Verified Test Bank Ch.20 Annuities And Sinking Funds

Chapter 20

Annuities and Sinking Funds

True/False Questions
 

1. An annuity is one lump sum payment. 
True    False

2. Maturity value is equal to principal plus interest. 
True    False

3. The value of an annuity is the series of payments and interest. 
True    False

4. Insurance companies do not use annuities. 
True    False

5. A contingent annuity has a fixed amount of payments. 
True    False

6. Annuities certain have a specific stated number of payments. 
True    False

7. There is only one class of annuities. 
True    False

8. An ordinary annuity results in the deposit or payment being made at end of the period. 
True    False

9. An annuity due requires that deposits or payments be made at the end of the period. 
True    False

10. Interest is not calculated in ordinary annuities. 
True    False

11. The maturity value in compounding is like the value of an annuity. 
True    False

12. Annuities can be done manually or by computer. 
True    False

13. An annuity due provides a lower final value compared with an ordinary annuity. 
True    False

14. The same formula can be used to find the value of an annuity or an annuity due by adding one payment.

True    False

15. All annuities due are based on a semiannual payment. 
True    False

16. The present value of an annuity looks from the present to the future. 
True    False

17. The amount of money one needs to invest in the future to receive a stream of payments in the present is called the present value of an ordinary annuity. 
True    False

18. Sinking funds accumulate money in the present to accumulate a specific sum at a predetermined present date. 
True    False

19. Sinking funds utilize the concept of compound interest. 
True    False

20. Companies that plan to retire bonds in the future could utilize sinking funds. 
True    False

Multiple Choice Questions
 

21. An annuity is: 
A. Not used by lotteries today
B. A one-time payment
C. A stream of payments
D. Never made up of equal payments
E. None of these

22. Contingent annuities: 
A. Have a fixed amount of payments
B. Pay for 30 years
C. Are only paid by the month
D. Have no fixed amount of payments
E. None of these

23. Annuity due payments are made: 
A. Monthly
B. At the beginning of the period
C. Yearly
D. At the end of the period
E. None of these

24. Ordinary annuity payments are made: 
A. At the end of the period
B. Yearly
C. Monthly
D. At the beginning of the period
E. None of these

25. In an ordinary annuity the interest on a yearly investment starts building interest: 
A. At the beginning of the first period
B. At the end of the first period
C. During the first period
D. After the second period ends
E. None of these

26. An annuity due compared with an ordinary annuity results in a: 
A. Higher value
B. Lower value
C. Same value
D. Value three times the annuity due
E. None of these

27. An annuity due can use the ordinary annuity formula if the ordinary annuity formula is adjusted: 
A. Add one payment to total value
B. Multiply results by 1+i
C. Add two payments to total value
D. Subtract three payments from total value
E. None of these

28. Payments in annuities must be made: 
A. Daily
B. Quarterly
C. Semiannually
D. Yearly
E. None of these

29. The present value of an ordinary annuity: 
A. Tells how much money one needs to invest in the future
B. Is a lump sum
C. Can only be calculated manually
D. Indicates how much money needs to be invested today
E. None of these

30. A sinking fund: 
A. Requires at the beginning one lump sum payment
B. Is really not an annuity
C. Aids in meeting a future obligation
D. Does not compound its money
E. None of these

31. Ted Williams made deposits of $500 at the end of each year for eight years. The rate is 8% compounded annually. The value of Ted's annuity at the end of eight years is: 
A. $5,318.31
B. $4,318.30
C. $2,837.03
D. $2,873.30
E. None of these

32. Nancy Billows promised to pay her son $600 quarterly for four years. If Nancy can invest her money at 6% in an ordinary annuity, she must invest how much today?

A. $10,759.38
B. $10,759.83
C. $8,478.76
D. $8,478.27
E. None of these

33. Joe Sullivan invests $9,000 at the end of each year for 20 years. The rate of interest Joe gets is 8% annually. The final value of Joe's investment at the end of the 20th year on this ordinary annuity is: 
A. $411,588.00
B. $88,362.90
C. $411,857.68
D. $88,632.90
E. None of these

34. Lance Rice has decided to invest $1,200 quarterly for eight years in an ordinary annuity at 4%. The total cash value of the annuity at end of year 8 is:
A. $46,642.80
B. $44,992.88
C. $46,246.80
D. $44,292.92
E. None of these

