CHAPTER 5 TIME VALUE OF MONEY (Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard) Note that there is some overlap between the T/F and the multiple choice questions, as some T/F statements are used in the MC questions. See the preface for information on the AACSB letter indicators (F, M, etc.) on the subject lines. Multiple Choice: True/False (5-2) Compounding 1. F J Answer: a EASY Starting to invest early for retirement increases the benefits of compound interest. a. True b. False (5-2) Compounding 2. F J Answer: b EASY Starting to invest early for retirement reduces the benefits of compound interest. a. True b. False (5-2) Compounding 3. F J Answer: a EASY A time line is meaningful even if all cash flows do not occur annually. a. True b. False (5-2) Compounding 4. F J Answer: b EASY A time line is not meaningful unless all cash flows occur annually. a. True b. False (5-2) Compounding F J Answer: a EASY 5. Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly. a. True b. False (5-2) Compounding 6. F J Answer: b EASY Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. a. True b. False Chapter 5: Time Value of Money True/False Page 135 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-2) Compounding 7. F J Answer: a EASY Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. a. True b. False (5-2) Compounding 8. F J Answer: b EASY Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods. a. True b. False (5-2) Compounding 9. F J Answer: a EASY Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts. a. True b. False (5-2) Compounding 10. F J Answer: b EASY Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts. a. True b. False (5-3) PV versus FV 11. C J Answer: b EASY If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series. a. True b. False (5-3) PV versus FV 12. C J Answer: a EASY If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. a. True b. False (5-3) PV versus FV 13. C J Answer: a EASY Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value. a. True b. False Page 136 True/False Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-3) PV versus FV 14. C J Answer: b EASY Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value. a. True b. False (5-16) Effective annual rate 15. C J Answer: b EASY If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate. a. True b. False (5-16) Effective annual rate 16. C J Answer: a EASY If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate. a. True b. False (5-2) Compounding 17. C J Answer: b MEDIUM The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date. a. True b. False (5-2) Compounding 18. C J Answer: a MEDIUM The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date. a. True b. False (5-2) Comparative compounding 19. C J Answer: a MEDIUM Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) a. True b. False Chapter 5: Time Value of Money True/False Page 137 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-2) Comparative compounding 20. C J Answer: b MEDIUM Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.) a. True b. False (5-3) PV of a sum 21. C J Answer: a MEDIUM The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant. a. True b. False (5-3) PV of a sum 22. C J Answer: b MEDIUM The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant. a. True b. False (5-9) PV of an annuity 23. C J Answer: a MEDIUM All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases. a. True b. False (5-9) PV of an annuity 24. C J Answer: b MEDIUM All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases. a. True b. False (5-15) Periodic and nominal rates 25. C J Answer: a MEDIUM If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year. a. True b. False (5-15) Periodic and nominal rates 26. C J Answer: b MEDIUM If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year. a. True b. False Page 138 True/False Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-16) Effective and nominal rates 27. C J Answer: a MEDIUM As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan). a. True b. False (5-16) Effective and nominal rates 28. C J Answer: b MEDIUM As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan). a. True b. False (5-18) Amortization 29. C J Answer: b MEDIUM When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years. a. True b. False (5-18) Amortization 30. C J Answer: a MEDIUM When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage increases in the loan's later years. a. True b. False (5-18) Amortization 31. C J Answer: a MEDIUM The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal. a. True b. False (5-18) Amortization 32. C J Answer: b MEDIUM The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal. a. True b. False Chapter 5: Time Value of Money True/False Page 139 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization 33. C J Answer: b HARD Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan. a. True b. False (5-18) Amortization 34. C J Answer: a HARD Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate. a. True b. False Multiple Choice: Conceptual The correct answers to most of these questions can be determined without doing any calculations, but calculations are required for a few of them, and calculations are useful to confirm the answers to others. You can see from the answer where calculations are required. Those questions generally take students longer to answer. (5-1) Time lines 35. F J Answer: b MEDIUM Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. (5-1) Time lines 36. F J Answer: d MEDIUM Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods. e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts. Page 140 Conceptual M/C Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-1) Time lines 37. F J Answer: c MEDIUM Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity. (5-1) Time lines 38. F J Answer: e MEDIUM Which of the following statements is CORRECT? a. A time line is not meaningful unless all cash flows occur annually. b. Time lines are not useful for visualizing complex problems prior to doing actual calculations. c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities. e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity. (5-3) Effects of factors on PVs 39. C J Answer: b MEDIUM You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment? a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000. b. The discount rate increases. c. The riskiness of the investment’s cash flows decreases. d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years. e. The discount rate decreases. (5-3) Effects of factors on PVs 40. C J Answer: b MEDIUM You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment? a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for 10 years rather than 5 years, hence that each payment is for $10,000 rather than for $20,000. b. The discount rate decreases. c. The riskiness of the investment’s cash flows