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Appendix B - Applying Present and Future Values

Appendix B

Applying Present and Future Values

These abbreviated tables can be used with the test questions that are tagged: Factor

Present Value of 1

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

3

4

0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118

0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355

5

6

7

8

0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674

0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066

0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523

0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039

9 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606

10 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220

Future Value of 1

Periods

3

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

1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049

4

5

6

7

8

1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735

1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623

1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738

1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107

1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760

9 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731

10 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058

Present Value of an Annuity of 1

Periods 3% 4% 5%

3

4

6% 7% 8% 9% 10% 12%

2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018

3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373

5

6

7

4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048

5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114

6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638

8

9

7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676

7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282

10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502

AppB-1

Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill

Education.


Future Value of an Annuity of 1

Periods 3% 4% 5%

3

4

6% 7% 8% 9% 10% 12%

3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744

4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793

5

6

7

8

9

5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528

6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152

7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.089

8.8923 9.2142 9.5491 9.8975 10.260 10.637 11.029 11.436 12.300

10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.580 14.776

10 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 17.549

True / False Questions

[Question]

1.

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

Answer: TRUE

Blooms Taxonomy: Remember

AACSB: Analytic

AACSB: Communications

AICPA BB: Critical Thinking

AICPA BB: Industry

AICPA FN: Measurement

AICPA FN: Reporting

Difficulty: 1 Easy

Learning Objective: B-C1

Topic: Interest

[Question]

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

Answer: FALSE

Blooms Taxonomy: Apply

AACSB: Analytic






Difficulty: 3 Hard


Topic: Interest

[Question]

AppB-2


Education.


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

Answer: TRUE


AACSB: Analytic








Topic: Interest

[Question]

4. A company can use present and future value computations to estimate the interest component of holding assets over time.

Answer: TRUE

Blooms Taxonomy: Understand

AACSB: Analytic






Difficulty: 2 Medium


Topic: Interest

[Question]

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

Answer: FALSE


AACSB: Analytic







Learning Objective: B-P1

Topic: Present Value

[Question]

6. The present value factor for determining the present value of a single sum to be received three years from today at 10% interest compounded semiannually is 0.7462.

Answer: TRUE

AppB-3


Education.



AACSB: Analytic









Topic: Factor

[ Question]

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 its worth at the future date.

Answer: FALSE


AACSB: Analytic









[ Question]

8. In a present value or future value table, the length of one time period may be one year, one month, or any other length of time depending on the situation.

Answer: TRUE


AACSB: Analytic










Topic: Future Value

[

Question]

9. The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000 (rounded to full dollar amount).

Answer: TRUE

AppB-4


Education.


Feedback: $2,000 x 0.5002 = $1,000


AACSB: Analytic









Topic: Factor

[Question]

10. Sandra has a savings account that is now $50,000. She started with $28,225 and earned interest at 10% compounded annually. It took five years to accumulate the $50,000.

Answer: FALSE

Feedback: $28,225/$50,000 = 0.5645. This is the present value of 1 factor, 10%, 6 periods.


AACSB: Analytic








Topic: PV

Topic: Factor

[Question]

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

Answer: TRUE


AACSB: Analytic









[Question]

AppB-5


Education.


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

Answer: FALSE


AACSB: Analytic









[ Question]

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

Answer: FALSE

Feedback: $100 x 1.4185 = $141.85


AACSB: Analytic









Topic: Factor

[Question]

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

$7,210.65 in five years.

Answer: FALSE

Feedback: $7,210.65/$5,300 = 1.3605. This is the future value of 1 factor for four periods, 8%.


AACSB: Analytic








Topic: Factor


[ Question]

AppB-6


Education.


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

Answer: TRUE


AACSB: Analytic








Topic: Annuity

[Question]

16. The present value of an annuity table can be used to determine the series of equal payments that are required by a loan agreement.

Answer: TRUE


AACSB: Analytic









[Question]

17. An ordinary annuity refers to a series of equal payments made or received at the end of equal intervals.

Answer: TRUE


AACSB: Analytic








Topic: Ordinary Annuity

[Question]

AppB-7


Education.


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

$12,009.

Answer: TRUE

Feedback: $5,000 x 2.4018 = $12,009


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

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%.

Answer: TRUE

Feedback: $5,000 x 7.7156 = $38,578


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

20. The future value of an ordinary annuity is the accumulated value of each annuity payment with interest one period after the date of the final payment.

Answer: FALSE


AACSB: Analytic









Multiple Choice Questions

AppB-8


Education.


[Question]

21. Interest is:

A. Time.

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

C. The same as a savings account.

D. Always a liability.

E. Always an asset.

Answer: B


AACSB: Analytic








Topic: Interest

[Question]

22. Which interest rate column would you use to determine the factor from a present value table or a future value table for 8% compounded quarterly?

A. 12%

B. 6%

C. 3%

D. 2%

E. 1%

Answer: D

Feedback: 8% /4 = 2%


AACSB: Analytic









Topic: Factor



Topic: Interest

[Question]

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

AppB-9


Education.

