To purchase $$12,200$ worth of restaurant equipment for his business, Miguel made a down payment of $$1400$ and took out a business loan for the rest. After $2$ years of paying monthly payments of $$478\mathrm{.}67,$ he finally patd off the loan.

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

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