APPENDICES
APPENDICES TABLE 1(a) Compound Interest Annual Compounding No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
(1 + i)n 14% per Annum i = 0.14 1.14 1.2996 1.48154 1.68896 1.92541 2.19497 2.50227 2.85258 3.25194 3.70722 4.22622 4.8179 5.4924 6.26,133 7.13792 8.13723 9.27644 10.5751 12.0557 12.7435
10% per Annum i = 0.10 1.1 1.21 1.331 1.4641 1.61051 1.77156 1.94872 2.14359 2.35795 2.59374 2.85312 3.13843 3.45227 3.7975 4.17725 4.59497 5.05447 5.55992 6.11591 6.7275
18% per Annum i = 0.18 1.18 1.3924 1.64303 1.93878 2.28776 2.69955 3.18547 3.75886 4.43546 5.23384 6.17593 7.28759 8.59936 10.1472 11.9738 14.129 16.6723 19.6733 23.2144 27.393
TABLE 1(b) Present Value of Re. 1 Annual Compounding No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10% per Annum .909091 .826446 .751315 .683014 .620921 .564474 .513158 .466507 .424098 .385543 .350494 .318631 .289664 .263331 .239392 .217629 .197845 .179859 .163508 .148644
STATISTICS
Copyright -The Institute of Chartered Accountants of India
(1 + i)–n 14% per Annum .877193 .769468 .674972 .592081 .519369 .455587 .399638 .35056 .307508 .269744 .236618 .20756 .18207 .15971 .140097 .122892 .1078 .0945614 .0829486 0.72762
18% per Annum .847458 .718184 .608631 .515789 .437109 .370432 .313925 .266038 .225456 .191064 .161919 .137219 .116288 .0985489 .083516 .0707763 .0599799 .0508304 .0430766 .0365056
A.1
APPENDICES TABLE 2(a) Present Value of an Annuity Annual Compounding No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
10% per Annum P(n, i) 1/P(n, i)
14% per Annum P(n, i) 1/P(n, i)
18% per Annum P(n, i) 1/P(n, i)
.909091 1.73554 2.48685 3.16987 3.79079 4.35526 4.86842 5.33493 5.75902 6.14457 6.49506 6.81369 7.10336 7.36669 7.60608 7.82371 8.02155 8.20141 8.36492
1.1 .576191 .402115 .315471 .263798 .229607 .205406 .187444 .173641 .162745 .153963 .146763 .140779 .135746 .131474 .127817 .124664 .12193 .119547
.877192 1.64666 2.32163 2.91371 3.43308 3.88867 4.2883 4.63886 4.94637 5.21611 5.45273 5.66029 5.84236 6.00207 6.14217 6.26506 6.37286 6.46742 6.55037
1.14 .60729 .430732 .343205 .291284 .257158 .233193 .21557 .202169 .191714 .183394 .176669 .171164 .166609 .162809 .159615 .156915 .154621 .152663
.847458 1.56564 2.17427 2.69006 3.12717 3.4976 3.81153 4.07757 4.30302 4.49409 4.65601 4.79323 4.90951 5.00806 5.09158 5.16236 5.22233 5.27316 5.31624
1.18 .638716 .459924 .371739 .319778 .28591 .262362 .245244 .232395 .222515 .214776 .208628 .203686 .199678 .196403 .19371 .191485 .189639 .188103
20
8.51356
.11746
6.62313
.150986
5.35275
.18682
TABLE 2(b) Amount of an Annuity Annual Computing No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10% per Annum A(n, i) 1/A(n, i) 1,000000 2.100000 3.310000 4,641000 6.105100 7.71561006 9,48717108 11.4358882 13.579477 15.9374248 18.5311672 21.384284 24.5227124 27.9749837 31.772482 35.9497303 40.5447033 45.5991737 51.1590911 57.274999
.999999994 .476190473 .302114802 .215470802 .16379748 .129607379 .105405499 .0874440168 0.736405385 .0627453949 0.539631415 .0467633146 .0407785234 .0357462229 .0314737765 .0278166204 .0246641341 .021930222 .019546868 .0174596250
14% per Annum A(n, i) 1/A(n, i) 1.00000001 2.14000001 3.43960003 4.92114404 6.61010421 8.53551881 10.7304915 13.2327603 16.0853467 19.3372953 23.0445166 27.270749 32.0886539 37.5810655 43.8424147 50.9803528 59.1176022 68.3940666 78.969236 91.0249291
A.2
Copyright -The Institute of Chartered Accountants of India
999999993 .467289717 .290731478 .203204782 .151283545 .117157495 .0931923765 0.755700232 .0621683833 0.517135403 .043394271 .0366693265 .0311636631 .0266091445 .0228089627 .0196153998 .0169154357 .0146211514 .0126631591 .0109860014
18% per Annum A(n, i) 1/A(n, i) 1 2.18000001 3.57240001 5.21543202 7.15420979 9.44196755 12.1415217 15.3269956 19.0858549 23.5213088 28.7551443 34.9310704 42.218663 50.8180224 60.9652664 72.9390144 87.0680371 103.740284 123.413535 146.627971
.999999996 .458715595 .27992386 .19173867 .139777841 .105910129 .082361999 .0652443586 .0523948237 .0425146411 .034776386 .0286278087 .0236862072 0.196780582 .0164027824 .0137100838 .011485271 .00963945696 .00810283897 .00681998115
COMMON PROFICIENCY TEST
TABLE 3 Future Value and Present Value i= n
(1 + i)n
1 4
%
i = rate of interest per period, n = number of periods 1 i= % 2 (1 + i)–n
(1 + i)n
(1 + i)–n
i= (1 + i)n
3 4
% (1 + i)–n
1 2 3 4 5
1.0025 1.0050 1.0075 1.0100 1.0125
0000 0625 1877 3756 6266
0.9975 0.9950 0.9925 0.9900 0.9875
0623 1869 3734 6219 9321
1.0050 1.0100 1.0150 1.0201 1.0252
0000 2500 7513 5050 5125
0.9950 0.9900 0.9851 0.9802 0.9753
2488 7450 4876 4752 7067
1.0075 1.0150 1.0226 1.0303 1.0380
0000 5625 6917 3919 6673
0.9925 0.9851 0.9778 0.9705 0.9633
5583 6708 3333 5417 2920
6 7 8 9 10
1.0150 1.0176 1.0201 1.0227 1.0252
9406 3180 7588 2632 8313
0.9851 0.9826 0.9802 0.9777 0.9753
3038 7370 2314 7869 4034
1.0303 1.0355 1.0407 1.0459 1.0511
7751 2940 0704 1058 4013
0.9705 0.9656 0.9608 0.9561 0.9513
1808 8963 8520 0468 4794
1.0458 1.0536 1.0615 1.0695 1.0775
5224 9613 9885 6084 8255
0.9561 0.9490 0.9419 0.9349 0.9280
5802 4022 7540 6318 0315
11 12 13 14 15
1.0278 1.0304 1.0329 1.0355 1.0381
4634 1596 9200 7448 6341
0.9729 0.9704 0.9680 0.9656 0.9632
0807 8187 6171 4759 3949
1.0563 1.0616 1.0669 1.0723 1.0776
9583 7781 8620 2113 8274
0.9466 0.9419 0.9372 0.9325 0.9279
1487 0534 1924 5646 1688
1.0856 1.0938 1.1020 1.1102 1.1186
6441 0690 1045 7553 0259
0.9210 0.9142 0.9074 0.9006 0.8939
9494 3815 3241 7733 7254
16 17 18 19 20
1.0407 1.0433 1.0459 1.0485 1.0512
5882 6072 6912 8404 0550
0.9608 0.9584 0.9560 0.9536 0.9512
3740 4130 5117 6700 8878
1.0830 1.0884 1.0939 1.0993 1.1048
7115 8651 2894 9858 9558
0.9233 0.9187 0.9141 0.9095 0.9050
0037 0684 3616 8822 6290
1.1269 1.1354 1.1439 1.1525 1.1611
9211 4455 6039 4009 8414
0.8873 0.8307 0.8741 0.8676 0.8611
1766 1231 5614 4878 8985
21 22 23 24 25
1.0538 1.0564 1.0591 1.0617 1.0644
3352 6810 0927 5704 1144
0.9489 0.9465 0.9441 0.9418 0.9394
1649 5011 8964 3505 8634
1.1104 1.1159 1.1215 1.1271 1.1327
2006 7216 5202 5978 9558
0.9005 0.8960 0.8916 0.8871 0.8827
6010 7971 2160 8567 7181
1.1698 1.1786 1.1875 1.1964 1.2053
9302 6722 0723 1353 8663
0.8547 0.8484 0.8421 0.8358 0.8296
7901 1589 0014 3140 0933
26 27 28 29 30
1.0670 1.0697 1.0724 1.0750 1.0777
7247 4015 1450 9553 8327
0.9371 0.9348 0.9324 0.9301 0.9278
4348 0646 7527 4990 3032
1.1384 1.1441 1.1498 1.1556 1.1614
5955 5185 7261 2197 0008
0.8783 0.8740 0.8696 0.8653 0.8610
7991 0986 6155 3488 2973
1.2144 1.2235 1.2327 1.2419 1.2512
2703 3523 1175 5709 7176
0.8234 0.8173 0.8112 0.8051 0.7991
3358 0380 1966 8080 8690
31 32 33 34 35
1.0804 1.0831 1.0858 1.0886 1.0913
7773 7892 8687 0159 2309
0.9255 0.9232 0.9209 0.9186 0.9163
1653 0851 0624 0972 1892
1.1672 1.1730 1.1789 1.1848 1.1907
0708 4312 0833 0288 2689
0.8567 0.8524 0.8482 0.8440 0.8398
4600 8358 4237 2226 2314
1.2606 1.2701 1.2796 1.2892 1.2989
5630 1122 3706 3434 0359
0.7932 0.7873 0.7814 0.7756 0.7698
3762 3262 7158 5418 8008
36 37 38 39 40
1.0940 1.0967 1.0995 1.1022 1.1050
5140 8653 2850 7732 3301
0.9140 0.9117 0.9094 0.9072 0.9049
3384 5445 8075 1272 5034
1.1966 1.2026 1.2086 1.2147 1.2207
8052 6393 7725 2063 9424
0.8356 0.8314 0.8273 0.8232 0.8191
4492 8748 5073 3455 3886
1.3086 1.3184 1.3283 1.3383 1.3483
4537 6021 4866 1128 4861
0.7641 0.7584 0.7528 0.7472 0.7416
4896 6051 1440 1032 4796
41 42 43 44 45
1.1077 1.1105 1.1133 1.1161 1.1189
9559 6508 4149 2485 1516
0.9026 0.9004 0.8981 0.8959 0.8937
9361 4250 9701 5712 2281
1.2268 1.2330 1.2391 1.2453 1.2516
9821 3270 9786 9385 2082
0.8150 0.8110 0.8069 0.8029 0.7989
6354 0850 7363 5884 6402
1.3584 1.3686 1.3789 1.3892 1.3996
6123 4969 1456 5642 7584
0.7361 0.7306 0.7252 0.7198 0.7144
2701 4716 0809 0952 5114
46 47 48 49 50
1.1217 1.1245 1.1273 1.1301 1.1329
1245 1673 2802 4634 7171
0.8914 0.8892 0.8870 0.8848 0.8826
9407 7090 5326 4116 3457
1.2578 1.2641 1.2704 1.2768 1.2832
7892 6832 8916 4161 2581
0.7949 0.7910 0.7870 0.7831 0.7792
8907 3390 9841 8250 8607
1.4101 1.4207 1.4314 1.4421 1.4529
7341 4971 0533 4087 5693
0.7091 0.7038 0.6986 0.6934 0.6882
3264 5374 1414 1353 5165
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.3
APPENDICES i =1
i =1% n
(1 + i)n
(1 + i)–n
(1 + i)n
1 4
i =1
% (1 + i)–n
(1 + i)n
1 2
% (1 + i)–n
1 2 3 4 5
1.0100 1.0201 1.0303 1.0406 1.0510
0000 0000 0100 0401 1005
0.9900 0.9802 0.9705 0.9609 0.9514
9901 9605 9015 8034 6569
1.0125 1.0251 1.0379 1.0509 1.0640
0000 5625 7070 4534 8215
0.9876 0.9754 0.9634 0.9515 0.9397
5432 6106 1833 2428 7706
1.0150 1.0302 1.0456 1.0613 1.0772
0000 2500 7838 6355 8400
0.9852 0.9706 0.9563 0.9421 0.9282
2167 6175 1699 8423 6033
6 7 8 9 10
1.0615 1.0721 1.0828 1.0936 1.1046
2015 3535 5671 8527 2213
0.9420 0.9327 0.9234 0.9143 0.9052
4524 1805 8322 3982 8695
1.0773 1.0908 1.1044 1.1182 1.1322
8318 5047 8610 9218 7083
0.9281 0.9167 0.9053 0.8942 0.8831
7488 1593 9845 2069 8093
1.0934 1.1098 1.1264 1.1433 1.1605
4326 4491 9259 8998 4083
0.9145 0.9010 0.8877 0.8745 0.8616
4219 2679 1112 9224 6723
11 12 13 14 15
1,1156 1.1268 1.1380 1.1494 1.1609
6835 2503 9328 7421 6896
0.8963 0.8874 0.8786 0.8699 0.8613
2372 4923 6260 6297 4947
1,1464 1.1607 1.1752 1.1899 1.2048
2422 5452 6395 5475 2918
0.8722 0.8615 0.8508 0.8403 0.8299
7746 0860 7269 6809 9318
1.1779 1.1956 1.2135 1.2317 1.2502
4894 1817 5244 5573 3207
0.8489 0.8363 0.8240 0.8118 0.7998
3323 8742 2702 4928 5150
16 17 18 19 20
1.1725 1.1843 1.1961 1.2081 1.2201
7864 0443 4748 0895 9004
0.8528 0.8443 0.8360 0.8277 0.8195
2126 7749 1731 3992 4447
1.2198 1.2351 1.2505 1.2662 1.2820
8955 3817 7739 0961 3723
0.8197 0.8096 0.7996 0.7897 0.7800
4635 2602 3064 5866 0855
1.2689 1.2880 1.3073 1.3269 1.3468
8555 2033 4064 5075 5501
0.7880 0.7763 0.7649 0.7536 0.7424
3104 8526 1159 0747 7042
21 22 23 24 25
1.2323 1.2447 1.2571 1.2697 1.2824
9194 1586 6302 3465 3200
0.8114 0.8033 0.7954 0.7875 0.7797
3017 9621 4179 6613 6844
1.2980 1.3142 1.3307 1.3473 1.3641
6270 8848 1709 5105 9294
0.7703 0.7608 0.7514 0.7421 0.7330
7881 6796 7453 9707 3414
1.3670 1.3875 1.4083 1.4295 1.4509
5783 6370 7715 0281 4535
0.7314 0.7206 0.7100 0.6995 0.6892
9795 8763 3708 4392 0583
26 27 28 29 30
1.2952 1.3082 1.3212 1.3345 1.3478
5631 0888 9097 0388 4892
0.7720 0.7644 0.7568 0.7493 0.7419
4796 0392 3557 4215 2292
1.3812 1.3985 1.4159 1.4336 1.4516
4535 1092 9230 9221 1336
0.7239 0.7150 0.7062 0.6974 0.6888
8434 4626 1853 9978 8867
1.4727 1.4948 1.5172 1.5399 1.5630
0953 0018 2218 8051 8022
0.6790 0.6689 0.6590 0.6493 0.6397
2052 8574 9925 5887 6243
31 32 33 34 35
1.3613 1.3749 1.3886 1.4025 1.4166
2740 4068 9009 7699 0276
0.7345 0.7273 0.7201 0.7129 0.7059
7715 0411 0307 7334 1420
1.4697 1.4881 1.5067 1.5255 1.5446
5853 3051 3214 6629 3587
0.6803 0.6719 0.6636 0.6554 0.6474
8387 8407 8797 9429 0177
1.5865 1.6103 1.6344 1.6589 1.6838
2642 2432 7918 9637 8132
0.6303 0.6209 0.6118 0.6027 0.5938
0781 9292 1568 7407 6608
36 37 38 39 40
1.4307 1.4450 1.4595 1.4741 1.4888
