Suppose you have a student loan of $$45,000$ with an APR of $6\%$ for $20$ years. Complete parts $($a$)$ through $($c$)$ below.

a$.$ What are your required monthly payments?

The required monthly payment is $

$($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 $10$ years instead of $20.$ What monthly payments will you need to make?

The monthly payment required to pay off the loan in $10$ years instead of $20$ is $

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

c$.$ Compare the total amount you'll pay over the loan term if you pay the loan off in $10$ years versus $20$ years.

Total payments for the $20-$year loan $=$$

Total payments for the $10-$year loan $=$$