On January 1, 2020, University Theatres issued $495,000 face value of bonds. The stated rate is 8%, and interest is paid semiannually on June 30 and December 31. The bonds mature in 15 years. Do not round interim calculations. If required, round your answers to the nearest whole dollar. Follow the format shown in present value tables as you complete the requirements below. a. Assuming the market rate of interest is 6%, calculate at what price the bonds are issued. $ b. Assuming the market rate of interest is 10%, calculate at what price the bonds are issue
On January 1, 2020, University Theatres issued $495,000 face value of bonds. The stated rate is 8%, and interest is paid semiannually on June 30 and December 31. The bonds mature in 15 years. Do not round interim calculations. If required, round your answers to the nearest whole dollar. Follow the format shown in present value tables as you complete the requirements below. a. Assuming the market rate of interest is 6%, calculate at what price the bonds are issued. $ b. Assuming the market rate of interest is 10%, calculate at what price the bonds are issue
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
Related questions
Question
On January 1, 2020, University Theatres issued $495,000 face value of bonds. The stated rate is 8%, and interest is paid semiannually on June 30 and December 31. The bonds mature in 15 years.
Do not round interim calculations. If required, round your answers to the nearest whole dollar. Follow the format shown in present value tables as you complete the requirements below.
a. Assuming the market rate of interest is 6%, calculate at what price the bonds are issued.
$
b. Assuming the market rate of interest is 10%, calculate at what price the bonds are issued.
$
![93719
Future Value of a Single Amount FV= 1(1+i)"
n/i
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
1.25000
1.56250
1.95313
2.44141
3.05176
3.81470
4.76837
5.96046
7.45058
9.31323
11.64153
14.55192
18.18909
22.73737
1.08000
1.16640
1.09000
1.18810
1.29503
1.41158
1.16000
1.34560
1.56090
1.81064
2.10034
2.43640
2.82622
3.27841
1,10000
1.14000
1.01000
2 1.02010 1.04040 1.06090 1.08160 1.10250 1.12360 1.14490
3 1.03030 1.06121 1.09273 1.12486 1.15763 1.19102 1.22504
4 1.04060 1.08243 1.12551 1.16986 1.21551 1.26248 1.31080
5 1.05101 1.10408 1.15927 1.21665 1.27628 133823 1.40255
6 1.06152 1.12616 1.1940S 1.26532 1.34010 141852 1.50073
7 1.07214 1.14869 1.22987 1.31593 1.40710 1.50363 1.60578
8 1.08286 1.17166 1.26677 1.36857 1.47746 159385 1.71819
9 1.09369 1.19509 1.30477 1,42331 1.55133 1.68948
1.30000
1.69000
2.19700
2.85610
3.71293
4.82681
6.27485
8.15731
10.60450
13.78585
17.92160
2329809
30 28751
39.37376
1.02000 1.03000 1.04000 1,05000 1.06000 1.07000
1.12000
1.18000
1.39240
1.64303
1.20000
1.29960
1,44000
1.25971
1.36049
146933
1.58687
1.71382
1.85093
1.99900
1.21000 1.25440
1.33100 1.40493
1.46410 1.57352
1.61051 1.76234
1.77156 1.97382
1.48154
1.68896
1.92541
2.19497
1.72800
2.07360
2.48832
1.93878
2.28776
2.69955
3.18547
3.75886
443545
5.23384
6.17593
7.28759
8.59936
10.14724
1.53862
1.67710
1.82804
1.99256
2.17189
2.98598
3.58318
4.29982
5.15978
6.19174
1.94872 221068
2.14359 2.47596
2.50227
2.85259
3.25195
3.70722
4.22623
4.81790
5.49241
626135
2.35795 2.77308
3.80296
10 1.10462 1.21899 1.34392 1.48024 1.62889 1.79085 1.96715 2.15892
11 1.11567 1.24337 1.38423
1.12683 1.26824 1,42576 1.60103 1.79586 2.01220 225219
2.36736
2.58043
281266
3.06580
2.59374 3.10585
2.85312 3.47855
3.13843 3.89598
3.45227
3.79750
4.41144
2.33164
2.51817
2.71962
5.11726
5.93603
6.88579
7.98752
9.26552
7.43008
8.91610
10.69932
12 83918
1.53945 1.71034 1.89830 2.10485
12
13
1.13809 1.29361 1,46853 1.66507 1.88565 2.13293 2.40985
14 1.14947 1.31948 1.51259 1.73168 1.97993 226090 257853
15 1.16097 1 34587 1.55797 1.80094 2.07893 239656 2.75903
3.34173
3.64248
397031
4 B8711
5 47357
413039
15.40702
18.48843
3.17217
3.42594
3.70002
3.99602
4.31570
4.66096
21 1.23239 1.51567 1.86029 2.27877 2.78596 3.39956 4.14056 5.03383
22 1.24472 1.54598 1.91610 2.36992 2.92526 3.60354 4.43040 5.43654
4.17725
7.13794
11.97375
28.42171
35 52714
44.40892
55.51115
69 38894
86.73617
46.00512 108.42022
55.20614 135 52527
51.18589
254035 295216
66.54166
86 S0416
4.59497
10 74800
12.46768
14.46251
8.61276 12.05569 16.77652
13.74349 19.46076
1,17258 1,37279 1.40471 187298 2.18287
8.13725
14.12902
16.67225
19.67325
23.21444
27.39303
16
4.32763
4.71712
5.14166
560441
6.10881
5.05447
5.55992
6.11591
6.72750 9.64629
22.18611
17 1.18430 1,40024 1,65285
18 1.19615 1.42825 1.70243 2.02582 2.40662
19 1.20811 1.45681 1.75351 2.10685 2.52695 3.02560 3.61653
20 1.22019 1.48595 1.80611 2.19112 2.65330 3.20714 3.86968
1.94790 2.29202 2.69277 3.15882
6.86604
9.27646
26.62333
31.94800
38.33760
2.85434
3.37993
7.68997 10.57517
112.45541
146.19203
190 04946
247.06453
321.18389
7.40025 10.80385 15.66758 22.57448
8.14027 12.10031 17.86104 26.18640
95430 13.5s235 20 36158
32.32378
6.65860
38.14206
30 37622
23 1.25716 1,57690 1,97359
24 1.26973 1.60844 2.03279 2.56330 3.22510 4.04893 5,07237
246472 3.07152 381975
66.24737 169.40659
79.49685 211 75824
7.25787
412.53905
5.87146
6.34118
6.84848
45.00763
53.10901
62 66863
73.94898
87.25980
102.96656
121.50054
143.37064
23.21221
10.83471 17.00006 26.46192 40.87424
542.80077
705.64100
917.33330
9.84973 15.17863
35.23642
25 1.28243 1.64061 2.09378 2.66584 3.38635 429187 5.42743
26 1.29526 1.67342 2.15659 2.77247 3.55567 454938 5.80735
27 1.30821 1.70689 222129 2.88337 3.73346 482235 621387
7.91108
8.62308
9.39916 11.91818 19.04007 30.16658 47.41412
10.24508
7.39635
7.98806
8.62711 11.16714 14.42099 23.88387 39.20449 63.80044
9.31727 12.17218 15.86309 26.74993 44.69312 74.00851
95.39622 264 69780
114.47546 330 87225
137.37055 413.59031
164.84466 516.98788
197.81359 646.23485 2015.38126
237 37631 807.79357 2619.99564
13.10999 21.32488 34.38991 55.00038
1192.53329
1550 29328
28 1.32129 1.74102 2.28793 2.99870 3.92013 5.11169 6.64884
29 1.33450 1.77584 2.35657 3.11865 4.11614 5.41839 7.11426
30 1.34785 1.81136 242726 3.24340 4.32194 5.74349 7.61226 10.06266 13.26768 17,44940 29.95992 50.95016 85.84988
1.8
Present Value of a Single Amount PV=
(1+i)"
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
0.80000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
0.83333
0.69444
0.57870
051579 0.48225
0.40188
0.33490
027908
023257
0.19381
0.16151
1.
