Car $-$ Maximum Price.

An SJSU alumnus just received a $$30,000$ bonus and plans to use this as a down payment on a car. He has been pre$-$approved for a $48-$month car loan with an APR of $6\mathrm{.}0\%,$ compounded monthly. If he makes $$500$ monthly payments on the car loan, what is the most he could pay for his new car? Hint: Solve for the loan amount, then add the down payment.

a$.$ $$51,290$

b$.$ $$68,553$

c$.$ $$55,528$

d$.$ $$58,626$

e$.$ $$49,075$