To pay for a $$17,400$ motorcycle, Alan made a down payment of $$3400$ and took out a loan for the rest. On the loan, he paid monthly payments of $$251\mathrm{.}57$ for $5$ years.

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

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

$$$