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Czynniki przyszłej wartości dla kapitalizacji odsetek od 1 zł
przy stopie procentowej k i n okresach dla płatności jednorazowej
Okres (n)
FV =(1+r)
n
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
1,00% 1,0100
1,0201
1,0303
1,0406
1,0510
1,0615
1,0721
1,0829
1,0937
1,1046
1,1157
1,1268
1,1381
1,1495
1,1610
1,1726
1,1843
1,1961
1,2081
1,2202
1,2324
1,2447
1,2572
1,2697
1,2824
1,2953
1,3082
1,3213
1,3345
1,3478
2,00% 1,0200
1,0404 1,0612
1,0824
1,1041
1,1262
1,1487
1,1717
1,1951
1,2190
1,2434
1,2682
1,2936
1,3195
1,3459
1,3728
1,4002
1,4282
1,4568
1,4859
1,5157
1,5460
1,5769
1,6084
1,6406
1,6734
1,7069
1,7410
1,7758
1,8114
3,00% 1,0300
1,0609
1,0927
1,1255
1,1593
1,1941
1,2299
1,2668
1,3048
1,3439
1,3842
1,4258
1,4685
1,5126
1,5580
1,6047
1,6528
1,7024
1,7535
1,8061
1,8603
1,9161
1,9736
2,0328
2,0938
2,1566
2,2213
2,2879
2,3566
2,4273
4,00% 1,0400
1,0816
1,1249
1,1699
1,2167
1,2653
1,3159
1,3686
1,4233
1,4802
1,5395
1,6010
1,6651
1,7317
1,8009
1,8730
1,9479
2,0258
2,1068
2,1911
2,2788
2,3699
2,4647
2,5633
2,6658
2,7725
2,8834
2,9987
3,1187
3,2434
5,00% 1,0500
1,1025
1,1576
1,2155
1,2763
1,3401
1,4071
1,4775
1,5513
1,6289
1,7103
1,7959
1,8856
1,9799
2,0789
2,1829
2,2920
2,4066
2,5270
2,6533
2,7860
2,9253
3,0715
3,2251
3,3864
3,5557
3,7335
3,9201
4,1161
4,3219
6,00% 1,0600
1,1236
1,1910
1,2625
1,3382
1,4185
1,5036
1,5938
1,6895
1,7908
1,8983
2,0122
2,1329
2,2609
2,3966
2,5404
2,6928
2,8543
3,0256
3,2071
3,3996
3,6035
3,8197
4,0489
4,2919
4,5494
4,8223
5,1117
5,4184
5,7435
7,00% 1,0700
1,1449
1,2250
1,3108
1,4026
1,5007
1,6058
1,7182
1,8385
1,9672
2,1049
2,2522
2,4098
2,5785
2,7590
2,9522
3,1588
3,3799
3,6165
3,8697
4,1406
4,4304
4,7405
5,0724
5,4274
5,8074
6,2139
6,6488
7,1143
7,6123
8,00% 1,0800
1,1664
1,2597
1,3605
1,4693
1,5869
1,7138
1,8509
1,9990
2,1589
2,3316
2,5182
2,7196
2,9372
3,1722
3,4259
3,7000
3,9960
4,3157
4,6610
5,0338
5,4365
5,8715
6,3412
6,8485
7,3964
7,9881
8,6271
9,3173
10,0627
9,00% 1,0900
1,1881
1,2950
1,4116
1,5386
1,6771
1,8280
1,9926
2,1719
2,3674
2,5804
2,8127
3,0658
3,3417
3,6425
3,9703
4,3276
4,7171
5,1417
5,6044
6,1088
6,6586
7,2579
7,9111
8,6231
9,3992
10,2451
11,1671
12,1722
13,2677
10,00% 1,1000
1,2100
1,3310
1,4641
1,6105
1,7716
1,9487
2,1436
2,3579
2,5937
2,8531
3,1384
3,4523
3,7975
4,1772
4,5950
5,0545
5,5599
6,1159
6,7275
7,4002
8,1403
8,9543
9,8497
10,8347
11,9182
13,1100
14,4210
15,8631
17,4494
11,00% 1,1100
1,2321
1,3676
1,5181
1,6851
1,8704
2,0762
2,3045
2,5580
2,8394
3,1518
3,4985
3,8833
4,3104
4,7846
5,3109
5,8951
6,5436
7,2633
8,0623
8,9492
9,9336
11,0263
12,2392
13,5855
15,0799
16,7386
18,5799
20,6237
22,8923
12,00% 1,1200
1,2544 1,4049
1,5735
1,7623
1,9738
2,2107
2,4760
2,7731
3,1058
3,4785
3,8960
4,3635
4,8871
5,4736
6,1304
6,8660
7,6900
8,6128
9,6463
10,8038
12,1003
13,5523
15,1786
17,0001
19,0401
21,3249
23,8839
26,7499
29,9599
13,00% 1,1300
1,2769
1,4429
1,6305
1,8424
2,0820
2,3526
2,6584
3,0040
3,3946
3,8359
4,3345
4,8980
5,5348
6,2543
7,0673
7,9861
9,0243
10,1974
11,5231
13,0211
14,7138
16,6266
18,7881
21,2305
23,9905
27,1093
30,6335
34,6158
39,1159
14,00% 1,1400
1,2996
1,4815
1,6890
1,9254
2,1950
2,5023
2,8526
3,2519
3,7072
4,2262
4,8179
5,4924
6,2613
7,1379
8,1372
9,2765
10,5752
12,0557
13,7435
15,6676
17,8610
20,3616
23,2122
26,4619
30,1666
34,3899
39,2045
44,6931
50,9502
15,00% 1,1500
1,3225
1,5209
1,7490
2,0114
2,3131
2,6600
3,0590
3,5179
4,0456
4,6524
5,3503
6,1528
7,0757
8,1371
9,3576 10,7613
12,3755
14,2318
16,3665
18,8215
21,6447
24,8915
28,6252
32,9190
37,8568
43,5353
50,0656
57,5755
66,2118
16,00% 1,1600
1,3456
1,5609
