Assume a borrower purchased a $$100,000$ house with a $$5,000$ down payment and a $30-$year loan with a fixed annual rate of $7\mathrm{.}50\%.$ The lender takes a private mortgage insurance that covers $20$ percent of the loan for the first $10$ years of the loan term. Compute the dollar amount of insurance premium if: a$)$ the premium is $2\mathrm{.}5\%$ of the loan amount and it is paid at closing as a one time premium; b$)$ the premium is $0\mathrm{.}5\%$ of outstanding mortgage balance and it is paid annually as a percentage of remaining loan balance; c$)$ the premium is $0\mathrm{.}05\%$ of outstanding mortgage balance and it is paid monthly as a percentage of remaining loan balance.

Topic $6$: Property Valuation via Sales Comparison

$33.$ You are appraising a property located adjacent to a high speed freeway. Total area of the property is $2,000$ sq$.$ ft$.$ Investigation disclosed the following transactions involving comparable properties in the neighborhood of the subject and in a similar value range as the subject.

$(1)$ One year ago a $2,400$ sq$.$ ft$.$ property not adjacent to freeway sold for $$160,000.$ Improvements were nearly identical to subject dwelling in all but size.

$(2)$ This year a $2,400$ sq$.$ ft$.$ property not adjacent to freeway sold for $$150,500.$ This dwelling was highly similar to subject in all respects except for size.

$(3)$ A $2,000$ sq$.$ ft$.$ property not adjacent to the freeway sold $1$ year ago for $$150,000.$ These improvements are highly similar to subject.

$(4)$ A $2,400$ sq$.$ ft$.$ property sold this year for $$140,300.$ Located adjacent to the freeway, it was very