You recently received a cash inheritance of $500,000 and have decided to buy a house that costs exactly that amount. You could pay cash for the house and use up the entire inheritance, but you are considering taking out a mortgage to help pay for the house that you can invest some of your inheritance in an investment account to fund your retirement. You plan to retire in exactly 30 years. Assume there are no taxes a. Upon talking with your mortgage banker you discover that you can borrow $400,000 with a 30-year mortgage at an interest rate of 3% (stated as an APR with monthly compounding ). What would be the monthly payment on this mortgage ? bIf you take out the mortgage to help buy the house and invest $400,000 from your inheritance today in an investment account earning 5% per year (assuming annual compounding)how much money will you have saved for retirement in 30 years? c. Now assume instead that you decide to use the entire $500,000 inheritance to pay for the house in cash. To save for retirement you will deposit in your investment account at the end of each year an amount equal to 12 times the monthly mortgage payment you calculated in part (a). Using the same 5% annual return as above (assuming annual compounding), how much money will you have saved for retirement in 30 years? d. Why are the answers to parts (b) and () different? Which strategy is better under these assumptions?