Test Bank Answers Ch19 Compound Interest And Present Value

Chapter 19

Compound Interest and Present Value

True/False Questions
 

1. Compounding always reduces the principal. 
True    False

2. Compounding looks into the present when we know what we have in the future. 
True    False

3. Annual means compounded once a year. 
True    False

4. Interest = principal × rate divided by the time. 
True    False

5. Compounding always requires the use of tables. 
True    False

6. Interest calculated on a balance every three months is said to be compounded quarterly. 
True    False

7. The rate to be used in compounding is found by taking the annual rate divided by the number of times compounded per day. 
True    False

8. The number of periods in compounding is found by multiplying the number of years times the number of times compounded per year. 
True    False

9. Compounding results in earning higher interest than simple interest. 
True    False

10. In the compound interest formula, i stands for periodic interest rate. 

True    False

11. A compound table factor of 1.2950 means that $1 at a certain rate of interest for a certain period of time will increase in value to approximately $1.30. 
True    False

12. Compound value = $ amount divided by

True    False

13. The number of periods for a table lookup on $5,000 at 12% compounded semiannually for 10 years is 10 periods. 
True    False

14. The rate for a table lookup on a $4,000, 12% investment compounded quarterly for four years is 4%. 
True    False

15. The factor for compounding $4,000 at 9% compounded annually for one year is 1.0900. 

True    False

16. The interest on $3,000 at 8% compounded semiannually for six years is $1,803.10. 

True    False

17. The annual rate a bank advertises is the same as the effective rate. 
True    False

18. The nominal rate is really the true rate. 
True    False

19. The effective rate (APY) can be calculated by the interest for one year divided by the principal. 
True    False

20. Effective rates can be seen in the compounding table for one dollar. 
True    False

21. Compounding interest daily is seldom used in comparison to compounding once a year. 
True    False

22. Using daily compounding, $700 would grow to $790 at the end of three years at 8% interest.
True    False

23. Present value starts with the future and tries to calculate its worth in the present. 
True    False

24. The present value is also less than the future value. 
True    False

25. Multiplying by means that if $.75 is invested at a certain rate of interest for a certain number of periods, it would be worth $1 in the past. 
True    False

26. The compound table can be used to prove a present value calculation. 
True    False

27. $14,182 is the present value of $21,000 that earns at a bank 12% compounded quarterly for four years.
True    False

Multiple Choice Questions
 

28. Compounding: 
A. Calculates interest periodically
B. Looks into the present when the future is known
C. Is done only on an annual basis
D. Results in less interest than simple interest
E. None of these

29. The number of periods is equal to: 
A. Number of years divided by rate
B. Number of years × rate
C. Number of years × number of times compounded per year
D. Number of years divided by number of times compounded per year
E. None of these

30. The rate used for calculating compound interest is found by: 
A. Annual rate × number of periods
B. Annual rate × number of times compounded per year
C. Annual rate divided by number of times compounded per year
D. Annual rate divided semiannually
E. None of these

31. The value of $60 deposited in a bank for six years at a rate of 10% compounded annually is: 
A. $96.63
B. $96.36
C. $106.29
D. $106.03
E. None of these

32. The interest on $6,000 at 6% compounded semiannually for eight years is

A. $3,628.24
B. $3,682.02
C. $362.82
D. $13,628.20
E. None of these

33. The effective rate (APY) is: 
A. The nominal rate
B. The stated rate
C. The true semiannual rate
D. The true annual rate
E. None of these

34. Effective rate (APY) is: 
A. Never related to compound table
B. Interest for one year divided by annual rate
C. Interest for one year divided by principal for two years
D. Interest for one year divided by principal
E. None of these

35.  $6,000 for six years at 8½% compounded daily will grow to: 
A. $8,991.02
B. $8,950.10
C. $9,991.35
D. $9,990.02
E. None of these

36. Present value does not: 
A. Know future amount
B. Know the present dollar amount
C. Find present dollar amount
D. Use tables
E. None of these

37. The present value of $1 means that for a certain rate of interest for a certain period of time will equal: 
 
A. $1
B. Over $1
C. Less than $1
D. Never equal
E. None of these

38. The present value of $12,000 for six years compounded at 6% semiannually is: 
A. $12,814.08
B. $8,461.08
C. $8,416.56
D. $8,614.80
E. None of these

39. $20,000 for 14 years compounded at 8% semiannually results in how many periods? 
A. 64
B. 28
C. 12
D. 14
E. None of these

40. $100,000 for 20 years compounded at 4% annually results in a rate per period of: 
A. 3%
B. 5%
C. 4%
D. 1%
E. None of these

41. Sam Monte deposits $21,500 into Legal Bank, which pays 6% interest that is compounded semiannually. What will Sam have in his account at the end of six years? 
A. $29,760.30
B. $30,653.83
C. $30,456.07
D. $29,670.03
E. None of these

42. Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will (round to nearest dollar)

A. $14,984
B. $16,857
C. $16,587
D. $14,484
E. None of these

43. Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is
A. $73,604.00
B. $53,604.00
C. $80,406.00
D. $98,636.18
E. None of these

44. Mia Kaminsky wants to attend Riverside Community College. She will need to have $25,000 six years from today. Mia is wondering what she will have to put in the bank today so that she will have $25,000 six years from now. Her bank pays 5% compounded semiannually. Round to nearest dollar.

