Question $1.$ You have decided to buy a $3,000$ square$-$feet house in Denton, close to a good public school. The average price in the area is $$150$ per square feet. The bank will finance $80\%$ of the house value, so you need savings for the $20\%$ down payment. You will take a $20-$year, $4\%$ fix rate mortgage.

a$)$ How much are your monthly payment?

b$)$ What is the loan balance after $2$ years?