Fin450 Testbank Ch 4

Chapter 04
Discounted Cash Flow Valuation

Multiple Choice Questions

1. An annuity stream of cash flow payments is a set of:
A. level cash flows occurring each time period for a fixed length of time.
B. level cash flows occurring each time period forever.
C. increasing cash flows occurring each time period for a fixed length of time.
D. increasing cash flows occurring each time period forever.
E. arbitrary cash flows occurring each time period for no more than 10 years.

2. Annuities where the payments occur at the end of each time period are called _____, whereas _____ refer to annuity streams with payments occurring at the beginning of each time period.
A. ordinary annuities; early annuities
B. late annuities; straight annuities
C. straight annuities; late annuities
D. annuities due; ordinary annuities
E. ordinary annuities; annuities due

3. An annuity stream where the payments occur forever is called a(n):
A. annuity due.
B. indemnity.
C. perpetuity.
D. amortized cash flow stream.
E. amortization table.

4. The interest rate expressed in terms of the interest payment made each period is called the _____ rate.
A. stated annual interest
B. compound annual interest
C. effective annual interest
D. periodic interest
E. daily interest

5. The interest rate expressed as if it were compounded once per year is called the _____ rate.
A. stated interest
B. compound interest
C. effective annual
D. periodic interest
E. daily interest

6. The interest rate charged per period multiplied by the number of periods per year is called the _____ rate.
A. effective annual
B. annual percentage
C. periodic interest
D. compound interest
E. daily interest

7. Paying off long-term debt by making installment payments is called:
A. foreclosing on the debt.
B. amortizing the debt.
C. funding the debt.
D. calling the debt.
E. None of the above.

8. You are comparing two annuities which offer monthly payments for ten years. Both annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity B pays on the last day of each month. Which one of the following statements is correct concerning these two annuities?
A. Both annuities are of equal value today.
B. Annuity B is an annuity due.
C. Annuity A has a higher future value than annuity B.
D. Annuity B has a higher present value than annuity A.
E. Both annuities have the same future value as of ten years from today.

9. You are comparing two investment options. The cost to invest in either option is the same today. Both options will provide you with $20,000 of income. Option A pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of the following statements is correct given these two investment options?
A. Both options are of equal value given that they both provide $20,000 of income.
B. Option A is the better choice of the two given any positive rate of return.
C. Option B has a higher present value than option A given a positive rate of return.
D. Option B has a lower future value at year 5 than option A given a zero rate of return.
E. Option A is preferable because it is an annuity due.

10. You are considering two projects with the following cash flows: [pic]
Which of the following statements are true concerning these two projects?
I. Both projects have the same future value at the end of year 4, given a positive rate of return.
II. Both projects have the same future value given a zero rate of return.
III. Both projects have the same future value at any point in time, given a positive rate of return.
IV. Project A has a higher future value than project B, given a positive rate of return.
A. II only
B. IV only
C. I and III only
D. II and IV only
E. I, II, and III only

11. A perpetuity differs from an annuity because:
A. perpetuity payments vary with the rate of inflation.
B. perpetuity payments vary with the market rate of interest.
C. perpetuity payments are variable while annuity payments are constant.
D. perpetuity payments never cease.
E. annuity payments never cease.

12. Which one of the following statements concerning the annual percentage rate is correct?
A. The annual percentage rate considers interest on interest.
B. The rate of interest you actually pay on a loan is called the annual percentage rate.
C. The effective annual rate is lower than the annual percentage rate when an interest rate is compounded quarterly.
D. When firms advertise the annual percentage rate they are violating U.S. truth-in-lending laws.
E. The annual percentage rate equals the effective annual rate when the rate on an account is designated as simple interest.

13. Which one of the following statements concerning interest rates is correct?
A. The stated rate is the same as the effective annual rate.
B. An effective annual rate is the rate that applies if interest were charged annually.
C. The annual percentage rate increases as the number of compounding periods per year increases.
D. Banks prefer more frequent compounding on their savings accounts.
E. For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate.

14. Which of the following statements concerning the effective annual rate are correct?
I. When making financial decisions, you should compare effective annual rates rather than annual percentage rates.
II. The more frequently interest is compounded, the higher the effective annual rate.
III. A quoted rate of 6% compounded continuously has a higher effective annual rate than if the rate were compounded daily.
IV. When borrowing and choosing which loan to accept, you should select the offer with the highest effective annual rate.
A. I and II only
B. I and IV only
C. I, II, and III only
D. II, III, and IV only
E. I, II, III, and IV

15. The highest effective annual rate that can be derived from an annual percentage rate of 9% is computed as:
A. .09e - 1.
B. e.09 ( q.
C. e ( (1 + .09).
D. e.09 - 1.
E. (1 + .09)q.

16. The time value of money concept can be defined as:
A. the relationship between the supply and demand of money.
B. the relationship between money spent versus money received.
C. the relationship between a dollar to be received in the future and a dollar today.
D. the relationship between interest rate stated and amount paid.
E. None of the above.

17. Discounting cash flows involves:
A. discounting only those cash flows that occur at least 10 years in the future.
B. estimating only the cash flows that occur in the first 4 years of a project.
C. multiplying expected future cash flows by the cost of capital.
D. discounting all expected future cash flows to reflect the time value of money.
E. taking the cash discount offered on trade merchandise.

18. Compound interest:
A. allows for the reinvestment of interest payments.
B. does not allow for the reinvestment of interest payments.
C. is the same as simple interest.
D. provides a value that is less than simple interest.
E. Both A and D.

19. An annuity:
A. is a debt instrument that pays no interest.
B. is a stream of payments that varies with current market interest rates.
C. is a level stream of equal payments through time.
D. has no value.
E. None of the above.

20. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?
A. annual compounding
B. monthly compounding
C. daily compounding
D. continuous compounding
E. It is impossible to tell without knowing the term of the loan.

21. The present value of future cash flows minus initial cost is called:
A. the future value of the project.
B. the net present value of the project.
C. the equivalent sum of the investment.
D. the initial investment risk equivalent value.
E. None of the above.

22. Find the present value of $5,325 to be received in one period if the rate is 6.5%.
A. $5,000.00
B. $5,023.58
C. $5,644.50
D. $5,671.13
E. None of the above.

23. If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compounded interest at 7.5% for three years which one will pay more and by how much?
A. Simple interest by $50.00
B. Compound interest by $22.97
C. Compound interest by $150.75
D. Compound interest by $150.00
E. None of the above.

24. Bradley Snapp has deposited $7,000 in a guaranteed investment account with a promised rate of 6% compounded annually. He plans to leave it there for 4 full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make?
A. $1,960.00
B. $2,175.57
C. $8,960.00
D. $8,837.34
E. $9,175.57

25. Your parents are giving you $100 a month for four years while you are in college. At a 6% discount rate, what are these payments worth to you when you first start college?
A. $3,797.40
B. $4,167.09
C. $4,198.79
D. $4,258.03
E. $4,279.32

26. You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today?
A. $87,003.69
B. $87,380.23
C. $87,962.77
D. $88,104.26
E. $90,723.76

27. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9%, how much can Todd afford to borrow to buy a car?
A. $6,961.36
B. $8,499.13
C. $8,533.84
D. $8,686.82
E. $9,588.05

28. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5% on your money. Which option should you take and why?
A. You should accept the payments because they are worth $56,451.91 today.
B. You should accept the payments because they are worth $56,523.74 today.
C. You should accept the payments because they are worth $56,737.08 today.
D. You should accept the $50,000 because the payments are only worth $47,757.69 today.
E. You should accept the $50,000 because the payments are only worth $47,808.17 today.

29. Your employer contributes $25 a week to your retirement plan. Assume that you work for your employer for another twenty years and that the applicable discount rate is 5%. Given these assumptions, what is this employee benefit worth to you today?
A. $13,144.43
B. $15,920.55
C. $16,430.54
D. $16,446.34
E. $16,519.02

30. You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today?
A. $180,238.81
B. $201,867.47
C. $210,618.19
D. $223,162.58
E. $224,267.10

31. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?
A. $82,964.59
B. $83,189.29
C. $83,428.87
D. $83,687.23
E. $84,998.01

32. You need some money today and the only friend you have that has any is your ‘miserly' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?
A. $113.94
B. $115.65
C. $119.34
D. $119.63
E. $119.96

33. You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the first day of each year. What is the value of this annuity today at a 7% discount rate?
A. $84,282.98
B. $87,138.04
C. $90,182.79
D. $96,191.91
E. $116,916.21

34. You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Your discount rate is 8.5%. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
A. $8,699
B. $9,217
C. $9,706
D. $10,000
E. $10,850

35. You are comparing two annuities with equal present values. The applicable discount rate is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year?
A. $4,651
B. $5,075
C. $5,000
D. $5,375
E. $5,405

36. Martha receives $100 on the first of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for five years. At an 8% discount rate, what is the difference in the present value of these two sets of payments?
A. $32.88
B. $40.00
C. $99.01
D. $108.00
E. $112.50

37. What is the future value of $1,000 a year for five years at a 6% rate of interest?
A. $4,212.36
B. $5,075.69
C. $5,637.09
D. $6,001.38
E. $6,801.91

38. What is the future value of $2,400 a year for three years at an 8% rate of interest?
A. $6,185.03
B. $6,847.26
C. $7,134.16
D. $7,791.36
E. $8,414.67

39. Janet plans on saving $3,000 a year and expects to earn 8.5%. How much will Janet have at the end of twenty-five years if she earns what she expects?
A. $219,317.82
B. $230,702.57
C. $236,003.38
D. $244,868.92
E. $256,063.66

40. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings on the last day of each year. They both earn a 9% rate of return. What is the difference in their savings account balances at the end of thirty years?
A. $35,822.73
B. $36,803.03
C. $38,911.21
D. $39,803.04
E. $40,115.31

41. You borrow $5,600 to buy a car. The terms of the loan call for monthly payments for four years at a 5.9% rate of interest. What is the amount of each payment?
A. $103.22
B. $103.73
C. $130.62
D. $131.26
E. $133.04

