Time Value of Money
Content
Time Value of Money Analysis
Compute interest rate factors and solve basic TVM problems, generates printable tables by rate, term, and frequency of compounding
User Information:
Annual Discount/Interest Rate
Frequency of Compounding
Time Horizon in Years
8.00%
2
10
Factors:
USCA
Name:
Definition:
General Formula:
SPCA
Future value of $1
deposited at time 0
V
n
Interest Rate Factor:
= V 0 (1 + r )
n
Future value of Uniform
series of deposits at the
end of each period
V
n
(1 + r ) n − 1
= P1
r
2.1911231
Calculation Utilities:
Known
Enter ==>
29.7780786
V0
$100.00
Vn
Unknown
Go to Tables
Solver
Result ==>
$219.11
Effective interest rate per period and number of periods:
4.00%
Interest rate per period = ' r ' in formulas
20
Number of Compounding Periods = 'n' in formulas
SFD
SPPV
Annual deposit at end of
Present value of $1
each period needed to
received at end of
have $1 at end of
period
horizon
r
P1 = V n
n
(1 + r ) − 1
V 0 = V n (1 + r ) −n
0.0335818
USPV
CR
Amount of uniform
Present value of uniform
payment at end of each
series of $1 payments at period to pay off a $1
end of each period
loan made at time 0
V
0
0.4563869
(1 + r ) n − 1
= P1
n
r (1 + r )
13.5903263
r (1 + r ) n
P1 = V 0
n
(1 + r ) − 1
0.0735818
P1
Vn
Vn
P1
V0
$100.00
Vn
$20,000.00
P1
$2,500.00
V0
$750.00
V0
$100,000.00
P1
$2,977.81
$671.64
$1,140.97
$10,192.75
$7,358.18
GoPrint
to Top
Table
Interest Factor Table
SPCA
USCA
SFD
SPPV
USPV
CR
Table For:
8.00%
Int. Rate/yr.
=r
Freq./yr. =2m
values
per
Future value of $1
deposited at time 0
Future value of Uniform
series of deposits at the
end of each period
Annual deposit at end of
Present value of $1
each period needed to
received at end of
have $1 at end of
period
horizon
Amount of uniform
Present value of uniform
series of $1 payments at payment at end of each
period to pay off a $1
end of each period
loan made at time 0
$1
V
End of Compounding
Year
period
1
1
2
0
3
2
4
0
5
3
6
0
7
4
8
0
9
5
10
0
11
6
12
0
13
7
14
0
15
8
16
0
17
9
18
0
19
10
20
0
21
11
22
0
23
12
24
0
25
13
26
0
27
14
28
0
29
15
30
0
31
16
32
0
33
17
34
0
35
18
36
0
37
19
38
0
39
20
40
0
41
21
42
0
43
22
44
0
45
23
46
0
47
24
48
0
49
25
50
0
51
26
52
0
53
27
54
0
55
28
56
0
57
29
58
0
59
30
60
0
61
31
62
0
63
32
64
0
65
33
66
0
67
34
68
0
69
35
70
0
71
36
72
0
73
37
74
0
75
38
76
0
77
39
78
0
79
40
80
0
81
41
82
0
83
42
84
0
85
43
86
0
87
44
88
0
89
45
90
0
91
46
92
0
93
47
94
0
95
48
96
0
97
49
98
0
99
50
100
0
101
51
102
0
103
52
104
0
105
53
106
0
107
54
108
0
109
55
110
0
111
56
112
0
113
57
114
0
115
58
116
0
117
59
118
0
119
60
120
0
121
61
122
0
123
62
124
0
125
63
126
0
127
64
128
0
129
65
130
0
131
66
132
0
133
67
134
0
135
68
136
0
137
69
138
0
139
70
140
0
141
71
142
0
143
72
144
0
145
73
146
0
147
74
148
0
149
75
150
0
151
76
152
0
153
77
154
0
155
78
156
0
157
79
158
0
159
80
160
0
161
81
162
0
163
82
164
0
165
83
166
0
167
84
168
0
169
85
170
0
171
86
172
0
173
87
174
0
175
88
176
0
177
89
178
0
179
90
180
0
181
91
182
0
183
92
184
0
185
93
186
0
187
94
188
0
189
95
190
0
191
96
192
0
193
97
194
0
195
98
196
0
197
99
198
0
199
100
200
0
201
101
202
0
203
102
204
0
205
103
206
0
207
104
208
0
209
105
210
0
211
106
212
0
213
107
214
0
215
108
216
0
217
109
218
0
219
110
220
0
221
111
222
0
223
112
224
0
225
113
226
0
227
114
228
0
229
115
230
0
231
116
232
0
233
117
234
0
235
118
236
0
237
119
238
0
239
120
240
0
241
121
242
0
243
122
244
0
245
123
246
0
247
124
248
0
249
125
250
0
251
126
252
0
253
127
254
0
255
128
256
0
257
129
258
0
259
130
260
0
261
131
262
0
263
132
264
0
265
133
266
0
267
134
268
0
269
135
270
0
271
136
272
0
273
137
274
0
275
138
276
0
277
139
278
0
279
140
280
0
281
141
282
0
283
142
284
0
285
143
286
0
287
144
288
0
289
145
290
0
291
146
292
0
293
147
294
0
295
148
296
0
297
149
298
0
299
150
300
0
301
151
302
0
303
152
304
0
305
153
306
0
307
154
308
0
309
155
310
0
311
156
312
0
313
157
314
0
315
158
316
0
317
159
318
0
319
160
320
0
321
161
322
0
323
162
324
0
325
163
326
0
327
164
328
0
329
165
330
0
331
166
332
0
333
167
334
0
335
168
336
0
337
169
338
0
339
170
340
0
341
171
342
0
343
172
344
0
345
173
346
0
347
174
348
0
349
175
350
0
351
176
352
0
353
177
354
0
355
178
356
0
357
179
358
0
359
180
360
n
= V 0 (1 + r )
n
SPCA
1.040000
1.081600
1.124864
1.169859
1.216653
1.265319
1.315932
1.368569
1.423312
1.480244
1.539454
1.601032
1.665074
1.731676
1.800944
1.872981
1.947900
2.025817
2.106849
2.191123
2.278768
2.369919
2.464716
2.563304
2.665836
2.772470
2.883369
2.998703
3.118651
3.243398
3.373133
3.508059
3.648381
3.794316
3.946089
4.103933
4.268090
4.438813
4.616366
4.801021
4.993061
5.192784
5.400495
5.616515
5.841176
6.074823
6.317816
6.570528
6.833349
7.106683
7.390951
7.686589
7.994052
8.313814
8.646367
8.992222
9.351910
9.725987
10.115026
10.519627
10.940413
11.378029
11.833150
12.306476
12.798735
13.310685
13.843112
14.396836
14.972710
15.571618
16.194483
16.842262
17.515953
18.216591
18.945255
19.703065
20.491187
21.310835
22.163268
23.049799
23.971791
24.930663
25.927889
26.965005
28.043605
29.165349
30.331963
31.545242
32.807051
34.119333
35.484107
36.903471
38.379610
39.914794
41.511386
43.171841
44.898715
46.694664
48.562450
50.504948
52.525146
54.626152
56.811198
59.083646
61.446992
63.904871
66.461066
69.119509
71.884289
74.759661
77.750047
80.860049
84.094451
87.458229
90.956558
94.594821
98.378614
102.313758
106.406308
110.662561
115.089063
119.692626
124.480331
129.459544
134.637926
140.023443
145.624381
151.449356
157.507330
163.807623
170.359928
177.174325
184.261298
191.631750
199.297020
207.268901
215.559657
224.182043
233.149325
242.475298
252.174310
262.261282
272.751734
283.661803
295.008275
306.808606
319.080950
331.844188
345.117956
358.922674
373.279581
388.210764
403.739195
419.888763
436.684313
454.151686
472.317753
491.210463
510.858882
531.293237
552.544967
574.646765
597.632636
621.537941
646.399459
672.255437
699.145655
727.111481
756.195940
786.443778
817.901529
850.617590
884.642294
920.027986
956.829105
995.102269
1034.906360
1076.302614
1119.354719
1164.128908
1210.694064
1259.121827
1309.486700
1361.866168
1416.340814
1472.994447
1531.914225
1593.190794
1656.918425
1723.195163
1792.122969
1863.807888
1938.360203
2015.894611
2096.530396
2180.391612
2267.607276
2358.311567
2452.644030
2550.749791
2652.779783
2758.890974
2869.246613
2984.016478
3103.377137
3227.512222
3356.612711
