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
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