Question 2 Milhouse, 22, is about to begin his career as a rocket scientist for a NASA contractor. Being a rocket scientist, Milhouse knows that he should begin saving for retirement immediately. Part of his inspiration came from reading an article on Social Security in Time. The article indicated that the ratio of workers paying taxes to retirees collecting checks will drop dramatically in the future. In fact, the number will drop to two workers for every retiree in 2040. Milhouse's retirement plan allows him to make equal yearly contributions, and it pays 9 percent interest annually. Upon retirement, Milhouse plans to buy a new boat, which he estimates will cost him $300,000 in 43 years, which is when he plans to retire (at age 65). He also estimates that in order to live comfortably he will require a yearly income of $80,000 for each year after he retires. Based on his family history, Milhouse expects to live until age 80 (that is, he would like to receive a payment of $80.000 at the end of each year for 15 years). When he retires, Milhouse will purchase his boat in one lump sum and place the remaining balance into an account that pays 6 percent interest, from which he will withdraw his $80,000 per year. If Milhouse's first contribution is made one year from today and his last is made the day he retires, how much money must he contribute each year to his retirement fund? Question 3 Having just inherited a large sum of money, you are trying to determine how much you should save for retirement and how much you can spend now. For retirement, you will deposit today (January 1, 2016) a lump sum in a bank account paying 10 percent compounded annually. You don't plan on touching this deposit until you retire in five years (January 1, 2021), and you plan on living for 20 additional years. During your retirement, you would like to receive a payment of $50,000 on the first day of each year, with the first payment on January 1, 2021, and the last payment on January 1, 2041. Complicating this objective is your desire to have one final three- year fling during which time you'd like to track down all the original cast members of Hey Dude and Saved by the Bell and get their autographs. To finance this, you want to receive $250,000 on January 1, 2036, and nothing on January 1, 2037. and January 1, 2038, because you will be on the road. In addition, after you pass on (January 1, 2041), you would like to have a total of $100,000 to leave to your children. a. How much must you deposit in the bank at 10 percent interest on January 1, 2016, to achieve your goal? (Use a timeline to answer this question. Keep in mind that the last second of December 31 is equivalent to the first second of January 1.) b. What kinds of problems are associated with this analysis and its assumptions