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Karen, age 27 saves 5% of her annual income of $55,000 at the end of every year

ID: 2730530 • Letter: K

Question

Karen, age 27 saves 5% of her annual income of $55,000 at the end of every year for her retirement. The current balance in her retirement accounts $70,000. She expects to retire at age 67 with a wage replacement ratio of 80%. She will need income at the beginning of each year during the post retirement period. How long her retirement fund is expected to last if expected return and inflation are 7% and 2% respectively? Assume that her salary is going to increase with inflation till retirement.

How wouldn't solve

Selected Answer: 34 years Answers: 15 years 19 years 34 years 9 years

Explanation / Answer

Present Salary

Period

Present value of Increased salary

Salary after adjustment of inflation rate

Present value of saving each year

FV Factor

Future value

55000

0

70000

14.97445784

1048212.049

0

2750

14.97445784

41179.75906

1

1100

56100

2805

13.99482041

39255.47125

2

1122

57222

2861.1

13.07927141

37421.10344

3

1144.44

58366.44

2918.322

12.22361814

35672.45374

4

1167.3288

59533.7688

2976.68844

11.42394219

34005.51665

5

1190.675376

60724.44418

3036.222209

10.67658148

32416.47382

6

1214.488884

61938.93306

3096.946653

9.978113537

30901.68532

7

1238.778661

63177.71172

3158.885586

9.325339754

29457.68133

8

1263.554234

64441.26596

3222.063298

8.715270798

28081.15417

9

1288.825319

65730.09127

3286.504564

8.145112896

26768.9507

10

1314.601825

67044.6931

3352.234655

7.612255043

25518.06516

11

1340.893862

68385.58696

3419.279348

7.114257049

24325.63221

12

1367.711739

69753.2987

3487.664935

6.648838364

23188.92042

13

1395.065974

71148.36467

3557.418234

6.21386763

22105.32601

14

1422.967293

72571.33197

3628.566598

5.807352925

21072.36685

15

1451.426639

74022.75861

3701.13793

5.42743264

20087.67681

16

1480.455172

75503.21378

3775.160689

5.072366953

19149.00032

17

1510.064276

77013.27806

3850.663903

4.740529863

18254.18722

18

1540.265561

78553.54362

3927.677181

4.430401741

17401.18782

19

1571.070872

80124.61449

4006.230724

4.140562375

16588.0482

20

1602.49229

81727.10678

4086.355339

3.869684462

15812.90576

21

1634.542136

83361.64891

4168.082446

3.616527535

15073.98493

22

1667.232978

85028.88189

4251.444095

3.379932276

14369.59311

23

1700.577638

86729.45953

4336.472977

3.158815211

13698.1168

24

1734.589191

88464.04872

4423.202436

2.952163749

13058.01788

25

1769.280974

90233.3297

4511.666485

2.759031541

12447.83013

26

1804.666594

92037.99629

4601.899814

2.57853415

11866.15583

27

1840.759926

93878.75622

4693.937811

2.409845

11311.66256

28

1877.575124

95756.33134

4787.816567

2.252191589

10783.0802

29

1915.126627

97671.45797

4883.572898

2.104851952

10279.19795

30

1953.429159

99624.88713

4981.244356

1.967151357

9798.861596

31

1992.497743

101617.3849

5080.869243

1.838459212

9340.970868

32

2032.347697

103649.7326

5182.486628

1.71818618

8904.476902

33

2072.994651

105722.7272

5286.136361

1.605781476

8488.37985

34

2114.454544

107837.1818

5391.859088

1.500730352

8091.726586

35

2156.743635

109993.9254

5499.69627

1.402551731

7713.608522

36

2199.878508

112193.8039

5609.690195

1.31079601

7353.159525

37

2243.876078

114437.68

5721.883999

1.225043

7009.55394

38

2288.7536

116726.4336

5836.321679

1.1449

6682.00469

39

2334.528672

119060.9623

5953.048113

1.07

6369.761481

40

2381.219245

121442.1815

6072.109075

1

6072.109075

169427.5628

1805587.867

Wage replacement ration(80%)

