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CHAPTER 5

The Time Value of Money

True/False

1. The future value of an investment increases as the number of years of compounding at a positive rate of interest declines.

DIFFICULTY: Easy

KEYWORDS: future value, lump sum

2. If we invest money for 10 years at 8% interest, compounded semi-annually, we are really investing money for 20 six-month periods, during which we receive 4% interest each period.

DIFFICULTY: Easy

KEYWORDS: non-annual periods

3. The present value interest factor is higher when the discount rate of

interest increases.

DIFFICULTY: Moderate

KEYWORDS: present value interest factor

4. As the compound interest rate increases, future values decrease.

DIFFICULTY: easy

KEYWORDS: future value, interest rate

5. The present value of a future sum of money increases as the number of years before the payment is received increases.

DIFFICULTY: Easy

KEYWORDS: present value

6. One characteristic of an annuity is that an equal sum of money is deposited or withdrawn each period.

DIFFICULTY: Easy

KEYWORDS: annuity

7. The present value of an annuity increases as the discount rate increases.

DIFFICULTY: Easy

KEYWORDS: present value of annuity

8. We can use the present value of an annuity formula to calculate constant annual loan payments.

DIFFICULTY: Moderate

KEYWORDS: present value of annuity

9. To evaluate and compare investment proposals, we must adjust all cash flows to a common date.

DIFFICULTY: Moderate

KEYWORDS: evaluating cash flows to common date

10. A compound annuity involves depositing or investing a single sum of money and allowing it to grow for a certain number of years.

DIFFICULTY: Easy

KEYWORDS: compound annuity

11. A bond paying interest of $120 per year forever is an example of a perpetuity.

DIFFICULTY: Easy

KEYWORDS: perpetuity

12. The formula for calculating the present value of a perpetuity is P = A/(1 + i).

DIFFICULTY: Easy

KEYWORDS: perpetuity formula

13. The discount rate for the time value of money should reflect delaying consumption.

DIFFICULTY: Moderate

KEYWORDS: consumption, time value of money

14. It is easy to choose a discount rate in an international setting due to stability of inflation.

DIFFICULTY: Moderate

KEYWORDS: multinational firms

15. A perpetuity is an investment that continues forever but pays a different dollar amount each year.

DIFFICULTY: Easy

KEYWORDS: perpetuity

16. The present value of the future sum of money is inversely related to both the number of years until payment is received and the opportunity rate.

DIFFICULTY: Moderate

KEYWORDS: present value

17. The present value of a $100 perpetuity discounted at 5% is $1200.

DIFFICULTY: Moderate

KEYWORDS: perpetuity

18. Determining the specified amount of money that you will receive at the maturity of an investment is an example of a future value equation.

DIFFICULTY: Easy

KEYWORDS: future value equation

19. The same basic formula is used for computing both the computation of future value and of present value.

DIFFICULTY: Moderate

KEYWORDS: future value equation

20. When repaying an amortized loan, the interest payments increase over time.

DIFFICULTY: Moderate

KEYWORDS: amortized loan

21. The more frequent the compounding periods in a year, the higher the future value.

DIFFICULTY: Moderate

KEYWORDS: non-annual periods

22. An amortized loan is a loan paid in unequal installments.

DIFFICULTY: Easy

KEYWORDS: amortized loan

23. A loan amortization schedule provides a breakdown of loan payments into principal and interest payments.

DIFFICULTY: Easy

KEYWORDS: amortized loan

24. Holding all other variables constant, payment per period for an annuity due will be higher than an ordinary annuity.

DIFFICULTY: Hard

KEYWORDS: annuity due payment

25. As the number of compounding periods per year increase, the nominal rate of interest increases.

DIFFICULTY: Moderate

KEYWORDS: nominal rate of interest

26. The annual percentage yield is equal to the nominal rate of interest.

DIFFICULTY: Easy

KEYWORDS: annual percentage yield

27. All else constant, an individual would be indifferent between receiving $2,000 today or receiving a $200 perpetuity when the discount rate is 10% annually.

DIFFICULTY: Moderate

KEYWORDS: perpetuities

28. The nominal interest rate on two different investments will equal the annual percentage yield on the two investments only if interest on both investments is compounded annually.

DIFFICULTY: Moderate

KEYWORDS: nominal interest rate, annual percentage rates

Multiple Choice

29. The present value of a single future sum:

a. increases as the number of discount periods increases.

b. is generally larger than the future sum.

c. depends upon the number of discount periods.

d. increases as the discount rate increases.

DIFFICULTY: Moderate

KEYWORDS: present value

30. Which of the following is the formula for compound value?

a. FVn = P(1+i)n

b. FVn = (1+i)/P

c. FVn = P/(1+i)n

d. FVn = P(1+i)-n

DIFFICULTY: Easy

KEYWORDS: compound value formula

31. At 8% compounded annually, how long will it take $750 to double?

a. 6.5 years

b. 48 months

c. 9 years

d. 12 years

DIFFICULTY: Moderate

KEYWORDS: number of periods

32. At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years?

a. 6%

b. 5%

c. 7%

d. 8%

DIFFICULTY: Moderate

KEYWORDS: compound interest rate

33. An increase in future value can be caused by an increase in the:

a. annual interest rate.

b. number of compounding periods.

c. original amount invested.

d. both a and b.

e. all of the above.

DIFFICULTY: Moderate

KEYWORDS: future value

34. Assuming two investments have equal lives, a high discount rate tends to favor:

a. the investment with large cash flow early.

b. the investment with large cash flow late.

c. the investment with even cash flow.

d. neither investment since they have equal lives.

DIFFICULTY: Moderate

KEYWORDS: discount rates and cash flows

35. You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12. The annual interest rate is:

a. 24%.

b. 8%.

c. 18%.

d. 12%.

DIFFICULTY: Moderate

KEYWORDS: annual interest rate, non-annual periods

36. If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?

a. $3,525.62

b. $5,008.76

c. $3,408.88

d. $2,465.78

DIFFICULTY: Moderate

KEYWORDS: annuity payment

37. If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?

a. $10,065

b. $10,193

c. $22,334

d. $21,731

DIFFICULTY: Moderate

KEYWORDS: compound annuity

38. A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today. If your friend can earn 5.0%, how much can your friend spend in four years on the purchase? Round off to the nearest $1.

a. $1,444

b. $1,604

c. $1,764

d. $1,283

DIFFICULTY: Moderate

KEYWORDS: future value, lump sum

39. You just purchased a parcel of land for $10,000. If you expect a 12% annual rate of return on your investment, how much will you sell the land for in 10 years?

a. $25,000

b. $31,060

c. $38,720

d. $34,310

DIFFICULTY: Moderate

KEYWORDS: future value, lump sum

40. You have just purchased a share of preferred stock for $50.00. The preferred stock pays an annual dividend of $5.50 per share forever. What is the rate of return on your investment?

a. .055

b. .010

c. .110

d. .220

DIFFICULTY: Moderate

KEYWORDS: perpetuity rate of return

41. A commercial bank will loan you $7,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 12% of the unpaid balance. What is the amount of the monthly payments?

a. $282.43

b. $390.52

c. $369.82

d. $353.05

DIFFICULTY: Moderate

KEYWORDS: annuity payments

42. Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?

