5-41A. (Comprehensive present value) You have just inherited a large sum of money, and 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 Ganuary 1,2004) 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 Ganual)'

1, 2009), and you plan on living for 20 additional years and then to drop dead on December 31, 2028. 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, 2009, and the last payment on January 1, 2028. 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 Leave It to Beaver and The Brady BU1U:h and get their autographs. To finance this, you want to receive $250,000 on January 1, 2024, and nothing onJanual)' 1, 2025 and January 1, 2026, because you will be on the road. In addition, after you pass on Ganuary 1, 2029), 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 on January 1, 2004, to achieve your goal? (Use a time line to answer this question.)

b. What kinds of problems are associated with this analysis and its assumptions?