1,8106
2,1003
2,4364
2,8262
3,2784
3,8030
4,4114
5,1173
5,9360
6,8858
7,9875
9,2655 10,7480 12,4677
14,4625
16,7765
19,4608
22,5745
26,1864
30,3762
35,2364
40,8742
47,4141
55,0004
63,8004
74,0085
85,8499
17,00% 1,1700
1,3689
1,6016
1,8739
2,1924
2,5652
3,0012
3,5115
4,1084
4,8068
5,6240
6,5801
7,6987
9,0075 10,5387
12,3303 14,4265
16,8790
19,7484
23,1056
27,0336
31,6293
37,0062
43,2973
50,6578
59,2697
69,3455
81,1342
94,9271
111,0647
18,00% 1,1800
1,3924
1,6430
1,9388
2,2878
2,6996
3,1855
3,7589
4,4355
5,2338
6,1759
7,2876
8,5994 10,1472
11,9737
14,1290 16,6722
19,6733
23,2144
27,3930
32,3238
38,1421
45,0076
53,1090
62,6686
73,9490
87,2598
102,9666
121,5005
143,3706
19,00% 1,1900
1,4161
1,6852
2,0053
2,3864
2,8398
3,3793
4,0214
4,7854
5,6947
6,7767
8,0642
9,5964 11,4198
13,5895 16,1715
19,2441
22,9005
27,2516
32,4294
38,5910
45,9233
54,6487
65,0320
77,3881
92,0918
109,5893
130,4112
155,1893
184,6753
20,00% 1,2000
1,4400
1,7280
2,0736
2,4883
2,9860
3,5832
4,2998
5,1598
6,1917
7,4301
8,9161 10,6993 12,8392 15,4070
18,4884 22,1861
26,6233
31,9480
38,3376
46,0051
55,2061
66,2474
79,4968
95,3962
114,4755
137,3706
164,8447
197,8136
237,3763
21,00% 1,2100
1,4641
1,7716
2,1436
2,5937
3,1384
3,7975
4,5950
5,5599
6,7275
8,1403
9,8497 11,9182
14,4210
17,4494 21,1138
25,5477
30,9127
37,4043
45,2593
54,7637
66,2641
80,1795
97,0172
117,3909
142,0429
171,8719
207,9651
251,6377
304,4816
22,00% 1,2200
1,4884
1,8158
2,2153
2,7027
3,2973
4,0227
4,9077
5,9874
7,3046
8,9117
10,8722 13,2641 16,1822
19,7423
24,0856 29,3844
35,8490
43,7358
53,3576
65,0963
79,4175
96,8894
118,2050 144,2101
175,9364
214,6424
261,8637
319,4737
389,7579
23,00% 1,2300
1,5129
1,8609
2,2889
2,8153
3,4628
4,2593
5,2389
6,4439
7,9259
9,7489
11,9912
14,7491
18,1414
22,3140
27,4462 33,7588
41,5233
51,0737
62,8206
77,2694
95,0413
116,9008
143,7880 176,8593
217,5369
267,5704
329,1115
404,8072
497,9129
24,00% 1,2400
1,5376
1,9066
2,3642
2,9316
3,6352
4,5077
5,5895
6,9310
8,5944 10,6571
13,2148 16,3863 20,3191
25,1956
31,2426 38,7408
48,0386
59,5679
73,8641
91,5915
113,5735 140,8312
174,6306 216,5420 268,5121
332,9550
412,8642
511,9516
634,8199
25,00% 1,2500
1,5625
1,9531
2,4414
3,0518
3,8147
4,7684
5,9605
7,4506
9,3132
11,6415
14,5519
18,1899
22,7374
28,4217
35,5271 44,4089
55,5112
69,3889
86,7362
108,4202
135,5253 169,4066
211,7582 264,6978 330,8722
413,5903
516,9879
646,2349
807,7936
26,00% 1,2600
1,5876
2,0004
2,5205
3,1758
4,0015
5,0419
6,3528
8,0045 10,0857 12,7080
16,0120 20,1752
25,4207 32,0301 40,3579 50,8510
64,0722
80,7310 101,7211
128,1685
161,4924 203,4804
256,3853 323,0454 407,0373
512,8670
646,2124
814,2276
1025,9267
27,00% 1,2700
1,6129
2,0484 2,6014
3,3038
4,1959
5,3288
6,7675
8,5948 10,9153
13,8625
17,6053 22,3588 28,3957 36,0625 45,7994 58,1652
73,8698
93,8147
119,1446
151,3137
192,1683 244,0538
309,9483 393,6344 499,9157
634,8929
806,3140
1 024,0187 1 300,5038
28,00% 1,2800
1,6384
2,0972
2,6844
3,4360
4,3980
5,6295
7,2058
9,2234 11,8059 15,1116
19,3428 24,7588 31,6913
40,5648 51,9230 66,4614
85,0706
108,8904 139,3797
178,4060
228,3596 292,3003
374,1444 478,9049
612,9982
784,6377 1 004,3363
1 285,5504 1 645,5046
29,00% 1,2900
1,6641
2,1467
2,7692
3,5723
4,6083
5,9447
7,6686
9,8925 12,7614
16,4622
21,2362 27,3947 35,3391 45,5875 58,8079 75,8621
97,8622
126,2422 162,8524
210,0796
271,0027 349,5935
450,9756 581,7585
750,4685
968,1044
1 248,8546
1 611,0225 2 078,2190
30,00% 1,3000
1,6900
2,1970
2,8561
3,7129
4,8268
6,2749
8,1573
10,6045 13,7858 17,9216
23,2981 30,2875 39,3738
51,1859
66,5417 86,5042 112,4554
146,1920 190,0496
247,0645 321,1839
417,5391
542,8008 705,6410