a. 15

b. 13

c. 12

d. 19

DIFFICULTY: Moderate

KEYWORDS: annuity payments

43. Which of the following provides the greatest annual interest?

a. 10% compounded annually

b. 9.5% compounded monthly

c. 9% compounded quarterly

d. 8.5% compounded daily

DIFFICULTY: Moderate

KEYWORDS: annual percentage yield

44. The effective annual rate increases when the _______ increases.

a. number of compounding periods in a year

b. number of years invested

c. quoted rate

d. both a and c

e. all of the above

DIFFICULTY: Moderate

KEYWORDS: effective annual rate

45. If you place $50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be worth at the end of five years (round to the nearest dollar)?

a. $72

b. $70

c. $71

d. $57

DIFFICULTY: Moderate

KEYWORDS: future value, non-annual periods

46. If you put $700 in a savings account with a 10% nominal rate of interest compounded monthly, what will the investment be worth in 21 months (round to the nearest dollar)?

a. $827

b. $833

c. $828

d. $1,176

DIFFICULTY: Moderate

KEYWORDS: future value, non-annual periods

47. What is the annual compounded interest rate of an investment with a stated interest rate of 6% compounded quarterly for seven years (round to the nearest .1%)?

a. 51.7%

b. 6.7%

c. 10.9%

d. 6.1%

DIFFICULTY: Moderate

KEYWORDS: compound interest rate, non-annual periods

48. You are considering two investments. Investment A yields 10% compounded quarterly. Investment B yields r% compounded semiannually. Both investments have equal annual yields. Find r.

a. 19.875%

b. 10%

c. 10.38%

d. 10.125%

DIFFICULTY: Hard

KEYWORDS: annual percentage yield

49. If you put $600 in a savings account that yields an 8% rate of interest compounded weekly, what will the investment be worth in 37 weeks (round to the nearest dollar)?

a. $648

b. $635

c. $634

d. $645

DIFFICULTY: Moderate

KEYWORDS: future value, non-annual periods

50. Which of the following formulas represents the future value of $500 invested at 8% compounded quarterly for five years?

a. 500(1+.08)⁵

b. 500(1+.08)²⁰

c. 500(1+.02)⁵

d. 500(1+.02)²⁰

DIFFICULTY: Moderate

KEYWORDS: future value formula

51. What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to the nearest $1)?

a. $1,048

b. $1,010

c. $1,038

d. $808

DIFFICULTY: Moderate

KEYWORDS: future value, non-annual periods

52. Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month)?

a. 73 months

b. 75 months

c. 77 months

d. 79 months

DIFFICULTY: Moderate

KEYWORDS: non-annual periods

53. If you want to have $10,000 in 10 years, which of the following formulas represents how much money you must put in a savings account today? Assume that the savings account pays 6% and it is compounded monthly.

a. 10,000/(1+.05)¹⁰

b. 10,000/(1+.005)¹²⁰

c. 10,000/(1+.06)¹⁰

d. 10,000/(1+.006)¹²⁰

DIFFICULTY: Moderate

KEYWORDS: present value formula

54. Discounting is the opposite of:

a. compounding.

b. future value.

c. opportunity costs.

d. both a and c.

DIFFICULTY: Easy

KEYWORDS: discounting

55. An increase in _______ will decrease present value.

a. the discount rate per period

b. the original amount invested

c. the number of periods

d. both a and c

e. all of the above

DIFFICULTY: Moderate

KEYWORDS: present value

56. ___________ annuities involve depositing money at the end of the period and allowing it to grow.

a. Discount

b. Compound

c. Annuity due

d. Both b and c

DIFFICULTY: Moderate

KEYWORDS: compound annuity

57. Dawn Swift discovered that 20 years ago, the average tuition for one year at an Ivy League school was $4,500. Today, the average cost is $29,000. What is the growth rate in tuition cost over this 20-year period? Round off to the nearest 0.1%.

a. 15.5%

b. 4.2%

c. 9.8%

d. 10.6%

DIFFICULTY: Moderate

KEYWORDS: growth rate, compound interest rate

58. When comparing annuity due to ordinary annuities, annuity due annuities will have higher:

a. present values.

b. annuity payments.

c. future values.

d. both a and c.

e. all of the above.

DIFFICULTY: Hard

KEYWORDS: annuity due versus ordinary annuities

59. If you want to have $1,700 in seven years, how much money must you put in a savings account today? Assume that the savings account pays 6% and it is compounded quarterly (round to the nearest $10).

a. $1,120

b. $1,130

c. $1,110

d. $1,140

DIFFICULTY: Easy

KEYWORDS: present value

60. If you want to have $90 in four years, how much money must you put in a savings account today? Assume that the savings account pays 8.5% and it is compounded monthly (round to the nearest $1).

a. $64

b. $65

c. $66

d. $71

DIFFICULTY: Easy

KEYWORDS: present value

61. What is the present value of $1,000 to be received 10 years from today? Assume that the investment pays 8.5% and it is compounded monthly (round to the nearest $1).

a. $893

b. $3,106

c. $429

d. $833

DIFFICULTY: Easy

KEYWORDS: present value

62. What is the present value of $12,500 to be received 10 years from today? Assume a discount rate of 8% compounded annually and round to the nearest $10.

a. $5,790

b. $11,574

c. $9,210

d. $17,010

DIFFICULTY: Moderate

KEYWORDS: present value

63. How much money must be put into a bank account yielding 5.5% (compounded annually) in order to have $250 at the end of five years (round to nearest $1)?

a. $237

b. $191

c. $187

d. $179

DIFFICULTY: Easy

KEYWORDS: present value

64. Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina’s plan is to invest her money by depositing into an IRA at the end of every year. What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%. Round off to the nearest $1.

a. $1,497

b. $5,281

c. $75

d. $3,622

DIFFICULTY: Moderate

KEYWORDS: annuity payment

65. If you want to have $1,200 in 27 months, how much money must you put in a savings account today? Assume that the savings account pays 14% and it is compounded monthly (round to the nearest $10).

a. $910

b. $890

c. $880

d. $860

DIFFICULTY: Moderate

KEYWORDS: present value

66. Three years from now, Barbara Waters will purchase a laptop computer that will cost $2,250. Assume that Barbara can earn 6.25% (compounded monthly) on her money. How much should she set aside today for the purchase? Round off to the nearest $1.

a. $1,250

b. $900

c. $1,866

d. $3,775

DIFFICULTY: Moderate

KEYWORDS: present value

67. Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.

a. $89,000,000

b. $38,163,612

c. $13,092,576

d. $41,083,128

DIFFICULTY: Moderate

KEYWORDS: present value of annuity

68. If you want to have $875 in 32 months, how much money must you put in a savings account today? Assume that the savings account pays 16% and it is compounded monthly (round to the nearest $10).

a. $630

b. $570

c. $650

d. $660

DIFFICULTY: Moderate

KEYWORDS: present value

68. As time increases for an amortized loan, the ___________ decreases.

a. interest paid per payment

b. principal paid per payment

c. the outstanding loan balance

d. both a and c

e. all of the above

DIFFICULTY: Moderate

KEYWORDS: amortized loan

70. The present value of a perpetuity decreases when the _______ decreases.

a. number of investment periods

b. annual discount rate

c. perpetuity payment

d. both b and c

DIFFICULTY: Moderate

KEYWORDS: perpetuities

71. What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest $10).

a. $120

b. $130

c. $100

d. $110

DIFFICULTY: Moderate

KEYWORDS: present value of annuity

72. What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today. Use a discount rate of 9%, and round your ANSWERwer to the nearest $10.

a. $1,360

b. $1,480

c. $1,250

d. $1,210

DIFFICULTY: Moderate

KEYWORDS: present value of annuity due

73. What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today. Use a discount rate of 12%, and round your ANSWERwer to the nearest $10.

a. $1,870

b. $2,090

c. $2,117

d. $3,243

DIFFICULTY: Moderate

KEYWORDS: present value of annuity due

74. What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%. The first payment will be received one year from today (round to the nearest $1).

a. $25

b. $40

c. $57

d. $118

DIFFICULTY: Moderate

KEYWORDS: present value of ordinary annuity

75. What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%.

a. $440

b. $43

c. $500

d. $1,040

DIFFICULTY: Moderate

KEYWORDS: present value of ordinary annuity

76. What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%. The first payment will be received one year from today (round to the nearest $1).

a. $42

b. $114

c. $88

d. $105

DIFFICULTY: Moderate

KEYWORDS: present value of ordinary annuity

77. Financial managers use the time value of money to:

a. make business decisions.

b. compare cash flows of different projects.

c. determine the price of common stock.

d. both a and b.

e. all of the above.

