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A Notes on Compound Interest and Interest Tables Appendix Interest is the cost of using money. It is the rental charge for funds, just as renting a building and equipment entails a rental charge. When the funds are used for a period of time, it is necessary to recognize interest as a cost of using the borrowed (“rented”) funds. This requirement applies even if the funds represent ownership capital and if interest does not entail an outlay of cash. Why must interest be consid- ered? Because the selection of one alternative automatically commits a given amount of funds that could otherwise be invested in some other alternative. Interest is generally important, even when short-term projects are under con- sideration. Interest looms correspondingly larger when long-run plans are studied. The rate of interest has significant enough impact to influence decisions regarding borrowing and investing funds. For example, $100,000 invested now and com- pounded annually for 10 years at 8% will accumulate to $215,900; at 20%, the $100,000 will accumulate to $619,200. Many computer programs and pocket calculators are available that handle computa- tions involving the time value of money. You may also turn to the following four basic tables to compute interest. Table 1—Future Amount of $1 Table 1 shows how much $1 invested now will accumulate in a given number of peri- ods at a given compounded interest rate per period. Consider investing $1,000 now for three years at 8% compound interest. A tabular presentation of how this $1,000 would accumulate to $1,259.70 follows: Cumulative Interest Called Compound Total at End of Year Interest per Year Interest Year 0 $— $ $1,000.00 1 80.00 80.00 1,080.00 2 86.40 166.40 1,166.40 3 93.30 259.70 1,259.70 interest tables
8

Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

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Page 1: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

ANotes on Compound Interest and Interest Tables

A p p e n d i x

Interest is the cost of using money. It is the rental charge for funds, just as renting abuilding and equipment entails a rental charge. When the funds are used for a periodof time, it is necessary to recognize interest as a cost of using the borrowed(“rented”) funds. This requirement applies even if the funds represent ownershipcapital and if interest does not entail an outlay of cash. Why must interest be consid-ered? Because the selection of one alternative automatically commits a given amountof funds that could otherwise be invested in some other alternative.

Interest is generally important, even when short-term projects are under con-sideration. Interest looms correspondingly larger when long-run plans are studied.The rate of interest has significant enough impact to influence decisions regardingborrowing and investing funds. For example, $100,000 invested now and com-pounded annually for 10 years at 8% will accumulate to $215,900; at 20%, the$100,000 will accumulate to $619,200.

Many computer programs and pocket calculators are available that handle computa-tions involving the time value of money. You may also turn to the following fourbasic tables to compute interest.

Table 1—Future Amount of $1Table 1 shows how much $1 invested now will accumulate in a given number of peri-ods at a given compounded interest rate per period. Consider investing $1,000 nowfor three years at 8% compound interest. A tabular presentation of how this $1,000would accumulate to $1,259.70 follows:

Cumulative InterestCalled Compound Total at End of

Year Interest per Year Interest Year

0 $ — $ — $1,000.001 80.00 80.00 1,080.002 86.40 166.40 1,166.403 93.30 259.70 1,259.70

interest tables

Horngren APP A.QXD 07/06/06 17:57 Page A-1

Page 2: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

This tabular presentation is a series of computations that could appear as follows:

S1 = $1,000(1.08)1

S2 = $1,000(1.08)2

S3 = $1,000(1.08)3

The formula for the “amount of 1,” often called the “future value of $1” or“future amount of $1,” can be written

S = P(1 + r)n

S = $1,000(1 + 0.08)3 = $1,259.70

S is the future value amount; P is the present value, $1,000 in this case; r is the rate ofinterest; and n is the number of time periods.

Fortunately, tables make key computations readily available. A facility in select-ing the proper table will minimize computations. Check the accuracy of the preced-ing answer using Table 1.

Table 2—Present Value of $1In the previous example, if $1,000 compounded at 8% per year will accumulate to$1,259.70 in 3 years, then $1,000 must be the present value of $1,259.70 due at theend of 3 years. The formula for the present value can be derived by reversing theprocess of accumulation (finding the future amount) that we just finished.

