Answer
a) $6435.1$
b) $8.24$ years
Work Step by Step
In $A(t)=P(1+\frac{r}{n})^{nt}$ for compound interest, $P,r,n,t$ respectively stand for the principal, interest rate per year, the number of times the interest is compounded per year and the number of years. $A(t)$ is the amount after $t$ years. So if we invest $P=5000$ at an interest rate of $r=0.085$ compounded quarterly ($n=4$), the amount after $t$ years is:
a) $A(3)=5000(1+\frac{0.085}{4})^{4(3)}\approx6435.1$
b) In this case: $A=10000$. So our equation is:
$10000=5000(1+\frac{0.085}{4})^{4(t)}\\2=(1+\frac{0.085}{4})^{4(t)}\\4t=\log_{1+\frac{0.085}{4}}(2)\approx32.96\\t\approx8.24$