917,3333 1 192,5333
1 550,2933
2 015,3813 2 619,9956
T
ABELE D
ABELE DY
SK
SK
ONT
ONTO
WE
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BIULETYN
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2
Czynniki obecnej wartości dla 1 zł zdyskontowanego
przy stopie procentowej k i n okresach dla płatności jednorazowej
Okres (n)
PV =
= 1/(1+r)
n
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
1,00%
0,9901
0,9803
0,9706
0,9610
0,9515
0,9420
0,9327
0,9235
0,9143
0,9053
0,8963
0,8874
0,8787
0,8700
0,8613
0,8528
0,8444
0,8360
0,8277
0,8195
0,8114
0,8034
0,7954
0,7876
0,7798
0,7720
0,7644
0,7568
0,7493
0,7419
2,00%
0,9804
0,9612
0,9423
0,9238
0,9057
0,8880
0,8706
0,8535
0,8368
0,8203
0,8043
0,7885
0,7730
0,7579
0,7430
0,7284
0,7142
0,7002
0,6864
0,6730
0,6598
0,6468
0,6342
0,6217
0,6095
0,5976
0,5859
0,5744
0,5631
0,5521
3,00%
0,9709
0,9426
0,9151
0,8885
0,8626
0,8375
0,8131
0,7894
0,7664
0,7441
0,7224
0,7014
0,6810
0,6611
0,6419
0,6232
0,6050
0,5874
0,5703
0,5537
0,5375
0,5219
0,5067
0,4919
0,4776
0,4637
0,4502
0,4371
0,4243
0,4120
4,00%
0,9615
0,9246
0,8890
0,8548
0,8219
0,7903
0,7599
0,7307
0,7026
0,6756
0,6496
0,6246
0,6006
0,5775
0,5553
0,5339
0,5134
0,4936
0,4746
0,4564
0,4388
0,4220
0,4057
0,3901
0,3751
0,3607
0,3468
0,3335
0,3207
0,3083
5,00%
0,9524
0,9070
0,8638
0,8227
0,7835
0,7462
0,7107
0,6768
0,6446
0,6139
0,5847
0,5568
0,5303
0,5051
0,4810
0,4581
0,4363
0,4155
0,3957
0,3769
0,3589
0,3418
0,3256
0,3101
0,2953
0,2812
0,2678
0,2551
0,2429
0,2314
6,00%
0,9434
0,8900
0,8396
0,7921
0,7473
0,7050
0,6651
0,6274
0,5919
0,5584
0,5268
0,4970
0,4688
0,4423
0,4173
0,3936
0,3714
0,3503
0,3305
0,3118
0,2942
0,2775
0,2618
0,2470
0,2330
0,2198
0,2074
0,1956
0,1846
0,1741
7,00%
0,9346
0,8734
0,8163
0,7629
0,7130
0,6663
0,6227
0,5820
0,5439
0,5083
0,4751
0,4440
0,4150
0,3878
0,3624
0,3387
0,3166
0,2959
0,2765
0,2584
0,2415
0,2257
0,2109
0,1971
0,1842
0,1722
0,1609
0,1504
0,1406
0,1314
8,00%
0,9259
0,8573
0,7938
0,7350
0,6806
0,6302
0,5835
0,5403
0,5002
0,4632
0,4289
0,3971
0,3677
0,3405
0,3152
0,2919
0,2703
0,2502
0,2317
0,2145
0,1987
0,1839
0,1703
0,1577
0,1460
0,1352
0,1252
0,1159
0,1073
0,0994
9,00%
0,9174
0,8417
0,7722
0,7084
0,6499
0,5963
0,5470
0,5019
0,4604
0,4224
0,3875
0,3555
0,3262
0,2992
0,2745
0,2519
0,2311
0,2120
0,1945
0,1784
0,1637
0,1502
0,1378
0,1264
0,1160
0,1064
0,0976
0,0895
0,0822
0,0754
10,00%
0,9091
0,8264
0,7513
0,6830
0,6209
0,5645
0,5132
0,4665
0,4241
0,3855
0,3505
0,3186
0,2897
0,2633
0,2394
0,2176
0,1978
0,1799
0,1635
0,1486
0,1351
0,1228
0,1117
0,1015
0,0923
0,0839
0,0763
0,0693
0,0630
0,0573
11,00%
0,9009
0,8116
0,7312
0,6587
0,5935
0,5346
0,4817
0,4339
0,3909
0,3522
0,3173
0,2858
0,2575
0,2320
0,2090
0,1883
0,1696
0,1528
0,1377
0,1240
0,1117
0,1007
0,0907
0,0817
0,0736
0,0663
0,0597
0,0538
0,0485
0,0437
12,00%
0,8929
0,7972
0,7118
0,6355
0,5674
0,5066
0,4523
0,4039
0,3606
0,3220
0,2875
0,2567
0,2292
0,2046
0,1827
0,1631
0,1456
0,1300
0,1161
0,1037
0,0926
0,0826
0,0738
0,0659
0,0588
0,0525
0,0469
0,0419
0,0374
0,0334
13,00%
0,8850
0,7831
0,6931
0,6133
0,5428
0,4803
0,4251
0,3762
0,3329
0,2946
0,2607
0,2307
0,2042
0,1807
0,1599
0,1415
0,1252
0,1108
0,0981
0,0868
0,0768
0,0680
0,0601
0,0532
0,0471
0,0417
0,0369
0,0326
0,0289
0,0256
14,00%
0,8772
0,7695
0,6750
0,5921
0,5194
0,4556
0,3996
0,3506
0,3075
0,2697
0,2366
0,2076
0,1821
0,1597
0,1401
0,1229
0,1078
0,0946
0,0829
0,0728
0,0638
0,0560
0,0491
0,0431
0,0378
0,0331
0,0291
0,0255
0,0224
0,0196
15,00%
0,8696
0,7561
0,6575
0,5718
0,4972
0,4323
0,3759
0,3269
0,2843
0,2472
0,2149
0,1869
0,1625
0,1413
0,1229
0,1069
0,0929
0,0808
0,0703
0,0611
0,0531
0,0462
0,0402
0,0349
