# Question

Over the past few years, Microsoft founder Bill Gates’s net worth has fluctuated between $20 and $130 billion. In early 2006, it was about $26 billion—after he reduced his stake in Microsoft from 21 percent to around 14 percent by moving billions into his charitable foundation. Let’s see what Bill Gates can do with his money in the following problems.

a. Manhattan’s native tribe sold Manhattan Island to Peter Minuit for $24 in 1626. Now, 387 years later in 2013, 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?

b. Bill Gates decides to pass on Manhattan and instead plans to buy the city of Seattle, Washington, for $50 billion in 10 years. How much would Bill have to invest today at 10 percent compounded annually in order to purchase Seattle in 10 years?

c. Now assume Bill Gates only wants to invest half his net worth today, $13 billion, in order to buy Seattle for $50 billion in 10 years. What annual rate of return would he have to earn in order to complete his purchase in 10 years?

d. 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 would invest his $20 billion fortune in safe investments with an expected annual rate of return of 7 percent. He also wants to make 40 equal annual withdrawals from this retirement fund beginning a year from today, running his retirement fund to $0 at the end of 40 years. How much can his annual withdrawal be in this case?

a. Manhattan’s native tribe sold Manhattan Island to Peter Minuit for $24 in 1626. Now, 387 years later in 2013, 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?

b. Bill Gates decides to pass on Manhattan and instead plans to buy the city of Seattle, Washington, for $50 billion in 10 years. How much would Bill have to invest today at 10 percent compounded annually in order to purchase Seattle in 10 years?

c. Now assume Bill Gates only wants to invest half his net worth today, $13 billion, in order to buy Seattle for $50 billion in 10 years. What annual rate of return would he have to earn in order to complete his purchase in 10 years?

d. 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 would invest his $20 billion fortune in safe investments with an expected annual rate of return of 7 percent. He also wants to make 40 equal annual withdrawals from this retirement fund beginning a year from today, running his retirement fund to $0 at the end of 40 years. How much can his annual withdrawal be in this case?

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