$(1$ point$)$

Fifteen years ago a couple purchased a house for $$190,000\mathrm{.}00$ by paying a $20\%$ down payment and financing the remaining balance with a $30-$year mortgage at $5\mathrm{.}3\%$ compounded monthly.

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

Monthly Payment: $

$($b$)$ Find the balance of the loan after $14$ years and after $15$ years. Let $m$ be how many payments are left on the loan.

$\backslash$table$[[$After $14$ years,,After $15$ years,$],[m=,19c,m=,18c$