Problem $7-8($LG $7-3)$ You plan to purchase a $\backslash (\backslash$$ $310,000\backslash )$ house using either a $25-$year mortgage obtained from your local savings bank with a rate of $7\mathrm{.}50$ percent, or a $10-$year mortgage with a rate of $6\mathrm{.}50$ 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$.,32\mathrm{.}16))$