The Kings bought a $$374,000$ condominium. They made a down payment of $$42,000$ and took out a mortgage for the rest. Over the course of $15$ years they made monthly payments of $$2801\mathrm{.}61$ on their mortgage until it was paid off.

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

$($b$)$ How much interest did they pay on the mortgage?