3490.877219
3630.512308
3775.732801
3926.762113
4083.832597
4247.185901
4417.073337
4593.756270
4777.506521
4968.606782
5167.351053
5374.045096
5589.006899
5812.567175
6045.069862
6286.872657
6538.347563
6799.881466
7071.876724
7354.751793
7648.941865
7954.899540
8273.095521
8604.019342
8948.180116
9306.107320
9678.351613
10065.485678
10468.105105
10886.829309
11322.302481
11775.194581
12246.202364
12736.050458
13245.492477
13775.312176
14326.324663
14899.377649
15495.352755
16115.166865
16759.773540
17430.164482
18127.371061
18852.465903
19606.564539
20390.827121
21206.460206
22054.718614
22936.907359
23854.383653
24808.558999
25800.901359
26832.937413
27906.254910
29022.505106
30183.405311
31390.741523
32646.371184
33952.226031
35310.315073
36722.727676
38191.636783
39719.302254
41308.074344
42960.397318
44678.813211
46465.965739
48324.604369
50257.588543
52267.892085
54358.607768
56532.952079
58794.270162
61146.040969
63591.882608
66135.557912
68780.980228
71532.219437
74393.508215
77369.248544
80464.018485
83682.579225
87029.882394
90511.077689
94131.520797
97896.781629
101812.652894
105885.159010
110120.565370
114525.387985
119106.403504
123870.659645
128825.486030
133978.505472
139337.645690
144911.151518
150707.597579
156735.901482
163005.337541
169525.551043
176306.573085
183358.836008
190693.189448
198320.917026
206253.753707
214503.903855
223084.060010
232007.422410
241287.719306
250939.228079
260976.797202
271415.869090
282272.503854
293563.404008
305305.940168
317518.177775
330218.904886
343427.661081
357164.767524
371451.358225
386309.412554
401761.789057
417832.260619
434545.551044
451927.373085
470004.468009
488804.646729
508356.832598
528691.105902
549838.750138
571832.300144
594705.592150
618493.815836
643233.568469
668962.911208
695721.427656
723550.284762
752492.296153
782591.987999
813895.667519
846451.494220
880309.553988
915521.936148
952142.813594
990228.526138
1029837.667183
1071031.173870
1113872.420825
1158427.317658
1204764.410365
1252954.986779
1303073.186250
1355196.113700
2.19E+00
0.0000000
(1 + r ) − 1
= P1
r
n
V
n
USCA
1.000000
2.040000
3.121600
4.246464
5.416323
6.632975
7.898294
9.214226
10.582795
12.006107
13.486351
15.025805
16.626838
18.291911
20.023588
21.824531
23.697512
25.645413
27.671229
29.778079
31.969202
34.247970
36.617889
39.082604
41.645908
44.311745
47.084214
49.967583
52.966286
56.084938
59.328335
62.701469
66.209527
69.857909
73.652225
77.598314
81.702246
85.970336
90.409150
95.025516
99.826536
104.819598
110.012382
115.412877
121.029392
126.870568
132.945390
139.263206
145.833734
152.667084
159.773767
167.164718
174.851306
182.845359
191.159173
199.805540
208.797762
218.149672
227.875659
237.990685
248.510313
259.450725
270.828754
282.661904
294.968380
307.767116
321.077800
334.920912
349.317749
364.290459
379.862077
396.056560
412.898823
430.414776
448.631367
467.576621
487.279686
507.770873
529.081708
551.244977
574.294776
598.266567
623.197230
649.125119
676.090123
704.133728
733.299078
763.631041
795.176282
827.983334
862.102667
897.586774
934.490245
972.869854
1012.784648
1054.296034
1097.467876
1142.366591
1189.061254
1237.623705
1288.128653
1340.653799
1395.279951
1452.091149
1511.174795
1572.621787
1636.526658
1702.987724
1772.107233
1843.991523
1918.751184
1996.501231
2077.361280
2161.455731
2248.913961
2339.870519
2434.465340
2532.843954
2635.157712
2741.564020
2852.226581
2967.315644
3087.008270
3211.488601
3340.948145
3475.586071
3615.609513
3761.233894
3912.683250
4070.190580
4233.998203
4404.358131
4581.532456
4765.793754
4957.425505
5156.722525
5363.991426
5579.551083
5803.733126
6036.882451
6279.357749
6531.532059
6793.793342
7066.545075
7350.206878
7645.215153
7952.023759
8271.104710
8602.948898
8948.066854
9306.989528
9680.269109
10068.479874
10472.219069
10892.107832
11328.792145
11782.943831
12255.261584
12746.472047
13257.330929
13788.624166
14341.169133
14915.815898
15513.448534
16134.986475
16781.385934
17453.641372
18152.787027
18879.898508
19636.094448
20422.538226
21240.439755
22091.057345
22975.699639
23895.727625
24852.556730
25847.658999
26882.565359
27958.867973
29078.222692
30242.351600
31453.045664
32712.167490
34021.654190
35383.520357
36799.861172
38272.855619
39804.769843
41397.960637
43054.879063
44778.074225
46570.197194
48434.005082
50372.365285
52388.259897
54484.790292
56665.181904
58932.789180
61291.100747
63743.744777
66294.494568
68947.274351
71706.165325
74575.411938
77559.428416
80662.805552
83890.317775
87246.930486
90737.807705
94368.320013
98144.052814
102070.814926
106154.647523
110401.833424
114818.906761
119412.663032
124190.169553
129158.776335
134326.127388
139700.172484
145289.179383
151101.746559
157146.816421
163433.689078
169972.036641
176771.918107
183843.794831
191198.546624
198847.488489
206802.388029
215075.483550
223679.502892
232627.683007
241933.790328
251612.141941
261677.627618
272145.732723
283032.562032
294354.864513
306130.059094
318376.261458
331112.311916
344357.804393
358133.116568
372459.441231
387358.818880
402854.171635
418969.338501
435729.112041
453159.276523
471286.647583
490139.113487
509745.678026
530136.505147
551342.965353
573397.683967
596334.591326
620188.974979
644997.533978
670798.435337
697631.372751
725537.627661
754560.132767
784743.538078
816134.279601
848780.650785
882732.876817
918043.191889
954765.919565
992957.556347
1032676.858601
1073984.932945
1116945.330263
1161624.143474
1208090.109213
1256414.713581
1306672.302124
1358940.194209
1413298.801978
1469831.754057
1528626.024219
1589772.065188
1653363.947796
1719499.505707
1788280.485936
1859812.705373
1934206.213588
2011575.462132
2092039.480617
2175722.059841
2262751.942235
2353263.019925
2447394.540721
2545291.322350
2647103.975244
2752989.134254
2863109.699624
2977635.087609
3096741.491114
3220612.150758
3349437.636789
3483416.142260
3622753.787950
3767664.939468
3918372.537047
4075108.438529
4238113.776070
4407639.327113
4583945.900198
4767304.736206
4957997.925654
5156318.842680
5362572.596387
5577076.500243
5800160.560252
6032167.982662
6273455.701969
6524394.930048
6785371.727250
7056787.596339
7339060.100193
7632623.504201
7937929.444369
8255447.622144
8585666.527029
8929094.188110
9286258.955635
9657710.313860
10044019.726415
10445781.515471
10863613.776090
11298159.327134
11750086.700219
12220091.168228
12708895.814957
13217252.647555
13745943.753458
14295782.503596
14867614.803740
