To purchase $$13,500$ worth of machinery for her business, Keiko made a down payment of $$1200$ and took out a business loan for the rest. After $3$ years of

paying monthly payments of $$374\mathrm{.}20,$ she finally paid off the loan.

$($a$)$ What was the total amount Keiko ended up paying for the machinery

$($including the down payment and monthly payments$)?$

$$]$

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

$