0,0304
0,0264
0,0230
0,0200
0,0174
0,0151
16,00%
0,8621
0,7432
0,6407
0,5523
0,4761
0,4104
0,3538
0,3050
0,2630
0,2267
0,1954
0,1685
0,1452
0,1252
0,1079
0,0930
0,0802
0,0691
0,0596
0,0514
0,0443
0,0382
0,0329
0,0284
0,0245
0,0211
0,0182
0,0157
0,0135
0,0116
17,00%
0,8547
0,7305
0,6244
0,5337
0,4561
0,3898
0,3332
0,2848
0,2434
0,2080
0,1778
0,1520
0,1299
0,1110
0,0949
0,0811
0,0693
0,0592
0,0506
0,0433
0,0370
0,0316
0,0270
0,0231
0,0197
0,0169
0,0144
0,0123
0,0105
0,0090
18,00%
0,8475
0,7182
0,6086
0,5158
0,4371
0,3704
0,3139
0,2660
0,2255
0,1911
0,1619
0,1372
0,1163
0,0985
0,0835
0,0708
0,0600
0,0508
0,0431
0,0365
0,0309
0,0262
0,0222
0,0188
0,0160
0,0135
0,0115
0,0097
0,0082
0,0070
19,00%
0,8403
0,7062
0,5934
0,4987
0,4190
0,3521
0,2959
0,2487
0,2090
0,1756
0,1476
0,1240
0,1042
0,0876
0,0736
0,0618
0,0520
0,0437
0,0367
0,0308
0,0259
0,0218
0,0183
0,0154
0,0129
0,0109
0,0091
0,0077
0,0064
0,0054
20,00%
0,8333
0,6944
0,5787
0,4823
0,4019
0,3349
0,2791
0,2326
0,1938
0,1615
0,1346
0,1122
0,0935
0,0779
0,0649
0,0541
0,0451
0,0376
0,0313
0,0261
0,0217
0,0181
0,0151
0,0126
0,0105
0,0087
0,0073
0,0061
0,0051
0,0042
21,00%
0,8264
0,6830
0,5645
0,4665
0,3855
0,3186
0,2633
0,2176
0,1799
0,1486
0,1228
0,1015
0,0839
0,0693
0,0573
0,0474
0,0391
0,0323
0,0267
0,0221
0,0183
0,0151
0,0125
0,0103
0,0085
0,0070
0,0058
0,0048
0,0040
0,0033
22,00%
0,8197
0,6719
0,5507
0,4514
0,3700
0,3033
0,2486
0,2038
0,1670
0,1369
0,1122
0,0920
0,0754
0,0618
0,0507
0,0415
0,0340
0,0279
0,0229
0,0187
0,0154
0,0126
0,0103
0,0085
0,0069
0,0057
0,0047
0,0038
0,0031
0,0026
23,00%
0,8130
0,6610
0,5374
0,4369
0,3552
0,2888
0,2348
0,1909
0,1552
0,1262
0,1026
0,0834
0,0678
0,0551
0,0448
0,0364
0,0296
0,0241
0,0196
0,0159
0,0129
0,0105
0,0086
0,0070
0,0057
0,0046
0,0037
0,0030
0,0025
0,0020
24,00%
0,8065
0,6504
0,5245
0,4230
0,3411
0,2751
0,2218
0,1789
0,1443
0,1164
0,0938
0,0757
0,0610
0,0492
0,0397
0,0320
0,0258
0,0208
0,0168
0,0135
0,0109
0,0088
0,0071
0,0057
0,0046
0,0037
0,0030
0,0024
0,0020
0,0016
25,00%
0,8000
0,6400
0,5120
0,4096
0,3277
0,2621
0,2097
0,1678
0,1342
0,1074
0,0859
0,0687
0,0550
0,0440
0,0352
0,0281
0,0225
0,0180
0,0144
0,0115
0,0092
0,0074
0,0059
0,0047
0,0038
0,0030
0,0024
0,0019
0,0015
0,0012
26,00%
0,7937
0,6299
0,4999
0,3968
0,3149
0,2499
0,1983
0,1574
0,1249
0,0992
0,0787
0,0625
0,0496
0,0393
0,0312
0,0248
0,0197
0,0156
0,0124
0,0098
0,0078
0,0062
0,0049
0,0039
0,0031
0,0025
0,0019
0,0015
0,0012
0,0010
27,00%
0,7874
0,6200
0,4882
0,3844
0,3027
0,2383
0,1877
0,1478
0,1164
0,0916
0,0721
0,0568
0,0447
0,0352
0,0277
0,0218
0,0172
0,0135
0,0107
0,0084
0,0066
0,0052
0,0041
0,0032
0,0025
0,0020
0,0016
0,0012
0,0010
0,0008
28,00%
0,7813
0,6104
0,4768
0,3725
0,2910
0,2274
0,1776
0,1388
0,1084
0,0847
0,0662
0,0517
0,0404
0,0316
0,0247
0,0193
0,0150
0,0118
0,0092
0,0072
0,0056
0,0044
0,0034
0,0027
0,0021
0,0016
0,0013
0,0010
0,0008
0,0006
29,00%
0,7752
0,6009
0,4658
0,3611
0,2799
0,2170
0,1682
0,1304
0,1011
0,0784
0,0607
0,0471
0,0365
0,0283
0,0219
0,0170
0,0132
0,0102
0,0079
0,0061
0,0048
0,0037
0,0029
0,0022
0,0017
0,0013
0,0010
0,0008
0,0006
0,0005
30,00%
0,7692
0,5917
0,4552
0,3501
0,2693
0,2072
0,1594
0,1226
0,0943
0,0725
0,0558
0,0429
0,0330
0,0254
0,0195
0,0150
0,0116
0,0089
0,0068
0,0053
0,0040
0,0031
0,0024
0,0018
0,0014
0,0011
0,0008
0,0006
0,0005
0,0004
T
ABELE D
ABELE DY
SK
SK
ONT
ONTO
WE
WE
BIULETYN
RACHUNKOWOŚCI
●
www.br.infor.pl
3
Czynniki przyszłej wartości dla kapitalizacji odsetek od 1 zł
płatności rocznej przy stopie procentowej k i n okresach. Wpłaty z dołu
*
* Dla wpłat z góry należy powiększyć liczbę wpłat o 1 i dodać jedną kwotę wpłat.