6878 7647 2724 2251 6373
0.6989 0.6920 0.6851 0.6783 0.6716
2495 0490 5337 6967 5314
1.5639 4382 1.5834 9312 1.6032 8678 16233 2787 1.6436 1946
0.6394 0916 0.6315 1522 0.6237 1873 06160 1850 0.6084 1334
1.7091 1.7347 1.7607 1.7872 1.8140
3954 7663 9828 1025 1841
0.5850 0.5764 0.5679 0.5595 0.5512
8974 4309 2423 3126 6232
41 42 43 44 45
1.5037 1.5187 1.5339 1.5493 1.5648
5237 8989 7779 1757 1075
0.6650 0.6584 0.6518 0.6454 0.6390
0311 1892 9992 4546 5492
1.6641 1.6849 1.7060 1.7273 1.7489
6471 6677 2885 5421 4614
0.6009 0.5934 0.5861 0.5789 0.5717
0206 8352 5656 2006 7290
1.8412 1.8688 1.8968 1.9253 1.9542
2868 4712 7982 3302 1301
0.5431 0.5350 0.5271 0.5193 0.5117
1559 8925 8153 9067 1494
46 47 48 49 50
1.5804 1.5962 1.6122 1.6283 1.6446
5885 6344 2608 4834 3182
0.6327 0.6264 0.6202 0.6141 0.6080
2764 6301 6041 1921 3882
1.7708 1.7929 1.8153 1.8380 1.8610
0797 4306 5485 4679 2237
0.5647 0.5577 0.5508 0.5440 0.5373
1397 4219 5649 5579 3905
1.9835 2.0132 2.0434 2.0741 2.1052
2621 7910 7829 3046 4242
0.5041 0.4967 0.4893 0.4821 0.4750
5265 0212 6170 2975 0468
A.4
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
3 i=1 % 4 n
(1 + i)n
1 i=2 % 4
i = 2% (1 + i)–n
(1 + i)n
(1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0175 1.0353 1.0534 1.0718 1.0906
0000 0625 2411 5903 1656
0.9828 0.9658 0.9492 0.9329 0.9169
0098 9777 8528 5851 1254
1.0200 1.0404 1.0612 1.0824 1.1040
0000 0000 0800 3216 8080
0.9803 0.9611 0.9423 0.9238 0.9057
9216 6878 2233 4543 3081
1.0225 1.0455 1.0690 1.0930 1.1176
0000 0625 3014 8332 7769
0.9779 0.9564 0.9354 0.9148 0.8947
9511 7444 2732 4335 1232
6 7 8 9 10
1.1097 1.1291 1.1488 1.1689 1.1894
0235 2215 8178 8721 4449
0.9011 0.8856 0.8704 0.8554 0.8407
4254 4378 1157 4135 2860
1.1261 1.1486 1.1716 1.1950 1.2189
6242 8567 5938 9257 9442
0.8879 0.8705 0.8534 0.8367 0.8203
7138 6018 9037 5527 4830
1.1428 1.1685 1.1948 1.2217 1.2492
2544 3901 3114 1484 0343
0.8750 0.8557 0.8369 0.8185 0.8005
2427 6946 3835 2161 1013
11 12 13 14 15
1.2102 1.2314 1.2529 1.2749 1.2972
5977 3931 8950 1682 2786
0.8262 0.8120 0.7980 0.7843 0.7708
6889 5788 9128 6490 7459
1.2433 1.2682 1.2936 1.3194 1.3458
7431 4179 0663 7876 6834
0.8042 0.7884 0.7730 0.7578 0.7430
6304 9318 3253 7502 1473
1.2773 1.3060 1.3354 1.3654 1.3962
1050 4999 3611 8343 0680
0.7828 0.7656 0.7488 0.7323 0.7162
9499 6748 1905 4137 2628
16 17 18 19 20
1.3199 1.3430 1.3665 1.3904 1.4147
2935 2811 3111 4540 7820
0.7576 0.7445 0.7317 0.7191 0.7068
1631 8605 7990 9401 2458
1.3727 1.4002 1.4282 1.4568 1.4859
8571 4142 4625 1117 4740
0.7284 0.7141 0.7001 0.6864 0.6729
4581 6256 5937 3076 7133
1.4276 1.4597 1.4925 1.5261 1.5605
2146 4294 8716 7037 0920
0.7004 0.6850 0.6699 0.6552 0.6408
6580 5212 7763 3484 1647
21 22 23 24 25
1.4395 1.4647 1.4903 1.5164 1.5429
3681 2871 6146 4279 8054
0.6946 0.6827 0.6709 0.6594 0.6480
6789 2028 7817 3800 9632
1.5156 1.5459 1.5768 1.6084 1.6406
6634 7967 9926 3725 0599
0.6597 0.6468 0.6341 0.6217 0.6095
7582 3904 5592 2149 3087
1.5956 1.6315 1.6682 1.7057 1.7441
2066 2212 3137 6658 4632
0.6267 0.6129 0.5994 0.5862 0.5733
1538 2457 3724 4668 4639
26 27 28 29 30
1.5699 1.5974 1.6254 1.6538 1.6828
8269 5739 1290 5762 0013
0.6369 0.6259 0.6152 0.6046 0.5942
4970 9479 2829 4697 4764
1.6734 1.7068 1.7410 1.7758 1.8113
1811 8648 2421 4469 6158
0.5975 0.5858 0.5743 0.5631 0.5520
7928 6204 7455 1231 7089
1.7833 1.8235 1.8645 1.9064 1.9493
8962 1588 4499 9725 9344
0.5607 0.5483 0.5363 0.5245 0.5129
2997 9117 2388 2213 8008
31 32 33 34 35
1.7122 1.7422 1.7727 1,8037 1.8352
4913 1349 0223 2452 8970
0.5840 0.5739 0.5641 0.5544 0.5448
2716 8247 1053 0839 7311
1.8475 1.8845 1.9222 1.9606 1.9998
8882 4059 3140 7603 8955
0.5412 0.5306 0.5205 0.5100 0.5000
4597 3330 2873 2817 2761
1.9932 2.0381 2.0839 2.1308 2.1787
5479 0303 6034 4945 9356
0.5016 0.4906 0.4798 0.4692 0.4589
9201 5233 5558 9641 6960
36 37 38 39 40
1.8674 1.9000 1.9333 1.9671 2.0015
0727 8689 3841 7184 9734
0.5355 0.5262 0.5172 0.5083 0.4996
0183 9172 4002 4400 0098
2.0398 2.0806 2.1222 2.1647 2.2080
8734 8509 9879 4477 3966
0.4902 0.4806 0.4711 0.4619 0.4528
2315 1093 8719 4822 9042
2.2278 2.2779 2.3291 2.3816 2.4351
1642 4229 9599 0290 8897
0.4488 0.4389 0.4293 0.4198 0.4106
7002 9268 3270 8528 4575
41 42 43 44 45
2.0366 2.0722 2.1085 2.1454 2.1829
2530 6624 3090 3019 7522
0.4910 0.4825 0.4742 0.4661 0.4580
0834 6348 6386 0699 9040
2.2522 2.2972 2.3431 2.3900 2.4378
0046 4447 8936 5314 5421
0.4440 0.4353 0.4267 0.4184 0.4101
1021 0413 6875 0074 9680
2.4899 2.5460 2.6032 2.6618 2.7217
8072 0528 9040 6444 5639
0.4016 0.3927 0.3841 0.3756 0.3674
0954 7216 2925 7653 0981
46 47 48 49 50
2.2211 2.2600 2.2995 2.3398 2.3807
7728 4789 9872 4170 8893
0.4502 0.4424 0.4348 0.4273 0.4200
1170 6850 5848 7934 2883
2.4866 2.5363 2.5870 2.6388 2.6915
1129 4352 7039 1179 8803
0.4021 0.3942 0.3865 0.3789 0.3715
5373 6836 3761 5844 2788
2.7829 2.8456 2.9096 2.9751 3.0420
9590 1331 3961 0650 4640
0.3593 0.3514 0.3436 0.3361 0.3287
2500 1809 8518 2242 2608
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.5
APPENDICES i=2 n
(1 + i)n
1 2
1 i=3 % 2
i = 3%
% (1 + i)–n
(1 + i)n
(1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0250 1.0506 1.0768 1.1038 1.1314
0000 2500 9063 1289 0821
0.9756 0.9518 0.9285 0.9059 0.8838
0976 1440 9941 5064 5429
1.0300 1.0609 1.0927 1.1255 1.1592
0000 0000 2700 0881 7407
0.9708 0.9425 0.9151 0.8884 0.8626
7379 9591 4166 8705 0878
1.0350 1.0712 1.1087 1.1475 1.1876
0000 2500 1788 2300 8631
0.9661 0.9335 0.9019 0.8714 0.8419
8357 1070 4271 4223 7317
6 7 8 9 10
1.1596 1.1886 1.2184 1.2488 1.2800
9342 8575 0290 6297 8454
0.8622 0.8412 0.8207 0.8007 0.7811
9687 6524 4657 2836 9840
1.1940 1.2298 1.2667 1.3047 1.3439
5230 7387 7008 7318 1638
0.8374 0.8130 0.7894 0.7664 0.7440
8426 9151 0923 1673 9391
1.2292 1.2722 1.3168 1.3628 1.4105
5533 7926 0904 9735 9876
0.8135 0.7859 0.7594 0.7337 0.7089
0064 9096 1156 3097 1881
11 12 13 14 15
1.3120 1.3448 1.3785 1.4129 1.4482
8666 8882 1104 7382 9817
0.7621 0.7435 0.7254 0.7077 0.6904
4478 5589 2038 2720 6556
1.3842 1.4257 1.4685 1.5125 1.5579
3387 6089 3371 8972 6742
0.7224 0.7013 0.6809 0.6611 0.6418
2128 7988 5134 1781 6195
1.4599 1.5110 1.5639 1.6186 1.6753
6972 6866 5606 9452 4883
0.6849 0.6617 0.6394 0.6177 0.5968
4571 8330 0415 8179 9062
16 17 18 19 20
1.4845 1.5216 1.5596 1.5986 1.6386
0562 1826 5872 5019 1644
0.6736 0.6571 0.6411 0.6255 0.6102
2493 9506 6591 2772 7094
1.6047 1.6528 1.7024 1.7535 1.8061
0644 4763 3306 0605 1123
0.6231 0.6050 0.5873 0.5702 0.5536
6694 1645 9461 8603 7575
1.7339 1.7946 1.8574 1.9225 1.9897
8604 7555 8920 0132 8886
0.5767 0.5572 0.5383 0.5201 0.5025
0591 0378 6114 5569 6588
21 22 23 24 25
1.6795 1,7215 1.7646 1.8087 1.8539
8185 7140 1068 2595 4410
0.5953 0.5808 0.5666 0.5528 0.5393
8629 6467 9724 7535 9059
1.8602 1,9161 1.9735 2.0327 2.0937
9457 0341 8651 9411 7793
0.5375 0.5218 0.5066 0.4919 0.4776
4928 9250 9175 3374 0557
2.0594 2,1315 2.2061 2.2833 2.3632
3147 1158 1448 2849 4498
0.4855 0.4691 0.4532 0.4379 0.4231
7090 5063 8563 5713 4699
26 27 28 29 30
1.9002 1.9478 1.9964 2.0464 2.0975
9270 0002 9502 0739 6758
0.5262 0.5133 0.5008 0.4886 0.4767
3472 9973 7778 6125 4269
2.1565 2.2212 2.2879 2.3565 2.4272
9127 8901 2768 6551 6247
0.4636 0.4501 0.4370 0.4243 0.4119
9473 8906 7675 4636 8676
2.4459 2.5315 2.6201 2.7118 2.8067
5856 6711 7196 7798 9370
0.4088 0.3950 0.3816 0.3687 0.3562
3767 1224 5434 4815 7841
31 32 33 34 35
2.1500 2.2037 2.2588 2.3153 2.3732
0677 5694 5086 2213 0519
0.4651 0.4537 0.4427 0.4319 0.4213
1481 7055 0298 0534 7107
2.5000 2.5750 2.6523 2.7319 2.8138
8035 8276 3524 0530 6245
0.3999 0.3883 0.3770 0.3660 0.3553
8715 3703 2625 4490 8340
2.9050 3.0067 3.1119 3.2208 3.3335
3148 0759 4235 6033 9045
0.3442 0.3325 0.3213 0.3104 0.2999
3035 8971 4271 7605 7686
36 37 38 39 40
2.4325 2.4933 2.5556 2.6195 2.6850
3532 4870 8242 7448 6384
0.4110 0.4010 0.3912 0.3817 0.3724
9372 6705 8492 4139 3062
2.8982 2.9852 3.0747 3.1670 3.2620
7833 2668 8348 2698 3779
0.3450 0.3349 0.3252 0.3157 0.3065
3243 8294 2615 5355 5684
3.4502 3.5710 3.6960 3.8253 3.9592
6611 2543 1132 7171 5972
0.2898 0.2800 0.2705 0.2614 0.2525
3272 3161 6194 1250 7247
41 42 43 44 45
2.7521 2.8209 2.8915 2.9638 3.0379
9043 9520 2008 0808 0328
0.3633 4695 0.3544 8483 0.3458 3886 03374 0376 0.3291 7440
3.3598 3.4606 3.5645 3.6714 3.7815
9893 9589 1677 5227 9584
0.2976 0.2889 0.2805 0.2723 0.2644
2800 5922 4294 7178 3862
4.0978 4.2412 4.3897 4.5433 4.7023
3381 5799 0202 4160 5855
0.2440 0.2357 0.2278 0.2201 0.2126
3137 7910 0590 0231 5924
46 47 48 49 50
3.1138 3.1916 3.2714 3.3532 3.4371
5086 9713 8956 7680 0872
0.3211 0.3133 0.3056 0.2982 0.2909
3.8950 4.0118 4.1322 4.2562 4.3839
4372 9503 5188 1944 0602
0.2567 0.2492 0.2419 0.2349 0.2281
3653 5876 9880 5029 0708
4.8669 5.0372 5.2135 5.3960 5.5849
4110 8404 8898 6459 2686
0.2054 0.1985 0.1918 0.1853 0.1790
6787 1968 0645 2024 5337
4576 1294 7116 1576 4221
A.6
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
1 i=4 % 2
i = 4% n
(1 + i)n
(1 + i)–n
(1 + i)n
i = 5% (1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0400 1.0816 1.1248 1.1698 1.2166
0000 0000 6400 5856 5290
0.9615 0.9245 0.8889 0.8548 0.8219
3846 5621 9636 0419 2711
1.0450 1.0920 1.1411 1.1925 1.2461
0000 2500 6613 1860 8194
0.9569 0.9157 0.8762 0.8382 0.8024
3780 2995 9660 6134 5105
1.0500 1.1025 1.1576 1.2155 1.2762
0000 0000 2500 0625 8156
0.9523 0.9070 0.8638 0.8227 0.7835
8095 2948 3760 0247 2617
6 7 8 9 10
1.2653 1.3159 1.3685 1.4233 1.4802
1902 3178 6905 1181 4428
0.7903 0.7599 0.7306 0.7025 0.6755
1453 1781 9021 8674 6417
1.3022 1.3608 1.4221 1.4860 1.5529
6012 6183 0061 9514 6942
0.7678 0.7348 0.7031 0.6729 0.6439
9574 2846 8513 0443 2768
1.3400 1.4071 1.4774 1.5513 1.6288
9564 0042 5544 2822 9463
0.7462 0.7106 0.6768 0.6446 0.6139
1540 8133 3936 0892 1325
11 12 13 14 15
1.5394 1.6010 1.6650 1.7316 1.8009
5406 3222 7351 7645 4351
0.6495 0.6245 0.6005 0.5774 0.5552
8093 9705 7409 7508 6450
1.6228 1.6958 1.7721 1.8519 1.9352
5305 8143 9610 4492 8244
0.6161 0.5896 0.5642 0.5399 0.5167
9874 6386 7164 7286 2044
1.7103 1.7958 1.8856 1.9799 2.0789
3936 5633 4914 3160 2818
0.5846 0.5568 0.5303 0.5050 0.4810
7929 3742 2135 6795 1710
16 17 18 19 20
1.8729 1.9479 2.0258 2.1068 2.1911
8125 0050 1652 4918 2314
0.5339 0.5133 0.4936 0.4746 0.4563
0818 7325 2812 4242 8695
2.0223 2.1133 2.2084 2.3078 2.4117
7015 7681 7877 6031 1402
0.4944 0.4731 0.4528 0.4333 0.4146
6932 7639 0037 0179 4286
2.1828 2.2920 2.4066 2.5269 2.6532
7459 1832 1923 5020 9771
0.4581 0.4362 0.4155 0.3957 0.3768
1152 9669 2065 3396 8948
21 22 23 24 25
2.2787 2.3699 2.4647 2.5633 2.6658
6807 1879 1554 0416 3633
0.4388 0.4219 0.4057 0.3901 0.3751
3360 5539 2633 2147 1680
2.5202 2.6336 2.7521 2.8760 3.0054
4116 5201 6635 1383 3446
0.3967 0.3797 0.3633 0.3477 0.3327
8743 0089 5013 0347 3060
2.7859 2.9252 3.0715 3.2250 3.3863
6259 6072 2376 9994 5494
0.3589 0.3418 0.3255 0.3100 0.2953
4236 4987 7131 6791 0277
26 27 28 29 30
