Lottery Ticket

Imagine that you stumble across a winning lottery ticket whose prize is a million dollars. Your first reaction, no doubt, would be to ask how the prize money will be paid out so that you could compute its present value.

1. Suppose it is to be paid out in 10 installments of $100,000 each. If the interest rate is 5%, what is the present value of the prize?
2. Now suppose the lottery commission offers you a choice: the 10 payments in part (1) or $50,000 per year forever. Which is better in terms of present value?
3. What if the stream of payments in part (2) only lasted 30 years instead of forever. What has the highest present value then? Hint: there is an easier way to solve this problem than adding up the present values of 30 payments one at a time.