To purchase $$13,100$ worth of machinery for his business, Keith made a down payment of $$1700$ and took out a business loan for the rest. After $3$ years of paying monthly payments of $$346\mathrm{.}82,$ he finally paid off the loan.

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

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