15462320.395889
16080814.211725
16724047.780194
17393010.691402
18088732.119058
18812282.403820
19564774.699973
20347366.687972
21161262.355491
22007713.849710
22888023.403699
23803545.339847
24755688.153440
25745916.679578
26775754.346761
27846785.520632
28960657.941457
30119085.259115
31323849.669480
32576804.656259
33879877.842509
2.98E+01
0.0000000
r
P1 = V n
n
(1 + r ) − 1
SFD
1.000000
0.490196
0.320349
0.235490
0.184627
0.150762
0.126610
0.108528
0.094493
0.083291
0.074149
0.066552
0.060144
0.054669
0.049941
0.045820
0.042199
0.038993
0.036139
0.033582
0.031280
0.029199
0.027309
0.025587
0.024012
0.022567
0.021239
0.020013
0.018880
0.017830
0.016855
0.015949
0.015104
0.014315
0.013577
0.012887
0.012240
0.011632
0.011061
0.010523
0.010017
0.009540
0.009090
0.008665
0.008262
0.007882
0.007522
0.007181
0.006857
0.006550
0.006259
0.005982
0.005719
0.005469
0.005231
0.005005
0.004789
0.004584
0.004388
0.004202
0.004024
0.003854
0.003692
0.003538
0.003390
0.003249
0.003115
0.002986
0.002863
0.002745
0.002633
0.002525
0.002422
0.002323
0.002229
0.002139
0.002052
0.001969
0.001890
0.001814
0.001741
0.001671
0.001605
0.001541
0.001479
0.001420
0.001364
0.001310
0.001258
0.001208
0.001160
0.001114
0.001070
0.001028
0.000987
0.000949
0.000911
0.000875
0.000841
0.000808
0.000776
0.000746
0.000717
0.000689
0.000662
0.000636
0.000611
0.000587
0.000564
0.000542
0.000521
0.000501
0.000481
0.000463
0.000445
0.000427
0.000411
0.000395
0.000379
0.000365
0.000351
0.000337
0.000324
0.000311
0.000299
0.000288
0.000277
0.000266
0.000256
0.000246
0.000236
0.000227
0.000218
0.000210
0.000202
0.000194
0.000186
0.000179
0.000172
0.000166
0.000159
0.000153
0.000147
0.000142
0.000136
0.000131
0.000126
0.000121
0.000116
0.000112
0.000107
0.000103
0.000099
0.000095
0.000092
0.000088
0.000085
0.000082
0.000078
0.000075
0.000073
0.000070
0.000067
0.000064
0.000062
0.000060
0.000057
0.000055
0.000053
0.000051
0.000049
0.000047
0.000045
0.000044
0.000042
0.000040
0.000039
0.000037
0.000036
0.000034
0.000033
0.000032
0.000031
0.000029
0.000028
0.000027
0.000026
0.000025
0.000024
0.000023
0.000022
0.000021
0.000021
0.000020
0.000019
0.000018
0.000018
0.000017
0.000016
0.000016
0.000015
0.000015
0.000014
0.000013
0.000013
0.000012
0.000012
0.000011
0.000011
0.000011
0.000010
0.000010
0.000009
0.000009
0.000009
0.000008
0.000008
0.000008
0.000007
0.000007
0.000007
0.000007
0.000006
0.000006
0.000006
0.000006
0.000005
0.000005
0.000005
0.000005
0.000005
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
3.36E-02
0.0000000
V
0
= V n (1 + r ) −n
SPPV
0.961538
0.924556
0.888996
0.854804
0.821927
0.790315
0.759918
0.730690
0.702587
0.675564
0.649581
0.624597
0.600574
0.577475
0.555265
0.533908
0.513373
0.493628
0.474642
0.456387
0.438834
0.421955
0.405726
0.390121
0.375117
0.360689
0.346817
0.333477
0.320651
0.308319
0.296460
0.285058
0.274094
0.263552
0.253415
0.243669
0.234297
0.225285
0.216621
0.208289
0.200278
0.192575
0.185168
0.178046
0.171198
0.164614
0.158283
0.152195
0.146341
0.140713
0.135301
0.130097
0.125093
0.120282
0.115656
0.111207
0.106930
0.102817
0.098863
0.095060
0.091404
0.087889
0.084508
0.081258
0.078133
0.075128
0.072238
0.069460
0.066788
0.064219
0.061749
0.059374
0.057091
0.054895
0.052784
0.050754
0.048801
0.046924
0.045120
0.043384
0.041716
0.040111
0.038569
0.037085
0.035659
0.034287
0.032969
0.031701
0.030481
0.029309
0.028182
0.027098
0.026056
0.025053
0.024090
0.023163
0.022272
0.021416
0.020592
0.019800
0.019039
0.018306
0.017602
0.016925
0.016274
0.015648
0.015046
0.014468
0.013911
0.013376
0.012862
0.012367
0.011891
0.011434
0.010994
0.010571
0.010165
0.009774
0.009398
0.009036
0.008689
0.008355
0.008033
0.007724
0.007427
0.007142
0.006867
0.006603
0.006349
0.006105
0.005870
0.005644
0.005427
0.005218
0.005018
0.004825
0.004639
0.004461
0.004289
0.004124
0.003966
0.003813
0.003666
0.003525
0.003390
0.003259
0.003134
0.003013
0.002898
0.002786
0.002679
0.002576
0.002477
0.002382
0.002290
0.002202
0.002117
0.002036
0.001957
0.001882
0.001810
0.001740
0.001673
0.001609
0.001547
0.001488
0.001430
0.001375
0.001322
0.001272
0.001223
0.001176
0.001130
0.001087
0.001045
0.001005
0.000966
0.000929
0.000893
0.000859
0.000826
0.000794
0.000764
0.000734
0.000706
0.000679
0.000653
0.000628
0.000604
0.000580
0.000558
0.000537
0.000516
0.000496
0.000477
0.000459
0.000441
0.000424
0.000408
0.000392
0.000377
0.000362
0.000349
0.000335
0.000322
0.000310
0.000298
0.000286
0.000275
0.000265
0.000255
0.000245
0.000235
0.000226
0.000218
0.000209
0.000201
0.000194
0.000186
0.000179
0.000172
0.000165
0.000159
0.000153
0.000147
0.000141
0.000136
0.000131
0.000126
0.000121
0.000116
0.000112
0.000107
0.000103
0.000099
0.000096
0.000092
0.000088
0.000085
0.000082
0.000079
0.000075
0.000073
0.000070
0.000067
0.000065
0.000062
0.000060
0.000057
0.000055
0.000053
0.000051
0.000049
0.000047
0.000045
0.000044
0.000042
0.000040
0.000039
0.000037
0.000036
0.000034
0.000033
0.000032
0.000031
0.000029
0.000028
0.000027
0.000026
0.000025
0.000024
0.000023
0.000022
0.000022
0.000021
0.000020
0.000019
0.000018
0.000018
0.000017
0.000016
0.000016
0.000015
0.000015
0.000014
0.000013
0.000013
0.000012
0.000012
0.000011
0.000011
0.000011
0.000010
0.000010
0.000009
0.000009
0.000009
0.000008
0.000008
0.000008
0.000007
0.000007
0.000007
0.000007
0.000006
0.000006
0.000006
0.000006
0.000005
0.000005
0.000005
0.000005
0.000005
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
4.56E-01
0.0000000
V
0
(1 + r ) n − 1
= P1
n
r (1 + r )
r (1 + r ) n
P1 = V 0
n
(1 + r ) − 1
USPV
0.961538
1.886095
2.775091
3.629895
4.451822
5.242137
6.002055
6.732745
7.435332
8.110896
8.760477
9.385074
9.985648
10.563123
11.118387
11.652296
12.165669
12.659297
13.133939
13.590326
14.029160
14.451115
14.856842
15.246963
15.622080
15.982769
16.329586
16.663063
16.983715
17.292033
17.588494
17.873551
18.147646
18.411198
18.664613
18.908282
19.142579
19.367864
19.584485
19.792774
19.993052
20.185627
20.370795
20.548841
20.720040
20.884654
21.042936
21.195131
21.341472
21.482185
21.617485
21.747582
21.872675
21.992957
22.108612
22.219819
22.326749
22.429567
22.528430
22.623490
22.714894
22.802783
22.887291
22.968549
23.046682
23.121810
23.194048
23.263507
23.330296
23.394515
23.456264
23.515639
23.572730
23.627625
23.680408
23.731162
23.779963
23.826888
23.872008
23.915392
23.957108
23.997219
24.035787
24.072872
24.108531
24.142818
24.175787
