A lottery winner must choose between receiving $1,500,000 in 40 years or $5,000 today. If the applicable discount rate is 12%, which option should the winner choose?
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- As the winner of a lottery you are promised 15 payments of $0.98 million each year starting a year from now. If the discount rate is 0.095, what is the present value of your winnings? Instruction: Type ONLY your numerical answer in the unit of millions,Suppose a state lottery prize is to be paid in 25 payments of $360,000 each at the end of each of the next 25 years. (a) What is the total of all payments received (the advertised value of the lottery prize)? (b) Instead of receiving annual payments, the winner opts to receive a single payment today equal to the present value of the prize. Find the amount of today's payment if: (Round your answer to the nearest cent.) interest is 8% $ interest is 12% $lottery winner has a decision between a lump sum of $1,000,000 or a 20 year annuity of $100,000 paid at the end of each of the next 20 years. If the lottery winner could invest or borrow funds at an annual effective interest rate of 5%, which alternative would be preferred and by how much in present value?
- Please do the following questions with full workingYou win the lottery and are offered the following choices. The appropriate discount rate is 7%. How much is each worth? Which would you choose? a. $3M today and $3M exactly 3 years from today b. $2M a year for 4 years, with the first payment starting exactly one year from today c. $350K a year forever, with the first payment starting one year from todayYou are the lucky winner of the $30 million state lottery. You can take your prize money either as (a) 30 payments of $1 million per year (starting in one year), or (b) $15 million paid today. If the interest rate is 5.5%, which option should you take? Select one: a. Option a, as it is equivalent to 15 333 101 $ b. Option a, as it is equivalent to 15 141 074 $ c. Option b d. Option a, as it is equivalent to 15 372 451 $
- The top prize for the state lottery is $115,700,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $115,700,000 in 25 equal payments of $4,628,000—one payment today and one payment at the end of each of the next 24 years. If you choose the cash payment, you will receive a one-time lump sum payment of $53,355,093.34. If you can invest the proceeds and earn 9 percent, which option should you choose? (Round factor values to 3 decimal places, e.g. 1.521.) Lump sum paymentAnnual paymentYou have just received notification that you have won the $1.25 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, 79 years from now. The appropriate discount rate is 6.4 percent. What is the present value of your winnings?The lottery commission is offering the winner of a recent jackpot a payout of 15 yearly payments $209,000 with the first payment occurring one year from today. As an alternative, the commission would also like to offer the winner (and their heirs) a series of yearly payments every year in perpetuity, again with the first payment occurring one year from today. If the commission uses a discount rate of 5%, what payment should the commission offer in the second option in order to make the two options equivalent in present value terms? Enter your answer as a positive number and round to the nearest dollar.
- The top prize for the state lottery is $105,000,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $105,000,000 in 20 equal payments of $5,250,000—one payment today and one payment at the end of each of the next 19 years. If you choose the cash payment, you will receive a one-time lump sum payment of $63,830,111.58. You can invest the proceeds and earn 7%. At what interest rate would you be indifferent between the cash and annual payment options? (Round factor values to 3 decimal places, e.g. 1.521 and final answer to 0 decimal places, e.g. 15%.)Click here to view the PV Table. Interest rate %Assume you win a lottery that will pay you $10,000 immediately, plus $20,000 one year from now, $30,000 two years from now, $40,000 three years from now, and $75,000 four years from now. You’re curious about how much the lottery commission might offer you as an immediate lump sum instead. What is the minimum amount you should consider accepting today instead? Use a 5% annual discount rate. Please remember that we are ignoring taxation and other considerations and basing this only on the math itself.The top prize for the state lottery is $105,704,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $105,704,000 in 25 equal payments of $4,228,160—one payment today and one payment at the end of each of the next 24 years. If you choose the cash payment, you will receive a one-time lump sum payment of $57,293,079.68. At what interest rate would you be indifferent between the cash and annual payment options? (Round answer to 0 decimal places, e.g. 15%.) Interest rate %
