$(1$ point$)$

Fifteen years ago a couple purchased a house for $$230,000\mathrm{.}00$ by paying a $20\%$ down payment and financing the remaining balance with a $30-$year mortgage at $5\mathrm{.}8\%$ compounded monthly.

$($a$)$ Find the monthly payment for this loan.

Monthly Payment: $

$($b$)$ Find the balance of the loan after $13$ years and after $14$ years. Let $m$ be how many payments are left on the loan.

$\backslash$table$[[$After $13$ years,After $14$ years$],[m=,m=$