42. You borrow $149,000 to buy a house. The mortgage rate is 7.5% and the loan period is 30 years. Payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay?
A. $138,086
B. $218,161
C. $226,059
D. $287,086
E. $375,059

43. The Great Giant Corp. has a management contract with its newly hired president. The contract requires a lump sum payment of $25 million be paid to the president upon the completion of her first ten years of service. The company wants to set aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 6.5% on these funds. How much must the company set aside each year for this purpose?
A. $1,775,042.93
B. $1,798,346.17
C. $1,801,033.67
D. $1,852,617.25
E. $1,938,018.22

44. You retire at age 60 and expect to live another 27 years. On the day you retire, you have $464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on your money during your retirement. How much can you withdraw from your retirement savings each month if you plan to die on the day you spend your last penny?
A. $2,001.96
B. $2,092.05
C. $2,398.17
D. $2,472.00
E. $2,481.27

45. The McDonald Group purchased a piece of property for $1.2 million. It paid a down payment of 20% in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75% compounded monthly. What is the amount of each mortgage payment?
A. $7,440.01
B. $8,978.26
C. $9,036.25
D. $9,399.18
E. $9,413.67

46. You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each month?
A. $471.30
B. $473.65
C. $476.79
D. $479.37
E. $480.40

47. You are buying a previously owned car today at a price of $6,890. You are paying $500 down in cash and financing the balance for 36 months at 7.9%. What is the amount of each loan payment?
A. $198.64
B. $199.94
C. $202.02
D. $214.78
E. $215.09

48. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500 per quarter for 25 years. You want to earn a minimum rate of return of 5.5%. What is the most you are willing to pay as a lump sum today to buy this annuity?
A. $26,988.16
B. $27,082.94
C. $27,455.33
D. $28,450.67
E. $28,806.30

49. Your car dealer is willing to lease you a new car for $299 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.9%, what is the current value of the lease?
A. $15,882.75
B. $15,906.14
C. $15,947.61
D. $16,235.42
E. $16,289.54

50. Your great-aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,500 on the first day of each year, starting immediately and continuing for fifty years. What is the value of this inheritance today if the applicable discount rate is 6.35%?
A. $36,811.30
B. $37,557.52
C. $39,204.04
D. $39,942.42
E. $40,006.09

51. Beatrice invests $1,000 in an account that pays 4% simple interest. How much more could she have earned over a five-year period if the interest had compounded annually?
A. $15.45
B. $15.97
C. $16.65
D. $17.09
E. $21.67

52. Your firm wants to save $250,000 to buy some new equipment three years from now. The plan is to set aside an equal amount of money on the first day of each year starting today. The firm can earn a 4.7% rate of return. How much does the firm have to save each year to achieve its goal?
A. $75,966.14
B. $76,896.16
C. $78,004.67
D. $81.414.14
E. $83,333.33

53. Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of ½ of 1 percent, how much will he have in his retirement account 35 years from now?
A. $199,45.944
B. $200,456.74
C. $249,981.21
D. $299,189.16
E. $300,685.11

54. You are considering an annuity which costs $100,000 today. The annuity pays $6,000 a year. The rate of return is 4.5%. What is the length of the annuity time period?
A. 24.96 years
B. 29.48 years
C. 31.49 years
D. 33.08 years
E. 38.00 years

55. Today, you signed loan papers agreeing to borrow $4,954.85 at 9% compounded monthly. The loan payment is $143.84 a month. How many loan payments must you make before the loan is paid in full?
A. 29.89
B. 36.00
C. 38.88
D. 40.00
E. 41.03

56. Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $136 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $450,000 a month for this purpose. The firm earns 6% compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations?
A. 184.61 months
B. 199.97 months
C. 234.34 months
D. 284.61 months
E. 299.97 months

57. Today, you are retiring. You have a total of $413,926 in your retirement savings and have the funds invested such that you expect to earn an average of 3%, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money?
A. 185.00 months
B. 213.29 months
C. 227.08 months
D. 236.84 months
E. 249.69 months

58. The Bad Guys Co. is notoriously known as a slow-payer. It currently needs to borrow $25,000 and only one company will even deal with Bad Guys. The terms of the loan call for daily payments of $30.76. The first payment is due today. The interest rate is 21% compounded daily. What is the time period of this loan?
A. 2.88 years
B. 2.94 years
C. 3.00 years
D. 3.13 years
E. 3.25 years

59. The Robertson Firm is considering a project which costs $123,900 to undertake. The project will yield cash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project?
A. 12.53%
B. 13.44%
C. 13.59%
D. 14.02%
E. 14.59%

60. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 a month for the next 40 years. What is the rate of return on this investment?
A. 3.45%
B. 3.47%
C. 3.50%
D. 3.52%
E. 3.55%

61. You have been investing $120 a month for the last 15 years. Today, your investment account is worth $47,341.19. What is your average rate of return on your investments?
A. 9.34%
B. 9.37%
C. 9.40%
D. 9.42%
E. 9.46%

62. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business venture. Today, Brinker sold that venture for $685,000. What is its rate of return on this venture?
A. 9.43%
B. 11.06%
C. 15.59%
D. 16.67%
E. 18.71%

63. Your mother helped you start saving $25 a month beginning on your 10th birthday. She always made you make your deposit on the first day of each month just to "start the month out right." Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?
A. 5.25%
B. 5.29%
C. 5.33%
D. 5.36%
E. 5.50%

64. Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $25 a day, every day until you turn 40. You open an investment account and deposit your first $25 today. What rate of return must you earn to achieve your goal?
A. 15.07%
B. 15.13%
C. 15.17%
D. 15.20%
E. 15.24%

65. Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $5,000, $9,000, and $15,000 over the next three years, respectively. After that time, Marko feels ABC will be worthless. Marko has determined that a 14% rate of return is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?
A. $19,201.76
B. $21,435.74
C. $23,457.96
D. $27,808.17
E. $31,758.00

66. You are considering two savings options. Both options offer a 4% rate of return. The first option is to save $1,200, $1,500, and $2,000 a year over the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?
A. $4,318.67
B. $4,491.42
C. $4,551.78
D. $4,607.23
E. $4,857.92

67. You are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 5%. What is the minimum amount that you will accept today if you are to select the lump sum offer?
A. $19,877.67
B. $20,203.00
C. $21,213.15
D. $23,387.50
E. $24,556.88

68. You are considering a job offer. The job offers an annual salary of $52,000, $55,000, and $60,000 a year for the next three years, respectively. The offer also includes a starting bonus of $2,000 payable immediately. What is this offer worth to you today at a discount rate of 6%?
A. $148,283.56
B. $148,383.56
C. $150,283.56
D. $150,383.56
E. $152,983.56

69. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given a 9% discount rate?
A. $4,713.62
B. $4,855.27
C. $5,103.18
D. $5,292.25
E. $6,853.61

70. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given an 11% discount rate?
A. $8,695.61
B. $8,700.89
C. $13,732.41
D. $13,812.03
E. $19,928.16

71. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given a 3% discount rate?
A. $13,732.41
B. $13,812.03
C. $14,308.08
D. $14,941.76
E. $14,987.69

72. You have some property for sale and have received two offers. The first offer is for $189,000 today in cash. The second offer is the payment of $100,000 today and an additional $100,000 two years from today. If the applicable discount rate is 8.75%, which offer should you accept and why?
A. You should accept the $189,000 today because it has the higher net present value.
B. You should accept the $189,000 today because it has the lower future value.
C. You should accept the second offer because you will receive $200,000 total.
D. You should accept the second offer because you will receive an extra $11,000.
E. You should accept the second offer because it has a present value of $194,555.42.

73. Your local travel agent is advertising an extravagant global vacation. The package deal requires that you pay $5,000 today, $15,000 one year from today, and a final payment of $25,000 on the day you leave two years from today. What is the cost of this vacation in today's dollars if the discount rate is 6%?
A. $39,057.41
B. $41,400.85
C. $43,082.39
D. $44,414.14
E. $46,518.00

74. One year ago, the Jenkins Family Fun Center deposited $3,600 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $5,000 to this account. It plans on making a final deposit of $7,500 to the account next year. How much will be available when it is ready to buy the equipment, assuming it earns a 7% rate of return?
A. $18,159.65
B. $19,430.84
C. $19,683.25
D. $20,194.54
E. $20,790.99

75. What is the future value of the following cash flows at the end of year 3 if the interest rate is 6%? The cash flows occur at the end of each year. [pic]
A. $15,916.78
B. $18,109.08
C. $18,246.25
D. $19,341.02
E. $19,608.07

76. What is the future value of the following cash flows at the end of year 3 if the interest rate is 9%? The cash flows occur at the end of each year. [pic]
A. $15,213.80
B. $15,619.70
C. $15,916.78
D. $16,177.14
E. $17,633.08

77. What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year. [pic]
A. $8,758.04
B. $8,806.39
C. $10,073.99
D. $10,314.00
E. $10,804.36

78. Suzette is going to receive $10,000 today as the result of an insurance settlement. In addition, she will receive $15,000 one year from today and $25,000 two years from today. She plans on saving all of this money and investing it for her retirement. If Suzette can earn an average of 11% on her investments, how much will she have in her account if she retires 25 years from today?
A. $536,124.93
B. $541,414.14
C. $546,072.91
D. $570,008.77
E. $595,098.67

79. The Bluebird Company has a $10,000 liability it must pay three years from today.
The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $2,500 a year for the next three years, starting one year from today. The account pays a 3% rate of return. How much does the Bluebird Company need to deposit today?
A. $1,867.74
B. $2,079.89
C. $3,108.09
D. $4,276.34
E. $4,642.28

80. The government has imposed a fine on the Not-So-Legal Company. The fine calls for annual payments of $100,000, $250,000, and $250,000, respectively over the next three years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including investment earnings, to a national health center. The government will earn 3.5% on the funds held. How much will the national health center receive three years from today?
A. $613,590.00
B. $614,622.50
C. $615,872.50
D. $616,006.00
E. $619,050.05

