Your annual income is $$75,000$ and you have $$53,000$ cash to cover down payment and closing cost of buying a house. You are looking at a house priced at $$300,000$ with monthly real estate tax and insurance cost amounting to $$375.$ The lender will accept a down payment of $15\%$ and the mortgage rate is $5\%.$ You have the funds to cover the estimated closing cost of $$6500$ and down payment. You have no other debt.

a$.$ Given the costs associated with the purchase of the above house and the mortgage rate, will you be able to take a $30-$year mortgage under rule $28$ to finance the purchase of this house with your income?

b$.$ What would be the highest house value you can afford with your income if the costs associated with the purchase are the same as in $($a$)?$