If S = P(1 + r)n

then P =

P = = $1,000

Use Table 2 to check this calculation.When accumulating, we advance or roll forward in time. The difference

between our original amount and our accumulated amount is called compound inter-est. When discounting, we retreat or roll back in time. The difference between thefuture amount and the present value is called compound discount. Note the followingformulas (where P = $1,000):

Compound interest = P[(1 + r)n − 1] = $259.70

Compound discount = S[1 − ] = $259.70

Table 3—Amount of Annuity of $1An (ordinary) annuity is a series of equal payments (receipts) to be paid (or received)at the end of successive periods of equal length. Assume that $1,000 is invested at theend of each of 3 years at 8%:

1(1 + r)n

$1,259.70(1.08)3

S(1 + r)n

A-2 APPENDIX A

End of Year Amount

1st payment $1,000.00 $1,080.00 $1,166.40, which is $1,000(1.08)2

2nd payment $1,000.00 1,080.00, which is $1,000(1.08)1

3rd payment 1,000.00Accumulation (future amount) $3,246.40

0 1 2 3

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The preceding arithmetic may be expressed algebraically as the amount of anordinary annuity of $1,000 for 3 years = $1,000(1 + r)2 + $1,000(1 + r)1 + $1,000.

We can develop the general formula for Sn, the amount of an ordinary annuityof $1, by using the example above as a basis:

1. Sn = 1 + (1 + r)1 + (1 + r)2

2. Substitute: Sn = 1 + (1.08)1 + (1.08)2

3. Multiply (2) by (1 + r): (1.08)Sn = (1.08)1 + (1.08)2 + (1.08)3

4. Subtract (2) from (3): 1.08Sn − Sn = (1.08)3 − 1Note that all terms onthe right-hand side areremoved except (1.08)3in equation (3) and 1in equation (2).

5. Factor (4): Sn(1.08 −1) = (1.08)3 − 1

6. Divide (5) by (1.08 − 1): Sn = =

7. The general formula forthe amount of an ordinaryannuity of $1 becomes: Sn = or

This formula is the basis for Table 3. Look at Table 3 or use the formula itselfto check the calculations.

Table 4—Present Value of an Ordinary Annuity of $1Using the same example as for Table 3, we can show how the formula of Pn, the pres-ent value of an ordinary annuity, is developed.

End of Year

1st payment = $ 925.93 $1,000

2nd payment = $ 857.34 $1,000

3rd payment = $ 793.83 $1,000

Total present value $2,577.10

For the general case, the present value of an ordinary annuity of $1 may beexpressed:

1. Pn � � �

2. Substitute Pn � � �

3. Multiply by : Pn � � �

4. Subtract (3) from (2): Pn − Pn = −

5. Factor: Pn (1 − ) = [1 − ]6. or Pn( ) = [1 − ]1

(1.08)31

1.08.08

1.08

1(1.08)3

11.08

1(1.08)

1(1.08)4

11.08

11.08

1(1.08)4

1(1.08)3

1(1.08)2

11.08

11.08

1(1.08)3

1(1.08)2

11.08

1(1 � r)3

1(1 � r)2

11 � r

1,000(1.08)3

1,000(1.08)2

1,000(1.08)1

Compound interestRate

(1 + r)n − 1r

(1.08)3 − 1.08

(1.08)3 − 1)1.08 − 1

A-3APPENDIX A

0 1 2 3

Horngren APP A.QXD 07/06/06 17:57 Page A-3

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7. Multiply by : Pn = [1 − ]The general formula for the present value of an annuity of $1.00 is:

Pn = [1 − ] =

Solving,

Pn = = 2.577

The formula is the basis for Table 4. Check the answer in the table. The pres-ent value tables, Tables 2 and 4, are used most frequently in capital budgeting.

The tables for annuities are not essential. With Tables 1 and 2, compoundinterest and compound discount can readily be computed. It is simply a matter ofdividing either of these by the rate to get values equivalent to those shown in Tables3 and 4.

0.20620.08

Compound discountRate

1(1 + r)n

1r

1(1.08)3

10.08

1.080.08

A-4 APPENDIX A

Horngren APP A.QXD 07/06/06 17:57 Page A-4

Page 5: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

TABL

E1

Com

poun

d Am

ount

of $

1.00

(The

Fut

ure

Valu

e of

$1.