81. George Jefferson established a trust fund that provides $150,000 in scholarships each year for worthy students. The trust fund earns a 4.25% rate of return. How much money did Mr. Jefferson contribute to the fund assuming that only the interest income is distributed?
A. $3,291,613.13
B. $3,529,411.77
C. $3,750,000.00
D. $4,328,970.44
E. $6,375,000.00

82. A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worth today?
A. $0.41
B. $4.50
C. $5.00
D. $45.00
E. $50.00

83. You would like to establish a trust fund that will provide $50,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 2.75%. How much money must you deposit today to fund this gift for your heirs?
A. $1,333,333.33
B. $1,375,000.00
C. $1,425,000.00
D. $1,666,666.67
E. $1,818,181.82

84. You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
A. 3.25%
B. 3.33%
C. 3.43%
D. 3.50%
E. 3.67%

85. The Eternal Gift Insurance Company is offering you a policy that will pay you and your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy?
A. 2.85%
B. 3.25%
C. 3.46%
D. 3.51%
E. 3.60%

86. Your rich uncle establishes a trust in your name and deposits $150,000 in it. The trust pays a guaranteed 4% rate of return. How much will you receive each year if the trust is required to pay you all of the interest earnings on an annual basis?
A. $3,750
B. $4,000
C. $4,500
D. $5,400
E. $6,000

87. The preferred stock of ABC Co. offers an 8.4% rate of return. The stock is currently priced at $50.00 per share. What is the amount of the annual dividend?
A. $2.10
B. $4.20
C. $5.00
D. $6.40
E. $8.60

88. Your credit card company charges you 1.5% per month. What is the annual percentage rate on your account?
A. 12.00%
B. 15.00%
C. 15.39%
D. 18.00%
E. 19.56%

89. What is the annual percentage rate on a loan with a stated rate of 2% per quarter?
A. 2.00%
B. 2.71%
C. 4.04%
D. 8.00%
E. 8.24%

90. You are paying an effective annual rate of 13.8% on your credit card. The interest is compounded monthly. What is the annual percentage rate on your account?
A. 11.50%
B. 12.00%
C. 13.00%
D. 13.80%
E. 14.71%

91. What is the effective annual rate if a bank charges you 7.64% compounded quarterly?
A. 7.79%
B. 7.86%
C. 7.95%
D. 7.98%
E. 8.01%

92. Your credit card company quotes you a rate of 14.9%. Interest is billed monthly. What is the actual rate of interest you are paying?
A. 13.97%
B. 14.90%
C. 15.48%
D. 15.96%
E. 16.10%

93. Mr. Miser loans money at an annual rate of 21%. Interest is compounded daily. What is the actual rate Mr. Miser is charging on his loans?
A. 22.97%
B. 23.08%
C. 23.21%
D. 23.36%
E. 23.43%

94. You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.45% compounded daily. Loan B offers a rate of 7.5% compounded semi-annually. Loan _____ is the better offer because ______.
A. A; you will pay less interest
B. A; the annual percentage rate is 7.45%
C. B; the annual percentage rate is 7.64%
D. B; the interest is compounded less frequently
E. B; the effective annual rate is 7.64%

95. You have $2,500 that you want to use to open a savings account. You have found five different accounts that are acceptable to you. All you have to do now is determine which account you want to use such that you can earn the highest rate of interest possible. Which account should you use based upon the annual percentage rates quoted by each bank? [pic]
A. Account A
B. Account B
C. Account C
D. Account D
E. Account E

96. What is the effective annual rate of 14.9% compounded continuously?
A. 15.96%
B. 16.01%
C. 16.05%
D. 16.07%
E. 16.17%

97. What is the effective annual rate of 9.75% compounded continuously?
A. 9.99%
B. 10.11%
C. 10.24%
D. 10.28%
E. 10.30%

98. The Smart Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.9 annual percentage rate. What is the maximum rate the bank can actually earn based on the quoted rate?
A. 7.90%
B. 8.18%
C. 8.20%
D. 8.22%
E. 8.39%

99. You are going to loan your friend $1,000 for one year at a 5% rate of interest. How much additional interest can you earn if you compound the rate continuously rather than annually?
A. $.97
B. $1.09
C. $1.27
D. $1.36
E. $1.49

100. Today you earn a salary of $28,500. What will be your annual salary fifteen years from now if you earn annual raises of 3.5%?
A. $47,035.35
B. $47,522.89
C. $47,747.44
D. $48,091.91
E. $48,201.60

101. You hope to buy your dream house six years from now. Today your dream house costs $189,900. You expect housing prices to rise by an average of 4.5% per year over the next six years. How much will your dream house cost by the time you are ready to buy it?
A. $240,284.08
B. $246,019.67
C. $246,396.67
D. $246,831.94
E. $247,299.20

102. Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
A. $2,700.00
B. $2,730.30
C. $2,750.00
D. $2,768.40
E. $2,774.90

103. You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your funds?
A. $17,750.00
B. $17,989.28
C. $18,077.05
D. $18,213.69
E. $18,395.00

104. One year ago, you invested $3,000. Today it is worth $3,142.50. What rate of interest did you earn?
A. 4.63%
B. 4.68%
C. 4.70%
D. 4.73%
E. 4.75%

105. Forty years ago, your father invested $2,500. Today that investment is worth $107,921. What is the average rate of return your father earned on his investment?
A. 8.50%
B. 9.33%
C. 9.50%
D. 9.87%
E. 9.99%

106. You want to have $10,000 saved ten years from now. How much less do you have to deposit today to reach this goal if you can earn 6% rather than 5% on your savings?
A. $555.18
B. $609.81
C. $615.48
D. $928.73
E. $1,046.22

107. You have deposited $1,500 in an account that promises to pay 8% compounded quarterly for the next five years. How much will you have in the account at the end?
A. $1,598.33
B. $2,203.99
C. $2,228.92
D. $6,991.44
E. None of the above.

108. What is the future value of investing $9,000 for 7 years at a continuously compounded rate of 11%?
A. $15,930.00
B. $18,685.44
C. $19,369.83
D. $19,437.90
E. None of the above.

109. What is the future value of investing $3,000 for 3/4 year at a continuously compounded rate of 12%?
A. $3,163
B. $3,263
C. $3,283
D. $3,287
E. $3,317

110. Which of the following amounts is closest to the end value of investing $5,000 for 14 months at a stated annual interest rate of 6% compounded monthly?
A. $5,293
B. $5,345
C. $5,352
D. $5,362
E. $6,183

111. Which of the following amounts is closest to the end value of investing $10,000 for 18 months at a stated annual interest rate of 12% compounded quarterly?
A. $11,800
B. $11,852
C. $11,940
D. $11,961
E. None of the above is within $100 of the correct answer.

112. Which of the following amounts is closest to the end value of investing $7,500 for 2.5 years at an effective annual interest rate of 12.36%. Interest is compounded semiannually.
A. $7,531
B. $8,427
C. $9,469
D. $9,818
E. $10,037

113. If the stated rate of interest is 12% and it is compounded monthly, what is the effective annual interest rate?
A. 12.00%
B. 12.25%
C. 12.46%
D. 12.68%
E. 12.92%

114. What is the present value of a payment of $21,000 three years from now if the effective annual interest rate is 4%?
A. $17,951
B. $18,480
C. $18,658
D. $18,669
E. $19,218

115. Thornton will receive an inheritance of $500,000 three years from now. Thorton's discount rate is 10% compounded semiannually. Which of the following values is closest to the amount that Thornton should accept today for the right to his inheritance?
A. $373,108.
B. $375,657.
C. $665,500.
D. $670,048.
E. None of the above is within $10 of the correct answer.

116. A mortgage instrument pays $1.5 million at the end of each of the next two years. An investor has an alternative investment with the same amount of risk that will pay interest at 8% compounded semiannually. Which of the following amounts is closest to what the investor should pay for the mortgage instrument?
A. $1,386,834
B. $1,388,889
C. $2,674,897
D. $2,669,041
E. $3,854,512

117. You are to receive $75 per year indefinitely. The market rate of interest for these types of payments is 8%. The price you would pay for this stream is:
A. $9.375.
B. $81.00.
C. $93.75.
D. $937.50.
E. None of the above.

118. Aunt Clarisse has promised to leave you an annuity that will pay $60 next year and grow at an annual rate of 4%. The payments are expected to go on indefinitely and the interest rate is 9%. What is the value of the growing perpetuity?
A. $667
B. $693
C. $1,200
D. $1,248
E. None of the above

119. A court settlement awarded an accident victim four payments of $50,000 to be paid at the end of each of the next four years. Using a discount rate of 4%, calculate the present value of the annuity.
A. $173,255
B. $178,495
C. $181,495
D. $184,095
E. $200,000

120. What is the present value of 10 annual payments of $500 at a discount rate of 12%?
A. $1,332
B. $1,761
C. $1,840
D. $2,825
E. $3,040

121. An S&L provides a loan with 15 yearly repayments of $8,000 with the first payment beginning immediately. Which of the following amounts comes closest to the present value of the loan if the interest rate is 7%?
A. $72,863
B. $77,964
C. $115,648
D. $120,000
E. Not enough information is given to determine the answer.

122. The great, great grandparents of one of your classmates sold their factory to the government 104 years ago for $150,000. If these proceeds had been invested at 6%, how much would this legacy be worth today? Assume annual compounding.
A. $936,000.00
B. $1,086,000.00
C. $60,467,131.54
D. $60,617,131.54
E. $64,254,159.44

123. If a business takes out a $10,000, 7 year, 12% loan, the annual payment is:
A. $1,976.38
B. $2,000.00
C. $2,111.78
D. $2,191.17
E. $2,456.54

124. If a business takes out a $10,000, 7 year, 12% loan, the decrease in principal in year 1 is: (assume annual payments).
A. $991.17
B. $1,976.38
C. $1,200.00
D. $2,191.17
E. $2,456.54

Essay Questions

125. Mr. Miser, who is 35 years old, has just inherited $11,000 and decides to use the windfall towards his retirement. He places the money in a bank which promises a return of 6% per year until his planned retirement in 30 years. If his funds earn 6% interest compounded annually, how much will he have at retirement? Repeat the analysis for both semi-annual and continuous compounding.

126. Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance?

127. If you invest $100,000 today at 12% per year over the next 15 years, what is the most you can spend in equal amounts out of the fund each year over that time.

128. Using the example of a savings account, explain the difference between the effective annual rate and the annual percentage rate.

129. There are three factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

130. There are three factors that affect the future value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity.

131. A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000. At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments?

132. What is the different between an ordinary annuity and an annuity due? Which occurs more in practice? Give a common example of both.

Chapter 04 Discounted Cash Flow Valuation Answer Key

Multiple Choice Questions

1. An annuity stream of cash flow payments is a set of:
A. level cash flows occurring each time period for a fixed length of time.
B. level cash flows occurring each time period forever.
C. increasing cash flows occurring each time period for a fixed length of time.
D. increasing cash flows occurring each time period forever.
E. arbitrary cash flows occurring each time period for no more than 10 years.

Difficulty level: Easy
Topic: ANNUITY
Type: DEFINITIONS

2. Annuities where the payments occur at the end of each time period are called _____, whereas _____ refer to annuity streams with payments occurring at the beginning of each time period.
A. ordinary annuities; early annuities
B. late annuities; straight annuities
C. straight annuities; late annuities
D. annuities due; ordinary annuities
E. ordinary annuities; annuities due

Difficulty level: Easy
Topic: ANNUITIES DUE
Type: DEFINITIONS

3. An annuity stream where the payments occur forever is called a(n):
A. annuity due.
B. indemnity.
C. perpetuity.
D. amortized cash flow stream.
E. amortization table.

Difficulty level: Easy
Topic: PERPETUITY
Type: DEFINITIONS

4. The interest rate expressed in terms of the interest payment made each period is called the _____ rate.
A. stated annual interest
B. compound annual interest
C. effective annual interest
D. periodic interest
E. daily interest

Difficulty level: Easy
Topic: STATED INTEREST RATES
Type: DEFINITIONS

5. The interest rate expressed as if it were compounded once per year is called the _____ rate.
A. stated interest
B. compound interest
C. effective annual
D. periodic interest
E. daily interest

Difficulty level: Easy
Topic: EFFECTIVE ANNUAL RATE
Type: DEFINITIONS

6. The interest rate charged per period multiplied by the number of periods per year is called the _____ rate.
A. effective annual
B. annual percentage
C. periodic interest
D. compound interest
E. daily interest

Difficulty level: Easy
Topic: ANNUAL PERCENTAGE RATE
Type: DEFINITIONS

7. Paying off long-term debt by making installment payments is called:
A. foreclosing on the debt.
B. amortizing the debt.
C. funding the debt.
D. calling the debt.
E. None of the above.

Difficulty level: Easy
Topic: AMORTIZATION
Type: DEFINITIONS

8. You are comparing two annuities which offer monthly payments for ten years. Both annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity B pays on the last day of each month. Which one of the following statements is correct concerning these two annuities?
A. Both annuities are of equal value today.
B. Annuity B is an annuity due.
C. Annuity A has a higher future value than annuity B.
D. Annuity B has a higher present value than annuity A.
E. Both annuities have the same future value as of ten years from today.

Difficulty level: Medium
Topic: ORDINARY ANNUITY VERSUS ANNUITY DUE
Type: CONCEPTS

9. You are comparing two investment options. The cost to invest in either option is the same today. Both options will provide you with $20,000 of income. Option A pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of the following statements is correct given these two investment options?
A. Both options are of equal value given that they both provide $20,000 of income.
B. Option A is the better choice of the two given any positive rate of return.
C. Option B has a higher present value than option A given a positive rate of return.
D. Option B has a lower future value at year 5 than option A given a zero rate of return.
E. Option A is preferable because it is an annuity due.

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: CONCEPTS

10. You are considering two projects with the following cash flows: [pic]
Which of the following statements are true concerning these two projects?
I. Both projects have the same future value at the end of year 4, given a positive rate of return.
II. Both projects have the same future value given a zero rate of return.
III. Both projects have the same future value at any point in time, given a positive rate of return.
IV. Project A has a higher future value than project B, given a positive rate of return.
A. II only
B. IV only
C. I and III only
D. II and IV only
E. I, II, and III only

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: CONCEPTS

11. A perpetuity differs from an annuity because:
A. perpetuity payments vary with the rate of inflation.
B. perpetuity payments vary with the market rate of interest.
C. perpetuity payments are variable while annuity payments are constant.
D. perpetuity payments never cease.
E. annuity payments never cease.

Difficulty level: Easy
Topic: PERPETUITY VERSUS ANNUITY
Type: CONCEPTS

12. Which one of the following statements concerning the annual percentage rate is correct?
A. The annual percentage rate considers interest on interest.
B. The rate of interest you actually pay on a loan is called the annual percentage rate.
C. The effective annual rate is lower than the annual percentage rate when an interest rate is compounded quarterly.
D. When firms advertise the annual percentage rate they are violating U.S. truth-in-lending laws.
E. The annual percentage rate equals the effective annual rate when the rate on an account is designated as simple interest.

Difficulty level: Medium
Topic: ANNUAL PERCENTAGE RATE
Type: CONCEPTS

13. Which one of the following statements concerning interest rates is correct?
A. The stated rate is the same as the effective annual rate.
B. An effective annual rate is the rate that applies if interest were charged annually.
C. The annual percentage rate increases as the number of compounding periods per year increases.
D. Banks prefer more frequent compounding on their savings accounts.
E. For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate.

Difficulty level: Medium
Topic: INTEREST RATES
Type: CONCEPTS

14. Which of the following statements concerning the effective annual rate are correct?
I. When making financial decisions, you should compare effective annual rates rather than annual percentage rates.
II. The more frequently interest is compounded, the higher the effective annual rate.
III. A quoted rate of 6% compounded continuously has a higher effective annual rate than if the rate were compounded daily.
IV. When borrowing and choosing which loan to accept, you should select the offer with the highest effective annual rate.
A. I and II only
B. I and IV only
C. I, II, and III only
D. II, III, and IV only
E. I, II, III, and IV

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: CONCEPTS

15. The highest effective annual rate that can be derived from an annual percentage rate of 9% is computed as:
A. .09e - 1.
B. e.09 ( q.
C. e ( (1 + .09).
D. e.09 - 1.
E. (1 + .09)q.

Difficulty level: Medium
Topic: CONTINUOUS COMPOUNDING
Type: CONCEPTS

16. The time value of money concept can be defined as:
A. the relationship between the supply and demand of money.
B. the relationship between money spent versus money received.
C. the relationship between a dollar to be received in the future and a dollar today.
D. the relationship between interest rate stated and amount paid.
E. None of the above.

Difficulty level: Easy
Topic: TIME VALUE
Type: CONCEPTS

17. Discounting cash flows involves:
A. discounting only those cash flows that occur at least 10 years in the future.
B. estimating only the cash flows that occur in the first 4 years of a project.
C. multiplying expected future cash flows by the cost of capital.
D. discounting all expected future cash flows to reflect the time value of money.
E. taking the cash discount offered on trade merchandise.

Difficulty level: Easy
Topic: CASH FLOWS
Type: CONCEPTS

18. Compound interest:
A. allows for the reinvestment of interest payments.
B. does not allow for the reinvestment of interest payments.
C. is the same as simple interest.
D. provides a value that is less than simple interest.
E. Both A and D.

Difficulty level: Easy
Topic: INTEREST
Type: CONCEPTS

19. An annuity:
A. is a debt instrument that pays no interest.
B. is a stream of payments that varies with current market interest rates.
C. is a level stream of equal payments through time.
D. has no value.
E. None of the above.

Difficulty level: Easy
Topic: ANNUITY
Type: CONCEPTS

20. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?
A. annual compounding
B. monthly compounding
C. daily compounding
D. continuous compounding
E. It is impossible to tell without knowing the term of the loan.

Difficulty level: Easy
Topic: COMPOUNDING
Type: CONCEPTS

21. The present value of future cash flows minus initial cost is called:
A. the future value of the project.
B. the net present value of the project.
C. the equivalent sum of the investment.
D. the initial investment risk equivalent value.
E. None of the above.

Difficulty level: Easy
Topic: PRESENT VALUE
Type: CONCEPTS

22. Find the present value of $5,325 to be received in one period if the rate is 6.5%.
A. $5,000.00
B. $5,023.58
C. $5,644.50
D. $5,671.13
E. None of the above.

[pic]

Difficulty level: Easy
Topic: PRESENT VALUE - SINGLE SUM
Type: PROBLEMS

23. If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compounded interest at 7.5% for three years which one will pay more and by how much?
A. Simple interest by $50.00
B. Compound interest by $22.97
C. Compound interest by $150.75
D. Compound interest by $150.00
E. None of the above.

Simple Interest = $10,000 (.08)(3) = $2,400;
Compound Interest = $10,000((1.075)3 - 1) = $2,422.97;
Difference = $2,422.97 - $2,400 = $22.97

Difficulty level: Easy
Topic: SIMPLE & COMPOUND INTEREST
Type: PROBLEMS

24. Bradley Snapp has deposited $7,000 in a guaranteed investment account with a promised rate of 6% compounded annually. He plans to leave it there for 4 full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make?
A. $1,960.00
B. $2,175.57
C. $8,960.00
D. $8,837.34
E. $9,175.57

$7,000 (1.06)4 = $8,837.34

Difficulty level: Easy
Topic: FUTURE VALUE - SINGLE SUM
Type: PROBLEMS

25. Your parents are giving you $100 a month for four years while you are in college. At a 6% discount rate, what are these payments worth to you when you first start college?
A. $3,797.40
B. $4,167.09
C. $4,198.79
D. $4,258.03
E. $4,279.32

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

26. You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today?
A. $87,003.69
B. $87,380.23
C. $87,962.77
D. $88,104.26
E. $90,723.76

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

27. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9%, how much can Todd afford to borrow to buy a car?
A. $6,961.36
B. $8,499.13
C. $8,533.84
D. $8,686.82
E. $9,588.05

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

28. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5% on your money. Which option should you take and why?
A. You should accept the payments because they are worth $56,451.91 today.
B. You should accept the payments because they are worth $56,523.74 today.
C. You should accept the payments because they are worth $56,737.08 today.
D. You should accept the $50,000 because the payments are only worth $47,757.69 today.
E. You should accept the $50,000 because the payments are only worth $47,808.17 today.

