Congratulations! You just won a very special kind of lottery. Instead of receiving a large lump...
Question:
Congratulations! You just won a very special kind of lottery. Instead of receiving a large lump sum now, for tax reasons this lottery makes equal yearly payments of $5,760 for the rest of your life! The only catch is that you have to wait 2 years for the first payment. What is the present value of this lottery prize? The annual rate of interest is 8%.
Perpetuity:
Investors purchase perpetuity plans to stabilize their prospective income and ensure constant earnings during their lifetime. Perpetuity calculation helps make a good retirement plan that allows the retired individual to earn money forever.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerCalculation using the present value of delayed perpetuity formula and present value factor:
{eq}\begin{align*} {\rm\text{Present Value}} &=...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.
Related to this Question
- Congratulations! You just won a very special kind of lottery. Instead of receiving a large lump sum now, for tax reasons this lottery makes equal annual payments of $ 2860 for the rest of your life! The only catch is that you have to wait to start receivi
- You just won a very special kind of lottery. Instead of receiving a large lump sum now, for tax reasons this lottery makes equal yearly payments of $4,539 for the rest of your life! The only catch is that you have to wait 3 years for the first payment. Wh
- You have won $386 million in the Mega lottery, to be paid out in 20 equal yearly installments. You are offered a lump sum payment instead. If your required rate of return is 6.2%, how large does the lumpsum have to be for you to take it over the yearly pa
- You just won the lottery. Congratulations! The jackpot is $85,000,000, paid in four equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won ..................................... assuming a
- You just won the lottery. Congratulations! The jackpot is $60,000,000, paid in 12 equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won _____ assuming annual interest rate of 6.50%.
- You just won the lottery. Congratulations! The jackpot is $60,000,000, paid in three equal, annual payments. The first payment on the lottery jackpot will be made today. In PV terms, how much did you really win? Use an annual interest rate of 11.00%
- You have just won the lottery. The lottery board offers you three different options for collecting your winnings: (i) You will receive payments of $500,000 at the end of each year for twenty years. (ii) You will receive a lump-sum payment of $4,500,000 to
- You've just won the Ohio Lottery's $100 million jackpot. You can either receive a sum payment of $50 million today or equal installments of $3,333,333 each year for the next 30 years. You believe you can invest any money received at 10% annualized returns
- You just won a lottery that will pay you $2,500 a year for twenty years. You will receive your first payment today. If you can earn 8 percent on your money, what are your winnings worth to you today? (Note that since you will receive your first payment to
- A state lottery gives a winner the choice of receiving the winning amount in equal monthly payments for 20 years or receiving a lump sum equal to the present value of an annuity with future value equa
- You have just won $110,000 from a lottery. If you invest all this amount in a tax-free money market fluid earning 8% compounded weekly, how long do you have to wait to become a millionaire?
- You win the Mightyball lottery, which promises a "$1 million" payout - yippeel But, there's a catch - your winnings will be paid as an annuity at a rate of $50,000 per year for 20 years, with the first payment beginning immediately. Alternatively, you may
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $510,000 per year. Thus, in one year you receive $1.51 million. In two years, you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $670,000 per year. Thus, in one year, you receive $1.67 million. In two years you get $
- Justice wins the lottery. He wins $20,000 per year to be paid to him for 10 years. The state offers him the choice of a cash settlement now instead of the annual payments for 10 years. If the interest rate is 6 percent, what is the amount the state will o
- You have won a small lottery of $1,000,000. However, instead of a lump sum amount, the lottery will pay you $50,000 per year for 20 years. If interest is 4%, what is the present value of your winnings, assuming payments are received at the end of each yea
- You hit the jackpot! The prize money is $900 million now in a lump sum, which, you have been told, is worth $1.3 billion in 30 years. Suppose no tax is involved. Determine the effective annual compoun
- You just won the California State Lottery. The amount awarded is paid in 20 equal annual installments at the beginning of each year. You can invest your money at 6.6%, compounded annually. You have calculated that the lottery is worth $20,975,400 today. H
- Congratulations! You have won the lottery! Would you rather have $1 million at the end of each of the next 21 years or $8.82 million today? (Assume a discount rate of 11%.) The present value, PV, of the $1 million at the end of each of the next 21 years i
- You have just won the lottery and received $ 10,000. You deposited your winnings into an account that pays 7.5% inerest compounded annually. How long will you have to wait until your winnings are wort
- Consider a lottery that pays to the winner an annuity of $150 that begins at the end of the first year and continues at the end of each consecutive year for a total of 6 years with one exception. Beca
- Consider a lottery that pays to the winner an annuity of $700 that begins at the end of the first year and continues at the end of each consecutive year for a total of 8 years with one exception. Beca
- You just won the lottery! Would you rather be given $2,500,00 right now or $500,000 per year for 6 years, assuming an 8% discount rate? Assume you are paid the installments at the end of the year.