35. At the beginning of each year, Bill Ross invests $1,400 semiannually at 8% for nine years. The cash value of the annuity due at the end of the ninth year is: 
A. $38,739.68
B. $37,399.68
C. $37,939.86
D. $37,339.72
E. None of these

36. Jones Co. borrowed money that is to be repaid in 12 years. So that the loan will be paid back at end of the 12th year, the company invests $8,000 at the end of each year at 5% compounded annually. The amount of the original loan was : 
A. $127,337.01
B. $70,905.60
C. $127,636.80
D. $70,950.60
E. None of these

37. Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.
A. $1,085.82
B. $1,463.13
C. $164,313.82
D. $163,313
E. None of these

38. Lee Associates borrowed $60,000. The company plans to set up a sinking fund that will pay back the loan at the end of 12 years. Assuming a rate of 8% compounded semiannually, the amount to be paid into the fund each period is: 
A. $1,350
B. $1,535.21
C. $1,653.33
D. $5,163.58
E. None of these

39. Ed Sloan invests $1,600 at the beginning of each year for eight years into an account that pays 10% compounded semiannually. The value of the annuity due is: 
A. $41,344.48
B. $1,600.00
C. $38,744.48
D. $37,744.48
E. None of these

40. How much would Howard Steele need to invest today so that he may withdraw $12,000 each year for the next 20 years, assuming a rate of 8% compounded annually? 
A. $117,817.77
B. $454,144.00
C. $112,817.20
D. $549,144
E. None of these

41. Scott deposits $5,000 at the end of each year into an account for five years. Assuming 6% interest annually, what is the value of his account in five years?

A. $67,060

B. $21,873

C. $30,100

D. $28,185.50

E. None of these

42. Connie made $2,100 deposits at the beginning of each year for four years. The rate she earned is 5% annually. What is the value of Connie’s account in four years?

A. $11,051.00

B. $8,260.20

C. $8,260.00

D. $9,051.26

E. None of these

43. Jorgen Grace made deposits of $250 at the end of each year for 12 years. The rate received was 6% annually. What is the value of the investment after 12 years?

A. $2,028

B. $3,000

C. $4,217.48

D. $4,200

E. None of these

45. Bram Johnson invests $500 at the end of each quarter for 10 years. The account earns 8% interest annually. What is the value of the account at the end of 10 years?

A. $37,700.89

B. $30,200.99

C. $37,000.99

D. $3,700

E. None of these

Short Answer Questions
 

46. 1. Annuities certain
2. Annuity
3. Annuity due
4. Contingent annuities
5. Ordinary annuities
6. Present value of annuity
7. Sinking fund
8. Value of an annuity
A. Beginning as well as ending dates, not fixed
B. Paid at beginning
C. Need to invest today to receive the stream
D. Paid at end
E. An annuity
F. Beginning as well as ending dates
G. Sum of series of payments
H. Stream of payments 

47. Complete this ordinary annuity:
   

48. Complete this ordinary annuity:
   

49. Assume there is an annuity due:
   

50. Complete present value of an ordinary annuity:
   

51. Complete present value of an ordinary annuity:
   

52. Using the financial calculator, complete:
   

53. Alice Wolf wants to know how much she will have to invest today in order to receive an annuity of $10,000 for six years if interest is earned at 7% annually. She will make all her withdrawals at the end of each year. How much should she invest? 

54. What must Bill McGuire invest today to receive an annuity of $12,000 for four years semiannually at a 10% annual rate? All withdrawals will be made at the end of each period. 

55. How much will the Apple Corporation have to set aside each year to have $60,000 ten years from now? Assume interest is at 10% compounded semiannually. 

56. Roger Fox made deposits of $900 semiannually to Reed Bank, which pays 6% interest compounded semiannually. After seven years Roger made no more deposits. What will be the balance in the account eight years after the last deposit? 

57. Jim Hunter has decided to retire to Florida in 10 years. What amount should Jim invest today so that he will be able to withdraw $25,000 at the end of each year for 30 years after he retires? Assume he can invest money at 9% interest compounded annually. 

58. Mike O'Brien plans to deposit $1,250 at the end of every six months for the next eight years at 6% interest compounded semiannually. What is the value of Mike's annuity at the end of eight years? 

59. Abby's Uncle Howard has promised her a gift upon graduation from high school of $2,000 or $200 every quarter for the next three years. If the money could be invested at 6%, which offer should Abby choose? (Show your calculations.) 

