You have two options when purchasing a house. The house costs $$300,000.$ The first option is a $30-$year mortgage with a rate of $7\mathrm{.}80$ percent and the second option is a $20-$year mortgage with a rate of $7\mathrm{.}20$ percent. You will make a down payment of $15$ percent of the purchase price.

a$.$ Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid?

b$.$ Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages?

$($For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

$\backslash$table$[[,,],[$a$.,$Interest under $20-$year mortgage,$],[,$Interest under $30-$year mortgage,$],[,$Difference in interest paid,$],[$b$.,$Monthly payment under $20-$year mortgage,$],[,$Monthly payment under $30-$year mortgage,$],[,$Difference in monthly payment,$]]$