Tablas Uso de Factores 2019

INGENIERÍA ECONÓMICA
Facultad de Ingeniería y Arquitectura
TABLA DE FACTORES DE
TASA DISCRETA DE RENDIMIENTO
UNIDAD DE ÁREA BÁSICA
Ing. Carlos Gerardo Vásquez Gallardo
NOMBRE FACTOR
Factor de Pago Simple,
Cantidad Compuesta
( SPCAF )
Factor de Pago Simple,
Valor Presente
( SPPWF )
FÓRMULAS Y FACTORES DE INGENIERÍA ECONOMICA
PARA
ENCONTRAR
DADO
FÓRMULA
UNIVERSIDAD POLITÉCNICA DE EL SALVADOR
FACTOR
DIAGRAMA
F
P
F  P(1  i )n
F=?
F = P ( F/ P )
( F/P, i %, n)
0
1
2
P
F
P  F (1  i )  n 
n
A
P
 i (1  i ) n 
A P

n
 (1  i )  1 
F
( P/F, i%, n)
P = F ( P/ F )
1
2 …… .....
P
A
 (1  i ) n  1 
P  A
n 
 i (1  i ) 
n
A=?
( A/P, i % , n )
A = P ( A/ P )
P
0
Factor Serie Uniforme,
Valor Presente
( USPWF )
……..…..
P=?
0
Factor de Recuperación
de Capital
( CRF )
ECUACIÓN
P
1
2
3
P =?
…………n
A
( P/A, i %, n )
P = A ( P/A )
0
1
2
3
…………
n
A=?
Factor de Depósito de
Fondo de Amortización
( SFDF )
A
F


i
A F

n
 (1  i )  1 
F
( A/F, i %, n )
A = F ( A/F )
0
1
2
3
…………n
A
Factor Serie Uniforme,
Cantidad Compuesta
( USCAF )
Factor de Serie
Aritmética
( ASF )
 (1  i)  1 
F  A

i


n
F
A
A
G
1

n
AG  G  

n
 i (1  i )  1 
F= ?
( F/A, i %, n )
F = A ( F/ A)
0
( AG /G, i %, n )
2G
1
3G
……….
2
3
(n-1) G
…………n

G
0 1 2 3 4 ......... n
AG = ?
AG = G( A/ G)
0 1 2 ..............
n
Factor de Valor
Presente Serie
Aritmética
( ASPWF )
P
G
Ing. Carlos Gerardo Vásquez Gallardo
1  (1  i ) n  1
n 
PG  G  


n
(1  i ) n  
 i  i (1  i )
(n-1) G
3G
( PG /G, i %, n )
2G
……….

PG = ?
G
0 1 2 3 4 ......... n
PG = G ( P/ G)
0 1 2 .............. n
Página 1
FÓRMULAS Y FACTORES DE INGENIERÍA ECONOMICA
NOMBRE FACTOR
PARA
ENCONTRAR
DADO
FÓRMULA
FACTOR
DIAGRAMA
ECUACIÓN
 (1  E )

 1

n
(1  i )

PE  D 
 ( E  i) 




n
Factor de Valor Presente
de la Serie Gradiente
Geométrica
PE
D;
E;
i
( PE/D,E; i %, n)
PE =?
1
0
2
3
4
n
D
D(1+E)
D(1+ E)2
Con E  I
5 ......
 n 
PE  D 

1  e 
. . . .. . .
D(1+E)3
Con E = i
D(1+E)4
D(1+E)
n-1
ECUACIÓN : PE = D(PE/D,E, i%,n)
VALORES LÍMITES DE LOS FACTORES CUANDO i = 0 % , n = 
FACTOR
F/P
P/F
A/P
P/A
A/F
F/A
A/ G
n= 

P/G
1 / i2
PE / D
1
;Cuando i  E
iE
;Cuando i  E
Ing. Carlos Gerardo Vásquez Gallardo
0
i
1/i
0

