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 $1,000,000 advertised jackpot. You can take annual payments of $20,000 at the end of the year for the next 50 years or $198,296 today. a. If your investment rate over the next 50 years is 11%, 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 $20,000 be the same as the lump-sum payment of $198,296? a. If your investment rate over the next 50 years is 11%, what is the present value of the $20,000 annual payments today? $ (Round to the nearest dollar.) Which payoff will you choose? (Select the best response.) O A. Choose the lump-sum payment of $198,296 today because its future value is lower. O B. Choose the annual payments of $20,000 for the next 50 years because its present value is higher. O C. Choose the annual payments of $20,000 for the next 50 years because its future value is lower. OD. Choose the lump-sum payment of $198,296 today because its present value is higher. b. If your investment rate over the next 50 years is 9%, what is the present value of the $20,000 annual payments today? $ (Round to the nearest dollar.) Which payoff will you choose? (Select the best response.) O A. Choose the annual payments of $20,000 for the next 50 years because its present value is higher. O B. Choose the annual payments of $20,000 for the next 50 years because its future value is lower. OC. Choose the lump-sum payment of $198,296 today because its future value is lower. OD. Choose the lump-sum payment of $198,296 today because its present value is higher. Click to select your answer(s)