Answer
$8081.13$
Work Step by Step
If in a one year we have $4$ quarters then in a $5$ years there will be $5 \times 4 =20$ quarters
Need to find the balance after $20$ quarters which can be found as:
$a_{20}=6000(1+\dfrac{0.06}{4})^{20}$
or, $=8081.13$