60. Rita Heckt wants to receive $4,200 each year for 15 years. How much must Rita invest today at 5% compounded annually? 

61. In 10 years, Longin Company will have to repay a $60,000 loan. Assume a 4% interest rate compounded quarterly. How much must Longin pay each period to have the $60,000 at the end of 10 years? Verify your result. 

62. Block Associates borrowed $75,000. The company plans to set up a sinking fund that will repay the loan after 15 years. Assume an 8% interest rate compounded semiannually. What must Block Associates pay into the fund each period? Verify your result. 

63. Angel Rowe wants to receive $7,500 each year for the next 25 years. Assume a 5% interest rate compounded annually. How much should Angel invest today? 

64. At the beginning of each period for nine years, Scott Sullivan invested $900 quarterly at 4% interest compounded quarterly. What is the value of this annuity due? 

65. Gail Korosa decided that in six years she will leave her job in publishing and retire to Arizona. What amount should Gail invest today so that she will be able to withdraw $50,000 at the end of each year for 30 years after she retires? Assume she can invest money at 5% interest compounded annually. 

66. Find the value of an investment after four years for a $7,000 ordinary annuity at 10% compounded annually. 

67. Find the value of an investment after five years for a $6,000 ordinary annuity at 8% compounded annually. 

68. Find the value of an investment after five years for a $7,000 annuity due at 10% compounded annually. 

69. Find the value of an investment after six years for a $7,000 annuity due at 8% compounded annually. 

70. Find the value of an investment after four years on $6,000 made quarterly at 8% for (A) an ordinary annuity and (B) an annuity due. 

71. Find the value of an investment after three years on $15,000 made quarterly at 8% for (A) an ordinary annuity and (B) an annuity due. 

72. Alice Wolf wants to know how much she will have to invest today in order to receive an annuity of $6,000 for four years if interest is earned at 10% annually. She will make all her withdrawals at the end of each year. How much should Alice invest? 

73. Art Newner wants to know how much he will have to invest today in order to receive an annuity of $8,000 for three years if interest is earned at 10% annually. He will make all his withdrawals at the end of each year. How much should Art invest? 

74. What must Bill McGuire invest today to receive an annuity of $9,000 for four years semiannually at an 8% annual rate? All withdrawals will be made at the end of each period. 

75. What must John Sullivan invest today to receive an annuity of $6,000 for three years semiannually at a 10% annual rate? All withdrawals will be made at the end of each period. 

76. How much will the Apple Corporation have to set aside each period to have $40,000 eight years from now? Assume money is at 12% compounded semiannually. 

77. How much will the Van Company have to set aside each period to have $60,000 twelve years from now? Assume money is at 12% compounded semiannually. 

78. Al Wright puts $2,000 in a bank at the end of every six months. The bank pays 8% compounded semiannually. Assuming Al does this for four years, what is the total interest he will receive? 

79. Alice Kate puts $2,500 in a bank at the end of every six months. The bank pays 12% compounded semiannually. Assuming Alice does this for four years, what is the total interest she will receive? 

80. Jim Hunter decides to retire to Florida in 10 years. What amount should Jim invest today so that he will be able to withdraw $25,000 at the end of each year for 30 years after he retires? Assume he can invest money at 9% interest compounded annually. 

81. Alice Hall made deposits of $300 semiannually to Rey Bank, which pays 8% interest compounded semiannually. After five years Alice made no more deposits. What would be the balance in the account four years from the last deposit? 

92. Pete Rool made deposits of $6,000 at the end of each quarter to Rote Bank, which pays 8% interest compounded quarterly. After three years, Pete made no more deposits. What would be the balance in the account two years after the last deposit? 

93. Rachel deposits $2,000 semiannually for three years. What is the value of her investment at the end of three years assuming she can earn 6% interest?

94. Lisa Schermer wants to receive $5,000 a year for 12 years. How much must she invest today at 12% interest compounded annually?

95. Doubletree Capital Investments deposits $700 semiannually for six years into an account that pays 6% interest. What is the balance after the last deposit?

96. Robin wants to receive $2,500 at the end of each year for the next 10 years. How much should she deposit today at 5% annually?

97. Sherry Siebert invests $2,000 at the end of each six months for five years. Assuming Sherry can receive 6% interest compounded semiannually, what is the value of her investment at the end of five years?