Earl Ezekiel wants to retire in San Diego when he is 65 years old. Earl is now 46. He believes he will need $440,000 to retire comfortably. To date, Earl has set aside no retirement money. Assume Earl gets 4% interest compounded semiannually. How much must Earl invest today to meet his $440,000 goal? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
Earl Ezekiel wants to retire in San Diego when he is 65 years old. Earl is now 46. He believes he will need $440,000 to retire comfortably. To date, Earl has set aside no retirement money. Assume Earl gets 4% interest compounded semiannually. How much must Earl invest today to meet his $440,000 goal? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 37E: Find the positive geometric mean between 4 and 64.
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Question
Earl Ezekiel wants to retire in San Diego when he is 65 years old. Earl is now 46. He believes he will need $440,000 to retire comfortably. To date, Earl has set aside no retirement money. Assume Earl gets 4% interest compounded semiannually.
How much must Earl invest today to meet his $440,000 goal? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest dollar amount.)
Transcribed Image Text:Period 0.5% 1.0%
1 0.9950 0.9901
0.9901
2
0.9901 0.9803
3
4
09
5
3
6
9
7
8
9
9
10
11
12
14
13
14
14
15
16
10
17
"7
18
10
19
19
20
21
21
22
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.9851 0.9706
0.9991
0.9609 0.9235
0.9009
0.9802
0.9002
0.9610
0.9754 0.9515
0.9794
0.9283
0.9919
0.9209
0.9705 0.9420
0.8880
0.9145
0.9709 0.9420
0.0000
0.9140
0.9657 0.9327 0.9010
0.9921
0.900
0.90 10
0.8706
0.9143
0.9513 0.9053
0.99 15
0.9901
0.9561
0.9372
0.991€
0.9326 0.8700
0.9920
0.9279 0.8613
0.9€19
0.9233
0.9295
0.9187
0.9141
0.9141
0.9096
0.9096
0.9466 0.8963
0.9400
0.9419 0.8874 0.8364 0.7885
0.94 19 0.0074 0.0904
0.9051
0.9091 0.8195
0.6 199
0.9006
0.9000
02740
0.8610
0.7419
0:0010 0:1970
0.8525
0.0040
0.8482
VOTUE
0.8440
CONTO
2.5%
1.5% 2.0%
0.9852 0.9804 0.9756
0.9707 0.9612 0.9518
0.9563 0.9423
0.9965 0.9429
Present value interest factor of $1 per period at i% for n periods, PVIF(i,n).
4.5% 5.0%
6.0%
0.8204
3.0%
3.5% 4.0%
5.5%
0.9709 0.9662 0.9615 0.9569 0.9524 0.9479
0.9426
0.9426 0.9335 0.9246 0.9157
0.9 197
0.9070 0.8985
0.9019
0.9286 0.9151
0.9260
0.8890 0.8763
0.90 19 0.0090
0.8638
0.6705
0.8516
0.8038
0.8714 0.8548 0.8386 0.8227 0.8072
0.6072
0.07 14 0.0040 0.0900 0.0221
0.7835 0.7651 0.7473 0.7299
