Your bank has decided to create a mortgage product that combines borrowing and saving. The idea is one where you make sufficiently large monthly payments, so that you get a loan upfront and a payout at the end. For example, consider a 15-year (180-month) mortgage that gives you $200,000 at time zero and gives you an additional $100,000 at the end of month 180. Assume the fixed annual rate is 4.2% APR (compounded monthly, so remember to adjust the rate for the number of payments per year).\ \ a. (10 points) What is your monthly payment?\ \ b. (10 points) At what point (after how many months) would you have a remaining balance on this loan equal to $0, so that you begin to build up savings towards the $100,000 you receive in month 180?\ \ c. (10 points) How much larger is the monthly payment for this product than the monthly payment on a conventional mortgage? The latter does not have the $100,000 (so-called balloon) payment at the end, but still involves borrowing $200,000 upfront.\ \ d. (5 points) If inflation is expected to be 3% per year over the life of this product, what will the $100,000 balloon payment at month 180 be able to buy in terms of todays purchasing power.