To purchase $$12,700$ worth of lab equipment for her business, Lena made a down payment of $$1500$ and took out a business loan for the rest. After $3$ years of paying monthly payments of $$340\mathrm{.}74,$ she finally paid off the loan.

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

$

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

$$$