2. You purchase a house and borrow $310,000 as part of the process. The bank lends you the money in a 30-year mortgage, 3.60% APR compounded monthly, with monthly payments starting next month. a. How much is each monthly loan payment? b. After your 180th payment (or 15 years), what is the remaining principal balance on the mortgage? 3. You win the lottery and take the lump-sum payment today of $83 million (already after- tax). You decide to invest this money into an investment account at a nominal 9.0% APR, compounded annually. You want to pay yourself a monthly CF from this investment account. You want the CFs to stay the same value every month, with the first payment next month, and you want the investment account to make monthly payments for the next 80 years (which is as long as you expect to live). a. How much would your investment account be able to pay you each month so that, exactly 80 years from now, the last payment would completely empty your investment account? Assume the first monthly payment would be exactly one month from now