Is this correct? Why or why not? Your dream of becoming rich has just...
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Is this correct? Why or why not?
Your dream of becoming rich has just come true. You have won the State of Tranquilitys 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.
a. If your investment rate over the next 20 years is 8%, which payoff will you choose?
b. If your investment rate over the next 20 years is 5%, which payoff will you choose?
c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?
Answers:
a. For the annuity payment plan: Present Value = CF * [(1 - (1 + r) ^ -n) / r] $2,769,115.84 Present Value = $250,000 * [(1 - (1 + 0.08) ^ -20) / 0.08] = $2,867,480
b. Present Value of annuity payments = $250,000 * [(1 - (1 + 0.05) ^ -20) / 0.05] $3,639,238.89
c. $250,000 * [(1 - (1 + r) ^ -20) / r] = $2,867,480 [(1 - (1 + r) ^ -20) / r] = $2,867,480 / $250,000 [(1 - (1 + r) ^ -20) / r] = 11.46992 r = 4.59%.
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