You’re planning for retirement, which you want to do in 30 years. By that time,
ID: 2654652 • Letter: Y
Question
You’re planning for retirement, which you want to do in 30 years. By that time, you expect to need $3000 per month, for 20 years. You find a long-term retirement account promising a fixed 7.8% APR compounded monthly, both during the saving period, and after beginning withdrawals. (You can’t begin withdrawing money from it prior to 30 years without penalty.)
A. To have enough to fund your withdrawals, how much will you have need to save by then?
B. In order to accumulate enough to retire, you begin monthly deposits into the account now. How much will you need to set aside each month to reach your retirement goal?
C. How much interest will have been earned overall, after the last withdrawal is made?
D. Assuming the same annual rate of inflation of 2.45% over the next 30 years, how much would that $3000 be worth in today’s money (i.e. what would the purchasing power be during the first year of retirement)?
Explanation / Answer
Part-A
Without considering inflation during the 20 years of retirement
We need to save: $3,000*12*20 = $720,000
By considering an inflation of 2.45% for the 20 years during retirement
We need to save $914,993
But with the interest of 7.8% compounded, the retirement corpus required will be $474,683
Part- B
A monthly saving of $336 is required for this. (Show in Table)
Part –C
Total Ineterst earned after the withdrawal of last installment is$ 816,465
Part –D
In today’s terms the value of $3,000 would be $1,451.32 :
$3,000/(1.0245)^30 =$1,451.32
Table (Working)
Growth of
Growth of
Total Corpus
corpus avail.
Monthly
Monthly
future
amt. inv.
accumulated
for annuity
Year
invest.
Expenses
mon. inv.
so far
(year-end)
(year-start)
0
1451
0
0
1
336
1487
4346
0
4346
0
2
336
1523
9032
0
9032
0
3
336
1561
14082
0
14082
0
4
336
1599
19527
0
19527
0
5
336
1638
25397
0
25397
0
6
336
1678
31724
0
31724
0
7
336
1719
38545
0
38545
0
8
336
1761
45898
0
45898
0
9
336
1805
53824
0
53824
0
10
336
1849
62369
0
62369
0
11
336
1894
71580
0
71580
0
12
336
1940
81509
0
81509
0
13
336
1988
92213
0
92213
0
14
336
2037
103752
0
103752
0
15
336
2087
116191
0
116191
0
16
336
2138
129601
0
129601
0
17
336
2190
144056
0
144056
0
18
336
2244
159638
0
159638
0
19
336
2299
176437
0
176437
0
20
336
2355
194545
0
194545
0
21
336
2413
214066
0
214066
0
22
336
2472
235109
0
235109
0
23
336
2532
257794
0
257794
0
24
336
2595
282248
0
282248
0
25
336
2658
308610
0
308610
0
26
336
2723
337028
0
337028
0
27
336
2790
367662
0
367662
0
28
336
2858
400686
0
400686
0
29
336
2928
436286
0
436286
0
Interest ernd.
30
336
3000
474663
0
474663
0
during wdl.
Interest End. Inv.
31
0
3074
0
0
471927
437780
34147
353703
32
0
3149
0
0
468004
434141
33863
33
0
3226
0
0
462777
429292
33485
34
0
3305
0
0
456120
423117
33003
35
0
3386
0
0
447896
415488
32408
36
0
3469
0
0
437957
406268
31689
37
0
3554
0
0
426144
395309
30834
38
0
3641
0
0
412282
382451
29831
39
0
3730
0
0
396186
367520
28667
40
0
3822
0
0
377652
350327
27325
41
0
3915
0
0
356461
330669
25792
42
0
4011
0
0
332377
308327
24050
43
0
4109
0
0
305142
283063
22079
44
0
4210
0
0
274481
254621
19860
45
0
4313
0
0
240094
222722
17372
46
0
4419
0
0
201658
187067
14591
47
0
4527
0
0
158823
147331
11492
48
0
4638
0
0
111213
103166
8047
49
0
4752
0
0
58418
54191
4227
50
0
4868
0
0
0
0
Total Int. earned
816465
0
0
0
0
0
0
0
Growth of
Growth of
Total Corpus
corpus avail.
Monthly
Monthly
future
amt. inv.
accumulated
for annuity
Year
invest.
Expenses
mon. inv.
so far
(year-end)
(year-start)
0
1451
0
0
1
336
1487
4346
0
4346
0
2
336
1523
9032
0
9032
0
3
336
1561
14082
0
14082
0
4
336
1599
19527
0
19527
0
5
336
1638
25397
0
25397
0
6
336
1678
31724
0
31724
0
7
336
1719
38545
0
38545
0
8
336
1761
45898
0
45898
0
9
336
1805
53824
0
53824
0
10
336
1849
62369
0
62369
0
11
336
1894
71580
0
71580
0
12
336
1940
81509
0
81509
0
13
336
1988
92213
0
92213
0
14
336
2037
103752
0
103752
0
15
336
2087
116191
0
116191
0
16
336
2138
129601
0
129601
0
17
336
2190
144056
0
144056
0
18
336
2244
159638
0
159638
0
19
336
2299
176437
0
176437
0
20
336
2355
194545
0
194545
0
21
336
2413
214066
0
214066
0
22
336
2472
235109
0
235109
0
23
336
2532
257794
0
257794
0
24
336
2595
282248
0
282248
0
25
336
2658
308610
0
308610
0
26
336
2723
337028
0
337028
0
27
336
2790
367662
0
367662
0
28
336
2858
400686
0
400686
0
29
336
2928
436286
0
436286
0
Interest ernd.
30
336
3000
474663
0
474663
0
during wdl.
Interest End. Inv.
31
0
3074
0
0
471927
437780
34147
353703
32
0
3149
0
0
468004
434141
33863
33
0
3226
0
0
462777
429292
33485
34
0
3305
0
0
456120
423117
33003
35
0
3386
0
0
447896
415488
32408
36
0
3469
0
0
437957
406268
31689
37
0
3554
0
0
426144
395309
30834
38
0
3641
0
0
412282
382451
29831
39
0
3730
0
0
396186
367520
28667
40
0
3822
0
0
377652
350327
27325
41
0
3915
0
0
356461
330669
25792
42
0
4011
0
0
332377
308327
24050
43
0
4109
0
0
305142
283063
22079
44
0
4210
0
0
274481
254621
19860
45
0
4313
0
0
240094
222722
17372
46
0
4419
0
0
201658
187067
14591
47
0
4527
0
0
158823
147331
11492
48
0
4638
0
0
111213
103166
8047
49
0
4752
0
0
58418
54191
4227
50
0
4868
0
0
0
0
Total Int. earned
816465
0
0
0
0
0
0
0
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