0.96154
0.92456
0.95238
0.90703 0.89000
0.94340 093458
0.87344
0.91743 0.90909 0.89286
0.76923
0.59172
0.45517
0.40960 0.35013
0.26933
0.20718
0.15937
0.12259
0.09430
0.99010 0.98039 0.97087
0.98030 0.96117 0.94260
0.97059 0.94232 0.91514 0.88900 0.86384 0.83962 0.81630
0.96098 0.9238s 0.88849
0.95147 0.90573
0.94205
0.93272
0.92348
0.91434
0.90529
0.89632
0.88745
0.87866
0.86996
0.86135
0.85282
0.84438
0.83602
0.82774
0.84168 0.82645 0.79719 076947
0.77218 0.75131 0.71178 0.67497 0.64066
0.68301 063552
0.87719 0.86207
0.74316
0.84746
0.71818
0.60863
0.64000
051200
0.55229
051937 0.47611
041044
0.35383
0.85480
0.82193
0.82270
0.78353
0.74622
0.71068
067684
0.79209 0.76290
0.70843
0.59208
0.86261
0.83748
0.81309
0.78941
0.43711
0.74726 0.71299
0.66634
0.62275
058201
0.54393
0.50835
047509
0.44401
0.41496
0.38782
036245
0.33873
031657
0.64993 0.62092 0.56743
0.56447
0.51316
0.46651
0.59627
054703
050187
0.46043
042241
0.32768
0.26214
0.20972
0.16777
0.13422
0.10737
0.88797
0.87056
0.85349
0.70496
0.66506
062741
0.45559
0.79031
0.75992
0.73069
050663
045235
0.40388
0.36061
032197
037043
031393
026604
022546
0.19106
0.39964
0.54027
0.50025
0.46319
0.42888
0.39711
0.36770
0.34046
031524
0.35056
0.4240
0.38554
0.30503
0.26295
0.83676
0.76642
0.82035
0.74409
0.80426
0.72242
0.78849
0.70138
0.77303 0.68095
0.70259
0.67556
0.64958
0.62460
0.64461
061391
0.58468
0.55684
0.53032
0.50507
0.48102
0.45811
0.59190
0 55839
030751
026974
023662
020756 0.16846
0.18207
0.15971
10
11
0.07254
0.05580
0.35049 028748
031863 025668
0.22917
0.20462
0.18270
0.16312
0.14564
0.19542
0.52679
0.49697
0.46884
0.44230
0.41727
038753
0.16192
0.13459
0.08590
0.06872
0.05498
0.04398
0.03518
035553
0.13722
0.11216
0.01292
0.03302
0.02540
0.01954
0.01503
12
13
0.60057
0.57748
0.55526
0.53391
0.32618 0.28966
0.26333
0.23939
021763
0.19784
0.17986
0.16351
0.14864
0.13513
0.12205
0.11168
0.10153
0.09230 0.05882
0.08391
0.14523
0.12520
0.10793
0.09304
0.11629
0.09855
0.08352
0.09346
0.07789
0.06491
0.75788 0.66112
0.74301
0.29925
0.27454
025187
023107
021199
14
15
0.64186
0.14010
029189
027027
0.25025
0.72845
0.07078 0.05409 0.02815
0.02252
0.01801
0.01441
0.01153
0.02174 0.00922
0.00738
0.00590
0.00472
042317
0.60502
0.39365
0.37136
0.35034
0.33051
0.31180
0.12209
16
17
0.71416
0.70016
0.68643
0.67297
065978
0.51337
0.49363
0.47464
0.45639
0.43883
042196
0.40573
0.43630
0.41552
0.39573
0.37689
0.05998 04507
0.05083 003756
0.04308 0.03130
0.10780 0.08021
0.09456 0.06914
0.08295 0.05961
0.01156
0.00889
0.00684
0.00526
0.00405
0.00311
0.00239
0.58739
0.29586
027651
0.25842
0.13004
0.11611
0.10367
0.09256 06383
0.08264
0.07379
18
0.57029
023171
0.19449
0.17843
0.16370
19
0.81954
0.81143
O.B0340
021455
003451 002608
0.03094
0.02622
0.02222
0.01883
001596
001352
0.01146
0.00971
0.00823
0.00697
20
21
22
007276 0.05139
0.04430
0.03819
0.55368
0.53755
0644 052109
0.63416 0.50669
0.62172 0.49193
0.47761
0.46369
0.45019
0.35894
0.34185
0.32557
0.31007
0.29530
0.20124
0.26785
0.25509
024295
0.23138
029416
0.27751
0.26180
0.24698
023300
021981
0.20737
0.19563
0.18456
0.17411
024151
0.22571
021095
0.19715
0.18425
0.17220
0.16093
0.19866
0.18394
0.17032
0.15770
0.15018
0 05599
0.01811
0.01509
0.79544
0.13778
23
24
0.04911
0.78757
0.77977
0,77205
0.76440
0.12640
0.11597
0.10639
0.09761
0.03292
0 04308 0.02838
0.03779 02447
003315 0.02109
0.39012
037512
0.06588
0.01258
0.01048
0.00874
0.00728
0.00184
0.14602
0.13520
0.60953
0.59758
0.58586
057437
0.56311
0.55207 0.41199
0.00378
0.00302
0.00242
0.00193
0.00155
0.00124
0.00142
0.00109
0.00064
25
036069
0.05252
0.04689
26
27
28
29
0.75684
0.74934
0.74192
0.34682
0.33348
0.32065
0.30832
0.12519
0.11591
0.10733
0.09938
0.07628
0.06934 0.04187
0.06304
0.02908 0.01818
0 02551
0.01567
0 02237
0.01351
001963
0.01165
0.43708
0.15040
0.14056
0.13137
0.08955
O 08215
0.07537
0.00607
0.00506
0.00421
0.00065
0.00050
0.00038
0.42435
0.03738
30
0.05731
0.03338](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a5b89dc-5707-415c-80f3-ec8a6690e4e9%2F5e175518-07e1-4988-814d-85ea0e5daeb8%2F2lzwo8_processed.png&w=3840&q=75)
Transcribed Image Text:93719
Future Value of a Single Amount FV= 1(1+i)"
n/i
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
1.25000
1.56250
1.95313
2.44141
3.05176
3.81470
4.76837
5.96046
7.45058
9.31323
11.64153
14.55192
18.18909
22.73737
1.08000
1.16640
1.09000
1.18810
1.29503