increases. d. The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years. e. The discount rate increases. Chapter 5: Time Value of Money Conceptual M/C Page 141 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-6) Annuities 41. F J Answer: d MEDIUM Which of the following statements is CORRECT? a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. c. The cash flows for an annuity due must all occur at the ends of the periods. d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. (5-6) Annuities 42. F J Answer: c MEDIUM Which of the following statements is CORRECT? a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods. b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity. c. The cash flows for an annuity due must all occur at the beginning of the periods. d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month. e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity. (5-16) Quarterly compounding 43. C J Answer: c MEDIUM Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? a. The periodic rate of interest interest is 3%. b. The periodic rate of interest interest is greater than 6%. c. The periodic rate of interest interest is greater than 6%. d. The periodic rate of interest interest is 6%. e. The periodic rate of interest interest is also 6%. Page 142 is 1.5% and the effective rate of is 6% and the effective rate of is 1.5% and the effective rate of is 3% and the effective rate of is 6% and the effective rate of Conceptual M/C Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-16) Quarterly compounding 44. C J MEDIUM Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT? a. The periodic rate of interest interest is 4%. b. The periodic rate of interest interest is greater than 8%. c. The periodic rate of interest interest is less than 8%. d. The periodic rate of interest interest is greater than 8%. e. The periodic rate of interest interest is also 8%. (5-18) Amortization 45. Answer: d is 2% and the effective rate of is 8% and the effective rate of is 4% and the effective rate of is 2% and the effective rate of is 8% and the effective rate of C J Answer: c MEDIUM A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. c. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower. d. The last payment would have a higher proportion of interest than the first payment. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments. (5-18) Amortization 46. C J Answer: d MEDIUM A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan. c. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower. d. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher. e. The proportion of interest versus principal repayment would be the same for each of the 7 payments. Chapter 5: Time Value of Money Conceptual M/C Page 143 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization 47. C J Answer: b MEDIUM Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. b. Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant. c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. e. The outstanding balance declines at a slower rate in the later years of the loan’s life. (5-18) Amortization 48. C J Answer: e MEDIUM Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.) a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years. b. Because the outstanding balance declines over time, the monthly payments will also decline over time. c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant. d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year. e. The outstanding balance declines at a faster rate in the later years of the loan’s life. (5-18) Amortization 49. C J Answer: b MEDIUM Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? a. The monthly payments will decline over time. b. A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment. c. The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity. d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%. e. Exactly 10% of the first monthly payment represents interest. Page 144 Conceptual M/C Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization 50. C J Answer: b MEDIUM Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT? a. The monthly payments will increase over time. b. A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal, than for the last monthly payment. c. The total dollar amount of interest being paid off each month gets larger as the loan approaches maturity. d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%. e. Exactly 10% of the first monthly payment represents interest. (Comp.) Time value concepts 51. C J Answer: a MEDIUM Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero. a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). d. Investment D pays $2,500 at the end of 10 years (just one payment). e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments). (Comp.) Time value concepts 52. C J Answer: d MEDIUM Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero. a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments). b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments). c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments). d. Investment D pays $2,500 at the end of 10 years (just one payment). e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments). (Comp.) Time value concepts 53. C J Answer: d MEDIUM A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT? a. The periodic interest rate is greater than 3%. b. The periodic rate is less than 3%. c. The present value would be greater if the lump sum were discounted back for more periods. d. The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually. e. The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity. Chapter 5: Time Value of Money Conceptual M/C Page 145 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (Comp.) Time value concepts 54. C J Answer: e MEDIUM A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT? a. The periodic interest rate is greater than 3%. b. The periodic rate is less than 3%. c. The present value would be greater if the lump sum were discounted back for more periods. d. The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually. e. The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity. (Comp.) Time value concepts 55. C J Answer: c MEDIUM Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity. b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage. c. A bank loan's nominal interest rate will always be equal to or less than its effective annual rate. d. If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%. e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit. (Comp.) Time value concepts 56. C J Answer: d MEDIUM Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant? a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity. b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage. c. A bank loan's nominal interest rate will always be equal to or greater than its effective annual