Present Value Tables
Content
Table
1
Present Value today of $1 at time t discounted at
rate i
PV = 1/(1 + i)t
Interest Rate (i)
Perio
d (t)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1%
0.990
10
0.980
30
0.970
59
0.960
98
0.951
47
0.942
05
0.932
72
0.923
48
0.914
34
0.905
29
0.896
32
0.887
45
0.878
66
0.869
96
0.861
35
2%
0.980
39
0.961
17
0.942
32
0.923
85
0.905
73
0.887
97
0.870
56
0.853
49
0.836
76
0.820
35
0.804
26
0.788
49
0.773
03
0.757
88
0.743
01
3%
0.970
87
0.942
60
0.915
14
0.888
49
0.862
61
0.837
48
0.813
09
0.789
41
0.766
42
0.744
09
0.722
42
0.701
38
0.680
95
0.661
12
0.641
86
4%
0.961
54
0.924
56
0.889
00
0.854
80
0.821
93
0.790
31
0.759
92
0.730
69
0.702
59
0.675
56
0.649
58
0.624
60
0.600
57
0.577
48
0.555
26
5%
0.952
38
0.907
03
0.863
84
0.822
70
0.783
53
0.746
22
0.710
68
0.676
84
0.644
61
0.613
91
0.584
68
0.556
84
0.530
32
0.505
07
0.481
02
6%
0.943
40
0.890
00
0.839
62
0.792
09
0.747
26
0.704
96
0.665
06
0.627
41
0.591
90
0.558
39
0.526
79
0.496
97
0.468
84
0.442
30
0.417
27
7%
0.934
58
0.873
44
0.816
30
0.762
90
0.712
99
0.666
34
0.622
75
0.582
01
0.543
93
0.508
35
0.475
09
0.444
01
0.414
96
0.387
82
0.362
45
8%
0.925
93
0.857
34
0.793
83
0.735
03
0.680
58
0.630
17
0.583
49
0.540
27
0.500
25
0.463
19
0.428
88
0.397
11
0.367
70
0.340
46
0.315
24
9%
0.917
43
0.841
68
0.772
18
0.708
43
0.649
93
0.596
27
0.547
03
0.501
87
0.460
43
0.422
41
0.387
53
0.355
53
0.326
18
0.299
25
0.274
54
10%
0.909
09
0.826
45
0.751
31
0.683
01
0.620
92
0.564
47
0.513
16
0.466
51
0.424
10
0.385
54
0.350
49
0.318
63
0.289
66
0.263
33
0.239
39
11%
0.900
90
0.811
62
0.731
19
0.658
73
0.593
45
0.534
64
0.481
66
0.433
93
0.390
92
0.352
18
0.317
28
0.285
84
0.257
51
0.231
99
0.209
00
12%
0.892
86
0.797
19
0.711
78
0.635
52
0.567
43
0.506
63
0.452
35
0.403
88
0.360
61
0.321
97
0.287
48
0.256
68
0.229
17
0.204
62
0.182
70
16
17
18
19
20
25
30
35
40
0.852
82
0.844
38
0.836
02
0.827
74
0.819
54
0.779
77
0.741
92
0.705
91
0.671
65
0.728
45
0.714
16
0.700
16
0.686
43
0.672
97
0.609
53
0.552
07
0.500
03
0.452
89
0.623
17
0.605
02
0.587
39
0.570
29
0.553
68
0.477
61
0.411
99
0.355
38
0.306
56
0.533
91
0.513
37
0.493
63
0.474
64
0.456
39
0.375
12
0.308
32
0.253
42
0.208
29
0.458
11
0.436
30
0.415
52
0.395
73
0.376
89
0.295
30
0.231
38
0.181
29
0.142
05
0.393
65
0.371
36
0.350
34
0.330
51
0.311