DIFFICULTY: Easy

KEYWORDS: financial management and the time value of money

78. The annual percentage yield is also referred to as the:

a. quoted rate.

b. nominal rate.

c. effective annual rate.

d. all of the above.

DIFFICULTY: Easy

KEYWORDS: annual percentage yield

79. You are considering two investments: A and B. Both investments provide a cash flow of $100 per year for n years. However, investment A receives the cash flow at the beginning of each year, while investment B receives the cash at the end of each year. If the present value of cash flows from investment A is P, and the discount rate is c, what is the present value of the cash flows from investment B?

a. P/(1+c)

b. P(1+c)

c. P/(1+c)n

d. P(1+c)n

DIFFICULTY: Moderate

KEYWORDS: present value of annuity due

80. What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year). Use a 10% discount rate, and round your answer to the nearest $100.

a. $1,100

b. $1,000

c. $900

d. $1,200

DIFFICULTY: Hard

KEYWORDS: present value of annuity due

81. Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually. If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.

a. $52,821

b. $57,901

c. $82,024

d. $64,132

DIFFICULTY: Moderate

KEYWORDS: present value of annuity due

82. What is the value on 1/1/05 of the following cash flows? Use a 10% discount rate, and round your answer to the nearest $10.

a. $490

b. $460

c. $420

d. $450

DIFFICULTY: Moderate

KEYWORDS: present value of complex stream

83. Consider the following cash flows:

What is the value on 1/1/05 of the above cash flows? Use an 8% discount rate, and round your answer to the nearest $10.

a. $600

b. $620

c. $630

d. $650

DIFFICULTY: Moderate

KEYWORDS: present value of complex stream

84. Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?

a. $500

b. $490

c. $540

d. $570

DIFFICULTY: Moderate

KEYWORDS: present value of annuity

85. It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account). Darwin will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total). How much money will Darwin have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually, and round to the nearest $1,000.

a. $93,000

b. $766,000

c. $767,000

d. $850,000

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

86. If you put $510 in a savings account at the beginning of each year for 30 years, how much money will be in the account at the end of the 30th year? Assume that the account earns 5%, and round to the nearest $100.

a. $33,300

b. $32,300

c. $33,900

d. None of the above

DIFFICULTY: Moderate

KEYWORDS: annuity due

87. If you put $10 in a savings account at the beginning of each year for 11 years, how much money will be in the account at the end of the 11th year? Assume that the account earns 11%, and round to the nearest $100.

a. $220

b. $200

c. $190

d. $180

DIFFICULTY: Moderate

KEYWORDS: annuity due

88. If you put $310 in a savings account at the beginning of each year for 10 years, how much money will be in the account at the end of the 10th year? Assume that the account earns 5.5%, and round to the nearest $100.

a. $3,800

b. $3,900

c. $4,000

d. $4,200

DIFFICULTY: Moderate

KEYWORDS: annuity due

89. If you put $200 in a savings account at the beginning of each year for 10 years and then allow the account to compound for an additional 10 years, how much will be in the account at the end of the 20th year? Assume that the account earns 10%, and round to the nearest $10.

a. $8,300

b. $9,100

c. $8,900

d. $9,700

DIFFICULTY: Moderate

KEYWORDS: annuity due

90. How much money must you pay into an account at the beginning of each of 30 years in order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.

a. $39

b. $46

c. $50

d. None of the above

DIFFICULTY: Moderate

KEYWORDS: annuity due

91. How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per annum, and round to the nearest $1.

a. $1,195

b. $111

c. $124

d. $139

DIFFICULTY: Moderate

KEYWORDS: annuity due

92. How much money must you pay into an account at the beginning of each of five years in order to have $5,000 at the end of the fifth year? Assume that the account pays 12% per year, and round to the nearest $10.

a. $700

b. $1,390

c. $1,550

d. $790

DIFFICULTY: Moderate

KEYWORDS: annuity due

93. How much money must you pay into an account at the beginning of each of 11 years in order to have $5,000 at the end of the 11th year? Assume that the account pays 8% per year, and round to the nearest $1.

a. $700

b. $257

c. $300

d. $278

DIFFICULTY: Moderate

KEYWORDS: annuity due

94. You are going to pay $800 into an account at the beginning of each of 20 years. The account will then be left to compound for an additional 20 years. At the end of the 41st year you will begin receiving a perpetuity from the account. If the account pays 14%, how much will you receive each year from the perpetuity (round to nearest $1,000)?

a. $140,000

b. $150,000

c. $160,000

d. $170,000

DIFFICULTY: Moderate

KEYWORDS: annuity due

The following information is to be used in solving the next two questions:

You are going to pay $100 into an account at the beginning of each of the next 40 years. At the beginning of the 41st year, you buy a 30-year annuity whose first payment comes at the end of the 41st year (the account pays 12%).

95. How much money will be in the account at the end of year 40 (round to the nearest $1,000)?

a. $77,000

b. $86,000

c. $69,000

d. $93,000

DIFFICULTY: Moderate

KEYWORDS: annuity due

96. How much will you receive at the end of the 41st year (i.e., the first annuity payment)? Round to the nearest $100.

a. $93,000

b. $7,800

c. $11,400

d. $10,700

DIFFICULTY: Moderate

KEYWORDS: annuity due

97. A retirement plan guarantees to pay you or your estate a fixed amount for 20 years. At the time of retirement, you will have $31,360 to your credit in the plan. The plan anticipates earning 8% interest annually over the period you receive benefits. How much will your annual benefits be, assuming the first payment occurs one year from your retirement date?

a. $682

b. $6,272

c. $2,000

d. $3,194

DIFFICULTY: Moderate

KEYWORDS: annuity payment

The following three questions refer to the following statement:

A Max, Inc. deposited $2,000 in a bank account that pays 12% interest annually.

98. What will the dollar amount be in four years?

a. $2,800

b. $3,100

c. $3,111

d. $3,148

DIFFICULTY: Moderate

KEYWORDS: future value

99. What will the dollar amount be if the interest is compounded semiannually for those four years?

a. $3,100

b. $3,188

c. $3,240

d. $3,290

DIFFICULTY: Moderate

KEYWORDS: future value

100. How many periods would it take for the deposit to grow to $6,798 if the interest is compounded semiannually?

a. 17

b. 19

c. 21

d. 25

DIFFICULTY: Moderate

KEYWORDS: future value, non-annual periods

101. SellUCars, Inc. offers you a car loan at an annual interest rate of 8% compounded quarterly. What is the annual percentage yield of the loan?

a. 8.00%

b. 8.24%

c. 8.32%

d. 8.44%

DIFFICULTY: Easy

KEYWORDS: annual percentage yield

102. An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven years. What is the present value of this investment if our opportunity rate is 5%?

a. $735

b. $865

c. $885

d. $900

DIFFICULTY: Moderate

KEYWORDS: present value, complex stream

103. The time value of money is created by:

a. the existence of profitable investment alternatives and interest rates.

b. the fact that the passing of time increases the value of money.

c. the elimination of the opportunity cost as a consideration.

d. the fact that the value of saving money for tomorrow could be more or less than spending it today.

