TABLE I The Present Value of $1 Due in n Periods*

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

12%

14%

15%

16%

18%

20%

1

.9901

.9804

.9709

.9615

.9524

.9434

.9346

.9259

.9174

.9091

.8929

.8772

.8696

.8621

.8475

.8333

2

.9803

.9612

.9426

.9246

.9070

.8900

.8734

.8573

.8417

.8264

.7972

.7695

.7561

.7432

.7182

.6944

3

.9706

.9423

.9151

.8890

.8638

.8396

.8163

.7938

.7722

.7513

.7118

.6750

.6575

.6407

.6086

.5787

4

.9610

.9238

.8885

.8548

.8227

.7921

.7629

.7350

.7084

.6830

.6355

.5921

.5718

.5523

.5158

.4823

5

.9515

.9057

.8626

.8219

.7835

.7473

.7130

.6806

.6499

.6209

.5674

.5194

.4972

.4761

.4371

.4019

6

.9420

.8880

.8375

.7903

.7462

.7050

.6663

.6302

.5963

.5645

.5066

.4556

.4323

.4104

.3704

.3349

7

.9327

.8706

.8131

.7599

.7107

.6651

.6227

.5835

.5470

.5132

.4523

.3996

.3759

.3538

.3139

.2791

8

.9235

.8535

.7894

.7307

.6768

.6274

.5820

.5403

.5019

.4665

.4039

.3506

.3269

.3050

.2660

.2326

9

.9143

.8368

.7664

.7026

.6446

.5919

.5439

.5002

.4604

.4241

.3606

.3075

.2843

.2630

.2255

.1938

10

.9053

.8203

.7441

.6756

.6139

.5584

.5083

.4632

.4224

.3855

.3220

.2697

.2472

.2267

.1911

.1615

11

.8963

.8043

.7224

.6496

.5847

.5268

.4751

.4289

.3875

.3503

.2875

.2366

.2149

.1954

.1619

.1346

12

.8874

.7885

.7014

.6246

.5568

.4970

.4440

.3971

.3555

.3186

.2567

.2076

.1869

.1685

.1372

.1122

13

.8787

.7730

.6810

.6006

.5303

.4688

.4150

.3677

.3262

.2897

.2292

.1821

.1625

.1452

.1163

.0935

14

.8700

.7579

.6611

.5775

.5051

.4423

.3878

.3405

.2992

.2633

.2046

.1597

.1413

.1252

.0985

.0779

15

.8613

.7430

.6419

.5553

.4810

.4173

.3624

.3152

.2745

.2394

.1827

.1401

.1229

.1079

.0835

.0649

16

.8528

.7284

.6232

.5339

.4581

.3936

.3387

.2919

.2519

.2176

.1631

.1229

.1069

.0930

.0708

.0541

17

.8444

.7142

.6050

.5134

.4363

.3714

.3166

.2703

.2311

.1978

.1456

.1078

.0929

.0802

.0600

.0451

18

.8360

.7002

.5874

.4936

.4155

.3503

.2959

.2502

.2120

.1799

.1300

.0946

.0808

.0691

.0508

.0376

19

.8277

.6864

.5703

.4746

.3957

.3305

.2765

.2317

.1945

.1635

.1161

.0829

.0703

.0596

.0431

.0313

20

.8195

.6730

.5537

.4564

.3769

.3118

.2584

.2145

.1784

.1486

.1037

.0728

.0611

.0514

.0365

.0261

25

.7798

.6095

.4476

.3751

.2953

.2330

.1842

.1460

.1160

.0923

.0588

.0378

.0304

.0245

.0160

.0105

30

.7419

.5521

.4120

.3083

.2314

.1741

.1314

.0994

.0754

.0573

.0334

.0196

.0151

.0116

.0070

.0042

40

.6717

.4529

.3066

.2083

.1420

.0972

.0668

.0460

.0318

.0221

.0107

.0053

.0037

.0026

.0013

.0007

50

.6080

.3715

.2281

.1407

.0872

.0543

.0339

.0213

.0134

.0085

.0035

.0014

.0009

.0006

.0003

.0001

60

.5504

.3048

.1697

.0951

.0535

.0303

.0173

.0099

.0057

.0033

.0011

.0004

.0002

.0001

*The formula used to derive the values in this table was PV = F1/(1 + i)n where PV = present value, F = future amount to be discounted, i = interest rate, and n = number of periods.