1.41158
1.16000
1.34560
1.56090
1.81064
2.10034
2.43640
2.82622
3.27841
1,10000
1.14000
1.01000
2 1.02010 1.04040 1.06090 1.08160 1.10250 1.12360 1.14490
3 1.03030 1.06121 1.09273 1.12486 1.15763 1.19102 1.22504
4 1.04060 1.08243 1.12551 1.16986 1.21551 1.26248 1.31080
5 1.05101 1.10408 1.15927 1.21665 1.27628 133823 1.40255
6 1.06152 1.12616 1.1940S 1.26532 1.34010 141852 1.50073
7 1.07214 1.14869 1.22987 1.31593 1.40710 1.50363 1.60578
8 1.08286 1.17166 1.26677 1.36857 1.47746 159385 1.71819
9 1.09369 1.19509 1.30477 1,42331 1.55133 1.68948
1.30000
1.69000
2.19700
2.85610
3.71293
4.82681
6.27485
8.15731
10.60450
13.78585
17.92160
2329809
30 28751
39.37376
1.02000 1.03000 1.04000 1,05000 1.06000 1.07000
1.12000
1.18000
1.39240
1.64303
1.20000
1.29960
1,44000
1.25971
1.36049
146933
1.58687
1.71382
1.85093
1.99900
1.21000 1.25440
1.33100 1.40493
1.46410 1.57352
1.61051 1.76234
1.77156 1.97382
1.48154
1.68896
1.92541
2.19497
1.72800
2.07360
2.48832
1.93878
2.28776
2.69955
3.18547
3.75886
443545
5.23384
6.17593
7.28759
8.59936
10.14724
1.53862
1.67710
1.82804
1.99256
2.17189
2.98598
3.58318
4.29982
5.15978
6.19174
1.94872 221068
2.14359 2.47596
2.50227
2.85259
3.25195
3.70722
4.22623
4.81790
5.49241
626135
2.35795 2.77308
3.80296
10 1.10462 1.21899 1.34392 1.48024 1.62889 1.79085 1.96715 2.15892
11 1.11567 1.24337 1.38423
1.12683 1.26824 1,42576 1.60103 1.79586 2.01220 225219
2.36736
2.58043
281266
3.06580
2.59374 3.10585
2.85312 3.47855
3.13843 3.89598
3.45227
3.79750
4.41144
2.33164
2.51817
2.71962
5.11726
5.93603
6.88579
7.98752
9.26552
7.43008
8.91610
10.69932
12 83918
1.53945 1.71034 1.89830 2.10485
12
13
1.13809 1.29361 1,46853 1.66507 1.88565 2.13293 2.40985
14 1.14947 1.31948 1.51259 1.73168 1.97993 226090 257853
15 1.16097 1 34587 1.55797 1.80094 2.07893 239656 2.75903
3.34173
3.64248
397031
4 B8711
5 47357
413039
15.40702
18.48843
3.17217
3.42594
3.70002
3.99602
4.31570
4.66096
21 1.23239 1.51567 1.86029 2.27877 2.78596 3.39956 4.14056 5.03383
22 1.24472 1.54598 1.91610 2.36992 2.92526 3.60354 4.43040 5.43654
4.17725
7.13794
11.97375
28.42171
35 52714
44.40892
55.51115
69 38894
86.73617
46.00512 108.42022
55.20614 135 52527
51.18589
254035 295216
66.54166
86 S0416
4.59497
10 74800
12.46768
14.46251
8.61276 12.05569 16.77652
13.74349 19.46076
1,17258 1,37279 1.40471 187298 2.18287
8.13725
14.12902
16.67225
19.67325
23.21444
27.39303
16
4.32763
4.71712
5.14166
560441
6.10881
5.05447
5.55992
6.11591
6.72750 9.64629
22.18611
17 1.18430 1,40024 1,65285
18 1.19615 1.42825 1.70243 2.02582 2.40662
19 1.20811 1.45681 1.75351 2.10685 2.52695 3.02560 3.61653
20 1.22019 1.48595 1.80611 2.19112 2.65330 3.20714 3.86968
1.94790 2.29202 2.69277 3.15882
6.86604
9.27646
26.62333
31.94800
38.33760
2.85434
3.37993
7.68997 10.57517
112.45541
146.19203
190 04946
247.06453
321.18389
7.40025 10.80385 15.66758 22.57448
8.14027 12.10031 17.86104 26.18640
95430 13.5s235 20 36158
32.32378
6.65860
38.14206
30 37622
23 1.25716 1,57690 1,97359
24 1.26973 1.60844 2.03279 2.56330 3.22510 4.04893 5,07237
246472 3.07152 381975
66.24737 169.40659
79.49685 211 75824
7.25787
412.53905
5.87146
6.34118
6.84848
45.00763
53.10901
62 66863
73.94898
87.25980
102.96656
121.50054
143.37064
23.21221
10.83471 17.00006 26.46192 40.87424
542.80077
705.64100
917.33330
9.84973 15.17863
35.23642
25 1.28243 1.64061 2.09378 2.66584 3.38635 429187 5.42743
26 1.29526 1.67342 2.15659 2.77247 3.55567 454938 5.80735
27 1.30821 1.70689 222129 2.88337 3.73346 482235 621387
7.91108
8.62308
9.39916 11.91818 19.04007 30.16658 47.41412
10.24508
7.39635
7.98806
8.62711 11.16714 14.42099 23.88387 39.20449 63.80044
9.31727 12.17218 15.86309 26.74993 44.69312 74.00851
95.39622 264 69780
114.47546 330 87225
137.37055 413.59031
164.84466 516.98788
197.81359 646.23485 2015.38126
237 37631 807.79357 2619.99564
13.10999 21.32488 34.38991 55.00038
1192.53329
1550 29328
28 1.32129 1.74102 2.28793 2.99870 3.92013 5.11169 6.64884
29 1.33450 1.77584 2.35657 3.11865 4.11614 5.41839 7.11426
30 1.34785 1.81136 242726 3.24340 4.32194 5.74349 7.61226 10.06266 13.26768 17,44940 29.95992 50.95016 85.84988
1.8
Present Value of a Single Amount PV=
(1+i)"
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
0.80000
0.92593
0.85734
0.79383
0.73503
0.68058
0.63017
0.58349
0.83333
0.69444
0.57870
051579 0.48225
0.40188
0.33490
027908
023257
0.19381
0.16151
1.
