Answer:
[tex]18.4\ 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=\$2,000\\ r=0.06\\n=4\\A=3*(\$2,000)=\$6,000[/tex]
substitute in the formula above
[tex]6,000=2,000(1+\frac{0.06}{4})^{4t}[/tex]
[tex]3=(1.015)^{4t}[/tex]
Applying log both sides
[tex]log(3)=4tlog(1.015)[/tex]
Solve for t
[tex]t=log(3)/(4log(1.015))=18.4\ years[/tex]