1/i
i=0%
1
1
1/n
n
1/n
n
n-1
2
n ( n-1 )
2
(1  E ) n  1
E
FÓRMULAS RELACIONADAS
1. ( F/ P ) = 1 / ( P/F )
2. ( P/F ) = 1 / ( F/P )
3. ( F/A ) = 1 / ( A/F )
4. ( A/F ) = 1 / ( F/A )
5. ( P/A ) = 1 / ( A/P )
6. ( A/P ) = 1/ ( P/A )
7. ( A/P ) = ( A/F ) + i
8.
(A/F )
= ( A/P ) - i
1  n( SFDF )
i
10.- P / G = ASF. USPWF
9.- A /G =
Página 2
i = 0.5 %
Factores de interes discreto capitalizado al : i = 0.00500
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.005000
1.010025
1.015075
1.020151
1.025251
0.995025
0.990075
0.985149
0.980248
0.975371
1.005000
0.503753
0.336672
0.253133
0.203010
0.995025
1.985099
2.970248
3.950496
4.925866
1.000000
2.005000
3.015025
4.030100
5.050251
1.000000
0.498753
0.331672
0.248133
0.198010
0.000000
0.990075
2.960372
5.901115
9.802597
0.000000
1.000000
3.005000
6.020025
10.050125
0.000000
0.498753
0.996675
1.493766
1.990025
6
7
8
9
10
1.030378
1.035529
1.040707
1.045911
1.051140
0.970518
0.965690
0.960885
0.956105
0.951348
0.169595
0.145729
0.127829
0.113907
0.102771
5.896384
6.862074
7.822959
8.779064
9.730412
6.075502
7.105879
8.141409
9.182116
10.228026
0.164595
0.140729
0.122829
0.108907
0.097771
14.655188
20.449325
27.175522
34.824359
43.386491
15.100376
21.175878
28.281757
36.423166
45.605282
2.485453
2.980050
3.473816
3.966751
4.458855
11
12
13
14
15
1.056396
1.061678
1.066986
1.072321
1.077683
0.946615
0.941905
0.937219
0.932556
0.927917
0.093659
0.086066
0.079642
0.074136
0.069364
10.677027
11.618932
12.556151
13.488708
14.416625
11.279167
12.335562
13.397240
14.464226
15.536548
0.088659
0.081066
0.074642
0.069136
0.064364
52.852639
63.213598
74.460229
86.583463
99.574299
55.833308
67.112475
79.448037
92.845277
107.309504
4.950127
5.440569
5.930179
6.418959
6.906908
16
17
18
19
20
1.083071
1.088487
1.093929
1.099399
1.104896
0.923300
0.918707
0.914136
0.909588
0.905063
0.065189
0.061506
0.058232
0.055303
0.052666
15.339925
16.258632
17.172768
18.082356
18.987419
16.614230
17.697301
18.785788
19.879717
20.979115
0.060189
0.056506
0.053232
0.050303
0.047666
113.423805
128.123114
143.663429
160.036017
177.232212
122.846051
139.460281
157.157583
175.943371
195.823087
7.394026
7.880313
8.365770
8.850396
9.334192
21
22
23
24
25
1.110420
1.115972
1.121552
1.127160
1.132796
0.900560
0.896080
0.891622
0.887186
0.882772
0.050282
0.048114
0.046135
0.044321
0.042652
19.887979
20.784059
21.675681
22.562866
23.445638
22.084011
23.194431
24.310403
25.431955
26.559115
0.045282
0.043114
0.041135
0.039321
0.037652
195.243414
214.061088
233.676763
254.082034
275.268557
216.802203
238.886214
262.080645
286.391048
311.823003
9.817157
10.299292
10.780596
11.261071
11.740715
26
27
28
29
30
1.138460
1.144152
1.149873
1.155622
1.161400
0.878380
0.874010
0.869662
0.865335
0.861030
0.041112
0.039686
0.038362
0.037129
0.035979
24.324018
25.198028
26.067689
26.933024
27.794054
27.691911
28.830370
29.974522
31.124395
32.280017
0.036112
0.034686
0.033362
0.032129
0.030979
297.228055
319.952311
343.433173
367.662550
392.632412
338.382118
366.074029
394.904399
424.878921
456.003316
12.219530
12.697514
13.174669
13.650994
14.126490
35
40
45
50
55
1.190727
1.220794
1.251621
1.283226
1.315629
0.839823
0.819139
0.798964
0.779286
0.760093
0.031215
0.027646
0.024871
0.022654
0.020841
32.035371
36.172228
40.207196
44.142786
47.981445
38.145378
44.158847
50.324164
56.645163
63.125775
0.026215
0.022646
0.019871
0.017654
0.015841
528.312260
681.334687
850.763117
1035.696587
1235.268565
629.075615
831.769459
1064.832831
1329.032597
1625.154992
16.491529
18.835851
21.159474
23.462420
25.744714
60
70
80
90
100
1.348850
1.417831
1.490339
1.566555
1.646668
0.741372
0.705303
0.670988
0.638344
0.607287
0.019333
0.016967
0.015197
0.013825
0.012732
51.725561
58.939418
65.802305
72.331300
78.542645
69.770031
83.566105
98.067714
113.310936
129.333698
0.014333
0.011967
0.010197
0.008825
0.007732
1448.645795
1913.642742
2424.645508
2976.076879
3562.793430
1954.006102
2713.221098
3613.542714
4662.187159
5866.739685
28.006382
32.467962
36.847425
41.145077
45.361261
Ing. Carlos Gerardo Vásquez Gallardo
Página 3
i=1%
Factores de interes discreto capitalizado al : i = 0.01000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.010000
1.020100
1.030301
1.040604
1.051010
0.990099
0.980296
0.970590
0.960980
0.951466
1.010000
0.507512
0.340022
0.256281
0.206040
0.990099
1.970395
2.940985
3.901966
4.853431
1.000000
2.010000
3.030100
4.060401
5.101005
1.000000
0.497512
0.330022
0.246281
0.196040
0.000000
0.980296
2.921476
5.804417
9.610280
0.000000
1.000000
3.010000
6.040100
10.100501
0.000000
0.497512
0.993367
1.487562
1.980100
6
7
8
9
10
1.061520
1.072135
1.082857
1.093685
1.104622
0.942045
0.932718
0.923483
0.914340
0.905287
0.172548
0.148628
0.130690
0.116740
0.105582
5.795476
6.728195
7.651678
8.566018
9.471305
6.152015
7.213535
8.285671
9.368527
10.462213
0.162548
0.138628
0.120690
0.106740
0.095582
14.320506
19.916815
26.381197
33.695916
41.843498
15.201506
21.353521
28.567056
36.852727
46.221254
2.470980
2.960202
3.447766
3.933673
4.417923
11
12
13
14
15
1.115668
1.126825
1.138093
1.149474
1.160969
0.896324
0.887449
0.878663
0.869963
0.861349
0.096454
0.088849
0.082415
0.076901
0.072124
10.367628
11.255077
12.133740
13.003703
13.865053
11.566835
12.682503
13.809328
14.947421
16.096896
0.086454
0.078849
0.072415
0.066901
0.062124
50.806736
60.568677
71.112628
82.422147
94.481039
56.683467
68.250301
80.932804
94.742132
109.689554
4.900517
5.381454
5.860734
6.338360
6.814330
16
17
18
19
20
1.172579
1.184304
1.196147
1.208109
1.220190
0.852821
0.844377
0.836017
0.827740
0.819544
0.067945
0.064258
0.060982
0.058052
0.055415
14.717874
15.562251
16.398269
17.226008
18.045553
17.257864
18.430443
19.614748
20.810895
22.019004
0.057945
0.054258
0.050982
0.048052
0.045415
107.273358
120.783398
134.995693
149.895011
165.466356
125.786449
143.044314
161.474757
181.089504
201.900399
7.288645
7.761306
8.232314
8.701668
9.169370
21
22
23
24
25
1.232392
1.244716
1.257163
1.269735
1.282432
0.811430
0.803396
0.795442
0.787566
0.779768
0.053031
0.050864
0.048886
0.047073
0.045407
18.856983
19.660379
20.455821
21.243387
22.023156
23.239194
24.471586
25.716302
26.973465
28.243200
0.043031
0.040864
0.038886
0.037073
0.035407
181.694959
198.566280
216.065999
234.180020
252.894463
223.919403
247.158598
271.630183
297.346485
324.319950
9.635420
10.099819
10.562568
11.023667
11.483116
26
27
28
29
30
1.295256
1.308209
1.321291
1.334504
1.347849
0.772048
0.764404
0.756836
0.749342
0.741923
0.043869
0.042446
0.041124
0.039895
0.038748
22.795204
23.559608
24.316443
25.065785
25.807708
29.525631
30.820888
32.129097
33.450388
34.784892
0.033869
0.032446
0.031124
0.029895
0.028748
272.195662
292.070164
312.504724
333.486304
355.002069
352.563150
382.088781
412.909669
445.038766
478.489153
11.940918
12.397073
12.851580
13.304443
13.755660
35
40
45
50
55
1.416603
1.488864
1.564811
1.644632
1.728525
0.705914
0.671653
0.639055
0.608039
0.578528
0.034004
0.030456
0.027705
0.025513
0.023726
29.408580
32.834686
36.094508
39.196118
42.147192
41.660276
48.886373
56.481075
64.463182
72.852457
0.024004
0.020456
0.017705
0.015513
0.013726
470.158312
596.856056
733.703724
879.417630
1032.814784
666.027560
888.637336
1148.107472
1446.318218
1785.245735
15.987114
18.177608
20.327295
22.436345
24.504949
60
70
80
90
100
1.816697
2.006763
2.216715
2.448633
2.704814
0.550450
0.498315
0.451118
0.408391
0.369711
0.022244
0.019933
0.018219
0.016903
0.015866
44.955038
50.168514
54.888206
59.160881
63.028879
81.669670
100.676337
121.671522
144.863267
170.481383
0.012244
0.009933
0.008219
0.006903
0.005866
1192.806145
1528.647439
1879.877099
2240.567482
2605.775753
2166.966986
3067.633684
4167.152172
5486.326746
7048.138294
26.533314
30.470255
34.249199
37.872449
41.342569
Ing. Carlos Gerardo Vásquez Gallardo
Página 4
i=2%
Factores de interes discreto capitalizado al : i = 0.02000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.020000
1.040400
1.061208
1.082432
1.104081
0.980392
0.961169
0.942322
0.923845
0.905731
1.020000
0.515050
0.346755
0.262624
0.212158
0.980392
1.941561
2.883883
3.807729
4.713460
1.000000
2.020000
3.060400
4.121608
5.204040
1.000000
0.495050
0.326755
0.242624
0.192158
0.000000
0.961169
2.845813
5.617350
9.240273
0.000000
1.000000
3.020000
6.080400
10.202008
0.000000
0.495050
0.986799
1.475249
1.960401
6
7
8
9
10
1.126162
1.148686
1.171659
1.195093
1.218994
0.887971
0.870560
0.853490
0.836755
0.820348
0.178526
0.154512
0.136510
0.122515
0.111327
5.601431
6.471991
7.325481
8.162237
8.982585
6.308121
7.434283
8.582969
9.754628
10.949721
0.158526
0.134512
0.116510
0.102515
0.091327
13.680130
18.903491
24.877924
31.571966
38.955100
15.406048
21.714169
29.148453
37.731422
47.486050
2.442256
2.920815
3.396080
3.868053
4.336736
11
12
13
14
15
1.243374
1.268242
1.293607
1.319479
1.345868
0.804263
0.788493
0.773033
0.757875
0.743015
0.102178
0.094560
0.088118
0.082602
0.077825
9.786848
10.575341
11.348374
12.106249
12.849264
12.168715
13.412090
14.680332
15.973938
17.293417
0.082178
0.074560
0.068118
0.062602
0.057825
46.997731
55.671156
64.947546
74.799921
85.202128
58.435771
70.604486
84.016576
98.696908
114.670846
4.802131
5.264242
5.723071
6.178621
6.630896
16
17
18
19
20
1.372786
1.400241
1.428246
1.456811
1.485947
0.728446
0.714163
0.700159
0.686431
0.672971
0.073650
0.069970
0.066702
0.063782
0.061157
13.577709
14.291872
14.992031
15.678462
16.351433
18.639285
20.012071
21.412312
22.840559
24.297370
0.053650
0.049970
0.046702
0.043782
0.041157