0.1999 0.7091 0.7475 0.7299
0.7252 0.7050
0.7402 0.7252 0.7090
6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0%
0.9434 0.9390 0.9346 0.9302 0.9259 0.9217 0.9174 0.9132 0.9091
0.8900 0.8817
0.8817 0.8734 0.8653 0.8573
0.6973 0.8495 0.8417
0.04 17
0.8340
0.7829
0.8396 0.8278 0.8163
0.6390
0.8050 0.7938
0.0 103
0.7617 0.7513
0.7829 0.7722
0.1990
0.7921 0.7773 0.7629
0.7350 0.7216 0.7084 0.6956
0.7488
0.7210
0.1029 1.1400 0.7990
0.7130 0.6966 0.6806
0.6499
0.7 130 1.0900
0.6650
0.0000
0.9060 0.8885
0.9000 0.0005
0.0020 0.8420
0.0420
0.8219
0.6219
0.8025
0.0029
0.0499
0.6352
0.7462
0.6853
0.0099
0.6480
0.6302
0.0302
0.6129
0.5963
0.5801
0.7107 0.6874 0.6651
0.6091
0.7 107 0.0074
0.5835
0.5470
0.5649
0.9699
0.5649
0.5298
0.5296
0.6768
0.5403
0.5002
0.6446
0.5002
0.6139
0.6139 0.5854
0.5654
0.8398
0.0990
0.9422
0.9422
0.8070
0.0070
0.9238
0.9236
0.9097
0.9057
0.8877 0.8535
0.6939
0.0077
0.8746 0.8368
0.6300
0.0740
0.8787 0.8240
0.0701 0.0240
0.8118 0.7579
0.0110
0.8617 0.8203
0.0011
0.8489 0.8043
0.0409
0.7999 0.7430
0.7999
0.7430
0.8839 0.8626
0.0099
0.6210 0.5306
0:0€ 10
0.8623
0.6023
0 5000
0.5202
0.8413
0.64 15
0.8007
0.0001
0.7812
0.7012
0.7621
0.7021
0.7436
0.7254
0.7730
0.7254
0.7894
0.8207
0.0201
0.7694
0.7077
0.7077
0.6905
0:0900
0.8375 0.8135
0.6579
0.8131
0.0191
0.4538
0-1000
0.4427
OFTE!
0.7664
0.7664
0.0199 0.1909
0.7903
0.7860 0.7599
0.7000 0.1999
0.7337 0.7026
0.7337
0.7020
0.6756
0.6496
0.6246
0.7014 0.6618
0.7014 0.00 10
0.6394 0.6006
0.0994 0.0000
0.6810
0.00 10
0.7441
0.7089
0.7441 0.7009
0.7224 0.6849
0.7994
0.7594
0.6611
0.0011
0.6419
0.7307
0.7907
0.7679
0.1019
0.1040
0.7348
0.3817
0.00
0.3687
0.000
0.3563
0.3083
0.0000 0.0000
0.7032
0.7092
0.6729
0.07.20
0.2534
0.600m
0.6439
0.6439
0.4970
0.4970 0.4697
0:4091
0.3971 0.3757 0.3555 0.3365
0.4410
0.3906
0.4150
0.3073
0:44 10
0.4190
0.3073
0.4986
0.4726
0.4141 0.3878
0.4425
0.4479 0.4173 0.3888 0.3624
0.4423
0.2807
0.2563
0.7880
0.8528
0.7284
0.6736
0.5767
0.5339
0.1978
0.1978
0.1799
0.1799
0.8114
0.7315
0.7207
0.8961 0 8034
0.5529
0.0598 0.5954 0.5375
0.9994
0.8034
0.6468
0.7207
0.5809 0.5219
0.8916 0.7954 0.7100 0.6342 0.5667 0.5067
0.8872 0.7876 0.6995 0.6217 0.5529 0.4919
0.8828 0.7798 0.6892
0.6095 0.5394 0.4776 0.4231 0.3751
0.8784 0.7720 0.6790 0.5976 0.5262 0.4637 0.4088
0.8740 0.7644 0.6690 0.5859 0.5134 0.4502
0.0000
0.4902
0.0007 7500
0.8697 0.7568 0.6591 0.5744 0.5009 0.4371
0.0097
0.000
FOO 0.0000
101
0.6494 0.5631 0.4887 0.4243
0:00
0-100!
