Answer:
[tex]13.0\ years[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\ P=\$7,500\\ r=0.06\\n=2\\ A=\$16,200[/tex]
substitute in the formula above
[tex]16,200=7,500(1+\frac{0.06}{2})^{2t}[/tex]
[tex](2.16)=(1.03)^{2t}[/tex]
Apply log both sides
[tex]log(2.16)=(2t)log(1.03)[/tex]
[tex]t=log(2.16)/[(2)log(1.03)][/tex]
[tex]t=13.0\ years[/tex]