96.128815
107.555416
119.458125
131.813879
144.600334
131.964263
150.603548
170.615619
192.027931
214.868490
7.079899
7.525635
7.968108
8.407322
8.843282
21
22
23
24
25
1.515666
1.545980
1.576899
1.608437
1.640606
0.659776
0.646839
0.634156
0.621721
0.609531
0.058785
0.056631
0.054668
0.052871
0.051220
17.011209
17.658048
18.292204
18.913926
19.523456
25.783317
27.298984
28.844963
30.421862
32.030300
0.038785
0.036631
0.034668
0.032871
0.031220
157.795850
171.379470
185.330900
199.630495
214.259236
239.165860
264.949177
292.248160
321.093124
351.514986
9.275993
9.705459
10.131688
10.554683
10.974452
26
27
28
29
30
1.673418
1.706886
1.741024
1.775845
1.811362
0.597579
0.585862
0.574375
0.563112
0.552071
0.049699
0.048293
0.046990
0.045778
0.044650
20.121036
20.706898
21.281272
21.844385
22.396456
33.670906
35.344324
37.051210
38.792235
40.568079
0.029699
0.028293
0.026990
0.025778
0.024650
229.198718
244.431131
259.939244
275.706388
291.716444
383.545286
417.216192
452.560515
489.611726
528.403960
11.391000
11.804334
12.214460
12.621385
13.025117
35
40
45
50
55
1.999890
2.208040
2.437854
2.691588
2.971731
0.500028
0.452890
0.410197
0.371528
0.336504
0.040002
0.036556
0.033910
0.031823
0.030143
24.998619
27.355479
29.490160
31.423606
33.174788
49.994478
60.401983
71.892710
84.579401
98.586534
0.020002
0.016556
0.013910
0.011823
0.010143
374.882643
461.993132
551.565188
642.360589
733.352690
749.723882
1020.099159
1344.635513
1728.970073
2179.326683
14.996134
16.888504
18.703364
20.441976
22.105724
60
70
80
90
100
3.281031
3.999558
4.875439
5.943133
7.244646
0.304782
0.250028
0.205110
0.168261
0.138033
0.028768
0.026668
0.025161
0.024046
0.023203
34.760887
37.498619
39.744514
41.586929
43.098352
114.051539
149.977911
193.771958
247.156656
312.232306
0.008768
0.006668
0.005161
0.004046
0.003203
823.697534
999.834315
1166.786767
1322.170082
1464.752746
2702.576971
3998.895557
5688.597890
7857.832816
10611.615296
23.696103
26.663230
29.357178
31.792924
33.986282
Ing. Carlos Gerardo Vásquez Gallardo
Página 5
i=3%
Factores de interes discreto capitalizado al : i =
0.03000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.030000
1.060900
1.092727
1.125509
1.159274
0.970874
0.942596
0.915142
0.888487
0.862609
1.030000
0.522611
0.353530
0.269027
0.218355
0.970874
1.913470
2.828611
3.717098
4.579707
1.000000
2.030000
3.090900
4.183627
5.309136
1.000000
0.492611
0.323530
0.239027
0.188355
0.000000
0.942596
2.772879
5.438340
8.888776
0.000000
1.000000
3.030000
6.120900
10.304527
0.000000
0.492611
0.980297
1.463061
1.940905
6
7
8
9
10
1.194052
1.229874
1.266770
1.304773
1.343916
0.837484
0.813092
0.789409
0.766417
0.744094
0.184598
0.160506
0.142456
0.128434
0.117231
5.417191
6.230283
7.019692
7.786109
8.530203
6.468410
7.662462
8.892336
10.159106
11.463879
0.154598
0.130506
0.112456
0.098434
0.087231
13.076197
17.954746
23.480611
29.611944
36.308790
15.613663
22.082073
29.744535
38.636871
48.795977
2.413833
2.881851
3.344963
3.803176
4.256498
11
12
13
14
15
1.384234
1.425761
1.468534
1.512590
1.557967
0.722421
0.701380
0.680951
0.661118
0.641862
0.108077
0.100462
0.094030
0.088526
0.083767
9.252624
9.954004
10.634955
11.296073
11.937935
12.807796
14.192030
15.617790
17.086324
18.598914
0.078077
0.070462
0.064030
0.058526
0.053767
43.533002
51.248181
59.419597
68.014129
77.000196
60.259856
73.067652
87.259682
102.877472
119.963796
4.704936
5.148499
5.587198
6.021042
6.450043
16
17
18
19
20
1.604706
1.652848
1.702433
1.753506
1.806111
0.623167
0.605016
0.587395
0.570286
0.553676
0.079611
0.075953
0.072709
0.069814
0.067216
12.561102
13.166118
13.753513
14.323799
14.877475
20.156881
21.761588
23.414435
25.116868
26.870374
0.049611
0.045953
0.042709
0.039814
0.037216
86.347700
96.027963
106.013671
116.278820
126.798659
138.562710
158.719591
180.481179
203.895615
229.012483
6.874214
7.293567
7.708116
8.117876
8.522862
21
22
23
24
25
1.860295
1.916103
1.973587
2.032794
2.093778
0.537549
0.521893
0.506692
0.491934
0.477606
0.064872
0.062747
0.060814
0.059047
0.057428
15.415024
15.936917
16.443608
16.935542
17.413148
28.676486
30.536780
32.452884
34.426470
36.459264
0.034872
0.032747
0.030814
0.029047
0.027428
137.549645
148.509387
159.656606
170.971082
182.433615
255.882857
284.559343
315.096123
347.549007
381.975477
8.923090
9.318577
9.709341
10.095401
10.476774
26
27
28
29
30
2.156591
2.221289
2.287928
2.356566
2.427262
0.463695
0.450189
0.437077
0.424346
0.411987
0.055938
0.054564
0.053293
0.052115
0.051019
17.876842
18.327031
18.764108
19.188455
19.600441
38.553042
40.709634
42.930923
45.218850
47.575416
0.025938
0.024564
0.023293
0.022115
0.021019
194.025984
205.730899
217.531971
229.413669
241.361285
418.434742
456.987784
497.697417
540.628340
585.847190
10.853482
11.225544
11.592982
11.955818
12.314074
35
40
45
50
55
2.813862
3.262038
3.781596
4.383906
5.082149
0.355383
0.306557
0.264439
0.228107
0.196767
0.046539
0.043262
0.040785
0.038865
0.037349
21.487220
23.114772
24.518713
25.729764
26.774428
60.462082
75.401260
92.719861
112.796867
136.071620
0.016539
0.013262
0.010785
0.008865
0.007349
301.626705
361.749945
420.632482
477.480334
531.741108
848.736060
1180.041991
1590.662046
2093.228910
2702.387324
14.037493
15.650163
17.155570
18.557509
19.860036
60
70
80
90
100
5.891603
7.917822
10.640891
14.300467
19.218632
0.169733
0.126297
0.093977
0.069928
0.052033
0.036133
0.034337
0.033112
0.032256
0.031647
27.675564
29.123421
30.200763
31.002407
31.598905
163.053437
230.594064
321.363019
443.348904
607.287733
0.006133
0.004337
0.003112
0.002256
0.001647
583.052609
676.086873
756.086524
823.630214
879.854045
3435.114560
5353.135458
8045.433952
11778.296788
16909.591090
21.067416
23.214541
25.035345
26.566654
27.844447
Ing. Carlos Gerardo Vásquez Gallardo
Página 6
i=4%
Factores de interes discreto capitalizado al : i =
0.04000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.040000
1.081600
1.124864
1.169859
1.216653
0.961538
0.924556
0.888996
0.854804
0.821927
1.040000
0.530196
0.360349
0.275490
0.224627
0.961538
1.886095
2.775091
3.629895
4.451822
1.000000
2.040000
3.121600
4.246464
5.416323
1.000000
0.490196
0.320349
0.235490
0.184627
0.000000
0.924556
2.702549
5.266962
8.554670
0.000000
1.000000
3.040000
6.161600
10.408064
0.000000
0.490196
0.973860
1.450995
1.921611
6
7
8
9
10
1.265319
1.315932
1.368569
1.423312
1.480244
0.790315
0.759918
0.730690
0.702587
0.675564
0.190762
0.166610
0.148528
0.134493
0.123291
5.242137
6.002055
6.732745
7.435332
8.110896
6.632975
7.898294
9.214226
10.582795
12.006107
0.150762
0.126610
0.108528
0.094493
0.083291
12.506243
17.065749
22.180581
27.801275
33.881352
15.824387
22.457362
30.355657
39.569883
50.152678
2.385715
2.843318
3.294434
3.739077
4.177264
11
12
13
14
15
1.539454
1.601032
1.665074
1.731676
1.800944
0.649581
0.624597
0.600574
0.577475
0.555265
0.114149
0.106552
0.100144
0.094669
0.089941
8.760477
9.385074
9.985648
10.563123
11.118387
13.486351
15.025805
16.626838
18.291911
20.023588
0.074149
0.066552
0.060144
0.054669
0.049941
40.377162
47.247729
54.454618
61.961794
69.735497
62.158785
75.645137
90.670942
107.297780
125.589691
4.609014
5.034348
5.453288
5.865859
6.272087
16
17
18
19
20
1.872981
1.947900
2.025817
2.106849
2.191123
0.533908
0.513373
0.493628
0.474642
0.456387
0.085820
0.082199
0.078993
0.076139
0.073582
11.652296
12.165669
12.659297
13.133939
13.590326
21.824531
23.697512
25.645413
27.671229
29.778079
0.045820
0.042199
0.038993
0.036139
0.033582
77.744120
85.958092
94.349770
102.893334
111.564686
145.613279
167.437810
191.135322
216.780735
244.451964
6.672000
7.065628
7.453002
7.834156
8.209125
21
22
23
24
25
2.278768
2.369919
2.464716
2.563304
2.665836
0.438834
0.421955
0.405726
0.390121
0.375117
0.071280
0.069199
0.067309
0.065587
0.064012
14.029160
14.451115
14.856842
15.246963
15.622080
31.969202
34.247970
36.617889
39.082604
41.645908
0.031280
0.029199
0.027309
0.025587
0.024012
120.341358
129.202421
138.128400
147.101194
156.103997
274.230043
306.199245
340.447214
377.065103
416.147707
8.577945
8.940654
9.297292
9.647901
9.992523
26
27
28
29
30
2.772470
2.883369
2.998703
3.118651
3.243398
0.360689
0.346817
0.333477
0.320651
0.308319
0.062567
0.061239
0.060013
0.058880
0.057830
15.982769
16.329586
16.663063
16.983715
17.292033
44.311745
47.084214
49.967583
52.966286
56.084938
0.022567
0.021239
0.020013
0.018880
0.017830
165.121228
174.138459
183.142351
192.120590
201.061832
457.793615
502.105360
549.189574
599.157157
652.123444
10.331203
10.663985
10.990917
11.312048
11.627426
35
40
45
50
55
3.946089
4.801021
5.841176
7.106683
8.646367
0.253415
0.208289
0.171198
0.140713
0.115656
0.053577
0.050523
0.048262
0.046550
0.045231
18.664613
19.792774
20.720040
21.482185
22.108612
73.652225
95.025516
121.029392
152.667084
191.159173
0.013577
0.010523
0.008262
0.006550
0.005231
244.876794
286.530302
325.402779
361.163846
393.688974
966.305621
1375.637892
1900.734801
2566.677091
3403.979325
13.119843
14.476511
15.704737
16.812249
17.807041
60
70
80
90
100
10.519627
15.571618
23.049799
34.119333
50.504948
0.095060
0.064219
0.043384
0.029309
0.019800
0.044202
0.042745
0.041814
0.041208
0.040808
22.623490
23.394515
23.915392
24.267278
24.504999
237.990685
364.290459
551.244977
827.983334
1237.623705
0.004202
0.002745
0.001814
0.001208
0.000808
422.996648
472.478923
511.116144
540.736923
563.124875
4449.767130
7357.261469
11781.124419
18449.583339
28440.592615
18.697232
20.196141
21.371849
22.282554
22.980000
Ing. Carlos Gerardo Vásquez Gallardo
