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Appendix one: tables

Table 1. Discount factors.

The present value of I received or spent in a given future year 'n' at a given discount 'i'.
Discount factor: 1/(1 + i)n

%

2

4

5

6

8

9

10

12

14

15

16

18

20

25

30

35

40

45

50

Yrs




















1

.980

.962

.952

.943

.926

.917

.909

.893

.877

.870

.862

.847

.833

.800

.769

.741

.714

.690

,667

2

.961

.925

.907

.890

.857

.842

.826

.797

.769

.756

.743

.718

.694

.640

.592

.549

.510

.476

.444

3

.942

.889

.864

.840

.794

.772

.751

.712

.675

.658

.641

.609

.579

.512

.455

.406

.364

.328

.296

4

.924

.855

.823

.792

.735

.708

.683

.636

.592

.572

.552

.516

.482

.410

.350

.301

.260

.226

.198

5

.906

.822

.784

.747

.681

.650

.621

.567

.519

.497

.476

.437

.402

.328

.269

.223

.186

.156

.132

6

.888

.790

.746

.705

.630

.596

.564

.507

.456

.432

.410

.370

.335

.262

.207

.165

.133

.108

.088

7

.871

.760

.711

.665

.583

.547

.513

.452

.400

.376

.354

.314

.279

.210

.159

.122

.095

.074

.059

8

.853

.731

.677

.627

.540

.502

.467

.404

.351

.327

.305

.266

.233

.168

.123

.091

.068

.051

.039

9

.837

.703

.645

.592

.500

.460

.424

.361

.308

.284

.263

.225

.194

.134

.094

.067

.048

.035

.026

10

.820

.676

.614

.558

.463

.422

.386

.322

.270

.247

.227

.191

.162

.107

.073

.050

.035

.024

.017

11

.804

.650

.585

.527

.429

.388

.350

.287

.237

.215

.195

.162

.135

.086

.056

.037

.025

.017

.012

12

.788

.625

.557

.497

.397

.356

.319

.257

.208

.187

.168

.137

.112

.069

.043

.027

.018

.012

.008

13

.773

.601

.530

.469

.368

.326

.290

.229

.182

.163

.145

.116

.093

.055

.033

.020

.013

.008

.005

14

.758

.577

.505

.442

.340

.299

.263

.205

.160

.141

.125

.099

.078

.044

.025

.015

.009

.006

.003

15

.743

.555

.481

.417

.315

.275

.239

.183

.140

.123

.108

.084

.065

.035

.020

.011

.006

.004

.002

16

.728

.534

.458

.394

.292

.252

.218

.163

.123

.107

.093

.071

.054

.028

.015

.008

.005

.003

.002

17

.714

.513

.436

.371

.270

.231

.198

.146

.108

.093

.080

.060

.045

.023

.012

.006

.003

.002

.001

18

.700

.494

.416

.350

.250

.212

.180

.130

.095

.081

.069

.051

.038

.018

.009

.005

.002

.001

.001

19

.686

.475

.396

.331

.232

.194

.164

.116

.083

.070

.060

.043

.031

.014

.007

.003

.002

.001

.000

20

.673

.456

.377

.312

.215

.178

.149

.104

.073

.061

.051

.037

.026

.012

.005

.002

.001

.001

.000

21

.660

.439

.359

.294

.199

.164

.135

.093

.064

.053

.044

.031

.022

.009

.004

.002

.001

.000

.000

22

.647

.422

342

.278

.184

.150

.123

.083

.056

.046

.038

.026

.018

.007

.003

.001

.001

.000

.000

23

.634

.406

.326

.262

.170

.138

.112

.074

.049

.040

.033

.022

.015

.006

.002

.001

.000

.000

.000

24

.622

.390

.310

.247

.158

.126

.102

.066

.043

.035

.028

.019

.013

.005

.002

.001

.000

.000

.000

25

.610

.375

.295

.233

.146

.116

.092

.059

.038

.030

.024

.016

.010

.004

.001

.001

.000

.000

.000

30

.552

.308

.231

.174

.099

.075

.057

.033

.020

.015

.012

.007

.004

.001

.000

.000

.000

.000

.000

35

.500

.253

.181

.130

.068

.049

.036

.019

.010

.008

.006

.003

.002

.000

.000

.000

.000

.000

.000

40

.453

.208

.142

.097

.046

.032

.022

.011

.005

.004

.003

.001

.001

.000

.000

.000

.000

.000

.000

45

.410

.171

.111

.073

.031

.021

.014

.006

.003

.002

.001

.001

.000

.000

.000

.000

.000

.000

.000

50

.372

.141

.087

.054

.021

.013

.009

.003

.001

.001

.001

.000

.000

.000

.000

.000

.000

.000

.000

Table 2. Present value of an annuity.