rate. d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%. e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit. Page 146 Conceptual M/C Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (Comp.) Time value concepts 57. C J Answer: a MEDIUM Which of the following statements is CORRECT? a. The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity. b. If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%. c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time. e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%. (Comp.) Time value concepts 58. C J Answer: b MEDIUM Which of the following statements is CORRECT? a. The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due. b. If a loan has a nominal annual rate of 8%, then the effective rate will never be less than 8%. c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different. d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time. e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%. (Comp.) Annuities 59. C J Answer: d MEDIUM You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? a. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE. b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD. e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant. Chapter 5: Time Value of Money Conceptual M/C Page 147 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (Comp.) Annuities 60. C J Answer: a MEDIUM You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT? a. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ. b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD. c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE. d. The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD. e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant. (5-14) Solving for I: uneven CFs 61. C J Answer: c HARD Which of the following statements is CORRECT? a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise. d. If you solve for I and get a negative number, then you must have made a mistake. e. If CF0 is positive and all the other CFs are negative, then you cannot solve for I. (5-14) Solving for I: uneven CFs 62. C J Answer: e HARD Which of the following statements is CORRECT? a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0. b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost. c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator. d. If you solve for I and get a negative number, then you must have made a mistake. e. If CF0 is positive and all the other CFs are negative, then you can still solve for I. Page 148 Conceptual M/C Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-16) Effective annual rate 63. HARD pays 8% nominal interest with monthly compounding. pays 8% nominal interest with annual compounding. pays 7% nominal interest with daily (365-day) pays 7% nominal interest with monthly compounding. pays 8% nominal interest with daily (365-day) (5-16) Effective annual rate C J Answer: d HARD Which of the following bank accounts has the lowest effective annual return? a. An account that b. An account that c. An account that compounding. d. An account that e. An account that compounding. pays 8% nominal interest with monthly compounding. pays 8% nominal interest with annual compounding. pays 7% nominal interest with daily (365-day) pays 7% nominal interest with monthly compounding. pays 8% nominal interest with daily (365-day) (5-16) Effective annual rate 65. Answer: e Which of the following bank accounts has the highest effective annual return? a. An account that b. An account that c. An account that compounding. d. An account that e. An account that compounding. 64. C J C J Answer: e HARD You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest? a. b. c. d. e. Bank Bank Bank Bank Bank 1; 2; 3; 4; 5; 6.1% 6.0% 6.0% 6.0% 6.0% with with with with with annual compounding. monthly compounding. annual compounding. quarterly compounding. daily (365-day) compounding. Multiple Choice: Problems (5-2) FV of a lump sum 66. Answer: d EASY Sue now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding? a. b. c. d. e. $205.83 $216.67 $228.07 $240.08 $252.08 (5-2) FV of a lump sum 67. C J C J Answer: d EASY Jose now has $500. How much would he have after 6 years if he leaves it invested at 5.5% with annual compounding? a. b. c. d. e. $591.09 $622.20 $654.95 $689.42 $723.89 Chapter 5: Time Value of Money M/C Problems Page 149 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-2) FV of a lump sum 68. Answer: a EASY $3,754.27 $3,941.99 $4,139.09 $4,346.04 $4,563.34 (5-2) FV of a lump sum C J Answer: c EASY Last year Rocco Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later? a. b. c. d. e. $271.74 $286.05 $301.10 $316.16 $331.96 (5-2) FV of a lump sum C J Answer: c EASY Last year Dania Corporation's sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later? a. b. c. d. e. $ 845.03 $ 889.51 $ 936.33 $ 983.14 $1,032.30 (5-2) FV of a lump sum 72. C J Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures? a. b. c. d. e. 71. EASY $1,781.53 $1,870.61 $1,964.14 $2,062.34 $2,165.46 (5-2) FV of a lump sum 70. Answer: a Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures? a. b. c. d. e. 69. C J C J Answer: b EASY How much would $1, growing at 3.5% per year, be worth after 75 years? a. b. c. d. e. Page 150 $12.54 $13.20 $13.86 $14.55 $15.28 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-2) FV of a lump sum 73. Answer: b EASY $2,245.08 $2,363.24 $2,481.41 $2,605.48 $2,735.75 (5-2) FV of a lump sum C J Answer: b EASY You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years? a. b. c. d. e. $1,122.54 $1,181.62 $1,240.70 $1,302.74 $1,367.88 (5-3) PV of a lump sum C J Answer: a EASY Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 5.5%, how much is the bond worth today? a. b. c. d. e. $585.43 $614.70 $645.44 $677.71 $711.59 (5-3) PV of a lump sum 77. C J You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years? a. b. c. d. e. 76. EASY $3,689.11 $3,883.27 $4,077.43 $4,281.30 $4,495.37 (5-2) FV of a lump sum 75. Answer: b How much would $100, growing at 5% per year, be worth after 75 years? a. b. c. d. e. 74. C J C J Answer: a EASY Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today? a. b. c. d. e. $651.60 $684.18 $718.39 $754.31 $792.02 Chapter 5: Time Value of Money M/C Problems Page 151 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-3) PV of a lump sum 78. Answer: e EASY $1,067.95 $1,124.16 $1,183.33 $1,245.61 $1,311.17 (5-3) PV of a lump sum C J Answer: b EASY Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today? a. b. c. d. e. $1,928.78 $2,030.30 $2,131.81 $2,238.40 $2,350.32 (5-3) PV of a lump sum C J Answer: b EASY Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today? a. b. c. d. e. $2,819.52 $2,967.92 $3,116.31 $3,272.13 $3,435.74 (5-4) Finding I 82. C J How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%? a. b. c. d. e. 81. EASY $438.03 $461.08 $485.35 $510.89 $537.78 (5-3) PV of a lump