You plan to purchase a $$340,000$ house using either a $25-$year mortgage obtained from your local savings bank with a rate of $8\mathrm{.}10$ percent, or a $10-$year mortgage with a rate of $7\mathrm{.}10$ percent. You will make a down payment of $20$ 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 $10-$year mortgage,$],[,$Interest under $25-$year mortgage,$],[,$Difference in interest paid,$],[$b$.,$Monthly payment under $10-$year mortgage,$],[,$Monthly payment under $25-$year mortgage,$],[,$Difference in monthly payment,$]]$