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 (ignore taxes)?

Explanation / Answer

Present value of lottery winning receipts P×[1-(1÷(1+r)^n)]÷r Here, 1 Interest rate per annum 7.00% 2 Number of years                                                            20 3 Number of compoundings per per annum                                                              1 4 = 1÷3 Interest rate per period ( r) 7.00% 5 = 2×3 Number of periods (n) 20 Payment per period (P) $                                         2,000,000 Present value of lottery winning receipts                                           21,188,028 2000000*[1-(1/(1+7%)^40)]/7%

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.