You and your wife are making plans for retirement. You plan on living 25 years a
ID: 2730665 • Letter: Y
Question
You and your wife are making plans for retirement. You plan on living 25 years after you retire and would like to have $80,000 annually on which to live. Your first withdrawal will be made one year after you retire and you anticipate that your retirement account will earn 12% annually.
Find and show work for the following answers using a financial calculator:
a) What amount do you need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
____________________
b) Assume that your first withdrawal will be made the day you retire. Under this assumption, what amount do you now need in your retirement account the day you retire? Round your answer to the nearest cent. Do not round intermediate calculations.
_____________________
Explanation / Answer
Answer 1: When withdrawal is made after 1 year of retirement
Period
PVF
Annual Withdrawal
Present value of annual withdrawal
1
0.893
80000
71428.57143
2
0.797
80000
63775.5102
3
0.712
80000
56942.41983
4
0.636
80000
50841.44627
5
0.567
80000
45394.14846
6
0.507
80000
40530.48969
7
0.452
80000
36187.93723
8
0.404
80000
32310.65824
9
0.361
80000
28848.802
10
0.322
80000
25757.85893
11
0.287
80000
22998.08833
12
0.257
80000
20534.00744
13
0.229
80000
18333.93521
14
0.205
80000
16369.58501
15
0.183
80000
14615.7009
16
0.163
80000
13049.73295
17
0.146
80000
11651.54727
18
0.130
80000
10403.16721
19
0.116
80000
9288.542151
20
0.104
80000
8293.341206
21
0.093
80000
7404.768934
22
0.083
80000
6611.400834
23
0.074
80000
5903.036459
24
0.066
80000
5270.568267
25
0.059
80000
4705.864524
Amount required at the time of retirement
627451.129
Proof of Answer 1:
Principal amount at the time of retirement
Period
Interest rate
Interest on Principal Amount
Amount of Withdrawal
Balance Principal
627451.129
1
0.12
75294.13548
80000
622,745.26
2
0.12
74729.43173
80000
617,474.70
3
0.12
74096.96354
80000
611,571.66
4
0.12
73388.59917
80000
604,960.26
5
0.12
72595.23107
80000
597,555.49
6
0.12
71706.65879
80000
589,262.15
7
0.12
70711.45785
80000
579,973.61
8
0.12
69596.83279
80000
569,570.44
9
0.12
68348.45273
80000
557,918.89
10
0.12
66950.26705
80000
544,869.16
11
0.12
65384.2991
80000
530,253.46
12
0.12
63630.41499
80000
513,883.87
13
0.12
61666.06479
80000
495,549.94
14
0.12
59465.99256
80000
475,015.93
15
0.12
57001.91167
80000
452,017.84
16
0.12
54242.14107
80000
426,259.98
17
0.12
51151.198
80000
397,411.18
18
0.12
47689.34176
80000
365,100.52
19
0.12
43812.06277
80000
328,912.59
20
0.12
39469.51031
80000
288,382.10
21
0.12
34605.85154
80000
242,987.95
22
0.12
29158.55373
80000
192,146.50
23
0.12
23057.58017
80000
135,204.08
24
0.12
16224.4898
80000
71,428.57
25
0.12
8571.428571
80000
(0.00)
Answer 2: When withdrawal is made at the time of retirement
Period
PVF
Annual Withdrawal
Present value of annual withdrawal
0
1.000
80000
80000
1
0.893
80000
71428.57143
2
0.797
80000
63775.5102
3
0.712
80000
56942.41983
4
0.636
80000
50841.44627
5
0.567
80000
45394.14846
6
0.507
80000
40530.48969
7
0.452
80000
36187.93723
8
0.404
80000
32310.65824
9
0.361
80000
28848.802
10
0.322
80000
25757.85893
11
0.287
80000
22998.08833
12
0.257
80000
20534.00744
13
0.229
80000
18333.93521
14
0.205
80000
16369.58501
15
0.183
80000
14615.7009
16
0.163
80000
13049.73295
17
0.146
80000
11651.54727
18
0.130
80000
10403.16721
19
0.116
80000
9288.542151
20
0.104
80000
8293.341206
21
0.093
80000
7404.768934
22
0.083
80000
6611.400834
23
0.074
80000
5903.036459
24
0.066
80000
5270.568267
Amount required at the time of retirement
702745.2644
Proof of Answer 2:
Principal amount at the time of retirement
Period
Interest rate
Interest on Principal Amount
Amount of Withdrawal
Balance Principal
702745.2644
0
0.12
80000
622,745.26
1
0.12
74729.43173
80000
617,474.70
2
0.12
74096.96354
80000
611,571.66
3
0.12
73388.59917
80000
604,960.26
4
0.12
72595.23107
80000
597,555.49
5
0.12
71706.65879
80000
589,262.15
6
0.12
70711.45785
80000
579,973.61
7
0.12
69596.83279
80000
569,570.44
8
0.12
68348.45273
80000
557,918.89
9
0.12
66950.26705
80000
544,869.16
10
0.12
65384.2991
80000
530,253.46
11
0.12
63630.41499
80000
513,883.87
12
0.12
61666.06479
80000
495,549.94
13
0.12
59465.99256
80000
475,015.93
14
0.12
57001.91167
80000
452,017.84
15
0.12
54242.14107
80000
426,259.98
16
0.12
51151.198
80000
397,411.18
17
0.12
47689.34176
80000
365,100.52
18
0.12
43812.06277
80000
328,912.59
19
0.12
39469.51031
80000
288,382.10
20
0.12
34605.85154
80000
242,987.95
21
0.12
29158.55373
80000
192,146.50
22
0.12
23057.58017
80000
135,204.08
23
0.12
16224.4898
80000
71,428.57
24
0.12
8571.428571
80000
(0.00)
Period
PVF
Annual Withdrawal
Present value of annual withdrawal
1
0.893
80000
71428.57143
2
0.797
80000
63775.5102
3
0.712
80000
56942.41983
4
0.636
80000
50841.44627
5
0.567
80000
45394.14846
6
0.507
80000
40530.48969
7
0.452
80000
36187.93723
8
0.404
80000
32310.65824
9
0.361
80000
28848.802
10
0.322
80000
25757.85893
11
0.287
80000
22998.08833
12
0.257
80000
20534.00744
13
0.229
80000
18333.93521
14
0.205
80000
16369.58501
15
0.183
80000
14615.7009
16
0.163
80000
13049.73295
17
0.146
80000
11651.54727
18
0.130
80000
10403.16721
19
0.116
80000
9288.542151
20
0.104
80000
8293.341206
21
0.093
80000
7404.768934
22
0.083
80000
6611.400834
23
0.074
80000
5903.036459
24
0.066
80000
5270.568267
25
0.059
80000
4705.864524
Amount required at the time of retirement
627451.129
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