A. $18,950
B. $33,226
C. $18,589
D. $33,622
E. None of these

45. Gracie Shay wants to buy a new Hummer in five years. Gracie estimates the cost of the Hummer will be $28,000. If she invests $12,000 now at a rate of 6% compounded semiannually, she: 
A. Will have enough money
B. Will have exactly $16,000
C. Will have $18,000
D. Will not have enough money
E. None of these

46. Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. The best deal is: 
A. Four Rivers
B. Four Rivers for first two years
C. Mystic
D. Mystic for last two years
E. None of these

47. Earl Miller deposited $25,000 at Y Bank at an interest rate of 12% compounded quarterly. The effective rate (APY) is: 
A. 12%
B. 12.55%
C. 12.15%
D. 13.2%
E. None of these

48. Al Miler, the owner of Al's Garage, estimates that he will need $29,000 for new equipment in 15 years. Al decides that he will put aside the money now so that in 15 years the $29,000 will be available. His bank offers him 10% interest compounded semiannually. Al must invest today: 
A. $6,709.95
B. $6,942.60
C. $6,701.60
D. $125,335.10
E. None of these

49. Burton Bush wants to retire in Arizona when he is 80 years of age. Burton, who is now 55, believes he will need $400,000 to retire comfortably. To date, he has set aside no retirement money. If he gets an interest rate of 6% compounded annually, he will have to invest today (to the nearest dollar)

A. $92,300
B. $69,900
C. $96,500
D. $93,200
E. None of these

50. Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is
A. $66,081.20
B. $50,000.00
C. $16,081.20
D. $88,555.42
E. None of these

51.  Interest on $2,630 at 3% compounded semiannually for five years is:

A. $3,052.22

B. $2,934.90

C. $3,044.49

D. $3,199.92

E. None of these

52. Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen’s balance have grown to, including interest?

A. $7,516.68

B. $7,516.88

C. $7,261.57

D. $6,836.78

E. None of these

53. Lisa Richter deposited $5,000 at 4% compounded semiannually for three years. At the beginning of the fourth year, Lisa deposited $2,500. What would her balance be at the end of five years assuming she is still earning 4% compounded semiannually?

A. $5,131

B. $8,131

C. $8,800

D. $8,801

E. None of these

54. Trisha Long wants to buy a boat in five years. She estimates the boat will cost $15,000 at that time. What must Trisha deposit today in an account earning 5% annually to have enough to buy the boat in five years?

A. $12,328.50

B. $11,527.50

C. $11,752.89

D. $11,077.50

E. None of these

55. Katie Hector wants to purchase a condo in Oxford, MS, in 20 years. The cost of the condo is expected to be $180,000. Assuming she can earn 6% annually, what should Katie deposit today?

A. $126,900

B. $56,125

C. $89,400

D. $180,000

E. None of these

Short Answer Questions
 

56. 1. Compound
2. Effective rate (APY)
3. Nominal rate
4. Periods
5. Present value
6. Rate
7. Interest
8. Semiannually
9. Quarterly
10. Monthly
A. Twice a year
B. Stated rate
C. Four times per year
D. Amount calculated on adjusted principal
E. Twelve times per year
F. Year times number of times compounded in one year
G. True rate of interest
H. Know future amount looking for present
I. Rate divided by number of times compounded per year
J. Periodically interest is calculated and added to principal 

57. Complete without using tables. (Show work.)
  
A. _______________
B. _______________
C. _______________ 

58. Solve by using compound table:
  
A. _____________
B. _____________
C. _____________ 

59. Solve by using financial calculator.
   

60. Solve by using compound formula:
   

61. Find effective rate (APY) and show work:
   

62. Use the present value formula to complete:
  
A. ______________
B. ______________
C. ______________
D. ______________ 

63. Use the financial calculator to complete
  
A. ______________
B. ______________
C. ______________
D. ______________ 

64. Juanita Finn deposits $12,000 into Valley Bank, which pays interest of 8% compounded annually for four years. How much will Juanita have in her account? 

65. John Riviera deposits $14,000 in National Bank at 8% compounded quarterly. What is the effective rate (APY) of interest? 

66. Jim Smith believes that in 30 years he will need $80,000 to buy a retirement cottage. Assuming he gets an interest rate of 9% compounded annually, how much will he have to invest today to reach his retirement goal? 

