Over the past few​ years, Microsoft founder Bill​ Gates' net worth has fluctuated between​ $20 billion 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 5 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 11 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?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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 Over the past few​ years, Microsoft founder Bill​ Gates' net worth has fluctuated between​ $20 billion 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
5
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
11
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
6
percent. He also wants to make
50
equal annual withdrawals from this retirement fund beginning a year from​ today, running his retirement fund to​ $0 at the end of
50
years. How much can his annual withdrawal be in this​ case?
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