$2.$ 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 mort$-$gage 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?

c$)$ Would your answers to $($a$)$ and $($b$)$ change if the second mortgage had a $10-$year term?

SHOW WORK $($NO EXCEL$)$