24.207487
24.237969
24.267278
24.295459
24.322557
24.348612
24.373666
24.397756
24.420919
24.443191
24.464607
24.485199
24.504999
24.524037
24.542344
24.559946
24.576871
24.593145
24.608794
24.623840
24.638308
24.652219
24.665595
24.678457
24.690824
24.702715
24.714149
24.725144
24.735715
24.745880
24.755654
24.765052
24.774088
24.782777
24.791132
24.799165
24.806889
24.814317
24.821458
24.828325
24.834928
24.841277
24.847382
24.853252
24.858896
24.864323
24.869541
24.874559
24.879384
24.884023
24.888483
24.892773
24.896897
24.900862
24.904675
24.908342
24.911867
24.915257
24.918516
24.921650
24.924663
24.927561
24.930347
24.933026
24.935602
24.938079
24.940460
24.942750
24.944952
24.947070
24.949105
24.951063
24.952945
24.954755
24.956495
24.958168
24.959777
24.961324
24.962812
24.964242
24.965617
24.966940
24.968211
24.969434
24.970610
24.971740
24.972827
24.973872
24.974877
24.975843
24.976772
24.977666
24.978525
24.979351
24.980145
24.980909
24.981643
24.982349
24.983028
24.983681
24.984308
24.984912
24.985492
24.986050
24.986587
24.987103
24.987599
24.988076
24.988534
24.988975
24.989399
24.989807
24.990199
24.990576
24.990938
24.991287
24.991622
24.991944
24.992254
24.992552
24.992838
24.993114
24.993379
24.993633
24.993878
24.994114
24.994340
24.994558
24.994767
24.994968
24.995162
24.995348
24.995527
24.995699
24.995864
24.996023
24.996176
24.996323
24.996465
24.996601
24.996732
24.996857
24.996978
24.997094
24.997206
24.997314
24.997417
24.997516
24.997612
24.997704
24.997792
24.997877
24.997959
24.998037
24.998113
24.998185
24.998255
24.998322
24.998387
24.998449
24.998508
24.998566
24.998621
24.998674
24.998725
24.998774
24.998821
24.998866
24.998910
24.998952
24.998992
24.999031
24.999068
24.999104
24.999139
24.999172
24.999204
24.999234
24.999264
24.999292
24.999319
24.999345
24.999371
24.999395
24.999418
24.999440
24.999462
24.999483
24.999503
24.999522
24.999540
24.999558
24.999575
24.999591
24.999607
24.999622
24.999637
24.999651
24.999664
24.999677
24.999689
24.999701
24.999713
24.999724
24.999734
24.999745
24.999754
24.999764
24.999773
24.999782
24.999790
24.999798
24.999806
24.999813
24.999821
24.999827
24.999834
24.999840
24.999847
24.999853
24.999858
24.999864
24.999869
24.999874
24.999879
24.999883
24.999888
24.999892
24.999896
24.999900
24.999904
24.999908
24.999911
24.999915
24.999918
24.999921
24.999924
24.999927
24.999930
24.999933
24.999935
24.999938
24.999940
24.999942
24.999945
24.999947
24.999949
24.999951
24.999953
24.999955
24.999956
24.999958
24.999960
24.999961
24.999963
24.999964
24.999965
24.999967
24.999968
24.999969
24.999970
24.999972
24.999973
24.999974
24.999975
24.999976
24.999977
24.999978
24.999978
24.999979
24.999980
24.999981
24.999982
CR
1.040000
0.530196
0.360349
0.275490
0.224627
0.190762
0.166610
0.148528
0.134493
0.123291
0.114149
0.106552
0.100144
0.094669
0.089941
0.085820
0.082199
0.078993
0.076139
0.073582
0.071280
0.069199
0.067309
0.065587
0.064012
0.062567
0.061239
0.060013
0.058880
0.057830
0.056855
0.055949
0.055104
0.054315
0.053577
0.052887
0.052240
0.051632
0.051061
0.050523
0.050017
0.049540
0.049090
0.048665
0.048262
0.047882
0.047522
0.047181
0.046857
0.046550
0.046259
0.045982
0.045719
0.045469
0.045231
0.045005
0.044789
0.044584
0.044388
0.044202
0.044024
0.043854
0.043692
0.043538
0.043390
0.043249
0.043115
0.042986
0.042863
0.042745
0.042633
0.042525
0.042422
0.042323
0.042229
0.042139
0.042052
0.041969
0.041890
0.041814
0.041741
0.041671
0.041605
0.041541
0.041479
0.041420
0.041364
0.041310
0.041258
0.041208
0.041160
0.041114
0.041070
0.041028
0.040987
0.040949
0.040911
0.040875
0.040841
0.040808
0.040776
0.040746
0.040717
0.040689
0.040662
0.040636
0.040611
0.040587
0.040564
0.040542
0.040521
0.040501
0.040481
0.040463
0.040445
0.040427
0.040411
0.040395
0.040379
0.040365
0.040351
0.040337
0.040324
0.040311
0.040299
0.040288
0.040277
0.040266
0.040256
0.040246
0.040236
0.040227
0.040218
0.040210
0.040202
0.040194
0.040186
0.040179
0.040172
0.040166
0.040159
0.040153
0.040147
0.040142
0.040136
0.040131
0.040126
0.040121
0.040116
0.040112
0.040107
0.040103
0.040099
0.040095
0.040092
0.040088
0.040085
0.040082
0.040078
0.040075
0.040073
0.040070
0.040067
0.040064
0.040062
0.040060
0.040057
0.040055
0.040053
0.040051
0.040049
0.040047
0.040045
0.040044
0.040042
0.040040
0.040039
0.040037
0.040036
0.040034
0.040033
0.040032
0.040031
0.040029
0.040028
0.040027
0.040026
0.040025
0.040024
0.040023
0.040022
0.040021
0.040021
0.040020
0.040019
0.040018
0.040018
0.040017
0.040016
0.040016
0.040015
0.040015
0.040014
0.040013
0.040013
0.040012
0.040012
0.040011
0.040011
0.040011
0.040010
0.040010
0.040009
0.040009
0.040009
0.040008
0.040008
0.040008
0.040007
0.040007
0.040007
0.040007
0.040006
0.040006
0.040006
0.040006
0.040005
0.040005
0.040005
0.040005
0.040005
0.040004
0.040004
0.040004
0.040004
0.040004
0.040004
0.040004
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
1.36E+01
0.0000000
7.36E-02
0.0000000
Compute interest rate factors and solve basic TVM problems, generates printable tables by rate, term, and frequency of compounding
User Information:
Annual Discount/Interest Rate
Frequency of Compounding
Time Horizon in Years
8.00%
2
10
Factors:
USCA
Name:
Definition:
General Formula:
SPCA
Future value of $1
deposited at time 0
V
n
Interest Rate Factor:
= V 0 (1 + r )
n
Future value of Uniform
series of deposits at the
end of each period
V
n
(1 + r ) n − 1
= P1
r
2.1911231
Calculation Utilities:
Known
Enter ==>
29.7780786
V0
$100.00
Vn
Unknown
Go to Tables
Solver
Result ==>
$219.11
Effective interest rate per period and number of periods:
4.00%
Interest rate per period = ' r ' in formulas
20
Number of Compounding Periods = 'n' in formulas
SFD
SPPV
Annual deposit at end of
Present value of $1
each period needed to
received at end of
have $1 at end of
period
horizon
r
P1 = V n
n
(1 + r ) − 1
V 0 = V n (1 + r ) −n
0.0335818
USPV
CR
Amount of uniform
Present value of uniform
payment at end of each
series of $1 payments at period to pay off a $1
end of each period
loan made at time 0
V
0
0.4563869
(1 + r ) n − 1
= P1
n
r (1 + r )
13.5903263
r (1 + r ) n
P1 = V 0
n
(1 + r ) − 1
0.0735818
P1
Vn
Vn
P1
V0
$100.00
Vn
$20,000.00
P1
$2,500.00
V0
$750.00
V0
$100,000.00
P1
$2,977.81
$671.64
$1,140.97
$10,192.75
$7,358.18
GoPrint
to Top
Table
Interest Factor Table
SPCA
USCA
SFD
SPPV
USPV
CR
Table For:
8.00%
Int. Rate/yr.
