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William and James are twin brothers aged 65.
1. William and James are twin brothers aged 65. Thirty-five years ago (at the end of the year when he reached age 30), William started an IRA (individual retirement account), putting $2,000 per year in the account at the end of each year. After 10 years of contributions, William stopped making new deposits but left the accumulated contributions in the IRA fund. The fund produced returns of 10 percent per year. No taxes are paid. James started his own IRA at the end of the year when he reached age 40 (25 years ago) and contributed $2,000 per year, making his last contribution today. Thus James invested 2½ times as much as William. James also earned 10 percent on his investments (tax free).
a) What are the values of William's and James' IRA funds today?
b) What personal finance lesson does this exercise suggest?
2. On her 20th birthday, Ima Tiger invests $3,000 in an IRA (Individual Retirement Account) that earns 8 percent per year. She continues to invest $3,000 on each birthday for the next 49 years. How much money will she have at age 69?
3. Columbia University is considering the purchase of one of two alternative Zambonis for Baker Rink to replace one of its failing Zambonis. The first Zamboni costs $58,000, lasts for nine years and has annual maintenance costs (paid at the end of the year) of $20,000 for each of the nine years. It would then have zero salvage value and would be given away at the end of the ninth year to the Harlem Globetrotter Ice Hockey Program as an attempt to improve town relationships. (It is assumed that the Zamboni would then be replaced, with the $58,000 payment for the new machine also made at the end of the ninth year.) The second Deluxe Zamboni costs $179,950, lasts for 10 years and is essentially maintenance free, requiring just $1,000 per year of maintenance at the end of each of the 10 years (provided the Zamboni driver does not crash the machine into the boards). It would also be given away at the end of 10 years and replaced at that time. The opportunity cost of funds for Columbia University is 10 percent. Which Zamboni should Columbia buy? Show all work. N.B. Round all numbers in present value tables to nearest tenth. This will make a part of the problem come out evenly.
