An investor has $$84,000$ to invest in a $$352,000$ property. He can either obtain a $$268,000$ loan at $9\mathrm{.}7$ percent for $20$ years or a $$204,000$ loan at $9$ percent for $20$ years and a second mortgage for $$64,000$ at $13$ percent.

Required:

a$.$ Calculate the effective cost of the combined loans if the second mortgage is for $20$ years and identify the best alternative for the borrower.

b$.$ Calculate the effective cost of the combined loans if the borrower plans to own the property for only five years and identify the best alternative for the borrower.

c$.$ Calculate the effective cost of the combined loans if the term is $10$ years and identify the best alternative for the borrower.