sum 80. Answer: e How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%? a. b. c. d. e. 79. C J C J Answer: d EASY Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price? a. b. c. d. e. Page 152 4.37% 4.86% 5.40% 6.00% 6.60% M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-4) Finding I 83. Answer: b EASY 15.17% 15.97% 16.77% 17.61% 18.49% (5-4) Growth rate C J Answer: b EASY Five years ago, Weed Go Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period? a. b. c. d. e. 15.54% 16.36% 17.18% 18.04% 18.94% (5-5) Finding N C J Answer: e Janice has $5,000 invested in a bank that pays 3.8% annually. will it take for her funds to triple? a. b. c. d. e. C J Bob has $2,500 invested in a bank that pays 4% annually. it take for his funds to double? a. b. c. d. e. EASY How long 23.99 25.26 26.58 27.98 29.46 (5-5) Finding N 87. C J Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period? a. b. c. d. e. 86. EASY 3.82% 4.25% 4.72% 5.24% 5.77% (5-4) Growth rate 85. Answer: d Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price? a. b. c. d. e. 84. C J Answer: e EASY How long will 14.39 15.15 15.95 16.79 17.67 Chapter 5: Time Value of Money M/C Problems Page 153 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-5) Finding N 88. Answer: e EASY 5.14 5.71 6.35 7.05 7.84 (5-5) Finding N C J Answer: e EASY You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000? a. b. c. d. e. 12.37 13.74 15.27 16.97 18.85 (5-7) FV of ordinary annuity C J Answer: c EASY You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now? a. b. c. d. e. $11,973 $12,603 $13,267 $13,930 $14,626 (5-7) FV of ordinary annuity 92. C J You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20? a. b. c. d. e. 91. EASY 9.29 10.33 11.47 12.75 14.02 (5-5) Finding N 90. Answer: d Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Thomson’s EPS to triple? a. b. c. d. e. 89. C J C J Answer: c EASY You want to buy a new ski boat 2 years from now, and you plan to save $8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now? a. b. c. d. e. Page 154 $15,260 $16,063 $16,908 $17,754 $18,642 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-7) FV of ordinary annuity 93. Answer: a EASY $16,112 $16,918 $17,763 $18,652 $19,584 (5-8) FV of annuity due C J Answer: c EASY You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today? a. b. c. d. e. $20,993 $22,098 $23,261 $24,424 $25,645 (5-9) PV of ordinary annuity C J Answer: e EASY What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%? a. b. c. d. e. $16,576 $17,449 $18,367 $19,334 $20,352 (5-9) PV of ordinary annuity 97. C J You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today? a. b. c. d. e. 96. EASY $18,369 $19,287 $20,251 $21,264 $22,327 (5-8) FV of annuity due 95. Answer: a You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now? a. b. c. d. e. 94. C J C J Answer: e EASY What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%? a. b. c. d. e. $16,806 $17,690 $18,621 $19,601 $20,633 Chapter 5: Time Value of Money M/C Problems Page 155 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-9) PV of ordinary annuity 98. Answer: e EASY $50,753 $53,424 $56,236 $59,195 $62,311 (5-9) PV of ordinary annuity C J Answer: b EASY Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today? a. b. c. d. e. $574,924 $605,183 $635,442 $667,214 $700,575 (5-9) PV of annuity due C J Answer: a EASY What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%? a. b. c. d. e. $11,262.88 $11,826.02 $12,417.32 $13,038.19 $13,690.10 (5-11) PV of a perpetuity 102. C J You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. b. c. d. e. 101. EASY $5,493.71 $5,782.85 $6,087.21 $6,407.59 $6,744.83 (5-9) PV of ordinary annuity 100. Answer: e You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. b. c. d. e. 99. C J C J Answer: b EASY What’s the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%? a. b. c. d. e. Page 156 $4,750 $5,000 $5,250 $5,513 $5,788 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-11) Return on a perpetuity 103. C J Answer: a EASY What’s the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year? a. 8.95% b. 9.39% c. 9.86% d. 10.36% e. 10.88% (5-9) PV of annuity due 104. C J Answer: c MEDIUM You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. b. c. d. e. $20,701 $21,791 $22,938 $24,085 $25,289 (5-9) PV of annuity due C J Answer: d MEDIUM Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today? a. b. c. d. e. $ 825,835 $ 869,300 $ 915,052 $ 963,213 $1,011,374 (5-9) PV of annuity due 107. MEDIUM $1,412.84 $1,487.20 $1,565.48 $1,643.75 $1,725.94 (5-9) PV of annuity due 106. Answer: c You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? a. b. c. d. e. 105. C J C J Answer: d MEDIUM Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today? a. b. c. d. e. $1,063,968 $1,119,966 $1,178,912 $1,240,960 $1,303,008 Chapter 5: Time Value of Money M/C Problems Page 157 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-9) PV of annuity due 108. Answer: b MEDIUM $225,367 $237,229 $249,090 $261,545 $274,622 (5-9) PV of ord. ann. & end. pmt. C J Answer: e MEDIUM What’s the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%? a. b. c. d. e. $ 8,509 $ 8,957 $ 9,428 $ 9,924 $10,446 (5-10) Ord. annuity payments C J Answer: a Suppose you inherited $275,000 and invested it at 8.25% per year. much could you withdraw at the end of each of the next 20 years? a. b. c. d. e. MEDIUM How $28,532 $29,959 $31,457 $33,030 $34,681 (5-10) Ord. annuity payments 112. C J Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity? a. b. c. d. e. 111. MEDIUM $284,595 $299,574 $314,553 $330,281 $346,795 (5-9) PV of annuity due 110. Answer: b You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it? a. b. c. d. e. 109. C J C J Answer: d MEDIUM Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account? a. b. c. d. e. Page 158 $28,843.38 $30,361.46 $31,959.43 $33,641.50 $35,323.58 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-10) Annuity due payments 113. C J Answer: c MEDIUM Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account? a. b. c. d. e. $24,736 $26,038 $27,409 $28,779 $30,218 (5-10) Annuity due payments C J Answer: d MEDIUM Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years? a. b. c. d. e. $22,598.63 $23,788.03 $25,040.03 $26,357.92 $27,675.82 (5-10) Finding annuity periods 116. MEDIUM $28,243.21 $29,729.70 $31,294.42 $32,859.14 $34,502.10 (5-10) Annuity due payments 115. Answer: c Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account? a. b. c. d. e. 114. C J C J Answer: a MEDIUM Your father's employer was just acquired, and he was given a severance payment of $375,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero? a. b. c. d. e. 22.50 23.63 24.81 26.05 27.35 Chapter 5: Time Value of Money M/C Problems Page 159 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-10) Finding annuity periods 117. C J 14.21 14.96 15.71 16.49 17.32 (5-10) Finding