978-0078025761 App B Part 1

APPENDIX B

PRESENT AND FUTURE VALUES IN ACCOUNTING

Present Value of 1

Period

s

3% 4% 5% 6% 7% 8% 9% 10% 12%

3 0.915

1

0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118

4 0.888

5

0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355

5 0.862

6

0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674

6 0.837

5

0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066

7 0.813

1

0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523

8 0.789

4

0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039

9 0.766

4

0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606

10 0.744

1

0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220

Future Value of 1

Period

s

3% 4% 5% 6% 7% 8% 9% 10% 12%

3 1.092

7

1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049

4 1.125

5

1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735

5 1.159

3

1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623

6 1.194

1

1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738

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7 1.229

9

1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107

8 1.266

8

1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760

9 1.304

8

1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731

10 1.343

9

1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058

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Present Value of an Annuity of 1

Period

s

3% 4% 5% 6% 7% 8% 9% 10% 12%

3 2.828

6

2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018

4 3.717

1

3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373

5 4.579

7

4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048

6 5.417

2

5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114

7 6.230

3

6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638

8 7.019

7

6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676

9 7.786

1

7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282

10 8.530

2

8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502

Future Value of an Annuity of 1

Period

s

3% 4% 5% 6% 7% 8% 9% 10% 12%

3 3.090

9

3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744

4 4.183

6

4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793

5 5.309

1

5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528

6 6.468

4

6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152

7 7.662

5

7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.089

8 8.892

3

9.2142 9.5491 9.8975 10.260 10.637 11.029 11.436 12.300

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9 10.15

9

10.583 11.027 11.491 11.978 12.488 13.021 13.580 14.776

10 11.46

4

12.006 12.578 13.181 13.816 14.487 15.193 15.937 17.549

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True / False Questions

1. Interest is the borrower’s payment to the owner of an asset for its use.

2. From the perspective of an account holder, a savings account is a liability with interest.

3. An interest rate is also called a discount rate.

4. Present and future value computations enable companies to measure or estimate the interest

component of holding assets or liabilities over time.

5. The number of periods in a present value calculation may only be expressed in years.

6. The present value factor for determining the present value of $6,300 to be received three

years from today at 10% interest compounded semiannually is 0.7462.

7. The present value of 1 formula is often useful when a borrowed asset must be repaid in full

at a later date and the borrower wants to know the worth of the asset at the future date.

8. In a present value or future value table, the length of one time period may be interpreted as

one year, one month, or any other length of time.

9. The present value of $2,000 to be received nine years from today at 8% interest

compounded annually is $1,000.

10. Sandra has a savings account that has accumulated to $50,000. She started with $28,225,

and earned interest at 10% compounded annually. It took her five years to accumulate the

$50,000.

11. Future value can be found if the interest rate (i), the number of periods (n), and the present

value (p) are known.

12. The number of periods in a future value calculation may only be expressed in years.

13. The future value of $100 compounded semiannually for 3 years at 12% equals $140.49.

14. At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total

of $7,210.65 in 5 years.

15. An annuity is a series of equal payments occurring at equal intervals.

16. The present value of an annuity table can be used to determine the value today of a series

of payments to be received in the future.

17. A series of equal payments made or received at the end of each period is an ordinary

annuity.

18. The present value of $5,000 per year for three years at 12% compounded annually is

$12,009.

19. With deposits of $5,000 at the end of each year, you will have accumulated $38,578 at the

end of the sixth year if the annual rate of interest is 10%.

20. The future value of an ordinary annuity is the accumulated value of each annuity payment

excluding interest as of the date of the final payment.

21. Interest may be defined as:

A. Time.

B. A borrower’s payment to the owner of an asset for its use.

C. The future value of a present amount.

D. Always a liability.

E. Always an asset.

22. If we want to know the value of present-day assets at a future date, we can use:

A. Present value computations

B. Annuity computations

C. Interest computations.

D. Future value computations.

E. Earnings computations.

23. Which interest rate column would you use from a present value or future value table for

8% interest compounded quarterly?

A. 12%

B. 6%

C. 3%

D. 2%

E. 1%

24. A company is considering investing in a project that is expected to return $350,000 four

years from now. How much is the company willing to pay for this investment if the company

requires a 12% return?

A. $ 55,606

B. $137,681

C. $222,425

D. $265,764

E. $350,000

25. Jason has a loan that requires a single payment of $4,000 at the end of 3 years. The loan’s

interest rate is 6%, compounded semiannually. How much did Jason borrow?

A. $3,358.40

B. $4,000.00

C. $3,660.40

D. $4,776.40

E. $3,350.00

26. Patricia wants to invest a sum of money today that will yield $10,000 at the end of 6

years. Assuming she can earn an interest rate of 6% compounded annually, how much must

she invest today?

