Phil Pittman is interested in a fixed$-$rate mortgage for $$100,000.$ He is undecided whether to choose a $15-$ or $30-$year mortgage. The current mortgage rate is $5\mathrm{.}5\%$ for the $15-$year mortgage and $6\mathrm{.}5\%$ for the $30-$year mortgage.

a$.$ What are the monthly principal and interest payments for each loan?

b$.$ Overall, how much more interest is paid by choosing the $30-$year mortgage?