Grady Zebrowski, age 25, just graduated from college, accepted his first job wit
ID: 2800014 • Letter: G
Question
Grady Zebrowski, age 25, just graduated from college, accepted his first job with a $47,000 salary, and is already looking forward to retirement in 40 years. He assumes a 2.9 percent inflation rate and plans to live in retirement for 20 years. He does not want to plan on any Social Security benefits. Assume Grady can earn a 6 percent rate of return on his investments prior to retirement and a 7 percent rate of return on his investments post-retirement to answer the following questions using your financial calculator.
a. Grady wants to replace 90 percent of his current net income. What is his annual need in today's
dollars?
b. Using the table Grady thinks he might have an average tax rate of 13 percent at retirement if he is married. Adjusting for taxes, how much does Grady really need per year, in today's dollars?
c. Adjusting for inflation, how much does Grady need per year in future dollars when he begins retirement in 40 years?
d. If he needs this amount for 20 years, how much does he need in total for retirement? (Hint: Use the inflation-adjusted rate of return.)
e. How much does Grady need to save per month to reach his retirement goal assuming he does not receive any employer match on his retirement savings?
Table 16.2 The Average Tax Rate
Average Tax Rate
Retirement Income
Couples Filling Jointly
Individuals
20,000
7%
10%
30,000
10
14
40,000
12
17
50,000
14
20
60,000
17
22
70,000
19
23
80,000
21
24
90,000
22
25
100,000
23
26
150,000
28
30
Compound Sum of $1 (FVIF)
n
5%
6%
7%
8%
9%
10%
11%
12%
24
3.2251
4.0489
5.0724
6.3412
7.9111
9.8497
12.2392
15.1786
25
3.3864
4.2919
5.4274
6.8485
8.6231
10.8347
13.5855
17.0001
26
3.5557
4.5494
5.8074
7.3964
9.3992
11.9182
15.0799
19.0401
27
3.7335
4.8223
6.2139
7.9881
10.2451
13.1100
16.7386
21.3249
28
3.9201
5.1117
6.6488
8.6271
11.1671
14.4210
18.5799
23.8839
29
4.1161
5.4184
7.1143
9.3173
12.1722
15.8631
20.6237
26.7499
30
4.3219
5.7435
7.6123
10.0627
13.2677
17.4494
22.8923
29.9599
31
4.5380
6.0881
8.1451
10.8677
14.4618
19.1943
25.4104
33.5551
32
4.7649
6.4534
8.7153
11.7371
15.7633
21.1138
28.2056
37.5817
33
5.0032
6.8406
9.3253
12.676
17.182
23.2252
31.3082
42.0915
34
5.2533
7.2510
9.9781
13.6901
18.7284
25.5477
34.7521
47.1425
35
5.5160
7.6861
10.6766
14.7853
20.4140
28.1024
38.5749
52.7996
Present Value of an Annuity (PVIFA)
n
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
15
13.8651
12.8493
11.9379
11.1184
10.3797
9.7122
9.1079
8.5595
8.0607
7.6061
16
14.7179
13.5777
12.5611
11.6523
10.8378
10.1059
9.4466
8.8514
8.3126
7.8237
17
15.5623
14.2919
13.1661
12.1657
11.2741
10.4773
9.7632
9.1216
8.5436
8.0216
18
16.3983
14.9920
13.7535
12.6593
11.6896
10.8276
10.0591
9.3719
8.7556
8.2014
19
17.2260
15.6785
14.3238
13.1339
12.0853
11.1581
10.3356
9.6036
8.9501
8.3649
20
18.0456
16.3514
14.8775
13.5903
12.4622
11.4699
10.5940
9.8181
9.1285
8.5136
21
18.8570
17.0112
15.4150
14.0292
12.8212
11.7641
10.8355
10.0168
9.2922
8.6487
22
19.6604
17.6580
15.9369
14.4511
13.1630
12.0416
11.0612
10.2007
9.4424
8.7715
23
20.4558
18.2922
16.4436
14.8568
13.4886
12.3034
11.2722
10.3711
9.5802
8.8832
24
21.2434
18.9139
16.9355
15.2470