00).

S=

P(1

+r)n . I

n th

is ta

ble

P=

$1.0

0.

Per

iods

2%4%

6%8%

10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

30%

32%

40%

Per

iods

11.

020

1.04

01.

060

1.08

01.

100

1.12

01.

140

1.16

01.

180

1.20

01.

220

1.24

01.

260

1.28

01.

300

1.32

01.

400

1

21.

040

1.08

21.

124

1.16

61.

210

1.25

41.

300

1.34

61.

392

1.44

01.

488

1.53

81.

588

1.63

81.

690

1.74

21.

960

2

31.

061

1,12

51.

191

1.26

01.

331

1.40

51.

482

1.56

11.

643

1.72

81.

816

1.90

72.

000

2.09

72.

197

2.30

02.

744

3

41.

082

1.17

01.

262

1.36

01.

464

1,57

41.

689

1.81

11.

939

2.07

42.

215

2.36

42.

520

2.68

42.

856

3.03

63.

842

4

51.

104

1.21

71.

338

1.46

91.

611

1.76

21.

925

2.10

02.

288

2.48

82.

703

2.93

23.

176

3.43

63.

713

4,00

75.

378

5

61.

126

1.26

51.

419

1.58

71.

772

1.97

4 2.

195

2.43

62.

700

2.98

63.

297

3.63

54.

002

4.39

84.

827

5.29

07.

530

6

71.

149

1.31

61.

504

1.71

41.

949

2.21

12.

502

2.82

63.

185

3.58

34.

023

4.50

85.

042

5.62

96.

275

6.98

310

.541

7

81.

172

1.36

91.

594

1.85

12.

144

2.47

62.

853

3.27

83.

759

4.30

04.

908

5.59

06.

353

7.20

68.

157

9.21

714

.758

8

91.

195

1.42

31.

689

1.99

92.

358

2.77

33.

252

3.80

34.

435

5.16

05.

987

6.93

18.

005

9.22

310

.604

12.1

6620

.661

9

101.

219

1.48

01.

791

2.15

92.

594

3.10

63.

707

4.41

15.

234

6.19

27.

305

8.59

410

.086

11.8

0613

.786

16.0

6028

.925

10

111.

243

1.53

91.

898

2.33

22.

853

3.47

94.

226

5.11

76.

176

7.43

08.

912

10.6

5712

.708

15.1

1217

.922

21.1

9940

.496

11

121.

268

1,60

12.

012

2.51

83.

138

3.89

64.

818

5.93

6 7.

288

8.91

610

.872

13.2

1516

.012

19.3

4323

.298

27.9

8356

.694

12

131.

294

1.66

52.

133

2.72

03.

452

4.36

35.

492

6.88

68.

599

10.6

9913

.264

16.3

8620

.175

24.7

5930

.288

36.9

3779

.371

13

141.

319

1,73

22.

261

2.93

73.

797

4.88

76.

261

7.98

810

.147

12.8

3916

.182

20.3

1925

.421

31.6

9139

.374

48.7

5711

1.12

014

151.

346

1.80

12.

397

3.17

24.

177

5.47

47.

138

9.26

611

.974

15.4

0719

.742

25.1

9632

.030

40.5

6551

.186

64.3

5915

5.56

815

161.

373

1.87

32.

540

3.42

64.

595

6.13

08.

137

10.7

4814

.129

18.4

8824

.086

31.2

4340

.358

51.9

2366

.542

84.9

5421

7.79

516

171.

400

1.94

82.

693

3.70

05.

054

6.86

69.

276

12.4

6816

.672

22.1

8629

.384

38.7

4150

.851

66.4

6186

.504

112.

139

304.

913

17

181.

428

2.02

62.

854

3.99

65.

560

7.69

010

.575

14.4

6319

.673

26.6

2335

.849

48.0

3964

.072

85.0

7111

2.45

514

8.02

442

6.87

918

191.

457

2.10

73.

026

4.31

66.