=r
Freq./yr. =2m
values
per
Future value of $1
deposited at time 0
Future value of Uniform
series of deposits at the
end of each period
Annual deposit at end of
Present value of $1
each period needed to
received at end of
have $1 at end of
period
horizon
Amount of uniform
Present value of uniform
series of $1 payments at payment at end of each
period to pay off a $1
end of each period
loan made at time 0
$1
V
End of Compounding
Year
period
1
1
2
0
3
2
4
0
5
3
6
0
7
4
8
0
9
5
10
0
11
6
12
0
13
7
14
0
15
8
16
0
17
9
18
0
19
10
20
0
21
11
22
0
23
12
24
0
25
13
26
0
27
14
28
0
29
15
30
0
31
16
32
0
33
17
34
0
35
18
36
0
37
19
38
0
39
20
40
0
41
21
42
0
43
22
44
0
45
23
46
0
47
24
48
0
49
25
50
0
51
26
52
0
53
27
54
0
55
28
56
0
57
29
58
0
59
30
60
0
61
31
62
0
63
32
64
0
65
33
66
0
67
34
68
0
69
35
70
0
71
36
72
0
73
37
74
0
75
38
76
0
77
39
78
0
79
40
80
0
81
41
82
0
83
42
84
0
85
43
86
0
87
44
88
0
89
45
90
0
91
46
92
0
93
47
94
0
95
48
96
0
97
49
98
0
99
50
100
0
101
51
102
0
103
52
104
0
105
53
106
0
107
54
108
0
109
55
110
0
111
56
112
0
113
57
114
0
115
58
116
0
117
59
118
0
119
60
120
0
121
61
122
0
123
62
124
0
125
63
126
0
127
64
128
0
129
65
130
0
131
66
132
0
133
67
134
0
135
68
136
0
137
69
138
0
139
70
140
0
141
71
142
0
143
72
144
0
145
73
146
0
147
74
148
0
149
75
150
0
151
76
152
0
153
77
154
0
155
78
156
0
157
79
158
0
159
80
160
0
161
81
162
0
163
82
164
0
165
83
166
0
167
84
168
0
169
85
170
0
171
86
172
0
173
87
174
0
175
88
176
0
177
89
178
0
179
90
180
0
181
91
182
0
183
92
184
0
185
93
186
0
187
94
188
0
189
95
190
0
191
96
192
0
193
97
194
0
195
98
196
0
197
99
198
0
199
100
200
0
201
101
202
0
203
102
204
0
205
103
206
0
207
104
208
0
209
105
210
0
211
106
212
0
213
107
214
0
215
108
216
0
217
109
218
0
219
110
220
0
221
111
222
0
223
112
224
0
225
113
226
0
227
114
228
0
229
115
230
0
231
116
232
0
233
117
234
0
235
118
236
0
237
119
238
0
239
120
240
0
241
121
242
0
243
122
244
0
245
123
246
0
247
124
248
0
249
125
250
0
251
126
252
0
253
127
254
0
255
128
256
0
257
129
258
0
259
130
260
0
261
131
262
0
263
132
264
0
265
133
266
0
267
134
268
0
269
135
270
0
271
136
272
0
273
137
274
0
275
138
276
0
277
139
278
0
279
140
280
0
281
141
282
0
283
142
284
0
285
143
286
0
287
144
288
0
289
145
290
0
291
146
292
0
293
147
294
0
295
148
296
0
297
149
298
0
299
150
300
0
301
151
302
0
303
152
304
0
305
153
306
0
307
154
308
0
309
155
310
0
311
156
312
0
313
157
314
0
315
158
316
0
317
159
318
0
319
160
320
0
321
161
322
0
323
162
324
0
325
163
326
0
327
164
328
0
329
165
330
0
331
166
332
0
333
167
334
0
335
168
336
0
337
169
338
0
339
170
340
0
341
171
342
0
343
172
344
0
345
173
346
0
347
174
348
0
349
175
350
0
351
176
352
0
353
177
354
0
355
178
356
0
357
179
358
0
359
180
360
n
= V 0 (1 + r )
n
SPCA
1.040000
1.081600
1.124864
1.169859
1.216653
1.265319
1.315932
1.368569
1.423312
1.480244
1.539454
1.601032
1.665074
1.731676
1.800944
1.872981
1.947900
2.025817
2.106849
2.191123
2.278768
2.369919
2.464716
2.563304
2.665836
2.772470
2.883369
2.998703
3.118651
3.243398
3.373133
3.508059
3.648381
3.794316
3.946089
4.103933
4.268090
4.438813
4.616366
4.801021
4.993061
5.192784
5.400495
5.616515
5.841176
6.074823
6.317816
6.570528
6.833349
7.106683
7.390951
7.686589
7.994052
8.313814
8.646367
8.992222
9.351910
9.725987
10.115026
10.519627
10.940413
11.378029
11.833150
12.306476
12.798735
13.310685
13.843112
14.396836
14.972710
15.571618
16.194483
16.842262
17.515953
18.216591
18.945255
19.703065
20.491187
21.310835
22.163268
23.049799
23.971791
24.930663
25.927889
26.965005
28.043605
29.165349
30.331963
31.545242
32.807051
34.119333
35.484107
36.903471
38.379610
39.914794
41.511386
43.171841
44.898715
46.694664
48.562450
50.504948
52.525146
54.626152
56.811198
59.083646
61.446992
63.904871
66.461066
69.119509
71.884289
74.759661
77.750047
80.860049
84.094451
87.458229
90.956558
94.594821
98.378614
102.313758
106.406308
110.662561
115.089063
119.692626
124.480331
129.459544
134.637926
140.023443
145.624381
151.449356
157.507330
163.807623
170.359928
177.174325
184.261298
191.631750
199.297020
207.268901
215.559657
224.182043
233.149325
242.475298
252.174310
262.261282
272.751734
283.661803
295.008275
306.808606
319.080950
331.844188
345.117956
358.922674
373.279581
388.210764
403.739195
419.888763
436.684313
454.151686
472.317753
491.210463
510.858882
531.293237
552.544967
574.646765
597.632636
621.537941
646.399459
672.255437
699.145655
727.111481
756.195940
786.443778
817.901529
850.617590
884.642294
920.027986
956.829105
995.102269
1034.906360
1076.302614
1119.354719
1164.128908
1210.694064
1259.121827
1309.486700
1361.866168
1416.340814
1472.994447
1531.914225
1593.190794
1656.918425
1723.195163
1792.122969
1863.807888
1938.360203
2015.894611
2096.530396
2180.391612
2267.607276
2358.311567
2452.644030
2550.749791
2652.779783
2758.890974
2869.246613
2984.016478
3103.377137
3227.512222
3356.612711
3490.877219
3630.512308
3775.732801
3926.762113
4083.832597
4247.185901
4417.073337
4593.756270
4777.506521
4968.606782
5167.351053
5374.045096
5589.006899
5812.567175
6045.069862
6286.872657
6538.347563
6799.881466
7071.876724
7354.751793
7648.941865
7954.899540
8273.095521
8604.019342
8948.180116
9306.107320
9678.351613
10065.485678
10468.105105
10886.829309
11322.302481
11775.194581
12246.202364
12736.050458
13245.492477
13775.312176
14326.324663
14899.377649
15495.352755
16115.166865
16759.773540
17430.164482
18127.371061
18852.465903
19606.564539
20390.827121
21206.460206
22054.718614
22936.907359
23854.383653
24808.558999
25800.901359
26832.937413
27906.254910
29022.505106
30183.405311
31390.741523
32646.371184
33952.226031
35310.315073
36722.727676
38191.636783
39719.302254
41308.074344
42960.397318
44678.813211
46465.965739
48324.604369