The value of 0 to four decimal places.

TABLE II The Present Value of an Annuity of $1 per Number of Payments*

Number of Payments

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

12%

14%

15%

16%

18%

20%

1

0.9901

0.9804

0.9709

0.9615

0.9524

0.9434

0.9346

0.9259

0.9174

0.9091

0.8929

0.8772

0.8596

0.8621

0.8475

0.8333

2

1.9704

1.9416

1.9135

1.8861

1.8594

1.8334

1.8080

1.7833

1.7591

1.7355

1.6901

1.6467

1.6257

1.6052

1.5656

1.5278

3

2.9410

2.8839

2.8286

2.7751

2.7232

2.6730

2.6243

2.5771

2.5313

2.4869

2.4018

2.3216

2.2832

2.2459

2.1743

2.1065

4

3.9820

3.8077

3.7171

3.6299

3.5460

3.4651

3.3872

3.3121

3.2397

3.1699

3.0373

2.9137

2.8550

2.7982

2.6901

2.5887

5

4.8884

4.7135

4.5797

4.4518

4.3295

4.2124

4.1002

3.9927

3.8897

3.7908

3.6048

3.4331

3.3522

3.2743

3.1272

2.9906

6

5.7985

5.6014

5.4172

5.2421

5.0757

4.9173

4.7665

4.6229

4.4859

4.3553

4.1114

3.8887

3.7845

3.6847

3.4976

3.3255

7

6.7282

6.4720

6.2303

6.0021

5.7864

5.5824

5.3893

5.2064

5.0330

4.8684

4.5638

4.2883

4.1604

4.0386

3.8115

3.6046

8

7.6517

7.3255

7.0197

6.7327

6.4632

6.2098

5.9713

5.7466

5.5348

5.3349

4.9676

4.6389

4.4873

4.3436

4.0776

3.8372

9

8.5660

8.1622

7.7861

7.4353

7.1078

6.8017

6.5152

6.2469

5.9952

5.7590

5.3282

4.9464

4.7716

4.6065

4.3030

4.0310

10

9.4713

8.9826

8.5302

8.1109

7.7217

7.3601

7.0236

6.7101

6.4177

6.1446

5.6502

5.2161

5.0188

4.8332

4.4941

4.1925

11

10.3676

9.7868

9.2526

8.7605

8.3064

7.8869

7.4987

7.1390

6.8052

6.4951

5.9377

5.4527

5.2337

5.0286

4.6560

4.3271

12

11.2551

10.5733

9.9540

9.3851

8.8633

8.3838

7.9427

7.5361

7.1607

6.8137

6.1944

5.6603

5.4206

5.1971

4.7932

4.4392

13

12.1337

11.3484

10.6350

9.9856

9.3936

8.8527

8.3577

7.9038

7.4869

7.1034

6.4235

5.8424