116

8.61

312

.056

16.7

7723

.214

31.9

4843

.736

59.5

6880

.731

108.

890

146.

192

195.

391

597.

630

19

201.

486

2.19

13.

207

4.66

16.

727

9.64

613

.743

19.4

6127

.393

38.3

3853

.358

73.8

6410

1.72

113

9.38

019

0.05

025

7.91

683

6.68

320

211.

516

2.27

93.

400

5.03

47.

400

10.8

0415

.668

22.5

7432

.324

46.0

0565

.096

91.5

9212

8.16

917

8.40

624

7.06

534

0.44

911

71.3

5621

221.

546

2.37

03.

604

5.43

78.

140

12.1

0017

.861

26.1

8638

.142

55.2

0679

.418

113.

574

161.

492

228.

360

321.

184

449.

393

1639

.898

22

231.

577

2.46

53.

820

5.87

18.

954

13.5

5220

.362

30.3

7645

.008

66.2

4796

.889

140.

831

203.

480

292.

300

417.

539

593.

199

2295

.857

23

241.

608

2.56

34.

049

6.34

19.

850

15.1

7923

.212

35.2

3653

.109

79.4

9711

8.20

517

4.63

125

6.38

537

4.14

454

2.80

178

3.02

332

14.2

0024

251.

641

2.66

64.

292

6.84

810

.835

17.0

0026

.462

40.8

7462

.669

95.3

9614

4.21

021

6.54

232

3.04

547

8.90

570

5.64

110

33.5

9044

99.8

8025

261.

673

2.77

24.

549

7.39

611

.918

19.0

4030

.167

47.4

14

73.9

4911

4.47

517

5.93

626

8.51

240

7.03

761

2.99

891

7.33

313

64.3

3962

99.8

3126

271.

707

2.88

34.

822

7.98

813

.110

21.3

2534

.390

55.0

0087

.260

137.

371

214.

642

332.

955

512.

867

784.

638

1192

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1800

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8819

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27

281.

741

2.99

95.

112

8.62

714

.421

23.8

8439

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63.8

0010

2.96

716

4.84

526

1.86

441

2.86

464

6.21

210

04.3

3615

50.2

9323

77.2

2412

347.

670

28

291.

776

3.11

95.

418

9.31

715

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26.7

5044

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74.0

0912

1.50

119

7.81

431

9.47

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1.95

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812

85.5

5020

15.3

8131

37.9

3517

286.

737

29

301.

811

3.24

35.

743

10.0

6317

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29.9

6050

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85.8

5014

3.37

123

7.37

638

9.75

863

4.82

010

25.9

2716

45.5

0526

19.9

9641

42.0

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432

30

352.

000

3.94

67.

686

14.7

8528

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52.8

0098

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180.

314

327.

997

590.

668

1053

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1861

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3258

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9727

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35

402.

208

4.80

110

.286

21.7

2545

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93.0

5118

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437

8.72

175

0.37

814

69.7

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3854

55.9

1310

347.

175

1942

6.68

936

118.

865

6652

0.76

770

0037

.697

40

Horngren APP A.QXD 07/06/06 17:57 Page A-5

Page 6: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

TABL

E2

(Pla

ce a

clip

on

this

pag

e fo

r eas

y re

fere

nce.

)Pr

esen

t Val

ue o

f $1.

00.

P=

.In

this

tabl

e S

= $1

.00.

S(1

+r)

n

Per

iods

2%4%

6%8%

10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

30%

32%

40%

Per

iods

10.

980

0.96

20.

943

0.92

60.

909

0.89

30.

877

0.86

20.

847

0.83

30.

820

0.80

60.

794

0.78

10.

769

0.75

80.

714

12

0.96

10.

925

0.89

00.

857

0.82

60.

797

0.76

90.

743

0.71

80.

694

0.67

20.

650

0.63

00.

610

0.59

20.

574

0.51

02

30.

942

0.88

90.

840

0.79

40.

751

0.71

20.

675

0.64

10.

609

0.57

90.

551

0.52

40.

500

0.47

70.

455

0.43

50.

364

34

0.92

40.

855

0.79

20.

