An investor has $$96,000$ to invest in a $$388,000$ property. He can obtain either

Alternative $1$: A $$292,000$ loan at $9\mathrm{.}8$ percent for $20$ years or

Alternative $2$: A $$216,000$ loan at $9$ percent for $20$ years and a second mortgage for $$76,000$ at $13$ percent for $20$ years.

All loans require monthly payments and are fully amortizing.

Required:

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

b$.$ Which alternative should the borrower choose if the borrower plans to own the property only five years?

c$1.$ Which alternative should the borrower choose, assuming he will own the property for the full loan term and the second mortgage has a $10-$year term?

c$2.$ Which alternative should the borrower choose, assuming that the borrower plans to own the property only for five years and the second mortgage has a $10-$year term?