A. $7,050

B. $9,400

C. $6,000

D. $8,836

E. $8,306

27. Marshall has received an inheritance and wants to invest a sum of money today that will

yield $5,000 at the end of each of the next 10 years. Assuming he can earn an interest rate of

5% compounded annually, how much of his inheritance must he invest today?

A. $50,000.00

B. $47,500.00

C. $45,125.00

D. $38,608.50

E. $100,000.00

28. Cody invests $1,800 per year from his summer wages at a 4% annual interest rate. He

plans to take a European vacation at the end of 4 years when he graduates from college. How

much will he have available to spend on his vacation?

A. $7,787.52

B. $7,488.00

C. $6,912.00

D. $7,200.00

E. $7,643.70

29. Jessica received a gift of $7,500 at the time of her high school graduation. She invests it

in an account that yields 10% compounded semi-annually. What will the value of Jessica’s

investment be at the end of 5 years?

A. $8,250.00

B. $11,250.00

C. $12,216.75

D. $9,375.00

E. $10,500.00

30. A company expects to invest $5,000 today at 12% annual interest and plans to receive

$15,529 at the end of the investment period. How many years will elapse before the company

accumulates the $15,529?

A. 0.322 years

B. 3.1058 years

C. 5 years

D. 8 years

E. 10 years

31. Keisha has $3,500 now and plans on investing it in a fund that will pay her 12% interest

compounded quarterly. How much will Keisha have accumulated after 2 years?

A. $4,433.80

B. $4,340.00

C. $4,390.40

D. $3,920.00

E. $3,500.00

32. How long will it take an investment of $25,000 at 6% compounded annually to

accumulate to a total of $35,462.50?

A. 4 years

B. 5 years

C. 6 years

D. 2 years

E. 10 years

33. What interest rate is required to accumulate $6,802.50 in four years from an investment of

$5,000?

A. 5%

B. 8%

C. 10%

D. 12%

E. 15%

34. Russell Company has acquired a building with a loan that requires payments of $20,000

every six months for 5 years. The annual interest rate on the loan is 12%. What is the present

value of the building?

A. $ 72,096

B. $113,004

C. $147,202

D. $ 86,590

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E. $200,000

35. Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is

earning 10% per year. How many annual payments will he receive?

A. Five payments

B. Six payments

C. Four payments

D. Three payments

E. More than six payments

36. A company is considering an investment that will return $22,000 semiannually at the end

of each semiannual period for 4 years. If the company requires an annual return of 10%, what

is the maximum amount it is willing to pay for this investment?

A. Not more than $69,738

B. Not more than $139,476

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C. Not more than $ 88,000

D. Not more than $142,190

E. Not more than $176,000

37. What amount can you borrow if you make six quarterly payments of $4,000 at a 12 %

annual rate of interest?

A. $24,838.00

B. $21,668.80

C. $31,049.00

D. $40,000.00

E. $44,800.00

38. What amount can you borrow if you make seven semiannual payments of $4,000 at an 8%

annual rate of interest?

A. $28,000.00

B. $25,760.00

C. $31,049.00

D. $24,008.40

E. $35,691.20

39. An individual is planning to set-up an education fund for her daughter. She plans to invest

$7,000 annually at the end of each year. She expects to withdraw money from the fund at the

end of 9 years and expects to earn an annual return of 8%. What will be the total value of the

fund at the end of 9 years?

A. $ 87,416

B. $ 68,040

C. $50,400

D. $126,000

E. $45,360

40. An individual is planning to set-up an education fund for his grandchildren. He plans to

invest $10,000 annually at the end of each year. He expects to withdraw money from the fund

at the end of 10 years and expects to earn an annual return of 8%. What will be the total value

of the fund at the end of 10 years?

A. $ 46,320

B. $ 67,107

C. $100,000

D. $144,870

E. $215,890

41. Clara is setting up a retirement fund, and she plans on depositing $5,000 per year in an

investment that will pay 7% annual interest. How long will it take her to reach her retirement

goal of $69,080?

A. 13.816 years

B. 0.072 years

C. 10 years

D. 20 years

E. 5 years

42. The Masterson family is setting up a vacation fund, and they plan on depositing $1,000

per quarter in an investment that will pay 12% annual interest. What amount will they have

available for their vacation at the end of 2 years?

A. $8,000.00

B. $8,960.00

C. $8,892.30

D. $8,240.00

E. $8,487.20

43. A company needs to have $150,000 in 5 years, and will create a fund to insure that the

$150,000 will be available. If it can earn a 6% return compounded annually, how much must

the company invest in the fund today to equal the $150,000 at the end of 5 years?

A. $141,000

B. $112,095

C. $100,000

D. $45,000

E. $105,000

44. Jackson has a loan that requires a $17,000 lump sum payment at the end of four years.

The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow

today?