0.96154
0.92456
0.95238
0.90703 0.89000
0.94340 093458
0.87344
0.91743 0.90909 0.89286
0.76923
0.59172
0.45517
0.40960 0.35013
0.26933
0.20718
0.15937
0.12259
0.09430
0.99010 0.98039 0.97087
0.98030 0.96117 0.94260
0.97059 0.94232 0.91514 0.88900 0.86384 0.83962 0.81630
0.96098 0.9238s 0.88849
0.95147 0.90573
0.94205
0.93272
0.92348
0.91434
0.90529
0.89632
0.88745
0.87866
0.86996
0.86135
0.85282
0.84438
0.83602
0.82774
0.84168 0.82645 0.79719 076947
0.77218 0.75131 0.71178 0.67497 0.64066
0.68301 063552
0.87719 0.86207
0.74316
0.84746
0.71818
0.60863
0.64000
051200
0.55229
051937 0.47611
041044
0.35383
0.85480
0.82193
0.82270
0.78353
0.74622
0.71068
067684
0.79209 0.76290
0.70843
0.59208
0.86261
0.83748
0.81309
0.78941
0.43711
0.74726 0.71299
0.66634
0.62275
058201
0.54393
0.50835
047509
0.44401
0.41496
0.38782
036245
0.33873
031657
0.64993 0.62092 0.56743
0.56447
0.51316
0.46651
0.59627
054703
050187
0.46043
042241
0.32768
0.26214
0.20972
0.16777
0.13422
0.10737
0.88797
0.87056
0.85349
0.70496
0.66506
062741
0.45559
0.79031
0.75992
0.73069
050663
045235
0.40388
0.36061
032197
037043
031393
026604
022546
0.19106
0.39964
0.54027
0.50025
0.46319
0.42888
0.39711
0.36770
0.34046
031524
0.35056
0.4240
0.38554
0.30503
0.26295
0.83676
0.76642
0.82035
0.74409
0.80426
0.72242
0.78849
0.70138
0.77303 0.68095
0.70259
0.67556
0.64958
0.62460
0.64461
061391
0.58468
0.55684
0.53032
0.50507
0.48102
0.45811
0.59190
0 55839
030751
026974
023662
020756 0.16846
0.18207
0.15971
10
11
0.07254
0.05580
0.35049 028748
031863 025668
0.22917
0.20462
0.18270
0.16312
0.14564
0.19542
0.52679
0.49697
0.46884
0.44230
0.41727
038753
0.16192
0.13459
0.08590
0.06872
0.05498
0.04398
0.03518
035553
0.13722
0.11216
0.01292
0.03302
0.02540
0.01954
0.01503
12
13
0.60057
0.57748
0.55526
0.53391
0.32618 0.28966
0.26333
0.23939
021763
0.19784
0.17986
0.16351
0.14864
0.13513
0.12205
0.11168
0.10153
0.09230 0.05882
0.08391
0.14523
0.12520
0.10793
0.09304
0.11629
0.09855
0.08352
0.09346
0.07789
0.06491
0.75788 0.66112
0.74301
0.29925
0.27454
025187
023107
021199
14
15
0.64186
0.14010
029189
027027
0.25025
0.72845
0.07078 0.05409 0.02815
0.02252
0.01801
0.01441
0.01153
0.02174 0.00922
0.00738
0.00590
0.00472
042317
0.60502
0.39365
0.37136
0.35034
0.33051
0.31180
0.12209
16
17
0.71416
0.70016
0.68643
0.67297
065978
0.51337
0.49363
0.47464
0.45639
0.43883
042196
0.40573
0.43630
0.41552
0.39573
0.37689
0.05998 04507
0.05083 003756
0.04308 0.03130
0.10780 0.08021
0.09456 0.06914
0.08295 0.05961
0.01156
0.00889
0.00684
0.00526
0.00405
0.00311
0.00239
0.58739
0.29586
027651
0.25842
0.13004
0.11611
0.10367
0.09256 06383
0.08264
0.07379
18
0.57029
023171
0.19449
0.17843
0.16370
19
0.81954
0.81143
O.B0340
021455
003451 002608
0.03094
0.02622
0.02222
0.01883
001596
001352
0.01146
0.00971
0.00823
0.00697
20
21
22
007276 0.05139
0.04430
0.03819
0.55368
0.53755
0644 052109
0.63416 0.50669
0.62172 0.49193
0.47761
0.46369
0.45019
0.35894
0.34185
0.32557
0.31007
0.29530
0.20124
0.26785
0.25509
024295
0.23138
029416
0.27751
0.26180
0.24698
023300
021981
0.20737
0.19563
0.18456
0.17411
024151
0.22571
021095
0.19715
0.18425
0.17220
0.16093
0.19866
0.18394
0.17032
0.15770
0.15018
0 05599
0.01811
0.01509
0.79544
0.13778
23
24
0.04911
0.78757
0.77977
0,77205
0.76440
0.12640
0.11597
0.10639
0.09761
0.03292
0 04308 0.02838
0.03779 02447
003315 0.02109
0.39012
037512
0.06588
0.01258
0.01048
0.00874
0.00728
0.00184
0.14602
0.13520
0.60953
0.59758
0.58586
057437
0.56311
0.55207 0.41199
0.00378
0.00302
0.00242
0.00193
0.00155
0.00124
0.00142
0.00109
0.00064
25
036069
0.05252
0.04689
26
27
28
29
0.75684
0.74934
0.74192
0.34682
0.33348
0.32065
0.30832
0.12519
0.11591
0.10733
0.09938
0.07628
0.06934 0.04187
0.06304
0.02908 0.01818
0 02551
0.01567
0 02237
0.01351
001963
0.01165
0.43708
0.15040
0.14056
0.13137
0.08955
O 08215
0.07537
0.00607
0.00506
0.00421
0.00065
0.00050
0.00038
0.42435
0.03738
30
0.05731
0.03338
![3.9
Future Value of an Annuity FVA
:
(1+ i)" – 1
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
1.00000
2.03000
3.09090
4.18363
1.00000
2.