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

29. Your employer contributes $25 a week to your retirement plan. Assume that you work for your employer for another twenty years and that the applicable discount rate is 5%. Given these assumptions, what is this employee benefit worth to you today?
A. $13,144.43
B. $15,920.55
C. $16,430.54
D. $16,446.34
E. $16,519.02

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

30. You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today?
A. $180,238.81
B. $201,867.47
C. $210,618.19
D. $223,162.58
E. $224,267.10

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY AND PRESENT VALUE
Type: PROBLEMS

31. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?
A. $82,964.59
B. $83,189.29
C. $83,428.87
D. $83,687.23
E. $84,998.01

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE AND PRESENT VALUE
Type: PROBLEMS

32. You need some money today and the only friend you have that has any is your ‘miserly' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?
A. $113.94
B. $115.65
C. $119.34
D. $119.63
E. $119.96

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE AND PRESENT VALUE
Type: PROBLEMS

33. You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the first day of each year. What is the value of this annuity today at a 7% discount rate?
A. $84,282.98
B. $87,138.04
C. $90,182.79
D. $96,191.91
E. $116,916.21

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE AND PRESENT VALUE
Type: PROBLEMS

34. You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Your discount rate is 8.5%. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
A. $8,699
B. $9,217
C. $9,706
D. $10,000
E. $10,850

[pic]

[pic]
Difference = $111,040.97 - $102,341.91 = $8,699.06 = $8,699 (rounded)
Note: The difference = .085 ( $102,341.91 = $8,699.06

Difficulty level: Medium
Topic: ORDINARY ANNUITY VERSUS ANNUITY DUE
Type: PROBLEMS

35. You are comparing two annuities with equal present values. The applicable discount rate is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year?
A. $4,651
B. $5,075
C. $5,000
D. $5,375
E. $5,405

[pic]
Because each payment is received one year later, then the cash flow has to equal: $5,000 ( (1 + .075) = $5,375

Difficulty level: Medium
Topic: ORDINARY ANNUITY VERSUS ANNUITY DUE
Type: PROBLEMS

36. Martha receives $100 on the first of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for five years. At an 8% discount rate, what is the difference in the present value of these two sets of payments?
A. $32.88
B. $40.00
C. $99.01
D. $108.00
E. $112.50

[pic]
Difference = $4,964.72 - $4,931.84 = $32.88
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY VERSUS ANNUITY DUE
Type: PROBLEMS

37. What is the future value of $1,000 a year for five years at a 6% rate of interest?
A. $4,212.36
B. $5,075.69
C. $5,637.09
D. $6,001.38
E. $6,801.91

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND FUTURE VALUE
Type: PROBLEMS

38. What is the future value of $2,400 a year for three years at an 8% rate of interest?
A. $6,185.03
B. $6,847.26
C. $7,134.16
D. $7,791.36
E. $8,414.67

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND FUTURE VALUE
Type: PROBLEMS

39. Janet plans on saving $3,000 a year and expects to earn 8.5%. How much will Janet have at the end of twenty-five years if she earns what she expects?
A. $219,317.82
B. $230,702.57
C. $236,003.38
D. $244,868.92
E. $256,063.66

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY AND FUTURE VALUE
Type: PROBLEMS

40. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings on the last day of each year. They both earn a 9% rate of return. What is the difference in their savings account balances at the end of thirty years?
A. $35,822.73
B. $36,803.03
C. $38,911.21
D. $39,803.04
E. $40,115.31

[pic]
Difference = $445,725.65 - $408,922.62 = $36,803.03
Note: Difference = $408,922.62 ( .09 = $36,803.03

Difficulty level: Medium
Topic: ANNUITY DUE VERSUS ORDINARY ANNUITY
Type: PROBLEMS

41. You borrow $5,600 to buy a car. The terms of the loan call for monthly payments for four years at a 5.9% rate of interest. What is the amount of each payment?
A. $103.22
B. $103.73
C. $130.62
D. $131.26
E. $133.04

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY PAYMENTS
Type: PROBLEMS

42. You borrow $149,000 to buy a house. The mortgage rate is 7.5% and the loan period is 30 years. Payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay?
A. $138,086
B. $218,161
C. $226,059
D. $287,086
E. $375,059

[pic]
Total interest = ($1,041.83 ( 30 ( 12) - $149,000 = $226,058.80 = $226,059 (rounded)

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND COST OF INTEREST
Type: PROBLEMS

43. The Great Giant Corp. has a management contract with its newly hired president. The contract requires a lump sum payment of $25 million be paid to the president upon the completion of her first ten years of service. The company wants to set aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 6.5% on these funds. How much must the company set aside each year for this purpose?
A. $1,775,042.93
B. $1,798,346.17
C. $1,801,033.67
D. $1,852,617.25
E. $1,938,018.22

[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY PAYMENTS AND FUTURE VALUE
Type: PROBLEMS

44. You retire at age 60 and expect to live another 27 years. On the day you retire, you have $464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on your money during your retirement. How much can you withdraw from your retirement savings each month if you plan to die on the day you spend your last penny?
A. $2,001.96
B. $2,092.05
C. $2,398.17
D. $2,472.00
E. $2,481.27

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

45. The McDonald Group purchased a piece of property for $1.2 million. It paid a down payment of 20% in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75% compounded monthly. What is the amount of each mortgage payment?
A. $7,440.01
B. $8,978.26
C. $9,036.25
D. $9,399.18
E. $9,413.67

Amount financed = $1,200,000 ( (1 - .2) = $960,000
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

46. You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each month?
A. $471.30
B. $473.65
C. $476.79
D. $479.37
E. $480.40

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

47. You are buying a previously owned car today at a price of $6,890. You are paying $500 down in cash and financing the balance for 36 months at 7.9%. What is the amount of each loan payment?
A. $198.64
B. $199.94
C. $202.02
D. $214.78
E. $215.09

Amount financed = $6,890 - $500 = $6,390
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

48. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500 per quarter for 25 years. You want to earn a minimum rate of return of 5.5%. What is the most you are willing to pay as a lump sum today to buy this annuity?
A. $26,988.16
B. $27,082.94
C. $27,455.33
D. $28,450.67
E. $28,806.30

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

49. Your car dealer is willing to lease you a new car for $299 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.9%, what is the current value of the lease?
A. $15,882.75
B. $15,906.14
C. $15,947.61
D. $16,235.42
E. $16,289.54

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

50. Your great-aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,500 on the first day of each year, starting immediately and continuing for fifty years. What is the value of this inheritance today if the applicable discount rate is 6.35%?
A. $36,811.30
B. $37,557.52
C. $39,204.04
D. $39,942.42
E. $40,006.09

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE PAYMENTS AND PRESENT VALUE
Type: PROBLEMS

51. Beatrice invests $1,000 in an account that pays 4% simple interest. How much more could she have earned over a five-year period if the interest had compounded annually?
A. $15.45
B. $15.97
C. $16.65
D. $17.09
E. $21.67

Ending value at 4% simple interest = $1,000 + ($1,000 ( .04 ( 5) = $1,200.00; Ending value at 4% compounded annually = $1,000 ( (1 +.04)5 = $1,216.65;
Difference = $1,216.65 - $1,200.00 = $16.65
[pic]

Difficulty level: Easy
Topic: SIMPLE VERSUS COMPOUND INTEREST
Type: PROBLEMS

52. Your firm wants to save $250,000 to buy some new equipment three years from now. The plan is to set aside an equal amount of money on the first day of each year starting today. The firm can earn a 4.7% rate of return. How much does the firm have to save each year to achieve its goal?
A. $75,966.14
B. $76,896.16
C. $78,004.67
D. $81.414.14
E. $83,333.33

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE PAYMENTS AND FUTURE VALUE
Type: PROBLEMS

53. Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of ½ of 1 percent, how much will he have in his retirement account 35 years from now?
A. $199,45.944
B. $200,456.74
C. $249,981.21
D. $299,189.16
E. $300,685.11

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE PAYMENTS AND FUTURE VALUE
Type: PROBLEMS

54. You are considering an annuity which costs $100,000 today. The annuity pays $6,000 a year. The rate of return is 4.5%. What is the length of the annuity time period?
A. 24.96 years
B. 29.48 years
C. 31.49 years
D. 33.08 years
E. 38.00 years

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE
Type: PROBLEMS

55. Today, you signed loan papers agreeing to borrow $4,954.85 at 9% compounded monthly. The loan payment is $143.84 a month. How many loan payments must you make before the loan is paid in full?
A. 29.89
B. 36.00
C. 38.88
D. 40.00
E. 41.03

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE
Type: PROBLEMS

56. Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $136 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $450,000 a month for this purpose. The firm earns 6% compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations?
A. 184.61 months
B. 199.97 months
C. 234.34 months
D. 284.61 months
E. 299.97 months

[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY TIME PERIODS AND FUTURE VALUE
Type: PROBLEMS

57. Today, you are retiring. You have a total of $413,926 in your retirement savings and have the funds invested such that you expect to earn an average of 3%, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money?
A. 185.00 months
B. 213.29 months
C. 227.08 months
D. 236.84 months
E. 249.69 months

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE TIME PERIODS AND PRESENT VALUE
Type: PROBLEMS

58. The Bad Guys Co. is notoriously known as a slow-payer. It currently needs to borrow $25,000 and only one company will even deal with Bad Guys. The terms of the loan call for daily payments of $30.76. The first payment is due today. The interest rate is 21% compounded daily. What is the time period of this loan?
A. 2.88 years
B. 2.94 years
C. 3.00 years
D. 3.13 years
E. 3.25 years