Appendix B - Applying Present and Future Values 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

Answer: C

Feedback: $350,000 x 0.6355 = $222,425


AACSB: Analytic








Topic: Factor


[Question]

24. Sam has a loan that requires a single payment of $4,000 at the end of three years. The loan's interest rate is 6%, compounded semiannually. How much did Sam borrow?

A. $3,358.40

B. $4,000.00

C. $3,660.40

D. $4,776.40

E. $3,350.00

Answer: E

Feedback: $4,000 x 0.8375 = $3,350.00


AACSB: Analytic








Topic: Factor


[Question]

AppB-10


Education.


25. 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

Answer: E

Feedback: $15,529/$5,000 = 3.1058

Future value of 1 factor of 3.1058 relates to 12%, 10 periods

Alternatively: $5,000/$15,529 = 0.3220

Present value of 1 factor of 0.3220 relates to 12%, 10 periods


AACSB: Analytic









Topic: Factor



[Question]

26. 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 two years?

A. $4,433.80

B. $4,340.00

C. $4,390.40

D. $3,920.00

E. $3,500.00

Answer: A

Feedback: $3,500 x 1.2668 = $4,433.80


AACSB: Analytic








AppB-11


Education.


Topic: Factor


[Question]

27. 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

Answer: C

Feedback: $35,462.50/$25,000 = 1.4185, the future value of 1 factor at 6% for six periods


AACSB: Analytic








Topic: Factor

[Question]

28. 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%

Answer: B

Feedback: $6802.50/$5,000 = 1.3605, the future value of 1 factor at 8% for four periods


AACSB: Analytic








Topic: Factor


AppB-12


Education.


[Question]

29.Crowe Company has acquired a building with a loan that requires payments of $20,000 every six months for five 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

E. $200,000

Answer: C

Feedback: $20,000 x 7.3601 = $147,202


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

30. Jon Shear 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

Answer: A

Feedback:

$25,000/$6,595 = 3.7908, the present value of an annuity of 1 factor at 10% for five periods


AACSB: Analytic








Topic: Factor


AppB-13


Education.


Topic: Annuity

[Question]

31. A company is considering an investment that will return $20,000 at the end of each semiannual period for four 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 $63,398

B. Not more than $126,796

C. Not more than $80,000

D. Not more than $129,264

E. Not more than $160,000

Answer: D

Feedback: $20,000 x 6.4632 = $129,264


AACSB: Analytic








Topic: Factor

Topic: Annuity


[Question]

32.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

Answer: B

Feedback: $4,000 x 5.4172 = $21,668.80


AACSB: Analytic








Topic: Factor

Topic: Annuity

AppB-14


Education.



[Question]

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

$10,000 annually at the end of each year. She 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

Answer: D

Feedback: $10,000 x 14.487 = $144,870


AACSB: Analytic








Topic: Factor

Topic: Annuity


[Question]

34.Chad is setting up a retirement fund, and he plans on depositing $5,000 per year in an investment that will pay 7% annual interest. How long will it take him to reach his retirement goal of $69,080?

A. 13.816 years

B. 0.072 years

C. 10 years

D. 20 years

E. 5 years

Answer: C

Feedback: $69,080/$5,000 = 13.816, the future value of an annuity of 1 factor at 7%, 10 periods


AACSB: Analytic







AppB-15


Education.



Topic: Factor


Topic: Annuity

Short Essay

[Question]

35.What is interest?

Answer:

Interest represents a borrower's payment to the owner of an asset in exchange for its use.


AACSB: Analytic








Topic: Interest

[Question]

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

Answer:

The present value of a single amount to be received at a future date is equal to the amount that can be invested now at the specified interest rate to yield the future value.


AACSB: Analytic









[Question]

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

Answer:

AppB-16


Education.


The future value of a single amount is equal to the amount that would accumulate at a future date at a specified rate of interest.


AACSB: Analytic









[Question]

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

Answer:

The present value of an annuity is the amount that can be invested now at the specified interest rate to yield a series of equal periodic payments.


AACSB: Analytic









Topic: Annuity

[Question]

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

Answer:

The future value of an annuity to be invested at a specified rate of interest is the amount that would accumulate at the date of the final periodic payment.


AACSB: Analytic









Topic: Annuity

AppB-17


Education.


Short Answer Questions

[Question]

40. A company needs to have $200,000 in four years, and will create a fund to ensure that the

$200,000 will be available. If they can earn a 7% return, how much must the company invest in the fund today to equal the $200,000 at the end of four years?

Answer: $200,000 x 0.7629 = $152,580


AACSB: Analytic









Topic: Factor

[Question]

41. Annette has a loan that requires a $25,000 payment at the end of three years. The interest rate on the loan is 5%, compounded annually. How much did Annette borrow today?

Answer: $25,000 x 0.8638 = $21,595


AACSB: Analytic









Topic: Factor

[Question]

42. Thompson Company has acquired a machine from a dealer which 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?

Answer: $45,000 x 0.6756 = $30,402

AppB-18


Education.



