An investor has $$60,000$ to invest in a $$280,000$ property. He can obtain either a $$220,000$ loan at $9\mathrm{.}5$ percent for $20$ years or a $$180,000$ loan at $9$ percent for $20$ years and a second mortgage for $$40,000$ at $13$ percent for $20$ years. All loans require monthly payments and are fully amortizing.

a$.$ Which alternative should the borrower choose, assuming he will own the property for the full loan term?

b$.$ Would your answer change if the borrower plans to own the property only five years?