5.5831

5.3423

4.9095

4.5327

14

13.0037

12.1062

11.2961

10.5631

9.8986

9.2950

8.7455

8.2442

7.7862

7.3667

6.6282

6.0021

5.7245

5.4675

5.0081

4.6106

15

13.8651

12.8493

11.9379

11.1184

10.3797

9.7122

9.1079

8.5595

8.0607

7.6061

6.8109

6.1422

5.8474

5.5755

5.0916

4.6755

16

14.7179

13.5777

12.5611

11.6523

10.8378

10.1059

9.4466

8.8514

8.3126

7.8237

6.9740

6.2651

5.9542

5.6685

5.1624

4.7296

17

15.5623

14.2919

13.1661

12.1657

11.2741

10.4773

9.7632

9.1216

8.5436

8.0216

7.1196

6.3729

6.0472

5.7487

5.2223

4.7746

18

16.3983

14.9920

13.7535

12.6593

11.6896

10.8276

10.0591

9.3719

8.7556

8.2014

7.2497

6.4674

6.1280

5.8178

5.2732

4.8122

19

17.2260

15.6785

14.3238

13.1339

12.0853

11.1581

10.3356

9.6036

8.9501

8.3649

7.3658

6.5504

6.1982

5.8775

5.3162

4.8435

20

18.0456

16.3514

14.8775

13.5903

12.4622

11.4699

10.5940

9.8181

9.1285

8.5136

7.4694

6.6231

6.2593

5.9288

5.3527

4.8696

25

22.0232

19.5235

17.4131

15.6221

14.0939

12.7834

11.6536

10.6748

9.8226

9.0770

7.8431

6.8729

6.4641

6.0971

5.4669

4.9476

30

25.8077

22.3965

19.6004

17.2920

15.3725

13.7648

12.4090

11.2578

10.2737

9.4269

8.0552

7.0027

6.5660

6.1772

5.5168

4.9789

40

32.8347

27.3555

23.1148

19.7928

17.1591

15.0463

13.3317

11.9246

10.7574

9.7791

8.2438

7.1050

6.6418

6.2335

5.5482

4.9966

50

39.1961

31.4236

25.7298

21.4822

18.2559

15.7619

13.8007

12.2335

10.9617

9.9148

8.3045

7.1327

6.6605

6.2463

5.5641

4.9995

60

44.9550

34.7609

27.6756

22.6235

18.9293

16.1614

14.0392

12.3766

11.0480

9.9672

8.3240

7.1401

6.6651

6.2482

5.5553

4.9999

*The formula used to derive the values in this table was PV = F(1 - 1/(1 + i)n/i) where PV = present value, F = periodic payment to be discounted, i = interest rate, and n = number of payments.

