Congratulations! You are the proud winner of the multi-state Sour Ball Lottery.

Question

Congratulations! You are the proud winner of the multi-state Sour Ball Lottery. You are to receive $2,000,000 at the end of each year for the next 20 years. While the Lottery Commission refers to this as a $40,000,000 jackpot, if you choose the "cash option" they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20 annual payments. If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7%, what is your payoff if you select the cash option? 18) A) $21,188,028 B) $26,945,332 C) $39,707,503 D) $42,977,401

Explanation / Answer

Price = P.V. of future payments
Price = 2000000{(1+i)-1 + (1+i)-2 + (1+i)-3 + ... + (1+i)-20} , where i = discount rate,i.e., 0.07
= 2000000*10.594
= $21,188,000

Thus, he receives $21,188,000.

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