annuity due periods Answer: e MEDIUM 18.62 19.60 20.63 21.71 22.86 (5-10) Finding annuity due periods C J Answer: c MEDIUM Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end? a. b. c. d. e. 15.54 16.36 17.22 18.08 18.99 (5-10) Finding I: annuity 120. C J Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero? a. b. c. d. e. 119. MEDIUM Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end? a. b. c. d. e. 118. Answer: b C J Answer: b MEDIUM Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes. a. b. c. d. e. Page 160 7.12% 7.49% 7.87% 8.26% 8.67% M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-10) Finding I: annuity 121. C J 3.44% 3.79% 4.17% 4.58% 5.04% (5-10) Finding I: annuity due C J MEDIUM 6.85% 7.21% 7.59% 7.99% 8.41% (5-11) Payments on a perpetuity C J Answer: b MEDIUM What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250? a. b. c. d. e. $77.19 $81.25 $85.31 $89.58 $94.06 (5-12) PV of uneven cash flows 124. Answer: e Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment? a. b. c. d. e. 123. MEDIUM Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity? a. b. c. d. e. 122. Answer: a C J Answer: e MEDIUM What is the present value of the following cash flow stream at a rate of 6.25%? Years: CFs: a. b. c. d. e. 0 | $0 1 | $75 2 | $225 3 | $0 4 | $300 $411.57 $433.23 $456.03 $480.03 $505.30 Chapter 5: Time Value of Money M/C Problems Page 161 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-12) PV of uneven cash flows 125. C J CFs: a. b. c. d. e. 0 | $0 1 | $1,500 3 | $4,500 4 | $6,000 C J Answer: d MEDIUM What is the present value of the following cash flow stream at a rate of 8.0%? Years: CFs: a. b. c. d. e. 0 | $750 1 | $2,450 2 | $3,175 3 | $4,400 $7,917 $8,333 $8,772 $9,233 $9,695 (5-12) PV of uneven cash flows C J Answer: a MEDIUM You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? Years: CFs: a. b. c. d. e. 0 | $0 1 | $1,000 2 | $2,000 3 | $2,000 4 | $2,000 $5,987 $6,286 $6,600 $6,930 $7,277 (5-13) FV of uneven cash flows 128. 2 | $3,000 $ 9,699 $10,210 $10,747 $11,284 $11,849 (5-12) PV of uneven cash flows 127. MEDIUM What is the present value of the following cash flow stream at a rate of 12.0%? Years: 126. Answer: c C J Answer: e MEDIUM At a rate of 6.5%, what is the future value of the following cash flow stream? Years: CFs: a. b. c. d. e. Page 162 0 | $0 1 | $75 2 | $225 3 | $0 4 | $300 $526.01 $553.69 $582.83 $613.51 $645.80 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-14) Rate in uneven cash flows 129. Answer: e MEDIUM 4.93% 5.19% 5.46% 5.75% 6.05% (5-15) FV, semiannual compounding C J Answer: c MEDIUM What’s the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually? a. b. c. d. e. $1,819 $1,915 $2,016 $2,117 $2,223 (5-15) FV, semiannual compounding C J Answer: d MEDIUM What’s the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually? a. b. c. d. e. $3,089 $3,251 $3,422 $3,602 $3,782 (5-15) FV, monthly compounding 133. C J You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset? a. b. c. d. e. 132. MEDIUM 6.77% 7.13% 7.50% 7.88% 8.27% (5-14) Rate in uneven cash flows 131. Answer: c Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment? a. b. c. d. e. 130. C J C J Answer: b MEDIUM What’s the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly? a. b. c. d. e. $1,537.69 $1,618.62 $1,699.55 $1,784.53 $1,873.76 Chapter 5: Time Value of Money M/C Problems Page 163 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-15) PV, monthly compounding 134. Answer: b MEDIUM 18.58% 19.56% 20.54% 21.57% 22.65% (5-16) Comparing EFF% C J Answer: d MEDIUM Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside? a. b. c. d. e. 0.52% 0.44% 0.36% 0.30% 0.24% (5-16) Nominal rate vs. EFF% C J Answer: a MEDIUM Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan? a. b. c. d. e. 8.24% 8.45% 8.66% 8.88% 9.10% (5-16) Nominal rate vs. EFF% 138. C J Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%? a. b. c. d. e. 137. MEDIUM $ 969 $1,020 $1,074 $1,131 $1,187 (5-16) APR vs. EFF% 136. Answer: d What’s the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly? a. b. c. d. e. 135. C J C J Answer: e MEDIUM Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan? a. 8.46% b. 8.90% c. 9.37% d. 9.86% e. 10.38% Page 164 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-16) Nominal rate vs. EFF% 139. Answer: b MEDIUM 15.27% 16.08% 16.88% 17.72% 18.61% (5-17) Simple interest C J Answer: a MEDIUM Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month? a. b. c. d. e. $120.83 $126.88 $133.22 $139.88 $146.87 (5-17) Fractional time periods C J Answer: a MEDIUM Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days? a. b. c. d. e. $5,178.09 $5,436.99 $5,708.84 $5,994.28 $6,294.00 (5-18) Amortization: payment 143. C J Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate? a. b. c. d. e. 142. MEDIUM 3.72% 4.13% 4.59% 5.05% 5.56% (5-16) Nominal rate vs. EFF% 141. Answer: c Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay? a. b. c. d. e. 140. C J C J Answer: a MEDIUM Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be? a. b. c. d. e. $3,704.02 $3,889.23 $4,083.69 $4,287.87 $4,502.26 Chapter 5: Time Value of Money M/C Problems Page 165 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization: payment 144. C J Answer: e MEDIUM Your uncle will sell you his bicycle shop for $250,000, with “seller financing,” at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be? a. b. c. d. e. $4,029.37 $4,241.44 $4,464.67 $4,699.66 $4,947.01 (5-18) Amortization: interest C J Answer: d MEDIUM Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year? a. b. c. d. e. $1,200.33 $1,263.50 $1,330.00 $1,400.00 $1,470.00 (5-18) Amortization: interest 147. MEDIUM $741.57 $780.60 $821.69 $862.77 $905.91 (5-18) Amortization: payment 146. Answer: c Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be? a. b. c. d. e. 145. C J C J Answer: d MEDIUM You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2? a. b. c. d. e. Page 166 $1,994.49 $2,099.46 $2,209.96 $2,326.27 $2,442.59 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization: interest 148. C J $7,531 $7,927 $8,323 $8,740 $9,177 (Comp.) N, ann. due, monthly comp. Answer: d MEDIUM 23 27 32 38 44 (Comp.) N, ann. due, monthly comp. C J Answer: b MEDIUM You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000? a. b. c. d. e. 39.60 44.00 48.40 53.24 58.57 (Comp.) Rate, ord. ann., monthly comp. 151. C J You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up. a. b. c. d. e. 150. MEDIUM Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2? a. b. c. d. e. 149. Answer: b C J Answer: d MEDIUM Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan? a. b. c. d. e. 12.31% 12.96% 13.64% 14.36% 15.08% Chapter 5: Time Value of Money M/C Problems Page 167 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-10) N, lifetime vs. yearly 152. C J Answer: e MEDIUM/HARD Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy? a. 7.48 b. 8.80 c. 10.35 d. 12.18 e. 14.33 (5-15) Non-annual compounding 153. C J $15,234.08 $16,035.87 $16,837.67 $17,679.55 $18,563.53 (5-16) Comparing EFF% C J Answer: d MEDIUM/HARD Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks? a. b. c. d. e. 1.56% 1.30% 1.09% 0.91% 0.72% (5-18) Amortization: princ. repymt. 