The present value of I received or spent annually at a given rate of interest 'i' for a given number of years 'n'.
Present value of an annuity factor: S 1/(1 + i)n

%

2

4

5

6

8

9

10

12

14

15

16

18

20

25

30

35

40

50

Yrs



















1

.9804

.9615

.9524

.9434

.9259

.9174

.9091

.8929

.8772

.8696

.8621

.8475

.8333

.8000

.7692

.7407

.7143

.6667

2

1.942

1.886

1.859

1.833

1.783

1.759

1.736

1.690

1.647

1.626

1.605

1.566

1.528

1.440

1.361

1.289

1.224

1.111

3

2.884

2.775

2.723

2.673

2.577

2.531

2.487

2.402

2.322

2.283

2.246

2.174

2.106

1.952

1.816

1.696

1.589

1.407

4

3.808

3.630

3.546

3.465

3.312

3.240

3.170

3.037

2.914

2.855

2.798

2.690

2.589

2.362

2.166

1.997

1.849

1.605

5

4.713

4.452

4.329

4.212

3.993

3.890

3.791

3.605

3.433

3.352

3.274

3,127

2.991

2.689

2.436

2.220

2.035

1.737

6

5.601

5.242

5.076

4.917

4.623

4.486

4.355

4.111

3.889

3.784

3.685

3.498

3.326

2.951

2.643

2.385

2.168

1.824

7

6.472

6.002

5.786

5.582

5.206

5.033

4.868

4.564

4.288

4.160

4.039

3.812

3.605

3.161

2.802

2.508

2.263

1.883

8

7.325

6.733

6.463

6.210

5.747

5.535

5.335

4.968

4.639

4.487

4.344

4.078

3.837

3.329

2.925

2.598

2.331

1.922

9

8.162

7.435

7.108

6.802

6.247

5.995

5.759

5.328

4.946

4.772

4.607

4.303

4.031

3.463

3.019

2.665

2.379

1.948

10

8.983

8.111

7.722

7.360

6.710

6.418

6.145

5.650

5.216

5.019

4.833

4.494

4.192

3.571

3.092

2.715

2.414

1.965

11

9.787

8.760

8.306

7.887

7.139

6.805

6.495

5.938

5.453

5.234

5.029

4.656

4.327

3.656

3.147

2.752

2.438

1.977

12

10.58

9.385

8.863

8.384

7.536

7.161

6.814

6.194

5.660

5.421

5.197

4.793

4.439

3.725

3.190

2.779

2.456

1.985

13

11.35

9.986

9.394

8.853

7.904

7.487

7.103

6.424

5.842

5.583

5.342

4.910

4.533

3.780

3.223

2.799

2.469

1.990

14

12.11

10.56

9.899

9.295

8.244

7.786

7.367

6.628

6.002

5.724

5.468

5.008

4.611

3.824

3.249

2.814

2.478

1.993

15

12.85

11.12

10.38

9.712

8.559

8.061

7.606

6.811

6.142

5.847

5.575

5.092

4.675

3.859

3.268

2.825

2.484

1.995

16

13.58

11.65

10.84

10.11

8.851

8.313

7.824

6.974

6.265

5.954

5.668

5.162

4.730

3.887

3.283

2.834

2.489

1.997

17

14.29

12.17

11.27

10.48

9.122

8.544

8.022

7.120

6.373

6.047

5.749

5.222

4.77

3.910

3.295

2.840

2.492

1.998

18

14.99

12.66

11.69

10.83

9.372

8.756

8.201

7.250

6.467

6.128

5.818

5.273

4.813

3.928

3.304

2.844

2.494

1.999

19

15.68

13.13

12.09

11.16

9.604

8.950

8.365

71366

6.550

6.198

5.877

5.316

4.843

3.942

3.311

2.848

2.496

1.999

20

16.35

13.59

12.46

11.47

9.818

9.129

8.514

7.469

6.623

6.259

5.929

5.353

4.870

3.954

3.316

2.850

2.497

1.999

21

17.01

14.03

12.82

11.76

10.02

9.292

8.649

7.562

6.687

6.312

5.973

5.384

4.891

3.963

3.320

2.852

2.498

2.000

22

17.66

14.45

13.16

12.04

10.20

9.442

8.772

7.645

6.743

6.359

6.011

5.410

4.909

3.970

3.323

2.853

2.498

2.000

23

18.29

14.86

13.49

12'30

10.37

9.580

8.883

7.718

6.792

6.399

6.044

5.432

4.925

3.976

3.325

2.854

2.499

2.000

24

18.91

15.25

13.80

12.55

10.53

9.707

8.985

7.784

6.835

6.434

6.073

5.451

4.937

3.981

3.327

2.855

2.499

2.000

25

19.52

15.62

14.09

12.78

10.67

9.823

9.077

7.843

6.873

6.464

6.097

5.467

4.948

3.985

3.329

2.856

2.499

2.000

30

22.40

17.29

15.37

13.76

11.26

10.27

9.427

8.055

7.003

6.566

6.177

5.517

4.979

3.995

3.332

2.857

2.500

2.000

35

25.00

18.66

16.37

14.50

11.65

10.57

9.644

8.176

7.070

6.617

6.215

5.539

4.992

3.998

3.333

2.857

2.500

2.000

40

27.36

19.79

17.16

15.05

11.92

10.76

9.779

8.244

7.105

6.642

6.233

5.548

4.997

3.999

3.333

2.857

2.500

2.000

45

29.49

20.72

17.77

15.46

12.11

10.88

9.863

8.283

7.123

6.654

6.242

5.552

4.999

4.000

3.333

2.857

2.500

2.000

50

31.42

21.48

18.26

15.76

12.23

10.96

9.915

8.304

7.133

6.661

6.246

5.554

4.999

4.000

3.333

2.857

2.500

2.000

Table 3. Compound interest factors.

The future value of I invested at a given rate of interest 'i' for a given number of years 'n'.
Compounding factor: 1 x (1 + i)n

