3: A 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?
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- 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?You are the lucky winner of the Ohio Lottery ! Congratulations. The Lottery tells you that you have won a $20,000,000 prize that will be paid in annual installments of $1,000,000 for 20 years. If interest rates on alternative investments in the market are 8%, what is the actual value (PV) of your prize? Round to the nearest 1,000, and show your work.Jane Bauer has won the lottery and has the following four options for receiving her winnings: Receive $100,000 at the beginning of the current year Receive $108,000 at the end of the year Receive $20,000 at the end of each year for eight years Receive $10,000 at the end of each year for 30 years Jane can invest her winnings at an interest rate of 8% compounded annually at a major bank. Use the appropriate present or future value table: FV of $1, PV of $1, FV of Annuity of $1 and PV of Annuity of $1 Calculate the Present value for each of the above options. Round all answers to the nearest dollar. Present Value Option 1 $fill in the blank 1 Option 2 $fill in the blank 2 Option 3 $fill in the blank 3 Option 4 $fill in the blank 4 Which of the payment options should Jane choose?
- Congratulations! You have just won a $40 million lottery and have electedto receive $2 million per year for 20 years. Assume that a 4 percent interestrate is used to evaluate the annuity and that you receive each payment atthe beginning of the year.a. What is the present value of the lottery?b. How much interest is earned on the present value to make the $2 millionper-year payment?A lottery offers you a choice of $1,000,000 per year for 30 years or a lump-sum payment. What lump-sum payment (rounded to the nearest dollar) would equal the annual payments if the current interest rate is 1.9% compounded annually? (a) State the type. A. amortization B. present value of an ordinary annuity C. future value of an ordinary annuity D.sinking fund E. none of these (b) Answer the question. (Round your answer to the nearest dollar.)A winner of the state lottery was given two choices: receive a single lump sum payment now of $50 million or receive 21 uniform payments, with the first payment to be made now, and the rest to be made at the end of each of the next 20 years. At an interest rate of 4% per year, the amount ofthe 21 uniform payments that would be equivalent to the $50 million lump-sum payment is closest to:a. $3,152,000b. $3,426,800c. $3,623,600d. $3,923,800
- How much would you accept in a lump sum today, in place of a lottery payment of $35,000 at the end of the next 20 years ($700,000 in total), assuming you could invest it at a 6 percent rate?A lottery winner will receive $1 million at the end of each of the next twelve years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 8.1% per year? A. $19.09 million B. $30.54 million C. $26.73 million D. $15.27 million. Lottery Winnings The winner of a “million dollar”lottery is to receive $50,000 plus $50,000 at theend of each year for 19 years or the present valueof this annuity in cash. How much cash wouldshe receive if money is worth 8%, compoundedannually?
- A lottery claims its grand prize is $15 million, payableover five years at $3,000,000 per year. If the firstpayment is made immediately, what is this grand prizereally worth? Use an interest rate of 7%A lottery winner will receive $1 million at the end of each of the next ten years. What is the future value (FV) of her winnings at the time of her final payment, given that the interest rate is 8.5% per year? A. $14.84 million B. $19.95 million C. $18.95 million D. $13.84 millionKA. An individual recently won a lottery and has the opportunity to receive $100,000 per year at the end of the year for the next 25 years. Assuming an annual interest rate of 5% is appropriate, the present value of 1 is 0.29530 × $100,000 = $29,530, the present value of an ordinary annuity is 14.09394 × $100,000 = $1,409,394, and the present value of an annuity due is 14.79864 × $100,000 = $1,479,864. What is the fair value of the lottery payments according to the Financial Accounting Standards Board (FASB)?