80
0.233
00
0.174
11
0.130
11
0.097
22
0.338
73
0.316
57
0.295
86
0.276
51
0.258
42
0.184
25
0.131
37
0.093
66
0.066
78
0.291
89
0.270
27
0.250
25
0.231
71
0.214
55
0.146
02
0.099
38
0.067
63
0.046
03
0.251
87
0.231
07
0.211
99
0.194
49
0.178
43
0.115
97
0.075
37
0.048
99
0.031
84
0.217
63
0.197
84
0.179
86
0.163
51
0.148
64
0.092
30
0.057
31
0.035
58
0.022
09
0.188
29
0.169
63
0.152
82
0.137
68
0.124
03
0.073
61
0.043
68
0.025
92
0.015
38
0.163
12
0.145
64
0.130
04
0.116
11
0.103
67
0.058
82
0.033
38
0.018
94
0.010
75
Table 2
Periods
(t)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Present Value of an ordinary annuity with $1 payments at the end of each period for t periods
discounted at rate i
PV = {1 - [1/(1 +
Interest Rate (i)
i)t]} / i
1%
0.9901
0
1.9704
0
2.9409
9
3.9019
7
4.8534
3
5.7954
8
6.7281
9
7.6516
8
8.5660
2
9.4713
0
10.367
63
11.255
08
12.133
74
13.003
70
13.865
05
2%
0.9803
9
1.9415
6
2.8838
8
3.8077
3
4.7134
6
5.6014
3
6.4719
9
7.3254
8
8.1622
4
8.9825
9
9.7868
5
10.575
34
11.348
37
12.106
25
12.849
26
3%
0.9708
7
1.9134
7
2.8286
1
3.7171
0
4.5797
1
5.4171
9
6.2302
8
7.0196
9
7.7861
1
8.5302
0
9.2526
2
9.9540
0
10.634
96
11.296
07
11.937
94
4%
0.9615
4
1.8860
9
2.7750
9
3.6299
0
4.4518
2
5.2421
4
6.0020
5
6.7327
4
7.4353
3
8.1109
0
8.7604
8
9.3850
7
9.9856
5
10.563
12
11.118
39
5%
0.9523
8
1.8594
1
2.7232
5
3.5459
5
4.3294
8
5.0756
9
5.7863
7
6.4632
1
7.1078
2
7.7217
3
8.3064
1
8.8632
5
9.3935
7
9.8986
4
10.379
66
6%
0.9434
0
1.8333
9
2.6730
1
3.4651
1
4.2123
6
4.9173
2
5.5823
8
6.2097
9
6.8016
9
7.3600
9
7.8868
7
8.3838
4
8.8526
8
9.2949
8
9.7122
5
7%
0.9345
8
1.8080
2
2.6243
2
3.3872
1
4.1002
0
4.7665
4
5.3892
9
5.9713
0
6.5152
3
7.0235
8
7.4986
7
7.9426
9
8.3576
5
8.7454
7
9.1079
1
8%
0.9259
3
1.7832
6
2.5771
0
3.3121
3
3.9927
1
4.6228
8
5.2063
7
5.7466
4
6.2468
9
6.7100
8
7.1389
6
7.5360
8
7.9037
8
8.2442
4
8.5594
8
9%
0.9174
3
1.7591
1
2.5312
9
3.2397
2
3.8896
5
4.4859
2
5.0329
5
5.5348
2
5.9952
5
6.4176
6
6.8051
9
7.1607
3
7.4869
0
7.7861
5
8.0606
9
10%
0.909
09
1.735
54
2.486
85
3.169
87
3.790
79
4.355
26
4.868
42
5.334
93
5.759
02
6.144
57
6.495
06
6.813
69
7.103
36
7.366
69
7.606
08
11%
0.900
90
1.712
52
2.443
71
3.102
45
3.695
90
4.230
54
4.712
20
5.146
12
5.537
05
5.889
23
6.206
52
6.492
36
6.749
87
6.981
87
7.190
87
12%
0.8928
6
1.6900
5
2.4018