%

2

4

5

6

8

9

10

12

14

15

16

18

20

25

30

35

40

45

50

Yrs




















1

1.020

1.040

1.050

1.060

1.080

1.090

1.100

1.120

1.140

1.150

1.160

.1.180

1.200

1.250

1.300

1.350

1.400

1.450

1.500

2

1.040

1.082

1.103

1.124

1.166

1.188

1.210

1.254

1.300

1.323

1.346

1.392

1.440

1.563

1.690

1.823

1.960

2.103

2.250

3

1.061

1.125

1.158

1.191

1.260

1.295

1.331

1.405

1.482

1.521

1.561

1.643

1.728

1.953

2.197

2.460

2.744

3.049

3.375

4

1.082

1.170

1.216

1.262

1.360

1.412

1.464

1.574

1.689

1.749

1.811

1.939

2.074

2.441

2.856

3.322

3.842

4.421

5.063

5

1.104

1.217

1.276

1.338

1.469

1.539

1.611

1.762

1.925

2.011

2.100

2.288

2.488

3.052

3.713

4.484

5.378

6.410

7.594

6

1.126

1.265

1.340

1.419

1.587

1.677

1.772

1.974

2.195

2.313

2.436

2.700

2.986

3.815

4.827

6.053

7.530

9.294

11.39

7

1.149

1.316

1.407

1.504

1.714

1.828

1.949

2.211

2.502

2.660

2.826

3.185

3.583

4.768

6.275

8.172

10.54

13.48

17.09

8

1.172

1.369

1.477

1.594

1.851

1.993

2.144

2.476

2.853

3.059

3.278

3.759

4.300

5.960

8.157

11.03

14.76

19.54

25.63

9

1.195

1.423

1.551

1.689

1.999

2.172

2.358

2.773

3.252

3.518

3.803

4.435

5.160

7.451

10.60

14.89

20.66

28.33

38.44

10

1.219

1.480

1.629

1.791

2.159

2.367

2.594

3.106

3.707

4.046

4.411

5.234

6.192

9.313

13.79

20.11

28.93

41.08

57.67

11

1.243

1.539

1.710

1.898

2.332

2.580

2.853

3.479

4.226

4.652

5.117

6.176

7.430

11.64

17.92

27.14

40.50

59.57

86.50

12

1.268

1.601

1.796

2.012

2.518

2.813

3.138

3.896

4.818

5.350

5.936

7.288

8.916

14.55

23.30

36.64

56.69

86.38

129.7

13

1.294

1.665

1.886

2.133

2.720

3.066

3.452

4.363

5.492

6.153

6.886

8.599

10.70

18.19

30.29

49.47

79.37

125.3

194.6

14

1.319

1.732

1.980

2.261

2.937

3.342

3.797

4.887

6.261

7.076

7.988

10.15

12.84

22.74

39.37

66.78

111.1

181.6

291.9

15

1.346

1.801

2.079

2.397

3.172

3.642

4.177

5.474

7.138

8.137

9.266

11.97

15.41

28.42

51.19

90.16

155.6

263.3

437.9

16

1.373

1.873

2.183

2.540

3.426

3.970

4.595

6.130

8.137

9.358

10.75

14.13

18.49

35.53

66.54

121.7

217.8

381.8

656.8

17

1.400

1.948

2.292

2.693

3.700

4.328

5.054

6.866

9.276

10.76

12.47

16.67

22.19

44.41

86.50

164.3

304.9

553.7

985.3

18

1.428

2.026

2.407

2.854

3.996

4.717

5.560

7.690

10.58

12.38

14.46

19.67

26.62

55.51

112.5

221.8

426.9

802.8

1478.

19

1.457

2.107

2.527

3.026

4.316

5.142

6.116

8.613

12.06

14.23

16.78

23.21

31.95

69.39

146.2

299.5

597.6

1164.

2217.

20

1.486

2.191

2.653

3.207

4.661

5.604

6.727

9.646

13.74

16.37

19.46

27.39

38.34

86.74

190.0

404.3

836.7

1688.

3325.

21

1.516

2.279

2.786

3.400

5.034

6.109

7.400

10.80

15.67

18.82

22.57

32.32

46.01

108.4

247.1

545.8

1171.

2448.

4988.

22

1.546

2.370

2.925

3.604

5.437

6.659

8.140

12.10

17,86

21.64

26.19

38.14

55.21

135.5

321.2

736.8

1640.

3549.

7482.

23

1.577

2.465

3.072

3.820

5.871

7.258

8.954

13.55

20.36

24.89

30.38

45.01

66.25

169.4

417.5

994.7

2296.

5146.

11223

24

1.608

2.563

3.225

4.049

6.341

7.911

9.850

15.18

23.21

28.63

35.24

53.11

79.50

211.8

542.8

1343.

3214.

7462.

16834

25

1.641

2.666

3.386

4.292

6.848

8.623

10.83

17.00

26.46

32.92

40.87

62.67

95.40

264.7

705.6

1813.

4500.

10819

25251

30

1.811

3.243

4.322

5.743

10.06

13.27

17.45

29.96

50.95

66.21

85.85

143.4

237.4

807.8

2620.

8129.

24210

69349

>100t

35

2.000

3.946

5.516

7.686

14.79

20.41

28.10

52.80

98.10

133.2

180.3

328.0

590.7

2465.

9728.

36449

>100t

>100t

>100t

40

2.208

4.801

7.040

10.29

21.72

31.41

45.26

93.05

188.9

267.9

378.7

750.4

1470.

7523.

36119

>100t

>100t

>100t

>100t

45

2.438

5.841

8.985

13.76

31.92

48.33

72.89

164.0

363.7

538.8

795.4

1717.

3657.

22959

>100t

>100t

>100t

>100t

>100t

50

2.692

7.107

11.47

18.42

46.90

74.36

117.4

289.0

700.2

1084.

1671.

3927.

9100.

70065

>100t

>100t

>100t

>100t

>100t

>100t indicates that the number exceeds 100 000.

Table 4. Future value of annuity.