TABLE III Amount of $1 Due in n Periods

Period

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

12%

14%

15%

16%

18%

20%

1

1.0100

1.0200

1.0300

1.0400

1.0500

1.0600

1.0700

1.0800

1.0900

1.1000

1.1200

1.1400

1.1500

1.1600

1.1800

1.2000

2

1.0201

1.0404

1.0609

1.0816

1.1025

1.1236

1.1449

1.1664

1.1881

1.2100

1.2544

1.2996

1.3225

1.3456

1.3924

1.4400

3

1.0303

1.0612

1.0927

1.1249

1.1576

1.1910

1.2250

1.2597

1.2950

1.3310

1.4049

1.4815

1.5209

1.5609

1.6430

1.7280

4

1.0406

1.0824

1.1255

1.1699

1.2155

1.2625

1.3108

1.3605

1.4116

1.4641

1.5735

1.6890

1.7490

1.8106

1.9388

2.0736

5

1.0510

1.1041

1.1593

1.2167

1.2763

1.3382

1.4026

1.4693

1.5386

1.6105

1.7623

1.9254

2.0114

2.1003

2.2878

2.4883

6

1.0615

1.1262

1.1941

1.2653

1.3401

1.4185

1.5007

1.5869

1.6771

1.7716

1.9738

2.1950

2.3131

2.4364

2.6996

2.9860

7

1.0721

1.1487

1.2299

1.3159

1.4071

1.5036

1.6058

1.7138

1.8280

1.9487

2.2107

2.5023

2.6600

2.8262

3.1855

3.5832

8

1.0829

1.1717

1.2668

1.3686

1.4775

1.5938

1.7182

1.8509

1.9926

2.1436

2.4760

2.8526

3.0590

3.2784

3.7589

4.2998

9

1.0937

1.1951

1.3048

1.4233

1.5513

1.6895

1.8385

1.9990

2.1719

2.3579

2.7731

3.2519

3.5179

3.8030

4.4355

5.1598

10

1.1046

1.2190

1.3439

1.4802

1.6289

1.7908

1.9672

2.1589

2.3674

2.5937

3.1058

3.7072

4.0456

4.4114

5.2338

6.1917

11

1.1157

1.2434

1.3842

1.5395

1.7103

1.8983

2.1049

2.3316

2.5804

2.8531

3.4785

4.2262

4.6524

5.1173

6.1759

7.4031

12

1.1268

1.2682

1.4258

1.6010

1.7959

2.0122

2.2522

2.5182

2.8127

3.1384

3.8960

4.8179

5.3502

5.9360

7.2876

8.9161

13

1.1381

1.2936

1.4685

1.6651

1.8856

2.1329

2.4098

2.7196

3.0658

3.4523

4.3635

5.4924

6.1528

6.8858

8.5994

10.699

14

1.1495

1.3195

1.5126

1.7317

1.9799

2.2609

2.5785

2.9372

3.3417

3.7975

4.8871

6.2613

7.0757

7.9875

10.147

12.839

15

1.1610

1.3459

1.5580

1.8009

2.0789

2.3966

2.7590

3.1722

3.6425

4.1772

5.4736

7.1379

8.1371

9.2655

11.973

15.407

16

1.1726

1.3728

1.6047

1.8730

2.1829

2.5404

2.9522

3.4259

3.9703

4.5950

6.1304

8.1372

9.3576

10.748

14.129

18.488

17

1.1843

1.4002

1.6528

1.9479

2.2920

2.6928

3.1588

3.7000

4.3276

5.0545

6.8660

9.2765

10.761

12.467

16.672

22.186

18

1.1961

1.4282

1.7024

2.0258

2.4066

2.8543

3.3799

3.9960

4.7171

5.5599

7.6900

10.575

12.375

14.462

19.673

26.623

19

1.2081

1.4568

1.7535

2.1068

2.5270

3.0256

3.6165

4.3157

5.1417

6.1159

8.6128

12.055

14.231

16.776

23.214

31.948

20

1.2202

1.4859

1.8061

2.1911

2.6533

3.2071

3.8697

4.6610

5.6044

6.7275

9.6463

13.743

16.366

19.460

27.393

38.337

30

1.3478

1.8114

2.4273

3.2434

4.3219

5.7435

7.6123

10.062

13.267

17.449

29.959

50.950

66.211

85.849

143.37

237.37

40

1.4889

2.2080

3.2620

4.8010

7.0400

10.285

14.974

21.724

31.409

45.259

93.050

188.88

267.86

378.72

750.37

1469.7

50

1.6446

2.6916

4.3839

7.1067

11.467

18.420

29.457

46.901

74.357

117.39

289.00

700.23

1083.6

1670.7

3927.3

9100.4

60

1.8167

3.2810

5.8916

10.519

18.679

32.987

57.946

101.25

176.03

304.48

897.59

2595.9

4383.9

7370.1

20555.

56347.

