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, 2013) 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, 2018), and you plan on living for 20 additional years. During your retirement, you would like to receive income of $50,000 per year to be received the first day of each year, with the first payment on January 1, 2018, and the last payment on January 1, 2037. 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 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, 2033, and nothing on January 1, 2034, and January 1, 2035, because you will be on the road. In addition, after you pass on (January 1, 2038), 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, 2013, to achieve your goal? (Use a timeline to answer this question. Keep in mind that the last second of December 31st is equivalent to the first second of January 1st.)
b. What kinds of problems are associated with this analysis and its assumptions?