3
3.0373
5
3.6047
8
4.1114
1
4.5637
6
4.9676
4
5.3282
5
5.6502
2
5.9377
0
6.1943
7
6.4235
5
6.6281
7
6.8108
6
16
17
18
19
20
25
30
35
40
14.717
87
15.562
25
16.398
27
17.226
01
18.045
55
22.023
16
25.807
71
29.408
58
32.834
69
13.577
71
14.291
87
14.992
03
15.678
46
16.351
43
19.523
46
22.396
46
24.998
62
27.355
48
12.561
10
13.166
12
13.753
51
14.323
80
14.877
47
17.413
15
19.600
44
21.487
22
23.114
77
11.652
30
12.165
67
12.659
30
13.133
94
13.590
33
15.622
08
17.292
03
18.664
61
19.792
77
10.837
77
11.274
07
11.689
59
12.085
32
12.462
21
14.093
94
15.372
45
16.374
19
17.159
09
10.105
90
10.477
26
10.827
60
11.158
12
11.469
92
12.783
36
13.764
83
14.498
25
15.046
30
9.4466
5
9.7632
2
10.059
09
10.335
60
10.594
01
11.653
58
12.409
04
12.947
67
13.331
71
8.8513
7
9.1216
4
9.3718
9
9.6036
0
9.8181
5
10.674
78
11.257
78
11.654
57
11.924
61
8.3125
6
8.5436
3
8.7556
3
8.9501
1
9.1285
5
9.8225
8
10.273
65
10.566
82
10.757
36
7.823
71
8.021
55
8.201
41
8.364
92
8.513
56
9.077
04
9.426
91
9.644
16
9.779
05
7.379
16
7.548
79
7.701
62
7.839
29
7.963
33
8.421
74
8.693
79
8.855
24
8.951
05
6.9739
9
7.1196
3
7.2496
7
7.3657
8
7.4694
4
7.8431
4
8.0551
8
8.1755
0
8.2437
8
1
Present Value today of $1 at time t discounted at
rate i
PV = 1/(1 + i)t
Interest Rate (i)
Perio
d (t)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1%
0.990
10
0.980
30
0.970
59
0.960
98
0.951
47
0.942
05
0.932
72
0.923
48
0.914
34
0.905
29
0.896
32
0.887
45
0.878
66
0.869
96
0.861
35
2%
0.980
39
0.961
17
0.942
32
0.923
85
0.905
73
0.887
97
0.870
56
0.853
49
0.836
76
0.820
35
0.804
26
0.788
49
0.773
03
0.757
88
0.743
01
3%
0.970
87
0.942
60
0.915
14
0.888
49
0.862
61
0.837
48
0.813
09
0.789
41
0.766
42
0.744
09
0.722
42
0.701
38
0.680
95
0.661
12
0.641
86
4%
0.961
54
0.924
56
0.889
00
0.854
80
0.821
93
0.790
31
0.759
92
0.730
69
0.702
59
0.675
56
0.649
58
0.624
60
0.600
57
0.577
48
0.555
26
5%
0.952
38
0.907
03
0.863
84
0.822
70
0.783
53
0.746
22
0.710
68
0.676
84
0.644
61
0.613
91
0.584
68
0.556
84
0.530
32
0.505
07
0.481
02
6%
0.943
40
0.890
00
0.839
62
0.792
09
0.747
26
0.704
96
0.665
06
0.627
41
0.591
90
0.558
39
0.526
79
0.496
97
0.468
84
0.442
30
0.417
27
7%
0.934
58
0.873
44
0.816
30
0.762
90
0.712
99
0.666
34
0.622
75
0.582
01
0.543
93
0.508
35
0.475
09
0.444
01
0.414
96
0.387
82
0.362
45
8%
0.925
93
0.857
34
