Questions: (Solving a comprehensive problem) Over the past few years, Microsoft founder Ball Gates' net worth has fluctuated between 20 billion and 130 billion. In early 2023, it was about 106 bilion-atter he reduced his stake in Microsoft from 21 percent to around 14 percent by moving bilions into his charitable foundation. Lets see what Ball 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, 397 years later in 2023, Bill Gates wants to buy the island from the "current natives". How much would Bal have to pay for Manhattan if the "current natives" want an annual return of 5 percent on the original 24 purchase price? b. Bar Gates decides to pass on Manhattan and instead plans to buy the city of Seattle, Washington, for 50 bilion in 9 years. How much would Bal have to invest today at 9 percent compounded annually in order to purchase Seattle in 9 years? c. Now, assume Bal Gates wants to invest only about 12 percent of his net worth, which stood at around 106 bilion in 2023, or 13 bilion, in order to buy Seattle for 50 bilion in 9 years. What annual rate of return would he have to earn in order to complete his purchase in 9 years? d. Instead of buying and running large cities, Ball Gates is considering quitting the rigors of the business world and retiring to work on his golf game. To fund his retirement, Ball would invest his 20 bifion 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?

Transcript text: (Solving a comprehensive problem) Over the past few years, Microsoft founder Ball Gates' net worth has fluctuated between $20 billion and $130 billion. In early 2023, it was about $106 bilion-atter he reduced his stake in Microsoft from 21 percent to around 14 percent by moving bilions into his charitable foundation. Lets see what Ball 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, 397 years later in 2023, Bill Gates wants to buy the island from the "current natives". How much would Bal have to pay for Manhattan if the "current natives" want an annual return of 5 percent on the original $24 purchase price? b. Bar Gates decides to pass on Manhattan and instead plans to buy the city of Seattle, Washington, for $50 bilion in 9 years. How much would Bal have to invest today at 9 percent compounded annually in order to purchase Seattle in 9 years? c. Now, assume Bal Gates wants to invest only about 12 percent of his net worth, which stood at around $106 bilion in 2023, or $13 bilion, in order to buy Seattle for $50 bilion in 9 years. What annual rate of return would he have to earn in order to complete his purchase in 9 years? d. Instead of buying and running large cities, Ball Gates is considering quitting the rigors of the business world and retiring to work on his golf game. To fund his retirement, Ball would invest his $20 bifion 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?