DIFFICULTY: Moderate

KEYWORDS: time value of money

104. All else constant, the future value of an investment will increase if:

a. the investment involves more risk.

b. the investment is compounded for fewer years.

c. the investment is compounded at a higher interest rate.

d. both b & c.

DIFFICULTY: Moderate

KEYWORDS: future value

105. To compound $100 quarterly for 20 years at 8%, we must use:

a. 40 periods at 4%.

b. five periods at 12%.

c. 10 periods at 4%.

d. 80 periods at 2%.

DIFFICULTY: Moderate

KEYWORDS: compound interest, non-annual periods

106. California Investors recently advertised the following claim: Invest your money with us at 21%, compounded annually, and we guarantee to double your money sooner than you imagine. Ignoring taxes, how long would it take to double your money at a nominal rate of 21%, compounded annually? Round off to the nearest year.

a. Approximately two years

b. Approximately four years

c. Approximately six years

d. Approximately eight years

DIFFICULTY: Moderate

KEYWORDS: compound interest, number of periods

107. How much money do I need to place into a bank account which pays a 6% rate in order to have $500 at the end of seven years?

a. $332.53

b. $381.82

c. $423.77

d. $489.52

DIFFICULTY: Moderate

KEYWORDS: present value

108. Bobby’s grandmother deposited $100 in a savings account for him when he was born. The money has been earning an annual rate of 12% interest, compounded quarterly for the last 25 years. He is getting married and would like to take his new bride on a fabulous honeymoon. How much does he have in this account to use?

a. $4,165

b. $1,700

c. $5,051

d. $1,922

DIFFICULTY: Moderate

KEYWORDS: compound interest, non-annual periods

109. George and Barbara will be retiring in four years and would like to buy a lake house. They estimate that they will need $150,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 16% on their money, compounded annually, over the next four years, how much must they invest at the end of each year for the next four years to have accumulated $150,000 by retirement?

a. $25,523

b. $29,606

c. $46,212

d. $43,500

e. $37,500

DIFFICULTY: Moderate

KEYWORDS: compound annuity

110. You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in Paris, France. You will need $15,000 every six months (beginning six months from now) for the next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your education. They want to make one deposit now in a bank account earning 6% interest, compounded semiannually, so that you can withdraw $15,000 every six months for the next three years. How much must they deposit now?

a. $97,026

b. $73,760

c. $90,000

d. $81,258

DIFFICULTY: Moderate

KEYWORDS: annuity due

111. You bought a painting 10 years ago as an investment. You originally paid $85,000 for it. If you sold it for $484,050, what was your annual return on investment?

a. 47%

b. 4.7%

c. 19%

d. 12.8%

DIFFICULTY: Moderate

KEYWORDS: compound interest

112. Jay Coleman just graduated. He plans to work for five years and then leave for the Australian "Outback" country. He figures that he can save $3,500 a year for the first three years and $5,000 a year for the next two years. These savings will start one year from now. In addition, his family gave him a $2,500 graduation gift. If he puts the gift, and the future savings when they start, into an account that pays 7.75% compounded annually, what will his financial "stake" be when he leaves for Australia five years from now? Round off to the nearest $1.

a. $36,082

b. $24,725

c. $30,003

d. $27,178

DIFFICULTY: Moderate

KEYWORDS: annuities due

113. You are thinking of buying a miniature golf course. It is expected to generate cash flows of $40,000 per year in years one through four and $50,000 per year in years five through eight. If the appropriate discount rate is 10%, what is the present value of these cash flows?

a. $285,288

b. $167,943

c. $235,048

d. $828,230

DIFFICULTY: Moderate

KEYWORDS: complex stream

114. You have been depositing money at the end of each year into an account drawing 8% interest. What is the balance in the account at the end of year four if you deposited the following amounts?

a. $1,622

b. $2,207

c. $2,384

d. $2,687

DIFFICULTY: Moderate

KEYWORDS: complex stream

115. What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments. Round to the nearest whole dollar.

Year Cash Flow

1 $3,000

2 $4,000

3 $5,000

a. PV = $3,000/[1.06]¹ + $4,000/[1.06]² + $5,000/[1.06]³

b. PV = $3,000 [1.06]¹ + $4,000 [1.06]² + $5,000 [1.06]³

c. PV = $3,000/[1.06]⁰ + $4,000/[1.06]¹ + $5,000/(1.06]²

d. PV = $3,000 [1.06]^-0 + $4,000 [1.06]^-1 + $5,000 [1.06]^-2

DIFFICULTY: Moderate

KEYWORDS: complex stream, compounding formula

116. Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing $95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make equal monthly installments over the next 20 years?

a. $1,046

b. $749

c. $1,722

d. $1,346

DIFFICULTY: Moderate

KEYWORDS: compound annuity payments

117. You are considering the purchase of XYZ Company’s perpetual preferred stock which pays a perpetual annual dividend of $8 per share. If the appropriate discount rate for this investment is 14%, what is the price of one share of this stock?

a. $7.02

b. $57.14

c. $36.43

d. Cannot be determined without maturity date

DIFFICULTY: Moderate

KEYWORDS: perpetuities

118. Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold’s monthly payments be? Round off to the nearest $1.

a. $1,450

b. $1,788

c. $3,200

d. $1,682

DIFFICULTY: Moderate

KEYWORDS: compound annuity payment

119. You buy a race horse, which has a winning streak for four years, bringing in $500,000 per year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what was your annual return over this four-year period?

a. 8%

b. 33%

c. 18%

d. 12%

DIFFICULTY: Moderate

KEYWORDS: annuity annual return

120. You are considering a monthly home loan with an annual percentage yield of 5.116%. What is the quoted rate of interest on the loan?

a. 4.5%

b. 4.75%

c. 5%

d. 6%

DIFFICULTY: Moderate

KEYWORDS: quoted rate

121. You want to travel to Europe to visit relatives when you graduate from college three years from now. The trip is expected to cost a total of $10,000. Your parents have deposited $5,000 for you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed to finance the balance. If you are going to put Aunt Hilda’s gift in an investment earning 10% over the next three years, how much must she deposit now so you can visit your relatives in three years?

a. $3,757

b. $3,039

c. $3,801

d. $3,345

DIFFICULTY: Moderate

KEYWORDS: annuities due

122. You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you plan to make $2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will calculate your bank balance just after the last payment is deposited?

a. FV = $2,000 [1.06]^-1 + $2,000 [1.06]^-2 + $2,000 [1.06]^-3

b. FV = $2,000 [1.06]¹ + $2,000 [1.06]² + $2,000 [1.06]³

c. FV = $2,000 [1.06]⁰ + $2,000 [1.06]¹ + $2,000 [1.06]²

d. FV = $2,000 [1.06]^-0 + $2,000 [1.06]^-1 + $2,000 [1.06]^-2 + $1,000 [1.06]^-3