Wartość przyszła annuity (płatne z dołu)
FV = CF ×
× ((1 + r)
n
–
– 1)/r
Okres (n)
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
1,00%
1,0000
2,0100
3,0301
4,0604
5,1010
6,1520
7,2135
8,2857
9,3685 10,4622 11,5668 12,6825 13,8093
14,9474
16,0969
17,2579
18,4304
19,6147
20,8109
22,0190
23,2392
24,4716
25,7163
26,9735
28,2432
29,5256
30,8209
32,1291
33,4504
34,7849
2,00%
1,0000
2,0200
3,0604
4,1216
5,2040
6,3081
7,4343
8,5830
9,7546 10,9497 12,1687
13,4121
14,6803
15,9739
17,2934
18,6393
20,0121
21,4123
22,8406
24,2974
25,7833
27,2990
28,8450
30,4219
32,0303
33,6709
35,3443
37,0512
38,7922
40,5681
3,00%
1,0000
2,0300
3,0909
4,1836
5,3091
6,4684
7,6625
8,8923 10,1591
11,4639 12,8078 14,1920
15,6178
17,0863
18,5989
20,1569
21,7616
23,4144
25,1169
26,8704
28,6765
30,5368
32,4529
34,4265
36,4593
38,5530
40,7096
42,9309
45,2189
47,5754
4,00%
1,0000
2,0400
3,1216
4,2465
5,4163
6,6330
7,8983
9,2142
10,5828 12,0061 13,4864 15,0258 16,6268
18,2919
20,0236
21,8245
23,6975
25,6454
27,6712
29,7781
31,9692
34,2480
36,6179
39,0826
41,6459
44,3117
47,0842
49,9676
52,9663
56,0849
5,00%
1,0000
2,0500
3,1525
4,3101
5,5256
6,8019
8,1420
9,5491
11,0266 12,5779 14,2068 15,9171
17,7130
19,5986
21,5786
23,6575
25,8404
28,1324
30,5390
33,0660
35,7193
38,5052
41,4305
44,5020
47,7271
51,1135
54,6691
58,4026
62,3227
66,4388
6,00%
1,0000
2,0600
3,1836
4,3746
5,6371
6,9753
8,3938
9,8975
11,4913 13,1808
14,9716 16,8699 18,8821
21,0151
23,2760
25,6725
28,2129
30,9057
33,7600
36,7856
39,9927
43,3923
46,9958
50,8156
54,8645
59,1564
63,7058
68,5281
73,6398
79,0582
7,00%
1,0000
2,0700
3,2149
4,4399
5,7507
7,1533
8,6540 10,2598
11,9780 13,8164 15,7836 17,8885 20,1406
22,5505
25,1290
27,8881
30,8402
33,9990
37,3790
40,9955
44,8652
49,0057
53,4361
58,1767
63,2490
68,6765
74,4838
80,6977
87,3465
94,4608
8,00%
1,0000
2,0800
3,2464
4,5061
5,8666
7,3359
8,9228 10,6366 12,4876 14,4866 16,6455 18,9771 21,4953
24,2149
27,1521
30,3243
33,7502
37,4502
41,4463
45,7620
50,4229
55,4568
60,8933
66,7648
73,1059
79,9544
87,3508
95,3388
103,9659
113,2832
9,00%
1,0000
2,0900
3,2781
4,5731
5,9847
7,5233
9,2004
11,0285
13,0210 15,1929
17,5603 20,1407
22,9534
26,0192
29,3609
33,0034
36,9737
41,3013
46,0185
51,1601
56,7645
62,8733
69,5319
76,7898
84,7009
93,3240
102,7231
112,9682
124,1354
136,3075
10,00%
1,0000
2,1000
3,3100
4,6410
6,1051
7,7156
9,4872
11,4359
13,5795 15,9374
18,5312 21,3843 24,5227
27,9750
31,7725
35,9497
40,5447
45,5992
51,1591
57,2750
64,0025
71,4027
79,5430
88,4973
98,3471
109,1818
121,0999
134,2099
148,6309
164,4940
11,00%
1,0000
2,1100
3,3421
4,7097
6,2278
7,9129
9,7833
11,8594
14,1640 16,7220 19,5614 22,7132 26,2116
30,0949
34,4054
39,1899
44,5008
50,3959
56,9395
64,2028
72,2651
81,2143
91,1479
102,1742
114,4133
127,9988
143,0786
159,8173
178,3972
199,0209
12,00%
1,0000
2,1200
3,3744
4,7793
6,3528
8,1152
10,0890
12,2997
14,7757 17,5487 20,6546 24,1331
28,0291
32,3926
37,2797
42,7533
48,8837
55,7497
63,4397
72,0524
81,6987
92,5026
104,6029
118,1552
133,3339
150,3339
169,3740
190,6989
214,5828
241,3327
13,00%
1,0000
2,1300
3,4069
4,8498
6,4803
8,3227 10,4047
12,7573 15,4157 18,4197
21,8143
25,6502 29,9847
34,8827
40,4175
46,6717
53,7391
61,7251
70,7494
80,9468
92,4699
105,4910
120,2048
136,8315
155,6196
176,8501
200,8406
227,9499
258,5834
293,1992
14,00%
1,0000
2,1400
3,4396
4,9211
6,6101
8,5355 10,7305
13,2328 16,0853 19,3373 23,0445 27,2707 32,0887
37,5811
43,8424
50,9804
59,1176
68,3941
78,9692
91,0249 104,7684
120,4360
138,2970
158,6586
181,8708
208,3327
238,4993
272,8892
312,0937
356,7868
15,00%
1,0000
2,1500
3,4725
4,9934
6,7424
8,7537
11,0668
13,7268 16,7858 20,3037 24,3493 29,0017 34,3519
40,5047
47,5804
55,7175
65,0751
75,8364
88,2118 102,4436 118,8101
137,6316
159,2764
184,1678
212,7930
245,7120
283,5688
327,1041
377,1697
434,7451
16,00%
1,0000
2,1600
3,5056
5,0665
6,8771
8,9775
11,4139
14,2401
17,5185 21,3215 25,7329 30,8502 36,7862
43,6720
51,6595
60,9250
71,6730
84,1407
98,6032 115,3797 134,8405
157,4150
183,6014
213,9776
249,2140
290,0883
337,5024
392,5028
456,3032
530,3117
17,00%
1,0000
2,1700
3,5389
5,1405
7,0144
9,2068
11,7720