Página 7
i=5%
Factores de interes discreto capitalizado al : i =
0.05000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.050000
1.102500
1.157625
1.215506
1.276282
0.952381
0.907029
0.863838
0.822702
0.783526
1.050000
0.537805
0.367209
0.282012
0.230975
0.952381
1.859410
2.723248
3.545951
4.329477
1.000000
2.050000
3.152500
4.310125
5.525631
1.000000
0.487805
0.317209
0.232012
0.180975
0.000000
0.907029
2.634705
5.102812
8.236917
0.000000
1.000000
3.050000
6.202500
10.512625
0.000000
0.487805
0.967486
1.439053
1.902520
6
7
8
9
10
1.340096
1.407100
1.477455
1.551328
1.628895
0.746215
0.710681
0.676839
0.644609
0.613913
0.197017
0.172820
0.154722
0.140690
0.129505
5.075692
5.786373
6.463213
7.107822
7.721735
6.801913
8.142008
9.549109
11.026564
12.577893
0.147017
0.122820
0.104722
0.090690
0.079505
11.967994
16.232082
20.969957
26.126829
31.652048
16.038256
22.840169
30.982178
40.531286
51.557851
2.357904
2.805225
3.244510
3.675786
4.099085
11
12
13
14
15
1.710339
1.795856
1.885649
1.979932
2.078928
0.584679
0.556837
0.530321
0.505068
0.481017
0.120389
0.112825
0.106456
0.101024
0.096342
8.306414
8.863252
9.393573
9.898641
10.379658
14.206787
15.917127
17.712983
19.598632
21.578564
0.070389
0.062825
0.056456
0.051024
0.046342
37.498841
43.624052
49.987909
56.553792
63.288031
64.135743
78.342530
94.259657
111.972640
131.571272
4.514444
4.921902
5.321501
5.713289
6.097314
16
17
18
19
20
2.182875
2.292018
2.406619
2.526950
2.653298
0.458112
0.436297
0.415521
0.395734
0.376889
0.092270
0.088699
0.085546
0.082745
0.080243
10.837770
11.274066
11.689587
12.085321
12.462210
23.657492
25.840366
28.132385
30.539004
33.065954
0.042270
0.038699
0.035546
0.032745
0.030243
70.159704
77.140451
84.204302
91.327514
98.488414
153.149835
176.807327
202.647693
230.780078
261.319082
6.473629
6.842292
7.203360
7.556896
7.902965
21
22
23
24
25
2.785963
2.925261
3.071524
3.225100
3.386355
0.358942
0.341850
0.325571
0.310068
0.295303
0.077996
0.075971
0.074137
0.072471
0.070952
12.821153
13.163003
13.488574
13.798642
14.093945
35.719252
38.505214
41.430475
44.501999
47.727099
0.027996
0.025971
0.024137
0.022471
0.020952
105.667261
112.846108
120.008677
127.140239
134.227505
294.385036
330.104288
368.609502
410.039977
454.541976
8.241635
8.572976
8.897062
9.213968
9.523771
26
27
28
29
30
3.555673
3.733456
3.920129
4.116136
4.321942
0.281241
0.267848
0.255094
0.242946
0.231377
0.069564
0.068292
0.067123
0.066046
0.065051
14.375185
14.643034
14.898127
15.141074
15.372451
51.113454
54.669126
58.402583
62.322712
66.438848
0.019564
0.018292
0.017123
0.016046
0.015051
141.258524
148.222580
155.110108
161.912605
168.622551
502.269075
553.382529
608.051655
666.454238
728.776950
9.826553
10.122396
10.411383
10.693601
10.969139
35
40
45
50
55
5.516015
7.039989
8.985008
11.467400
14.635631
0.181290
0.142046
0.111297
0.087204
0.068326
0.061072
0.058278
0.056262
0.054777
0.053667
16.374194
17.159086
17.774070
18.255925
18.633472
90.320307
120.799774
159.700156
209.347996
272.712618
0.011072
0.008278
0.006262
0.004777
0.003667
200.580686
229.545181
255.314538
277.914782
297.510397
1106.406147
1615.995485
2294.003117
3186.959914
4354.252367
12.249805
13.377471
14.364439
15.223265
15.966450
60
70
80
90
100
18.679186
30.426426
49.561441
80.730365
131.501258
0.053536
0.032866
0.020177
0.012387
0.007604
0.052828
0.051699
0.051030
0.050627
0.050383
18.929290
19.342677
19.596460
19.752262
19.847910
353.583718
588.528511
971.228821
1594.607301
2610.025157
0.002828
0.001699
0.001030
0.000627
0.000383
314.343162
340.840898
359.646048
372.748792
381.749224
5871.674358
10370.570214
17824.576427
30092.146020
50200.503139
16.606179
17.621186
18.352602
18.871195
19.233724
Ing. Carlos Gerardo Vásquez Gallardo
Página 8
i=6%
Factores de interes discreto capitalizado al : i = 0.06000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.060000
1.123600
1.191016
1.262477
1.338226
0.943396
0.889996
0.839619
0.792094
0.747258
1.060000
0.545437
0.374110
0.288591
0.237396
0.943396
1.833393
2.673012
3.465106
4.212364
1.000000
2.060000
3.183600
4.374616
5.637093
1.000000
0.485437
0.314110
0.228591
0.177396
0.000000
0.889996
2.569235
4.945516
7.934549
0.000000
1.000000
3.060000
6.243600
10.618216
0.000000
0.485437
0.961176
1.427234
1.883633
6
7
8
9
10
1.418519
1.503630
1.593848
1.689479
1.790848
0.704961
0.665057
0.627412
0.591898
0.558395
0.203363
0.179135
0.161036
0.147022
0.135868
4.917324
5.582381
6.209794
6.801692
7.360087
6.975319
8.393838
9.897468
11.491316
13.180795
0.143363
0.119135
0.101036
0.087022
0.075868
11.459351
15.449694
19.841581
24.576768
29.602321
16.255309
23.230627
31.624465
41.521933
53.013249
2.330404
2.767581
3.195208
3.613331
4.022007
11
12
13
14
15
1.898299
2.012196
2.132928
2.260904
2.396558
0.526788
0.496969
0.468839
0.442301
0.417265
0.126793
0.119277
0.112960
0.107585
0.102963
7.886875
8.383844
8.852683
9.294984
9.712249
14.971643
16.869941
18.882138
21.015066
23.275970
0.066793
0.059277
0.052960
0.047585
0.042963
34.870197
40.336860
45.962928
51.712840
57.554551
66.194044
81.165687
98.035628
116.917765
137.932831
4.421295
4.811261
5.191977
5.563521
5.925976
16
17
18
19
20
2.540352
2.692773
2.854339
3.025600
3.207135
0.393646
0.371364
0.350344
0.330513
0.311805
0.098952
0.095445
0.092357
0.089621
0.087185
10.105895
10.477260
10.827603
11.158116
11.469921
25.672528
28.212880
30.905653
33.759992
36.785591
0.038952
0.035445
0.032357
0.029621
0.027185
63.459246
69.401076
75.356921
81.306155
87.230445
161.208801
186.881329
215.094209
245.999862
279.759853
6.279428
6.623972
6.959705
7.286728
7.605148
21
22
23
24
25
3.399564
3.603537
3.819750
4.048935
4.291871
0.294155
0.277505
0.261797
0.246979
0.232999
0.085005
0.083046
0.081278
0.079679
0.078227
11.764077
12.041582
12.303379
12.550358
12.783356
39.992727
43.392290
46.995828
50.815577
54.864512
0.025005
0.023046
0.021278
0.019679
0.018227
93.113553
98.941160
104.700700
110.381206
115.973173
316.545445
356.538171
399.930462
446.926289
497.741867
7.915075
8.216625
8.509914
8.795065
9.072201
26
27
28
29
30
4.549383
4.822346
5.111687
5.418388
5.743491
0.219810
0.207368
0.195630
0.184557
0.174110
0.076904
0.075697
0.074593
0.073580
0.072649
13.003166
13.210534
13.406164
13.590721
13.764831
59.156383
63.705766
68.528112
73.639798
79.058186
0.016904
0.015697
0.014593
0.013580
0.012649
121.468424
126.859991
132.142005
137.309593
142.358787
552.606379
611.762761
675.468527
743.996639
817.636437
9.341450
9.602942
9.856809
10.103187
10.342211
35
40
45
50
55
7.686087
10.285718
13.764611
18.420154
24.650322
0.130105
0.097222
0.072650
0.054288
0.040567
0.068974
0.066462
0.064700
0.063444
0.062537
14.498246
15.046297
15.455832
15.761861
15.990543
111.434780
154.761966
212.743514
290.335905
394.172027
0.008974
0.006462
0.004700
0.003444
0.002537
165.742729
185.956823
203.109646
217.457376
229.322246
1273.912998
1912.699427
2795.725230
4005.598410
5652.867109
11.431916
12.358976
13.141295
13.796428
14.341117
60
70
80
90
100
32.987691
59.075930
105.795993
189.464511
339.302084
0.030314
0.016927
0.009452
0.005278
0.002947
0.061876
0.061033
0.060573
0.060318
0.060177
16.161428
16.384544
16.509131
16.578699
16.617546
533.128181
967.932170
1746.599891
3141.075187
5638.368059
0.001876
0.001033
0.000573
0.000318
0.000177
239.042791
253.327135
262.549308
268.394607
272.047060
7885.469681
14965.536161
27776.664856
50851.253120
92306.134310
14.790945
15.461348
15.903279
16.189123
16.371073
Ing. Carlos Gerardo Vásquez Gallardo
Página 9
i=7%
Factores de interes discreto capitalizado al : i = 0.07000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.070000
1.144900
1.225043
1.310796
1.402552
0.934579
0.873439
0.816298
0.762895
0.712986
1.070000
0.553092
0.381052
0.295228
0.243891
0.934579
1.808018
2.624316
3.387211
4.100197
1.000000
2.070000
3.214900
4.439943
5.750739
1.000000
0.483092
0.311052
0.225228
0.173891
0.000000
0.873439
2.506034
4.794720
7.646665
0.000000
1.000000
3.070000
6.284900
10.724843
0.000000
0.483092
0.954929
1.415536
1.864950
6
7
8
9
10
1.500730
1.605781
1.718186
1.838459
1.967151
0.666342
0.622750
0.582009
0.543934
0.508349
0.209796
0.185553
0.167468
0.153486
0.142378
4.766540
5.389289
5.971299
6.515232
7.023582
7.153291
8.654021
10.259803
11.977989
13.816448
0.139796
0.115553
0.097468
0.083486
0.072378
10.978376
14.714874
18.788938
23.140408
27.715552
16.475582
23.628873
32.282894
42.542696
54.520685
2.303217
2.730392
3.146541
3.551740
3.946071
11
12
13
14
15
2.104852
2.252192
2.409845
2.578534
2.759032
0.475093
0.444012
0.414964
0.387817
0.362446
0.133357
0.125902
0.119651
0.114345
0.109795
7.498674
7.942686
8.357651
8.745468
9.107914
15.783599
17.888451
20.140643
22.550488
25.129022
0.063357
0.055902
0.049651
0.044345
0.039795
32.466480
37.350611
42.330185
47.371809
52.446053
68.337133
84.120732
102.009184
122.149827
144.700314
4.329629
4.702516
5.064842
5.416727
5.758295
16
17
18
19
20
2.952164
3.158815
3.379932
3.616528
3.869684
0.338735
0.316574
0.295864
0.276508
0.258419
0.105858
0.102425
0.099413
0.096753
0.094393
9.446649
9.763223
10.059087
10.335595
10.594014
27.888054
30.840217
33.999033
37.378965
40.995492
0.035858
0.032425
0.029413
0.026753
0.024393
57.527072
62.592262
67.621949
72.599099
77.509060
169.829336
197.717390
228.557607
262.556640
299.935605
6.089681
6.411025
6.722474
7.024182
7.316307
21
22
23
24
25
4.140562
4.430402
4.740530
5.072367
5.427433
0.241513
0.225713
0.210947
0.197147
0.184249
0.092289
0.090406
0.088714
0.087189
0.085811
10.835527
11.061240
11.272187