DIFFICULTY: Moderate

KEYWORDS: compound annuity, annuity due

123. What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments. Round to the nearest whole dollar.

Year Cash Flow

1 $3,000

2 $4,000

3 $5,000

a. $10,588

b. $11,461

c. $12,688

d. $13,591

DIFFICULTY: Moderate

KEYWORDS: complex stream

124. As a part of your savings plan at work, you have been depositing $250 per quarter in a savings account earning 8% interest compounded quarterly for the last 10 years. You will retire in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by increasing your contribution every four months from $250 to $500. Additionally, you have just inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually for the next 15 years. How much money will you have in savings when you retire 15 years from now?

a. $126,862

b. $73,012

c. $161,307

d. $194,415

DIFFICULTY: Moderate

KEYWORDS: compound annuity

125. Ronald Slump purchased a real estate investment with the following end-of-year cash flows:

Year EOY Cash Flow

1 $ 200

2 $ -350

3 $ -430

4 $ 950

What is the present value of these cash flows if the appropriate discount rate is 20%?

a. $178

b. $160

c. $133

d. $767

DIFFICULTY: Moderate

KEYWORDS: complex stream

126. You have just won a magazine sweepstakes and have a choice of three alternatives. You can get $100,000 now, or $10,000 per year in perpetuity, or $50,000 now and $150,000 at the end of 10 years. If the appropriate discount rate is 12%, which option should you choose?

a. $100,000 now

b. $10,000 perpetuity

c. $50,000 now and $150,000 in 10 years

DIFFICULTY: Moderate

KEYWORDS: future value, present value, perpetuities

127. Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back the principal and interest in five equal annual installments beginning one year from now. Determine the amount of Harry’s annual payment.

a. $8,322

b. $9,600

c. $9,709

d. $6,720

DIFFICULTY: Moderate

KEYWORDS: amortized loan

128. Middletown, USA currently has a population of 1.5 million people. It has been one of the fastest growing cities in the nation, growing by an average of 4% per year for the last five years. If this city’s population continues to grow at 4% per year, what will the population be 10 years from now?

a. 1,560,000

b. 2,220,366

c. 2,100,000

d. 1,824,979

DIFFICULTY: Moderate

KEYWORDS: future value

129. Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.

a. $245

b. $265

c. $285

d. $305

e. $315

DIFFICULTY: Moderate

KEYWORDS: annuity

130. You deposit $5,000 today in an account drawing 12% compounded quarterly. How much will you have in the account at the end of 2 1/2 years?

a. $7,401

b. $5,523

c. $7,128

d. $6,720

DIFFICULTY: Easy

KEYWORDS: compound interest, non-annual periods

131. The future value of $500 deposited into an account paying 8% annually for three years is:

a. $500.

b. $630.

c. $700.

d. $620.

DIFFICULTY: Moderate

KEYWORDS: future value

132. You have borrowed $70,000 to buy a sports car. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the total amount of interest dollars you will pay the bank over the life of the loan. Round to the nearest dollar and assume end-of-year payments.

a. $47,451

b. $51,644

c. $54,776

d. $57,798

DIFFICULTY: Hard

KEYWORDS: annuity, amortized loan

133. How many years will it take for an initial investment of $200 to grow to $544 if it is invested today at 8% compounded annually?

a. 8 years

b. 10 years

c. 11 years

d. 13 years

DIFFICULTY: Easy

KEYWORDS: future value, number of years

134. You have borrowed $70,000 to buy rental property. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the principal paid to the bank in month two of the loan. Assume end-of-period payments.

a. $184.01

b. $186.38

c. $188.46

d. $190.64

e. $192.73

DIFFICULTY: Hard

KEYWORDS: amortized loan

135. The future value of $200 deposited today in an account for four years paying semiannual interest when the annual interest rate is 12% is:

a. $309.40.

b. $318.80.

c. $320.20.

d. $296.00.

DIFFICULTY: Easy

KEYWORDS: future value

136. The present value of $400 to be received at the end of 10 years, if the discount rate is 5%, is:

a. $400.00.

b. $248.40.

c. $313.60.

d. $245.60.

DIFFICULTY: Easy

KEYWORDS: present value

137. The present value of $1,000 to be received at the end of five years, if the discount rate is 10%, is:

a. $621.

b. $784.

c. $614.

d. $500.

DIFFICULTY: Easy

KEYWORDS: present value

138. What is the present value of an investment that pays $400 at the end of three years and $700 at the end of 10 years if the discount rate is 5%?

a. $1,100.00

b. $675.30

c. $775.40

d. $424.60

DIFFICULTY: Moderate

KEYWORDS: present value, complex stream

139. A friend of yours plans to begin saving for retirement by depositing $2,000 at the end of each year for the next 25 years. If she can earn 10% annually on her investment, how much will she have accumulated at the end of 25 years?

a. $50,000

b. $196,692

c. $100,000

d. $216,361

DIFFICULTY: Moderate

KEYWORDS: compound annuities

140. Which of the following statements is false?

a. Quarterly compounding has a higher annual percentage yield than monthly compounding.

b. On monthly compounding loans, the annual percentage yield will be less than the nominal or quoted rate of interest.

c. Compounding essentially means earning interest on interest on an initial balance.

d. Perpetuities pay an equal payment forever.

DIFFICULTY: Moderate

KEYWORDS: compounding, annual percentage yield, perpetuities

141. How much must you deposit at the end of each of the next 10 years in a savings account paying 5% annually in order to have $10,000 saved by the end of the 10th year?

a. $1,000

b. $1,638

c. $1,500

d. $795

DIFFICULTY: Easy

KEYWORDS: compound annuity payment

142. What is the value today of an investment that pays $500 every year at year-end during the next 15 years if the annual interest rate is 9%?

a. $4,030.50

b. $7,500.00

c. $3,500.00

d. $7,000.00

DIFFICULTY: Easy

KEYWORDS: present value of annuity

143. How much would an investor be willing to pay today for an investment that returns $1,000 every year at year-end for five years if he wants to earn a 10% annual return on the investment?

a. $1,000

b. $3,791

c. $5,000

d. $7,700

DIFFICULTY: Easy

KEYWORDS: present value of annuity, annual return

144. A friend of yours would like you to lend him $5,000 today for the next five years. What would be the equal annual end-of-year payment on this loan if you charge your friend 7% interest?

a. $869.45

b. $1,000.00

c. $1,219.51

d. $1,350.00

DIFFICULTY: Moderate

KEYWORDS: annuity payment

145. Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in equal annual payments which begin today, and will continue to be payable at the beginning of each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan payment?

a. $3,756.85

b. $4,200.00

c. $3,478.31

d. $3,000.00

DIFFICULTY: Moderate

KEYWORDS: annuity due payment

146. A friend of yours borrows $19,500 from the bank at 8% annually to be repaid in 10 equal annual end-of-year installments. The interest paid on this loan in year three is:

a. $1,336.01.

b. $1,560.00.

c. $2,906.11.

d. $1,947.10.

