Question

Q 29,30,32,34,35

e present value of the cash flows? Sent is the discutate, what is the present value of 000 payments the end of each of the next 19 flows? If 20 percent is the discount at what is the recent value of the discount rate, what is the value of this stream of 6-29. Calculating the future value of an an t he future value of an an that pays 8.000 a year for 10 years at 6 percent compounded annually will be the future value if it was compounded at 10 percent 6-30. Calculating the present value of an annuity dual What will be the presenta annuity due of £800 a year for 12 years. di t hack to the present at an anno rate of 5 percent? What will be the most value of this nuity of the discount Il be the present value of an 8 percent? 6-31. (Calculating the present value of annuity You have agreed to invest in a no ness scheme that has promised to pay Year S from now, assuming it ears very year starting at the end of t the same amount each year for 10 years on . This will continue to of this business opportunity be? dared What will the present 6–32. (Calculating the (Calculating the components of an annuity payment) You have just bought a house for €270.000 by taking a 20-year montage for the same amount at 8 percent per a num payable in monthly installments What will your monthly payments be? Use a spreadsheet to calculate your answer. Now calculate the amounts in the 50th monthly payment that goes toward interest and principal, respectively. 6-33. (Solving a comprehensive problem) 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, 390 years later in 2016, Bill Gates wants to buy the island from the current natives." How much will Bill have to pay for Manhattan if the current natives" want a 6 percent annual return on the original S24 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 will Bill have to invest today at 10 percent compounded annually in order to purchase Seattle in 10 years? c. Now assume Bill Gates wants to invest only about 17 percent of his net worth, which stood at around $76 billion in 2016, or $13 billion, in order to buy Seattle for $50 billion in 10 years. What annual rate of return will 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 wants to 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 an- nual 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 with drawal be in this case? 6-34. (Calculating annuity payments) (Related to Checkpoint 6.1 on page 196) Sheryl Williams wants to have a million dollars when she retires, 40 years from now. She is planning to do this by depositing an equal amount at the end of every year for the next 40 years. If her tax-free savings account pays her 9 percent per annum, how much does she need to deposit every year? Pallating the present value of annuity) (Related to Checkpoint 6.2 on na 190 Xiang Lu received €80,000 four years as an inheritance, which he immediately deposited in an account paying him 5 percent every year. Now he has started to in €3,000 every year in the same account, starting now. How much money will be have at the end of 25 years? 6-35.

Answer 1

29.
Future value at 6%=8000/6%*(1.06^10-1)=105446.3595

Future value at 10%=8000/10%*(1.1^10-1)=127499.3968

30.
Present value at 5%=800/5%*(1-1/1.05^12)*1.05=7445.131375

Present value at 8%=800/8%*(1-1/1.08^12)*1.08=6511.171407

32.
Monthly payments=PMT(8%/12,12*20,-270000)=2258.39

Interest=FV(8%/12,49,2258.39,-270000)*8%/12=1623.59517

Principal=2258.39-1623.59517=634.79483

34.
=1000000*9%/(1.09^40-1)=2959.609221

35.
=80000*1.05^29+3000/5%*(1.05^25-1)*1.05=479631.2089