735

0.68

30.

636

0.59

20.

552

0.51

60.

482

0.45

10.

423

0.39

70.

373

0.35

00.

329

0.26

04

50.

906

0.82

20.

747

0.68

10.

621

0.56

70.

519

0.47

60.

437

0.40

20.

370

0.34

10.

315

0.29

10.

269

0.25

00.

186

56

0.88

80.

790

0.70

50.

630

0.56

40.

507

0.45

60.

410

0.37

00.

335

0.30

30.

275

0.25

00.

227

0.20

70.

189

0.13

36

70.

871

0.76

00.

665

0.58

30.

513

0.45

20.

400

0.35

40.

314

0.27

90.

249

0.22

20.

198

0.17

80.

159

0.14

30.

095

78

0.85

30.

731

0.62

70.

540

0.46

70.

404

0.35

10.

305

0.26

60.

233

0.20

40.

179

0.15

70.

139

0.12

30.

108

0.06

88

90.

837

0.70

30.

592

0.50

00.

424

0.36

10.

308

0.26

30.

225

0.19

40.

167

0.14

40.

125

0.10

80.

094

0.08

20.

048

910

0.82

00.

676

0.55

80.

463

0.38

60.

322

0.27

00.

227

0.19

10.

162

0.13

70.

116

0.09

90.

085

0.07

30.

062

0.03

510

110.

804

0.65

00.

527

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90.

350

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237

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162

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112

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079

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60.

056

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025

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0.78

80.

625

0.49

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397

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257

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168

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112

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20.

076

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30.

036

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812

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773

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469

0.36

80.

290

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90.

182

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116

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075

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10.

050

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00.

033

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013

1314

0.75

80.

577

0.44

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340

0.26

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205

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00.

125

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90.

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417

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239

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140

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084

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1516

0.72

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163

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0.51

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371

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198

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108

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003

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294

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000

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040

Horngren APP A.QXD 07/06/06 17:57 Page A-6

Page 7: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

TABL

E3

Com

poun

d Am

ount

of A

nnui

ty o

f $1.

00 in

Arr

ears

* (F

utur

e Va

lue

of A

nnui

ty).

S n=

(1 +

r)n

− 1

r

Per

iods

2%4%

6%8%

10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

30%

32%

40%

Per

iods

11.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1.00

01.

000

1

22.

020

2.04

02.

060

2.08

02.

100

2.12

02.

140

2.16

02.

180

2.20

02.

220

2.24

02.

260

2.28

02.

300

2.32

02.

400

2

33.

060

3.12

23.

184

3.24

63.

310

3.37

43.

440

3.50

63.

572

3.64

03.

708

3.77

83.

848

3.91

83.

990

4.06

24.

360

3

44.

122

4.24

64.

375

4.50

64.

641

4.77

94.

921

5.06

65.

215

5.36

85.

524

5.68

45.

848

6.01

66.

187

6.36

27.

104

4

55.

204

5.41

65.

637

5.86

76.

105

6.35

36.

610

6.87

77.

154

7.44

27.

740

8.04

88.

368

8.70

09.

043

9.39

810

.946

5

66.

308

6.63

36.

975

7.33

67.

716

8.11

58.

536

8.97

79.

442

9.93

010

.442

10.9

8011

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12.1

3612

.756

13.4

0616

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6

77.

434

7.89

88.

394

8.92

39.

487

10.0

8910

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11.4

1412

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12.9

1613

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14.6

1515

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16.5

3417

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18.6

9623

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7

88.

583

9.21

49.

897

10.6

3711

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12.3

0013

.233

14.2

4015

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16.4

9917

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19.1

2320

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22.1

6323

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25.6

7834

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8

99.

