Peter and Blair recently reviewed their future retirement income and expense pro

Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 3535 years and anticipate they will need funding for an additional 2525 years. They determined that they would have a retirement income of $56,000 in today's dollars, but they would actually need

$77,040 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 33 percent inflation rate and a return of 11 percent.

Question - The total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 33 percent inflation rate and a return of 11 percent is $___________ (Round to the nearest cent.)

Compound Sum of $1 (FVIF)

n

2.00%

3.00%

4.00%

5.00%

24

1.6084

2.0328

2.5633

3.2251

252

1.6406

2.0938

2.6658

3.3864

26

1.6734

2.1566

2.7725

3.5557

27

1.7069

2.2213

2.8834

3.7335

28

‘1.7410

2.2879

2.9987

3.9201

29

1.7758

2.3566

3.1187

4.1161

30

1.8114

2.4273

3.2434

4.3219

31

1.8476

2.5001

3.3731

‘4.5380

32

1.8845

2.5751

3.5081

4.7649

33

1.9222

2.6523

3.6484

5.0032

34

1.9607

2.7319

3.7943

5.2533

35

1.9999

2.8139

3.9461

‘5.5160

Present Value of an Annuity (PVIFA)

n

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

13

11.3484

‘10.6350

9.9856

9.3936

8.8527

8.3577

7.9038

7.4869

7.1034

14

12.1062

11.2961

10.5631

9.8986

‘9.2950

8.7455

8.2442

7.7862

7.3667

15

12.8493

11.9379

11.1184

10.3797

9.7122

9.1079

8.5595

8.0607

7.6061

16

13.5777

12.5611

11.6523

10.8378

10.1059

9.4466

8.8514

8.3126

7.8237

17

14.2919

13.1661

12.1657

11.2741

10.4773

9.7632

9.1216

8.5436

8.0216

18

‘14.9920

13.7535

12.6593

11.6896

10.8276

10.0591

9.3719

8.7556

8.2014

19

15.6785

14.3238

13.1339

12.0853

11.1581

10.3356

9.6036

8.9501

8.3649

20

16.3514

14.8775

13.5903

12.4622

11.4699

10.5940

9.8181

9.1285

8.5136

21

17.0112

‘15.4150

14.0292

12.8212

11.7641

10.8355

10.0168

9.2922

8.6487

22

17.6580

15.9369

14.4511

‘13.1630

12.0416

11.0612

10.2007

9.4424

8.7715

23

18.2922

16.4436

14.8568

13.4886

12.3034

11.2722

10.3711

9.5802

8.8832

24

18.9139

16.9355

‘15.2470

13.7986

12.5504

11.4693

10.5288

9.7066

8.9847

25

19.5235

17.4131

15.6221

14.0939

12.7834

11.6536

10.6748

9.8226

‘9.0770

26

'20.1210

17.8768

15.9828

14.3752

13.0032

11.8258

‘10.8100

‘9.9290

9.1609

27

20.7069

‘18.3270

16.3296

‘14.6430

13.2105

11.9867

10.9352

10.0266

9.2372

Compound Sum of $1 (FVIF)

n

2.00%

3.00%

4.00%

5.00%

24

1.6084

2.0328

2.5633

3.2251

252

1.6406

2.0938

2.6658

3.3864

26

1.6734

2.1566

2.7725

3.5557

27

1.7069

2.2213

2.8834

3.7335

28

‘1.7410

2.2879

2.9987

3.9201

29

1.7758

2.3566

3.1187

4.1161

30

1.8114

2.4273

3.2434

4.3219

31

1.8476

2.5001

3.3731

‘4.5380

32

1.8845

2.5751

3.5081

4.7649

33

1.9222

2.6523

3.6484

5.0032

34

1.9607

2.7319

3.7943

5.2533

35

1.9999

2.8139

3.9461

‘5.5160

Explanation / Answer

Short fall = 77040 - 56000 = 21040

Value of short fall after 35 years at 3% inflation

FV = 21040*2.8139= 59204.46

Real return = (1+11%)/(1+3%) - 1 = 7.77%

After retirment for 25 years

PV = 59204.46*(1-(1+7.77%)-25)/7.77%

   = 644779.04 after 35 years

Annual payments

PMT = (644779.04*11%) / ((1+11%)35 - 1) = 1887.58 every year

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