0 5504
0.5521 0.4767
05440
07400
0.8653
0.7493
0.0000
0.3207
0.0630
0:00
0.6398
0.0000
0.8567 0.7346
0.0719
0.0002
0.0657 0.0573
0.0000 000
0.0521
0.0000 0:00
0.0548 0.0474
0.5900
0.3677
0.3900
0.3463 0.3262
0.3677
0.3405 0.3191 0.2992
0.3633
0.3191
0.3095 0.5409
0.2992
0.4810
0.3380 0.3152 0.2941
0.3380
0.2745
0.3152 0.2941
0.7600 0.7284
0.6232
0.0730
0.9707 0.9999 0.4945 0.4581 0.4246 0.3936 0.3651 0.3387 0.3144 0.2919 0.2711 0.2519 0.2341
0.4949 0.4961
0.2919
0.2341
0.8444 0.7764 0.7142 0.6572 0.6050 0.5572 0.5134 0.4732 0.4363 0.4024
0.4303
0.3714 0.3428 0.3166 0.2925 0.2703
0.2925
0.2499 0.2311 0.2138
0.7704
0.8360 0.7649 0.7002 0.6412 0.5874 0.5384 0.4936
0.4936 0.4528
0.4920 0.4155 0.3815 0.3503
0.5905 0.3219 0.2959 0.2720 0.2502
0.2902 0.2303 0.2120 0.1952
0.8277 0.7536
0.7950 0.6864 0.6255 0.5703 0.5202 0.4746 0.4333 0.3957 0.3616 0.3305
0.5509 0.3022 0.2765 0.2531 0.2317 0.2122 0.1945
0.1949 0.1783
0.1783 0.1635
0.7425 0.6730 0.6103 0.5537 0.5026 0.4564 0.4146
0.4564
0.3769
02838
0.3427 0.3118
0.2584
0.2838
0.2354 0.2145 0.1956 0.1784
0.1429
0.1628 0.1486
0.6598
0.4856 0.4388
0.4090
0.3968 0.3589 0.3249 0.2942 0.2665
01803
0.2415 0.2190 0.1987
0.1803 0.1637 0.1487 0.1351
0.4692 0.4220 0.3797 0.3418 0.3079 0.2775 0.2502 0.2257 0.2037 0.1839 0.1662
0. 1839
0 1358
0.1502 0.1358 0.1228
0 4533 0.4057
0.4533
0.3634 0.3256 0.2919 0.2618 0.2349 0.2109 0.1895
0.1703
0.1531 0.1378 0.1240 0.1117
0.4380 0.3901 0.3477 0.3101 0.2767 0.2470 0.2206 0.1971 0.1763
01577 0 1412
0.1412
01264 0.1133 0.1015
0.3327 0.2953 0.2622 0.2330 0.2071 0.1842 0.1640 0.1460 0.1301 0.1160 0.1034 0.0923
0.3607 0.3184 0.2812 0.2486 0.2198 0.1945 0.1722 0.1525 0.1352 0.1199 0.1064 0.0945 0.0839
20
0.3950 0.3468 0.3047 0.2678 0.2356 0.2074 0.1826
0.1419
0.2010
0.1609
0.1252 0.1105 0.0976 0.0863 0.0763
00700
1.2390
0.0970
0.4056
*150* Fo
01040
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0.3335 0.2916 0.2551 0.2233 0.1956 0.1715 0.1504 0.1320 0.1159 0.1019 0.0895 0.0788 0.0693
0.000 0910
0-2400 0-1000
100 0-1799
04406
0.0000 0.0099 0.0740 00000
0.2790 0.2429 0.2117 0.1846 0.1610 0.1406 0.1228 0.1073 0.0939 0.0822
0.2790
01070
0.0044 0.0006
1010
01640
0.0022
0404
0.0004 0.0000
0.2670 0.2314 0.2006 0.1741 0.1512 0.1314 0.1142 0.0994 0.0865 0.0754
0.2010
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0.0709
0 4000
0.0000
0.2204 0.1902
0.1643 0.1420 0.1228 0.1063 0.0920 0.0797 0.0691 0.0600
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04447
0.0050 00206
0.1803 0.1550 0.1333 0.1147 0.0988 0.0852 0.0735 0.0634
0.1990
0.1009
0.0092
9-1990
0 4000
04030 0.0040
00000
0.1999 0.1709 0.1462 0.1252 0.1072 0.0919 0.0789 0.0677 0.0582
0-1700
01000
1996 0.149€ TOTE 0:00 10 0.0108 0.000 0.000€ 0.0000
0.1904 0.1620 0.1379 0.1175 0.1002 0.0855 0.0730 0.0624 0.0534 0.0457
0.1904
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09000 0.0000
9-1919
9.1991 0.00
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0.009 0:00.00 0:00 0:00
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0.4902 0.4111 0.3450 0.2898
0.1727 0.1455 0.1227 0.1036 0.0875 0.0740 0.0626 0.0530 0.0449 0.0381
0.1006 www
0.4000 0:44O!
