12. 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 $80,000 ot the end of the year for the next 25 years or $673,740 today. a. If your investment rate over the next 25 years is 12%, which payoff will you choose? b. If your investment rate over the next 25 years is 9%, which payoff will you choose? c. Al what investment rate will the annuity stream of $80,000 to the same as the lump-sum payment of $873,7407 If your investment rate over the next 25 years in 12%, what is the present value of the $80,000 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 3673,740 today because its present value is higher OB. Choose the lump-sum payment of 5673,740 today because its future value is lower OC. Choose the annual payments of $80,000 for the next 25 years because its present value is higher OD. Choose the annual payments of $80,000 for the next 25 years because its future value is lower b. If your investment rate over the next 25 years is 9%, what is the present value of the $80,000 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 $673.740 today because its present value is higher O B. Choose the lump sum payment of $673.740 today because its future value is lower OC. Choose the annual payments of $80,000 for the next 25 years because its future value is lower OD. Choose the annual payments of $80,000 for the next 25 years because its present value is higher c. At what investment rate will the annulty stream of $80,000 be the same as the lump-sum payment of $673,740? % (Round to two decimal places)