To purchase $$12,600$ worth of machinery for his business, Ali made a down payment of $$1400$ and took out a business loan for the rest. After $3$ years of paying monthly payments of $$340\mathrm{.}74,$ he finally paid off the loan.

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

$$$

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

$$$