11.469334
11.653583
44.865177
49.005739
53.436141
58.176671
63.249038
0.022289
0.020406
0.018714
0.017189
0.015811
82.339322
87.079298
91.720129
96.254502
100.676482
340.931097
385.796274
434.802013
488.238154
546.414825
7.599014
7.872471
8.136853
8.392336
8.639101
26
27
28
29
30
5.807353
6.213868
6.648838
7.114257
7.612255
0.172195
0.160930
0.150402
0.140563
0.131367
0.084561
0.083426
0.082392
0.081449
0.080586
11.825779
11.986709
12.137111
12.277674
12.409041
68.676470
74.483823
80.697691
87.346529
94.460786
0.014561
0.013426
0.012392
0.011449
0.010586
104.981369
109.165559
113.226419
117.162177
120.971824
609.663862
678.340333
752.824156
833.521847
920.868376
8.877332
9.107217
9.328943
9.542701
9.748684
35
40
45
50
55
10.676581
14.974458
21.002452
29.457025
41.315001
0.093663
0.066780
0.047613
0.033948
0.024204
0.077234
0.075009
0.073500
0.072460
0.071736
12.947672
13.331709
13.605522
13.800746
13.939939
138.236878
199.635112
285.749311
406.528929
575.928593
0.007234
0.005009
0.003500
0.002460
0.001736
138.135278
152.292766
163.755923
172.905119
180.124332
1474.812548
2280.501600
3439.275869
5093.270421
7441.837037
10.668734
11.423349
12.035990
12.528679
12.921458
60
70
80
90
100
57.946427
113.989392
224.234388
441.102980
867.716326
0.017257
0.008773
0.004460
0.002267
0.001152
0.071229
0.070620
0.070314
0.070159
0.070081
14.039181
14.160389
14.222005
14.253328
14.269251
813.520383
1614.134174
3189.062680
6287.185427
12381.661794
0.001229
0.000620
0.000314
0.000159
0.000081
185.767743
193.518530
198.074799
200.704199
202.200081
10764.576905
22059.059632
44415.181138
88531.220383
13.232092
13.666187
13.927347
14.081217
14.170336
Ing. Carlos Gerardo Vásquez Gallardo
Página 10
i=8%
Factores de interes discreto capitalizado al : i = 0.08000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.080000
1.166400
1.259712
1.360489
1.469328
0.925926
0.857339
0.793832
0.735030
0.680583
1.080000
0.560769
0.388034
0.301921
0.250456
0.925926
1.783265
2.577097
3.312127
3.992710
1.000000
2.080000
3.246400
4.506112
5.866601
1.000000
0.480769
0.308034
0.221921
0.170456
0.000000
0.857339
2.445003
4.650093
7.372426
0.000000
1.000000
3.080000
6.326400
10.832512
0.000000
0.480769
0.948743
1.403960
1.846472
6
7
8
9
10
1.586874
1.713824
1.850930
1.999005
2.158925
0.630170
0.583490
0.540269
0.500249
0.463193
0.216315
0.192072
0.174015
0.160080
0.149029
4.622880
5.206370
5.746639
6.246888
6.710081
7.335929
8.922803
10.636628
12.487558
14.486562
0.136315
0.112072
0.094015
0.080080
0.069029
10.523274
14.024216
17.806098
21.808090
25.976831
16.699113
24.035042
32.957845
43.594473
56.082031
2.276346
2.693665
3.098524
3.491033
3.871314
11
12
13
14
15
2.331639
2.518170
2.719624
2.937194
3.172169
0.428883
0.397114
0.367698
0.340461
0.315242
0.140076
0.132695
0.126522
0.121297
0.116830
7.138964
7.536078
7.903776
8.244237
8.559479
16.645487
18.977126
21.495297
24.214920
27.152114
0.060076
0.052695
0.046522
0.041297
0.036830
30.265660
34.633911
39.046287
43.472280
47.885664
70.568593
87.214081
106.191207
127.686504
151.901424
4.239503
4.595747
4.940207
5.273051
5.594460
16
17
18
19
20
3.425943
3.700018
3.996019
4.315701
4.660957
0.291890
0.270269
0.250249
0.231712
0.214548
0.112977
0.109629
0.106702
0.104128
0.101852
8.851369
9.121638
9.371887
9.603599
9.818147
30.324283
33.750226
37.450244
41.446263
45.761964
0.032977
0.029629
0.026702
0.024128
0.021852
52.264021
56.588324
60.842558
65.013375
69.089791
179.053538
209.377821
243.128047
280.578290
322.024554
5.904626
6.203746
6.492028
6.769688
7.036948
21
22
23
24
25
5.033834
5.436540
5.871464
6.341181
6.848475
0.198656
0.183941
0.170315
0.157699
0.146018
0.099832
0.098032
0.096422
0.094978
0.093679
10.016803
10.200744
10.371059
10.528758
10.674776
50.422921
55.456755
60.893296
66.764759
73.105940
0.019832
0.018032
0.016422
0.014978
0.013679
73.062906
76.925656
80.672593
84.299677
87.804107
367.786518
418.209439
473.666195
534.559490
601.324249
7.294034
7.541181
7.778626
8.006612
8.225382
26
27
28
29
30
7.396353
7.988061
8.627106
9.317275
10.062657
0.135202
0.125187
0.115914
0.107328
0.099377
0.092507
0.091448
0.090489
0.089619
0.088827
10.809978
10.935165
11.051078
11.158406
11.257783
79.954415
87.350768
95.338830
103.965936
113.283211
0.012507
0.011448
0.010489
0.009619
0.008827
91.184151
94.439008
97.568679
100.573849
103.455792
674.430189
754.384605
841.735373
937.074203
1041.040139
8.435184
8.636268
8.828883
9.013281
9.189712
35
40
45
50
55
14.785344
21.724521
31.920449
46.901613
68.913856
0.067635
0.046031
0.031328
0.021321
0.014511
0.085803
0.083860
0.082587
0.081743
0.081178
11.654568
11.924613
12.108402
12.233485
12.318614
172.316804
259.056519
386.505617
573.770156
848.923201
0.005803
0.003860
0.002587
0.001743
0.001178
116.091990
126.042200
133.733086
139.592790
144.006454
1716.460046
2738.206484
4268.820217
6547.126955
9924.040018
9.961072
10.569919
11.044652
11.410714
11.690151
0.009876
0.004574
0.002119
0.000981
0.000455
0.080798
0.080368
0.080170
0.080079
0.080036
12.376552
12.442820
12.473514
12.487732
12.494318
1253.213296
2720.080074
5886.935428
12723.938616
27484.515704
0.000798
0.000368
0.000170
0.000079
0.000036
147.300007
151.532618
153.800083
154.992535
155.610726
14915.166198
33126.000922
72586.692854
11.901538
12.178318
12.330132
12.411584
12.454520
60
101.257064
70
218.606406
80
471.954834
90 1018.915089
100 2199.761256
Ing. Carlos Gerardo Vásquez Gallardo
Página 11
i=9%
Factores de interes discreto capitalizado al : i =
0.09000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.09000
1.188100
1.295029
1.411582
1.538624
0.91743
0.841680
0.772183
0.708425
0.649931
1.09000
0.568469
0.395055
0.308669
0.257092
0.91743
1.759111
2.531295
3.239720
3.889651
1.00000
2.090000
3.278100
4.573129
5.984711
1.00000
0.478469
0.305055
0.218669
0.167092
0.00000
0.841680
2.386047
4.511323
7.111048
0.00000
1.000000
3.090000
6.368100
10.941229
0.00000
0.478469
0.942619
1.392504
1.828197
6
7
8
9
10
1.677100
1.828039
1.992563
2.171893
2.367364
0.596267
0.547034
0.501866
0.460428
0.422411
0.222920
0.198691
0.180674
0.166799
0.155820
4.485919
5.032953
5.534819
5.995247
6.417658
7.523335
9.200435
11.028474
13.021036
15.192930
0.132920
0.108691
0.090674
0.076799
0.065820
10.092385
13.374590
16.887654
20.571076
24.372774
16.925940
24.449274
33.649709
44.678183
57.699219
2.249792
2.657404
3.051166
3.431231
3.797768
11
12
13
14
15
2.580426
2.812665
3.065805
3.341727
3.642482
0.387533
0.355535
0.326179
0.299246
0.274538
0.146947
0.139651
0.133567
0.128433
0.124059
6.805191
7.160725
7.486904
7.786150
8.060688
17.560293
20.140720
22.953385
26.019189
29.360916
0.056947
0.049651
0.043567
0.038433
0.034059
28.248102
32.158984
36.073128
39.963332
43.806865
72.892149
90.452442
110.593162
133.546547
159.565736
4.150964
4.491023
4.818164
5.132618
5.434631
16
17
18
19
20
3.970306
4.327633
4.717120
5.141661
5.604411
0.251870
0.231073
0.211994
0.194490
0.178431
0.120300
0.117046
0.114212
0.111730
0.109546
8.312558
8.543631
8.755625
8.950115
9.128546
33.003399
36.973705
41.301338
46.018458
51.160120
0.030300
0.027046
0.024212
0.021730
0.019546
47.584911
51.282082
54.885975
58.386789
61.776976
188.926652
221.930051
258.903755
300.205093
346.223552
5.724460
6.002375
6.268653
6.523580
6.767450
21
22
23
24
25
6.108808
6.658600
7.257874
7.911083
8.623081
0.163698
0.150182
0.137781
0.126405
0.115968
0.107617
0.105905
0.104382
0.103023
0.101806
9.292244
9.442425
9.580207
9.706612
9.822580
56.764530
62.873338
69.531939
76.789813
84.700896
0.017617
0.015905
0.014382
0.013023
0.011806
65.050938
68.204754
71.235944
74.143258
76.926486
397.383671
454.148202
517.021540
586.553478
663.343291
7.000563
7.223224
7.435742
7.638428
7.831597
26
27
28
29
30
9.399158
10.245082
11.167140
12.172182
13.267678
0.106393
0.097608
0.089548
0.082155
0.075371
0.100715
0.099735
0.098852
0.098056
0.097336
9.928972
10.026580
10.116128
10.198283
10.273654
93.323977
102.723135
112.968217
124.135356
136.307539
0.010715
0.009735
0.008852
0.008056
0.007336
79.586298
82.124101
84.541910
86.842237
89.028000
748.044188
841.368165
944.091299
1057.059516
1181.194873
8.015563
8.190639
8.357141
8.515378
8.665661
35
40
45
50
55
20.413968
31.409420
48.327286
74.357520
114.408262
0.048986
0.031838
0.020692
0.013449
0.008741
0.094636
0.092960
0.091902
0.091227
0.090794
10.566821
10.757360
10.881197
10.961683
11.013993
215.710755
337.882445
525.858734
815.083556
1260.091796
0.004636
0.002960
0.001902
0.001227
0.000794
98.358990
105.376188
110.556070
114.325066
117.036206
2007.897274
3309.804945
5342.874828
8500.928404
13389.908841
9.308285
9.795729
10.160285
10.429518
10.626138
60
70
80
90
100
176.031292
416.730086
986.551668
2335.526582
5529.040792
0.005681
0.002400
0.001014
0.000428
0.000181
0.090514
0.090216
0.090091
0.090039
0.090016
11.047991
11.084449
11.099849
11.106354
11.109102
1944.792133
4619.223180
10950.574090
25939.184247
61422.675465
0.000514
0.000216
0.000091
118.968250
121.294156
122.430644
122.975761
123.233502
20942.134810
50546.924220
10.768315
10.942733
11.029938
11.072559
11.093022
Ing. Carlos Gerardo Vásquez Gallardo
Página 12
i = 10 %
Factores de interes discreto capitalizado al : i = 0.10000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.100000
1.210000
1.331000
1.464100
1.610510
0.909091
0.826446
0.751315
0.683013
0.620921
1.100000
0.576190
0.402115
0.315471
0.263797
0.909091
1.735537
2.486852
3.169865
3.790787
1.000000
2.100000
3.310000
4.641000
6.105100
1.000000
0.476190
0.302115
0.215471
0.163797
0.000000
