$(1$ point$)$

Fifteen years ago a couple purchased a house for $$250,000\mathrm{.}00$ by paying a $20\%$ down payment and financing the remaining balance with a $30$year mortgage at $4\mathrm{.}84\%$ compounded monthly.

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

Monthly Payment: $

$($b$)$ Find the balance of the loan after $17$ years and after $18$ years. Let $m$ be how many payments are left on the loan.

$\backslash$table$[[\backslash$table$[[$After $17],[$years$]],,\backslash$table$[[$After $18],[$years$]],],[m=,,m=,],[\backslash$table$[[$Loan$],[$Balance: $$]],,\backslash$table$[[$Loan$],[$Balance: $$]],]]$

$($c$)$ Find the total amount of interest paid by the couple during the $18$th year.

Interest Paid During $18$th year: $