50257.588543
52267.892085
54358.607768
56532.952079
58794.270162
61146.040969
63591.882608
66135.557912
68780.980228
71532.219437
74393.508215
77369.248544
80464.018485
83682.579225
87029.882394
90511.077689
94131.520797
97896.781629
101812.652894
105885.159010
110120.565370
114525.387985
119106.403504
123870.659645
128825.486030
133978.505472
139337.645690
144911.151518
150707.597579
156735.901482
163005.337541
169525.551043
176306.573085
183358.836008
190693.189448
198320.917026
206253.753707
214503.903855
223084.060010
232007.422410
241287.719306
250939.228079
260976.797202
271415.869090
282272.503854
293563.404008
305305.940168
317518.177775
330218.904886
343427.661081
357164.767524
371451.358225
386309.412554
401761.789057
417832.260619
434545.551044
451927.373085
470004.468009
488804.646729
508356.832598
528691.105902
549838.750138
571832.300144
594705.592150
618493.815836
643233.568469
668962.911208
695721.427656
723550.284762
752492.296153
782591.987999
813895.667519
846451.494220
880309.553988
915521.936148
952142.813594
990228.526138
1029837.667183
1071031.173870
1113872.420825
1158427.317658
1204764.410365
1252954.986779
1303073.186250
1355196.113700
2.19E+00
0.0000000
(1 + r ) − 1
= P1
r
n
V
n
USCA
1.000000
2.040000
3.121600
4.246464
5.416323
6.632975
7.898294
9.214226
10.582795
12.006107
13.486351
15.025805
16.626838
18.291911
20.023588
21.824531
23.697512
25.645413
27.671229
29.778079
31.969202
34.247970
36.617889
39.082604
41.645908
44.311745
47.084214
49.967583
52.966286
56.084938
59.328335
62.701469
66.209527
69.857909
73.652225
77.598314
81.702246
85.970336
90.409150
95.025516
99.826536
104.819598
110.012382
115.412877
121.029392
126.870568
132.945390
139.263206
145.833734
152.667084
159.773767
167.164718
174.851306
182.845359
191.159173
199.805540
208.797762
218.149672
227.875659
237.990685
248.510313
259.450725
270.828754
282.661904
294.968380
307.767116
321.077800
334.920912
349.317749
364.290459
379.862077
396.056560
412.898823
430.414776
448.631367
467.576621
487.279686
507.770873
529.081708
551.244977
574.294776
598.266567
623.197230
649.125119
676.090123
704.133728
733.299078
763.631041
795.176282
827.983334
862.102667
897.586774
934.490245
972.869854
1012.784648
1054.296034
1097.467876
1142.366591
1189.061254
1237.623705
1288.128653
1340.653799
1395.279951
1452.091149
1511.174795
1572.621787
1636.526658
1702.987724
1772.107233
1843.991523
1918.751184
1996.501231
2077.361280
2161.455731
2248.913961
2339.870519
2434.465340
2532.843954
2635.157712
2741.564020
2852.226581
2967.315644
3087.008270
3211.488601
3340.948145
3475.586071
3615.609513
3761.233894
3912.683250
4070.190580
4233.998203
4404.358131
4581.532456
4765.793754
4957.425505
5156.722525
5363.991426
5579.551083
5803.733126
6036.882451
6279.357749
6531.532059
6793.793342
7066.545075
7350.206878
7645.215153
7952.023759
8271.104710
8602.948898
8948.066854
9306.989528
9680.269109
10068.479874
10472.219069
10892.107832
11328.792145
11782.943831
12255.261584
12746.472047
13257.330929
13788.624166
14341.169133
14915.815898
15513.448534
16134.986475
16781.385934
17453.641372
18152.787027
18879.898508
19636.094448
20422.538226
21240.439755
22091.057345
22975.699639
23895.727625
24852.556730
25847.658999
26882.565359
27958.867973
29078.222692
30242.351600
31453.045664
32712.167490
34021.654190
35383.520357
36799.861172
38272.855619
39804.769843
41397.960637
43054.879063
44778.074225
46570.197194
48434.005082
50372.365285
52388.259897
54484.790292
56665.181904
58932.789180
61291.100747
63743.744777
66294.494568
68947.274351
71706.165325
74575.411938
77559.428416
80662.805552
83890.317775
87246.930486
90737.807705
94368.320013
98144.052814
102070.814926
106154.647523
110401.833424
114818.906761
119412.663032
124190.169553
129158.776335
134326.127388
139700.172484
145289.179383
151101.746559
157146.816421
163433.689078
169972.036641
176771.918107
183843.794831
191198.546624
198847.488489
206802.388029
215075.483550
223679.502892
232627.683007
241933.790328
251612.141941
261677.627618
272145.732723
283032.562032
294354.864513
306130.059094
318376.261458
331112.311916
344357.804393
358133.116568
372459.441231
387358.818880
402854.171635
418969.338501
435729.112041
453159.276523
471286.647583
490139.113487
509745.678026
530136.505147
551342.965353
573397.683967
596334.591326
620188.974979
644997.533978
670798.435337
697631.372751
725537.627661
754560.132767
784743.538078
816134.279601
848780.650785
882732.876817
918043.191889
954765.919565
992957.556347
1032676.858601
1073984.932945
1116945.330263
1161624.143474
1208090.109213
1256414.713581
1306672.302124
1358940.194209
1413298.801978
1469831.754057
1528626.024219
1589772.065188
1653363.947796
1719499.505707
1788280.485936
1859812.705373
1934206.213588
2011575.462132
2092039.480617
2175722.059841
2262751.942235
2353263.019925
2447394.540721
2545291.322350
2647103.975244
2752989.134254
2863109.699624
2977635.087609
3096741.491114
3220612.150758
3349437.636789
3483416.142260
3622753.787950
3767664.939468
3918372.537047
4075108.438529
4238113.776070
4407639.327113
4583945.900198
4767304.736206
4957997.925654
5156318.842680
5362572.596387
5577076.500243
5800160.560252
6032167.982662
6273455.701969
6524394.930048
6785371.727250
7056787.596339
7339060.100193
7632623.504201
7937929.444369
8255447.622144
8585666.527029
8929094.188110
9286258.955635
9657710.313860
10044019.726415
10445781.515471
10863613.776090
11298159.327134
11750086.700219
12220091.168228
12708895.814957
13217252.647555
13745943.753458
14295782.503596
14867614.803740
15462320.395889
16080814.211725
16724047.780194
17393010.691402
18088732.119058
18812282.403820
19564774.699973
20347366.687972
21161262.355491
22007713.849710
22888023.403699
23803545.339847
24755688.153440