DIFFICULTY: Moderate

KEYWORDS: loan amortization, annuity due, interest paid

147. If a loan of $10,000 is paid back in equal annual end-of-year payments of $2,570.69 during the next five years, what is the annual interest rate on the loan?

a. 2%

b. 5%

c. 9%

d. 12%

DIFFICULTY: Moderate

KEYWORDS: annuity annual interest rate

148. What is the present value of an investment that pays $10,000 every year at year-end for the next five years and $15,000 every year at year-end for years six through 10? The annual rate of interest for the investment is 9%.

a. $125,000.00

b. $97,250.00

c. $135,173.00

d. $76,827.50

DIFFICULTY: Moderate

KEYWORDS: complex stream, annual interest rate

149. Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house that pleases your parents costs $200,000, but they expect inflation to increase the price of the house at a rate of 4% over the next 20 years. In order to buy a house upon retirement, what must they save each year in equal annual end-of-year deposits if they can earn 10% annually?

a. $21,910.00

b. $7,650.94

c. $10,000.00

d. $14,715.52

DIFFICULTY: Moderate

KEYWORDS: annuity due

150. Michael Bilkman has an opportunity to buy a perpetuity that pays $24,350 annually. His required rate of return on this investment is 14.25%. At what price would Michael be indifferent to buying or not buying the investment? Round off to the nearest $1.

a. $83,470

b. $170,877

c. $95,621

d. $121,709

DIFFICULTY: Moderate

KEYWORDS: perpetuity

151. What is the present value of a $200 perpetuity when the discount rate is 10%?

a. $2,000

b. $20,000

c. $4,000

d. $40,000

DIFFICULTY: Easy

KEYWORDS: perpetuities

152. An investment has a nominal interest rate of 12% annually, but interest on the investment is compounded monthly. Therefore, the annual percentage yield on the investment is:

a. 12%.

b. 12.68%.

c. 13.89%.

d. 12.36%.

DIFFICULTY: Moderate

KEYWORDS: annual percentage yield

153. An investment has a nominal interest rate of 12% annually, but interest on the investment is compounded semiannually. Therefore, the annual percentage yield on the investment is:

a. 12%.

b. 12.68%.

c. 13.89%.

d. 12.36%.

DIFFICULTY: Moderate

KEYWORDS: annual percentage yield

154. The future value of a single sum:

a. increases as the compound rate decreases.

b. decreases as the compound rate increases.

c. increases as the number of compound periods decreases.

d. increases as the compound rate increases.

e. none of the above.

DIFFICULTY: Moderate

KEYWORDS: future value

155. The present value of a single sum:

a. increases as the discount rate decreases.

b. decreases as the discount rate decreases.

c. increases as the number of discount periods increases.

d. increases as the discount rate increases.

e. none of the above.

DIFFICULTY: Moderate

KEYWORDS: present value

156. You intend to purchase your dream PC upon graduation in two years. It will have a cost of $2,975, including all attachments and sales tax. You just received a $3,000 pre-graduation gift from your rich uncle that you intend to deposit in a money market account that pays 6% interest, compounded monthly. How much of your pre-graduation gift will you need to deposit in order to have $2,975 available for the purchase of the PC upon graduation?

a. $1,275

b. $2,588

c. $2,975

d. $1,567

e. $2,639

DIFFICULTY: Hard

KEYWORDS: non-annual periods

157. If you were to deposit $2,000 in an IRA that would earn interest of 7.5%, compounded quarterly for 18 years, how much would you have accumulated?

a. $9,621

b. $36,000

c. $22,419

d. $12,363

e. $7,619

DIFFICULTY: Moderate

KEYWORDS: future value

158. Congratulations. You just won the California State Lottery. The amount awarded is paid in 20 equal annual installments, at the beginning of each year. You can invest your money at 6.6%, compounded annually. You have calculated that the lottery is worth $20,975,400 today. How much was the amount awarded?

a. $75,310,294

b. $36,000,000

c. $81,047,770

d. $42,000,000

DIFFICULTY: Moderate

KEYWORDS: annuities due

159. Your rich great, great aunt just passed away at the age of 91. She liked you more than she let on and left you in her will. You will receive 100 British bonds that pay interest forever. The amount of annual interest payments that you will receive is $5,000. If you could invest your money at 4.25%, how much are these bonds worth today?

a. $64,480

b. $197,250

c. $250,000

d. $117,647

e. $55,000

DIFFICULTY: Moderate

KEYWORDS: perpetuities

160. Assume that two investments have a three-year life and generate the cash flows shown below. Which of the two would you prefer?

Year Investment A Investment B

1 $5,000 $8,000

2 $5,000 $5,000

3 $5,000 $2,000

a. Investment A, since it has the most even cash flows

b. Investment B, since it gives you the largest cash flows in earlier years

c. Neither, since they both have equal lives

d. Both investments are equally attractive

e. None of the above

DIFFICULTY: Moderate

KEYWORDS: present value of annuity, present value of complex stream

161. You have just purchased an investment that generates the cash flows that are shown below. You are able to invest your money at 5.75%, compounded annually. How much is this investment worth today?

Year Amount

0 $ 0

1 $1,250

2 $1,585

3 $1,750

4 $2,225

5 $3,450

a. $7,758

b. $4,521

c. $10,260

d. $8,467

e. $6,583

DIFFICULTY: Moderate

KEYWORDS: complex stream

162. At 8%, compounded annually, how long will it take $750 to double?

a. 9 years

b. 8 years

c. 12 years

d. 4 years

e. 6 years

DIFFICULTY: Easy

KEYWORDS: number of periods

163. If you have $375,000 in an account earning 9% annually, what constant amount could you withdraw each year and have nothing remaining at the end of 20 years?

a. $7,500

b. $18,750

c. $66,912

d. $5,575

e. $41,080

DIFFICULTY: Moderate

KEYWORDS: annuity payment

164. Which of the following provides the greatest annual interest?

a. 10%, compounded annually

b. 10%, compounded semiannually

c. 10%, compounded quarterly

d. 10%, compounded monthly

e. 10%, compounded daily

DIFFICULTY: Easy

KEYWORDS: effective annual rate

165. You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual interest rate is:

a. 10.50%.

b. 12.75%.

c. 15.25%.

d. 6.50%.

e. 8.80%.

DIFFICULTY: Moderate

KEYWORDS: annual interest rate, non-annual periods

166. You wish to purchase a condo at a cost of $175,000. You are able to make a down payment of $35,000 and will borrow $140,000 for 30 years at an interest rate of 7.25%. How much is your monthly payment?

a. $650

b. $955

c. $1,092

d. $1,023

e. $875

DIFFICULTY: Moderate

KEYWORDS: monthly payment

167. A bank pays a quoted annual (nominal) interest rate of 4.25%, compounded daily (365-day year). What is the annual percentage yield (APY)?

a. 4.25%

b. 5.56%

c. 4.75%

d. 6.20%

e. 4.34%

DIFFICULTY: Moderate

KEYWORDS: annual percentage yield

168. Northwest Bank pays a quoted annual (nominal) interest rate of 4.75%. However, it pays interest (compounds) daily using a 365-day year. What is the effective annual rate of return (APY)?

a. 4.75%

b. 5.02%

c. 3.61%

d. 4.86%

DIFFICULTY: Moderate

KEYWORDS: effective annual return

169. Suppose that you wish to save for your child's college education by opening up an educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume that you will be able to earn 10%, compounded monthly, on your investment. How much will you have accumulated at the end of 18 years?

a. $21,600

b. $54,719

c. $33,548

d. $85,920

e. $60,056

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

170. Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next 35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each month. Assume that Edward will earn 8.75% over the life of the IRA. How much will he have at the end of 35 years?

a. $125,250

b. $250,321

c. $363,000

d. $414,405

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

171. When George Washington was president of the United States in 1797, his salary was $25,000. If you assume an annual rate of inflation of 2.5%, how much would his salary have been in 1997?

a. $1,025,000

b. $954,719

c. $2,525,548

d. $4,085,920

e. $3,489,097

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

172. If you are an investor, which of the following would you prefer?

a. Earnings on funds invested would compound annually.

b. Earnings on funds invested would compound daily.

c. Earnings on funds invested would compound monthly.

d. Earnings on funds invested would compound quarterly.

