Accounting Appendix B 1 The Future Value Ordinary Annuity The Accumulated

APPENDIX B

PRESENT AND FUTURE VALUES IN ACCOUNTING

Present Value of 1

Periods

3%

4%

5%

6%

7%

8%

9%

10%

12%

3

0.9151

0.8890

0.8638

0.8396

0.8163

0.7938

0.7722

0.7513

0.7118

4

0.8885

0.8548

0.8227

0.7921

0.7629

0.7350

0.7084

0.6830

0.6355

5

0.8626

0.8219

0.7835

0.7473

0.7130

0.6806

0.6499

0.6209

0.5674

6

0.8375

0.7903

0.7462

0.7050

0.6663

0.6302

0.5963

0.5645

0.5066

7

0.8131

0.7599

0.7107

0.6651

0.6227

0.5835

0.5470

0.5132

0.4523

8

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%

4%

5%

6%

7%

8%

9%

10%

12%

3

1.0927

1.1249

1.1576

1.1910

1.2250

1.2597

1.2950

1.3310

1.4049

4

1.1255

1.1699

1.2155

1.2625

1.3108

1.3605

1.4116

1.4641

1.5735

5

1.1593

1.2167

1.2763

1.3382

1.4026

1.4693

1.5386

1.6105

1.7623

6

1.1941

1.2653

1.3401

1.4185

1.5007

1.5869

1.6771

1.7716

1.9738

7

1.2299

1.3159

1.4071

1.5036

1.6058

1.7138

1.8280

1.9487

2.2107

8

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%

6%

7%

8%

9%

10%

12%

3

2.8286

2.7751

2.7232

2.6730

2.6243

2.5771

2.5313

2.4869

2.4018

4

3.7171

3.6299

3.5460

3.4651

3.3872

3.3121

3.2397

3.1699

3.0373

5

4.5797

4.4518

4.3295

4.2124

4.1002

3.9927

3.8897

3.7908

3.6048

6

5.4172

5.2421

5.0757

4.9173

4.7665

4.6229

4.4859

4.3553

4.1114

7

6.2303

6.0021

5.7864

5.5824

5.3893

5.2064

5.0330

4.8684

4.5638

8

7.0197

6.7327

6.4632

6.2098

5.9713

5.7466

5.5348

5.3349

4.9676

9

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

Future Value of an Annuity of 1

Periods

3%

4%

5%

6%

7%

8%

9%

10%

12%

3

3.0909

3.1216

3.1525

3.1836

3.2149

3.2464

3.2781

3.3100

3.3744

4

4.1836

4.2465

4.3101

4.3746

4.4399

4.5061

4.5731

4.6410

4.7793

5

5.3091

5.4163

5.5256

5.6371

5.7507

5.8666

5.9847

6.1051

6.3528

6

6.4684

6.6330

6.8019

6.9753

7.1533

7.3359

7.5233

7.7156

8.1152

7

7.6625

7.8983

8.1420

8.3938

8.6540

8.9228

9.2004

9.4872

10.089

8

8.8923

9.2142

9.5491

9.8975

10.260

10.637

11.029

11.436

12.300

9

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

1. Interest is the payment to the owner of an asset for its use by a borrower.

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

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

4. A company can use present and future value computations to estimate the interest

component of holding assets over time.

5. The number of periods in a present value calculation can 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.

0.5645 is the present value of $1 factor, 10%, 6 periods

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 can 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.

1.3605 is the future value of $1 factor, 8%, 4 periods

15. An annuity is a series of equal payments.

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.

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

each period.

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

$12,009.

2.4018 is the interest factor on the Present Value of an Annuity table; n = 3; i = 12%

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%.

7.7156 is the interest factor on the Future Value of an Annuity table; n = 6; i = 10%

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.

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.

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

table for 8% compounded quarterly?

A. 12%

B. 6%

C. 3%

D. 2%

E. 1%

23. 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

0.6355 is the interest factor on the Present Value table; n =4; i = 12%

24. Sam 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 Sam borrow?

A. $3,358.40

B. $4,000.00

C. $3,660.40

D. $4,776.40

E. $3,350.00

0.8375 is the interest factor on the Present Value table; n =3*2 = 6; i = 6/2 = 3%

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

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 2 years?

A. $4,433.80

B. $4,340.00

C. $4,390.40

D. $3,920.00

E. $3,500.00

1.2668 is the interest factor on the Future Value table; i = 12%/4 = 3%; n = 2*4 = 8

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

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%

1.3605 is the interest factor on the Future Value table; n = 4; i = 8%

29. Crowe 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

E. $200,000

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