67. Jarad Rodriguez deposits $10,000 at 10% compounded semiannually. At the start of year 6, Jarad deposits an additional $5,000 that is compounded at the same rate. At the end of 10 years, what is the balance in Jarad's account? 

68. Kathy Crag, the owner of The Fabric Corner, lent $15,000 to Dani Flynn to open her own card shop. Dani plans to repay Kathy at the end of 12 years with 8% interest compounded quarterly. How much will Kathy receive at the end of 12 years? 

69. Molly Scupper wants to attend Clarke University. She will need $90,000 eight years from today. Assume Molly's bank pays 6% interest compounded quarterly. What must Molly deposit today to have $90,000 in eight years? Verify your answer. 

70. Moxie Fox deposited $30,000 in a savings account at 6% interest compounded semiannually. At the beginning of year 4, Moxie deposits an additional $60,000 at 6% interest compounded semiannually. At the end of six years, what is the balance in Moxie's account? 

71. Pete Sist wants to buy a new Chevrolet in five years. He estimates the car will cost $24,000. Assuming Pete invests $15,000 now at 10% interest compounded semiannually, will he have enough money to buy the car at the end of five years? 

72. Jim Ryan deposited $8,000 at National Bank at 6% interest compounded quarterly. What was the effective rate (APY)? (Round to the nearest hundredth percent.) 

73. Jane Ring estimates she will need $35,000 for a new computerized office system. Janet decided to put aside the money today so that it will be available in 10 years. Pod Bank offers Janet 9% interest compounded semiannually. How much must Janet invest today to have $35,000 in 10 years? 

74. Complete without using table:
   

75. Complete without using table:
   

76. Solve by using compound formula:
   

77. Solve by using financial calculator:
   

78. Solve by using compound formula. Find future value.
   

79. Solve by using compound formula. Find future value.
   

80. Solve by using financial calculator. Find future value.    

81. Solve by financial calculator. Find future value.    

82. Find effective rate (APY) and show work:    

83. Find effective rate (APY) and show work:
   

88. Don Williams wants to buy a boat five years from today. He will need $40,000. Don wants you to calculate how much he needs today to put in the bank (10% compounded semiannually) to reach his goal in the future. 

89. Paul Lospennato wants to buy a house. Five years from now, he will need $90,000. Paul wants you to calculate how much he needs today to put in the bank (10% compounded semiannually) to reach his goal in the future. 

90. Joe Diamond deposited $9,000 into the Rong Bank, which pays 12% interest, compounded quarterly. Calculate the amount Joe will have in his account at the end of four years. 

91. John James lent Mel Karras $8,000 to open a pottery shop. Mel will repay John at the end of five years with interest, compounded quarterly, at 8%. How much will John receive at the end of five years? 

92. Al Safe deposited $15,000 at Q Bank at an interest rate of 16%, compounded quarterly. What was the effective rate (APY)? 

93. Mark Larken promised his grandson Ralph that he would give him $3,000 six years from today for graduating high school. If money is worth 10% compounded semiannually, what is the present value of this money? 

94. Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000? 

95. Mel Ross thinks he would like to buy a used car in five years for $8,000. He wants to put the money aside now so that in five years the $8,000 will be available. His bank offers him 12% interest, compounded semiannually. Can you calculate what Mel must invest today? 

96. Jim Ring wants to attend Northeast College. He will need $20,000 four years from today. If Jim's bank pays 8% compounded quarterly, what must he deposit today so that he will have the $20,000 in the future? 

97. Check your answer by use of the financial calculator. 

98. Al Derover wants to buy a used jeep in five years. He estimates that the cost will be $12,000. If he invests $8,500 now at a rate of 10% compounded semiannually, will he have enough money to buy the jeep at the end of five years? Show your work. 

99. Abe Frill wants to attend AVP Tech. He will need to have $15,000 seven years from today. How much should Abe put in the bank today (12% quarterly) to reach his goal in the future? 

100. Ryan deposits $12,000 into a fixed asset account that earns 6% compounded quarterly. What is Ryan’s balance at the end of five years?

101. Jackie wants to purchase a lakeside condo in Cuba, MO, in 20 years. Jackie will invest in a mutual fund earning 8% compounded semiannually. How much will she need to deposit today in that fund to purchase her $100,000 lakeside condo?

102. Kelly Kuhn wants to purchase a new Ford F-150 for her son in five years. She estimates that the truck will cost $30,000 after all rebates. Assuming she invests at 8% compounded semiannually for five years, what must she invest today?

103. Helga Thalhimer will need to replace the registration software for her agency in five years. She received an estimate that it will cost $40,000 when she is ready to replace. What must Helga deposit today at 6% compounded quarterly to have enough to update her system?

104. Travis Brown deposited $17,500 into Browning Bank, which pays 4% compounded quarterly. Calculate how much Travis will have in his account at the end of seven years.