Peter and Blair recently reviewed their future retirement income and expense pro
ID: 2797150 • Letter: P
Question
Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 35 years and anticipate they will need funding for an additional 23 years. They determined that they would have a retirement income of $46,000 in today's dollars, but they would actually need $65,222 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 3percent inflation rate and a return of 7percent.
Question - The total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 3 percent inflation rate and a return of 7 percent is $_________(Round to the nearest cent.)
.
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
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
Explanation / Answer
Shortfall =$65,222 - 46,000 =$19,222
Inflation Asjusted Amount =$19,222 x (1+0.03)23 =$19,222 x 1.9736 =$37,936.28
Real Return after Retirement = (1+0.07)/(1+0.03) -1 =1.07/1.03 -1 =1.0388 -1 =0.0388 or 3.88%
So, they will require this amount of $37,936.28 per year and earning 3.88% real returns after retirement.
This will form an annuity whose present value at the retirement start =37,936.28 x PVIFA(23,3.88%)
=$37,936.28 x 15.0349
=$570,369.80
To get this amount, we will save P amount each year and invest at 7%.
i.e P x FVIA(35,7%) =570,369.80
P = 570,369.80/138.24 =$4,126.03
Hence, they need to save $4,126.03 per year to achieve their goal.
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