Question 2 You just won the lottery! The jackpot was advertised as $1.5 billion. However, you discover that the $1.5 billion figure is actually the sum of the annuity payments: 30 annual payments of $50 million made at the end of each year. If you want the money as an immediate lump sum, you will only get $930 million.

Part a: Assume the inflation rate is 2%, compounded annually. What is the present value of the annuity payments, discounted for inflation? Is it greater or less than the lump sum offered?

Part b: At what discount rate does the lump sum offered by lottery officials equal the present value of the annuity payments? An approximation is okay here (within 1%).

Part c: Assume that you won't spend any of your lottery winnings for 30 years, regardless of whether you choose lump sum or annuity. Instead, you plan to invest all of your winnings and earn a 10% annual return. Will the future value (at the end of 30 years) be greater with the lump sum, or the annuity? Hint: Calculate the future value in each case and compare. Assume interest compounds annually.