You want to buy an apartment and you have $$2,000,000$ for a down payment and closing costs $($i$.$e$.,$ down payment $+$ closing costs $=2,000,000).$ Closing costs are estimated to be $4\%$ of the loan value. You have an annual salary of $$360,000$ and the bank is willing to allow your monthly mortgage payment to be equal to $40\%$ of your monthly income. The interest rate on the loan is $6\%$ per year with monthly compounding $(0\mathrm{.}5\%$ per month$)$ for a $30-$year fixed rate loan. How much money will the bank loan you? How much can you offer for the apartment? You need to show your steps to earn full points.