97153.7452

No. of years her retirement funds will last (FV of savings/wage replacement rate)

18.58485089

Answer is 19 years

Present Salary

Period

Present value of Increased salary

Salary after adjustment of inflation rate

Present value of saving each year

FV Factor

Future value

55000

0

70000

14.97445784

1048212.049

0

2750

14.97445784

41179.75906

1

1100

56100

2805

13.99482041

39255.47125

2

1122

57222

2861.1

13.07927141

37421.10344

3

1144.44

58366.44

2918.322

12.22361814

35672.45374

4

1167.3288

59533.7688

2976.68844

11.42394219

34005.51665

5

1190.675376

60724.44418

3036.222209

10.67658148

32416.47382

6

1214.488884

61938.93306

3096.946653

9.978113537

30901.68532

7

1238.778661

63177.71172

3158.885586

9.325339754

29457.68133

8

1263.554234

64441.26596

3222.063298

8.715270798

28081.15417

9

1288.825319

65730.09127

3286.504564

8.145112896

26768.9507

10

1314.601825

67044.6931

3352.234655

7.612255043

25518.06516

11

1340.893862

68385.58696

3419.279348

7.114257049

24325.63221

12

1367.711739

69753.2987

3487.664935

6.648838364

23188.92042

13

1395.065974

71148.36467

3557.418234

6.21386763

22105.32601

14

1422.967293

72571.33197

3628.566598

5.807352925

21072.36685

15

1451.426639

74022.75861

3701.13793

5.42743264

20087.67681

16

1480.455172

75503.21378

3775.160689

5.072366953

19149.00032

17

1510.064276

77013.27806

3850.663903

4.740529863

18254.18722

18

1540.265561

78553.54362

3927.677181

4.430401741

17401.18782

19

1571.070872

80124.61449

4006.230724

4.140562375

16588.0482

20

1602.49229

81727.10678

4086.355339

3.869684462

15812.90576

21

1634.542136

83361.64891

4168.082446

3.616527535

15073.98493

22

1667.232978

85028.88189

4251.444095

3.379932276

14369.59311

23

1700.577638

86729.45953

4336.472977

3.158815211

13698.1168

24

1734.589191

88464.04872

4423.202436

2.952163749

13058.01788

25

1769.280974

90233.3297

4511.666485

2.759031541

12447.83013

26

1804.666594

92037.99629

4601.899814

2.57853415

11866.15583

27

1840.759926

93878.75622

4693.937811

2.409845

11311.66256

28

1877.575124

95756.33134

4787.816567

2.252191589

10783.0802

29

1915.126627

97671.45797

4883.572898

2.104851952

10279.19795

30

1953.429159

99624.88713

4981.244356

1.967151357

9798.861596

31

1992.497743

101617.3849

5080.869243

1.838459212

9340.970868

32

2032.347697

103649.7326

5182.486628

1.71818618

8904.476902

33

2072.994651

105722.7272

5286.136361

1.605781476

8488.37985

34

2114.454544

107837.1818

5391.859088

1.500730352

8091.726586

35

2156.743635

109993.9254

5499.69627

1.402551731

7713.608522

36

2199.878508

112193.8039

5609.690195

1.31079601

7353.159525

37

2243.876078

114437.68

5721.883999

1.225043

7009.55394

38

2288.7536

116726.4336

5836.321679

1.1449

6682.00469

39

2334.528672

119060.9623

5953.048113

1.07

6369.761481

40

2381.219245

121442.1815

6072.109075

1

6072.109075

169427.5628

1805587.867

Wage replacement ration(80%)

97153.7452

No. of years her retirement funds will last (FV of savings/wage replacement rate)

18.58485089