Bernie's Mortgage. Bernie Madeoff pays $$220\mathrm{.}000$ for a new four$-$bedroom $2,400-$square$-$foot home outside Tonopah, Nevada. He plans to make a $20\%$ down payment, but is having trouble deciding whether he wants a $15-$year fixed rate $(6\mathrm{.}398\%)$ or a $30-$year fixed rate $(6\mathrm{.}874\%)$ mortgage

a$.$ What is the monthly payment for both the $15-$ and $30-$year mortgages, assuming a fully amortizing loan of equal payments for the life of the mortgage?

b$.$ Assume that instead of making a $20\%$ down payment, he makes a $10\%$ down payment, and finances the remainder at $7\mathrm{.}123\%$ fixed interest for $15$ years. What is his monthly payment?

c$.$ Assume that the home's total value falls by $25\%.$ If Bernie sells the house at the new market value, what would be his gain or loss on the home and mortgage, assuming all of the mortgage principal remains? Use the same assumptions as in part a$.$