[pic]

Difficulty level: Medium
Topic: ANNUITY DUE TIME PERIODS
Type: PROBLEMS

59. The Robertson Firm is considering a project which costs $123,900 to undertake. The project will yield cash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project?
A. 12.53%
B. 13.44%
C. 13.59%
D. 14.02%
E. 14.59%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that your answer is correct.
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY INTEREST RATE
Type: PROBLEMS

60. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 a month for the next 40 years. What is the rate of return on this investment?
A. 3.45%
B. 3.47%
C. 3.50%
D. 3.52%
E. 3.55%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct.
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY INTEREST RATE
Type: PROBLEMS

61. You have been investing $120 a month for the last 15 years. Today, your investment account is worth $47,341.19. What is your average rate of return on your investments?
A. 9.34%
B. 9.37%
C. 9.40%
D. 9.42%
E. 9.46%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct.
[pic]

Difficulty level: Medium
Topic: ORDINARY ANNUITY INTEREST RATE
Type: PROBLEMS

62. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business venture. Today, Brinker sold that venture for $685,000. What is its rate of return on this venture?
A. 9.43%
B. 11.06%
C. 15.59%
D. 16.67%
E. 18.71%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct.
[pic]

Difficulty level: Easy
Topic: ORDINARY ANNUITY INTEREST RATE
Type: PROBLEMS

63. Your mother helped you start saving $25 a month beginning on your 10th birthday. She always made you make your deposit on the first day of each month just to "start the month out right." Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?
A. 5.25%
B. 5.29%
C. 5.33%
D. 5.36%
E. 5.50%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct.
[pic]
To more decimal places, the answer is 5.28632%.

Difficulty level: Easy
Topic: ANNUITY DUE INTEREST RATE
Type: PROBLEMS

64. Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $25 a day, every day until you turn 40. You open an investment account and deposit your first $25 today. What rate of return must you earn to achieve your goal?
A. 15.07%
B. 15.13%
C. 15.17%
D. 15.20%
E. 15.24%

[pic]
This can not be solved directly, so it's easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct.
[pic]
To more decimal places, the answer is 15.0697117%.

Difficulty level: Easy
Topic: ANNUITY DUE INTEREST RATE
Type: PROBLEMS

65. Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $5,000, $9,000, and $15,000 over the next three years, respectively. After that time, Marko feels ABC will be worthless. Marko has determined that a 14% rate of return is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?
A. $19,201.76
B. $21,435.74
C. $23,457.96
D. $27,808.17
E. $31,758.00

[pic]
Present value = $4,385.96 + $6,925.21 + $10,124.57 = $21,435.74

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

66. You are considering two savings options. Both options offer a 4% rate of return. The first option is to save $1,200, $1,500, and $2,000 a year over the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?
A. $4,318.67
B. $4,491.42
C. $4,551.78
D. $4,607.23
E. $4,857.92

[pic]
Present value = $1,153.85 + $1,386.83 + $1,777.99 = $4,318.67

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

67. You are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 5%. What is the minimum amount that you will accept today if you are to select the lump sum offer?
A. $19,877.67
B. $20,203.00
C. $21,213.15
D. $23,387.50
E. $24,556.88

[pic]
Present value = $4,761.90 + $6,802.72 + $8,638.38 = $20,203.00

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

68. You are considering a job offer. The job offers an annual salary of $52,000, $55,000, and $60,000 a year for the next three years, respectively. The offer also includes a starting bonus of $2,000 payable immediately. What is this offer worth to you today at a discount rate of 6%?
A. $148,283.56
B. $148,383.56
C. $150,283.56
D. $150,383.56
E. $152,983.56

[pic]
Present value = $2,000 + $49,056.60 + $48,949.80 + $50,377.16 = $150,383.56

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

69. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given a 9% discount rate?
A. $4,713.62
B. $4,855.27
C. $5,103.18
D. $5,292.25
E. $6,853.61

[pic]
Present value = $1,100.92 + $1,515.02 + $2,239.33 = $4,855.27

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

70. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given an 11% discount rate?
A. $8,695.61
B. $8,700.89
C. $13,732.41
D. $13,812.03
E. $19,928.16

[pic]
Present value = $5,045.05 + $7,304.60 + $1,462.38 = $13,812.03

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

71. You are considering a project with the following cash flows: [pic]
What is the present value of these cash flows, given a 3% discount rate?
A. $13,732.41
B. $13,812.03
C. $14,308.08
D. $14,941.76
E. $14,987.69

[pic]
Present value = $4,077.67 + $4,712.98 + $4,941.76 = $13,732.41

Difficulty level: Easy
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

72. You have some property for sale and have received two offers. The first offer is for $189,000 today in cash. The second offer is the payment of $100,000 today and an additional $100,000 two years from today. If the applicable discount rate is 8.75%, which offer should you accept and why?
A. You should accept the $189,000 today because it has the higher net present value.
B. You should accept the $189,000 today because it has the lower future value.
C. You should accept the second offer because you will receive $200,000 total.
D. You should accept the second offer because you will receive an extra $11,000.
E. You should accept the second offer because it has a present value of $194,555.42.

[pic]
Present value = $100,000 + $84,555.42 = $184,555.42
You should accept the $189,000 today since it is the higher net present value.

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

73. Your local travel agent is advertising an extravagant global vacation. The package deal requires that you pay $5,000 today, $15,000 one year from today, and a final payment of $25,000 on the day you leave two years from today. What is the cost of this vacation in today's dollars if the discount rate is 6%?
A. $39,057.41
B. $41,400.85
C. $43,082.39
D. $44,414.14
E. $46,518.00

[pic]
Present value = $5,000.00 + $14,150.94 + $22,249.91 = $41,400.85

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND PRESENT VALUE
Type: PROBLEMS

74. One year ago, the Jenkins Family Fun Center deposited $3,600 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $5,000 to this account. It plans on making a final deposit of $7,500 to the account next year. How much will be available when it is ready to buy the equipment, assuming it earns a 7% rate of return?
A. $18,159.65
B. $19,430.84
C. $19,683.25
D. $20,194.54
E. $20,790.99

[pic]
Future value = $5,049.19 + $6,553.98 + $9,187.82 = $20,790.99

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

75. What is the future value of the following cash flows at the end of year 3 if the interest rate is 6%? The cash flows occur at the end of each year. [pic]
A. $15,916.78
B. $18,109.08
C. $18,246.25
D. $19,341.02
E. $19,608.07

[pic]
Future value = $5,820.25 + $10,176.00 + $2,250.00 = $18,246.25

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

76. What is the future value of the following cash flows at the end of year 3 if the interest rate is 9%? The cash flows occur at the end of each year. [pic]
A. $15,213.80
B. $15,619.70
C. $15,916.78
D. $16,177.14
E. $17,633.08

[pic]
Future value = $11,667.14 + $0 + $4,510.00 = $16,177.14

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

77. What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year. [pic]
A. $8,758.04
B. $8,806.39
C. $10,073.99
D. $10,314.00
E. $10,804.36

[pic]
Future value = $7,821.74 + $2,252.25 + $0 = $10,073.99

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

78. Suzette is going to receive $10,000 today as the result of an insurance settlement. In addition, she will receive $15,000 one year from today and $25,000 two years from today. She plans on saving all of this money and investing it for her retirement. If Suzette can earn an average of 11% on her investments, how much will she have in her account if she retires 25 years from today?
A. $536,124.93
B. $541,414.14
C. $546,072.91
D. $570,008.77
E. $595,098.67

[pic]
Future value = $135,854.64 + $183,587.35 + $275,656.68 = $595,098.67

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

79. The Bluebird Company has a $10,000 liability it must pay three years from today.
The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $2,500 a year for the next three years, starting one year from today. The account pays a 3% rate of return. How much does the Bluebird Company need to deposit today?
A. $1,867.74
B. $2,079.89
C. $3,108.09
D. $4,276.34
E. $4,642.28

[pic]

Difficulty level: Medium
Topic: PRESENT VALUE, PAYMENTS AND FUTURE VALUE
Type: PROBLEMS

80. The government has imposed a fine on the Not-So-Legal Company. The fine calls for annual payments of $100,000, $250,000, and $250,000, respectively over the next three years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including investment earnings, to a national health center. The government will earn 3.5% on the funds held. How much will the national health center receive three years from today?
A. $613,590.00
B. $614,622.50
C. $615,872.50
D. $616,006.00
E. $619,050.05

[pic]
FV = $107,122.50 + $258,750.00 + $250,000 = $615,872.50

Difficulty level: Medium
Topic: UNEVEN CASH FLOWS AND FUTURE VALUE
Type: PROBLEMS

81. George Jefferson established a trust fund that provides $150,000 in scholarships each year for worthy students. The trust fund earns a 4.25% rate of return. How much money did Mr. Jefferson contribute to the fund assuming that only the interest income is distributed?
A. $3,291,613.13
B. $3,529,411.77
C. $3,750,000.00
D. $4,328,970.44
E. $6,375,000.00

[pic]

Difficulty level: Easy
Topic: PERPETUITY PRESENT VALUE
Type: PROBLEMS

82. A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worth today?
A. $0.41
B. $4.50
C. $5.00
D. $45.00
E. $50.00

[pic]

Difficulty level: Easy
Topic: PERPETUITY PRESENT VALUE
Type: PROBLEMS

83. You would like to establish a trust fund that will provide $50,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 2.75%. How much money must you deposit today to fund this gift for your heirs?
A. $1,333,333.33
B. $1,375,000.00
C. $1,425,000.00
D. $1,666,666.67
E. $1,818,181.82

[pic]

Difficulty level: Easy
Topic: PERPETUITY PRESENT VALUE
Type: PROBLEMS

84. You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
A. 3.25%
B. 3.33%
C. 3.43%
D. 3.50%
E. 3.67%

[pic]

