Answer:
[tex]7.4\ 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=\$9,000\\ r=0.06\\n=12\\ A=\$14,000[/tex]
substitute in the formula above
[tex]14,000=9,000(1+\frac{0.06}{12})^{12t}[/tex]
[tex](14/9)=(1.005)^{12t}[/tex]
Apply log both sides
[tex]log(14/9)=(12t)log(1.005)[/tex]
[tex]t=log(14/9)/[(12)log(1.005)][/tex]
[tex]t=7.4\ years[/tex]