155. MEDIUM/HARD You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now? a. b. c. d. e. 154. Answer: b C J Answer: b MEDIUM/HARD Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year? a. b. c. d. e. Page 168 $2,404.91 $2,531.49 $2,658.06 $2,790.96 $2,930.51 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization: ending bal. 156. C J Answer: c MEDIUM/HARD Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year. a. b. c. d. e. $58,601 $61,686 $64,932 $68,179 $71,588 (5-10) Finding I: annuity due C J Answer: a HARD You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning? a. b. c. d. e. 7.62% 8.00% 8.40% 8.82% 9.26% (5-18) Amortization 159. MEDIUM/HARD $10,155.68 $10,690.19 $11,252.83 $11,845.09 $12,468.51 (Comp.) Retirement planning 158. Answer: e Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment? a. b. c. d. e. 157. C J C J Answer: e HARD Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal? a. b. c. d. e. 73.67% 77.55% 81.63% 85.93% 90.45% Chapter 5: Time Value of Money M/C Problems Page 169 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (5-18) Amortization: interest 160. C J $17,419.55 $17,593.75 $17,769.68 $17,947.38 $18,126.85 (Comp.) Retirement planning C J Answer: a HARD Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate's trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Steve's 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a “trust fund baby,” but he also wants to ensure that Steve is provided for in his old age. Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed's trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday? a. b. c. d. e. $3,726 $3,912 $4,107 $4,313 $4,528 (Comp.) FV comb. CF lump sum & ann. 162. HARD On January 1, 2010, your brother's business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for 2010? a. b. c. d. e. 161. Answer: a C J Answer: d HARD After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now? a. b. c. d. e. Page 170 $238,176 $250,712 $263,907 $277,797 $291,687 M/C Problems Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. (Comp.) CF for given return 163. Answer: c HARD You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X? a. b. c. d. e. $4,271.67 $4,496.49 $4,733.15 $4,969.81 $5,218.30 (Comp.) Saving for college 164. C J C J Answer: e HARD John and Daphne are saving for their daughter Ellen's college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years--if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen's anticipated college costs? a. b. c. d. e. $1,965.21 $2,068.64 $2,177.51 $2,292.12 $2,412.76 Chapter 5: Time Value of Money M/C Problems Page 171 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. CHAPTER 5 ANSWERS AND SOLUTIONS 1. (5-2) Compounding F J Answer: a EASY 2. (5-2) Compounding F J Answer: b EASY 3. (5-2) Compounding F J Answer: a EASY 4. (5-2) Compounding F J Answer: b EASY 5. (5-2) Compounding F J Answer: a EASY 6. (5-2) Compounding F J Answer: b EASY 7. (5-2) Compounding F J Answer: a EASY 8. (5-2) Compounding F J Answer: b EASY 9. (5-2) Compounding F J Answer: a EASY 10. (5-2) Compounding F J Answer: b EASY 11. (5-3) PV versus FV C J Answer: b EASY 12. (5-3) PV versus FV C J Answer: a EASY 13. (5-3) PV versus FV C J Answer: a EASY 14. (5-3) PV versus FV C J Answer: b EASY 15. (5-16) Effective annual rate C J Answer: b EASY 16. (5-16) Effective annual rate C J Answer: a EASY 17. (5-2) Compounding C J Answer: b MEDIUM 18. (5-2) Compounding C J Answer: a MEDIUM 19. (5-2) Comparative compounding C J Answer: a MEDIUM Answer: b MEDIUM Work out the numbers with a calculator: PV 1000 FVA = $1,710.34 Rate on A 5% 2 × FVA = $3,420.68 Rate on B 12% FVB = $3,478.55 Years 11 FVB > 2 × FVA, so TRUE 20. (5-2) Comparative compounding C J Work out the numbers with a calculator: PV 1000 FVA = $1,710.34 Rate on A 5% 2 × FVA = $3,420.68 Rate on B 12% FVB = $3,478.55 Years 11 FVB > 2 × FVA, so FALSE Page 172 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 21. (5-3) PV of a sum C J Answer: a MEDIUM 22. (5-3) PV of a sum C J Answer: b MEDIUM 23. (5-9) PV of an annuity C J Answer: a MEDIUM One could make up an example and see that the statement is true. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. 24. (5-9) PV of an annuity C J Answer: b MEDIUM One could make up an example and see that the statement is false. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. 25. (5-15) Periodic and nominal rates C J Answer: a MEDIUM 26. (5-15) Periodic and nominal rates C J Answer: b MEDIUM 27. (5-16) Effective and nominal rates C J Answer: a MEDIUM 28. (5-16) Effective and nominal rates C J Answer: b MEDIUM 29. (5-18) Amortization C J Answer: b MEDIUM 30. (5-18) Amortization C J Answer: a MEDIUM 31. (5-18) Amortization C J Answer: a MEDIUM 32. (5-18) Amortization C J Answer: b MEDIUM 33. (5-18) Amortization C J Answer: b HARD There is no reason to think that this statement would always be true. The portion of the payment representing interest declines, while the portion representing principal repayment increases. Therefore, the statement is false. We could also work out some numbers to prove this point. Here's an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is not equal to the principal repayment component except at the high interest rate. Original loan Rate Life Payment 1 2 3 Beg. Balance Interest $1,000.00 $100.00 $697.89 $69.79 $365.56 $36.56 Chapter 5: Time Value of Money $1,000 10% 3 $402.11 Original loan Rate Life Payment Principal End. Bal. $302.11 $697.89 $332.33 $365.56 $365.56 $0.00 Answers 1 2 3 Beg. Balance $1,000.00 $773.52 $453.15 $1,000 41.45% 3 $640.98 Interest $414.50 $320.62 $187.83 Principal End. Bal. $226.48 $773.52 $320.36 $453.15 $453.15 $0.00 Page 173 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 34. (5-18) Amortization C J Answer: a HARD This statement is true. The portion of the payment representing interest declines, while the portion representing principal repayment increases. The interest portion could be equal to, greater than, or less than the principal portion. We can work out some numbers to prove this point. Here's an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is less than the principal at 10%, equal at about 41.45%, and greater at rates above 41.45%. Original loan Rate Life Payment 1 2 3 Beg. Balance Interest $1,000.00 $100.00 $697.89 $69.79 $365.56 $36.56 $1,000 10% 3 $402.11 Original loan Rate Life Payment Principal End. Bal. $302.11 $697.89 $332.33 $365.56 $365.56 $0.00 1 2 3 $1,000 41.45% 3 $640.98 Beg. Balance $1,000.00 $773.52 $453.15 Interest $414.50 $320.62 $187.83 Principal End. Bal. $226.48 $773.52 $320.36 $453.15 $453.15 $0.00 35. (5-1) Time lines F J Answer: b MEDIUM 36. (5-1) Time lines F J Answer: d MEDIUM 37. (5-1) Time lines F J Answer: c MEDIUM 38. (5-1) Time lines F J Answer: e MEDIUM 39. (5-3) Effects of factors on PVs C J Answer: b MEDIUM 40. (5-3) Effects of factors on PVs C J Answer: b MEDIUM 41. (5-6) Annuities F J Answer: d MEDIUM 42. (5-6) Annuities F J Answer: c MEDIUM 43. (5-16) Quarterly compounding C J Answer: c MEDIUM 44. (5-16) Quarterly compounding C J Answer: d MEDIUM 45. (5-18) Amortization C J Answer: c MEDIUM a, d, and e can be ruled out as incorrect by simple reasoning. b is also incorrect because interest in the first year would be Loan amount × interest rate regardless of the life of the loan, so the interest payment would be identical for the first payment. Think about the situation whe re r = 0%, statement c is the "most logical guess." One could also set up an amortization schedule and change the numbers to confirm that only c is correct. 