You are ready to buy a house, and you have $$80,000$ for a down payment and closing costs. Closing costs are estimated to be $3\%$ of the loan value. You have an annual salary of $$105,000.$ The bank will allow your monthly mortgage payment to equal $28\%$ of your monthly income. The interest rate on the loan is $6\%$ per year with monthly compounding $(\mathrm{.}5\%$ per month$)$ for a $30-$year fixed$-$rate loan.

a$.$ How much money will the bank loan you?

b$.$ How much can you offer for the house?