Answer:
[tex]5.3\ 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]A=\$9,000\\ P=\$6,500\\ r=0.0625\\n=2[/tex]
substitute in the formula above and solve for t
[tex]9,000=6,500(1+\frac{0.0625}{2})^{2t}[/tex]
[tex]1.38462=(1.03125)^{2t}[/tex]
applying log both sides
[tex]log(1.38462)=(2t)log(1.03125)[/tex]
[tex]t=log(1.38462)/2log(1.03125)=5.3\ years[/tex]