0.826446
2.329076
4.378116
6.861802
0.000000
1.000000
3.100000
6.410000
11.051000
0.000000
0.476190
0.936556
1.381168
1.810126
6
7
8
9
10
1.771561
1.948717
2.143589
2.357948
2.593742
0.564474
0.513158
0.466507
0.424098
0.385543
0.229607
0.205405
0.187444
0.173641
0.162745
4.355261
4.868419
5.334926
5.759024
6.144567
7.715610
9.487171
11.435888
13.579477
15.937425
0.129607
0.105405
0.087444
0.073641
0.062745
9.684171
12.763120
16.028672
19.421453
22.891342
17.156100
24.871710
34.358881
45.794769
59.374246
2.223557
2.621615
3.004479
3.372351
3.725461
11
12
13
14
15
2.853117
3.138428
3.452271
3.797498
4.177248
0.350494
0.318631
0.289664
0.263331
0.239392
0.153963
0.146763
0.140779
0.135746
0.131474
6.495061
6.813692
7.103356
7.366687
7.606080
18.531167
21.384284
24.522712
27.974983
31.772482
0.053963
0.046763
0.040779
0.035746
0.031474
26.396281
29.901220
33.377193
36.800499
40.151988
75.311671
93.842838
115.227121
139.749834
167.724817
4.064054
4.388402
4.698792
4.995529
5.278933
16
17
18
19
20
4.594973
5.054470
5.559917
6.115909
6.727500
0.217629
0.197845
0.179859
0.163508
0.148644
0.127817
0.124664
0.121930
0.119547
0.117460
7.823709
8.021553
8.201412
8.364920
8.513564
35.949730
40.544703
45.599173
51.159090
57.274999
0.027817
0.024664
0.021930
0.019547
0.017460
43.416425
46.581939
49.639539
52.582683
55.406912
199.497299
235.447028
275.991731
321.590904
372.749995
5.549341
5.807097
6.052560
6.286095
6.508075
21
22
23
24
25
7.400250
8.140275
8.954302
9.849733
10.834706
0.135131
0.122846
0.111678
0.101526
0.092296
0.115624
0.114005
0.112572
0.111300
0.110168
8.648694
8.771540
8.883218
8.984744
9.077040
64.002499
71.402749
79.543024
88.497327
98.347059
0.015624
0.014005
0.012572
0.011300
0.010168
58.109523
60.689288
63.146208
65.481297
67.696401
430.024994
494.027494
565.430243
644.973268
733.470594
6.718878
6.918886
7.108483
7.288054
7.457982
26
27
28
29
30
11.918177
13.109994
14.420994
15.863093
17.449402
0.083905
0.076278
0.069343
0.063039
0.057309
0.109159
0.108258
0.107451
0.106728
0.106079
9.160945
9.237223
9.306567
9.369606
9.426914
109.181765
121.099942
134.209936
148.630930
164.494023
0.009159
0.008258
0.007451
0.006728
0.006079
69.794037
71.777257
73.649527
75.414631
77.076579
831.817654
940.999419
1062.099361
1196.309297
1344.940227
7.618650
7.770437
7.913716
8.048858
8.176226
35
40
45
50
55
28.102437
45.259256
72.890484
117.390853
189.059142
0.035584
0.022095
0.013719
0.008519
0.005289
0.103690
0.102259
0.101391
0.100859
0.100532
9.644159
9.779051
9.862808
9.914814
9.947106
271.024368
442.592556
718.904837
1163.908529
1880.591425
0.003690
0.002259
0.001391
0.000859
0.000532
83.987154
88.952536
92.454433
94.888869
96.561922
2360.243685
4025.925557
6739.048369
11139.085288
18255.914247
8.708603
9.096234
9.374048
9.570413
9.707539
0.003284
0.001266
0.000488
0.000188
0.000073
0.100330
0.100127
0.100049
9.967157
9.987338
9.995118
9.998118
9.999274
3034.816395
7887.469568
20474.002146
53120.226118
0.000330
0.000127
97.701011
98.987017
99.560633
99.811783
99.920178
29748.163954
78174.695680
9.802294
9.911252
9.960926
9.983057
9.992743
60
304.481640
70
789.746957
80
2048.400215
90
5313.022612
100 13780.612340
Ing. Carlos Gerardo Vásquez Gallardo
Página 13
i = 12 %
Factores de interes discreto capitalizado al : i = 0.12000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.120000
1.254400
1.404928
1.573519
1.762342
0.892857
0.797194
0.711780
0.635518
0.567427
1.120000
0.591698
0.416349
0.329234
0.277410
0.892857
1.690051
2.401831
3.037349
3.604776
1.000000
2.120000
3.374400
4.779328
6.352847
1.000000
0.471698
0.296349
0.209234
0.157410
0.000000
0.797194
2.220754
4.127309
6.397016
0.000000
1.000000
3.120000
6.494400
11.273728
0.000000
0.471698
0.924609
1.358852
1.774595
6
7
8
9
10
1.973823
2.210681
2.475963
2.773079
3.105848
0.506631
0.452349
0.403883
0.360610
0.321973
0.243226
0.219118
0.201303
0.187679
0.176984
4.111407
4.563757
4.967640
5.328250
5.650223
8.115189
10.089012
12.299693
14.775656
17.548735
0.123226
0.099118
0.081303
0.067679
0.056984
8.930172
11.644267
14.471450
17.356330
20.254089
17.626575
25.741764
35.830776
48.130469
62.906126
2.172047
2.551465
2.913144
3.257417
3.584653
11
12
13
14
15
3.478550
3.895976
4.363493
4.887112
5.473566
0.287476
0.256675
0.229174
0.204620
0.182696
0.168415
0.161437
0.155677
0.150871
0.146824
5.937699
6.194374
6.423548
6.628168
6.810864
20.654583
24.133133
28.029109
32.392602
37.279715
0.048415
0.041437
0.035677
0.030871
0.026824
23.128850
25.952276
28.702366
31.362424
33.920171
80.454861
101.109444
125.242577
153.271686
185.664289
3.895255
4.189653
4.468304
4.731688
4.980303
16
17
18
19
20
6.130394
6.866041
7.689966
8.612762
9.646293
0.163122
0.145644
0.130040
0.116107
0.103667
0.143390
0.140457
0.137937
0.135763
0.133879
6.973986
7.119630
7.249670
7.365777
7.469444
42.753280
48.883674
55.749715
63.439681
72.052442
0.023390
0.020457
0.017937
0.015763
0.013879
36.366996
38.697306
40.907979
42.997901
44.967569
222.944003
265.697284
314.580958
370.330673
433.770354
5.214664
5.435297
5.642737
5.837524
6.020203
21
22
23
24
25
10.803848
12.100310
13.552347
15.178629
17.000064
0.092560
0.082643
0.073788
0.065882
0.058823
0.132240
0.130811
0.129560
0.128463
0.127500
7.562003
7.644646
7.718434
7.784316
7.843139
81.698736
92.502584
104.602894
118.155241
133.333870
0.012240
0.010811
0.009560
0.008463
0.007500
46.818762
48.554254
50.177589
51.692878
53.104637
505.822796
587.521532
680.024115
784.627009
902.782250
6.191317
6.351407
6.501007
6.640645
6.770840
26
27
28
29
30
19.040072
21.324881
23.883866
26.749930
29.959922
0.052521
0.046894
0.041869
0.037383
0.033378
0.126652
0.125904
0.125244
0.124660
0.124144
7.895660
7.942554
7.984423
8.021806
8.055184
150.333934
169.374007
190.698887
214.582754
241.332684
0.006652
0.005904
0.005244
0.004660
0.004144
54.417657
55.636890
56.767361
57.814092
58.782052
1036.116121
1186.450055
1355.824062
1546.522949
1761.105703
6.892097
7.004912
7.109764
7.207117
7.297419
35
40
45
50
55
52.799620
93.050970
163.987604
289.002190
509.320606
0.018940
0.010747
0.006098
0.003460
0.001963
0.122317
0.121304
0.120736
0.120417
0.120236
8.175504
8.243777
8.282516
8.304498
8.316972
431.663496
767.091420
1358.230032
2400.018249
4236.005047
0.002317
0.001304
0.000736
0.000417
0.000236
62.605170 3305.529137
65.115873 6059.095170
66.734212 10943.583602
67.762412 19583.485405
68.408206 34841.708727
7.657653
7.898791
8.057239
8.159724
8.225134
0.001114
0.000359
0.000115
0.120134
0.120043
8.324049
8.330344
8.332371
8.333023
8.333234
7471.641112
23223.331897
72145.692501
0.000134
68.810034 61763.675937
69.210289
69.359428
69.413973
69.433636
8.266414
8.308215
8.324093
8.329986
8.332136
60
897.596933
70
2787.799828
80
8658.483100
90 26891.934223
100 83522.265727
Ing. Carlos Gerardo Vásquez Gallardo
Página 14
i = 15 %
Factores de interes discreto capitalizado al : i = 0.15000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.150000
1.322500
1.520875
1.749006
2.011357
0.869565
0.756144
0.657516
0.571753
0.497177
1.150000
0.615116
0.437977
0.350265
0.298316
0.869565
1.625709
2.283225
2.854978
3.352155
1.000000
2.150000
3.472500
4.993375
6.742381
1.000000
0.465116
0.287977
0.200265
0.148316
0.000000
0.756144
2.071176
3.786436
5.775143
0.000000
1.000000
3.150000
6.622500
11.615875
0.000000
0.465116
0.907127
1.326257
1.722815
6
7
8
9
10
2.313061
2.660020
3.059023
3.517876
4.045558
0.432328
0.375937
0.326902
0.284262
0.247185
0.264237
0.240360
0.222850
0.209574
0.199252
3.784483
4.160420
4.487322
4.771584
5.018769
8.753738
11.066799
13.726819
16.785842
20.303718
0.114237
0.090360
0.072850
0.059574
0.049252
7.936781
10.192403
12.480715
14.754815
16.979477
18.358256
27.111995
38.178794
51.905613
68.691455
2.097190
2.449850
2.781329
3.092226
3.383196
11
12
13
14
15
4.652391
5.350250
6.152788
7.075706
8.137062
0.214943
0.186907
0.162528
0.141329
0.122894
0.191069
0.184481
0.179110
0.174688
0.171017
5.233712
5.420619
5.583147
5.724476
5.847370
24.349276
29.001667
34.351917
40.504705
47.580411
0.041069
0.034481
0.029110
0.024688
0.021017
19.128909
21.184888
23.135223
24.972496
26.693019
88.995173
113.344449
142.346117
176.698034
217.202739
3.654941
3.908205
4.143760
4.362408
4.564961
16
17
18
19
20
9.357621
10.761264
12.375454
14.231772
16.366537
0.106865
0.092926
0.080805
0.070265
0.061100
0.167948
0.165367
0.163186
0.161336
0.159761
5.954235
6.047161
6.127966
6.198231
6.259331
55.717472
65.075093
75.836357
88.211811
102.443583
0.017948
0.015367
0.013186
0.011336
0.009761
28.295990
29.782805
31.156492
32.421267
33.582173
264.783150
320.500622
385.575716
461.412073
549.623884
4.752246
4.925089
5.084312
5.230729
5.365137
21
22
23
24
25
18.821518
21.644746
24.891458
28.625176
32.918953
0.053131
0.046201
0.040174
0.034934
0.030378
0.158417
0.157266
0.156278
0.155430
0.154699
6.312462
6.358663
6.398837
6.433771
6.464149
118.810120
137.631638
159.276384
184.167841
212.793017
0.008417
0.007266
0.006278
0.005430
0.004699
34.644786
35.614999
36.498836
37.302324
38.031388
652.067467
770.877587
908.509225
1067.785608
1251.953450
5.488316
5.601020
5.703979
5.797894
5.883433
26
27
28
29
30
37.856796
43.535315
50.065612
57.575454
66.211772
0.026415
0.022970
0.019974
0.017369
0.015103
0.154070
0.153526
0.153057
0.152651
0.152300
6.490564
6.513534
6.533508
6.550877
6.565980
245.711970
283.568766
327.104080
377.169693
434.745146
0.004070
0.003526
0.003057
0.002651
0.002300
38.691771
39.288987
39.828280
40.314598
40.752587
1464.746467
1710.458437
1994.027203
2321.131283