The future value of I invested annually at a given rate of interest 'i' for a given number of years 'n'.
Future value of an annuity factor: S (1 + i)n

%

2

4

5

6

8

9

10

12

14

15

16

18

120

25

30

35

40

50

Yrs



















1

1.02

1.04

1.05

1.06

1.08

1.09

1.1

1.12

1.14

1.15

1.16

1.18

1.2

1.25

1.3

1.35

1.4

1.5

2

2.060

2.122

2.153

2.184

2.246

2.278

2.310

2.374

2.440

2.473

2.506

2.572

2.640

2.813

2.990

3.173

3.360

3.750

3

3.122

3.246

3.310

3.375

3.506

3.573

3.641

3.779

3.921

3.993

4.066

4.215

4.368

4.766

5.187

5.633

6.104

7.125

4

4.204

4.416

4.526

4.637

4.867

4.985

5.105

5.353

5.610

5.742

5.877

6.154

6.442

7.207

8.043

8.954

9.946

12.19

5

5.308

5.633

5.802

5.975

6.336

6.523

6.716

7.115

7.536

7.754

7.977

8.442

8.930

10.26

11.76

13.44

15.32

19.78

6

6.434

6.898

7.142

7.394

7.923

8.200

8.487

9.089

9.730

10.07

10.41

11.14

11.92

14.07

16.58

19.49

22.85

31.17

7

7.583

8.214

8.549

8.897

9.637

10.03

10.44

11.30

12.23

12.73

13.24

14.33

15.50

18.84

22.86

27.66

33.39

48.26

8

8.755

9.583

10.03

10.49

11.49

12.02

12.58

13.78

15.09

15.79

16.52

18.09

19.80

24.80

31.01

38.70

48.15

73.89

9

9.950

11.01

11.58

12.18

13.49

14.19

14.94

16.55

18.34

19.30

20.32

22.52

24.96

32.25

41.62

53.59

68.81

112.3

10

11.17

12.49

13.21

13.97

15.65

16.56

17.53

19.65

22.04

23.35

24.73

27.76

31.15

41.57

55.41

73.70

97.74

170.0

11

12.41

14.03

14.92

15.87

17.98

19.14

20.38

23.13

26.27

28.00

29.85

33.93

38.58

53.21

73.33

100.8

138.2

256.5

12

13.68

15.63

16.71

17.88

20.50

21.95

23.52

27.03

31.09

33.35

35.79

41.22

47.50

67.76

96.63

137.5

194.9

386.2

13

14.97

17.29

18.60

20.02

23.21

25.02

26.97

31.39

36.58

39.50

42.67

49.82

58.20

85.95

126.9

187.0

274.3

580.9

14

16.29

19.02

20.58

22.28

26.15

28.36

30.77

36.28

42.84

46.58

50.66

59.97

71.04

108.7

166.3

253.7

385.4

872.8

15

17.64

20.82

22.66

24.67

29.32

32.00

34.95

41.75

49.98

54.72

59.93

71.94

86.44

137.1

217.5

343.9

541.0

1311.

16

19.01

22.70

24.84

27.21

32.75

35.97

39.54

47.88

58.12

64.08

70.67

86.07

104.9

172.6

284.0

465.6

758.8

1968.

17

20.41

24.65

27.13

29.91

36.45

40.30

44.60

54.75

67.39

74.84

83.14

102.7

127.1

217.0

370.5

629.9

1064.

2953.

18

21.84

26.67

29.54

32.76

40.45

45.02

50.16

62.44

77.97

87.21

97.60

122.4

153.7

272.6

483.0

851.7

1491.

4431.

19

23.30

28.78

32.07

35.79

44.76

50.16

56.27

71.05

90.02

101.4

114.4

145.6

195.7

341.9

629.2

1151.

2088.

6648.

20

24.78

30.97

34.72

38.99

49.42

55.76

63.00

80.70

103.8

117.8

133.8

173.0

224.0

428.7

819.2

1555.

2925.

9973.

21

26.30

33.25

37.51

42.39

54.46

61.87

70.40

91.50

119.4

136.6

156.4

205.3

270.0

537.1

1066.

2101.

4096.

14961

22

27.84

35.62

40.43

46.00

59.89

68.53

78.54

103.6

137.3

158.3

182.6

243.5

325.2

672.6

1387.

2838.

5736.