14,7733 18,2847 22,3931 27,1999
32,8239 39,4040
47,1027
56,1101
66,6488
78,9792
93,4056 110,2846 130,0329 153,1385
180,1721
211,8013
248,8076
292,1049
342,7627
402,0323
471,3778
552,5121
647,4391
18,00%
1,0000
2,1800
3,5724
5,2154
7,1542
9,4420 12,1415
15,3270 19,0859 23,5213 28,7551 34,9311 42,2187
50,8180
60,9653
72,9390
87,0680 103,7403 123,4135 146,6280 174,0210
206,3448
244,4868
289,4945
342,6035
405,2721
479,2211
566,4809
669,4475
790,9480
19,00%
1,0000
2,1900
3,6061
5,2913
7,2966
9,6830 12,5227 15,9020 19,9234 24,7089 30,4035 37,1802 45,2445
54,8409
66,2607
79,8502
96,0218 115,2659 138,1664 165,4180 197,8474
236,4385
282,3618
337,0105
402,0425
479,4306
571,5224
681,1116
811,5228
966,7122
20,00%
1,0000
2,2000
3,6400
5,3680
7,4416
9,9299 12,9159
16,4991 20,7989 25,9587 32,1504 39,5805 48,4966
59,1959
72,0351
87,4421 105,9306 128,1167 154,7400 186,6880 225,0256
271,0307
326,2369
392,4842
471,9811
567,3773
681,8528
819,2233
984,0680
1 181,8816
21,00%
1,0000
2,2100
3,6741
5,4457
7,5892 10,1830
13,3214
17,1189
21,7139 27,2738 34,0013 42,1416
51,9913
63,9095
78,3305
95,7799 116,8937 142,4413 173,3540 210,7584 256,0176
310,7813
377,0454
457,2249
554,2422
671,6330
813,6759
985,5479 1 193,5129
1 445,1507
22,00%
1,0000
2,2200
3,7084
5,5242
7,7396 10,4423 13,7396
17,7623 22,6700 28,6574 35,9620 44,8737 55,7459
69,0100
85,1922 104,9345 129,0201 158,4045 194,2535 237,9893 291,3469
356,4432
435,8607
532,7501
650,9551
795,1653
971,1016
1 185,7440 1 447,6077 1 767,0813
23,00%
1,0000
2,2300
3,7429
5,6038
7,8926 10,7079
14,1708
18,4300 23,6690 30,1128
38,0388 47,7877 59,7788
74,5280
92,6694 114,9834 142,4295 176,1883 217,7116 268,7853 331,6059
408,8753
503,9166
620,8174
764,6054
941,4647 1 159,0016 1 426,5719 1 755,6835 2 160,4907
24,00%
1,0000
2,2400
3,7776
5,6842
8,0484 10,9801
14,6153
19,1229
24,7125 31,6434 40,2379 50,8950 64,1097
80,4961 100,8151 126,0108 157,2534 195,9942 244,0328 303,6006 377,4648
469,0563
582,6298
723,4610
898,0916 1 114,6336 1 383,1457
1 716,1007 2 128,9648 2 640,9164
25,00%
1,0000
2,2500
3,8125
5,7656
8,2070
11,2588
15,0735
19,8419
25,8023 33,2529 42,5661 54,2077 68,7596
86,9495 109,6868 138,1085
173,6357 218,0446 273,5558 342,9447 429,6809
538,1011
673,6264
843,0329 1 054,7912 1 319,4890 1 650,3612 2 063,9515 2 580,9394 3 227,1743
26,00%
1,0000
2,2600
3,8476
5,8480
8,3684
11,5442 15,5458 20,5876 26,9404 34,9449 45,0306 57,7386 73,7506
93,9258 119,3465 151,3766 191,7345 242,5855 306,6577 387,3887 489,1098
617,2783
778,7707
982,2511
1 238,6363 1 561,6818 1 968,7191 2 481,5860 3 127,7984 3 942,0260
27,00%
1,0000
2,2700
3,8829
5,9313
8,5327
11,8366
16,0324 21,3612
28,1287 36,7235 47,6388 61,5013 79,1066 101,4654 129,8611 165,9236 211,7230 269,8882 343,7580 437,5726 556,7173
708,0309
900,1993 1 144,2531 1 454,2014 1 847,8358 2 347,7515 2 982,6443 3 788,9583 4 812,9771
28,00%
1,0000
2,2800
3,9184
6,0156
8,6999 12,1359
16,5339 22,1634
29,3692 38,5926 50,3985 65,5100 84,8529 109,6117
141,3029 181,8677 233,7907 300,2521 385,3227 494,2131 633,5927
811,9987 1 040,3583 1 332,6586 1 706,8031 2 185,7079 2 798,7061 3 583,3438 4 587,6801 5 873,2306
29,00%
1,0000
2,2900
3,9541
6,1008
8,8700
12,4423 17,0506 22,9953 30,6639 40,5564 53,3178 69,7800 91,0161
118,4108 153,7500 199,3374 258,1453 334,0074 431,8696 558,1118
720,9642
931,0438 1 202,0465 1 551,6400 2 002,6156 2 584,3741 3 334,8426 4 302,9470 5 551,8016 7 162,8241
30,00%
1,0000
2,3000
3,9900
6,1870
9,0431 12,7560
17,5828 23,8577 32,0150 42,6195 56,4053 74,3270 97,6250 127,9125 167,2863 218,4722 285,0139 371,5180 483,9734 630,1655 820,2151 1 067,2796 1 388,4635 1 806,0026 2 348,8033 3 054,4443 3 971,7776 5 164,3109 6 714,6042 8 729,9855
T
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SK
SK
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ONTO
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WE
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4
Czynniki obecnej wartości dla 1 zł płatności rocznej
przy stopie dyskontowej k i n okresach. Wpłaty z dołu
*
* W przypadku wpłat z góry należy pomniejszyć liczbę wpłat o 1 i dodać jedną kwotę wpłat.
