Answer :
Answer:
[tex]t= 9.43\ 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=\$5,200\\ r=8.6\%=8.6\100=0.086\\n=4\\A=\$11,600[/tex]
substitute in the formula above
[tex]11,600=5,200(1+\frac{0.086}{4})^{4t}[/tex]
[tex]11,600=5,200(1.0215)^{4t}[/tex]
[tex](11,600/5,200)=(1.0215)^{4t}[/tex]
Applying log both sides
[tex]log(11,600/5,200)=log(1.0215)^{4t}[/tex]
applying property of logarithms
[tex]log(11,600/5,200)=(4t)log(1.0215)[/tex]
[tex]t=log(11,600/5,200)/[(4)log(1.0215)][/tex]
[tex]t= 9.43\ years[/tex]