- You just won $100,000 on a scratch-off lottery ticket. You plan to save the money in a retirement account expected to return 8% annual interest per year. If you intend to retire in 45 years, how much are these lottery winnings expected to be worth when yo
- You are the lucky winner of a $50 million state lottery. You decide to take your prize money as 10 payments of $5 million per year (starting today). If the interest rate is 8%, what is the present value of your prize money? a) $31.28 million b) $33.55 m
- You just won a lottery of $1,000,000. The lottery payment is made in the form of an annuity due with the first payment made today. The lottery pays $10,000 every month for 100 months (8 years and 4 months). If the proper discount rate is 4% per year, what
- A $1,000,000 state lottery prize is spread evenly over 10 years ($100,000 a year), or you may take a lump sum distribution of $654,000. If you can earn 7 percent interest, which alternative is better?
- You have just received that you have won the $2 million first prize in the lottery. However, the prize will be awarded on your 100th birthday (assuming you're around to collect) 73 years from now. What is the present value of your windfall, if the appropr
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years, and the payments will increase 2.5% per year. If the appropriate discount rate is 6.5%, w
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 35 years and the payments will increase by 2.1% per year. If the appropriate discount rate is 6.1%,
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 35 years and the payments will increase 2.4 per cent per year. If the appropriate discount rate is
- You have just won the lottery and received $10,000. You deposited your winnings into an account that pays 7.5 % interest compounded annually. How long will you have to wait until your winnings are wor
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years and the payments will increase by 3.9 percent per year. If the appropriate discount rate i
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 25 years and the payments will increase by 3.5 percent per year. If the appropriate discount rate i
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 25 years and the payments will increase 3.2 percent per year. If the appropriate discount rate is 7
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 25 years and the payments will increase by 2 percent per year. If the appropriate discount rate is
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $660,000 per year. Thus, in one year you receive $1.66 million. In two years, you get $
- You have just won the lottery and received $10,000. You deposited your winnings into an account that pays 7.5 percent interest compounded annually. How long will you have to wait until your winnings are worth $15,000?
- Thaddeus won the lottery, $250 million was the grand prize which will be paid in equal installments over the next 25 years (so 25 payments of $10 million per year, starting today). He also has the option to take a lump sum immediately which will be calcul
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $590,000 per year. Thus, in one year you receive $1.59 million. In two years, you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $610,000 per year. Thus, in one year, you receive $1.61 million. In two years you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $560,000 per year. Thus, in one year, you receive $1.56 million. In two years you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $650,000 per year. Thus, in one year, you receive $1.65 million. In two years, you get
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $630,000 per year. Thus, in one year you receive $1.63 million. In two years, you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $550,000 per year. Thus, in one year you receive $1.55 million. In two years, you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $690,000 per year. Thus, in one year, you receive $1.69 million. In two years you get $
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments that increase by $350,000 per year. Thus, in one year you receive $1.35 million. In two years, you get $
- Sally has won the grand prize in a lottery and must choose between the following three options: A. Receive a lump sum payment of $10,000,000. B. Receive annual end-of-year payments of $2,000,000 for the next 8 years. C. Receive annual end-of-the year pay
- You win your state lottery. The lottery officials offer you the option of taking your winnings in one lump-sum payment, or fixed annual payments for the next 20 years. The sum of the 20 annual payments is larger than the lump-sum payment. Before deciding,
- You just won the lottery. You and your heirs will receive $40,000 per year forever, beginning one year from now. If the present value of the lottery is $500,000, what is the discount rate used to valu
- You recently won the lottery for $100,000,000 and found out that they will pay you $5,000,000 per year for 20 years. Assume that the payments will be made to a tax shelter that you had previously set
- You just won the lottery. You won $5,000 per week for the rest of your life. You're 25 and you expect to live to 95. At a 10% annual interest rate, what is the value of the lottery? a. $600 K. b. $2.6 M. c. $4.2 M. d. $18.2 M.