2698.300976
5.961234
6.031900
6.096002
6.154077
6.206627
35
40
45
50
55
133.175523
267.863546
538.769269
1083.657442
2179.622184
0.007509
0.003733
0.001856
0.000923
0.000459
0.151135
0.150562
0.150279
0.150139
6.616607
6.641778
6.654293
6.660515
6.663608
881.170156
1779.090308
3585.128460
7217.716277
14524.147893
0.001135
0.000562
0.000279
0.000139
42.358642
43.282991
43.805127
44.095831
44.255829
5641.134374
11593.935388
23600.856399
47784.775182
96460.985952
6.401867
6.516777
6.582988
6.620484
6.641421
60
70
80
90
100
4383.998746
17735.720039
71750.879401
0.000228
0.000056
6.665146
6.666291
6.666574
29219.991638
Ing. Carlos Gerardo Vásquez Gallardo
44.343066
44.415626
44.436392
44.442224
44.443839
6.652977
6.662720
6.665552
6.666357
6.666582
Página 15
i = 18 %
Factores de interes discreto capitalizado al : i = 0.18000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.180000
1.392400
1.643032
1.938778
2.287758
0.847458
0.718184
0.608631
0.515789
0.437109
1.180000
0.638716
0.459924
0.371739
0.319778
0.847458
1.565642
2.174273
2.690062
3.127171
1.000000
2.180000
3.572400
5.215432
7.154210
1.000000
0.458716
0.279924
0.191739
0.139778
0.000000
0.718184
1.935446
3.482813
5.231250
0.000000
1.000000
3.180000
6.752400
11.967832
0.000000
0.458716
0.890158
1.294696
1.672838
6
7
8
9
10
2.699554
3.185474
3.758859
4.435454
5.233836
0.370432
0.313925
0.266038
0.225456
0.191064
0.285910
0.262362
0.245244
0.232395
0.222515
3.497603
3.811528
4.077566
4.303022
4.494086
9.441968
12.141522
15.326996
19.085855
23.521309
0.105910
0.082362
0.065244
0.052395
0.042515
7.083407
8.966958
10.829225
12.632873
14.352453
19.122042
28.564009
40.705531
56.032527
75.118381
2.025218
2.352589
2.655806
2.935814
3.193631
11
12
13
14
15
6.175926
7.287593
8.599359
10.147244
11.973748
0.161919
0.137220
0.116288
0.098549
0.083516
0.214776
0.208628
0.203686
0.199678
0.196403
4.656005
4.793225
4.909513
5.008062
5.091578
28.755144
34.931070
42.218663
50.818022
60.965266
0.034776
0.028628
0.023686
0.019678
0.016403
15.971644
17.481059
18.876511
20.157647
21.326872
98.639690
127.394834
162.325904
204.544567
255.362589
3.430332
3.647035
3.844885
4.025040
4.188657
16
17
18
19
20
14.129023
16.672247
19.673251
23.214436
27.393035
0.070776
0.059980
0.050830
0.043077
0.036506
0.193710
0.191485
0.189639
0.188103
0.186820
5.162354
5.222334
5.273164
5.316241
5.352746
72.939014
87.068036
103.740283
123.413534
146.627970
0.013710
0.011485
0.009639
0.008103
0.006820
22.388517
23.348195
24.212313
24.987692
25.681299
316.327855
389.266869
476.334905
580.075188
703.488722
4.336881
4.470836
4.591610
4.700256
4.797780
21
22
23
24
25
32.323781
38.142061
45.007632
53.109006
62.668627
0.030937
0.026218
0.022218
0.018829
0.015957
0.185746
0.184846
0.184090
0.183454
0.182919
5.383683
5.409901
5.432120
5.450949
5.466906
174.021005
206.344785
244.486847
289.494479
342.603486
0.005746
0.004846
0.004090
0.003454
0.002919
26.300039
26.850612
27.339418
27.772490
28.155456
850.116692
1024.137697
1230.482482
1474.969329
1764.463809
4.885138
4.963235
5.032919
5.094983
5.150163
26
27
28
29
30
73.948980
87.259797
102.966560
121.500541
143.370638
0.013523
0.011460
0.009712
0.008230
0.006975
0.182467
0.182087
0.181765
0.181494
0.181264
5.480429
5.491889
5.501601
5.509831
5.516806
405.272113
479.221093
566.480890
669.447450
790.947991
0.002467
0.002087
0.001765
0.001494
0.001264
28.493527
28.791488
29.053709
29.284161
29.486434
2107.067294
2512.339407
2991.560500
3558.041390
4227.488841
5.199142
5.242548
5.280956
5.314893
5.344838
35
40
45
50
55
327.997290
750.378345
1716.683879
3927.356860
8984.841120
0.003049
0.001333
0.000583
0.000255
0.000111
0.180550
0.180240
0.180105
0.180046
5.538618
5.548152
5.552319
5.554141
5.554937
1816.651612
4163.213027
9531.577105
21813.093666
49910.228445
0.000550
0.000240
0.000105
30.177275 9898.064512
30.526919 22906.739038
30.700589 52703.206139
30.785610
30.826754
5.448521
5.502178
5.529327
5.542821
5.549433
60
70
80
90
100
20555.139966
30.846479
30.860296
30.863353
30.864017
30.864160
5.552636
5.554905
5.555413
5.555525
Ing. Carlos Gerardo Vásquez Gallardo
5.555285
5.555504
Página 16
i = 20 %
Factores de interes discreto capitalizado al : i =
0.20000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.200000
1.440000
1.728000
2.073600
2.488320
0.833333
0.694444
0.578704
0.482253
0.401878
1.200000
0.654545
0.474725
0.386289
0.334380
0.833333
1.527778
2.106481
2.588735
2.990612
1.000000
2.200000
3.640000
5.368000
7.441600
1.000000
0.454545
0.274725
0.186289
0.134380
0.000000
0.694444
1.851852
3.298611
4.906121
0.000000
1.000000
3.200000
6.840000
12.208000
0.000000
0.454545
0.879121
1.274218
1.640507
6
7
8
9
10
2.985984
3.583181
4.299817
5.159780
6.191736
0.334898
0.279082
0.232568
0.193807
0.161506
0.300706
0.277424
0.260609
0.248079
0.238523
3.325510
3.604592
3.837160
4.030967
4.192472
9.929920
12.915904
16.499085
20.798902
25.958682
0.100706
0.077424
0.060609
0.048079
0.038523
6.580611
8.255101
9.883077
11.433531
12.887081
19.649600
29.579520
42.495424
58.994509
79.793411
1.978828
2.290163
2.575623
2.836424
3.073862
11
12
13
14
15
7.430084
8.916100
10.699321
12.839185
15.407022
0.134588
0.112157
0.093464
0.077887
0.064905
0.231104
0.225265
0.220620
0.216893
0.213882
4.327060
4.439217
4.532681
4.610567
4.675473
32.150419
39.580502
48.496603
59.195923
72.035108
0.031104
0.025265
0.020620
0.016893
0.013882
14.232961
15.466684
16.588251
17.600776
18.509453
105.752093
137.902511
177.483013
225.979616
285.175539
3.289291
3.484102
3.659700
3.817486
3.958841
16
17
18
19
20
18.488426
22.186111
26.623333
31.948000
38.337600
0.054088
0.045073
0.037561
0.031301
0.026084
0.211436
0.209440
0.207805
0.206462
0.205357
4.729561
4.774634
4.812195
4.843496
4.869580
87.442129
105.930555
128.116666
154.740000
186.688000
0.011436
0.009440
0.007805
0.006462
0.005357
19.320771
20.041943
20.680481
21.243896
21.739493
357.210647
444.652777
550.583332
678.699998
833.439998
4.085109
4.197588
4.297515
4.386067
4.464347
21
22
23
24
25
46.005120
55.206144
66.247373
79.496847
95.396217
0.021737
0.018114
0.015095
0.012579
0.010483
0.204444
0.203690
0.203065
0.202548
0.202119
4.891316
4.909430
4.924525
4.937104
4.947587
225.025600
271.030719
326.236863
392.484236
471.981083
0.004444
0.003690
0.003065
0.002548
0.002119
22.174228
22.554620
22.886709
23.176028
23.427611
1020.127998
1245.153597
1516.184317
1842.421180
2234.905416
4.533386
4.594142
4.647495
4.694255
4.735159
26
27
28
29
30
114.475460
137.370552
164.844662
197.813595
237.376314
0.008735
0.007280
0.006066
0.005055
0.004213
0.201762
0.201467
0.201221
0.201016
0.200846
4.956323
4.963602
4.969668
4.974724
4.978936
567.377300
681.852760
819.223312
984.067974
1181.881569
0.001762
0.001467
0.001221
0.001016
0.000846
23.645998
23.835267
23.999058
24.140605
24.262774
2706.886499
3274.263799
3956.116559
4775.339871
5759.407845
4.770876
4.802010
4.829106
4.852652
4.873084
35
40
45
50
55
590.668229
1469.771568
3657.261988
9100.438150
22644.802257
0.001693
0.000680
0.000273
0.000110
0.200339
0.200136
4.991535
4.996598
4.998633
4.999451
4.999779
2948.341146
7343.857840
18281.309940
45497.190750
0.000339
0.000136
24.661400
24.846915
24.931643
24.969782
24.986752
14566.705729
36519.289199
91181.549700
4.940645
4.972766
4.987692
4.994505
4.997571
60
70
80
90
100
56347.514353
Ing. Carlos Gerardo Vásquez Gallardo
4.999911
4.999986
24.994232
24.998925
24.999803
4.998935
4.999799
4.999963
Página 17
i = 25 %
Factores de interes discreto capitalizado al : i =
0.25000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.250000
1.562500
1.953125
2.441406
3.051758
0.800000
0.640000
0.512000
0.409600
0.327680
1.250000
0.694444
0.512295
0.423442
0.371847
0.800000
1.440000
1.952000
2.361600
2.689280
1.000000
2.250000
3.812500
5.765625
8.207031
1.000000
0.444444
0.262295
0.173442
0.121847
0.000000
0.640000
1.664000
2.892800
4.203520
0.000000
1.000000
3.250000
7.062500
12.828125
0.000000
0.444444
0.852459
1.224932
1.563065
6
7
8
9
10
3.814697
4.768372
5.960464
7.450581
9.313226
0.262144
0.209715
0.167772
0.134218
0.107374
0.338819
0.316342
0.300399
0.288756
0.280073
2.951424
3.161139
3.328911
3.463129
3.570503
11.258789
15.073486
19.841858
25.802322
33.252903
0.088819
0.066342
0.050399
0.038756
0.030073
5.514240
6.772531
7.946936
9.020678
9.987046
21.035156
32.293945
47.367432
67.209290
93.011612
1.868332
2.142434
2.387248
2.604777
2.797098
11
12
13
14
15
11.641532
14.551915
18.189894
22.737368
28.421709
0.085899
0.068719
0.054976
0.043980
0.035184
0.273493
0.268448
0.264543
0.261501
0.259117
3.656403
3.725122
3.780098
3.824078
3.859263
42.566129
54.207661
68.759576
86.949470
109.686838
0.023493
0.018448
0.014543
0.011501
0.009117
10.846039
11.601953
12.261660
12.833407
13.325988
126.264515
168.830644
223.038305
291.797881
378.747351
2.966314
3.114516
3.243742
3.355948
3.452988
16
17
18
19
20
35.527137
44.408921
55.511151
69.388939
86.736174
0.028147
0.022518
0.018014
0.014412
0.011529
0.257241
0.255759
0.254586
0.253656
0.252916
3.887410
3.909928
3.927942
3.942354
3.953883
138.108547
173.635684
218.044605
273.555756
342.944695
0.007241
0.005759
0.004586
0.003656
0.002916
13.748200
14.108488
14.414733
14.674140
14.893195
488.434189
626.542736
800.178420
1018.223025
1291.778781
3.536596
3.608375
3.669792
3.722177
3.766726
21
22
23
24
25
108.420217
135.525272
169.406589
211.758237
264.697796
0.009223
0.007379
0.005903
0.004722
0.003778
0.252327
0.251858
0.251485
0.251186
0.250948
3.963107
3.970485
3.976388
3.981111
3.984888
429.680869
