To pay for a $$22,400$ car, Hong made a down payment of $$3,600$ and took out a loan for the rest. On the loan, he paid monthly payments of $$416\mathrm{.}14$ for $4$years.

$($a$)$ What was the total amount Hong ended up paying for the car $($including the down payment and monthly payments$)?$

$($b$)$ How much interest did Hong pay on the loan?