3.03010
4.06040
5.10101
6.15202
721354
1.00000
2.04000 0
3.12160
424646
5.30914 541632
ఉ
7.89829
921423
1,00000
2.08000 2.09000
3.27810
4.57313
1.00000
1.00000
2.02000
3.06040
4.12161
5.20404
1.00000
2.14000
3.43960
4.92114
661010
1.00000
2.05000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
2.10000
3.31000
2.06000
3.18360
437462
563709
6.97532
8.39384
207000
321490
4.43994
5.75074
220000
3.64000
5.36800
7.44160
9.92992
12.91590
16.49908
2.30000
3.99000
6.18700
9.04310
12.75603
17.58284
23.85769
2.01000
2.12000
2.16000
2.18000
225000
3.37440
477933
6.35205
8.11519
3.50560
5.06650
687714
3.57240
521543
7.15421
944197
3.15250
431013
324640
4.50611
5.86660
733593
4.64100
6.10510
7.71561
3.81250
5.76563
820703
11.25879
15.07349
5.52563
5.96471
6.30812
7.43428
8.58297
6.46841
7.66246
8.89234
6.80191
8.14201
9.54911
7.15329
8.65402
10.25980
7.52333
8.92280 920043 9.48717 10.08901
8.53552
10.73049
1323276
8.97748
11.41387
12.14152
15.32700
8.28567
9.89747
10.63663 11.02847
11.43589 12.29969
14.24009
19.84186
936853
10 10.46221 10.94972 11.46388
11.56683 12.16872
12.68250 13.41209
13
16.08535 17.51851
20.79890
25 80232
33 25290
4256613
54 20766
48.49660 68.75958 9762504
59.19592 86.94947 127.91255
72.03511 109.68684 167 28631
9.75463 10.15911 10.58280 11.02656
11.49132 11.97799
12.48756 13.02104 13.57948
14.77566
19.08585
32.01500
12.00611 12.57789 13.18079
13.48635 14.20679
15.02581 15.91713
1381645
15.78360
16.86994 1788845
17.71298 1888214 20.14064
14.48656 15.19293 15.93742 17.54874 1933730 21.32147 23.52131
16.64549 17.56029 18.53117 20.65458 23.04452 25.73290 28.75514
18.97713 20.14072 21.38428 24.13313 27 27075 3085017 34.93107
21.49530 22.95338 24.52271 28.02911
24.21492 26.01919 27.97498 32.39260 37 58107
42.61950
56.40535
25.95868
12.80780
14.19203
14.68033 15.61779
15.97394 17.08632
14.97164
32.15042
39.58050
11
12
743295
13.80933
1494742
15
16.62684
32.06865 36.78620
4221866
18.29191 19.59863 21.01507 2255049 43.67199 50.81802
60.96527
60.92503 72.93901
14
16.09690 17.29342 18.59891
20.02359 21.57856 23.27597 25.12902 27.15211
29 36092 31.77248 37.27971
43.84241 51.65951
16 17.25786 18.63929 20.15688 21.82453 23.65749 25.67253 27.88805
30.32428
33.00340 35.94973 42.75328 50.98035
87.44213 138.10855 218.47220
17
18.43044 20.01207 21.76159 23.69751 25.84037 28.21288 30.84022
33.75023 36.97370 40.54470 48.88367 59.11760 71.67303 87.06804 105.93056 173.63568 285.01386
18 1961475 21.41231 23.41444 25.64541 28.13238 30.9O56S 33.99903
19 20.81090 2284056 25.11687 2767123 30.53900 3375999 37 37896
20 2201900 2429737 26.87037 29.7780e 33.06595 36 78559 40.99549
84.14072 103.74028 128.11667 218.04460 37151802
8 78.96923 98.60323 123.41353 154.74000 273.55576 483.97343
45.76196 51.16012 57.27500 72.05244 91.02493 115.37975 146 62797 186.68800 342.94470 630.16546
50.42292 56.76453 64.00250 81.69874 104.76842 13484051 174.02100 225.02560 429 68087 82021510
55.45676 6287334 71.4027S 92.50258 120.43600 157.41499 206.34479 271.03072 538. 10109 1067 27963
69.53194 79.54302 104.60289 13829704 183.60138 244.48685 326 23686 673.62636 1388.46351
37.45024
41.44626 46.01846 51.15909 63 43968
41.30134 45.59917 55.74971
68.39407
21 23.23919 25.78332 28.67649 31.96920 35.71925 39.99273 4486518
22 24.47159 27.29898 3053678 3424797 38.50521 43.39229 49.00574
23 25.71630 28.84496 32.45288 36.61789 41.43048 46.99583 53.43614 60.89330
24 26.97346 30.42186 34.42647 39.08260 44.50200 50.81558 58.17667
66.76476 76.78981 88.49733 118.15524 158.65862 213.97761 289.49448 392.48424 843.03295 1806.00257
73.1OS94 84.70090 98.34706 133.33387 181.87083 249 21402 34260349 471.9810e 1054.79118 2348.80334
79.95442 93.32398 109.18177 150.33393 208.33274 290.06827 405.27211 567.37730 1319.48898 3054.44434
87.35077 102.72313 121.09994 169.37401 238.49933 337.50239 479 22109 681.85276 1650.36123 3971.7764
25 28.24320 32.03030 36.45926
26 29 52563 33.67091 38.55304 4431174 51.11345 59.15638 68.67647
27 30.82009 35.34432 40.70963
28 32.12910 37.05121 4293092 4996758 58.40258 6852811 8069769
29 33.45039 38.79223 4521885 5296629 6232271 73.63980 8734653 103.96594 124.13536 148.63093 214.58275 312.09373 456 30322 66944745 984.06797 2580.93941 6714.60421
30 34.78489 40 56808 4757542 56.08494 66.43885 79.05819 94.46079 113.28321 136 30754 164.49402 241.33268 356 78685 53031173 79094799 1181.88157 3227.17427 8729.98548
41.64591
47.72710 54.86451 6324904
47.06421
54.66913 63.70577
74.48382
95.33883 112.96822 134.20994 190.699 272.88923 392.50277 S66.4809 81922331 2063.95153 S164.31093
1
1 –
(1+i)"
3.10
-
Present Value of an Annuity PVA :
=
i
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
0.95238
0.83333 0.80000
1.52778 1.44000
2.10648 1.95200
2.36160
268928
0.99010 0.98039 0.97087 0.96154 0.94340 0.93458 0.92593
0.91743 0.90909 0.89286 O.87719
0.86207
0.84746
0.76923
1.97040 1.94156
1.91347 1.88609 1.85941
1.83339
1.80802
1.78326 1.75911 1.73554 1.69005
1.64666 1.60523
1.56564
1.36095
2.88388
181611
2.16624
2.94099 2.77509
3.90197 3.80773 3.71710 3.62990
4.85343
5.79548 5.60143
2.82861
2.72325
2.67301
2.62432
2.57710
2.53129 2.48685 2.40183 2.32163 224589
2.17427
4.