AACSB: Analytic









Topic: Factor

[Question]

43. A company is creating a fund by depositing $65,763 today. The fund will grow to $90,000 after eight years. What annual interest rate is the company earning on the fund?

Answer: $65,763/$90,000 = 0.7307

This is the present value of 1 factor for eight periods at 4%.

Alternatively: $90,000/$65,763 = 1.3686

This is the future value of 1 factor for 8 periods at 4%.


AACSB: Analytic









Topic: Factor



[Question]

44. 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?

Answer: $21,354/$30,000 = 0.7118

This is the present value of 1 factor for three periods at 12%. This implies the company must

AppB-19


Education.

Appendix B - Applying Present and Future Values earn 12%.

Alternatively: $30,000/$21,354 = 1.4049. This is the future value of 1 factor for three periods at

12%.


AACSB: Analytic









Topic: Factor



AppB-20


Education.


[Question]

45. 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 eight years?

Answer: $50,000 x 1.7182 = $85,910


AACSB: Analytic








Topic: Factor


[Question]

46.Troy has $105,000 now. He has a loan of $175,000 that he must pay at the end of five years.

He can invest his $105,000 at 10% interest compounded semiannually. Will Troy have enough to pay his loan at the end of the five years?

Answer: $105,000 x 1.6289 = $171,034.50

No, Troy will be $3,965.50 short of his goal of $175,000.


AACSB: Analytic








Topic: Factor


AppB-21


Education.


[Question]

47. Madera Iron Sculpting is planning to save the money needed to replace one of its robotic welders 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 Madera have accumulated at the end of five years to replace the welder?

Answer:

Future value of $20,000 deposit $20,000 x 1.6105 = $32,210

Future value of $5,000 payments $5,000 x 4.6410 = 23,205

Total accumulated $55,415


AACSB: Analytic









Topic: Factor


Topic: Annuity

[Question]

48. A company borrows money from the bank by promising to make six annual year-end payments of $25,000 each. How much is the company able to borrow if the interest rate is 9%?

Answer: $25,000 x 4.4859 = $112,147.50


AACSB: Analytic








Topic: Factor


Topic: Annuity

AppB-22


Education.


[Question]

49. A company borrows money from the bank by promising to make eight semiannual payments of $9,000 each. How much is the company able to borrow if the interest rate is 10% compounded annually?

Answer: $9,000 x 6.4632 = $58,168.80


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

50. 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?

Answer: Nine years.

Feedback: $100,000/$14,702 = 6.8017, the present value of 1 annuity factor at 6% for nine periods.


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

AppB-23


Education.


51. Big League Sports borrowed $883,212 and must make annual year-end payments of

$120,000 each. If the applicable interest rate is 6%, how many years will it take Big League

Sports to pay off the loan?

Answer: $883,212/$120,000 = 7.3601

This is the present value of an annuity factor at 6% for 10 periods. It will take 10 years to pay off the loan.


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

52. Daley Co. lends $524,210 to Davis Corporation. The terms of the loan require that Davis repay the loan with six semiannual period-end payments of $100,000 each. What semiannual interest rate is Davis paying on the loan?

Answer: $524,210/$100,000 = 5.2421

This is the present value of an annuity factor for 6 periods at 4%.

Davis is paying a 4% semiannual rate, or 8% annual rate of interest.


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

AppB-24


Education.


53. A company is beginning a savings plan. It will save $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?

Answer: $15,000 x 15.937 = $239,055


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

54. You hope to retire in 10 years. Regrettably you are only just now beginning to save money for this purpose. You expect to save $6,000 a year at an annual rate of 8%. How much will you have accumulated when you retire?

Answer:

$6,000 x 14.487 = $86,922


AACSB: Analytic








Topic: Factor


Topic: Annuity

[Question]

55. A company is setting up a sinking fund to pay off $8,654,000 in bonds that are due in seven years. The fund will earn 7% interest, and the company intends to put away a series of equal year-end amounts for seven years. What amount must the company deposit annually?

Answer: $8,654,000/8.654 = $1,000,000 annually


AACSB: Analytic






AppB-25


Education.




Topic: Factor

Topic: Annuity


Fill-in-the-Blank

[Question]

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

Answer: Interest


AACSB: Analytic








Topic: Interest

[Question]

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

Answer: discount


AACSB: Analytic








Topic: Interest

[Question]

58. To calculate present value of an amount, two factors are required: __________________ and

___________________.

Answer: interest rate ( i ); number of time periods ( n )


AACSB: Analytic




AppB-26


Education.







[ Question]

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

Answer: annuity


AACSB: Analytic








Topic: Annuity

[Question]

60.The future value of an ________________ annuity is the accumulated value of each annuity payment with interest as of the date of the final payment.

Answer: ordinary


AACSB: Analytic









AppB-27


Education.

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Appendix B

Applying Present and Future Values

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Applying Present and Future Values

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