0.0020
0-1740
64030
0.1441
0.0000
0.0000 0:0440 0.0001
0.0073
0.8315 0.6920 0.5764 0.4806 0.4011 0.3350 0.2800 0.2343 0.1962 0.1644 0.1379 0.1158
0.4000
0.0973 0.0818 0.0688 0.0580 0.0489 0.0412 0.0348
0:0010
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0-1100
04007
0.0000
0 5670
0.04.14 0.0040
0.0640
0.0450
0.8274 0.6852 0.5679 0.4712 0.3913 0.3252 0.2706 0.2253 0.1878 0.1566 0.1307 0.1092 0.0914 0.0765 0.0640 0.0537 0.0450 0.0378 0.0318
0:0€14
0.47 12 0.99 19 0.0206 0.4100 0.4400 9.1970 0-1000
0.0937
0.1007 9.1994 0:00
06704
0:0979 0.00.10
00506
0.8232 0.6784 0.5595 0.4619 0.3817 0.3158 0.2614
0.0292
0.2166 0.1797 0.1491
0.0596 0.0497 0.0415 0.0347 0.0290
09990 0:4018 03704
0:9100
0€ 100
0.6747
0:00
0.0497
0:0947 0:0€90
04740
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0.0554
0.8191 0.6717 0.5513 0.4529 0.3724 0.3066 0.2526 0.2083 0.1719 0.1420
0.0668 0.0554 0.0460 0.0383 0.0318 0.0265
0.0191 0:00
1-4040 0.9764 0.0000 0.4040 0.2000
0.1920
0:0912
0.0004
0:0009
0.0400
0.0200
0.0004
04945
0.0000
0.3633 0.2976 0.2440 0.2003 0.1645 0.1353 0.1113
0.9099
0.0917 0.0756 0.0624 0.0516 0.0426 0.0353 0.0292 0.0242
0.2970 0.4440 0.2000
0.1999
0:09 1 0.0100 0:00€4 0.0010 0.04.20 0.0000 0.0292 0.0242
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4055
0.5351 0.4353 0.3545 0.2890 0.2358 0.1926 0.1574 0.1288 0.1055 0.0865 0.0710 0.0583 0.0480 0.0395 0.0325 0.0268 0.0221 0.0183
0.9991
0.0040 0.2090 0.6000 0.1920
0.1200
1000
0.0009
0:0909
0.0899
200
0.0020 0.0200
0.0007
0.0241 0.0109
0.5272
0:9212 0.4268 0.3458 0.2805 0.2278 0.1852 0.1507 0.1227
0.2210
0.1000 0.0816 0.0667 0.0545 0.0446 0.0365 0.0300 0.0246 0.0202 0.0166
0:4200 0.94990 0.2000
0.1002 www
0.00.10 0.0007
0.0040
0.0040
0.0809
0.0240
0.0000
0.0202
00445
0.0100
0.5194 0.4184 0.3374 0.2724 0.2201 0.1780 0.1442 0.1169 0.0948 0.0770 0.0626 0.0509 0.0415 0.0338 0.0276 0.0226 0.0184 0.0151
0:04994 0:3194 0:4 104
0.2724
0-1700
0.0000
0.0000
0.0040
0.0210
0.0407
0.0009
0.0104 0.0101
0.0000
0.0220
0.7990 0.6391 0.5117 0.4102 0.3292 0.2644
0.1712 0.1380 0.1113
0.2127
0.0899 0.0727 0.0588 0.0476 0.0386 0.0313 0.0254 0.0207 0.0168 0.0137
0.0091 9:31 0:4106
0.2049 0.2121
0904
9-1712
0.0121 0.0000
0.0204
2014 0.0000
04000
0.08.19
0.0207
0.0100
0.7950 0.6327 0.5042 0.4022 0.3211 0.2567 0.2055 0.1646 0.1320 0.1060 0.0852 0.0685 0.0552 0.0445 0.0359 0.0290 0.0235 0.0190 0.0154 0.0125
