Chapter 5.2, Problem 37E

Lottery Winnings and Risk Analysis. Lucky Larry wins $1,000,000 in a state lottery. The standard way in which a state pays such lottery winnings is at a constant rate of $50,000 per year for 20 yr.

a. If Lucky invests each payment from the state at 4.4%, compounded continuously, what is the accumulated future value of the income stream? Round your answer to the nearest $10.

b. What is the accumulated present value of the income stream 4.4%, compounded continuously? This amount represents what the state has to invest at the start of its lottery payments, assuming the 4.4% interest rate holds.

c. The risk for Lucky is that he doesn’t know how long he will live or what the future interest rate will be; it might drop or rise, or it could vary considerably over 20 yr. This is the risk he assumes in accepting payments of $50,000 a year over 20 yr. Lucky has taken a course in business calculus so he is aware of the formulas for accumulated future value and present value. He calculates the accumulated present value of the income stream for interest rates of 3%, 4%, and 5%. What values does he obtain?

d. Lucky thinks “a bird in the hand (present value) is worth two in the bush (future value)” and decides to negotiate with the state for immediate payment of his lottery winnings. He asks the state for $750,000. They offer $600,000. Discuss the pros and cons of each amount. Lucky finally accepts $675,000. Is this a good decision? Why or why not?