- Most government lotteries pay out jackpots in the form of a twenty or thirty-year annuity, but they also give winners the option to collect their winnings as a much smaller lump sum. Explain how you w
- If you receive a $4,950 tax refund, bonus, or another lump sum of money, how much will it be worth in 25 years if you invest it today at 5% interest compounded annually? (Do not round intermediate cal
- A lottery claims its grand prize is $10 million, payable over 20 years at $500,000 per year. If the first payment is made immediately, what is this grand prize really worth? Use a discount rate of 6%.
- You just won the Powerball, as a result you have the choice between taking $250 million today or taking a 20-year annuity. Interest rates are expected to hold at 3.75% over the next 20 years. How much would the annuity need to be annually for you to be in
- Play-2-Win is the latest lottery game in your country, and you happen to be the latest winner of $10.5 million. Your government has a guarantee on the funds and will not be paid before 3 years from to
- Play-2-Win is the latest lottery game in your country, and you happen to be the latest winner of $2.5 million. Your government has a guarantee on the funds and will not be paid before 10 years from to
- A lottery claims its grand prize is $15 million, payable over 5 years at $3,000,000 per year. If the first payment is made immediately, what is the grand prize real worth? Use an interest rate of 7%.
- You just won the lottery. As your prize, you will receive $1,500 a month for 150 months. If you can earn 7 percent, compounded monthly, on your money, what is this prize worth to you today?
- The Florida lottery agrees to pay the winner $256,000 at the end of each year for 20 years. What is the future value of this prize if each payment is put in a account earning 10%?
- Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum payout, you get $2,950 today. If you pick the payments over time payout, you
- You win a lottery with a prize of $1.5 million. Unfortunately the prize is paid in 10 annual installments. The first payment is next year. How much is the prize really worth? The discount rate is 8 percent.
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 35 years and the payments will increase by 2.7 percent per year. If the appropriate discount rate is 6.7 percent, what is the present value of your winnin
- Sue wins the lottery. The State of Florida offers her $134,351 a year for 20 years as her prize. She also has the option of accepting a lump sum payment now. What is the present value of the yearly p
- You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. If the present value of the lottery is $416,667, what is the discount rate used to value this perpetuity?
- The Florida lottery pays out winnings, after taxes, on the basis of 20 equal annual installments, providing the first installment at the time that the winning ticket is turned in. a. What type of cash flow pattern is the distribution of lottery winnings?
- You win a lottery, with a prize of $1.5 million. Unfortunately, the prize is paid in 10 annual installments. The first payment is next year. How much is the prize really worth? The discount rate is 8%
- You just won $100,000 on a scratch-off lottery ticket. You plan to save the money in a retirement account expected to return 7% per year. If you intend to retire in 45 years, how much are these lottery winnings expected to be worth when you retire? $2, 1
- Suppose the Texas lottery advertises that it pays its winner $10 million. However, this prize money is paid at the rate of $500,000 each year (with the first payment being immediate) for a total of 20
- Sarah just won a $3,000,000.00 lottery. According to the lottery, they will pay her a lump sum of $500,000.00 on October 1, 2012 and the balance in equal annual installments for 10 years. Assuming tha
- You have won this week's lottery jackpot of $200 million. You have the option of receiving the jackpot in 25 annual payments of $8 million starting today or receiving a lump sum today. If the appropriate annual interest rate is 6%, the value of the lump s
- Assume that you just won $260 million in the Mega-Millions lottery, and hence the state will pay you 20 annual payments of $103 million each beginning immediately. If the rate of return on securities of similar risk to the lottery earnings (e.g., The rate
- You have just paid $20 million in the secondary market for the winning Powerball lottery ticket, The prize is $2 million at the end of each year for the next 25 years. If your required rate of return is 8%, what is the net present value (NPV) of the deal?
