Suppose you win a raffle held at a county fair and are given the choice between two different ways to be paid. You can either accept the money in a lump sum immediately or in a series of payments over time. If you choose the lump sum payout, you receive $$3,100$ today. If you choose to collect payments over time, you receive three payments: $$1,000$ today, $$1,0001$ year from today, and $$1,0002$ years from today.

At an interest rate of $7\%$ per year, the winner would be better off accepting the value. $,$ since that choice has the greater present

At an interest rate of $9\%$ per year, the winner would be better off accepting the payments over time grad, since it has the greater present value.