TheMortgageReports.com reported the median price of a home sold in the United States hit a record high in $2020$ at just above

$$320,000.$ Juan Carlos Soto, Jr$.,$ wants to purchase a new home for $$317,500.$ Juan puts $20\%$ down and will finance the remainder of

the purchase. Compare the following two mortgage options he has: $10$ years at $5\mathrm{.}5\%$ or $15$ years at $6\mathrm{.}0\%.($Use Table $15\mathrm{.}1.)$

Note: Round your intermediate calculations and final answers to the nearest cent.

a$.$ Calculate Juan's monthly payment for both the $10$ and $15$ year mortgage?

b$.$ Calculate Juan's total cost of interest for both the $10$ and $15$ year mortgage?