Many State Lotteries Have Advertised "Instant Millionaire" Lottery Games A)Since the Winner Will Be Given Actually a Million Dollars

Many state lotteries have advertised "instant millionaire" lottery games. However, if one wins the game, the state does not write a check for a million dollars. Rather it pays $50,000 a year for 20 years. Using the tables shown and assuming the interest rate is 4, which of the following statements must be true? $\begin{array}{|r|l|}\hline\begin{array}{c} \text { Annuity Table } \\ \text { (value now of \$1 Per year To be } \\ \text { received for x-years) } \\\begin{array}{c|c|c|c}\hline {\text { Year }} & \mathbf{3 \%} & \mathbf{4 \%} & \mathbf{6 \%} \\\hline 10 & 8.53 & 8.11 & 7.36 \\\hline 15 & 11.94 & 11.12 & 9.71 \\\hline 20 & 14.88 & 13.59 & 11.47 \\\hline 30 & 19.60 & 17.29 & 13.76 \\\hline\end{array}\end{array}& \begin{array}{c} \text { Present Value Table } \\ \text { (Value now to \$ 1 to be received} \\ \text { x-years un the future) } \\\begin{array}{c|c|c|c}\hline \text { Year } & \mathbf{3} \% & \mathbf{4 \%} & \mathbf{6 \%} \\\hline 10 & 0.74 & 0.68 & 0.53 \\\hline 15 & 0.64 & 0.56 & 0.42 \\\hline 20 & 0.55 & 0.46 & 0.31 \\\hline 30 & 0.41 & 0.31 & 0.17 \\\hline\end{array}\end{array}\\\hline\end{array}$

A) Since the winner will be given actually a million dollars over 20 years, the state is correct in advertising these games as "instant millionaire."
B) If the winner invests his annual payout, at the end of 20 years he will have a lot more than a million dollars. Hence the state is understating the winnings when it advertises these games as "instant millionaire."
C) The true value of winning is much less than a million. The state has misrepresented the true value of the payout.
D) The state does not care whether it gives a million as a lump sum or spread over 20 years.