755

10.5

8311

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12.4

8813

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14.7

7616

.085

17.5

1919

.086

20.7

9922

.670

24.7

1226

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29.3

6932

.015

34.8

9549

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9

1010

.950

12.0

0613

.181

14.4

8715

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17.5

4919

.337

21.3

2123

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25.9

5928

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31.6

4334

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33.5

9342

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47.0

6269

.814

10

ll12

.169

13.4

8614

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16.6

4518

.531

20.6

5523

.045

25.7

3328

.755

32.1

5035

.962

40.2

3845

.031

50.3

9856

.405

63.1

2298

.739

11

1213

.412

15.0

2616

.870

18.9

7721

.384

24.1

3327

.271

30.8

5034

.931

39.5

8144

.874

50.8

9557

.739

65.5

1074

.327

84.3

2013

9.23

512

1314

.680

16.6

2718

.882

21.4

9524

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28.0

2932

.089

36.7

8642

.219

48.4

9755

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64.1

1073

.751

84.8

5397

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112.

303

195.

929

13

1415

.974

18.2

9221

.015

24 2

1527

.975

32.3

9337

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43.6

7250

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59.1

9669

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80.4

9693

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109.

612

127.

913

149.

240

275.

300

14

1517

.293

20.0

2423

.276

27.1

5231

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37.2

8043

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51.6

6060

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72.0

3585

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100.

815

119.

347

141.

303

167.

286

197.

997

386.

420

15

1618

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21.8

2525

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30.3

2435

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42.7

5350

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60.9

2572

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87.4

4210

4.93

512

6.01

115

1.37

718

1.86

821

8.47

226

2.35

654

1.98

816

1720

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23.6

9828

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33.7

5040

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48.8

8459

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71.6

7387

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105.

931

129.

020

157.

253

191.

735

233.

791

285.

014

347.

309

759.

784

17

1821

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25.6

4530

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37.4

5045

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55.7

5068

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84.1

4110

3.74

012

8.11

715

8.40

519

5.99

424

2.58

530

0.25

237

1.51

845

9.44

910

64.6

9718

1922

.841

27.6

7133

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41.4

4651

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63.4

4078

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98.6

0312

3.41

415

4.74

019

4.25

424

4.03

330

6.65

838

5.32

348

3.97

360

7.47

214

91.5

7619

2024

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29.7

7836

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45.7

6257

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72.0

5291

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115.

380

146.

628

186.

688

237.

989

303.

601

387.

389

494.

213

630.

165

802.

863

2089

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20

2125

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31.9

6939

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50.4

2364

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81.6

9910

4.76

813

4.84

117

4.02

122

5.02

629

1.34

737

7.46

548

9.11

063

3.59

382

0.21

510

60.7

7929

25.8

8921

2227

.299

34.2

4843

.392

55.4

5771

.403

92.5

0312

0.43

615

7.41

520

6.34

527

1.03

135

6.44

346

9.05

661

7.27

881

1.99

910

67.2

8014

01.2

2940

97.2

4522

2328

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36.6

1846

.996

60.8

9379

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104.

603

138.

297

183.

601

244.

487

326.

237

435.

861

582.

630

778.

771

1040

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1388

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1850

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5737

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23

2430

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39.0

8350

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66.7

6588

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118.

155

158.

659

213.

978

289.

494

392.

484

532.

750

723.

461

982.

251

1332

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1806

.003

2443

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8032

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24

2532

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41.6

4654

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73.1

0698

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133.

334

181.

871

249.

214

342.

603

471.

981

650.

955

898.

092

1238

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1706

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2348

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3226

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1124

7.19

925

2633

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44.3

1259

.156

79.9

5410

9.18

215

0.33

420

8.33

329

0.08

840

5.27

256

7.37

779

5.16

511

14.6

3415

61.6

8221

85.7

0830

54.4

4442

60.4

3415

747.

079

26

2735

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47.0

8463

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87.3

5112

1.10

016

9.37

423

8.49

933

7.50

247

9.22

168

1.85

397

1.10

213

83.1

4619

68.7

1927

98.7

0639

71.7

7856

24.7

7222

046.

910

27

2837

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49.9

6868

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95.3

3913

4.21

019

0.69

927

2.88

939

2.50

358

6.48

181

9.22

311

85.7

4417

16.1

0124

81.5

8635

83.3

4451

64.3

1174

25.6

9930

366.

674

28

2938

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52.9

6673

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103.

966

148.

631

214.

583

312.

094

456.

303

669.

447

984.