Wartość bieżąca annuity (płatne z dołu)
Okres (n)
PV = CF × (1 –
– (1/(1+r)
n
))/r
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
1,00%
0,9901
1,9704
2,9410
3,9020
4,8534
5,7955
6,7282
7,6517
8,5660
9,4713
10,3676
11,2551
12,1337
13,0037
13,8651
14,7179
15,5623 16,3983
17,2260
18,0456
18,8570
19,6604
20,4558
21,2434
22,0232
22,7952
23,5596
24,3164
25,0658
25,8077
2,00%
0,9804
1,9416
2,8839
3,8077
4,7135
5,6014
6,4720
7,3255
8,1622
8,9826
9,7868
10,5753
11,3484
12,1062
12,8493
13,5777
14,2919 14,9920
15,6785
16,3514
17,0112
17,6580
18,2922
18,9139
19,5235
20,1210
20,7069
21,2813
21,8444
22,3965
3,00%
0,9709
1,9135
2,8286
3,7171
4,5797
5,4172
6,2303
7,0197
7,7861
8,5302
9,2526
9,9540
10,6350
11,2961
11,9379
12,5611
13,1661
13,7535
14,3238
14,8775
15,4150
15,9369
16,4436
16,9355
17,4131
17,8768
18,3270
18,7641
19,1885
19,6004
4,00%
0,9615
1,8861
2,7751
3,6299
4,4518
5,2421
6,0021
6,7327
7,4353
8,1109
8,7605
9,3851
9,9856
10,5631
11,1184
11,6523
12,1657
12,6593
13,1339
13,5903
14,0292
14,4511
14,8568
15,2470
15,6221
15,9828
16,3296
16,6631
16,9837
17,2920
5,00%
0,9524
1,8594
2,7232
3,5460
4,3295
5,0757
5,7864
6,4632
7,1078
7,7217
8,3064
8,8633
9,3936
9,8986
10,3797
10,8378
11,2741
11,6896
12,0853
12,4622
12,8212
13,1630
13,4886
13,7986
14,0939
14,3752
14,6430
14,8981
15,1411
15,3725
6,00%
0,9434
1,8334
2,6730
3,4651
4,2124
4,9173
5,5824
6,2098
6,8017
7,3601
7,8869
8,3838
8,8527
9,2950
9,7122
10,1059
10,4773 10,8276
11,1581
11,4699
11,7641
12,0416
12,3034
12,5504
12,7834
13,0032
13,2105
13,4062
13,5907
13,7648
7,00%
0,9346
1,8080
2,6243
3,3872
4,1002
4,7665
5,3893
5,9713
6,5152
7,0236
7,4987
7,9427
8,3577
8,7455
9,1079
9,4466
9,7632 10,0591
10,3356
10,5940
10,8355
11,0612
11,2722
11,4693
11,6536
11,8258
11,9867
12,1371
12,2777
12,4090
8,00%
0,9259
1,7833
2,5771
3,3121
3,9927
4,6229
5,2064
5,7466
6,2469
6,7101
7,1390
7,5361
7,9038
8,2442
8,5595
8,8514
9,1216
9,3719
9,6036
9,8181
10,0168
10,2007
10,3711
10,5288
10,6748
10,8100
10,9352
11,0511
11,1584
11,2578
9,00%
0,9174
1,7591
2,5313
3,2397
3,8897
4,4859
5,0330
5,5348
5,9952
6,4177
6,8052
7,1607
7,4869
7,7862
8,0607
8,3126
8,5436
8,7556
8,9501
9,1285
9,2922
9,4424
9,5802
9,7066
9,8226
9,9290
10,0266
10,1161
10,1983
10,2737
10,00%
0,9091
1,7355
2,4869
3,1699
3,7908
4,3553
4,8684
5,3349
5,7590
6,1446
6,4951
6,8137
7,1034
7,3667
7,6061
7,8237
8,0216
8,2014
8,3649
8,5136
8,6487
8,7715
8,8832
8,9847
9,0770
9,1609
9,2372
9,3066
9,3696
9,4269
11,00%
0,9009
1,7125
2,4437
3,1024
3,6959
4,2305
4,7122
5,1461
5,5370
5,8892
6,2065
6,4924
6,7499
6,9819
7,1909
7,3792
7,5488
7,7016
7,8393
7,9633
8,0751
8,1757
8,2664
8,3481
8,4217
8,4881
8,5478
8,6016
8,6501
8,6938
12,00%
0,8929
1,6901
2,4018
3,0373
3,6048
4,1114
4,5638
4,9676
5,3282
5,6502
5,9377
6,1944
6,4235
6,6282
6,8109
6,9740
7,1196
7,2497
7,3658
7,4694
7,5620
7,6446
7,7184
7,7843
7,8431
7,8957
7,9426
7,9844
8,0218
8,0552
13,00%
0,8850
1,6681
2,3612
2,9745
3,5172
3,9975
4,4226
4,7988
5,1317
5,4262
5,6869
5,9176
6,1218
6,3025
6,4624
6,6039
6,7291
6,8399
6,9380
7,0248
7,1016
7,1695
7,2297
7,2829
7,3300
7,3717
7,4086
7,4412
7,4701
7,4957
14,00%
0,8772
1,6467
2,3216
2,9137
3,4331
3,8887
4,2883
4,6389
4,9464
5,2161
5,4527
5,6603
5,8424
6,0021
6,1422
6,2651
6,3729
6,4674
6,5504
6,6231
6,6870
6,7429
6,7921
6,8351
6,8729
6,9061
6,9352
6,9607
6,9830
7,0027
15,00%
0,8696
1,6257
2,2832
2,8550
3,3522
3,7845
4,1604
4,4873
4,7716
5,0188
5,2337
5,4206
5,5831
5,7245
5,8474
5,9542
6,0472
6,1280
6,1982
6,2593
6,3125
6,3587
6,3988
6,4338
6,4641
6,4906
6,5135
6,5335
6,5509
6,5660
16,00%
0,8621
1,6052
2,2459
2,7982
3,2743
3,6847
4,0386
4,3436
4,6065