331213
3.99271
4.62288
5.20637
5.74664
624689
6.71008
7.13896 6.80519
7.53608
3.23972
3.16987 3.03735
2.91371 279v818
2.58873
2.99061
3.32551
3.60459
3.83716
4.03097
4.19247
3.54595
3.46511
3.38721
2.69006
4.57971
4.45182
5.24214
4.21236
4.91732
5.58238
4.71346
43294
4.10020
3.88965 3.79079 3.60478
3.43306
3.27429
3.12717
2.43557
3.49760
3.81153
4.07757
4.30302
4.49409
2.64275
2.80211
6.
5.41719
5.07569
4.76654
4.48592 435526 4.11141
3.88867
3.68474
2.95142
6.00205
6.23028
701969
7.78611
5.78637
6.46321
7.10782
7.72173
8.30641
5.38929
5.97130
6.51523
7.02358
5.03295
5.53482 5.33493
5.99525 5.75902
4.86842 4.56376
4.28830
4.63886
3.16114
3.32891
3.46313 3.01900
3.57050
4.32706 3.65640
4.43922 3.72512
6.72819 6.47199
4.03857
7.32548
8.16224
7.65168
6.73274
6.20979
4.96764
4.34359
2.92470
7.43533
8.11090
8.76048
9.38507
8.56602
6.80169
5.32825
4.94637
4.60654
7.36009
4.83323
3.09154
3.14734
3.19026
3.22328
3.24867
10
9.47130 8.98259
8.53020
6.41766
6.14457 5.65022 5.21612
9.25262
9.95400
12.13374 11.34837 10.63496 9.98565 9.39357
6.49506 5.93770
6.81369 6.19437
5.45273 5.02864
5.66029
5.84236
6.00207
11
10.36763 9.78685
7.88687
7.49867
4.65601
11.25508 10.57534
7.16073
7 48690
4.79322
4.90951
5.00806
12
8.86325
8.38384
7.94269
5.19711
8.85268
9.29498
9.71225
14.71787 13.57771 12.56110O 11.65230 10.83777 10.10590
15.56225 14.29187 13.16612 12.16567 11.27407 10.47726
8.35765
8.74547
9.10791
7.10336 6.4235s
6.62817
13
7.90378
5.34233
4.53268
3.78010
14
13.00370 12.10625 11.29607 10.56312
9.89864
8.24424
7.78615 7.36669
4.61057
5.46753
6.14217 5.57546
3.82408
8.55948
8.85137
9.12164
9.37189
9.60360
9.81815
18.85698 17.01121 15.41502 14.02916 12.82115 11.76408 10.83553 10.01680
19.66038 17.65s80s 15.93692 14.45112 13.16300 12.04158 11.06124 10.20074
15
13.86505 12.84926 11.93794 11.11839 10.37966
8.06069 7.60608
6.81086
5.09158 4.67547
385926
3.26821
7.82371
8.54363 8.02155
8.75563 820141
16
9.44665
8.31256
6.97399
6.26506
5.66850
5.16235
4.72956
3.88741
3.28324
17
9.76322
7,11963
6.37286
4.77443
3.90993
5.74870
5.81785
5.22233
5.27316
3.29480
3.30369
3.31053
331579
3.31984
3.32296
3.32535
3.32719
16.39827 14.99203 13.75351 12.65930 11.68959 10.82760 10.05909
17.22601
6.46742
6.55037 5.87746
18
7.24967
4.81219 3.92794
4.84350 3.94235
4.86958 3.95388
4.89132 3.96311
4.90943 3.97049
4.92453 3.97639
19
15.67846 14.32380 13.13394 12.08532 11.15812 10.33560
8.95011
8.36492 736578
5.31624
5.35275
5.38368
5.40990
5.43212
5.45095
5.46691
6.11818 5.48043
6.62313 5.92884
6.68696
6.74294
20
18.04555 16.35143 14.87747 13.59033 12.46221 11.46992 10.59401
9.12855 8.51356
7.46944
21
8.64869
9.44243 8.77154
9.58021
9.70661
9.82258 9.07704
9.29224
7.56200
5.97314
6.01133
6.04425
22
4
7.64465
23
20.45582 18.29220 16.44361 14.85684 13.48857 12.30338 11.27219 1037106
8.88322 7.71843
6.79206
24
21.24339 18.91393 16.93554 15.24696 13.79864 12.55036 11.46933 10.52876
8.98474 7.78432
6.83514
6.07263
4.93710 3.98111
3.98489
4.95632 3.98791
4.96360 3.99033
4.96967 3.99226
4.97472 3.99381
4.97894 3.995os
25
22.02316 19.52346 1741315 15.62208 14.09394 12.78336 11.65358 10.67478
7.84314
6.87293
6.09709
4.94759
3.32861
3.32970
3.33054
26
22.79520 20.12104 1787684 15.98277 1437519 13.00317 11.82578 10.80998 9.92897
9.16095 7.89566
6.90608
923722
7.94255
6.13636
6.15204
5.50160
6.16555
5.50983
6.17720 5.51681
27
23.55961 20.70690 18.32703 16.32959 14.64303 13.21053 11.98671 10.93516 10.02658
6.93515
5.49189
28
29
9.30657 7.98442
9.36961 8.02181
9.42691
6.96066
6.98304
24.31644 21.28127 18.76411 16.66306 14.89813 13.40616 12.13711 11.05108 10.11613
3.33118
25.06579 21.84438 19.18845 16.98371 15.14107 13.59072 12.27767 11.15841 10.19828
3.33168
30
25.80771 2239646 19.60044 17.29203 15.37245 13.76483 12.40904 11.25778 10.27365
8.05518
7.00266
3.33206](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a5b89dc-5707-415c-80f3-ec8a6690e4e9%2F5e175518-07e1-4988-814d-85ea0e5daeb8%2Fhtx2izr_processed.png&w=3840&q=75)
Transcribed Image Text:3.9
Future Value of an Annuity FVA
:
(1+ i)" – 1
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
1.00000
2.03000
3.09090
4.18363
1.00000
2.
