Fineen 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 $5\mathrm{.}62\%$ compounded monthly.

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

Monthly Payment:

$[$Note: Your answer is a dollar amount and should have a dollar sign and exactly two decimal places.$]$

$($b$)$ Find the balance of the loan after $18$ years and after $19$ years?

$\backslash$table$[[$After $18$ years,After $19$ years$],[n=,n=$