13.7986
12.5504
11.4693
10.5288
9.7066
8.9847
25
22.0232
19.5235
17.4131
15.6221
14.0939
12.7834
11.6536
10.6748
9.8226
9.0770
26
22.7952
20.1210
17.8768
15.9828
14.3752
13.0032
11.8258
10.8100
9.9290
9.1609
27
23.5596
20.7069
18.3270
16.3296
14.6430
13.2105
11.9867
10.9352
10.0266
9.2372
28
24.3164
21.2813
18.7641
16.6631
14.8981
13.4062
12.1371
11.0511
10.1161
9.3066
29
25.0658
21.8444
19.1885
16.9837
15.1411
13.5907
12.2777
11.1584
10.1983
9.3696
30
25.8077
22.3965
19.6004
17.2920
15.3725
13.7648
12.4090
11.2578
10.2737
9.4269
Future Value of an Annuity (FVIFA)
n
6%
7%
8%
9%
10%
11%
12%
13%
24
50.8156
58.1767
66.7648
76.7898
88.4973
102.174
118.1552
136.8315
25
54.8645
63.2490
73.1059
84.7009
98.3471
114.413
133.3339
155.6196
26
59.1564
68.6765
79.9544
93.3240
109.1818
127.999
150.3339
176.8501
27
63.7058
74.4838
87.3508
102.7231
121.0999
143.079
169.3740
200.8406
28
68.5281
80.6977
95.3388
112.9682
134.2099
159.817
190.6989
227.9499
29
73.6398
87.3465
103.9659
124.1354
148.6309
178.397
214.5828
258.5834
30
79.0582
94.4608
113.2832
136.3075
164.4940
199.021
241.3327
293.1992
31
84.8017
102.0730
123.3459
149.5752
181.9434
221.913
271.2926
332.3151
32
90.8898
110.2182
134.2135
164.0370
201.1378
247.324
304.8477
376.5161
33
97.3432
118.9334
145.9506
179.8003
222.2515
275.529
342.4294
426.4632
34
104.1838
128.2588
158.6267
196.9823
245.4767
306.837
384.5210
482.9034
35
111.4348
138.2369
172.3168
215.7108
271.0244
341.59
431.6635
546.6808
Table 16.2 The Average Tax Rate
Average Tax Rate
Retirement Income
Couples Filling Jointly
Individuals
20,000
7%
10%
30,000
10
14
40,000
12
17
50,000
14
20
60,000
17
22
70,000
19
23
80,000
21
24
90,000
22
25
100,000
23
26
150,000
28
30
Explanation / Answer
a. Grady wants to replace 90 percent of his current net income. What is his annual need in today's dollars?
Annual need = Salary *90% = $47000*90% = $42,300
b. Using the table Grady thinks he might have an average tax rate of 13 percent at retirement if he is married. Adjusting for taxes, how much does Grady really need per year, in today's dollars?
Annual requirement = annual need/ (1-tax rate) = $42,300/(1-0.13) = $48,620.68
c. Adjusting for inflation, how much does Grady need per year in future dollars when he begins retirement in 40 years?
Annual requirement= annual need after taxes*(1+Inflation rate)n = $48,620.68*(1+0.029)40
Annual requirement= $48,620.68*3.13772= $152,558.36
therefore, Grady would need $152,558.36 per year in future dollars when he begins retirement in 40 years.
d. If he needs this amount for 20 years, how much does he need in total for retirement? (Hint: Use the inflation-adjusted rate of return.)
The inflation adjusted rate of return = rate of return- Inflation = 6%-2.9%= 3.1%
From the table PVIFA of 3.1% for 20 years can be seen which is 14.7409
Total requirement = Annual need * PVIFA factor = $152,558.36*14.7409 = $2,248,847.53
e. How much does Grady need to save per month to reach his retirement goal assuming he does not receive any employer match on his retirement savings?
Annual saving = total requirement*FVIFA factor = $2,248,847.53/154.7620 = $14,531
Hence Grady should save $14,531 annualy to meet his retirement goal.
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