068

1447

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2128

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3127

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4587

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6714

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9802

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4321

4.34

329

3040

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56.0

8579

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113.

263

164.

494

241.

333

356.

787

530.

312

790.

948

1181

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1767

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2640

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3942

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5873

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8729

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1294

0.85

960

501.

081

30

3549

.994

73.6

5211

1.43

517

2.31

727

1.02

443

1.66

369

3.57

311

20.7

1318

16.6

5229

48.3

4147

83.6

4577

50.2

2512

527.

442

2018

8.96

632

422.

868

5186

9.42

732

5400

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35

4060

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95.0

2615

4.76

225

9.05

744

2.59

376

7.09

113

42.0

2523

60.7

5741

63.2

1373

43.8

5812

936.

535

2272

8.80

339

792.

982

6937

7.46

012

0392

.883

2078

74.2

7217

5009

1.74

140

*Pay

men

ts (o

r re

ceip

ts) a

t the

end

of e

ach

peri

od.

Horngren APP A.QXD 07/06/06 17:57 Page A-7

Page 8: Notes on Compound Interest and Interest Tableswps.prenhall.com/wps/media/objects/3554/3640175/Horngren_app_ A.pdfNotes on Compound Interest and Interest Tables Appendix Interest is

TABL

E4

(Pla

ce a

clip

on

this

pag

e fo

r eas

y re

fere

nce.

)Pr

esen

t Val

ue o

f Ann

uity

$1.

00 in

Arr

ears

.*

P n=

[1 −

]1

(1 +

r)n

1 r

Per

iods

2%4%

6%8%

10%

12%

14%

16%

18%

20%

22%

24%

26%

28%

30%

32%

40%

Per

iods

10.

980

0.96

20.

943

0.92

60.

909

0.89

30.

877

0.86

20.

847

0.83

30.

820

0.80

60.

794

0.78

10.

769

0.75

80.

714

12

1.94

21.

886

1.83

31.

783

1.73

61.

690

1.64

71.

605

1.56

61.

528

1.49

21.

457

1.42

41.

392

1.36

11.

331

1.22

42

32.

884

2.77

52.

673

2.57

72.

487

2.40

22.

322

2.24

62.

174

2.10

62.

042

1.98

11.

923

1.86

81.

816

1.76

61.

589

34

3.80

83.

630

3.46

53.

312

3.17

03.

037

2.91

42.

798

2.69

02.

589

2.49

42.

404

2.32

02.

241

2.16

62.

096

1.84

94

54.

713

4.45

24.

212

3.99

33.

791

3.60

53.

433

3.27

43.

127

2.99

12.

864

2.74

52.

635

2.53

22.

436

2.34

52.

035

56

5.60

15.

242

4.91

74.

623

4.35

54.

111

3.88

93.

685

3.49

83.

326

3.16

73.

020

2.88

52.

759

2.64

32.

534

2.16

86

76.

472

6.00

25.

582

5.20

64.

868

4.56

44.

288

4.03

93.

812

3.60

53.

416

3.24

23.

083

2.93

72.

802

2.67

72.

263

78

7.32

56.

733

6.21

05.

747

5.33

54.

968

4.63

94.

344

4.07

83.

837

3.61

93.

421

3.24

13.

076

2.92

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786

2.33

18

98.

162

7.43

56.

802

6.24

75.

759

5.32

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946

4.60

74.

303

4.03

13.

786

3.56

63.

366

3.18

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019

2.86

82.

379

910

8.98

38.

111

7.36

06.

710

6.14

55.

650

5.21

64.

833

4.49

44.

192

3.92

33.

682

3.46

53.

269

3.09

22.

930

2.41

410

119.

787

8.76

07.

887

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495

5.93

85.

453

5.02

94.

656

4.32

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035

3.77

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543

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147

2.97

82.

438

1112

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385

8.38

47.

536

6.81

46.

194

5.66

05.

197

4.79

34.

439

4.12

73.

851

3.60

63.

387

3.19

03.

013

2.45

612

1311

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9.98

68.

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Horngren APP A.QXD 07/06/06 17:57 Page A-8