46. (5-18) Amortization C J Answer: d MEDIUM a, c, and e are obviously incorrect. b is also incorrect because interest in the first year would be Loan amount × interest rate regardless of the life of the loan. That makes d the "most logical guess." One could also set up an amortization schedule and change the numbers to confirm that only d is corre ct. 47. (5-18) Amortization C J Answer: b MEDIUM b is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement b is correct. Page 174 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 48. (5-18) Amortization C J Answer: e MEDIUM e is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement e is correct. 49. (5-18) Amortization C J Answer: b MEDIUM b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see: Loan Rate Periodic rate 100000 10% 0.008333333 Payment -$877.57 Interest as % of total #360 payment: 1% Principal as % of total #360 payment 99% 50. (5-18) Amortization Term Periods/Year Total periods 30 12 360 Interest, Month 1 Interest, Month 360 Principal, Month 360 C J $833.33 $7.25 $870.32 Answer: b MEDIUM b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see: Loan Rate Periodic rate 100000 10% 0.00833333 Payment Interest as % of total payment: 51. Term Periods/Year Total periods 30 12 360 -$877.57 Interest Month 1 95%, which is much larger than 10%. (Comp.) Time value concepts C J $833.33 Answer: a MEDIUM A dominates B because it provides the same total amount, but it comes faster, hence it can earn more interest over the 10 years. A also dominates C and E for the same re ason, and it dominates D because with D no interest whatever is earned. We could also do these calculations to answer the question: A B C D E 52. $4,382.79 $4,081.59 $4,280.81 $2,500.00 $3,984.36 Largest (Comp.) Time value concepts EFF% 10.00% NOM% 9.76% 10 C J 250 125 125 2500 250 Answer: d MEDIUM A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B because a larger annuity is received later. So, now the choice comes down to either A or D . Since all of D is received at the end, this is the logical choice. We could also do these calculations to answer the question: A B C D E $1,536.14 $1,573.63 $1,650.44 $963.86 $1,689.76 Chapter 5: Time Value of Money EFF% 10.00% NOM% 9.76% Smallest Answers 10 250 125 125 2500 250 Page 175 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 53. (Comp.) Time value concepts C J Answer: d MEDIUM 54. (Comp.) Time value concepts C J Answer: e MEDIUM 55. (Comp.) Time value concepts C J Answer: c MEDIUM 56. (Comp.) Time value concepts C J Answer: d MEDIUM 57. (Comp.) Time value concepts C J Answer: a MEDIUM 58. (Comp.) Time value concepts C J Answer: b MEDIUM 59. (Comp.) Annuities C J Answer: d MEDIUM 60. (Comp.) Annuities C J Answer: a MEDIUM 61. (5-14) Solving for I: uneven CFs C J Answer: c HARD 62. (5-14) Solving for I: uneven CFs C J Answer: e HARD 63. (5-16) Effective annual rate C J Answer: e HARD By inspection, we can see that e dominates a and b, and that c dominates d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either e or c. Moreover, we can see by inspection that since c and e have the same compounding frequency yet e has the higher nominal rate, e must have the higher EFF%. You could also prove that e is the correct choice by calculating the EFF%s: a. b. c. d. e. 64. 8.300% = (1+0.08/12)12-1 8.000% = (1+0.08/1)1-1 7.250% = (1+0.07/365)365-1 7.229% = (1+0.07/12)12-1 8.328% = (1+0.08/365)365-1 (5-16) Effective annual rate C J Answer: d HARD By inspection, we can see that b must have a lower EFF% than either a or e because they all pay the same nominal rate but b is compounded least frequently. Similarly, c and d pay the same rate, but d is compounded less frequently, hence d must have the lower EFF%. So, the correct answer must be either b or d. It is not obvious which of these two has the lower EFF%, so we must do a quick calculation to determine the correct response. As the following calculations show, d is the correct answer. a. b. c. d. e. Page 176 8.300% = (1+0.08/12)12-1 8.000% = (1+0.08/1)1-1 7.250% = (1+0.07/365)365-1 7.229% = (1+0.07/12)12-1 8.328% = (1+0.08/365)365-1 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 65. (5-16) Effective annual rate C J Answer: e HARD By inspection, we can see that e dominates b, c, and d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either a or e. However, we cannot tell by inspection whether a or e provides the higher EFF%. We know that with one compounding period a’s EFF% is 6.1%, so we can calculate e's EFF%. It is 6.183%, so e is the correct answer. a. = (1+0.061/12)12-1 = 6.100% e. = (1+0.06/365)365-1 = 6.183% 66. (5-2) FV of a lump sum N I/YR PV PMT FV 67. 68. 69. 70. Answer: d EASY C J Answer: a EASY C J Answer: a EASY C J Answer: c EASY 10 6.5% $2,000 $0 $3,754.27 (5-2) FV of a lump sum N I/YR PV PMT FV C J 5 3.5% $1,500 $0 $1,781.53 (5-2) FV of a lump sum N I/YR PV PMT FV EASY 6 5.5% $500 $0 $689.42 (5-2) FV of a lump sum N I/YR PV PMT FV Answer: d 8 8.5% $125 $0 $240.08 (5-2) FV of a lump sum N I/YR PV PMT FV C J 5 6.0% $225.00 $0.00 $301.10 Chapter 5: Time Value of Money Answers Page 177 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 71. (5-2) FV of a lump sum N I/YR PV PMT FV 72. 73. 74. 75. 76. 77. Page 178 C J Answer: b EASY C J Answer: b EASY C J Answer: b EASY C J Answer: a EASY C J Answer: a EASY 10 5.5% $0 $1,000.00 $585.43 (5-3) PV of a lump sum N I/YR PMT FV PV EASY 25 3.5% $500 $0 $1,181.62 (5-3) PV of a lump sum N I/YR PMT FV PV Answer: b 25 3.5% $1,000 $0 $2,363.24 (5-2) FV of a lump sum N I/YR PV PMT FV C J 75 5.0% $100.00 $0.00 $3,883.27 (5-2) FV of a lump sum N I/YR PV PMT FV EASY 75 3.5% $1.00 $0.00 $13.20 (5-2) FV of a lump sum N I/YR PV PMT FV Answer: c 8 7.5% $525.00 $0.00 $936.33 (5-2) FV of a lump sum N I/YR PV PMT FV C J 8 5.5% $0 $1,000.00 $651.60 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 78. (5-3) PV of a lump sum N I/YR PMT FV PV 79. 