frac{\log_{}(\frac{FV}{P})}{\log_{}(1+\frac{r}{n})}[/tex][tex]\text{Where n=2, FV=\$6000, P=\$3000, r=0.0525, t=?}[/tex]substituting these values, we get
[tex]2t=\frac{\log _{}(\frac{6000}{3000})}{\log _{}(1+\frac{0.0525}{2})}[/tex][tex]2t=\frac{\log _{}2}{\log _{}(1+0.02625)}[/tex][tex]2t=\frac{\log _{}2}{\log _{}(1.02625)}=\frac{0.3010}{0.01125}=26.7556[/tex][tex]\begin{gathered} \text{Dividing both sides by 2, we get} \\ t=\frac{26.7556}{2}=13.3778\approx13\text{ years} \end{gathered}[/tex]Therefore, the correct answer is 13 years (4th option)