0.793
83
0.735
03
0.680
58
0.630
17
0.583
49
0.540
27
0.500
25
0.463
19
0.428
88
0.397
11
0.367
70
0.340
46
0.315
24
9%
0.917
43
0.841
68
0.772
18
0.708
43
0.649
93
0.596
27
0.547
03
0.501
87
0.460
43
0.422
41
0.387
53
0.355
53
0.326
18
0.299
25
0.274
54
10%
0.909
09
0.826
45
0.751
31
0.683
01
0.620
92
0.564
47
0.513
16
0.466
51
0.424
10
0.385
54
0.350
49
0.318
63
0.289
66
0.263
33
0.239
39
11%
0.900
90
0.811
62
0.731
19
0.658
73
0.593
45
0.534
64
0.481
66
0.433
93
0.390
92
0.352
18
0.317
28
0.285
84
0.257
51
0.231
99
0.209
00
12%
0.892
86
0.797
19
0.711
78
0.635
52
0.567
43
0.506
63
0.452
35
0.403
88
0.360
61
0.321
97
0.287
48
0.256
68
0.229
17
0.204
62
0.182
70
16
17
18
19
20
25
30
35
40
0.852
82
0.844
38
0.836
02
0.827
74
0.819
54
0.779
77
0.741
92
0.705
91
0.671
65
0.728
45
0.714
16
0.700
16
0.686
43
0.672
97
0.609
53
0.552
07
0.500
03
0.452
89
0.623
17
0.605
02
0.587
39
0.570
29
0.553
68
0.477
61
0.411
99
0.355
38
0.306
56
0.533
91
0.513
37
0.493
63
0.474
64
0.456
39
0.375
12
0.308
32
0.253
42
0.208
29
0.458
11
0.436
30
0.415
52
0.395
73
0.376
89
0.295
30
0.231
38
0.181
29
0.142
05
0.393
65
0.371
36
0.350
34
0.330
51
0.311
80
0.233
00
0.174
11
0.130
11
0.097
22
0.338
73
0.316
57
0.295
86
0.276
51
0.258
42
0.184
25
0.131
37
0.093
66
0.066
78
0.291
89
0.270
27
0.250
25
0.231
71
0.214
55
0.146
02
0.099
38
0.067
63
0.046
03
0.251
87
0.231
07
0.211
99
0.194
49
0.178
43
0.115
97
0.075
37
0.048
99
0.031
84
0.217
63
0.197
84
0.179
86
0.163
51
0.148
64
0.092
30
0.057
31
0.035
58
0.022
09
0.188
29
0.169
63
0.152
82
0.137
68
0.124
03
0.073
61
0.043
68
0.025
92
0.015
38
0.163
12
0.145
64
0.130
04
0.116
11
0.103
67
0.058
82
0.033
38
0.018
94
0.010
75
Table 2
Periods
(t)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Present Value of an ordinary annuity with $1 payments at the end of each period for t periods
discounted at rate i
PV = {1 - [1/(1 +
Interest Rate (i)
i)t]} / i
1%
0.9901
0
1.9704
0
2.9409
9
3.9019
7
4.8534
3
5.7954
8
6.7281
9
7.6516
8
8.5660
2
9.4713
0
10.367
63
11.255
08
12.133
74
13.003
70
13.865
05
2%
0.9803
9
1.9415
6
2.8838
8
3.8077
3
4.7134
6
5.6014
3
6.4719
9
7.3254
8
8.1622
4
8.9825
9
9.7868
5
10.575
34
11.348
37
12.106
25
12.849
26
3%
0.9708
7
1.9134
7
2.8286
1
3.7171
0
4.5797
1
5.4171
9
6.2302
8
7.0196
9
7.7861
1
8.5302
0
9.2526
2
9.9540
0
10.634
96
11.296
07
