Answer:
[tex]t=17.04\ 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]P=\$3,000\\A=\$9,000\\ r=6.5\%=6.5/100=0.065\\n=4[/tex]
substitute in the formula above
[tex]9,000=3,000(1+\frac{0.065}{4})^{4t}[/tex]
solve for t
Simplify
[tex]3=(1.01625)^{4t}[/tex]
Apply log both sides
[tex]log(3)=log[(1.01625)^{4t}][/tex]
Apply property of logarithms
[tex]log(3)=(4t)log(1.01625)[/tex]
[tex]t=log(3)/[4log(1.01625)][/tex]
[tex]t=17.04\ years[/tex]
