Please answer parts a, b, and c.

Lottery. Your dreams of becoming rich have just come true. You have won the State of Tranquility's Lottery. The State offers you two payment plans for the $2,000,000 advertised jackpot. You can take annual payments of $40,000 at the end of the year for the next 50 years or $361,666 today. a. If your investment rate over the next 50 years is 13%, which payoff will you choose? b. If your investment rate over the next 50 years is 9%, which payoff will you choose? c. At what investment rate will the annuity stream of $40,000 be the same as the lump-sum payment of $361,666? a. If your investment rate over the next 50 years is 13%, what is the present value of the $40,000 annual payments today? $ (Round to the nearest dollar.)