Answer
8.75 years
Work Step by Step
$A=P*(1+r/n)^{n*t}$
$A=10000$
$P=5000$
$r=.08$
$n=4$
$A=P*(1+r/n)^{n*t}$
$10000=5000*(1+.08/4)^{4*t}$
$10000/5000=5000/5000*(1.02)^{4*t}$
$2=1.02^{4*t}$
$log 2 = 4*t log 1.02$
$.30103 = 4*t*.0086$
$.30103 = .0344*t$
$.30103/.0344 =.0344*t/.0344$
$t =8.75$