2.7724 2.8833 2.9987 3.1186 3.2433
6978 6858 0332 5145 9751
0.3606 0.3468 0.3334 0.3206 0.3083
8923 1657 7747 5141 1867
3.1406 3.2820 3.4296 3.5840 3.7453
7901 0956 9999 3649 1813
0.3184 0.3046 0.2915 0.2790 0.2670
0248 9137 7069 1502 0002
3.5556 3.7334 3.9201 4.1161 4.3219
7269 5632 2914 3560 4238
0.2812 0.2678 0.2550 0.2429 0.2313
4073 4832 9364 4632 7745
31 32 33 34 35
3.3731 3.5080 3.6483 3.7943 3.9460
3341 5875 8110 1634 8899
0.2964 0.2850 0.2740 0.2635 0.2534
6026 5794 9417 5209 1547
3.9138 4.0899 4.2740 4.4663 4.6673
5745 8104 3018 6154 4781
0.2555 0.2444 0.2339 0.2238 0.2142
0241 9991 7121 9589 5444
4.5380 4.7649 5.0031 5.2533 5.5160
3949 4147 8854 4797 1537
0.2203 0.2098 0.1998 0.1903 0.1812
5947 6617 7254 5480 9029
36 37 38 39 40
4.1039 4.2680 4.4388 4.6163 4.8010
3255 8986 1345 6599 2063
0.2436 0.2342 0.2252 0.2166 0.2082
6872 9685 8543 2061 8904
4.8773 5.0968 5.3262 5.5658 5.8163
7846 6049 1921 9908 6454
0.2050 0.1961 0.1877 0.1796 0.1719
2817 9921 5044 6549 2870
5.7918 6.0814 6.3854 6.7047 7.0399
1614 0694 7729 5115 8871
0.1726 0.1644 0.1566 0.1491 0.1420
5741 3563 0536 4797 4568
41 42 43 44 45
4.9930 5.1927 5.4004 5.6165 5.8411
6145 8391 9527 1508 7568
0.2002 0.1925 0.1851 0.1780 0.1711
7793 7493 6820 4635 9841
6.0781 6.3516 6.6374 6.9361 7.2482
0094 1548 3818 2290 4843
0.1645 0.1574 0.1506 0.1441 0.1379
2507 4026 6054 7276 6437
7.3919 7.7615 8.1496 8.5571 8.9850
8815 8756 6693 5028 0779
0.1352 0.1288 0.1227 0.1168 0.1112
8160 3962 0440 6133 9651
46 47 48 49 50
6.0748 6.3178 6.5705 6.8333 7.1066
2271 1562 2824 4937 8335
0.1646 0.1582 0.1521 0.1463 0.1407
1386 8256 9476 4112 1262
7.5744 7.9152 8.2714 8.6436 9.0326
1961 6849 5557 7107 3627
0.1320 0.1263 0.1208 0.1156 0.1107
2332 3810 9771 9158 0965
9.4342 5818 9.9059 7109 10.4012 6965 10.9213 3313 11.4673 9979
0.1059 0.1009 0.0961 0.0915 0.0872
9668 4921 4211 6391 0373
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.7
APPENDICES i = 6% n
(1 + i)n
i = 7% (1 + i)–n
(1 + i)n
i = 8% (1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0600 1.1236 1.1910 1.2624 1.3382
0000 0000 1600 7696 2558
0.9433 0.8899 0.8396 0.7920 0.7472
9623 9644 1928 9366 5817
1.0700 1.1449 1.2250 1.3107 1.4025
0000 0000 4300 9601 5173
0.9345 0.8734 0.8162 0.7628 0.7129
7944 3873 9788 9521 8618
1.0800 1.1664 1.2597 1.3604 1.4693
0000 0000 1200 8896 2808
0.9259 0.8573 0.7938 0.7350 0.6805
2593 3882 3224 2985 8320
6 7 8 9 10
1.4185 1.5036 1.5938 1.6894 1.7908
1911 3026 4807 7896 4770
0.7049 0.6650 0.6274 0.5918 0.5583
6054 5711 1237 9846 9478
1.5007 1.6057 1.7181 1.8384 1.9671
3035 8148 8618 5921 5136
0.6663 0.6227 0.5820 0.5439 0.5083
4222 4974 0910 3374 4929
1.5868 1.7138 1.8509 1.9990 2.1589
7432 2427 3021 0463 2500
0.6301 0.5834 0.5402 0.5002 0.4631
6963 9040 6888 4897 9349
11 12 13 14 15
1.8982 2.0121 2.1329 2.2609 2.3965
9856 9647 2826 0396 5819
0.5267 0.4969 0.4688 04423 0.4172
8753 6936 3902 0096 6506
2.1048 2.2521 2.4098 2.5785 2.7590
5195 9159 4500 3415 3154
0.4750 0.4440 0.4149 0.3878 0.3624
9280 1196 6445 1724 4602
2.3316 2.5181 2.7196 2.9371 3.1721
3900 7012 2373 9362 6911
0.4288 0.3971 0.3676 0.3404 0.3152
8286 1376 9792 6104 4170
16 17 18 19 20
2.5403 2.6927 2.8543 3.0255 3.2071
5168 7279 3915 9950 3547
0.3936 0.3713 0.3503 0.3305 0.3118
4628 6442 4379 1301 0473
2.9521 3.1588 3.3799 3.6165 3.8696
6375 1521 3228 2754 8446
0.3387 0.3165 0.2958 0.2765 0.2584
3460 7439 6392 0833 1900
3.4259 3.7000 3.9960 4.3157 4.6609
4264 1805 1950 0106 5714
0.2918 0.2702 0.2502 0.2317 0.2145
9047 6895 4903 1206 4821
21 22 23 24 25
3.3995 3.6035 3.8197 4.0489 4.2918
6360 3742 4966 3464 7072
0.2941 0.2775 0.2617 0.2469 0.2329
5540 0510 9726 7855 9863
4.1405 4.4304 4.7405 5.0723 5.4274
6237 0174 2986 6695 3264
0.2415 0.2257 0.2109 0.1971 0.1842
1309 1317 4688 4662 4918
5.0338 5.4365 5.8714 6.3411 6.8484
3372 4041 6365 8074 7520
0.1986 0.1839 0.1703 0.1576 0.1460
5575 4051 1528 9934 1790
26 27 28 29 30
4.5493 4.8223 5.1116 5.4183 5.7434
8296 4594 8670 8790 9117
0.2198 0.2073 0.1956 0.1845 0.1741
1003 6795 3014 5674 1013
5.8073 6.2138 6.6488 7.1142 7.6122
5292 6763 3836 5705 5504
0.1721 0.1609 0.1504 0.1405 0.1313
9549 3037 0221 6282 6712
7.3963 7.9880 8.6271 9.3172 10.0626
5321 6147 0639 7490 5689
0.1352 0.1251 0.1159 0.1073 0.0993
0176 8682 1372 2752 7733
31 32 33 34 35
6.0881 6.4533 6.8405 7.2510 7.6860
0064 8668 8988 2528 8679
0.1642 0.1549 0.1461 0.1379 0.1301
5484 5740 8622 1153 0522
8.1451 8.7152 9.3253 9.9781 10.6765
1290 7080 3975 1354 8148
0.1227 0.1147 0.1072 0.1002 0.0936
7301 4113 3470 1934 6294
10.8676 11.7370 12.6760 13.6901 14.7853
6944 8300 4964 3361 4429
0.0920 0.0852 0.0788 0.0730 0.0676
1605 0005 8893 4531 3454
36 37 38 39 40
8.1472 8.6360 9.1542 9.7035 10.2857
5200 8712 5235 0749 1794
0.1227 0.1157 0.1092 0.1030 0.0972
4077 9318 3885 5552 2219
11.4239 12.2236 13.0792 13.9948 14.9744
4219 1814 7141 2041 5784
0.0875 0.0818 0.0764 0.0714 0.0667
3546 0884 5686 5501 8038
15.9681 17.2456 18.6252 20.1152 21.7245
7184 2558 7563 9768 2150
0.0626 0.0579 0.0536 0.0497 0.0460
2458 8572 9048 1341 3093
41 42 43 44 45
10.9028 11.5570 12.2504 12.9854 13.7646
6101 3267 5463 8191 1083
0.0917 0.0865 0.0816 0.0770 0.0726
1905 2740 2962 0908 5007
16.0226 17.1442 18.3443 19.6284 21.0024
6989 5678 5475 5959 5176
0.0624 0.0583 0.0545 0.0509 0.0476
1157 2857 1268 4643 1349
23.4624 25.3394 27.3666 29.5559 31.9204
8322 8187 4042 7166 4939
0.0426 0.0394 0.0365 0.0338 0.0313
2123 6411 4084 3411 2788
46 47 48 49 50
14.5904 15.4659 16.3938 17.3775 18.4201
8748 1673 7173 0403 5427
0.0685 0.0646 0.0609 0.0575 0.0542
3781 5831 9840 4566 8836
22.4726 24.0457 25.7289 27.5299 29.4570
2338 0702 0651 2997 2506
0.0444 0.0415 0.0388 0.0363 0.0339
9859 8747 6679 2410 4776
34.4740 37.2320 40.2105 43.4274 46.9016
8534 1217 7314 1899 1251
0.0290 0.0268 0.0248 0.0230 0.0213
0730 5861 6908 2693 2123
A.8
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
TABLE 4 Log-Tables LOGARITHAMS
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.9
APPENDICES LOG-TABLES
A.10
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
TABLE 5 ANTILOGARITHMS LOG-TABLES
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.11
APPENDICES LOG-TABLES
A.12
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.13
To find the area under the curve between the mean and a point 2.24 standard deviations to the right of the mean, look up the value opposite 2.2 and under 0.04 in the table; 0.4875 of the area under the curve lies between the mean and a z Value of 2.24
Example:
0.00 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.2257 0.2580 0.2881 0.3159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987
x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4649 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987
0.01
0.02
z = 2.24
0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.2324 0.2642 0.2939 0.3212 0.3461 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4726 0.4783 0.4830 0.4868 0.4898 0.4922 0.4941 04956 0.4967 0.4976 0.4982 0.4987
Mean
0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.4834 0.4871 0.4901 0.4925 0.4943 0.4957 0.4968 0.4977 0.4983 0.4988
0.03
0.4875 of Area
0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988
0.04 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.2454 0.2764 0.3051 0.3315 0.3554 0.3770 0.3962 0.4131 0.4279 0.4406 0.4515 0.4608 0.4686 0.4750 0.4803 0.4846 0.4881 0.4909 0.4931 0.4948 0.4961 0.4971 0.4979 0.4985 0.4989
0.4989
0.06
0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.2422 0.2734 0.3023 0.3289 0.3531 0.3749 0.3944 0.4115 0.4265 0.4394 0.4505 0.4599 0.4678 0.4744 0.4798 0.4842 0.4878 0.4906 0.4929 0.4946 0.4960 0.4970 0.4978 0.4984
0.05
0.4989
0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 0.4525 0.4616 0.4693 0.4756 0.4808 0.4850 0.4884 0.4911 0.4932 0.4949 0.4962 0.4972 0.4979 0.4985
0.07
0.4990
0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.2517 0.2823 0.3106 0.3365 0.3599 0.3810 0.3997 0.4162 0.4306 0.4429 0.4535 0.4625 0.4699 0.4761 0.4812 0.4854 0.4887 0.4913 0.4934 0.4951 0.4963 0.4973 0.4980 0.4986
0.08
Areas under the Standard Normal Probability Distribution between the Mean and Positive Values of z
Table 6
0.4990
0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952 0.4964 0.4974 0.4981 0.4986
0.09
To find the value of t that corresponds to an area of 0.10 in both tails of the distribution combined, when there are 19 degress of freedom, look under the 0.10 column, and proceed down to the 19 degrees of freedom row; the appropriate t value there is 1.729
Example: 0.10 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645
Freedom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 Normal Distribution
Degree of 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960
0.05 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326
0.02
Area in Both Tails Combined
Areas in Both Tails Combined for Student’s t Distribution
Table 7
63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576
0.01
APPENDICES
A.14
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.15
6
the curve (the
11
the 11 degrees
value is 14.631
chi-squares
the appropriate
of freedom row,
5.229 5.812 6.408 7.015 7.633
15 16 17 18 19
8.260
4.660
14
20
4.107
3.571
13
12
2.558
10
the table and 3.053
2.088
9
0.20 column in
look under the
1.646
1.239
8
in the right tail)
coloured area 7
0.554
5
the area under 0.872
0.297
4
value of 0.20 of
the chi-square
0.115
0.0201
0.00016
0.99
3
freedom, to find
2
1
distribution with
11 degrees of
Freedom
of
Degrees
In a chi-square
Example:
9.591
8.907
8.231
7.564
6.908
6.262
5.629
5.009
4.404
3.816
3.247
2.700
2.180
1.690
1.237
0.831
0.484
0.216
0.0506
0.00098
0.975
10.851
10.117
9.390
8.672
7.962
7.261
6.571
5.892
5.226
4.575
3.940
3.325
2.733
2.167
1.635
1.145
0.711
0.352
0.103
0.00398
0.95
12.443
11.651
10.865
10.085
9.312
8.547
7.790
7.042
6.304
5.578
4.865
4.168
3.490
2.833
2.204
1.610
1.064
0.584
0.211
0.0158
14.578
13.716
12.857
12.002
11.152
10.307
9.467
8.634
7.807
6.989
6.179
5.380
4.594
3.822
3.070
2.343
1.649
1.005
0.446
0.0642
0.800
Area in Right Tail 0.90
1
25.038
23.900
22.760
21.615
20.465
19.311
18.151
16.985
15.812
14.631
13.442
12.242
11.030
9.803
8.558
7.289
5.989
4.642
3.219
1.642
0.20
28.412
27.204
25.989
24.769
23.542
22.307
21.064
19.812
18.549
17.275
15.987
14.684
13.362
12.017
10.645
9.236
7.779
6.251
4.605
2.706
0.10
31.410
30.144
28.869
27.587
26.296
24.996
23.685
22.362
21.026
19.675
18.307
16.919
15.507
14.067
12.592
11.070
9.488
7.815
5.991
3.841
0.05
34.170
32.852
31.526
30.191
28.845
27.488
26.119
24.736
23.337
21.920
20.483
19.023
17.535
16.013
14.449
12.833
11.143
9.348
7.378
5.024
0.025
Area in the Right Tail of a Chi-square ( 243 2) Distribution
Table 8
37.566
36.191
34.805
33.409
32.000
30.578
29.141
27.688
26.217
24.725
23.209
21.666
20.090
18.475
16.812
15.086
13.277
11.345
9.210
6.635
0.01
A.16
Copyright -The Institute of Chartered Accountants of India
F value is 3.94.