- Suppose you just won a $10 million lottery jackpot. How can TVM help you decide whether to take the lump sum one-time payment for $5 million or be paid the entire $10 million over the course of 15 yea
- You just won $100,000 on a scratch-off lottery ticket. You plan to save the money in a retirement account expected to return 8% interest per year with interest paid monthly. If you intend to retire in 45 years, how much are these lottery winnings expected
- The lottery's million-dollar payout provides $1 million to be paid over 19 years in 20 payments of $50,000. The first $50,000 is paid immediately, and the remaining 19 $50,000 dollar payments occur at the end of each of the next 19 years. a) If 10%is the
- You can receive lottery winnings of either $800,000 now or $100,000 per year for the next 10 years. If your interest rate is 5 % per year, which do you prefer?
- You won the lottery, you are going to get paid 23 annual payments, starting today that adds up to $40,443,585. Using a 0.05 discount rate how much did you really win?
- You have just won the lottery and will receive dollar 1,000,000 in one year. You will receive payments for 35 years and the payments will increase 2.1 percent per year. If the appropriate discount rate is 6.1 percent, what is the present value of your win
- Jane Bauer has won the lottery and has the following four options for receiving her winnings: 1. Receive $100,000 at the beginning of the current year 2. Receive $108,000 at the end of the year 3. Receive $20,000 at the end of each year for eight years 4.
- A state's lottery winner is promised $200,000 a year for twenty years (starting at the end of the first year). How much must the state invest now to guarantee the prize if the state can earn annually
- You just won the TVM Lottery. You will receive $100,000 today plus another four years of (7%) semiannual payments that increase by $15,000 per payment. Thus, you will receive the first semiannual paym
- Winners of the Georgia Lotto drawing are given the choice of receiving the winning amount divided equally over 19 years or as a lump-sum cash option amount. The cash option amount is determined by discounting the annual winning payment at 6% over 19 years
- You have just won the lottery and will receive $570,000 in one year. You will receive payments for 29 years, which will increase 3 percent per year. The appropriate discount rate is 11%. What is the present value of your winnings?
- You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years, which will increase 3% per year. If the appropriate discount rate is 7%, what is the pres
- You have just won lottery of 11,000,000. Your winnings will be paid to you in 26 equal installments with the first payment made immediately. If you had the money now you could invest it in an account
- Assume that you just won the state lottery. Your prize can be taken either in the form of $40,000 at the end of each of the next twenty-five years (i.e., $1 million over twenty-five years) or as a lump sum of $500,000 paid immediately. a. If you expect t
- You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments t... You just won the TVM Lottery. You will receive $1 million today plus another 10 annual payments tha
- You just won the million-dollar lottery- you will receive $50,000 per year for 20 years. Assuming your personal discount rate is 5%, what is the PV of what you just won?
- You just won the lottery, which promises you $200,000 per year for the next 20 years. You receive the first payment today (hint: annuity due). If your discount rate is 9.25%, what is the present value
- You have just won the Strayer Lottery jackpot of $11,000,000. You will be paid in 26 equal annual instalments beginning immediately. If you had the money now, you could invest it in an account with a quoted annual interest rate of 9% with monthly compound
- Assume that you just won the state lottery. Your prize can be taken either in the form of $42,000 at the end of each of the next 25 years (i.e., $1.05 million over 25 years) or as a lump sum of $490,0
- Your grandfather won a lottery years ago. The value of his winnings at the time was $50,000. He invested this money such that it will provide annual payments of $2,400 a year to his heirs forever. What is the percentage of rate of return?
- The Florida lottery agrees to pay the winner 243000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 0.07?
- The Florida lottery agrees to pay the winner $242,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put into an account earning 0.07?
- The Florida lottery agrees to pay the winner $261,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 0.08?
- The Florida lottery agrees to pay the winner $249,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 0.08?
- The Florida lottery agrees to pay the winner $281,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 0.07?
- The Florida lottery agrees to pay the winner $247,000 at the end of each year for the next 20 years. What is the future value of this prize if each payment is put in an account earning 0.08?