25745916.679578
26775754.346761
27846785.520632
28960657.941457
30119085.259115
31323849.669480
32576804.656259
33879877.842509
2.98E+01
0.0000000
r
P1 = V n
n
(1 + r ) − 1
SFD
1.000000
0.490196
0.320349
0.235490
0.184627
0.150762
0.126610
0.108528
0.094493
0.083291
0.074149
0.066552
0.060144
0.054669
0.049941
0.045820
0.042199
0.038993
0.036139
0.033582
0.031280
0.029199
0.027309
0.025587
0.024012
0.022567
0.021239
0.020013
0.018880
0.017830
0.016855
0.015949
0.015104
0.014315
0.013577
0.012887
0.012240
0.011632
0.011061
0.010523
0.010017
0.009540
0.009090
0.008665
0.008262
0.007882
0.007522
0.007181
0.006857
0.006550
0.006259
0.005982
0.005719
0.005469
0.005231
0.005005
0.004789
0.004584
0.004388
0.004202
0.004024
0.003854
0.003692
0.003538
0.003390
0.003249
0.003115
0.002986
0.002863
0.002745
0.002633
0.002525
0.002422
0.002323
0.002229
0.002139
0.002052
0.001969
0.001890
0.001814
0.001741
0.001671
0.001605
0.001541
0.001479
0.001420
0.001364
0.001310
0.001258
0.001208
0.001160
0.001114
0.001070
0.001028
0.000987
0.000949
0.000911
0.000875
0.000841
0.000808
0.000776
0.000746
0.000717
0.000689
0.000662
0.000636
0.000611
0.000587
0.000564
0.000542
0.000521
0.000501
0.000481
0.000463
0.000445
0.000427
0.000411
0.000395
0.000379
0.000365
0.000351
0.000337
0.000324
0.000311
0.000299
0.000288
0.000277
0.000266
0.000256
0.000246
0.000236
0.000227
0.000218
0.000210
0.000202
0.000194
0.000186
0.000179
0.000172
0.000166
0.000159
0.000153
0.000147
0.000142
0.000136
0.000131
0.000126
0.000121
0.000116
0.000112
0.000107
0.000103
0.000099
0.000095
0.000092
0.000088
0.000085
0.000082
0.000078
0.000075
0.000073
0.000070
0.000067
0.000064
0.000062
0.000060
0.000057
0.000055
0.000053
0.000051
0.000049
0.000047
0.000045
0.000044
0.000042
0.000040
0.000039
0.000037
0.000036
0.000034
0.000033
0.000032
0.000031
0.000029
0.000028
0.000027
0.000026
0.000025
0.000024
0.000023
0.000022
0.000021
0.000021
0.000020
0.000019
0.000018
0.000018
0.000017
0.000016
0.000016
0.000015
0.000015
0.000014
0.000013
0.000013
0.000012
0.000012
0.000011
0.000011
0.000011
0.000010
0.000010
0.000009
0.000009
0.000009
0.000008
0.000008
0.000008
0.000007
0.000007
0.000007
0.000007
0.000006
0.000006
0.000006
0.000006
0.000005
0.000005
0.000005
0.000005
0.000005
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
3.36E-02
0.0000000
V
0
= V n (1 + r ) −n
SPPV
0.961538
0.924556
0.888996
0.854804
0.821927
0.790315
0.759918
0.730690
0.702587
0.675564
0.649581
0.624597
0.600574
0.577475
0.555265
0.533908
0.513373
0.493628
0.474642
0.456387
0.438834
0.421955
0.405726
0.390121
0.375117
0.360689
0.346817
0.333477
0.320651
0.308319
0.296460
0.285058
0.274094
0.263552
0.253415
0.243669
0.234297
0.225285
0.216621
0.208289
0.200278
0.192575
0.185168
0.178046
0.171198
0.164614
0.158283
0.152195
0.146341
0.140713
0.135301
0.130097
0.125093
0.120282
0.115656
0.111207
0.106930
0.102817
0.098863
0.095060
0.091404
0.087889
0.084508
0.081258
0.078133
0.075128
0.072238
0.069460
0.066788
0.064219
0.061749
0.059374
0.057091
0.054895
0.052784
0.050754
0.048801
0.046924
0.045120
0.043384
0.041716
0.040111
0.038569
0.037085
0.035659
0.034287
0.032969
0.031701
0.030481
0.029309
0.028182
0.027098
0.026056
0.025053
0.024090
0.023163
0.022272
0.021416
0.020592
0.019800
0.019039
0.018306
0.017602
0.016925
0.016274
0.015648
0.015046
0.014468
0.013911
0.013376
0.012862
0.012367
0.011891
0.011434
0.010994
0.010571
0.010165
0.009774
0.009398
0.009036
0.008689
0.008355
0.008033
0.007724
0.007427
0.007142
0.006867
0.006603
0.006349
0.006105
0.005870
0.005644
0.005427
0.005218
0.005018
0.004825
0.004639
0.004461
0.004289
0.004124
0.003966
0.003813
0.003666
0.003525
0.003390
0.003259
0.003134
0.003013
0.002898
0.002786
0.002679
0.002576
0.002477
0.002382
0.002290
0.002202
0.002117
0.002036
0.001957
0.001882
0.001810
0.001740
0.001673
0.001609
0.001547
0.001488
0.001430
0.001375
0.001322
0.001272
0.001223
0.001176
0.001130
0.001087
0.001045
0.001005
0.000966
0.000929
0.000893
0.000859
0.000826
0.000794
0.000764
0.000734
0.000706
0.000679
0.000653
0.000628
0.000604
0.000580
0.000558
0.000537
0.000516
0.000496
0.000477
0.000459
0.000441
0.000424
0.000408
0.000392
0.000377
0.000362
0.000349
0.000335
0.000322
0.000310
0.000298
0.000286
0.000275
0.000265
0.000255
0.000245
0.000235
0.000226
0.000218
0.000209
0.000201
0.000194
0.000186
0.000179
0.000172
0.000165
0.000159
0.000153
0.000147
0.000141
0.000136
0.000131
0.000126
0.000121
0.000116
0.000112
0.000107
0.000103
0.000099
0.000096
0.000092
0.000088
0.000085
0.000082
0.000079
0.000075
0.000073
0.000070
0.000067
0.000065
0.000062
0.000060
0.000057
0.000055
0.000053
0.000051
0.000049
0.000047
0.000045
0.000044
0.000042
0.000040
0.000039
0.000037
0.000036
0.000034
0.000033
0.000032
0.000031
0.000029
0.000028
0.000027
0.000026
0.000025
0.000024
0.000023
0.000022
0.000022
0.000021
0.000020
0.000019
0.000018
0.000018
0.000017
0.000016
0.000016
0.000015
0.000015
0.000014
0.000013
0.000013
0.000012
0.000012
0.000011
0.000011
0.000011
0.000010
0.000010
0.000009
0.000009
0.000009
0.000008
0.000008
0.000008
0.000007
0.000007
0.000007
0.000007
0.000006
0.000006
0.000006
0.000006
0.000005
0.000005
0.000005
0.000005
0.000005
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000004
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000003
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000002
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
0.000001
4.56E-01
0.0000000
V
0
(1 + r ) n − 1
= P1
n
r (1 + r )
r (1 + r ) n
P1 = V 0
n
(1 + r ) − 1
USPV
0.961538
1.886095
2.775091
3.629895
4.451822
5.242137
6.002055
6.732745
7.435332
8.110896
8.760477
9.385074
9.985648
10.563123
11.118387
11.652296
12.165669
12.659297
13.133939
13.590326
14.029160
14.451115
14.856842
15.246963
15.622080
15.982769