Difficulty level: Medium
Topic: PERPETUITY DISCOUNT RATE
Type: PROBLEMS

85. The Eternal Gift Insurance Company is offering you a policy that will pay you and your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy?
A. 2.85%
B. 3.25%
C. 3.46%
D. 3.51%
E. 3.60%

[pic]

Difficulty level: Easy
Topic: PERPETUITY DISCOUNT RATE
Type: PROBLEMS

86. Your rich uncle establishes a trust in your name and deposits $150,000 in it. The trust pays a guaranteed 4% rate of return. How much will you receive each year if the trust is required to pay you all of the interest earnings on an annual basis?
A. $3,750
B. $4,000
C. $4,500
D. $5,400
E. $6,000

[pic]

Difficulty level: Easy
Topic: PERPETUITY PAYMENT
Type: PROBLEMS

87. The preferred stock of ABC Co. offers an 8.4% rate of return. The stock is currently priced at $50.00 per share. What is the amount of the annual dividend?
A. $2.10
B. $4.20
C. $5.00
D. $6.40
E. $8.60

[pic]

Difficulty level: Easy
Topic: PERPETUITY PAYMENT
Type: PROBLEMS

88. Your credit card company charges you 1.5% per month. What is the annual percentage rate on your account?
A. 12.00%
B. 15.00%
C. 15.39%
D. 18.00%
E. 19.56%

APR = .015 ( 12 = .18 = 18%

Difficulty level: Medium
Topic: ANNUAL PERCENTAGE RATE
Type: PROBLEMS

89. What is the annual percentage rate on a loan with a stated rate of 2% per quarter?
A. 2.00%
B. 2.71%
C. 4.04%
D. 8.00%
E. 8.24%

APR = .02 ( 4 = .08 = 8%

Difficulty level: Medium
Topic: ANNUAL PERCENTAGE RATE
Type: PROBLEMS

90. You are paying an effective annual rate of 13.8% on your credit card. The interest is compounded monthly. What is the annual percentage rate on your account?
A. 11.50%
B. 12.00%
C. 13.00%
D. 13.80%
E. 14.71%

[pic]

Difficulty level: Medium
Topic: ANNUAL PERCENTAGE RATE
Type: PROBLEMS

91. What is the effective annual rate if a bank charges you 7.64% compounded quarterly?
A. 7.79%
B. 7.86%
C. 7.95%
D. 7.98%
E. 8.01%

[pic]

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: PROBLEMS

92. Your credit card company quotes you a rate of 14.9%. Interest is billed monthly. What is the actual rate of interest you are paying?
A. 13.97%
B. 14.90%
C. 15.48%
D. 15.96%
E. 16.10%

[pic]

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: PROBLEMS

93. Mr. Miser loans money at an annual rate of 21%. Interest is compounded daily. What is the actual rate Mr. Miser is charging on his loans?
A. 22.97%
B. 23.08%
C. 23.21%
D. 23.36%
E. 23.43%

[pic]

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: PROBLEMS

94. You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.45% compounded daily. Loan B offers a rate of 7.5% compounded semi-annually. Loan _____ is the better offer because ______.
A. A; you will pay less interest
B. A; the annual percentage rate is 7.45%
C. B; the annual percentage rate is 7.64%
D. B; the interest is compounded less frequently
E. B; the effective annual rate is 7.64%

[pic]
[pic]

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: PROBLEMS

95. You have $2,500 that you want to use to open a savings account. You have found five different accounts that are acceptable to you. All you have to do now is determine which account you want to use such that you can earn the highest rate of interest possible. Which account should you use based upon the annual percentage rates quoted by each bank? [pic]
A. Account A
B. Account B
C. Account C
D. Account D
E. Account E

[pic]
[pic]
Using ex on a financial calculator: EAR = 3.72% On the Texas Instruments BA II Plus, the input is: .0365, 2nd, ex, -1, = .0372 = 3.72%
[pic]
Account B offers the highest effective annual rate at 3.76%.

Difficulty level: Medium
Topic: EFFECTIVE ANNUAL RATE
Type: PROBLEMS

96. What is the effective annual rate of 14.9% compounded continuously?
A. 15.96%
B. 16.01%
C. 16.05%
D. 16.07%
E. 16.17%

[pic]
Using ex on a financial calculator: EAR = 16.07% On the Texas Instruments BA II Plus, the input is: .149, 2nd, ex, -1, = .1607 = 16.07%

Difficulty level: Medium
Topic: CONTINUOUS COMPOUNDING
Type: PROBLEMS

97. What is the effective annual rate of 9.75% compounded continuously?
A. 9.99%
B. 10.11%
C. 10.24%
D. 10.28%
E. 10.30%

[pic]
Using ex on a financial calculator: EAR = 10.24% On the Texas Instruments BA II Plus, the input is: .0975, 2nd, ex, -1, = .1024 = 10.24%

Difficulty level: Medium
Topic: CONTINUOUS COMPOUNDING
Type: PROBLEMS

98. The Smart Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.9 annual percentage rate. What is the maximum rate the bank can actually earn based on the quoted rate?
A. 7.90%
B. 8.18%
C. 8.20%
D. 8.22%
E. 8.39%

[pic]
Using ex on a financial calculator: EAR = 8.22% On the Texas Instruments BA II Plus, the input is: .079, 2nd, ex, -1, = .0822 = 8.22%

Difficulty level: Medium
Topic: CONTINUOUS COMPOUNDING
Type: PROBLEMS

99. You are going to loan your friend $1,000 for one year at a 5% rate of interest. How much additional interest can you earn if you compound the rate continuously rather than annually?
A. $.97
B. $1.09
C. $1.27
D. $1.36
E. $1.49

[pic]
Using ex on a financial calculator: EAR = 5.127% On the Texas Instruments BA II Plus, the input is: .05, 2nd, ex, -1, = .05127 = 5.127%
Additional interest = $1,000 ( (.05127 - .05) = $1.27

Difficulty level: Medium
Topic: CONTINUOUS COMPOUNDING VERSUS ANNUAL COMPOUNDING
Type: PROBLEMS

100. Today you earn a salary of $28,500. What will be your annual salary fifteen years from now if you earn annual raises of 3.5%?
A. $47,035.35
B. $47,522.89
C. $47,747.44
D. $48,091.91
E. $48,201.60

Future value = $28,500 ( (1 + .035)15 = $47,747.44
[pic]

Difficulty level: Medium
Topic: FUTURE VALUE
Type: PROBLEMS

101. You hope to buy your dream house six years from now. Today your dream house costs $189,900. You expect housing prices to rise by an average of 4.5% per year over the next six years. How much will your dream house cost by the time you are ready to buy it?
A. $240,284.08
B. $246,019.67
C. $246,396.67
D. $246,831.94
E. $247,299.20

Future value = $189,900 ( (1 + .045)6 = $247,299.20
[pic]

Difficulty level: Medium
Topic: FUTURE VALUE
Type: PROBLEMS

102. Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest?
A. $2,700.00
B. $2,730.30
C. $2,750.00
D. $2,768.40
E. $2,774.90

Present value = $5,539.92 ( [1 ( (1 + .0425)17] = $2,730.30
[pic]

Difficulty level: Medium
Topic: PRESENT VALUE
Type: PROBLEMS

103. You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your funds?
A. $17,750.00
B. $17,989.28
C. $18,077.05
D. $18,213.69
E. $18,395.00

Present value = $40,000 ( [1 ( (1 + .063)13] = $18,077.05
[pic]

Difficulty level: Medium
Topic: PRESENT VALUE
Type: PROBLEMS

104. One year ago, you invested $3,000. Today it is worth $3,142.50. What rate of interest did you earn?
A. 4.63%
B. 4.68%
C. 4.70%
D. 4.73%
E. 4.75%

$3,142.50 = $3,000 ( (1 + r)1; r = 4.75%
[pic]

Difficulty level: Easy
Topic: INTEREST RATE FOR A SINGLE PERIOD
Type: PROBLEMS

105. Forty years ago, your father invested $2,500. Today that investment is worth $107,921. What is the average rate of return your father earned on his investment?
A. 8.50%
B. 9.33%
C. 9.50%
D. 9.87%
E. 9.99%

$107,921 = $2,500 ( (1 + r)40; r = 9.87%
[pic]

Difficulty level: Easy
Topic: INTEREST RATE FOR MULTIPLE PERIODS
Type: PROBLEMS

106. You want to have $10,000 saved ten years from now. How much less do you have to deposit today to reach this goal if you can earn 6% rather than 5% on your savings?
A. $555.18
B. $609.81
C. $615.48
D. $928.73
E. $1,046.22

Present value = $10,000 ( [1 ( (1 + .06)10] = $5,583.95; Present value = $10,000 ( [1 ( (1 + .05)10] = $6,139.13; Difference = $6,139.13 - $5,583.95 = $555.18
[pic]

Difficulty level: Medium
Topic: PRESENT VALUE AND RATE CHANGES
Type: PROBLEMS

107. You have deposited $1,500 in an account that promises to pay 8% compounded quarterly for the next five years. How much will you have in the account at the end?
A. $1,598.33
B. $2,203.99
C. $2,228.92
D. $6,991.44
E. None of the above.

$1,500(1.02)20 = $2,228.92

Difficulty level: Easy
Topic: FUTURE VALUE - SINGLE SUM
Type: PROBLEMS

108. What is the future value of investing $9,000 for 7 years at a continuously compounded rate of 11%?
A. $15,930.00
B. $18,685.44
C. $19,369.83
D. $19,437.90
E. None of the above.

