For a student loan of $$20,300$ at $2\mathrm{.}75\%$ for $15$ years, complete the following.

$($a$)$ Calculate the monthly payment necessary to amortize the loan amount.

$($b$)$ Find the amount of money saved over the lifetime of the loan if an additional $$100$ is added to the monthly payment.

$($a$)$ The monthly payment is $

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

$($b$)$ The amount saved over the lifetime of the loan is :

$($Round the final answer to the nearest cent as needed. Round all intermediate values to the nearest ten$-$thousandth as needed.$)$