3.03010
4.06040
5.10101
6.15202
721354
1.00000
2.04000 0
3.12160
424646
5.30914 541632
ఉ
7.89829
921423
1,00000
2.08000 2.09000
3.27810
4.57313
1.00000
1.00000
2.02000
3.06040
4.12161
5.20404
1.00000
2.14000
3.43960
4.92114
661010
1.00000
2.05000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
2.10000
3.31000
2.06000
3.18360
437462
563709
6.97532
8.39384
207000
321490
4.43994
5.75074
220000
3.64000
5.36800
7.44160
9.92992
12.91590
16.49908
2.30000
3.99000
6.18700
9.04310
12.75603
17.58284
23.85769
2.01000
2.12000
2.16000
2.18000
225000
3.37440
477933
6.35205
8.11519
3.50560
5.06650
687714
3.57240
521543
7.15421
944197
3.15250
431013
324640
4.50611
5.86660
733593
4.64100
6.10510
7.71561
3.81250
5.76563
820703
11.25879
15.07349
5.52563
5.96471
6.30812
7.43428
8.58297
6.46841
7.66246
8.89234
6.80191
8.14201
9.54911
7.15329
8.65402
10.25980
7.52333
8.92280 920043 9.48717 10.08901
8.53552
10.73049
1323276
8.97748
11.41387
12.14152
15.32700
8.28567
9.89747
10.63663 11.02847
11.43589 12.29969
14.24009
19.84186
936853
10 10.46221 10.94972 11.46388
11.56683 12.16872
12.68250 13.41209
13
16.08535 17.51851
20.79890
25 80232
33 25290
4256613
54 20766
48.49660 68.75958 9762504
59.19592 86.94947 127.91255
72.03511 109.68684 167 28631
9.75463 10.15911 10.58280 11.02656
11.49132 11.97799
12.48756 13.02104 13.57948
14.77566
19.08585
32.01500
12.00611 12.57789 13.18079
13.48635 14.20679
15.02581 15.91713
1381645
15.78360
16.86994 1788845
17.71298 1888214 20.14064
14.48656 15.19293 15.93742 17.54874 1933730 21.32147 23.52131
16.64549 17.56029 18.53117 20.65458 23.04452 25.73290 28.75514
18.97713 20.14072 21.38428 24.13313 27 27075 3085017 34.93107
21.49530 22.95338 24.52271 28.02911
24.21492 26.01919 27.97498 32.39260 37 58107
42.61950
56.40535
25.95868
12.80780
14.19203
14.68033 15.61779
15.97394 17.08632
14.97164
32.15042
39.58050
11
12
743295
13.80933
1494742
15
16.62684
32.06865 36.78620
4221866
18.29191 19.59863 21.01507 2255049 43.67199 50.81802
60.96527
60.92503 72.93901
14
16.09690 17.29342 18.59891
20.02359 21.57856 23.27597 25.12902 27.15211
29 36092 31.77248 37.27971
43.84241 51.65951
16 17.25786 18.63929 20.15688 21.82453 23.65749 25.67253 27.88805
30.32428
33.00340 35.94973 42.75328 50.98035
87.44213 138.10855 218.47220
17
18.43044 20.01207 21.76159 23.69751 25.84037 28.21288 30.84022
33.75023 36.97370 40.54470 48.88367 59.11760 71.67303 87.06804 105.93056 173.63568 285.01386
18 1961475 21.41231 23.41444 25.64541 28.13238 30.9O56S 33.99903
19 20.81090 2284056 25.11687 2767123 30.53900 3375999 37 37896
20 2201900 2429737 26.87037 29.7780e 33.06595 36 78559 40.99549
84.14072 103.74028 128.11667 218.04460 37151802
8 78.96923 98.60323 123.41353 154.74000 273.55576 483.97343
45.76196 51.16012 57.27500 72.05244 91.02493 115.37975 146 62797 186.68800 342.94470 630.16546
50.42292 56.76453 64.00250 81.69874 104.76842 13484051 174.02100 225.02560 429 68087 82021510
55.45676 6287334 71.4027S 92.50258 120.43600 157.41499 206.34479 271.03072 538. 10109 1067 27963
69.53194 79.54302 104.60289 13829704 183.60138 244.48685 326 23686 673.62636 1388.46351
37.45024
41.44626 46.01846 51.15909 63 43968
41.30134 45.59917 55.74971
68.39407
21 23.23919 25.78332 28.67649 31.96920 35.71925 39.99273 4486518
22 24.47159 27.29898 3053678 3424797 38.50521 43.39229 49.00574
23 25.71630 28.84496 32.45288 36.61789 41.43048 46.99583 53.43614 60.89330
24 26.97346 30.42186 34.42647 39.08260 44.50200 50.81558 58.17667
66.76476 76.78981 88.49733 118.15524 158.65862 213.97761 289.49448 392.48424 843.03295 1806.00257
73.1OS94 84.70090 98.34706 133.33387 181.87083 249 21402 34260349 471.9810e 1054.79118 2348.80334
79.95442 93.32398 109.18177 150.33393 208.33274 290.06827 405.27211 567.37730 1319.48898 3054.44434
87.35077 102.72313 121.09994 169.37401 238.49933 337.50239 479 22109 681.85276 1650.36123 3971.7764
25 28.24320 32.03030 36.45926
26 29 52563 33.67091 38.55304 4431174 51.11345 59.15638 68.67647
27 30.82009 35.34432 40.70963
28 32.12910 37.05121 4293092 4996758 58.40258 6852811 8069769
29 33.45039 38.79223 4521885 5296629 6232271 73.63980 8734653 103.96594 124.13536 148.63093 214.58275 312.09373 456 30322 66944745 984.06797 2580.93941 6714.60421
30 34.78489 40 56808 4757542 56.08494 66.43885 79.05819 94.46079 113.28321 136 30754 164.49402 241.33268 356 78685 53031173 79094799 1181.88157 3227.17427 8729.98548
41.64591
47.72710 54.86451 6324904
47.06421
54.66913 63.70577
74.48382
95.33883 112.96822 134.20994 190.699 272.88923 392.50277 S66.4809 81922331 2063.95153 S164.31093
1
1 –
(1+i)"
3.10
-
Present Value of an Annuity PVA :
=
i
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
12%
14%
16%
18%
20%
25%
30%
0.95238
0.83333 0.80000
1.52778 1.44000
2.10648 1.95200
2.36160
268928
0.99010 0.98039 0.97087 0.96154 0.94340 0.93458 0.92593
0.91743 0.90909 0.89286 O.87719
0.86207
0.84746
0.76923
1.97040 1.94156
1.91347 1.88609 1.85941
1.83339
1.80802
1.78326 1.75911 1.73554 1.69005
1.64666 1.60523
1.56564
1.36095
2.88388
181611
2.16624
2.94099 2.77509
3.90197 3.80773 3.71710 3.62990
4.85343
5.79548 5.60143
2.82861
2.72325
2.67301
2.62432
2.57710
2.53129 2.48685 2.40183 2.32163 224589
2.17427
4.
