Ten years ago, the Budai family bought a home and financed $$144,000$ with a $20-$year mortgage at $7\mathrm{.}6\%.$ Complete parts $($a$)$ through $($d$).$

$($a$)$ Find their monthly payment, the total amount of their payments, and the total amount of interest they will pay over the life of this loan.

Their monthly payment is $$.$

$($Do not round until the final answer. Then round to the nearest cent as needed.$)$