22442

23

29.42

38.08

43.50

49.82

65.76

75.79

87.50

117.2

157.7

183.2

213.0

288.5

391.5

842.0

1805.

3833.

8032.

33665

24

31.03

40.65

46.73

53.86

72.11

83.70

97.35

132.3

180.9

211.8

248.2

341.6

471.0

1054.

2348.

5176.

11246

50499

25

32.67

43.31

50.11

58.16

78.95

92.32

108.2

149.3

207.3

244.7

289.1

404.3

566.4

1318.

3053.

6988.

15746

75751

30

41.38

58.33

69.76

83.80

122.3

148.6

180.9

270.3

406.7

500.0

615.2

933.3

1418.

4034.

11349

31349

84702

>100t

35

50.99

76.60

94.84

118.1

186.1

235.1

298.1

483.5

790.7

1013.

1300.

2144.

3538.

12321

42150

>100t

>100t

>100t

40

61.61

98.83

126.8

164.0

279.8

368.3

486.9

859.1

1530.

2046.

2738.

4913.

8813.

37611

>100t

>100t

>100t

>100t

45

73.33

125.9

167.7

223.5

417.4

573.2

790.8

1521.

2953.

4123.

5760.

11247

21938

>100t

>100t

>100t

>100t

>100t

50

86.27

158.8

219.8

307.8

619.7

888.4

1280.

2688.

5694.

8300.

12105

25739

54597

>100t

>100t

>100t

>100t

>100t

> 100t indicates that the number exceeds 100 000. !

Table 5. Annual repayments or capital recovery factors.

The amount that must be repaid annually for every I unit borrowed for 'n' years at 'i' rate of interest.
Capital recovery factor: 1/ [S (1 + i)n]