DIFFICULTY: Easy

KEYWORDS: compounding and non-annual periods

173. You have $10,000 to invest. You do not want to take any risk, so you will put the funds in a savings account at the local bank. Of the following choices, which one will produce the largest sum at the end of 22 years?

a. An account that compounds interest annually

b. An account that compounds interest daily

c. An account that compounds interest quarterly

d. An account that compounds interest monthly

DIFFICULTY: Easy

KEYWORDS: compounding and non-annual periods

174. Which of the following statements is true about the time value of money?

a. The future value of a single sum will be greater if funds earn 5% instead of 10%.

b. The future value of a single sum will be unaffected by the rate of return at which funds grow.

c. The future value of a single sum will be greater if funds earn 12% instead of 6%.

d. The future value of a single sum will be unaffected by the length of time funds are invested.

DIFFICULTY: Easy

KEYWORDS: future value, time value of money

175. Which of the following statements is true?

a. The future value of an annuity would be greater if funds are invested at the beginning of each period instead of at the end of each period.

b. An annuity is a series of equal payments that are made, or received, forever.

c. The effective annual rate (APR) of a loan is higher the less frequently payments are made.

d. The future value of an annuity would be greater if funds are invested at the end of each period rather than at the beginning of each period.

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

176. Which of the following statements is true about the time value of money?

a. The present value of a future amount will be greater if funds earn 5% instead of 10%.

b. The present value of a single sum will be unaffected by the rate of return at which funds grow.

c. The present value of a future amount will be greater if funds earn 12% instead of 6%.

d. The present value of a future amount will be unaffected by how far in the future funds would be received.

DIFFICULTY: Moderate

KEYWORDS: present value

177. If you are a borrower, which of the choices would lower your APR?

a. Repay your loan in monthly installments.

b. Repay your loan in quarterly installments.

c. Repay your loan in semiannual installments.

d. Repay your loan in annual installments.

e. You would be indifferent to how frequent your loan payments are.

DIFFICULTY: Moderate

KEYWORDS: annual percentage rate

178. As the number of compounding periods increases, the ________ increases.

a. quoted

b. annual percentage yield

c. effective annual rate

d. both b & c

DIFFICULTY: Moderate

KEYWORDS: annual rate of interest

179. What is a series of equal payments for a finite period of time called?

a. A perpetuity

b. An axiom

c. A lump sum

d. An annuity

DIFFICULTY: Easy

KEYWORDS: annuities

180. What is a series of equal payments for an infinite period of time called?

a. A perpetuity

b. An axiom

c. A cash cow

d. An annuity

DIFFICULTY: Easy

KEYWORDS: perpetuities

181. Which of the following statements is false?

a. The effective annual rate (APR) of a loan is always the same as the quoted rate.

b. The payments of an ordinary annuity are made or received at the end of each period.

c. The effective annual rate (APR) of a loan is always equal to or greater than the quoted rate.

d. A perpetuity is a series of equal payments, which are made for an infinite period of time.

DIFFICULTY: Moderate

KEYWORDS: effective annual rate

182. What is a series of equal payments to be received at the end of each period, for a finite period of time, called?

a. A perpetuity

b. An annuity due

c. A cash cow

d. A deferred annuity

DIFFICULTY: Easy

KEYWORDS: deferred annuity

183. What is a series of equal payments to be received at the beginning of each period, for a finite period of time, called?

a. A perpetuity

b. An annuity due

c. A cash cow

d. A deferred annuity

DIFFICULTY: Easy

KEYWORDS: annuity due

184. Which of the following provides the lowest return to an investor?

a. 12%, compounded annually

b. 12%, compounded semiannually

c. 12%, compounded quarterly

d. 12%, compounded monthly

e. 12%, compounded daily

DIFFICULTY: Easy

KEYWORDS: annual percentage yield

185. If you purchased a share of Mico.com stock on March 1, 1993 for $45 and you sold the stock at $168 on February 28, 1998, what was your annual rate of return on the stock?

a. 83%

b. 75%

c. 20%

d. 30%

e. 50%

DIFFICULTY: Moderate

KEYWORDS: future value, annual interest

Short Answer

186. Briefly discuss how non-annual compounding is preferable to annual compounding if you are an investor.

DIFFICULTY: Easy

KEYWORDS: non-annual compounding

187. Why is the concept of the time value of money so important to financial managers?

DIFFICULTY: Moderate

KEYWORDS: financial management, time value of money

188. If you deposit $1,000 each year in a savings account earning 4%, compounded annually, how much will you have in 10 years?

DIFFICULTY: Easy

KEYWORDS: future value

189. If you have an opportunity cost of 10%, how much are you willing to invest each year to have $4,000 accumulated in 10 years?

A = $250.99

DIFFICULTY: Easy

KEYWORDS: future value

190. Consider an investment that has cash flows of $500 the first year and $400 for the next four years. If your opportunity cost is 10%, how much is this investment worth to you?

PV = $400(3.170)(.909) = $1,152.61

454.50 + 1152.61 = $1,607.11

DIFFICULTY: Moderate

KEYWORDS: complex stream

191. Your bank has agreed to loan you $3,000 if you agree to pay a lump sum of $5,775 in five years. What annual rate of interest will you be paying?

FVIF[? %, 5 yr] $3,000 = $5,775

FVIF[? %, 5 yr] = $1.925

i = 14%

DIFFICULTY: Moderate

KEYWORDS: annual rate of interest

192. If your opportunity cost is 12%, how much will you pay for a bond that pays $100 per year forever?

DIFFICULTY: Easy

KEYWORDS: perpetuities

193. If you invest $450 today and it increases to $6,185 at the end of 20 years, what rate of return have you earned?

$6,185 = $450 FVIF[? %, 20 yr]

13.743 = FVIF[? %, 20 yr]

i = 14%

DIFFICULTY: Easy

KEYWORDS: future value

194. If your opportunity cost is 10%, how much are you willing to pay for an investment promising $750 per year for the first four years and $450 for the next six years?

PV = $750(3.17) = $2,377.50

PV = $450(4.355)(.683) = $1,338.51

2377.50 + 1338.51 = $3,716.01

DIFFICULTY: Moderate

KEYWORDS: present value, complex stream

195. You have just received an endowment of $32,976. You plan to put the entire amount in an account earning 8 percent compounded annually and to withdraw $4000 at the end of each year. How many years can you continue to make the withdrawals?

$32,976 = $4,000 PVIFA[8%, ? yr]

8.244 = PVIFA[8%, ? yr]

14 years

DIFFICULTY: Moderate

KEYWORDS: number of periods, annuity

196. Earnings per share for XYZ, Inc. grew constantly from $7.99 in 1974 to $12.68 in 1980. What was the compound annual growth rate in earnings-per-share over the period?

$12.68 = $7.99 FVIF[? %, 6 yr]

1.587 = FVIF[? %, 6 yr]

g = 8%

DIFFICULTY: Moderate

KEYWORDS: annual growth rate

197. To repay a $2,000 loan from your bank, you promise to make equal payments every six months for the next five years totaling $3,116.20. What annual rate of interest will you be paying?

Total payments of $3,116.20 indicates that each payment is $311.62.

