Chapter 5, Problem 62SP

(Future and present value using a calculator) In 2016 Bill Gates was worth about $82 billion. Let’s see what Bill Gates can do with his money in the following problems.

1. a. I’ll take Manhattan? Manhattan’s native tribe sold Manhattan Island to Peter Minuit for $24 in 1626. Now, 393 years later in 2019, Bill Gates wants to buy the island from the “current natives.” How much would Bill have to pay for Manhattan if the “current natives” want a 6 percent annual return on the original $24 purchase price?
2. b. (Nonannual compounding using a calculator) How much would Bill have to pay for Manhattan if the “current natives” want an APR of 6 percent compounded monthly on the original $24 purchase price?
3. c. Microsoft Seattle? Bill Gates decides to pass on Manhattan and instead plans to buy the city of Seattle, Washington, for $100 billion in 10 years. How much would Mr. Gates have to invest today at 10 percent compounded annually in order to purchase Seattle in 10 years?
4. d. Now assume Bill Gates wants to invest only about half his net worth today, $41 billion, in order to buy Seattle for $100 billion in 10 years. What annual rate of return would he have to earn in order to complete his purchase in 10 years?
5. e. Margaritaville? Instead of buying and running large cities, Bill Gates is considering quitting the rigors of the business world and retiring to work on his golf game. To fund his retirement, Bill Gates would invest his $82 billion fortune in safe investments with an expected annual rate of return of 7 percent. Also, Mr. Gates wants to make 40 equal annual withdrawals from this retirement fund beginning a year from today. How much can Mr. Gates’s annual withdrawal be in this case?