$5.$ You have a choice between the following two identical properties: Property A is priced at $$150,000$ with $80$ percent financing at a $10\mathrm{.}5$ percent interest rate for $20$ years. Property B is priced at $$160,000$ with an assumable mortgage of $$100,000$ at $9$ percent interest with $20$ years remaining. Monthly payments are $$899\mathrm{.}73.$ A second mortgage for $$20,000$ can be obtained at $13$ percent interest for $20$ years. All loans require monthly payments and are fully amortizing.

a$.$ With no preference other than financing, which property would you choose?

b$.$ How would your answer change if the seller of Property B provided a second mortgage for $$20,000$ at the same $9$ percent rate as the assumable loan?

c$.$ How would your answer change if the seller of Property B provided a second mortgage for $$30,000$ at the same $9$ percent rate as the assumable loan so that no additional down payment would be required by the buyer if the loan were assumed?

SHOW WORK $($NO EXCEL$)$