Suppose you have a student loan of $$40,000$ with an APR of $6\%$ for $30$ years. Complete parts $($a$)$ through $($c$)$ below.

a$.$ What are your required monthly payments?

The required monthly payment is $$239\mathrm{.}82.$

$($Do not round until the final answer. Then round to the nearest cent as needed.$)$

b$.$ Suppose you would like to pay the loan off in $15$ years instead of $30.$ What monthly payments will you need to make?

The monthly payment required to pay off the loan in $15$ years instead of $30$ is $

$($Do not round until the final answer. Then round to the nearest cent as needed.$)$