$(10$ pts$)$ A couple purchased a $$230,000$ house by making a down payment of $$20,000$ and financing the remaining balance $($$$210,000)$ with a $30-$year mortgage at $5\mathrm{.}914\%$ compounded monthly. The couple's mortgage payment is $$1247\mathrm{.}47$ per month.

$($a$)$ How much equity will the couple have in the house after $18$ years of payments? Round your final answer to $2$ decimal places.

$($b$)$ What is the total amount of interest paid by the couple over the lifetime of the loan? Round your final answer to $2$ decimal places.