Chapter 9 Time Value of Money

Transcription

1 Chapter 9 Time Value of Money Problems 2. Present value (LO9-3) What is the present value of a. $7,900 in 10 years at 11 percent? b. $16,600 in 5 years at 9 percent? c. $26,000 in 14 years at 6 percent? 9-2. Solution: (a) , ,900 Answer: $2, (b) , ,600 Answer: $10, (c) , ,000 Answer: $11,499.83

2 3. Present Value (LO9-3) a. What is the present value of $140,000 to be received after 30 years with a 14 percent discount rate? b. Would the present value of the funds in part a be enough to buy a $2,900 concert ticket? 9-3. Solution: (a) ,000 Answer: $ (b) No. You only have $ If you invest $9,000 today, how much will you have a. In 2 years at 9 percent? b. In 7 years at 12 percent? c. In 25 years at 14 percent? d. In 25 years at 14 percent (compounded semiannually)? 9-5. Solution: (a) 2 9 9,000 0 CPT FV 10, Answer: $10, (b) ,000 0 CPT FV 19, Answer: $19, (c) ,000 0 CPT FV 238, Answer: $238, (d) ,000 0 CPT FV 265, Answer: $265,113.23

3 6. Present value (LO9-3) Your aunt offers you a choice of $20,100 in 20 years or $870 today. If money is discounted at 17 percent, which should you choose? 9-6. Solution: ,100 Answer: $ Present Value (LO9-3) Your uncle offers you a choice of $105,000 in 10 years or $47,000 today. If money is discounted at 9 percent, which should you choose? 9-7. Solution: , ,000 Answer: $44,353.13

4 8. Present Value (LO9-3) Your father offers you a choice of $105,000 in 12 years or $47,000 today. a. If money is discounted at 8 percent, which should you choose? b. If money is still discounted at 8 percent, but your choice is between $105,000 in 9 years or $47,000 today, which should you choose? 9-8. Solution: (a) & (b) , ,000 Answer: $41, (c) & (d) , ,000 Answer: $52, Present Value (LO9-3) You are going to receive $205,000 in 18 years. What is the difference in present value between using a discount rate of 12 percent versus 9 percent? 9-9. Solution: At 12% , ,000 Answer: $26, At 9% , ,000 Answer: $43, The difference is 43, , = $16,800.60

5 10. How much would you have to invest today to receive a. $15,000 in 8 years at 10 percent? b. $20,000 in 12 years at 13 percent? c. $6,000 each year for 10 years at 9 percent? d. $50,000 each year for 50 years at 7 percent? Solution: (a) , ,000 Answer: $6, (b) , ,000 Answer: $4, (c) , ,000 0 Answer: $38, (d) , ,000 0 Answer: $690,037.31

6 11. Future value (LO9-2) If you invest $8,500 per period for the following number of periods, how much would you have? a. 12 years at 10 percent. b. 50 years at 9 percent Solution: (a) ,500 CPT FV 181, Answer: $181, (b) ,500 CPT FV 6,928, Answer: $6,928, You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you take the proceeds and invest them for 12 years at 15 percent. How much will you have after 17 years? Solution: First step: ,000 0 CPT FV 16, Answer: $16, Second step: , CPT FV 86, Answer: $86,166.31

7 13. Present value (LO9-3) Mrs. Crawford will receive $7,600 a year for the next 19 years from her trust. If a 14 percent interest rate is applied, what is the current value of the future payments? Solution: , ,600 0 Answer: $49, Phil Goode will receive $175,000 in 50 years. His friends are very jealous of him. If the funds are discounted back at a rate of 14 percent, what is the present value of his future pot of gold? Solution: ,000 Answer: $249.92

8 15. Present value (LO9-3) Sherwin Williams will receive $18,500 a year for the next 25 years as a result of a picture he has painted. If a discount rate of 12 percent is applied, should he be willing to sell out his future rights now for $165,000? Solution: , ,500 0 Answer: $145, Carrie Tune will receive $19,500 for the next 20 years as a payment for a new song she has written. If a 10 percent rate is applied, should she be willing to sell out her future rights now for $160,000? Solution: , ,500 0 Answer: $166,014.49

9 17. The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount rate of 10 percent, what is the present value of your winnings? Solution: , ,000 0 Answer: $198, Future value (LO9-2) Christy Reed made a $2,000 deposit in her savings account on her 21 st birthday, and she has made another $2,000 deposit on every birthday since then. Her account earns 7 percent compounded annually. How much will she have in her account after she makes the deposit on her 32 nd birthday? Solution: ,000 CPT FV 35, Answer: $35,776.90

10 21. Future value (LO9-2) At a growth (interest) rate of 10 percent annually, how long will it take for a sum to double? To triple? Select the year that is closest to the correct answer Solution: To double: CPT N Answer: 7.27 years To triple: CPT N Answer: years 25. Juan Garza invested $20, years ago at 12 percent, compounded quarterly. How much has he accumulated? Solution: Ten years with quarterly compounding means ,000 0 CPT FV 65, Answer: $65,240.76

11 26. Special compounding (LO9-5) Determine the amount of money in a savings account at the end of 10 years, given an initial deposit of $5,500 and a 12 percent annual interest rate when interest is compounded (a) annually, (b) semiannually, and (c) quarterly Solution: (a) ,500 0 CPT FV 17, Answer: $17, (b) ,500 0 CPT FV 17, Answer: $17, (c) ,500 0 CPT FV 17, Answer: $17,941.21

12 27. Annuity due (LO9-4) What is the future value of a 15-year annuity of $1,800 per period where payments come at the beginning of each period? The interest rate is 12 percent Solution: Set calculator beginning ,800 CPT FV 75, Answer: $75, Annuity due (LO9-4) What is the present value of a 10-year annuity of $3,000 per period in which payments come at the beginning of each period? The interest rate is 12 percent Solution: Set calculator to beginning , ,000 0 Answer: $18,984.75