the appropriate
freedom row;
degrees of
across the 6
column and
Freedom
15 degrees of
look under the
under the curve
of the area
Value for 0.05
to find the F
denominator,
freedom for the
6 degrees of
numerator and
freedom for the
degrees of
bution with 15
In an F distri-
Example:
4.32 4.30 4.28 4.26 4.24 4.17 4.08 4.00 3.92 3.84
30 40 60 120 º
4.49 4.45 4.41 4.38 4.35
21 22 23 24 25
16 17 18 19 20
4.84 4.75 4.67 4.60 4.54
5.99 5.59 5.32 5.12 4.96
6 7 8 9 10 11 12 13 14 15
161 18.5 10.1 7.71 6.61
1 2 3 4 5
1
3.32 3.23 3.15 3.07 3.00
3.47 3.44 3.42 3.40 3.39
3.63 3.59 3.55 3.52 3.49
3.98 3.89 3.81 3.74 3.68
5.14 4.74 4.46 4.26 4.10
200 19.0 9.55 6.94 5.79
2
2.92 2.84 2.76 2.68 2.60
3.07 3.05 3.03 3.01 2.99
3.24 3.20 3.16 3.13 3.10
3.59 3.49 3.41 3.34 3.29
4.76 4.35 4.07 3.86 3.71
216 19.2 9.28 6.59 5.41
3
3.94
2.69 2.61 2.53 2.45 2.37
2.84 2.82 2.80 2.78 2.76
3.01 2.96 2.93 2.90 2.87
3.36 3.26 3.18 3.11 3.06
4.53 4.12 3.84 3.63 3.48
225 19.2 9.12 6.39 5.19
4
5
2.53 2.45 2.37 2.29 2.21
2.68 2.66 2.64 2.62 2.60
2.85 2.81 2.77 2.74 2.71
3.20 3.11 3.03 2.96 2.90
4.39 3.97 3.69 3.48 3.33
230 19.3 9.01 6.26 5.05
0.05 of area
2.42 2.34 2.25 2.18 2.10
2.57 2.55 2.53 2.51 2.49
2.74 2.70 2.66 2.63 2.60
3.09 3.00 2.92 2.85 2.79
4.28 3.87 3.58 3.37 3.22
234 19.3 8.94 6.16 4.95
6
2.33 2.25 2.17 2.09 2.01
2.49 2.46 2.44 2.42 2.40
2.66 2.61 2.58 2.54 2.51
3.01 2.91 2.83 2.76 2.71
4.21 3.79 3.50 3.29 3.14
237 19.4 8.89 6.09 4.88
7
2.27 2.18 2.10 2.02 1.94
2.42 2.40 2.37 2.36 2.34
2.59 2.55 2.51 2.48 2.45
2.95 2.85 2.77 2.70 2.64
4.15 3.73 3.44 3.23 3.07
239 19.4 8.85 6.04 4.82
8
2.21 2.12 2.04 1.96 1.88
2.37 2.34 2.32 2.30 2.28
2.54 2.49 2.46 2.42 2.39
2.90 2.80 2.71 2.65 2.59
4.10 3.68 3.39 3.18 3.02
241 19.4 8.81 6.00 4.77
9
2.16 2.08 1.99 1.91 1.83
2.32 2.30 2.27 2.25 2.24
2.49 2.45 2.41 2.38 2.35
2.85 2.75 2.67 2.60 2.54
4.06 3.64 3.35 3.14 2.98
242 19.4 8.79 5.96 4.74
10
2.09 2.00 1.92 1.83 1.75
2.25 2.23 2.20 2.18 2.16
2.42 2.38 2.34 2.31 2.28
2.79 2.69 2.60 2.53 2.48
4.00 3.57 3.28 3.07 2.91
244 19.4 8.74 5.91 4.68
12
2.01 1.92 1.84 1.75 1.67
2.18 2.15 2.13 2.11 2.09
2.35 2.31 2.27 2.23 2.20
2.72 2.62 2.53 2.46 2.40
3.94 3.51 3.22 3.01 2.85
246 19.4 8.70 5.86 4.62
15
1.93 1.84 1.75 1.66 1.57
2.10 2.07 2.05 2.03 2.01
2.28 2.23 2.19 2.16 2.12
2.65 2.54 2.46 2.39 2.33
3.87 3.44 3.15 2.94 2.77
248 19.4 8.66 5.80 4.56
20
Degrees of Freedom for Numerator
1.89 1.79 1.70 1.61 1.52
2.05 2.03 2.01 1.98 1.96
2.24 2.19 2.15 2.11 2.08
2.61 2.51 2.42 2.35 2.29
3.84 3.41 3.12 2.90 2.74
249 19.5 8.64 5.77 4.53
24
1.84 1.74 1.65 1.55 1.46
2.01 1.98 1.96 1.94 1.92
2.19 2.15 2.11 2.07 2.04
2.57 2.47 2.38 2.31 2.25
3.81 3.38 3.08 2.86 2.70
250 19.5 8.62 5.75 4.50
30
1.79 1.69 1.59 1.50 1.39
1.96 1.94 1.91 1.89 1.87
2.15 2.10 2.06 2.03 1.99
2.53 2.43 2.34 2.27 2.20
3.77 3.34 3.04 2.83 2.66
251 19.5 8.59 5.72 4.46
40
Values of F for F Distribution with 0.05 of the Area in the Right Tail
Table 9 (a)
1.74 1.64 1.53 1.43 1.32
1.92 1.89 1.86 1.84 1.82
2.11 2.06 2.02 1.98 1.95
2.49 2.38 2.30 2.22 2.16
3.74 3.30 3.01 2.79 2.62
252 19.5 8.57 5.69 4.43
60
1.68 1.58 1.47 1.35 1.22
1.87 1.84 1.81 1.79 1.77
2.06 2.01 1.97 1.93 1.90
2.45 2.34 2.25 2.18 2.11
3.70 3.27 2.97 2.75 2.58
253 19.5 8.55 5.66 4.40
120
1.62 1.51 1.39 1.25 1.00
1.81 1.78 1.76 1.73 1.71
2.01 1.96 1.92 1.88 1.84
2.40 2.30 2.21 2.13 2.07
3.67 3.23 2.93 2.71 2.54
254 19.5 8.53 5.63 4.37
∞
APPENDICES
COMMON PROFICIENCY TEST
Degrees of Freedom for Denominator
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.17
F value is 10.5
the appropriate
freedom row;
degrees of
across the 5
column and
freedom
17 degrees of
look under the
under the curve
of the area
Value for 0.01
to find the F
denominator,
freedom for the
5 degrees of
numerator and
freedom for the
degrees of
bution with 7
In an F distri-
Example:
Degrees of Freedom for Denominator
4,052 98.5 34.1 21.2 16.3 13.7 12.2 11.3 10.6 10.0 9.65 9.33 9.07 8.86 8.68 8.53 8.40 8.29 8.19 8.10 8.02 7.95 7.88 7.82 7.77 7.56 7.31 7.08 6.85 6.63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 60 120 º
1
5.39 5.18 4.98 4.79 4.61
5.78 5.72 5.66 5.61 5.57
6.23 6.11 6.01 5.93 5.85
7.21 6.93 6.70 6.51 6.36
10.9 9.55 8.65 8.02 7.56
5,000 99.0 30.8 18.0 13.3
2
4.51 4.31 4.13 3.95 3.78
4.87 4.82 4.76 4.72 4.68
5.29 5.19 5.09 5.01 4.94
6.22 5.95 5.74 5.56 5.42
9.78 8.45 7.59 6.99 6.55
5,403 99.2 29.5 16.7 12.1
3
4.02 3.83 3.65 3.48 3.32
4.37 4.31 4.26 4.22 4.18
4.77 4.67 4.58 4.50 4.43
5.67 5.41 5.21 5.04 4.89
9.15 7.85 7.01 6.42 5.99
5,625 99.2 28.7 16.0 11.4
4
10.5
3.70 3.51 3.34 3.17 3.02
4.04 3.99 3.94 3.90 3.86
4.44 4.34 4.25 4.17 4.10
5.32 5.06 4.86 4.70 4.56
8.75 7.46 6.63 6.06 5.64
5,764 99.3 28.2 15.5 11.0
5
6
3.47 3.29 3.12 2.96 2.80
3.81 3.76 3.71 3.67 3.63
4.20 4.10 4.01 3.94 3.87
5.07 4.82 4.62 4.46 4.32
8.47 7.19 6.37 5.80 5.39
5,859 99.3 27.9 15.2 10.7
0.01 of area
3.30 3.12 2.95 2.79 2.64
3.64 3.59 3.54 3.50 3.46
4.03 3.93 3.84 3.77 3.70
4.89 4.64 4.44 4.28 4.14
8.26 6.99 6.18 5.61 5.20
5,928 99.4 27.7 15.0 10.5
7
3.17 2.99 2.82 2.66 2.51
3.51 3.45 3.41 3.36 3.32
3.89 3.79 3.71 3.63 3.56
4.74 4.50 4.30 4.14 4.00
8.10 6.84 6.03 5.47 5.06
5,982 99.4 27.5 14.8 10.3
8
3.07 2.89 2.72 2.56 2.41
3.40 3.35 3.30 3.26 3.22
3.78 3.68 3.60 3.52 3.46
4.63 4.39 4.19 4.03 3.89
7.98 6.72 5.91 5.35 4.94
6,023 99.4 27.3 14.7 10.2
9
2.98 2.80 2.63 2.47 2.32
3.31 3.26 3.21 3.17 3.13
3.69 3.59 3.51 3.43 3.37
4.54 4.30 4.10 3.94 3.80
7.87 6.62 5.81 5.26 4.85
6,056 99.4 27.2 14.5 10.1
10
2.84 2.66 2.50 2.34 2.18
3.17 3.12 3.07 3.03 2.99
3.55 3.46 3.37 3.30 3.23
4.40 4.16 3.96 3.80 3.67
7.72 6.47 5.67 5.11 4.71
6,106 99.4 27.1 14.4 9.89
12
2.70 2.52 2.35 2.19 2.04
3.03 2.98 2.93 2.89 2.85
3.41 3.31 3.23 3.15 3.09
4.25 4.01 3.82 3.66 3.52
7.56 6.31 5.52 4.96 4.56
6,157 99.4 26.9 14.2 9.72
15
2.55 2.37 2.20 2.03 1.88
2.88 2.83 2.78 2.74 2.70
3.26 3.16 3.08 3.00 2.94
4.10 3.86 3.66 3.51 3.37
7.40 6.16 5.36 4.81 4.41
6,209 99.4 26.7 14.0 9.55
20
Degrees of Freedom for Numerator
2.47 2.29 2.12 1.95 1.79
2.80 2.75 2.70 2.66 2.62
3.18 3.08 3.00 2.92 2.86
4.02 3.78 3.59 3.43 3.29
7.31 6.07 5.28 4.73 4.33
6,235 99.5 26.6 13.9 9.47
24
2.39 2.20 2.03 1.86 1.70
2.72 2.67 2.62 2.58 2.53
3.10 3.00 2.92 2.84 2.78
3.94 3.70 3.51 3.35 3.21
7.23 5.99 5.20 4.65 4.25
6,261 99.5 26.5 13.8 9.38
30
2.30 2.11 1.94 1.76 1.59
2.64 2.58 2.54 2.49 2.45
3.02 2.92 2.84 2.76 2.69
3.86 3.62 3.43 3.27 3.13
7.14 5.91 5.12 4.57 4.17
6,287 99.5 26.4 13.7 9.29
40
Values of F for F Distributions with 0.01 of the Area in the Right Tail
Table 9 (b)
2.21 2.02 1.84 1.66 1.47
2.55 2.50 2.45 2.40 2.36
2.93 2.83 2.75 2.67 2.61
3.78 3.54 3.34 3.18 3.05
7.06 5.82 5.03 4.48 4.08
6,313 99.5 26.3 13.7 9.20
60
2.11 1.92 1.73 1.53 1.32
2.46 2.40 2.35 2.31 2.27
2.84 2.75 2.66 2.58 2.52
3.69 3.45 3.25 3.09 2.96
6.97 5.74 4.95 4.40 4.00
6,339 99.5 26.2 13.6 9.11
120
2.01 1.80 1.60 1.38 1.00
2.36 2.31 2.26 2.21 2.17
2.75 2.65 2.57 2.49 2.42
3.60 3.36 3.17 3.00 2.87
6.88 5.65 4.86 4.31 3.91
6,366 99.5 26.1 13.5 9.02
∞
(1 + i)n 14% per Annum i = 0.14 1.14 1.2996 1.48154 1.68896 1.92541 2.19497 2.50227 2.85258 3.25194 3.70722 4.22622 4.8179 5.4924 6.26,133 7.13792 8.13723 9.27644 10.5751 12.0557 12.7435
10% per Annum i = 0.10 1.1 1.21 1.331 1.4641 1.61051 1.77156 1.94872 2.14359 2.35795 2.59374 2.85312 3.13843 3.45227 3.7975 4.17725 4.59497 5.05447 5.55992 6.11591 6.7275
18% per Annum i = 0.18 1.18 1.3924 1.64303 1.93878 2.28776 2.69955 3.18547 3.75886 4.43546 5.23384 6.17593 7.28759 8.59936 10.1472 11.9738 14.129 16.6723 19.6733 23.2144 27.393
TABLE 1(b) Present Value of Re. 1 Annual Compounding No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10% per Annum .909091 .826446 .751315 .683014 .620921 .564474 .513158 .466507 .424098 .385543 .350494 .318631 .289664 .263331 .239392 .217629 .197845 .179859 .163508 .148644
STATISTICS
Copyright -The Institute of Chartered Accountants of India
(1 + i)–n 14% per Annum .877193 .769468 .674972 .592081 .519369 .455587 .399638 .35056 .307508 .269744 .236618 .20756 .18207 .15971 .140097 .122892 .1078 .0945614 .0829486 0.72762
18% per Annum .847458 .718184 .608631 .515789 .437109 .370432 .313925 .266038 .225456 .191064 .161919 .137219 .116288 .0985489 .083516 .0707763 .0599799 .0508304 .0430766 .0365056
A.1
APPENDICES TABLE 2(a) Present Value of an Annuity Annual Compounding No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
10% per Annum P(n, i) 1/P(n, i)
14% per Annum P(n, i) 1/P(n, i)
18% per Annum P(n, i) 1/P(n, i)
.909091 1.73554 2.48685 3.16987 3.79079 4.35526 4.86842 5.33493 5.75902 6.14457 6.49506 6.81369 7.10336 7.36669 7.60608 7.82371 8.02155 8.20141 8.36492
1.1 .576191 .402115 .315471 .263798 .229607 .205406 .187444 .173641 .162745 .153963 .146763 .140779 .135746 .131474 .127817 .124664 .12193 .119547
.877192 1.64666 2.32163 2.91371 3.43308 3.88867 4.2883 4.63886 4.94637 5.21611 5.45273 5.66029 5.84236 6.00207 6.14217 6.26506 6.37286 6.46742 6.55037
1.14 .60729 .430732 .343205 .291284 .257158 .233193 .21557 .202169 .191714 .183394 .176669 .171164 .166609 .162809 .159615 .156915 .154621 .152663
.847458 1.56564 2.17427 2.69006 3.12717 3.4976 3.81153 4.07757 4.30302 4.49409 4.65601 4.79323 4.90951 5.00806 5.09158 5.16236 5.22233 5.27316 5.31624
1.18 .638716 .459924 .371739 .319778 .28591 .262362 .245244 .232395 .222515 .214776 .208628 .203686 .199678 .196403 .19371 .191485 .189639 .188103
20
8.51356
.11746
6.62313
.150986
5.35275
.18682
TABLE 2(b) Amount of an Annuity Annual Computing No. of Periods n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10% per Annum A(n, i) 1/A(n, i) 1,000000 2.100000 3.310000 4,641000 6.105100 7.71561006 9,48717108 11.4358882 13.579477 15.9374248 18.5311672 21.384284 24.5227124 27.9749837 31.772482 35.9497303 40.5447033 45.5991737 51.1590911 57.274999
.999999994 .476190473 .302114802 .215470802 .16379748 .129607379 .105405499 .0874440168 0.736405385 .0627453949 0.539631415 .0467633146 .0407785234 .0357462229 .0314737765 .0278166204 .0246641341 .021930222 .019546868 .0174596250