331213
3.99271
4.62288
5.20637
5.74664
624689
6.71008
7.13896 6.80519
7.53608
3.23972
3.16987 3.03735
2.91371 279v818
2.58873
2.99061
3.32551
3.60459
3.83716
4.03097
4.19247
3.54595
3.46511
3.38721
2.69006
4.57971
4.45182
5.24214
4.21236
4.91732
5.58238
4.71346
43294
4.10020
3.88965 3.79079 3.60478
3.43306
3.27429
3.12717
2.43557
3.49760
3.81153
4.07757
4.30302
4.49409
2.64275
2.80211
6.
5.41719
5.07569
4.76654
4.48592 435526 4.11141
3.88867
3.68474
2.95142
6.00205
6.23028
701969
7.78611
5.78637
6.46321
7.10782
7.72173
8.30641
5.38929
5.97130
6.51523
7.02358
5.03295
5.53482 5.33493
5.99525 5.75902
4.86842 4.56376
4.28830
4.63886
3.16114
3.32891
3.46313 3.01900
3.57050
4.32706 3.65640
4.43922 3.72512
6.72819 6.47199
4.03857
7.32548
8.16224
7.65168
6.73274
6.20979
4.96764
4.34359
2.92470
7.43533
8.11090
8.76048
9.38507
8.56602
6.80169
5.32825
4.94637
4.60654
7.36009
4.83323
3.09154
3.14734
3.19026
3.22328
3.24867
10
9.47130 8.98259
8.53020
6.41766
6.14457 5.65022 5.21612
9.25262
9.95400
12.13374 11.34837 10.63496 9.98565 9.39357
6.49506 5.93770
6.81369 6.19437
5.45273 5.02864
5.66029
5.84236
6.00207
11
10.36763 9.78685
7.88687
7.49867
4.65601
11.25508 10.57534
7.16073
7 48690
4.79322
4.90951
5.00806
12
8.86325
8.38384
7.94269
5.19711
8.85268
9.29498
9.71225
14.71787 13.57771 12.56110O 11.65230 10.83777 10.10590
15.56225 14.29187 13.16612 12.16567 11.27407 10.47726
8.35765
8.74547
9.10791
7.10336 6.4235s
6.62817
13
7.90378
5.34233
4.53268
3.78010
14
13.00370 12.10625 11.29607 10.56312
9.89864
8.24424
7.78615 7.36669
4.61057
5.46753
6.14217 5.57546
3.82408
8.55948
8.85137
9.12164
9.37189
9.60360
9.81815
18.85698 17.01121 15.41502 14.02916 12.82115 11.76408 10.83553 10.01680
19.66038 17.65s80s 15.93692 14.45112 13.16300 12.04158 11.06124 10.20074
15
13.86505 12.84926 11.93794 11.11839 10.37966
8.06069 7.60608
6.81086
5.09158 4.67547
385926
3.26821
7.82371
8.54363 8.02155
8.75563 820141
16
9.44665
8.31256
6.97399
6.26506
5.66850
5.16235
4.72956
3.88741
3.28324
17
9.76322
7,11963
6.37286
4.77443
3.90993
5.74870
5.81785
5.22233
5.27316
3.29480
3.30369
3.31053
331579
3.31984
3.32296
3.32535
3.32719
16.39827 14.99203 13.75351 12.65930 11.68959 10.82760 10.05909
17.22601
6.46742
6.55037 5.87746
18
7.24967
4.81219 3.92794
4.84350 3.94235
4.86958 3.95388
4.89132 3.96311
4.90943 3.97049
4.92453 3.97639
19
15.67846 14.32380 13.13394 12.08532 11.15812 10.33560
8.95011
8.36492 736578
5.31624
5.35275
5.38368
5.40990
5.43212
5.45095
5.46691
6.11818 5.48043
6.62313 5.92884
6.68696
6.74294
20
18.04555 16.35143 14.87747 13.59033 12.46221 11.46992 10.59401
9.12855 8.51356
7.46944
21
8.64869
9.44243 8.77154
9.58021
9.70661
9.82258 9.07704
9.29224
7.56200
5.97314
6.01133
6.04425
22
4
7.64465
23
20.45582 18.29220 16.44361 14.85684 13.48857 12.30338 11.27219 1037106
8.88322 7.71843
6.79206
24
21.24339 18.91393 16.93554 15.24696 13.79864 12.55036 11.46933 10.52876
8.98474 7.78432
6.83514
6.07263
4.93710 3.98111
3.98489
4.95632 3.98791
4.96360 3.99033
4.96967 3.99226
4.97472 3.99381
4.97894 3.995os
25
22.02316 19.52346 1741315 15.62208 14.09394 12.78336 11.65358 10.67478
7.84314
6.87293
6.09709
4.94759
3.32861
3.32970
3.33054
26
22.79520 20.12104 1787684 15.98277 1437519 13.00317 11.82578 10.80998 9.92897
9.16095 7.89566
6.90608
923722
7.94255
6.13636
6.15204
5.50160
6.16555
5.50983
6.17720 5.51681
27
23.55961 20.70690 18.32703 16.32959 14.64303 13.21053 11.98671 10.93516 10.02658
6.93515
5.49189
28
29
9.30657 7.98442
9.36961 8.02181
9.42691
6.96066
6.98304
24.31644 21.28127 18.76411 16.66306 14.89813 13.40616 12.13711 11.05108 10.11613
3.33118
25.06579 21.84438 19.18845 16.98371 15.14107 13.59072 12.27767 11.15841 10.19828
3.33168
30
25.80771 2239646 19.60044 17.29203 15.37245 13.76483 12.40904 11.25778 10.27365
8.05518
7.00266
3.33206
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