$2,000 = $311.62 PVIFA[? %, 10 periods]

6.418 = PVIFA[? %, 10 periods]

i = 9%

Annual interest rate = (.09)(2) = .18 = 18%

DIFFICULTY: Moderate

KEYWORDS: annual interest rate, non-annual periods

198. You have been offered the opportunity to invest in a project which will pay $1,000 per year at the end of years one through 10 and $2,000 per year at the end of years 21 through 30. If the appropriate discount rate is 8%, what is the present value of this cash flow pattern?

Present value of $1,000 per year for years 1 through 10 = $1,000(6.710) = $6,710 i = 8%

Value in year 20 of annuity of $2,000 per year for years 21 through 30 = $2,000(6.710) = $13,420

Present value of annuity of $2,000 per year for years 21 through 30 = $13,420(.215) = $2,885.30

Total present value = $6,710 + $2,885.30 = $9,595.30

DIFFICULTY: Moderate

KEYWORDS: complex stream

199. You are saving money to buy a house. You will need $7,473.50 to make the down payment. If you can deposit $500 per month in a savings account which pays 1% per month, how long will it take you to save the $7,473.50?

$7,473.50 = $500 FVIFA[1%, n periods]

14.947 = FVIFA[1%, n periods]

n = 14 months

DIFFICULTY: Moderate

KEYWORDS: number of periods, annuity

200. You have a credit card with a balance of $18,000. The annual interest rate on the card is 18% compounded monthly, and the minimum payment is $400 per month. If you pay only the minimum payment each month and do not make any new charges on the card, how many years will it take for you to pay off the $18,000 balance?

Calculator steps:

18,000 PV

-400 PMT

12 I/yr or I

N = Approximately 75 months = 6.25 years

DIFFICULTY: Moderate

KEYWORDS: compound annuity, non-annual periods

201. You are considering purchasing common stock in AMZ Corporation. You anticipate that the company will pay dividends of $5.00 per share next year and $7.50 per share in the following year. You also believe that you can sell the common stock two years from now for $30.00 per share. If you require a 14% rate of return on this investment, what is the maximum price that you would be willing to pay for a share of AMZ common stock?

PV = $5.00 PVIF[14%, 1 yr] + ($7.50 + $30.00) PVIF[14%, 2 yr]

= $5.00 (.877) + ($37.50)(.769)

= $33.22

DIFFICULTY: Moderate

KEYWORDS: complex stream

202. How does the risk-return tradeoff relate to the time value of money and the multinational firm?

DIFFICULTY: Easy

KEYWORDS: inflation and multinational firms

203. You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of 12%, what do you estimate that you will have in this account at retirement?

Calculator steps:

-500 PV

-500 PMT

40 N

12 I/yr or I

FV = $430,071

DIFFICULTY: Moderate

KEYWORDS: compound annuity

204. You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today?

FV = $10,000 FVIF[5%, 5 yr]

= $10,000(1.276) = $12,760

Amount to invest in remaining three years = $12,760 - $7,500 = $5,260

FV = $5,260 FVIF[5%, 3 yr]

= $5,260(1.158) = $6,091.08

DIFFICULTY: Moderate

KEYWORDS: future value

205. You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an amortization schedule for the first two months of the loan.

MO Beg PMT Int. Princ. End

1 $70,000 $709.99 $525 $184.99 $69,815.01

2 $69,815.01 $709.99 $523.61 $186.38 $69,628.63

DIFFICULTY: Moderate

KEYWORDS: amortized loan

206. Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you will need to withdraw $5,000 per year from a retirement fund to supplement your social security payments. You expect to live to the age of 85. How much money should you place in the retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12% interest per year from the fund?

Amount in fund at age 60 = $5,000 PVIFA[12%, 25 yr]

= $5,000(7.843) = $39,215

$39,215 = (annual contribution) FVIFA[12%, 20 yr]

$39,215 = (annual contribution)(72.052)

Annual contribution = $39,215/72.052 = $544.26

DIFFICULTY: Moderate

KEYWORDS: annuities due

207. You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%. How many payments must you make?

$ 6,000 = $317.22 PVIFA[2%, ? periods]

18.914 = PVIFA[2%, ? periods] n = 24 months

DIFFICULTY: Moderate

KEYWORDS: annuity, number of payments

208. An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?

PV = $500(1/(1.06)3) + $700(1/1.06)5) + $1000(1/(1.06)9)

PV = $500(.840) + $700(.747) + $1000(.592)

= $420.00 + $522.90 + $592.00

= $1,534.90

DIFFICULTY: Moderate

KEYWORDS: complex stream

209. a.) If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account that pays 5% interest, how much money will Sparco have at the end of eight years?

b.) Suppose Sparco decides that they need to have $5,300 at the end of the eight years. How much will they have to deposit at the end of each year?

a. FV = $150 FVIFA [5%, 8 yr]

FV = $150 (9.549)

= $1,432.35

b. $5,300 = PMT FVIFA [5%, 8 yr]

$5,300 = PMT(9.549)

PMT = $555.03

DIFFICULTY: Moderate

KEYWORDS: future value of annuity

210. What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.

Bond value =

= $400 [12.462] + $10,000 [.377]

= $4984.80 + $3,770 = $8,754.80

DIFFICULTY: Moderate

KEYWORDS: present value of annuity

211. Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows:

Because Frank has enough savings for only one investment, his broker has proposed the third alternative to be, according to his expertise, the best in town. However, Frank questions his broker and wants to eliminate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative?

Investment A

PV = $300 PVIFA [15%, 4 yr]

PV = $856.49

Investment B

PV = $300 pymt beginning at the end of the fourth year, 5 years, 15%

= $300 × PVIFA [15%, 8 yr] - $300 × PVIFA [15%, 3 yr]

= $300 [4.487] - $300 [2.204]

PV = $1,346.2 - $684.97

PV = $661.23

Investment C

PV = ($400, 1 year, 15%) + ($600, 4 years 15%) + ($600, 8 years, 15%)

PV = $348 + $343.05 + $196.14

PV = $887.19

Thus, investment C is the best as it has the highest NPV.

DIFFICULTY: Hard

KEYWORDS: present value investment alternatives

212. What is the present value of the following perpetuities?

a. $600 discounted at 7%

b. $450 discounted at 12%

c. $1,000 discounted at 6%

d. $880 discounted at 9%

a. PV = $600/.07

PV = $8,571.43

b. PV = $450/.12

PV = $3,750

c. PV = $1,000/.06

PV = $16,666.67

d. PV = $880/.09

PV = $9,777.78

DIFFICULTY: Moderate

KEYWORDS: perpetuities

213. Delight Candy, Inc. is choosing between two bonds in which to invest their cash. One bond is being offered from Hershey’s and will mature in 10 years and pays 12% per year, compounded quarterly. The other alternative is a Mars bond that will mature in 20 years and that pays 12% per year, compounded quarterly. What would be the present value of each bond if the discount rate is 10%?

Bond A

PV = $1,000, 10 years, 12% interest compounded quarterly, 10% discount rate

PV = $1,125.51

Bond B

PV = $1,000, 20 years, 12% interest compounded quarterly, 10% discount rate

PV = $1,172.26

DIFFICULTY: Moderate

KEYWORDS: investment alternatives

214. In order to send your oldest child to law school when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if:

a. you want to deposit an amount annually at the end of each year?

b. you want to deposit one large lump sum today?

a. Pymt = $1,294.26

b. Pymt = $14,013.75

DIFFICULTY: Moderate

KEYWORDS: annuity payment