14% per Annum A(n, i) 1/A(n, i) 1.00000001 2.14000001 3.43960003 4.92114404 6.61010421 8.53551881 10.7304915 13.2327603 16.0853467 19.3372953 23.0445166 27.270749 32.0886539 37.5810655 43.8424147 50.9803528 59.1176022 68.3940666 78.969236 91.0249291
A.2
Copyright -The Institute of Chartered Accountants of India
999999993 .467289717 .290731478 .203204782 .151283545 .117157495 .0931923765 0.755700232 .0621683833 0.517135403 .043394271 .0366693265 .0311636631 .0266091445 .0228089627 .0196153998 .0169154357 .0146211514 .0126631591 .0109860014
18% per Annum A(n, i) 1/A(n, i) 1 2.18000001 3.57240001 5.21543202 7.15420979 9.44196755 12.1415217 15.3269956 19.0858549 23.5213088 28.7551443 34.9310704 42.218663 50.8180224 60.9652664 72.9390144 87.0680371 103.740284 123.413535 146.627971
.999999996 .458715595 .27992386 .19173867 .139777841 .105910129 .082361999 .0652443586 .0523948237 .0425146411 .034776386 .0286278087 .0236862072 0.196780582 .0164027824 .0137100838 .011485271 .00963945696 .00810283897 .00681998115
COMMON PROFICIENCY TEST
TABLE 3 Future Value and Present Value i= n
(1 + i)n
1 4
%
i = rate of interest per period, n = number of periods 1 i= % 2 (1 + i)–n
(1 + i)n
(1 + i)–n
i= (1 + i)n
3 4
% (1 + i)–n
1 2 3 4 5
1.0025 1.0050 1.0075 1.0100 1.0125
0000 0625 1877 3756 6266
0.9975 0.9950 0.9925 0.9900 0.9875
0623 1869 3734 6219 9321
1.0050 1.0100 1.0150 1.0201 1.0252
0000 2500 7513 5050 5125
0.9950 0.9900 0.9851 0.9802 0.9753
2488 7450 4876 4752 7067
1.0075 1.0150 1.0226 1.0303 1.0380
0000 5625 6917 3919 6673
0.9925 0.9851 0.9778 0.9705 0.9633
5583 6708 3333 5417 2920
6 7 8 9 10
1.0150 1.0176 1.0201 1.0227 1.0252
9406 3180 7588 2632 8313
0.9851 0.9826 0.9802 0.9777 0.9753
3038 7370 2314 7869 4034
1.0303 1.0355 1.0407 1.0459 1.0511
7751 2940 0704 1058 4013
0.9705 0.9656 0.9608 0.9561 0.9513
1808 8963 8520 0468 4794
1.0458 1.0536 1.0615 1.0695 1.0775
5224 9613 9885 6084 8255
0.9561 0.9490 0.9419 0.9349 0.9280
5802 4022 7540 6318 0315
11 12 13 14 15
1.0278 1.0304 1.0329 1.0355 1.0381
4634 1596 9200 7448 6341
0.9729 0.9704 0.9680 0.9656 0.9632
0807 8187 6171 4759 3949
1.0563 1.0616 1.0669 1.0723 1.0776
9583 7781 8620 2113 8274
0.9466 0.9419 0.9372 0.9325 0.9279
1487 0534 1924 5646 1688
1.0856 1.0938 1.1020 1.1102 1.1186
6441 0690 1045 7553 0259
0.9210 0.9142 0.9074 0.9006 0.8939
9494 3815 3241 7733 7254
16 17 18 19 20
1.0407 1.0433 1.0459 1.0485 1.0512
5882 6072 6912 8404 0550
0.9608 0.9584 0.9560 0.9536 0.9512
3740 4130 5117 6700 8878
1.0830 1.0884 1.0939 1.0993 1.1048
7115 8651 2894 9858 9558
0.9233 0.9187 0.9141 0.9095 0.9050
0037 0684 3616 8822 6290
1.1269 1.1354 1.1439 1.1525 1.1611
9211 4455 6039 4009 8414
0.8873 0.8307 0.8741 0.8676 0.8611
1766 1231 5614 4878 8985
21 22 23 24 25
1.0538 1.0564 1.0591 1.0617 1.0644
3352 6810 0927 5704 1144
0.9489 0.9465 0.9441 0.9418 0.9394
1649 5011 8964 3505 8634
1.1104 1.1159 1.1215 1.1271 1.1327
2006 7216 5202 5978 9558
0.9005 0.8960 0.8916 0.8871 0.8827
6010 7971 2160 8567 7181
1.1698 1.1786 1.1875 1.1964 1.2053
9302 6722 0723 1353 8663
0.8547 0.8484 0.8421 0.8358 0.8296
7901 1589 0014 3140 0933
26 27 28 29 30
1.0670 1.0697 1.0724 1.0750 1.0777
7247 4015 1450 9553 8327
0.9371 0.9348 0.9324 0.9301 0.9278
4348 0646 7527 4990 3032
1.1384 1.1441 1.1498 1.1556 1.1614
5955 5185 7261 2197 0008
0.8783 0.8740 0.8696 0.8653 0.8610
7991 0986 6155 3488 2973
1.2144 1.2235 1.2327 1.2419 1.2512
2703 3523 1175 5709 7176
0.8234 0.8173 0.8112 0.8051 0.7991
3358 0380 1966 8080 8690
31 32 33 34 35
1.0804 1.0831 1.0858 1.0886 1.0913
7773 7892 8687 0159 2309
0.9255 0.9232 0.9209 0.9186 0.9163
1653 0851 0624 0972 1892
1.1672 1.1730 1.1789 1.1848 1.1907
0708 4312 0833 0288 2689
0.8567 0.8524 0.8482 0.8440 0.8398
4600 8358 4237 2226 2314
1.2606 1.2701 1.2796 1.2892 1.2989
5630 1122 3706 3434 0359
0.7932 0.7873 0.7814 0.7756 0.7698
3762 3262 7158 5418 8008
36 37 38 39 40
1.0940 1.0967 1.0995 1.1022 1.1050
5140 8653 2850 7732 3301
0.9140 0.9117 0.9094 0.9072 0.9049
3384 5445 8075 1272 5034
1.1966 1.2026 1.2086 1.2147 1.2207
8052 6393 7725 2063 9424
0.8356 0.8314 0.8273 0.8232 0.8191
4492 8748 5073 3455 3886
1.3086 1.3184 1.3283 1.3383 1.3483
4537 6021 4866 1128 4861
0.7641 0.7584 0.7528 0.7472 0.7416
4896 6051 1440 1032 4796
41 42 43 44 45
1.1077 1.1105 1.1133 1.1161 1.1189
9559 6508 4149 2485 1516
0.9026 0.9004 0.8981 0.8959 0.8937
9361 4250 9701 5712 2281
1.2268 1.2330 1.2391 1.2453 1.2516
9821 3270 9786 9385 2082
0.8150 0.8110 0.8069 0.8029 0.7989
6354 0850 7363 5884 6402
1.3584 1.3686 1.3789 1.3892 1.3996
6123 4969 1456 5642 7584
0.7361 0.7306 0.7252 0.7198 0.7144
2701 4716 0809 0952 5114
46 47 48 49 50
1.1217 1.1245 1.1273 1.1301 1.1329
1245 1673 2802 4634 7171
0.8914 0.8892 0.8870 0.8848 0.8826
9407 7090 5326 4116 3457
1.2578 1.2641 1.2704 1.2768 1.2832
7892 6832 8916 4161 2581
0.7949 0.7910 0.7870 0.7831 0.7792
8907 3390 9841 8250 8607
1.4101 1.4207 1.4314 1.4421 1.4529
7341 4971 0533 4087 5693
0.7091 0.7038 0.6986 0.6934 0.6882
3264 5374 1414 1353 5165
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.3
APPENDICES i =1
i =1% n
(1 + i)n
(1 + i)–n
(1 + i)n
1 4
i =1
% (1 + i)–n
(1 + i)n
1 2
% (1 + i)–n
1 2 3 4 5
1.0100 1.0201 1.0303 1.0406 1.0510
0000 0000 0100 0401 1005
0.9900 0.9802 0.9705 0.9609 0.9514
9901 9605 9015 8034 6569
1.0125 1.0251 1.0379 1.0509 1.0640
0000 5625 7070 4534 8215
0.9876 0.9754 0.9634 0.9515 0.9397
5432 6106 1833 2428 7706
1.0150 1.0302 1.0456 1.0613 1.0772
0000 2500 7838 6355 8400
0.9852 0.9706 0.9563 0.9421 0.9282
2167 6175 1699 8423 6033
6 7 8 9 10
1.0615 1.0721 1.0828 1.0936 1.1046
2015 3535 5671 8527 2213
0.9420 0.9327 0.9234 0.9143 0.9052
4524 1805 8322 3982 8695
1.0773 1.0908 1.1044 1.1182 1.1322
8318 5047 8610 9218 7083
0.9281 0.9167 0.9053 0.8942 0.8831
7488 1593 9845 2069 8093
1.0934 1.1098 1.1264 1.1433 1.1605
4326 4491 9259 8998 4083
0.9145 0.9010 0.8877 0.8745 0.8616
4219 2679 1112 9224 6723
11 12 13 14 15
1,1156 1.1268 1.1380 1.1494 1.1609
6835 2503 9328 7421 6896
0.8963 0.8874 0.8786 0.8699 0.8613
2372 4923 6260 6297 4947
1,1464 1.1607 1.1752 1.1899 1.2048
2422 5452 6395 5475 2918
0.8722 0.8615 0.8508 0.8403 0.8299
7746 0860 7269 6809 9318
1.1779 1.1956 1.2135 1.2317 1.2502
4894 1817 5244 5573 3207
0.8489 0.8363 0.8240 0.8118 0.7998
3323 8742 2702 4928 5150
16 17 18 19 20
1.1725 1.1843 1.1961 1.2081 1.2201
7864 0443 4748 0895 9004
0.8528 0.8443 0.8360 0.8277 0.8195
2126 7749 1731 3992 4447
1.2198 1.2351 1.2505 1.2662 1.2820
8955 3817 7739 0961 3723
0.8197 0.8096 0.7996 0.7897 0.7800
4635 2602 3064 5866 0855
1.2689 1.2880 1.3073 1.3269 1.3468
8555 2033 4064 5075 5501
0.7880 0.7763 0.7649 0.7536 0.7424
3104 8526 1159 0747 7042
21 22 23 24 25
1.2323 1.2447 1.2571 1.2697 1.2824
9194 1586 6302 3465 3200
0.8114 0.8033 0.7954 0.7875 0.7797
3017 9621 4179 6613 6844
1.2980 1.3142 1.3307 1.3473 1.3641
6270 8848 1709 5105 9294
0.7703 0.7608 0.7514 0.7421 0.7330
7881 6796 7453 9707 3414
1.3670 1.3875 1.4083 1.4295 1.4509
5783 6370 7715 0281 4535
0.7314 0.7206 0.7100 0.6995 0.6892
9795 8763 3708 4392 0583
26 27 28 29 30
1.2952 1.3082 1.3212 1.3345 1.3478
5631 0888 9097 0388 4892
0.7720 0.7644 0.7568 0.7493 0.7419
4796 0392 3557 4215 2292
1.3812 1.3985 1.4159 1.4336 1.4516
4535 1092 9230 9221 1336
0.7239 0.7150 0.7062 0.6974 0.6888
8434 4626 1853 9978 8867
1.4727 1.4948 1.5172 1.5399 1.5630
0953 0018 2218 8051 8022
0.6790 0.6689 0.6590 0.6493 0.6397
2052 8574 9925 5887 6243
31 32 33 34 35
1.3613 1.3749 1.3886 1.4025 1.4166
2740 4068 9009 7699 0276
0.7345 0.7273 0.7201 0.7129 0.7059
7715 0411 0307 7334 1420
1.4697 1.4881 1.5067 1.5255 1.5446
5853 3051 3214 6629 3587
0.6803 0.6719 0.6636 0.6554 0.6474
8387 8407 8797 9429 0177
1.5865 1.6103 1.6344 1.6589 1.6838
2642 2432 7918 9637 8132
0.6303 0.6209 0.6118 0.6027 0.5938
0781 9292 1568 7407 6608
36 37 38 39 40
1.4307 1.4450 1.4595 1.4741 1.4888
6878 7647 2724 2251 6373
0.6989 0.6920 0.6851 0.6783 0.6716
2495 0490 5337 6967 5314
1.5639 4382 1.5834 9312 1.6032 8678 16233 2787 1.6436 1946
0.6394 0916 0.6315 1522 0.6237 1873 06160 1850 0.6084 1334
1.7091 1.7347 1.7607 1.7872 1.8140
3954 7663 9828 1025 1841
0.5850 0.5764 0.5679 0.5595 0.5512
8974 4309 2423 3126 6232
41 42 43 44 45
1.5037 1.5187 1.5339 1.5493 1.5648
5237 8989 7779 1757 1075
0.6650 0.6584 0.6518 0.6454 0.6390
0311 1892 9992 4546 5492
1.6641 1.6849 1.7060 1.7273 1.7489
6471 6677 2885 5421 4614
0.6009 0.5934 0.5861 0.5789 0.5717
0206 8352 5656 2006 7290
1.8412 1.8688 1.8968 1.9253 1.9542
2868 4712 7982 3302 1301
0.5431 0.5350 0.5271 0.5193 0.5117
1559 8925 8153 9067 1494
46 47 48 49 50
1.5804 1.5962 1.6122 1.6283 1.6446
5885 6344 2608 4834 3182
0.6327 0.6264 0.6202 0.6141 0.6080
2764 6301 6041 1921 3882
1.7708 1.7929 1.8153 1.8380 1.8610
0797 4306 5485 4679 2237
0.5647 0.5577 0.5508 0.5440 0.5373
1397 4219 5649 5579 3905
1.9835 2.0132 2.0434 2.0741 2.1052
2621 7910 7829 3046 4242
0.5041 0.4967 0.4893 0.4821 0.4750
5265 0212 6170 2975 0468
A.4
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
3 i=1 % 4 n
(1 + i)n
1 i=2 % 4
i = 2% (1 + i)–n
(1 + i)n
(1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0175 1.0353 1.0534 1.0718 1.0906
0000 0625 2411 5903 1656
0.9828 0.9658 0.9492 0.9329 0.9169
0098 9777 8528 5851 1254
1.0200 1.0404 1.0612 1.0824 1.1040
0000 0000 0800 3216 8080
0.9803 0.9611 0.9423 0.9238 0.9057
9216 6878 2233 4543 3081
1.0225 1.0455 1.0690 1.0930 1.1176
0000 0625 3014 8332 7769
0.9779 0.9564 0.9354 0.9148 0.8947
9511 7444 2732 4335 1232
6 7 8 9 10
1.1097 1.1291 1.1488 1.1689 1.1894
0235 2215 8178 8721 4449
0.9011 0.8856 0.8704 0.8554 0.8407
4254 4378 1157 4135 2860
1.1261 1.1486 1.1716 1.1950 1.2189
6242 8567 5938 9257 9442
0.8879 0.8705 0.8534 0.8367 0.8203
7138 6018 9037 5527 4830
1.1428 1.1685 1.1948 1.2217 1.2492
2544 3901 3114 1484 0343
0.8750 0.8557 0.8369 0.8185 0.8005
2427 6946 3835 2161 1013
11 12 13 14 15
1.2102 1.2314 1.2529 1.2749 1.2972
5977 3931 8950 1682 2786
0.8262 0.8120 0.7980 0.7843 0.7708
6889 5788 9128 6490 7459
1.2433 1.2682 1.2936 1.3194 1.3458
7431 4179 0663 7876 6834
0.8042 0.7884 0.7730 0.7578 0.7430
6304 9318 3253 7502 1473
1.2773 1.3060 1.3354 1.3654 1.3962
1050 4999 3611 8343 0680
0.7828 0.7656 0.7488 0.7323 0.7162
9499 6748 1905 4137 2628
16 17 18 19 20
1.3199 1.3430 1.3665 1.3904 1.4147