TABLE IV Amount of an Annuity of $1 per Number of Payments

Number of Payments

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

12%

14%

15%

16%

18%

20%

1

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

1.0000

2

2.0100

2.0200

2.0300

2.0400

2.0500

2.0600

2.0700

2.0800

2.0900

2.1000

2.1200

2.1400

2.1500

2.1600

2.1800

2.2000

3

3.0301

3.0604

3.0909

3.1216

3.1525

3.1836

3.2149

3.2464

3.2781

3.3100

3.3744

3.4396

3.4725

3.5056

3.5724

3.6400

4

4.0604

4.1216

4.1836

4.2465

4.3101

4.3746

4.4399

4.5061

4.5731

4.6410

4.7793

4.9211

4.9934

5.0665

5.2154

5.3680

5

5.1010

5.2040

5.3091

5.4163

5.5256

5.6371

5.7507

5.8666

5.9847

6.1051

6.3528

6.6101

6.7424

6.8771

7.1542

7.4416

6

6.1520

6.3081

6.4684

6.6330

6.8019

6.9753

7.1533

7.3359

7.5233

7.7156

8.1152

8.5355

8.7537

8.9775

9.4420

9.9299

7

7.2135

7.4343

7.6625

7.8983

8.1420

8.3938

8.6540

8.9228

9.2004

9.4872

10.8090

10.7305

11.0668

11.4139

12.1415

12.9159

8

8.2857

8.5830

8.8923

9.2142

9.5491

9.8975

10.2598

10.6366

11.0285

11.4359

12.2997

13.2328

13.7268

14.2401

15.3270

16.4991

9

9.3685

9.7546

10.1591

10.5828

11.0266

11.4913

11.9780

12.4876

13.0210

13.5795

14.7757

16.0853

16.7858

17.5185

19.0859

20.7989

10

10.4622

10.9497

11.4639

12.0061

12.5779

13.1808

13.8164

14.4866

15.1929

15.9374

17.5487

19.3373

20.3037

21.3215

23.5213

25.9587

11

11.5668

12.1687

12.8078

13.4864

14.2068

14.9716

15.7836

16.6455

17.5603

18.5312

20.6546

23.0445

24.3493

25.7329

28.7551

32.1504

12

12.6825

13.4121

14.1920

15.0258

15.9171

16.8699

17.8885

18.9771

20.1407

21.2843

24.1331

27.2707

29.0017

30.8502

34.9311

39.5805

13

13.8093

14.6803

15.6178

16.6268

17.7130

18.8821

20.1406

21.4953

22.9534

24.5227

28.0291

32.0887

34.3519

36.7862

42.2187

48.4966

14

14.9474

15.9739

17.0863

18.2919

19.5986

21.0151

22.5505

24.2149

26.0192

27.9750

32.3926

37.5811

40.5047

43.6720

50.8180

59.1959

15

16.0969

17.2934

18.5989

20.0236

21.5786

23.2760

25.1290

27.1521

29.3609

31.7725

37.2797

43.8424

47.5804

51.6595

60.9653

72.0351

16

17.2579

18.6393

20.1569

21.8248

23.6575

25.6725

27.8881

30.3243

33.0034

35.9497

42.7535

50.9804

55.7178

60.9250

72.9390

87.4421

17

18.4304

20.0121

21.7616

23.6975

25.8404

28.2129

30.8402

33.7502

36.9737

40.5447

48.8837

59.1176

65.0751

71.6730

87.0680

105.9306

18

19.6147

21.4123

23.4144

25.6454

28.1324

30.9057

33.9990

37.4502

41.3013

45.5992

55.7497

68.3941

75.8364

84.1407

103.7403

128.1167

19

20.8190

22.8406

25.1169

27.6712

30.5390

33.7600

37.3790

41.4463

46.0185

51.1591

63.4397

78.9692

88.2118

98.6032

123.4135

154.7400

20

22.0190

24.2974

26.8704

29.7781

33.0660

36.7856

40.9955

45.7620

51.1601

57.2750

72.0524

91.0249

102.4436

115.3797

146.6280

186.6880

30

34.7849

40.5681

47.5754

56.0849

66.4388

79.0582

94.4608

113.2832

136.3075

164.4940

241.3327

356.7868

434.7451

530.3117

790.9480

1181.8816

40

48.8864

60.4020

75.4013

95.0255

120.7998

154.7620

199.6351

259.0565

337.8824

442.5926

767.0914

1342.0251

1779.0903

2360.7572

4163.2130

7343.8578

50

64.4632

84.5794

112.7969

152.6671

209.3480

290.3359

406.5289

573.7702

815.0836

1163.9085

2400.0182

4994.5213

7217.7163

10435.6488

21813.0937

45497.1908

60

81.6697

114.0515

163.0534

237.9907

353.5837

533.1282

813.5204

1253.2133

1944.7921

3034.8164

7471.6411

18535.1333

29219.9916

46057.5085

114189.6665

281732.5718