Your dream of becoming rich has just come true you have won the state of tranquillities lottery the state offers you two payment plans for the $$5$ million jackpot you can take annual payments of $$250,000$ for the next $20$ years or $$2,867,480$ today if you investment rate over the next $20$ years is $8\%$ which payoff will you choose if your investment rate over the next $20$ years is $5\%$ which payoff will you choose at what investment rate will the annuity stream of $250,000$ be the same as the lump sum payment of $2,867,480$