A. $16,150

B. $13,600

C. $11,504

D. $13,986

E. $15,343

45. A company has $46,000 today to invest in a fund that will earn 4% compounded annually.

How much will the fund contain at the end of 6 years?

A. $58,204

B. $47,840

C. $58,075

D. $57,040

E. $62,582

46. Define interest.

47. Explain the concept of the present value of a single amount.

48. Explain the concept of the future value of a single amount.

49. Explain the concept of the present value of an annuity.

50. Explain the concept of the future value of an annuity.

51. A company needs to have $200,000 in 4 years, and will create a fund to insure that the

$200,000 will be available. If it can earn a 7% return compounded annually, how much must

the company invest in the fund today to equal the $200,000 at the end of 4 years?

52. A company needs to have $150,000 in 5 years, and will create a fund to insure that the

$150,000 will be available. If it can earn a 6% return compounded annually, how much must

the company invest in the fund today to equal the $150,000 at the end of 5 years?

53. Kelsey has a loan that requires a $25,000 lump sum payment at the end of three years.

The interest rate on the loan is 5%, compounded annually. How much did Kelsey borrow

today?

54. Jackson has a loan that requires a $17,000 lump sum payment at the end of four years.

The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow

today?

55. Mason Company has acquired a machine from a dealer that requires a payment of $45,000

at the end of five years. This transaction includes interest at 8%, compounded semiannually.

What is the value of the machine today?

56. Protocol Company has acquired equipment from a dealer that requires equal payments of

$12,000 at the end of the next five years. This transaction includes interest at 9%,

compounded annually. What is the value of the machine today?

57. A company is creating a fund today by depositing $65,763. The fund will grow to

$90,000 after 8 years. What annual interest rate is the company earning on the fund?

58. A company is setting aside $21,354 today, and wishes to have $30,000 at the end of three

years for a down payment on a piece of property. What interest rate must the company earn?

59. A company has $50,000 today to invest in a fund that will earn 7%. How much will the

fund contain at the end of 8 years?

60. A company has $46,000 today to invest in a fund that will earn 4% compounded annually.

How much will the fund contain at the end of 6 years?

61. Trey has $105,000 now. He has a loan of $175,000 that he must pay at the end of 5 years.

He can invest his $105,000 at 10% interest compounded semiannually. Will Trey have

enough to pay his loan at the end of the 5 years?

62. Garcia Brass Fixtures is planning on replacing one of its machines in five years by

making a one-time deposit of $20,000 today and four yearly contributions of $5,000

beginning at the end of year 1. The deposits will earn 10% interest. How much money will

Garcia have accumulated at the end of five years to replace the machine?

63. A company borrows money from the bank by promising to make 6 annual year-end

payments of $27,000 each. How much is the company able to borrow if the interest rate is

9%?

64. A company borrows money from the bank by promising to make 8 semiannual payments

of $9,000 each. How much is the company able to borrow if the interest rate is 10%

compounded semiannually?

65. When you reach retirement age, you will have one fund of $100,000 from which you are

going to make annual withdrawals of $14,702. The fund will earn 6% per year. For how

many years will you be able to draw an even amount of $14,702?

66. City Peewee League borrowed $883,212, and must make annual year-end payments of

$120,000 each. If City’s interest rate is 6%, how many years will it take to pay off the loan?

67. Giuliani Co. lends $524,210 to Craig Corporation. The terms of the loan require that

Craig make six semiannual period-end payments of $100,000 each. What semiannual interest

rate is Craig paying on the loan?

68. A company is beginning a savings plan. It will be saving $15,000 per year for the next 10

years. How much will the company have accumulated after the tenth year-end deposit,

assuming the fund earns 10% interest?

69. A company is beginning a savings plan to purchase a new building. It will be saving

$43,000 per year for the next 10 years. How much will the company have accumulated after

the tenth year-end deposit, assuming the fund earns 9% interest?

70. You are little late planning your retirement, but are looking forward to retiring in 10 years.

You expect to save $6,000 a year at an annual rate of 8%. How much will you have

accumulated when you retire?

71. A company is setting up a sinking fund to pay off $8,654,000 in bonds that are due in 7

years. The fund will earn 7% interest, and the company intends to put away a series of equal

year-end amounts for 7 years. What is the amount of the annual deposits that the company

must make?

72. _____________ is a borrower’s payment to the owner of an asset for its use.

73. The interest rate is also called the __________________ rate.

74. To calculate present value of an amount, two factors are required: The

__________________ and the___________________.

75. An _____________ is a series of equal payments occurring at equal intervals.

76. The future value of an ________________ annuity is the accumulated value of each

annuity payment with interest as of the date of the final payment.