To purchase $$12,300$ worth of machinery for her business, Laura made a down payment of $$1900$ and took out a business loan for the rest. After $2$ years of paying monthly payments of $$460\mathrm{.}94,$ she finally paid off the loan.

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

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

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