Answer
$\$25,172.96$
Work Step by Step
We know that Chuck will need to pay $\$420.27$ per month for four years ($4*12=48$ months). Thus the total sum of monthly payments will be:
$\$420.27/month*48~months=\$20,172.96$
In addition, Chuck will pay the down payment of $\$5000$. Therefore, his total car payments will be:
$\$20,172.96+\$5,000=\$25,172.96$