3. A business is considering purchasing a machine that is projected to yield cash, savings of $1,000 per ear over a 10-year period. Using a 12 percent discount rate, calculate the present value of the savings (Assume that the cash savings occur at the end of each year) 4. Yolanda William is 35 years old today and is beginning to plan for her retirement. She wants to set aside an equal amount at the end of each of the next 25 years so that she can retire at age 60. She expects to live to an age of 80 and wants to be able to withdraw $50,000 per year from the account on har 61M through 80th birthdays. The account is expected to eam 10 percent per year for the entire period of time. Determine the size of the annual deposits that she must make 5. How much must you deposit at the end of each year in an account that pays a nominal annual rate of 20 percent, if at the end of five years you want $10,000 in the account? 6. A leading broker has advertised money multiplier certificates that will triple your money in nine years, that is, if you buy one for $333 33 today, it will pay you $1.000 at the end of nine years. What rate of retum will you earn on these money multiplier certificates? 7. Your great-uncle Claude is 82 years old. Over the years, he has accumulated savings of $80,000. He estimates that he will live another 10 years at the most and wants to spend his savings by then. (If he lives longer than that, he figures you will be happy to take care of him) Uncle Claude places his $80,000 into an account earning 10 percent annually and sets it up in such a way that he will be making 10 equal withdrawals the first one occurring one year from now such that his account balance will be zero at the end of 10 years. How much will he be able to withdraw each year? 8. Jim Nance has been offered a future payment of $500 three years from today. If his opportunity cost is 798 compounded annually, what value should he place on this opportunity today? What is the most he should pay to purchase this payment today