Madeoff's Mortgage. Bernie Madeoff pays $$$$240$ comma $000$ for a new$$ 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 $(6\mathrm{.}404\%)$ or a $30-$year fixed rate $(6\mathrm{.}879\%)$ 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 $7\mathrm{.}129\%$ 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$.$