4,8332
5,0286
5,1971
5,3423
5,4675
5,5755
5,6685
5,7487
5,8178
5,8775
5,9288
5,9731
6,0113
6,0442
6,0726
6,0971
6,1182
6,1364
6,1520
6,1656
6,1772
17,00%
0,8547
1,5852
2,2096
2,7432
3,1993
3,5892
3,9224
4,2072
4,4506
4,6586
4,8364
4,9884
5,1183
5,2293
5,3242
5,4053
5,4746
5,5339
5,5845
5,6278
5,6648
5,6964
5,7234
5,7465
5,7662
5,7831
5,7975
5,8099
5,8204
5,8294
18,00%
0,8475
1,5656
2,1743
2,6901
3,1272
3,4976
3,8115
4,0776
4,3030
4,4941
4,6560
4,7932
4,9095
5,0081
5,0916
5,1624
5,2223
5,2732
5,3162
5,3527
5,3837
5,4099
5,4321
5,4509
5,4669
5,4804
5,4919
5,5016
5,5098
5,5168
19,00%
0,8403
1,5465
2,1399
2,6386
3,0576
3,4098
3,7057
3,9544
4,1633
4,3389
4,4865
4,6105
4,7147
4,8023
4,8759
4,9377
4,9897
5,0333
5,0700
5,1009
5,1268
5,1486
5,1668
5,1822
5,1951
5,2060
5,2151
5,2228
5,2292
5,2347
20,00%
0,8333
1,5278
2,1065
2,5887
2,9906
3,3255
3,6046
3,8372
4,0310
4,1925
4,3271
4,4392
4,5327
4,6106
4,6755
4,7296
4,7746
4,8122
4,8435
4,8696
4,8913
4,9094
4,9245
4,9371
4,9476
4,9563
4,9636
4,9697
4,9747
4,9789
21,00%
0,8264
1,5095
2,0739
2,5404
2,9260
3,2446
3,5079
3,7256
3,9054
4,0541
4,1769
4,2784
4,3624
4,4317
4,4890
4,5364
4,5755
4,6079
4,6346
4,6567
4,6750
4,6900
4,7025
4,7128
4,7213
4,7284
4,7342
4,7390
4,7430
4,7463
22,00%
0,8197
1,4915
2,0422
2,4936
2,8636
3,1669
3,4155
3,6193
3,7863
3,9232
4,0354
4,1274
4,2028
4,2646
4,3152
4,3567
4,3908
4,4187
4,4415
4,4603
4,4756
4,4882
4,4985
4,5070
4,5139
4,5196
4,5243
4,5281
4,5312
4,5338
23,00%
0,8130
1,4740
2,0114
2,4483
2,8035
3,0923
3,3270
3,5179
3,6731
3,7993
3,9018
3,9852
4,0530
4,1082
4,1530
4,1894
4,2190
4,2431
4,2627
4,2786
4,2916
4,3021
4,3106
4,3176
4,3232
4,3278
4,3316
4,3346
4,3371
4,3391
24,00%
0,8065
1,4568
1,9813
2,4043
2,7454
3,0205
3,2423
3,4212
3,5655
3,6819
3,7757
3,8514
3,9124
3,9616
4,0013
4,0333
4,0591
4,0799
4,0967
4,1103
4,1212
4,1300
4,1371
4,1428
4,1474
4,1511
4,1542
4,1566
4,1585
4,1601
25,00%
0,8000
1,4400
1,9520
2,3616
2,6893
2,9514
3,1611
3,3289
3,4631
3,5705
3,6564
3,7251
3,7801
3,8241
3,8593
3,8874
3,9099
3,9279
3,9424
3,9539
3,9631
3,9705
3,9764
3,9811
3,9849
3,9879
3,9903
3,9923
3,9938
3,9950
26,00%
0,7937
1,4235
1,9234
2,3202
2,6351
2,8850
3,0833
3,2407
3,3657
3,4648
3,5435
3,6059
3,6555
3,6949
3,7261
3,7509
3,7705
3,7861
3,7985
3,8083
3,8161
3,8223
3,8273
3,8312
3,8342
3,8367
3,8387
3,8402
3,8414
3,8424
27,00%
0,7874
1,4074
1,8956
2,2800
2,5827
2,8210
3,0087
3,1564
3,2728
3,3644
3,4365
3,4933
3,5381
3,5733
3,6010
3,6228
3,6400
3,6536
3,6642
3,6726
3,6792
3,6844
3,6885
3,6918
3,6943
3,6963
3,6979
3,6991
3,7001
3,7009
28,00%
0,7813
1,3916
1,8684
2,2410
2,5320
2,7594
2,9370
3,0758
3,1842
3,2689
3,3351
3,3868
3,4272
3,4587
3,4834
3,5026
3,5177
3,5294
3,5386
3,5458
3,5514
3,5558
3,5592
3,5619
3,5640
3,5656
3,5669
3,5679
3,5687
3,5693
29,00%
0,7752
1,3761
1,8420
2,2031
2,4830
2,7000
2,8682
2,9986
3,0997
3,1781
3,2388
3,2859
3,3224
3,3507
3,3726
3,3896
3,4028
3,4130
3,4210
3,4271
3,4319
3,4356
3,4384
3,4406
3,4423
3,4437
3,4447
3,4455
3,4461
3,4466
30,00%
0,7692
1,3609
1,8161
2,1662
2,4356
2,6427
2,8021
2,9247
3,0190
3,0915
3,1473
3,1903
3,2233
3,2487
3,2682
3,2832
3,2948
3,3037
3,3105
3,3158
3,3198
3,3230
3,3254
3,3272
3,3286
3,3297
3,3305
3,3312
3,3317
3,3321
T
ABELE D
ABELE DY
SK
SK
ONT
ONTO
WE
WE
BIULETYN
RACHUNKOWOŚCI
●
www.br.infor.pl
Plik z chomika:
Pajak77
Inne pliki z tego folderu:
2900.pdf
(1782 KB)
Biuletyn Rachunkowości 10_2010 z 15.05.2010.pdf
(1799 KB)
3056.pdf
(944 KB)
Biuletyn Rachunkowości 11_2010 z 01.06.2010.pdf
(1115 KB)
Biuletyn Rachunkowości 12_2010 z 15.06.2010.pdf
(2025 KB)
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