0.0129
0.1583 0.1263 0.1009 0.0807 0.0647 0.0518 0.0416 0.0334 0.0269 0.0216 0.0174 0.0140 0.0113
0.1522 0.1209 0.0961 0.0765 0.0610 0.0487 0.0389 0.0311 0.0249 0.0199 0.0160 0.0128 0.0103
0.1463 0.1157 0.0916 0.0725 0.0575 0.0457 0.0363 0.0289 0.0230 0.0184 0.0147 0.0117
0.0094
0.1407 0.1107 0.0872 0.0688 0.0543 0.0429 0.0339 0.0269 0.0213 0.0169 0.0134 0.0107 0.0085
0.6303 0.5412 0.4651
0.0000
0.2555
0.0007
0.9412
02030
0-100
0:2000
0*20*
0.7273
0.2099
02600
0:0940
0.7201
0.6118
0.0500
0500
0.010 05406
0.7130 0.6028 0.5100
0000
0:0020
000
0.7059 0.5939 0.5000
7000
0.8356 0.6989 0.5851
0.0000 10000
0.3000
0.0000
0.2437
0.2050
0.4000
0.0000
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0.1239 0.1031 0.0858 0.0715
0.1091 0.0000
04478
0.1175 0.0972 0.0805
00000
0.0201
0.8151 0.6650 0.5431 0.4440
0.0191
O GERA
0.8110 0.6584
0.0110
GEAD
0.6519
0.0019
0.8030 0.6454
0.0090
0.7910 0.6265 0.4967 0.3943 0.3133 0.2493 0.1985
0.7871 0.6203 0.4894 0.3865 0.3057 0.2420 0.1918
0.7832 0.6141 0.4821 0.3790 0.2982 0.2350 0.1853
0.7793 0.6080 0.4750 0.3715 0.2909 0.2281 0.1791
0.6162
0.0102
0.5897
0.5897
0.5775
0.6178
0.0170
0.5969 0.5553 0.5167
0.5553
0.9900
0.4120
07760
0.4000 0.3442 0.2965
0.000
0.3883 0.3326
0.0064
0.2851 0.2445
0.9999
0.0040
3
0.3770 0.3213 0.2741 0.2340
0.0000
VET 0600
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0.4319 0.3660 0.3105
9:4010
0:9100
0.2636 0.2239
0.4000
0.4214 0.3554
0.5643 0.5303
0.9045 0.9505
0.5051
0.5400
0.2143
060
0.6516 0.6274
0.09 10
0.6042
0.0274 0.0042
0.5919
0.6176
0.5674
0.9919 0.9074
0.5847
0.5549
0.9047 0.9949 0.9200
0.5268
0.5584 0.5327
0.0004 0.99€!
0.5568
0.5260
0.9900
0.6435
0.0499
0.4688
0.4000
0.5002
0.0002
0.6663
0.0009
0.0221
0.6227
0.5820
0.9020
0.6028
0.6028
0.5607
0.5007
0.5439 0.5216
0.9499
0.5083 0.4852
0.0009
0.4440
0.4440
0.4751 0.4513
0.4751 0.49 13
0.4199
0.5019 0.4838
0.4090
0.5207
0.5207
0.4799 0.4604
0.4423
0.4632
0.4032
0.4289
0.4076
0.4209
0.4224
0.4224
0.3875
0.4418
0.44 16
0.4035
0.3685
0.6830
0.6830
0.6209
0.5645
0.9049
0.5132
0.9132
0.4665
0.4009
0.4241
0.4241
0.3855
0.3099
0.9900
0.3505
0.3186
0.2897
0.2897
0.2099
0.2633
0.2394
0.2176
0.2170
0.0431
0.049
0.0391
0.009
0.0356
0.0980
0.0323
0.0020
0.0294
0.0267
0:00
0.0207
0.0243
0.0240
0.0221
0:0€€
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