16.329586
16.663063
16.983715
17.292033
17.588494
17.873551
18.147646
18.411198
18.664613
18.908282
19.142579
19.367864
19.584485
19.792774
19.993052
20.185627
20.370795
20.548841
20.720040
20.884654
21.042936
21.195131
21.341472
21.482185
21.617485
21.747582
21.872675
21.992957
22.108612
22.219819
22.326749
22.429567
22.528430
22.623490
22.714894
22.802783
22.887291
22.968549
23.046682
23.121810
23.194048
23.263507
23.330296
23.394515
23.456264
23.515639
23.572730
23.627625
23.680408
23.731162
23.779963
23.826888
23.872008
23.915392
23.957108
23.997219
24.035787
24.072872
24.108531
24.142818
24.175787
24.207487
24.237969
24.267278
24.295459
24.322557
24.348612
24.373666
24.397756
24.420919
24.443191
24.464607
24.485199
24.504999
24.524037
24.542344
24.559946
24.576871
24.593145
24.608794
24.623840
24.638308
24.652219
24.665595
24.678457
24.690824
24.702715
24.714149
24.725144
24.735715
24.745880
24.755654
24.765052
24.774088
24.782777
24.791132
24.799165
24.806889
24.814317
24.821458
24.828325
24.834928
24.841277
24.847382
24.853252
24.858896
24.864323
24.869541
24.874559
24.879384
24.884023
24.888483
24.892773
24.896897
24.900862
24.904675
24.908342
24.911867
24.915257
24.918516
24.921650
24.924663
24.927561
24.930347
24.933026
24.935602
24.938079
24.940460
24.942750
24.944952
24.947070
24.949105
24.951063
24.952945
24.954755
24.956495
24.958168
24.959777
24.961324
24.962812
24.964242
24.965617
24.966940
24.968211
24.969434
24.970610
24.971740
24.972827
24.973872
24.974877
24.975843
24.976772
24.977666
24.978525
24.979351
24.980145
24.980909
24.981643
24.982349
24.983028
24.983681
24.984308
24.984912
24.985492
24.986050
24.986587
24.987103
24.987599
24.988076
24.988534
24.988975
24.989399
24.989807
24.990199
24.990576
24.990938
24.991287
24.991622
24.991944
24.992254
24.992552
24.992838
24.993114
24.993379
24.993633
24.993878
24.994114
24.994340
24.994558
24.994767
24.994968
24.995162
24.995348
24.995527
24.995699
24.995864
24.996023
24.996176
24.996323
24.996465
24.996601
24.996732
24.996857
24.996978
24.997094
24.997206
24.997314
24.997417
24.997516
24.997612
24.997704
24.997792
24.997877
24.997959
24.998037
24.998113
24.998185
24.998255
24.998322
24.998387
24.998449
24.998508
24.998566
24.998621
24.998674
24.998725
24.998774
24.998821
24.998866
24.998910
24.998952
24.998992
24.999031
24.999068
24.999104
24.999139
24.999172
24.999204
24.999234
24.999264
24.999292
24.999319
24.999345
24.999371
24.999395
24.999418
24.999440
24.999462
24.999483
24.999503
24.999522
24.999540
24.999558
24.999575
24.999591
24.999607
24.999622
24.999637
24.999651
24.999664
24.999677
24.999689
24.999701
24.999713
24.999724
24.999734
24.999745
24.999754
24.999764
24.999773
24.999782
24.999790
24.999798
24.999806
24.999813
24.999821
24.999827
24.999834
24.999840
24.999847
24.999853
24.999858
24.999864
24.999869
24.999874
24.999879
24.999883
24.999888
24.999892
24.999896
24.999900
24.999904
24.999908
24.999911
24.999915
24.999918
24.999921
24.999924
24.999927
24.999930
24.999933
24.999935
24.999938
24.999940
24.999942
24.999945
24.999947
24.999949
24.999951
24.999953
24.999955
24.999956
24.999958
24.999960
24.999961
24.999963
24.999964
24.999965
24.999967
24.999968
24.999969
24.999970
24.999972
24.999973
24.999974
24.999975
24.999976
24.999977
24.999978
24.999978
24.999979
24.999980
24.999981
24.999982
CR
1.040000
0.530196
0.360349
0.275490
0.224627
0.190762
0.166610
0.148528
0.134493
0.123291
0.114149
0.106552
0.100144
0.094669
0.089941
0.085820
0.082199
0.078993
0.076139
0.073582
0.071280
0.069199
0.067309
0.065587
0.064012
0.062567
0.061239
0.060013
0.058880
0.057830
0.056855
0.055949
0.055104
0.054315
0.053577
0.052887
0.052240
0.051632
0.051061
0.050523
0.050017
0.049540
0.049090
0.048665
0.048262
0.047882
0.047522
0.047181
0.046857
0.046550
0.046259
0.045982
0.045719
0.045469
0.045231
0.045005
0.044789
0.044584
0.044388
0.044202
0.044024
0.043854
0.043692
0.043538
0.043390
0.043249
0.043115
0.042986
0.042863
0.042745
0.042633
0.042525
0.042422
0.042323
0.042229
0.042139
0.042052
0.041969
0.041890
0.041814
0.041741
0.041671
0.041605
0.041541
0.041479
0.041420
0.041364
0.041310
0.041258
0.041208
0.041160
0.041114
0.041070
0.041028
0.040987
0.040949
0.040911
0.040875
0.040841
0.040808
0.040776
0.040746
0.040717
0.040689
0.040662
0.040636
0.040611
0.040587
0.040564
0.040542
0.040521
0.040501
0.040481
0.040463
0.040445
0.040427
0.040411
0.040395
0.040379
0.040365
0.040351
0.040337
0.040324
0.040311
0.040299
0.040288
0.040277
0.040266
0.040256
0.040246
0.040236
0.040227
0.040218
0.040210
0.040202
0.040194
0.040186
0.040179
0.040172
0.040166
0.040159
0.040153
0.040147
0.040142
0.040136
0.040131
0.040126
0.040121
0.040116
0.040112
0.040107
0.040103
0.040099
0.040095
0.040092
0.040088
0.040085
0.040082
0.040078
0.040075
0.040073
0.040070
0.040067
0.040064
0.040062
0.040060
0.040057
0.040055
0.040053
0.040051
0.040049
0.040047
0.040045
0.040044
0.040042
0.040040
0.040039
0.040037
0.040036
0.040034
0.040033
0.040032
0.040031
0.040029
0.040028
0.040027
0.040026
0.040025
0.040024
0.040023
0.040022
0.040021
0.040021
0.040020
0.040019
0.040018
0.040018
0.040017
0.040016
0.040016
0.040015
0.040015
0.040014
0.040013
0.040013
0.040012
0.040012
0.040011
0.040011
0.040011
0.040010
0.040010
0.040009
0.040009
0.040009
0.040008
0.040008
0.040008
0.040007
0.040007
0.040007
0.040007
0.040006
0.040006
0.040006
0.040006
0.040005
0.040005
0.040005
0.040005
0.040005
0.040004
0.040004
0.040004
0.040004
0.040004
0.040004
0.040004
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040003
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040002
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040001
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
0.040000
1.36E+01
0.0000000
7.36E-02
0.0000000