538.101086
673.626358
843.032947
1054.791184
0.002327
0.001858
0.001485
0.001186
0.000948
15.077663
15.232615
15.362481
15.471095
15.561764
1634.723476
2064.404345
2602.505431
3276.131789
4119.164736
3.804506
3.836462
3.863426
3.886125
3.905195
26
27
28
29
30
330.872245
413.590306
516.987883
646.234854
807.793567
0.003022
0.002418
0.001934
0.001547
0.001238
0.250758
0.250606
0.250485
0.250387
0.250310
3.987911
3.990329
3.992263
3.993810
3.995048
1319.488980
1650.361225
2063.951531
2580.939414
3227.174268
0.000758
0.000606
0.000485
0.000387
0.000310
15.637322
15.700186
15.752412
15.795740
15.831640
5173.955920
6493.444900
8143.806126
10207.757657
12788.697071
3.921182
3.934560
3.945735
3.955055
3.962816
35
40
45
50
55
2465.190329
7523.163845
22958.874039
70064.923216
0.000406
0.000133
0.000044
0.250101
0.250033
3.998377
3.999468
3.999826
3.999943
3.999981
9856.761315
30088.655381
91831.496158
0.000101
0.000033
15.936719
15.976606
15.991463
15.996917
15.998896
39287.045261
3.985797
3.994682
3.998040
3.999286
3.999743
60
70
80
90
100
Ing. Carlos Gerardo Vásquez Gallardo
15.999608
15.999951
3.999908
3.999988
Página 18
i = 30 %
Factores de interes discreto capitalizado al : i = 0.30000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.300000
1.690000
2.197000
2.856100
3.712930
0.769231
0.591716
0.455166
0.350128
0.269329
1.300000
0.734783
0.550627
0.461629
0.410582
0.769231
1.360947
1.816113
2.166241
2.435570
1.000000
2.300000
3.990000
6.187000
9.043100
1.000000
0.434783
0.250627
0.161629
0.110582
0.000000
0.591716
1.502048
2.552432
3.629748
0.000000
1.000000
3.300000
7.290000
13.477000
0.000000
0.434783
0.827068
1.178277
1.490308
6
7
8
9
10
4.826809
6.274852
8.157307
10.604499
13.785849
0.207176
0.159366
0.122589
0.094300
0.072538
0.378394
0.356874
0.341915
0.331235
0.323463
2.642746
2.802112
2.924702
3.019001
3.091539
12.756030
17.582839
23.857691
32.014998
42.619497
0.078394
0.056874
0.041915
0.031235
0.023463
4.665629
5.621827
6.479953
7.234350
7.887193
22.520100
35.276130
52.858969
76.716660
108.731658
1.765447
2.006282
2.215595
2.396273
2.551219
11
12
13
14
15
17.921604
23.298085
30.287511
39.373764
51.185893
0.055799
0.042922
0.033017
0.025398
0.019537
0.317729
0.313454
0.310243
0.307818
0.305978
3.147338
3.190260
3.223277
3.248675
3.268211
56.405346
74.326950
97.625036
127.912546
167.286310
0.017729
0.013454
0.010243
0.007818
0.005978
8.445179
8.917321
9.313524
9.643693
9.917206
151.351155
207.756501
282.083452
379.708487
507.621033
2.683277
2.795171
2.889458
2.968501
3.034445
16
17
18
19
20
66.541661
86.504159
112.455407
146.192029
190.049638
0.015028
0.011560
0.008892
0.006840
0.005262
0.304577
0.303509
0.302692
0.302066
0.301587
3.283239
3.294800
3.303692
3.310532
3.315794
218.472203
285.013864
371.518023
483.973430
630.165459
0.004577
0.003509
0.002692
0.002066
0.001587
10.142628
10.327591
10.478762
10.601887
10.701861
674.907344
893.379547
1178.393411
1549.911434
2033.884864
3.089214
3.134513
3.171834
3.202472
3.227541
21
22
23
24
25
247.064529
321.183888
417.539054
542.800770
705.641001
0.004048
0.003113
0.002395
0.001842
0.001417
0.301219
0.300937
0.300720
0.300554
0.300426
3.319842
3.322955
3.325350
3.327192
3.328609
820.215097
1067.279626
1388.463514
1806.002568
2348.803338
0.001219
0.000937
0.000720
0.000554
0.000426
10.782812
10.848195
10.900885
10.943257
10.977269
2664.050323
3484.265420
4551.545046
5940.008560
7746.011128
3.247990
3.264623
3.278116
3.289037
3.297854
26
27
28
29
30
917.333302
1192.533293
1550.293280
2015.381264
2619.995644
0.001090
0.000839
0.000645
0.000496
0.000382
0.300327
0.300252
0.300194
0.300149
3.329700
3.330538
3.331183
3.331679
3.332061
3054.444340
3971.777642
5164.310934
6714.604214
8729.985479
0.000327
0.000252
0.000194
0.000149
11.004522
11.026324
11.043740
11.057633
11.068702
10094.814466
13149.258806
17121.036447
22285.347382
28999.951596
3.304959
3.310673
3.315261
3.318937
3.321879
35
40
45
50
55
9727.860425
36118.864808
0.000103
3.332991
3.333241
3.333308
32422.868084
60
70
80
90
100
Ing. Carlos Gerardo Vásquez Gallardo
11.097976
11.107112
11.109910
11.110754
11.111006
3.329735
3.332226
3.332998
3.333233
3.333304
11.111080
Página 19
i = 40 %
Factores de interes discreto capitalizado al : i = 0.40000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.400000
1.960000
2.744000
3.841600
5.378240
0.714286
0.510204
0.364431
0.260308
0.185934
1.400000
0.816667
0.629358
0.540766
0.491361
0.714286
1.224490
1.588921
1.849229
2.035164
1.000000
2.400000
4.360000
7.104000
10.945600
1.000000
0.416667
0.229358
0.140766
0.091361
0.000000
0.510204
1.239067
2.019992
2.763729
0.000000
1.000000
3.400000
7.760000
14.864000
0.000000
0.416667
0.779817
1.092342
1.357989
6
7
8
9
10
7.529536
10.541350
14.757891
20.661047
28.925465
0.132810
0.094865
0.067760
0.048400
0.034572
0.461260
0.441923
0.429074
0.420345
0.414324
2.167974
2.262839
2.330599
2.378999
2.413571
16.323840
23.853376
34.394726
49.152617
69.813664
0.061260
0.041923
0.029074
0.020345
0.014324
3.427781
3.996968
4.471291
4.858493
5.169637
25.809600
42.133440
65.986816
100.381542
149.534159
1.581099
1.766351
1.918516
2.042242
2.141904
11
12
13
14
15
40.495652
56.693912
79.371477
111.120068
155.568096
0.024694
0.017639
0.012599
0.008999
0.006428
0.410128
0.407182
0.405104
0.403632
0.402588
2.438265
2.455904
2.468503
2.477502
2.483930
98.739129
139.234781
195.928693
275.300171
386.420239
0.010128
0.007182
0.005104
0.003632
0.002588
5.416577
5.610602
5.761789
5.878780
5.968773
219.347823
318.086952
457.321733
653.250427
928.550597
2.221488
2.284537
2.334123
2.372866
2.402955
16
17
18
19
20
217.795334
304.913467
426.878854
597.630396
836.682554
0.004591
0.003280
0.002343
0.001673
0.001195
0.401845
0.401316
0.400939
0.400670
0.400479
2.488521
2.491801
2.494144
2.495817
2.497012
541.988334
759.783668
1064.697136
1491.575990
2089.206386
0.001845
0.001316
0.000939
0.000670
0.000479
6.037645
6.090119
6.129943
6.160061
6.182770
1314.970836
1856.959171
2616.742839
3681.439974
5173.015964
2.426198
2.444063
2.457734
2.468154
2.476067
21
22
23
24
25
1171.355576
1639.897806
2295.856929
3214.199700
4499.879581
0.000854
0.000610
0.000436
0.000311
0.000222
0.400342
0.400244
0.400174
0.400124
2.497866
2.498476
2.498911
2.499222
2.499444
2925.888940
4097.244516
5737.142322
8032.999251
11247.198951
0.000342
0.000244
0.000174
0.000124
6.199844
6.212650
6.222233
6.229388
6.234722
7262.222350
10188.111290
14285.355805
20022.498128
28055.497379
2.482057
2.486576
2.489978
2.492531
2.494443
26
27
28
29
30
6299.831413
8819.763978
12347.669569
17286.737397
24201.432355
0.000159
0.000113
2.499603
2.499717
2.499798
2.499855
15747.078532
22046.909945
30866.673923
43214.343492
60501.080889
6.238690
6.241638
6.243825
6.245444
6.246643
39302.696330
55049.774862
77096.684807
2.495872
2.496938
2.497732
2.498322
2.498760
35
40
45
50
55
6.249280
6.249848
6.249968
2.499731
2.499943
2.499988
60
70
80
90
100
Ing. Carlos Gerardo Vásquez Gallardo
Página 20
i = 50 %
Factores de interes discreto capitalizado al : i = 0.50000
n
(F/P,i,n)
(P/F,i,n)
(A/P,i,n)
(P/A,i,n)
(F/A,i,n)
(A/F,i,n)
(P/G,i,n)
(F/G,i,n)
(A/G,i,n)
1
2
3
4
5
1.500000
2.250000
3.375000
5.062500
7.593750
0.666667
0.444444
0.296296
0.197531
0.131687
1.500000
0.900000
0.710526
0.623077
0.575829
0.666667
1.111111
1.407407
1.604938
1.736626
1.000000
2.500000
4.750000
8.125000
13.187500
1.000000
0.400000
0.210526
0.123077
0.075829
0.000000
0.444444
1.037037
1.629630
2.156379
0.000000
1.000000
3.500000
8.250000
16.375000
0.000000
0.400000
0.736842
1.015385
1.241706
6
7
8
9
10
11.390625
17.085938
25.628906
38.443359
57.665039
0.087791
0.058528
0.039018
0.026012
0.017342
0.548120
0.531083
0.520301
0.513354
0.508824
1.824417
1.882945
1.921963
1.947975
1.965317
20.781250
32.171875
49.257813
74.886719
113.330078
0.048120
0.031083
0.020301
0.013354
0.008824
2.595336
2.946502
3.219631
3.427730
3.583803
29.562500
50.343750
82.515625
131.773438
206.660156
1.422556
1.564837
1.675178
1.759637
1.823524
11
12
13
14
15
86.497559
129.746338
194.619507
291.929260
437.893890
0.011561
0.007707
0.005138
0.003425
0.002284
0.505848
0.503884
0.502582
0.501719
0.501144
1.976878
1.984585
1.989724
1.993149
1.995433
170.995117
257.492676
387.239014
581.858521
873.787781
0.005848
0.003884
0.002582
0.001719
0.001144
3.699413
3.784194
3.845853
3.890384
3.922356
319.990234
490.985352
748.478027
1135.717041
1717.575562
1.871341
1.906793
1.932858
1.951878
1.965667
16
17
18
19
20
656.840836
985.261253
1477.891880
2216.837820
3325.256730
0.001522
0.001015
0.000677
0.000451
0.000301
0.500762
0.500508
0.500339
0.500226
0.500150
1.996955
1.997970
1.998647
1.999098
1.999399
1311.681671
1968.522507
2953.783760
4431.675640
6648.513460
0.000762
0.000508
0.000339
0.000226
3.945192
3.961432
3.972934
3.981054
3.986768
2591.363342
3903.045013
5871.567520
8825.351280
13257.026920
1.975604
1.982728
1.987812
1.991425
1.993984
21
22
23
24
25
4987.885095
7481.827643
11222.741464
16834.112196
25251.168294
0.000200
0.000134
0.500100
1.999599
1.999733
1.999822
1.999881
9973.770190
14961.655285
22443.482928
33666.224392
50500.336588
0.000100
3.990778
3.993584
3.995545
3.996911
3.997861
19905.540380
29879.310571
44840.965856
67284.448784
1.995789
1.997059
1.997950
1.998574
1.999010
26
27
28
29
30
37876.752441
56815.128662
85222.692992
35
40
45
50
55
75751.504882
3.998522
3.998979
3.999296
3.999515
3.999666
1.999314
1.999525
1.999671
1.999773
1.999844
3.999949
3.999992
1.999976
60
70
80
90
100
Ing. Carlos Gerardo Vásquez Gallardo
Página 21