11.937
94
4%
0.9615
4
1.8860
9
2.7750
9
3.6299
0
4.4518
2
5.2421
4
6.0020
5
6.7327
4
7.4353
3
8.1109
0
8.7604
8
9.3850
7
9.9856
5
10.563
12
11.118
39
5%
0.9523
8
1.8594
1
2.7232
5
3.5459
5
4.3294
8
5.0756
9
5.7863
7
6.4632
1
7.1078
2
7.7217
3
8.3064
1
8.8632
5
9.3935
7
9.8986
4
10.379
66
6%
0.9434
0
1.8333
9
2.6730
1
3.4651
1
4.2123
6
4.9173
2
5.5823
8
6.2097
9
6.8016
9
7.3600
9
7.8868
7
8.3838
4
8.8526
8
9.2949
8
9.7122
5
7%
0.9345
8
1.8080
2
2.6243
2
3.3872
1
4.1002
0
4.7665
4
5.3892
9
5.9713
0
6.5152
3
7.0235
8
7.4986
7
7.9426
9
8.3576
5
8.7454
7
9.1079
1
8%
0.9259
3
1.7832
6
2.5771
0
3.3121
3
3.9927
1
4.6228
8
5.2063
7
5.7466
4
6.2468
9
6.7100
8
7.1389
6
7.5360
8
7.9037
8
8.2442
4
8.5594
8
9%
0.9174
3
1.7591
1
2.5312
9
3.2397
2
3.8896
5
4.4859
2
5.0329
5
5.5348
2
5.9952
5
6.4176
6
6.8051
9
7.1607
3
7.4869
0
7.7861
5
8.0606
9
10%
0.909
09
1.735
54
2.486
85
3.169
87
3.790
79
4.355
26
4.868
42
5.334
93
5.759
02
6.144
57
6.495
06
6.813
69
7.103
36
7.366
69
7.606
08
11%
0.900
90
1.712
52
2.443
71
3.102
45
3.695
90
4.230
54
4.712
20
5.146
12
5.537
05
5.889
23
6.206
52
6.492
36
6.749
87
6.981
87
7.190
87
12%
0.8928
6
1.6900
5
2.4018
3
3.0373
5
3.6047
8
4.1114
1
4.5637
6
4.9676
4
5.3282
5
5.6502
2
5.9377
0
6.1943
7
6.4235
5
6.6281
7
6.8108
6
16
17
18
19
20
25
30
35
40
14.717
87
15.562
25
16.398
27
17.226
01
18.045
55
22.023
16
25.807
71
29.408
58
32.834
69
13.577
71
14.291
87
14.992
03
15.678
46
16.351
43
19.523
46
22.396
46
24.998
62
27.355
48
12.561
10
13.166
12
13.753
51
14.323
80
14.877
47
17.413
15
19.600
44
21.487
22
23.114
77
11.652
30
12.165
67
12.659
30
13.133
94
13.590
33
15.622
08
17.292
03
18.664
61
19.792
77
10.837
77
11.274
07
11.689
59
12.085
32
12.462
21
14.093
94
15.372
45
16.374
19
17.159
09
10.105
90
10.477
26
10.827
60
11.158
12
11.469
92
12.783
36
13.764
83
14.498
25
15.046
30
9.4466
5
9.7632
2
10.059
09
10.335
60
10.594
01
11.653
58
12.409
04
12.947
67
13.331
71
8.8513
7
9.1216
4
9.3718
9
9.6036
0
9.8181
5
10.674
78
11.257
78
11.654
57
11.924
61
8.3125
6
8.5436
3
8.7556
3
8.9501
1
9.1285
5
9.8225
8
10.273
65
10.566
82
10.757
36
7.823
71
8.021
55
8.201
41
8.364
92
8.513
56
9.077
04
9.426
91
9.644
16
9.779
05
7.379
16
7.548
79
7.701
62
7.839
29
7.963
33
8.421
74
8.693
79
8.855
24
8.951
05
6.9739
9
7.1196
3
7.2496
7
7.3657
8
7.4694
4
7.8431
4
8.0551
8
8.1755
0
8.2437
8
