Phil Pittman is interested in a fixed$-$rate mortgage for $$400,000.$ He is undecided whether to choose a $15-$ or $30-$year mortgage. The current mortgage rate is $4\mathrm{.}5\%$ for the $15-$year mortgage and $5\%$ for the $30-$year mortgage. $($Round your answers to the nearest dollar. Use this table, if necessary.$)$

$($a$)$ What are the monthly principal and interest payments $($in $ $)$ for each loan?

$15-$year mortgage $ $$

$30-$year mortgage $ $$

$($b$)$ What is the total amount of interest $($in $ $)$ paid on each loan?

$15-$year mortgage $ $q,$

$30-$year mortgage $ $$

$($c$)$ Overall, how much more interest $($in $ $)$ is paid by choosing the $30-$year mortgage?

$ $$