2935 2811 3111 4540 7820
0.7576 0.7445 0.7317 0.7191 0.7068
1631 8605 7990 9401 2458
1.3727 1.4002 1.4282 1.4568 1.4859
8571 4142 4625 1117 4740
0.7284 0.7141 0.7001 0.6864 0.6729
4581 6256 5937 3076 7133
1.4276 1.4597 1.4925 1.5261 1.5605
2146 4294 8716 7037 0920
0.7004 0.6850 0.6699 0.6552 0.6408
6580 5212 7763 3484 1647
21 22 23 24 25
1.4395 1.4647 1.4903 1.5164 1.5429
3681 2871 6146 4279 8054
0.6946 0.6827 0.6709 0.6594 0.6480
6789 2028 7817 3800 9632
1.5156 1.5459 1.5768 1.6084 1.6406
6634 7967 9926 3725 0599
0.6597 0.6468 0.6341 0.6217 0.6095
7582 3904 5592 2149 3087
1.5956 1.6315 1.6682 1.7057 1.7441
2066 2212 3137 6658 4632
0.6267 0.6129 0.5994 0.5862 0.5733
1538 2457 3724 4668 4639
26 27 28 29 30
1.5699 1.5974 1.6254 1.6538 1.6828
8269 5739 1290 5762 0013
0.6369 0.6259 0.6152 0.6046 0.5942
4970 9479 2829 4697 4764
1.6734 1.7068 1.7410 1.7758 1.8113
1811 8648 2421 4469 6158
0.5975 0.5858 0.5743 0.5631 0.5520
7928 6204 7455 1231 7089
1.7833 1.8235 1.8645 1.9064 1.9493
8962 1588 4499 9725 9344
0.5607 0.5483 0.5363 0.5245 0.5129
2997 9117 2388 2213 8008
31 32 33 34 35
1.7122 1.7422 1.7727 1,8037 1.8352
4913 1349 0223 2452 8970
0.5840 0.5739 0.5641 0.5544 0.5448
2716 8247 1053 0839 7311
1.8475 1.8845 1.9222 1.9606 1.9998
8882 4059 3140 7603 8955
0.5412 0.5306 0.5205 0.5100 0.5000
4597 3330 2873 2817 2761
1.9932 2.0381 2.0839 2.1308 2.1787
5479 0303 6034 4945 9356
0.5016 0.4906 0.4798 0.4692 0.4589
9201 5233 5558 9641 6960
36 37 38 39 40
1.8674 1.9000 1.9333 1.9671 2.0015
0727 8689 3841 7184 9734
0.5355 0.5262 0.5172 0.5083 0.4996
0183 9172 4002 4400 0098
2.0398 2.0806 2.1222 2.1647 2.2080
8734 8509 9879 4477 3966
0.4902 0.4806 0.4711 0.4619 0.4528
2315 1093 8719 4822 9042
2.2278 2.2779 2.3291 2.3816 2.4351
1642 4229 9599 0290 8897
0.4488 0.4389 0.4293 0.4198 0.4106
7002 9268 3270 8528 4575
41 42 43 44 45
2.0366 2.0722 2.1085 2.1454 2.1829
2530 6624 3090 3019 7522
0.4910 0.4825 0.4742 0.4661 0.4580
0834 6348 6386 0699 9040
2.2522 2.2972 2.3431 2.3900 2.4378
0046 4447 8936 5314 5421
0.4440 0.4353 0.4267 0.4184 0.4101
1021 0413 6875 0074 9680
2.4899 2.5460 2.6032 2.6618 2.7217
8072 0528 9040 6444 5639
0.4016 0.3927 0.3841 0.3756 0.3674
0954 7216 2925 7653 0981
46 47 48 49 50
2.2211 2.2600 2.2995 2.3398 2.3807
7728 4789 9872 4170 8893
0.4502 0.4424 0.4348 0.4273 0.4200
1170 6850 5848 7934 2883
2.4866 2.5363 2.5870 2.6388 2.6915
1129 4352 7039 1179 8803
0.4021 0.3942 0.3865 0.3789 0.3715
5373 6836 3761 5844 2788
2.7829 2.8456 2.9096 2.9751 3.0420
9590 1331 3961 0650 4640
0.3593 0.3514 0.3436 0.3361 0.3287
2500 1809 8518 2242 2608
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.5
APPENDICES i=2 n
(1 + i)n
1 2
1 i=3 % 2
i = 3%
% (1 + i)–n
(1 + i)n
(1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0250 1.0506 1.0768 1.1038 1.1314
0000 2500 9063 1289 0821
0.9756 0.9518 0.9285 0.9059 0.8838
0976 1440 9941 5064 5429
1.0300 1.0609 1.0927 1.1255 1.1592
0000 0000 2700 0881 7407
0.9708 0.9425 0.9151 0.8884 0.8626
7379 9591 4166 8705 0878
1.0350 1.0712 1.1087 1.1475 1.1876
0000 2500 1788 2300 8631
0.9661 0.9335 0.9019 0.8714 0.8419
8357 1070 4271 4223 7317
6 7 8 9 10
1.1596 1.1886 1.2184 1.2488 1.2800
9342 8575 0290 6297 8454
0.8622 0.8412 0.8207 0.8007 0.7811
9687 6524 4657 2836 9840
1.1940 1.2298 1.2667 1.3047 1.3439
5230 7387 7008 7318 1638
0.8374 0.8130 0.7894 0.7664 0.7440
8426 9151 0923 1673 9391
1.2292 1.2722 1.3168 1.3628 1.4105
5533 7926 0904 9735 9876
0.8135 0.7859 0.7594 0.7337 0.7089
0064 9096 1156 3097 1881
11 12 13 14 15
1.3120 1.3448 1.3785 1.4129 1.4482
8666 8882 1104 7382 9817
0.7621 0.7435 0.7254 0.7077 0.6904
4478 5589 2038 2720 6556
1.3842 1.4257 1.4685 1.5125 1.5579
3387 6089 3371 8972 6742
0.7224 0.7013 0.6809 0.6611 0.6418
2128 7988 5134 1781 6195
1.4599 1.5110 1.5639 1.6186 1.6753
6972 6866 5606 9452 4883
0.6849 0.6617 0.6394 0.6177 0.5968
4571 8330 0415 8179 9062
16 17 18 19 20
1.4845 1.5216 1.5596 1.5986 1.6386
0562 1826 5872 5019 1644
0.6736 0.6571 0.6411 0.6255 0.6102
2493 9506 6591 2772 7094
1.6047 1.6528 1.7024 1.7535 1.8061
0644 4763 3306 0605 1123
0.6231 0.6050 0.5873 0.5702 0.5536
6694 1645 9461 8603 7575
1.7339 1.7946 1.8574 1.9225 1.9897
8604 7555 8920 0132 8886
0.5767 0.5572 0.5383 0.5201 0.5025
0591 0378 6114 5569 6588
21 22 23 24 25
1.6795 1,7215 1.7646 1.8087 1.8539
8185 7140 1068 2595 4410
0.5953 0.5808 0.5666 0.5528 0.5393
8629 6467 9724 7535 9059
1.8602 1,9161 1.9735 2.0327 2.0937
9457 0341 8651 9411 7793
0.5375 0.5218 0.5066 0.4919 0.4776
4928 9250 9175 3374 0557
2.0594 2,1315 2.2061 2.2833 2.3632
3147 1158 1448 2849 4498
0.4855 0.4691 0.4532 0.4379 0.4231
7090 5063 8563 5713 4699
26 27 28 29 30
1.9002 1.9478 1.9964 2.0464 2.0975
9270 0002 9502 0739 6758
0.5262 0.5133 0.5008 0.4886 0.4767
3472 9973 7778 6125 4269
2.1565 2.2212 2.2879 2.3565 2.4272
9127 8901 2768 6551 6247
0.4636 0.4501 0.4370 0.4243 0.4119
9473 8906 7675 4636 8676
2.4459 2.5315 2.6201 2.7118 2.8067
5856 6711 7196 7798 9370
0.4088 0.3950 0.3816 0.3687 0.3562
3767 1224 5434 4815 7841
31 32 33 34 35
2.1500 2.2037 2.2588 2.3153 2.3732
0677 5694 5086 2213 0519
0.4651 0.4537 0.4427 0.4319 0.4213
1481 7055 0298 0534 7107
2.5000 2.5750 2.6523 2.7319 2.8138
8035 8276 3524 0530 6245
0.3999 0.3883 0.3770 0.3660 0.3553
8715 3703 2625 4490 8340
2.9050 3.0067 3.1119 3.2208 3.3335
3148 0759 4235 6033 9045
0.3442 0.3325 0.3213 0.3104 0.2999
3035 8971 4271 7605 7686
36 37 38 39 40
2.4325 2.4933 2.5556 2.6195 2.6850
3532 4870 8242 7448 6384
0.4110 0.4010 0.3912 0.3817 0.3724
9372 6705 8492 4139 3062
2.8982 2.9852 3.0747 3.1670 3.2620
7833 2668 8348 2698 3779
0.3450 0.3349 0.3252 0.3157 0.3065
3243 8294 2615 5355 5684
3.4502 3.5710 3.6960 3.8253 3.9592
6611 2543 1132 7171 5972
0.2898 0.2800 0.2705 0.2614 0.2525
3272 3161 6194 1250 7247
41 42 43 44 45
2.7521 2.8209 2.8915 2.9638 3.0379
9043 9520 2008 0808 0328
0.3633 4695 0.3544 8483 0.3458 3886 03374 0376 0.3291 7440
3.3598 3.4606 3.5645 3.6714 3.7815
9893 9589 1677 5227 9584
0.2976 0.2889 0.2805 0.2723 0.2644
2800 5922 4294 7178 3862
4.0978 4.2412 4.3897 4.5433 4.7023
3381 5799 0202 4160 5855
0.2440 0.2357 0.2278 0.2201 0.2126
3137 7910 0590 0231 5924
46 47 48 49 50
3.1138 3.1916 3.2714 3.3532 3.4371
5086 9713 8956 7680 0872
0.3211 0.3133 0.3056 0.2982 0.2909
3.8950 4.0118 4.1322 4.2562 4.3839
4372 9503 5188 1944 0602
0.2567 0.2492 0.2419 0.2349 0.2281
3653 5876 9880 5029 0708
4.8669 5.0372 5.2135 5.3960 5.5849
4110 8404 8898 6459 2686
0.2054 0.1985 0.1918 0.1853 0.1790
6787 1968 0645 2024 5337
4576 1294 7116 1576 4221
A.6
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
1 i=4 % 2
i = 4% n
(1 + i)n
(1 + i)–n
(1 + i)n
i = 5% (1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0400 1.0816 1.1248 1.1698 1.2166
0000 0000 6400 5856 5290
0.9615 0.9245 0.8889 0.8548 0.8219
3846 5621 9636 0419 2711
1.0450 1.0920 1.1411 1.1925 1.2461
0000 2500 6613 1860 8194
0.9569 0.9157 0.8762 0.8382 0.8024
3780 2995 9660 6134 5105
1.0500 1.1025 1.1576 1.2155 1.2762
0000 0000 2500 0625 8156
0.9523 0.9070 0.8638 0.8227 0.7835
8095 2948 3760 0247 2617
6 7 8 9 10
1.2653 1.3159 1.3685 1.4233 1.4802
1902 3178 6905 1181 4428
0.7903 0.7599 0.7306 0.7025 0.6755
1453 1781 9021 8674 6417
1.3022 1.3608 1.4221 1.4860 1.5529
6012 6183 0061 9514 6942
0.7678 0.7348 0.7031 0.6729 0.6439
9574 2846 8513 0443 2768
1.3400 1.4071 1.4774 1.5513 1.6288
9564 0042 5544 2822 9463
0.7462 0.7106 0.6768 0.6446 0.6139
1540 8133 3936 0892 1325
11 12 13 14 15
1.5394 1.6010 1.6650 1.7316 1.8009
5406 3222 7351 7645 4351
0.6495 0.6245 0.6005 0.5774 0.5552
8093 9705 7409 7508 6450
1.6228 1.6958 1.7721 1.8519 1.9352
5305 8143 9610 4492 8244
0.6161 0.5896 0.5642 0.5399 0.5167
9874 6386 7164 7286 2044
1.7103 1.7958 1.8856 1.9799 2.0789
3936 5633 4914 3160 2818
0.5846 0.5568 0.5303 0.5050 0.4810
7929 3742 2135 6795 1710
16 17 18 19 20
1.8729 1.9479 2.0258 2.1068 2.1911
8125 0050 1652 4918 2314
0.5339 0.5133 0.4936 0.4746 0.4563
0818 7325 2812 4242 8695
2.0223 2.1133 2.2084 2.3078 2.4117
7015 7681 7877 6031 1402
0.4944 0.4731 0.4528 0.4333 0.4146
6932 7639 0037 0179 4286
2.1828 2.2920 2.4066 2.5269 2.6532
7459 1832 1923 5020 9771
0.4581 0.4362 0.4155 0.3957 0.3768
1152 9669 2065 3396 8948
21 22 23 24 25
2.2787 2.3699 2.4647 2.5633 2.6658
6807 1879 1554 0416 3633
0.4388 0.4219 0.4057 0.3901 0.3751
3360 5539 2633 2147 1680
2.5202 2.6336 2.7521 2.8760 3.0054
4116 5201 6635 1383 3446
0.3967 0.3797 0.3633 0.3477 0.3327
8743 0089 5013 0347 3060
2.7859 2.9252 3.0715 3.2250 3.3863
6259 6072 2376 9994 5494
0.3589 0.3418 0.3255 0.3100 0.2953
4236 4987 7131 6791 0277
26 27 28 29 30
2.7724 2.8833 2.9987 3.1186 3.2433
6978 6858 0332 5145 9751
0.3606 0.3468 0.3334 0.3206 0.3083
8923 1657 7747 5141 1867
3.1406 3.2820 3.4296 3.5840 3.7453
7901 0956 9999 3649 1813
0.3184 0.3046 0.2915 0.2790 0.2670
0248 9137 7069 1502 0002
3.5556 3.7334 3.9201 4.1161 4.3219
7269 5632 2914 3560 4238
0.2812 0.2678 0.2550 0.2429 0.2313
4073 4832 9364 4632 7745
31 32 33 34 35
3.3731 3.5080 3.6483 3.7943 3.9460
3341 5875 8110 1634 8899
0.2964 0.2850 0.2740 0.2635 0.2534
6026 5794 9417 5209 1547
3.9138 4.0899 4.2740 4.4663 4.6673
5745 8104 3018 6154 4781
0.2555 0.2444 0.2339 0.2238 0.2142
0241 9991 7121 9589 5444
4.5380 4.7649 5.0031 5.2533 5.5160
3949 4147 8854 4797 1537
0.2203 0.2098 0.1998 0.1903 0.1812
5947 6617 7254 5480 9029
36 37 38 39 40
4.1039 4.2680 4.4388 4.6163 4.8010
3255 8986 1345 6599 2063
0.2436 0.2342 0.2252 0.2166 0.2082
6872 9685 8543 2061 8904
4.8773 5.0968 5.3262 5.5658 5.8163
7846 6049 1921 9908 6454
0.2050 0.1961 0.1877 0.1796 0.1719
2817 9921 5044 6549 2870
5.7918 6.0814 6.3854 6.7047 7.0399
1614 0694 7729 5115 8871
0.1726 0.1644 0.1566 0.1491 0.1420
5741 3563 0536 4797 4568
41 42 43 44 45
4.9930 5.1927 5.4004 5.6165 5.8411
6145 8391 9527 1508 7568
0.2002 0.1925 0.1851 0.1780 0.1711
7793 7493 6820 4635 9841
6.0781 6.3516 6.6374 6.9361 7.2482
0094 1548 3818 2290 4843
0.1645 0.1574 0.1506 0.1441 0.1379
2507 4026 6054 7276 6437
7.3919 7.7615 8.1496 8.5571 8.9850
8815 8756 6693 5028 0779
0.1352 0.1288 0.1227 0.1168 0.1112
8160 3962 0440 6133 9651
46 47 48 49 50
6.0748 6.3178 6.5705 6.8333 7.1066
2271 1562 2824 4937 8335