%

2

4

5

6

8

9

10

12

14

15

16

18

20

25

30

35

40

45

50

Yrs




















1

1.02

1.04

1.05

1.06

1.08

1.09

1.10

1.12

1.14

1.15

1.16

1.18

1.20

1.25

1.30

1.35

1.40

1.45

1.50

2

.515

.530

.538

.545

.561

.568

.576

.592

.607

.615

.623

.639

.655

.694

.735

.776

.817

.858

.900

3

.347

.360

.367

.374

.388

.395

.402

.416

.431

.438

.445

.460

.475

.512

.551

.590

.629

.670

.711

4

.263

.275

.282

.289

.302

.309

.315

.329

.343

.350

.357

.372

.386

.423

.462

.501

.541

.582

.623

5

.212

.225

.231

.237

.250

.257

.264

.277

.291

.298

.305

.320

.334

.372

.411

.450

.491

.533

.576

6

.179

.191

.197

.203

.216

.223

.230

.243

.257

.264

.271

.286

.301

.339

.378

.419

.461

.504

.548

7

.155

.167

.173

.179

.192

.199

.205

.219

.233

.240

.248

.262

.277

.316

.357

.399

.442

.486

.531

8

.137

.149

.155

.161

.174

.181

.187

.201

.216

.223

.230

.245

.261

.300

.342

.385

.429

.474

.520

9

.123

.134

.141

.147

.160

.167

.174

.188

.202

.210

.217

.232

.248

.289

.331

.375

.420

.466

.513

10

.111

.123

.130

.136

.149

.156

.163

.177

.192

.199

.207

.223

.239

.280

.323

.368

.414

.461

.509

11

.102

.114

.120

.127

.140

.147

.154

.168

.183

.191

.199

.215

.231

.273

.318

.363

.410

.458

.506

12

.095

.107

.113

.119

.133

.140

.147

.161

.177

.184

.192

.209

.225

.268

.313

.360

.407

.455

.504

13

.088

.100

.106

.113

.127

.134

.141

.156

.171

.179

.187

.204

.221

.265

.310

.357

.405

.454

.503

14

.083

.095

.101

.108

.121

.128

.136

.151

.167

.175

.183

.200

.217

.262

.308

.355

.404

.452

.502

15

.078

.090

.096

.103

.117

.124

.131

.147

.163

.171

.179

.196

.214

.259

.306

.354

.403

.452

.501

16

.074

.086

.092

.099

.113

.120

.128

.143

.160

.168

.176

.194

.211

.257

.305

.353

.402

.451

.501

17

.070

.082

.089

.095

.110

.117

.125

.140

.157

.165

.174

.191

.209

.256

.304

.352

.401

.451

.501

18

.067

.079

.086

.092

.107

.114

.122

.138

.155

.163

.172

.190

.208

.255

.303

.352

.401

.451

.500

19

.064

.076

.083

.090

.104

.112

.120

.136

.153

.161

.170

.188

.206

.254

.302

.351

.401

.450

.500

20

.061

.074

.080

.087

.102

.110

.117

.134

.151

.160

.169

.187

.205

.253

.302

.351

.400

.450

.500

21

.059

.071

.078

.085

.100

.109

.116

.132

.150

.158

.167

.186

.204

.252

.301

.351

.400

.450

.500

22

.057

.069

.076

.083

.098

.106

.114

.131

.148

.157

.166

.185

.204

.252

.301

.350

.400

.450

.500

23

.055

.067

.074

.081

.096

.104

.113

.130

.147

.156

.165

.184

.203

.251

.301

.350

.400

.450

.500

24

.053

.066

.072

.080

.095