80. 81. 82. 83. 84. C J Answer: b EASY C J Answer: b EASY C J Answer: d EASY C J Answer: d EASY C J Answer: b EASY 10 $3,000.00 $0 $5,000.00 5.24% (5-4) Growth rate N PV PMT FV I/YR EASY 5 $747.25 $0 $1,000.00 6.00% (5-4) Finding I N PV PMT FV I/YR Answer: e 10 4.25% $0 $4,500.00 $2,967.92 (5-4) Finding I N PV PMT FV I/YR C J 5 4.25% $0 $2,500.00 $2,030.30 (5-3) PV of a lump sum N I/YR PMT FV PV EASY 25 5.5% $0 $5,000 $1,311.17 (5-3) PV of a lump sum N I/YR PMT FV PV Answer: e 50 7.5% $0 $20,000 $537.78 (5-3) PV of a lump sum N I/YR PMT FV PV C J 10 $0.50 $0 $2.20 15.97% Chapter 5: Time Value of Money Answers Page 179 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 85. (5-4) Growth rate N PV PMT FV I/YR 86. 87. 88. 89. 90. 91. Page 180 C J Answer: e EASY C J Answer: d EASY C J Answer: e EASY C J Answer: e EASY C J Answer: c EASY 6.0% $10,000.00 $0 $30,000.00 18.85 (5-7) FV of ordinary annuity N I/YR PV PMT FV EASY 8.0% $5,000.00 $0 $9,140.20 7.84 (5-5) Finding N I/YR PV PMT FV N Answer: e 9.0% $3.50 $0 $10.50 12.75 (5-5) Finding N I/YR PV PMT FV N C J 4.0% $2,500.00 $0 $5,000.00 17.67 (5-5) Finding N I/YR PV PMT FV N EASY 3.8% $5,000.00 $0 $15,000.00 29.46 (5-5) Finding N I/YR PV PMT FV N Answer: b 5 $1.50 $0 $3.20 16.36% (5-5) Finding N I/YR PV PMT FV N C J 3 5.2% $0.00 $4,200 $13,266.56 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 92. (5-7) FV of ordinary annuity N I/YR PV PMT FV 93. 94. 95. 96. Answer: a EASY C J Answer: a EASY 3 5.2% $0.00 $7,000 $23,261 2 $3,500 3 $3,500 4 FV = $16,112 C J Alternative setup: 0 1 $7,000 $7,000 Answer: c 2 $7,000 EASY 3 $7,000 FV = $23,261 C J Answer: e EASY C J Answer: e EASY 10 5.5% $2,700 $0.00 $20,352 (5-9) PV of ordinary annuity N I/YR PMT FV PV C J Alternative setup: 0 1 $3,500 $3,500 (5-9) PV of ordinary annuity N I/YR PMT FV PV 97. 4 5.7% $0.00 $3,500 $16,112 (5-8) FV of annuity due BEGIN Mode N I/YR PV PMT FV EASY 5 8.5% $0.00 $3,100 $18,369 (5-8) FV of annuity due BEGIN Mode N I/YR PV PMT FV Answer: c 2 6.2% $0.00 $8,200 $16,908 (5-7) FV of ordinary annuity N I/YR PV PMT FV C J 5 4.5% $4,700 $0.00 $20,633 Chapter 5: Time Value of Money Answers Page 181 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 98. (5-9) PV of ordinary annuity N I/YR PMT FV PV 99. 100. 101. EASY C J Answer: e EASY C J Answer: b EASY C J Answer: a EASY C J Answer: b EASY C J Answer: a EASY 20 5.0% $5,000 $0.00 $62,311 (5-9) PV of ordinary annuity N I/YR PMT FV PV Answer: e 3 5.5% $2,500 $0.00 $6,744.83 (5-9) PV of ordinary annuity N I/YR PMT FV PV C J 30 7.25% $50,000 $0.00 $605,183 (5-9) PV of annuity due BEGIN Mode N 5 I/YR 5.5% PMT $2,500 FV $0.00 PV $11,262.88 102. (5-11) PV of a perpetuity I/YR PMT PV 103. (5-11) Return on a perpetuity Cost (PV) PMT I/YR 104. 5.0% $250 $5,000 $950 $85 8.95% (5-9) PV of annuity due BEGIN Mode N I/YR PMT FV PV Page 182 C J Answer: c MEDIUM 3 5.5% $550 $0.00 $1,565.48 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 105. (5-9) PV of annuity due C J Answer: c MEDIUM C J Answer: d MEDIUM C J Answer: d MEDIUM C J Answer: b MEDIUM C J Answer: b MEDIUM (5-9) PV of ord. ann. & end. pmt. C J Answer: e MEDIUM BEGIN Mode N I/YR PMT FV PV 106. (5-9) PV of annuity due BEGIN Mode N I/YR PMT FV PV 107. 5 4.5% $5,000 $0.00 $22,938 20 5.25% $75,000 $0.00 $963,213 (5-9) PV of annuity due BEGIN Mode N 25 I/YR 5.15% PMT $85,000 FV $0.00 PV $1,240,960 108. (5-9) PV of annuity due BEGIN Mode N I/YR PMT FV PV 109. (5-9) PV of annuity due BEGIN Mode N I/YR PMT FV PV 110. 25 7.5% $25,000 $0.00 $299,574 N I/YR PMT FV PV 15 7.5% $25,000 $0.00 $237,229 4 5.0% $2,250 $3,000 $10,446 Chapter 5: Time Value of Money Alternative setup: 0 1 $2,250 2 $2,250 3 $2,250 $2,250 $2,250 $2,250 4 $2,250 $3,000 $5,250 PV = $10,446.50 Answers Page 183 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 111. (5-10) Ord. annuity payments N I/YR PV FV PMT 112. 113. Answer: a MEDIUM C J Answer: d MEDIUM C J Answer: c MEDIUM C J Answer: c MEDIUM C J Answer: d MEDIUM C J Answer: a MEDIUM 20 8.25% $275,000 $0.00 $28,532 (5-10) Ord. annuity payments N I/YR PV FV PMT C J 25 7.5% $375,000 $0.00 $33,641.50 (5-10) Annuity due payments BEGIN Mode N 25 I/YR 7.5% PV $375,000 FV $0.00 PMT $31,294.42 114. (5-10) Annuity due payments BEGIN Mode N I/YR PV FV PMT 115. 4 6.5% $100,000 $0.00 $27,409 (5-10) Annuity due payments BEGIN Mode N 20 I/YR 8.25% PV $275,000 FV $0.00 PMT $26,357.92 116. (5-10) Finding annuity periods I/YR PV PMT FV N Page 184 7.5% $375,000 $35,000 $0.00 22.50 Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 117. (5-10) Finding annuity periods I/YR PV PMT FV N 118. 119. 120. 121. 122. 123. C J Answer: c MEDIUM C J Answer: b MEDIUM C J Answer: a MEDIUM C J Answer: e MEDIUM C J Answer: b MEDIUM 12 $120,000 $15,000 $0.00 8.41% (5-11) Payments on a perpetuity Cost (PV) I/YR PMT MEDIUM 20 $15,000,000 $1,050,000 $0.00 3.44% (5-10) Finding I: annuity due BEGIN Mode N PV PMT FV I/YR Answer: e 20 $2,550,000 $250,000 $0.00 7.49% (5-10) Finding I: annuity N PV PMT FV I/YR C J 5.5% $500,000 $45,000 $50,000 17.22 (5-10) Finding I: annuity N PV PMT FV I/YR MEDIUM 6.5% $500,000 $40,000 $0.00 22.86 (5-10) Finding annuity due periods BEGIN Mode I/YR PV PMT FV N Answer: b 7.50% $300,000 $35,000 $25,000 14.96 (5-10) Finding annuity due periods BEGIN Mode I/YR PV PMT FV N C J $1,250 6.5% $81.25 Chapter 5: Time Value of Money Multiply Cost by I/YR. Answers Page 185 © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. 124. (5-12) PV of uneven cash flows C J Answer: e MEDIUM I/YR = 6.25% CFs: PV of CFs: PV = $505.30 PV = $505.30 0 $0 $0 1 $75 $71 2 $225 $199 3 $0 $0 4 $300 $235 Found using the Excel NPV function. Found by summing individual PVs. You can find the individual PVs and sum them. Alternately, you can automate the process using Excel or a calculator, by inputting the data into the cash flow register and pressing the NPV key. 125. (5-12) PV of uneven cash flows C J Answer: c MEDIUM Answer: d MEDIUM I/YR = 12.0% CFs: PV of CFs: PV = $10,747 PV = $10,747 PV = $10,747 126. 0 $0 $0 1 $1,500 $1,339 2 $3,000 $2,392 3 $4,500 $3,203 4 $6,000 $3,813 Found using the Excel NPV function. Found by summing individual PVs. Found using the calculator NPV key. (5-12) PV of uneven cash flows C J I/YR = 8.0% CFs: PV of CFs: PV = $9,233 PV = $9,233 127. 0 $750 1 $2,450 2 $3,175 3 $4,400 $750 $2,269 $2,722 $3,493 Found by summing individual PVs. Found with a calculator or Excel to automate the process. With a calculator, input the cash flows and I into the cash flow register, then press the NPV key. (5-12) PV of uneven cash flows C J Answer: a MEDIUM I/YR = 6.0% CFs: PV of CFs: PV = $5,987 PV = $5,987 PV = $5,987 Page 186 0 $0 $0 1 $1,000 $943 2 $2,000 $1,780 3 $2,000 $1,679 4 $2,000 $1,584 Found using the Excel NPV function. Found by summing individual PVs. Found using the calculator NPV key. Answers Chapter 5: Time Value of Money © 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or ...