0.1646 0.1582 0.1521 0.1463 0.1407
1386 8256 9476 4112 1262
7.5744 7.9152 8.2714 8.6436 9.0326
1961 6849 5557 7107 3627
0.1320 0.1263 0.1208 0.1156 0.1107
2332 3810 9771 9158 0965
9.4342 5818 9.9059 7109 10.4012 6965 10.9213 3313 11.4673 9979
0.1059 0.1009 0.0961 0.0915 0.0872
9668 4921 4211 6391 0373
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.7
APPENDICES i = 6% n
(1 + i)n
i = 7% (1 + i)–n
(1 + i)n
i = 8% (1 + i)–n
(1 + i)n
(1 + i)–n
1 2 3 4 5
1.0600 1.1236 1.1910 1.2624 1.3382
0000 0000 1600 7696 2558
0.9433 0.8899 0.8396 0.7920 0.7472
9623 9644 1928 9366 5817
1.0700 1.1449 1.2250 1.3107 1.4025
0000 0000 4300 9601 5173
0.9345 0.8734 0.8162 0.7628 0.7129
7944 3873 9788 9521 8618
1.0800 1.1664 1.2597 1.3604 1.4693
0000 0000 1200 8896 2808
0.9259 0.8573 0.7938 0.7350 0.6805
2593 3882 3224 2985 8320
6 7 8 9 10
1.4185 1.5036 1.5938 1.6894 1.7908
1911 3026 4807 7896 4770
0.7049 0.6650 0.6274 0.5918 0.5583
6054 5711 1237 9846 9478
1.5007 1.6057 1.7181 1.8384 1.9671
3035 8148 8618 5921 5136
0.6663 0.6227 0.5820 0.5439 0.5083
4222 4974 0910 3374 4929
1.5868 1.7138 1.8509 1.9990 2.1589
7432 2427 3021 0463 2500
0.6301 0.5834 0.5402 0.5002 0.4631
6963 9040 6888 4897 9349
11 12 13 14 15
1.8982 2.0121 2.1329 2.2609 2.3965
9856 9647 2826 0396 5819
0.5267 0.4969 0.4688 04423 0.4172
8753 6936 3902 0096 6506
2.1048 2.2521 2.4098 2.5785 2.7590
5195 9159 4500 3415 3154
0.4750 0.4440 0.4149 0.3878 0.3624
9280 1196 6445 1724 4602
2.3316 2.5181 2.7196 2.9371 3.1721
3900 7012 2373 9362 6911
0.4288 0.3971 0.3676 0.3404 0.3152
8286 1376 9792 6104 4170
16 17 18 19 20
2.5403 2.6927 2.8543 3.0255 3.2071
5168 7279 3915 9950 3547
0.3936 0.3713 0.3503 0.3305 0.3118
4628 6442 4379 1301 0473
2.9521 3.1588 3.3799 3.6165 3.8696
6375 1521 3228 2754 8446
0.3387 0.3165 0.2958 0.2765 0.2584
3460 7439 6392 0833 1900
3.4259 3.7000 3.9960 4.3157 4.6609
4264 1805 1950 0106 5714
0.2918 0.2702 0.2502 0.2317 0.2145
9047 6895 4903 1206 4821
21 22 23 24 25
3.3995 3.6035 3.8197 4.0489 4.2918
6360 3742 4966 3464 7072
0.2941 0.2775 0.2617 0.2469 0.2329
5540 0510 9726 7855 9863
4.1405 4.4304 4.7405 5.0723 5.4274
6237 0174 2986 6695 3264
0.2415 0.2257 0.2109 0.1971 0.1842
1309 1317 4688 4662 4918
5.0338 5.4365 5.8714 6.3411 6.8484
3372 4041 6365 8074 7520
0.1986 0.1839 0.1703 0.1576 0.1460
5575 4051 1528 9934 1790
26 27 28 29 30
4.5493 4.8223 5.1116 5.4183 5.7434
8296 4594 8670 8790 9117
0.2198 0.2073 0.1956 0.1845 0.1741
1003 6795 3014 5674 1013
5.8073 6.2138 6.6488 7.1142 7.6122
5292 6763 3836 5705 5504
0.1721 0.1609 0.1504 0.1405 0.1313
9549 3037 0221 6282 6712
7.3963 7.9880 8.6271 9.3172 10.0626
5321 6147 0639 7490 5689
0.1352 0.1251 0.1159 0.1073 0.0993
0176 8682 1372 2752 7733
31 32 33 34 35
6.0881 6.4533 6.8405 7.2510 7.6860
0064 8668 8988 2528 8679
0.1642 0.1549 0.1461 0.1379 0.1301
5484 5740 8622 1153 0522
8.1451 8.7152 9.3253 9.9781 10.6765
1290 7080 3975 1354 8148
0.1227 0.1147 0.1072 0.1002 0.0936
7301 4113 3470 1934 6294
10.8676 11.7370 12.6760 13.6901 14.7853
6944 8300 4964 3361 4429
0.0920 0.0852 0.0788 0.0730 0.0676
1605 0005 8893 4531 3454
36 37 38 39 40
8.1472 8.6360 9.1542 9.7035 10.2857
5200 8712 5235 0749 1794
0.1227 0.1157 0.1092 0.1030 0.0972
4077 9318 3885 5552 2219
11.4239 12.2236 13.0792 13.9948 14.9744
4219 1814 7141 2041 5784
0.0875 0.0818 0.0764 0.0714 0.0667
3546 0884 5686 5501 8038
15.9681 17.2456 18.6252 20.1152 21.7245
7184 2558 7563 9768 2150
0.0626 0.0579 0.0536 0.0497 0.0460
2458 8572 9048 1341 3093
41 42 43 44 45
10.9028 11.5570 12.2504 12.9854 13.7646
6101 3267 5463 8191 1083
0.0917 0.0865 0.0816 0.0770 0.0726
1905 2740 2962 0908 5007
16.0226 17.1442 18.3443 19.6284 21.0024
6989 5678 5475 5959 5176
0.0624 0.0583 0.0545 0.0509 0.0476
1157 2857 1268 4643 1349
23.4624 25.3394 27.3666 29.5559 31.9204
8322 8187 4042 7166 4939
0.0426 0.0394 0.0365 0.0338 0.0313
2123 6411 4084 3411 2788
46 47 48 49 50
14.5904 15.4659 16.3938 17.3775 18.4201
8748 1673 7173 0403 5427
0.0685 0.0646 0.0609 0.0575 0.0542
3781 5831 9840 4566 8836
22.4726 24.0457 25.7289 27.5299 29.4570
2338 0702 0651 2997 2506
0.0444 0.0415 0.0388 0.0363 0.0339
9859 8747 6679 2410 4776
34.4740 37.2320 40.2105 43.4274 46.9016
8534 1217 7314 1899 1251
0.0290 0.0268 0.0248 0.0230 0.0213
0730 5861 6908 2693 2123
A.8
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
TABLE 4 Log-Tables LOGARITHAMS
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.9
APPENDICES LOG-TABLES
A.10
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
TABLE 5 ANTILOGARITHMS LOG-TABLES
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.11
APPENDICES LOG-TABLES
A.12
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.13
To find the area under the curve between the mean and a point 2.24 standard deviations to the right of the mean, look up the value opposite 2.2 and under 0.04 in the table; 0.4875 of the area under the curve lies between the mean and a z Value of 2.24
Example:
0.00 0.0000 0.0398 0.0793 0.1179 0.1554 0.1915 0.2257 0.2580 0.2881 0.3159 0.3413 0.3643 0.3849 0.4032 0.4192 0.4332 0.4452 0.4554 0.4641 0.4713 0.4772 0.4821 0.4861 0.4893 0.4918 0.4938 0.4953 0.4965 0.4974 0.4981 0.4987
x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
0.0040 0.0438 0.0832 0.1217 0.1591 0.1950 0.2291 0.2611 0.2910 0.3186 0.3438 0.3665 0.3869 0.4049 0.4207 0.4345 0.4463 0.4564 0.4649 0.4719 0.4778 0.4826 0.4864 0.4896 0.4920 0.4940 0.4955 0.4966 0.4975 0.4982 0.4987
0.01
0.02
z = 2.24
0.0080 0.0478 0.0871 0.1255 0.1628 0.1985 0.2324 0.2642 0.2939 0.3212 0.3461 0.3686 0.3888 0.4066 0.4222 0.4357 0.4474 0.4573 0.4656 0.4726 0.4783 0.4830 0.4868 0.4898 0.4922 0.4941 04956 0.4967 0.4976 0.4982 0.4987
Mean
0.0120 0.0517 0.0910 0.1293 0.1664 0.2019 0.2357 0.2673 0.2967 0.3238 0.3485 0.3708 0.3907 0.4082 0.4236 0.4370 0.4484 0.4582 0.4664 0.4732 0.4788 0.4834 0.4871 0.4901 0.4925 0.4943 0.4957 0.4968 0.4977 0.4983 0.4988
0.03
0.4875 of Area
0.0160 0.0557 0.0948 0.1331 0.1700 0.2054 0.2389 0.2704 0.2995 0.3264 0.3508 0.3729 0.3925 0.4099 0.4251 0.4382 0.4495 0.4591 0.4671 0.4738 0.4793 0.4838 0.4875 0.4904 0.4927 0.4945 0.4959 0.4969 0.4977 0.4984 0.4988
0.04 0.0239 0.0636 0.1026 0.1406 0.1772 0.2123 0.2454 0.2764 0.3051 0.3315 0.3554 0.3770 0.3962 0.4131 0.4279 0.4406 0.4515 0.4608 0.4686 0.4750 0.4803 0.4846 0.4881 0.4909 0.4931 0.4948 0.4961 0.4971 0.4979 0.4985 0.4989
0.4989
0.06
0.0199 0.0596 0.0987 0.1368 0.1736 0.2088 0.2422 0.2734 0.3023 0.3289 0.3531 0.3749 0.3944 0.4115 0.4265 0.4394 0.4505 0.4599 0.4678 0.4744 0.4798 0.4842 0.4878 0.4906 0.4929 0.4946 0.4960 0.4970 0.4978 0.4984
0.05
0.4989
0.0279 0.0675 0.1064 0.1443 0.1808 0.2157 0.2486 0.2794 0.3078 0.3340 0.3577 0.3790 0.3980 0.4147 0.4292 0.4418 0.4525 0.4616 0.4693 0.4756 0.4808 0.4850 0.4884 0.4911 0.4932 0.4949 0.4962 0.4972 0.4979 0.4985
0.07
0.4990
0.0319 0.0714 0.1103 0.1480 0.1844 0.2190 0.2517 0.2823 0.3106 0.3365 0.3599 0.3810 0.3997 0.4162 0.4306 0.4429 0.4535 0.4625 0.4699 0.4761 0.4812 0.4854 0.4887 0.4913 0.4934 0.4951 0.4963 0.4973 0.4980 0.4986
0.08
Areas under the Standard Normal Probability Distribution between the Mean and Positive Values of z
Table 6
0.4990
0.0359 0.0753 0.1141 0.1517 0.1879 0.2224 0.2549 0.2852 0.3133 0.3389 0.3621 0.3830 0.4015 0.4177 0.4319 0.4441 0.4545 0.4633 0.4706 0.4767 0.4817 0.4857 0.4890 0.4916 0.4936 0.4952 0.4964 0.4974 0.4981 0.4986
0.09
To find the value of t that corresponds to an area of 0.10 in both tails of the distribution combined, when there are 19 degress of freedom, look under the 0.10 column, and proceed down to the 19 degrees of freedom row; the appropriate t value there is 1.729
Example: 0.10 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645
Freedom 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 Normal Distribution
Degree of 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960
0.05 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326
0.02
Area in Both Tails Combined
Areas in Both Tails Combined for Student’s t Distribution
Table 7
63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576
0.01
APPENDICES
A.14
Copyright -The Institute of Chartered Accountants of India
COMMON PROFICIENCY TEST
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.15
6
the curve (the
11
the 11 degrees
value is 14.631
chi-squares
the appropriate
of freedom row,
5.229 5.812 6.408 7.015 7.633
15 16 17 18 19
8.260
4.660
14
20
4.107
3.571
13
12
2.558
10
the table and 3.053
2.088
9
0.20 column in
look under the
1.646
1.239
8
in the right tail)
coloured area 7
0.554
5
the area under 0.872
0.297
4
value of 0.20 of
the chi-square
0.115
0.0201
0.00016
0.99
3
freedom, to find
2
1
distribution with
11 degrees of
Freedom
of
Degrees
In a chi-square
Example:
9.591
8.907
8.231
7.564
6.908
6.262
5.629
5.009
4.404
3.816
3.247
2.700
2.180
1.690
1.237
0.831
0.484
0.216
0.0506
0.00098
0.975
10.851
10.117
9.390
8.672
7.962
7.261
6.571
5.892
5.226
4.575
3.940
3.325
2.733
2.167
1.635
1.145
0.711
0.352
0.103
0.00398
0.95
12.443
11.651
10.865
10.085
9.312
8.547
7.790
7.042
6.304
5.578
4.865
4.168
3.490
2.833
2.204
1.610
1.064
0.584
0.211
0.0158
14.578
13.716
12.857
12.002
11.152
10.307
9.467
8.634
7.807
6.989
6.179
5.380
4.594
3.822
3.070
2.343
1.649
1.005
0.446
0.0642
0.800
Area in Right Tail 0.90
1
25.038
23.900
22.760
21.615
20.465
19.311
18.151
16.985
15.812
14.631
13.442
12.242
11.030
9.803
8.558
7.289
5.989
4.642
3.219
1.642
0.20
28.412
27.204
25.989
24.769
23.542
22.307
21.064
19.812
18.549
17.275
15.987
14.684
13.362
12.017
10.645
9.236
7.779
6.251
4.605
2.706
0.10
31.410
30.144
28.869
27.587
26.296
24.996
23.685
22.362
21.026
19.675
18.307
16.919
15.507
14.067
12.592
11.070
9.488
7.815
5.991
3.841
0.05
34.170
32.852
31.526
30.191
28.845
27.488
26.119
24.736
23.337
21.920
20.483
19.023
17.535
16.013
14.449
12.833
11.143
9.348
7.378
5.024
0.025
Area in the Right Tail of a Chi-square ( 243 2) Distribution
Table 8
37.566
36.191
34.805
33.409
32.000
30.578
29.141
27.688
26.217
24.725
23.209
21.666
20.090
18.475
16.812
15.086
13.277
11.345
9.210
6.635
0.01
A.16
Copyright -The Institute of Chartered Accountants of India
F value is 3.94.