.103

.111

.128

.146

.155

.165

.183

.203

.251

.301

.350

.400

.450

.500

25

.051

.064

.071

.078

.094

.102

.110

.127

.145

.155

.164

.183

.202

.251

.300

.350

.400

.450

.500

30

.045

.058

.065

.073

.089

.097

.106

.124

.143

.152

.162

.181

.201

.250

.300

.350

A00

.450

.500

35

.040

.054

.061

.069

.086

.095

.104

.122

.141

.151

.161

.181

.200

.250

.300

.350

.400

.450

.500

40

.037

.051

.058

.066

.084

.093

.102

.121

.141

.151

.161

.181

.200

.250

.300

.350

.400

.450

.500

45

.034

.048

.056

.065

.083

.092

.101

.121

.140

.150

.160

.180

.200

.250

.300

.350

.400

.450

.500

50

.032

.047

.055

.063

.082

.091

.101

.120

.140

.150

.160

.180

.200

.250

.300

.350

.400

.450

.500

Table 6. Random numbers.

52687

36466

31250

10750

81154

76239

02937

00804

14571

35636

99891

39300

20363

81053

87126

68315

66018

99258

23050

51628

95686

65633

03927

49542

62015

76279

30667

47457

08370

55493

80297

42941

53954

89751

81720

75500

52079

18983

09517

54467

43840

05978

64461

88503

13868

38579

51074

06421

11489

91794

58253

16172

43289

36508

92507

19955

47069

69382

72355

41264

76842

44975

72445

60619

76206

78458

57261

20480

14159

77540

11049

93629

75978

09284

74560

35337

41350

19829

72905

81083

18417

09269

04931

02875

66460

78901

90850

56802

64686

00483

84721

02891

04851

28690

78929

55718

76640

34683

24470

72028

81587

94552

19714

14725

30418

50040

10905

21456

96274

21497

71360

84488

27826

38847

42635

00011

44324

87077

86266

36286

52016

02138

99081

33774

60456

86-051

92892

00108

80450

08016

34409

63265

03569

53389

94802

78443

14874

34622

01461

12809

75493

85249

68259

78254

04969

90573

80572

22936

75494

65843

54777

82846

07602

12542

13438

38729

51739

21464

23261

50418

88106

84632

13687

13245

91385

54043

49706

01643

92906

70078

94555

90339

44937

93688

03769

35063

29841

00717

55934

92701

55639

92813

52547

32590

50596

85757

17311

50801

05721

06699

59503

06371

57022

46540

51404

87963

87201

72295

93739

92461

86958

93697

84126

18507

15149

68452

10995

18637

63589

10291

34068

50072

01118

19281

78744

46676

26528

60506

84982

55870

85367

84104

62187

75449

71417

95366

24359

76252

95341

59073

91119

15355

25554

72685

71664

41397

85554

18196

80180

91959

07223

59851

13118

7,8283

55640

89046

36486

58435

91206

29737

73846

81192

03205

96028

75043

51927

06520

35374

13506

86271

17397

38235

89714

63479

99097

57960

64607

89019

08505

68026

46860

04838

47212

07890

53116

61106

64073

75536

37865

65796


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