$9,000(e.11(7)) -1 = $9,000 (2.15976625) = $19,437.90

Difficulty level: Easy
Topic: FUTURE VALUE - SINGLE SUM
Type: PROBLEMS

109. What is the future value of investing $3,000 for 3/4 year at a continuously compounded rate of 12%?
A. $3,163
B. $3,263
C. $3,283
D. $3,287
E. $3,317

EAR = (er - 1) = e.12 - 1 = 0.1275 (12.75%)
End value after 3/4 year = $3000(1 + 0.1275)3/4 = $3,282.53

Difficulty level: Challenge
Topic: FUTURE VALUE - CONTINUOUS COMPOUNDING
Type: PROBLEMS

110. Which of the following amounts is closest to the end value of investing $5,000 for 14 months at a stated annual interest rate of 6% compounded monthly?
A. $5,293
B. $5,345
C. $5,352
D. $5,362
E. $6,183

EAR = (1 + r/m)m-1 = [1 + (0.06/12)]12- 1 = 0.06167781
End value = $5,000(1 + 0.06167781)14/12 = $5,361.61

Difficulty level: Medium
Topic: EAR & FUTURE VALUE
Type: PROBLEMS

111. Which of the following amounts is closest to the end value of investing $10,000 for 18 months at a stated annual interest rate of 12% compounded quarterly?
A. $11,800
B. $11,852
C. $11,940
D. $11,961
E. None of the above is within $100 of the correct answer.

EAR = (1 + r/m)m-1 = [1 + (0.12/4)]4-1 = 0.1255
End value = $10,000(1 + 0.1255)1.5 = $11,940.38

Difficulty level: Medium
Topic: EAR & FUTURE VALUE
Type: PROBLEMS

112. Which of the following amounts is closest to the end value of investing $7,500 for 2.5 years at an effective annual interest rate of 12.36%. Interest is compounded semiannually.
A. $7,531
B. $8,427
C. $9,469
D. $9,818
E. $10,037

End value = $7,500(1 + 0.1236)2.5 = $10,036.69

Difficulty level: Medium
Topic: FUTURE VALUE
Type: PROBLEMS

113. If the stated rate of interest is 12% and it is compounded monthly, what is the effective annual interest rate?
A. 12.00%
B. 12.25%
C. 12.46%
D. 12.68%
E. 12.92%

(1 + .12/12)12 - 1 = 12.68%

Difficulty level: Medium
Topic: EAR
Type: PROBLEMS

114. What is the present value of a payment of $21,000 three years from now if the effective annual interest rate is 4%?
A. $17,951
B. $18,480
C. $18,658
D. $18,669
E. $19,218

PV = FV/(1 + r)n = $21,000/(1 + .04)3 = $18,668.92

Difficulty level: Easy
Topic: PRESENT VALUE - SINGLE SUM
Type: PROBLEMS

115. Thornton will receive an inheritance of $500,000 three years from now. Thorton's discount rate is 10% compounded semiannually. Which of the following values is closest to the amount that Thornton should accept today for the right to his inheritance?
A. $373,108.
B. $375,657.
C. $665,500.
D. $670,048.
E. None of the above is within $10 of the correct answer.

EAR = (1 + r/m)m-1 = [1 + (0.1/2)]2-1 = 0.1025
PV = $500,000/(1 + 0.1025)3 = $373,107.70

Difficulty level: Medium
Topic: PRESENT VALUE - FUTURE SUM
Type: PROBLEMS

116. A mortgage instrument pays $1.5 million at the end of each of the next two years. An investor has an alternative investment with the same amount of risk that will pay interest at 8% compounded semiannually. Which of the following amounts is closest to what the investor should pay for the mortgage instrument?
A. $1,386,834
B. $1,388,889
C. $2,674,897
D. $2,669,041
E. $3,854,512

EAR = (1 + r/m)m-1 = (1 + 0.08/2)2-1 = 0.0816
PV = $1.5/(1.0816)1 + $1.5/(1.0816)2 = $2,669,041

Difficulty level: Easy
Topic: PRESENT VALUE - FUTURE SUM
Type: PROBLEMS

117. You are to receive $75 per year indefinitely. The market rate of interest for these types of payments is 8%. The price you would pay for this stream is:
A. $9.375.
B. $81.00.
C. $93.75.
D. $937.50.
E. None of the above.

PVperpertuity = C/r = $75/.08 = $937.50.

Difficulty level: Easy
Topic: PERPETUITY
Type: PROBLEMS

118. Aunt Clarisse has promised to leave you an annuity that will pay $60 next year and grow at an annual rate of 4%. The payments are expected to go on indefinitely and the interest rate is 9%. What is the value of the growing perpetuity?
A. $667
B. $693
C. $1,200
D. $1,248
E. None of the above

PVgrowing perpetuity = C/(r - g) = $60/(.09 - .04) = $1,200

Difficulty level: Medium
Topic: GROWING PERPETUITY
Type: PROBLEMS

119. A court settlement awarded an accident victim four payments of $50,000 to be paid at the end of each of the next four years. Using a discount rate of 4%, calculate the present value of the annuity.
A. $173,255
B. $178,495
C. $181,495
D. $184,095
E. $200,000

PVannuity = PMT(PVIFA4%,4) = $50,000(3.6299) = $181,495

Difficulty level: Medium
Topic: PRESENT VALUE - ANNUITY
Type: PROBLEMS

120. What is the present value of 10 annual payments of $500 at a discount rate of 12%?
A. $1,332
B. $1,761
C. $1,840
D. $2,825
E. $3,040

CALC: N = 10 FV = 0 PV = ? I = 12 PMT = $500; PV = $2,825

Difficulty level: Medium
Topic: PRESENT VALUE - ANNUITY
Type: PROBLEMS

121. An S&L provides a loan with 15 yearly repayments of $8,000 with the first payment beginning immediately. Which of the following amounts comes closest to the present value of the loan if the interest rate is 7%?
A. $72,863
B. $77,964
C. $115,648
D. $120,000
E. Not enough information is given to determine the answer.

PV = Immediate Pmt + Pmt(PVIFA7%,14) = $8,000 + $8,000(8.7455) = $77,964

Difficulty level: Medium
Topic: PRESENT VALUE - ANNUITY
Type: PROBLEMS

122. The great, great grandparents of one of your classmates sold their factory to the government 104 years ago for $150,000. If these proceeds had been invested at 6%, how much would this legacy be worth today? Assume annual compounding.
A. $936,000.00
B. $1,086,000.00
C. $60,467,131.54
D. $60,617,131.54
E. $64,254,159.44

$150,000(1.06)104 = $64,254,159.44

Difficulty level: Medium
Topic: FUTURE VALUE - SINGLE SUM
Type: PROBLEMS

123. If a business takes out a $10,000, 7 year, 12% loan, the annual payment is:
A. $1,976.38
B. $2,000.00
C. $2,111.78
D. $2,191.17
E. $2,456.54

10,000 PV, 7N, 12%, CPT PMT = $2,191.17

Difficulty level: Medium
Topic: LOAN AMORTIZATION
Type: PROBLEMS

124. If a business takes out a $10,000, 7 year, 12% loan, the decrease in principal in year 1 is: (assume annual payments).
A. $991.17
B. $1,976.38
C. $1,200.00
D. $2,191.17
E. $2,456.54

$2,191.17 (above) - 1,200 (interest) = $991.17

Difficulty level: Medium
Topic: LOAN AMORTIZATION
Type: PROBLEMS

Essay Questions

125. Mr. Miser, who is 35 years old, has just inherited $11,000 and decides to use the windfall towards his retirement. He places the money in a bank which promises a return of 6% per year until his planned retirement in 30 years. If his funds earn 6% interest compounded annually, how much will he have at retirement? Repeat the analysis for both semi-annual and continuous compounding.

$11,000(1.06)30 = $63,178.40
$11,000(1.03)60 = $64,807.63
$11,000 e(.06)(30) = $66,546.12

Topic: FUTURE VALUE
Type: ESSAYS

126. Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance?

$5,000 + $5,000(1.05)/(.12 - .05) = $80,000

Topic: PRESENT VALUE OF A PERPETUITY
Type: ESSAYS

127. If you invest $100,000 today at 12% per year over the next 15 years, what is the most you can spend in equal amounts out of the fund each year over that time.

$100,000 = Annuity Payment * Annuity Factor(.12,15)6.8109 = $14,682.42 or
PV = $-100,000 I/YR = 12 N = 15 PMT = ? = $14,682.42

Topic: PRESENT VALUE OF AN ANNUITY
Type: ESSAYS

128. Using the example of a savings account, explain the difference between the effective annual rate and the annual percentage rate.

The effective annual rate is what you actually earn, the annual percentage rate is a quoted rate. If interest is compounded during the year, the ending balance of a savings account cannot be calculated directly using the annual percentage rate. Also, in the case of the savings account, the effective annual rate will always be higher than the annual percentage rate as long as the account is compounded more than once a year and the interest rate is greater than zero.

Topic: EFFECTIVE ANNUAL RATE VERSUS ANNUAL PERCENTAGE RATE
Type: ESSAYS

129. There are three factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity.

The factors are the interest rate, payment amount, and number of payments. An increase in the payment and number of payments will increase the present value, while an increase in the interest rate will decrease the present value.

Topic: PRESENT VALUE OF AN ANNUITY
Type: ESSAYS

130. There are three factors that affect the future value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity.

The factors are the interest rate, payment amount, and number of payments. An increase in any of these three will increase the future value of the annuity.

Topic: FUTURE VALUE OF AN ANNUITY
Type: ESSAYS

131. A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000. At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments?

The present value of the perpetuity is $10,000, and the present value of the first 25 payments is $9,077.04, thus you should be willing to pay only $922.96 for payments 26 and onwards. This suggests that the value of a perpetuity is derived primarily from the payments received early in its life, and the payments to be received later have little worth today.

Topic: PERPETUITY PAYMENTS
Type: ESSAYS

132. What is the different between an ordinary annuity and an annuity due? Which occurs more in practice? Give a common example of both.

An annuity is a stream of payments to be received in the future. An ordinary annuity is when each payment occurs at the end of the period and an annuity due is when the payment occurs at the beginning of the period. From a valuation perspective, one will need to adjust the annuity formula to account for an annuity due. The most common type of annuity is the ordinary annuity with examples being monthly paychecks, monthly bills for services performed, or savings deposited at the end of the period. Examples of annuity due include most leases and mortgages.

Topic: ANNUITY DUE
Type: ESSAYS