the appropriate
freedom row;
degrees of
across the 6
column and
Freedom
15 degrees of
look under the
under the curve
of the area
Value for 0.05
to find the F
denominator,
freedom for the
6 degrees of
numerator and
freedom for the
degrees of
bution with 15
In an F distri-
Example:
4.32 4.30 4.28 4.26 4.24 4.17 4.08 4.00 3.92 3.84
30 40 60 120 º
4.49 4.45 4.41 4.38 4.35
21 22 23 24 25
16 17 18 19 20
4.84 4.75 4.67 4.60 4.54
5.99 5.59 5.32 5.12 4.96
6 7 8 9 10 11 12 13 14 15
161 18.5 10.1 7.71 6.61
1 2 3 4 5
1
3.32 3.23 3.15 3.07 3.00
3.47 3.44 3.42 3.40 3.39
3.63 3.59 3.55 3.52 3.49
3.98 3.89 3.81 3.74 3.68
5.14 4.74 4.46 4.26 4.10
200 19.0 9.55 6.94 5.79
2
2.92 2.84 2.76 2.68 2.60
3.07 3.05 3.03 3.01 2.99
3.24 3.20 3.16 3.13 3.10
3.59 3.49 3.41 3.34 3.29
4.76 4.35 4.07 3.86 3.71
216 19.2 9.28 6.59 5.41
3
3.94
2.69 2.61 2.53 2.45 2.37
2.84 2.82 2.80 2.78 2.76
3.01 2.96 2.93 2.90 2.87
3.36 3.26 3.18 3.11 3.06
4.53 4.12 3.84 3.63 3.48
225 19.2 9.12 6.39 5.19
4
5
2.53 2.45 2.37 2.29 2.21
2.68 2.66 2.64 2.62 2.60
2.85 2.81 2.77 2.74 2.71
3.20 3.11 3.03 2.96 2.90
4.39 3.97 3.69 3.48 3.33
230 19.3 9.01 6.26 5.05
0.05 of area
2.42 2.34 2.25 2.18 2.10
2.57 2.55 2.53 2.51 2.49
2.74 2.70 2.66 2.63 2.60
3.09 3.00 2.92 2.85 2.79
4.28 3.87 3.58 3.37 3.22
234 19.3 8.94 6.16 4.95
6
2.33 2.25 2.17 2.09 2.01
2.49 2.46 2.44 2.42 2.40
2.66 2.61 2.58 2.54 2.51
3.01 2.91 2.83 2.76 2.71
4.21 3.79 3.50 3.29 3.14
237 19.4 8.89 6.09 4.88
7
2.27 2.18 2.10 2.02 1.94
2.42 2.40 2.37 2.36 2.34
2.59 2.55 2.51 2.48 2.45
2.95 2.85 2.77 2.70 2.64
4.15 3.73 3.44 3.23 3.07
239 19.4 8.85 6.04 4.82
8
2.21 2.12 2.04 1.96 1.88
2.37 2.34 2.32 2.30 2.28
2.54 2.49 2.46 2.42 2.39
2.90 2.80 2.71 2.65 2.59
4.10 3.68 3.39 3.18 3.02
241 19.4 8.81 6.00 4.77
9
2.16 2.08 1.99 1.91 1.83
2.32 2.30 2.27 2.25 2.24
2.49 2.45 2.41 2.38 2.35
2.85 2.75 2.67 2.60 2.54
4.06 3.64 3.35 3.14 2.98
242 19.4 8.79 5.96 4.74
10
2.09 2.00 1.92 1.83 1.75
2.25 2.23 2.20 2.18 2.16
2.42 2.38 2.34 2.31 2.28
2.79 2.69 2.60 2.53 2.48
4.00 3.57 3.28 3.07 2.91
244 19.4 8.74 5.91 4.68
12
2.01 1.92 1.84 1.75 1.67
2.18 2.15 2.13 2.11 2.09
2.35 2.31 2.27 2.23 2.20
2.72 2.62 2.53 2.46 2.40
3.94 3.51 3.22 3.01 2.85
246 19.4 8.70 5.86 4.62
15
1.93 1.84 1.75 1.66 1.57
2.10 2.07 2.05 2.03 2.01
2.28 2.23 2.19 2.16 2.12
2.65 2.54 2.46 2.39 2.33
3.87 3.44 3.15 2.94 2.77
248 19.4 8.66 5.80 4.56
20
Degrees of Freedom for Numerator
1.89 1.79 1.70 1.61 1.52
2.05 2.03 2.01 1.98 1.96
2.24 2.19 2.15 2.11 2.08
2.61 2.51 2.42 2.35 2.29
3.84 3.41 3.12 2.90 2.74
249 19.5 8.64 5.77 4.53
24
1.84 1.74 1.65 1.55 1.46
2.01 1.98 1.96 1.94 1.92
2.19 2.15 2.11 2.07 2.04
2.57 2.47 2.38 2.31 2.25
3.81 3.38 3.08 2.86 2.70
250 19.5 8.62 5.75 4.50
30
1.79 1.69 1.59 1.50 1.39
1.96 1.94 1.91 1.89 1.87
2.15 2.10 2.06 2.03 1.99
2.53 2.43 2.34 2.27 2.20
3.77 3.34 3.04 2.83 2.66
251 19.5 8.59 5.72 4.46
40
Values of F for F Distribution with 0.05 of the Area in the Right Tail
Table 9 (a)
1.74 1.64 1.53 1.43 1.32
1.92 1.89 1.86 1.84 1.82
2.11 2.06 2.02 1.98 1.95
2.49 2.38 2.30 2.22 2.16
3.74 3.30 3.01 2.79 2.62
252 19.5 8.57 5.69 4.43
60
1.68 1.58 1.47 1.35 1.22
1.87 1.84 1.81 1.79 1.77
2.06 2.01 1.97 1.93 1.90
2.45 2.34 2.25 2.18 2.11
3.70 3.27 2.97 2.75 2.58
253 19.5 8.55 5.66 4.40
120
1.62 1.51 1.39 1.25 1.00
1.81 1.78 1.76 1.73 1.71
2.01 1.96 1.92 1.88 1.84
2.40 2.30 2.21 2.13 2.07
3.67 3.23 2.93 2.71 2.54
254 19.5 8.53 5.63 4.37
∞
APPENDICES
COMMON PROFICIENCY TEST
Degrees of Freedom for Denominator
STATISTICS
Copyright -The Institute of Chartered Accountants of India
A.17
F value is 10.5
the appropriate
freedom row;
degrees of
across the 5
column and
freedom
17 degrees of
look under the
under the curve
of the area
Value for 0.01
to find the F
denominator,
freedom for the
5 degrees of
numerator and
freedom for the
degrees of
bution with 7
In an F distri-
Example:
Degrees of Freedom for Denominator
4,052 98.5 34.1 21.2 16.3 13.7 12.2 11.3 10.6 10.0 9.65 9.33 9.07 8.86 8.68 8.53 8.40 8.29 8.19 8.10 8.02 7.95 7.88 7.82 7.77 7.56 7.31 7.08 6.85 6.63
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 30 40 60 120 º
1
5.39 5.18 4.98 4.79 4.61
5.78 5.72 5.66 5.61 5.57
6.23 6.11 6.01 5.93 5.85
7.21 6.93 6.70 6.51 6.36
10.9 9.55 8.65 8.02 7.56
5,000 99.0 30.8 18.0 13.3
2
4.51 4.31 4.13 3.95 3.78
4.87 4.82 4.76 4.72 4.68
5.29 5.19 5.09 5.01 4.94
6.22 5.95 5.74 5.56 5.42
9.78 8.45 7.59 6.99 6.55
5,403 99.2 29.5 16.7 12.1
3
4.02 3.83 3.65 3.48 3.32
4.37 4.31 4.26 4.22 4.18
4.77 4.67 4.58 4.50 4.43
5.67 5.41 5.21 5.04 4.89
9.15 7.85 7.01 6.42 5.99
5,625 99.2 28.7 16.0 11.4
4
10.5
3.70 3.51 3.34 3.17 3.02
4.04 3.99 3.94 3.90 3.86
4.44 4.34 4.25 4.17 4.10
5.32 5.06 4.86 4.70 4.56
8.75 7.46 6.63 6.06 5.64
5,764 99.3 28.2 15.5 11.0
5
6
3.47 3.29 3.12 2.96 2.80
3.81 3.76 3.71 3.67 3.63
4.20 4.10 4.01 3.94 3.87
5.07 4.82 4.62 4.46 4.32
8.47 7.19 6.37 5.80 5.39
5,859 99.3 27.9 15.2 10.7
0.01 of area
3.30 3.12 2.95 2.79 2.64
3.64 3.59 3.54 3.50 3.46
4.03 3.93 3.84 3.77 3.70
4.89 4.64 4.44 4.28 4.14
8.26 6.99 6.18 5.61 5.20
5,928 99.4 27.7 15.0 10.5
7
3.17 2.99 2.82 2.66 2.51
3.51 3.45 3.41 3.36 3.32
3.89 3.79 3.71 3.63 3.56
4.74 4.50 4.30 4.14 4.00
8.10 6.84 6.03 5.47 5.06
5,982 99.4 27.5 14.8 10.3
8
3.07 2.89 2.72 2.56 2.41
3.40 3.35 3.30 3.26 3.22
3.78 3.68 3.60 3.52 3.46
4.63 4.39 4.19 4.03 3.89
7.98 6.72 5.91 5.35 4.94
6,023 99.4 27.3 14.7 10.2
9
2.98 2.80 2.63 2.47 2.32
3.31 3.26 3.21 3.17 3.13
3.69 3.59 3.51 3.43 3.37
4.54 4.30 4.10 3.94 3.80
7.87 6.62 5.81 5.26 4.85
6,056 99.4 27.2 14.5 10.1
10
2.84 2.66 2.50 2.34 2.18
3.17 3.12 3.07 3.03 2.99
3.55 3.46 3.37 3.30 3.23
4.40 4.16 3.96 3.80 3.67
7.72 6.47 5.67 5.11 4.71
6,106 99.4 27.1 14.4 9.89
12
2.70 2.52 2.35 2.19 2.04
3.03 2.98 2.93 2.89 2.85
3.41 3.31 3.23 3.15 3.09
4.25 4.01 3.82 3.66 3.52
7.56 6.31 5.52 4.96 4.56
6,157 99.4 26.9 14.2 9.72
15
2.55 2.37 2.20 2.03 1.88
2.88 2.83 2.78 2.74 2.70
3.26 3.16 3.08 3.00 2.94
4.10 3.86 3.66 3.51 3.37
7.40 6.16 5.36 4.81 4.41
6,209 99.4 26.7 14.0 9.55
20
Degrees of Freedom for Numerator
2.47 2.29 2.12 1.95 1.79
2.80 2.75 2.70 2.66 2.62
3.18 3.08 3.00 2.92 2.86
4.02 3.78 3.59 3.43 3.29
7.31 6.07 5.28 4.73 4.33
6,235 99.5 26.6 13.9 9.47
24
2.39 2.20 2.03 1.86 1.70
2.72 2.67 2.62 2.58 2.53
3.10 3.00 2.92 2.84 2.78
3.94 3.70 3.51 3.35 3.21
7.23 5.99 5.20 4.65 4.25
6,261 99.5 26.5 13.8 9.38
30
2.30 2.11 1.94 1.76 1.59
2.64 2.58 2.54 2.49 2.45
3.02 2.92 2.84 2.76 2.69
3.86 3.62 3.43 3.27 3.13
7.14 5.91 5.12 4.57 4.17
6,287 99.5 26.4 13.7 9.29
40
Values of F for F Distributions with 0.01 of the Area in the Right Tail
Table 9 (b)
2.21 2.02 1.84 1.66 1.47
2.55 2.50 2.45 2.40 2.36
2.93 2.83 2.75 2.67 2.61
3.78 3.54 3.34 3.18 3.05
7.06 5.82 5.03 4.48 4.08
6,313 99.5 26.3 13.7 9.20
60
2.11 1.92 1.73 1.53 1.32
2.46 2.40 2.35 2.31 2.27
2.84 2.75 2.66 2.58 2.52
3.69 3.45 3.25 3.09 2.96
6.97 5.74 4.95 4.40 4.00
6,339 99.5 26.2 13.6 9.11
120
2.01 1.80 1.60 1.38 1.00
2.36 2.31 2.26 2.21 2.17
2.75 2.65 2.57 2.49 2.42
3.60 3.36 3.17 3.00 2.87
6.88 5.65 4.86 4.31 3.91
6,366 99.5 26.1 13.5 9.02
∞
