Note: For example, if the interest rate is 10% per year, the investment of $1 received in each of the next 5 years is $3.791.
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A-3
Present Value Tables
APPENDIX TABLE 4
Values of ert. Future value of $1 invested at a continuously compounded rate r for t years.
rt
.00
.01
.02
.03
.04
.05
.06
.07
.08
.00
.10
.20
.30
.40
1.000
1.105
1.221
1.350
1.492
1.010
1.116
1.234
1.363
1.507
.50
.60
.70
.80
.90
1.649
1.822
2.014
2.226
2.460
1.00
1.10
1.20
1.30
1.40
.09
1.020
1.127
1.246
1.377
1.522
1.030
1.139
1.259
1.391
1.537
1.041
1.150
1.271
1.405
1.553
1.051
1.162
1.284
1.419
1.568
1.062
1.174
1.297
1.433
1.584
1.073
1.185
1.310
1.448
1.600
1.083
1.197
1.323
1.462
1.616
1.094
1.209
1.336
1.477
1.632
1.665
1.840
2.034
2.248
2.484
1.682
1.859
2.054
2.271
2.509
1.699
1.878
2.075
2.293
2.535
1.716
1.896
2.096
2.316
2.560
1.733
1.916
2.117
2.340
2.586
1.751
1.935
2.138
2.363
2.612
1.768
1.954
2.160
2.387
2.638
1.786
1.974
2.181
2.411
2.664
1.804
1.994
2.203
2.435
2.691
2.718
3.004
3.320
3.669
4.055
2.746
3.034
3.353
3.706
4.096
2.773
3.065
3.387
3.743
4.137
2.801
3.096
3.421
3.781
4.179
2.829
3.127
3.456
3.819
4.221
2.858
3.158
3.490
3.857
4.263
2.886
3.190
3.525
3.896
4.306
2.915
3.222
3.561
3.935
4.349
2.945
3.254
3.597
3.975
4.393
2.974
3.287
3.633
4.015
4.437
1.50
1.60
1.70
1.80
1.90
4.482
4.953
5.474
6.050
6.686
4.527
5.003
5.529
6.110
6.753
4.572
5.053
5.585
6.172
6.821
4.618
5.104
5.641
6.234
6.890
4.665
5.155
5.697
6.297
6.959
4.711
5.207
5.755
6.360
7.029
4.759
5.259
5.812
6.424
7.099
4.807
5.312
5.871
6.488
7.171
4.855
5.366
5.930
6.553
7.243
4.904
5.419
5.989
6.619
7.316
2.00
2.10
2.20
2.30
2.40
7.389
8.166
9.025
9.974
11.02
7.463
8.248
9.116
10.07
11.13
7.538
8.331
9.207
10.18
11.25
7.614
8.415
9.300
10.28
11.36
7.691
8.499
9.393
10.38
11.47
7.768
8.585
9.488
10.49
11.59
7.846
8.671
9.583
10.59
11.70
7.925
8.758
9.679
10.70
11.82
8.004
8.846
9.777
10.80
11.94
8.085
8.935
9.875
10.91
12.06
2.50
2.60
2.70
2.80
2.90
12.18
13.46
14.88
16.44
18.17
12.30
13.60
15.03
16.61
18.36
12.43
13.74
15.18
16.78
18.54
12.55
13.87
15.33
16.95
18.73
12.68
14.01
15.49
17.12
18.92
12.81
14.15
15.64
17.29
19.11
12.94
14.30
15.80
17.46
19.30
13.07
14.44
15.96
17.64
19.49
13.20
14.59
16.12
17.81
19.69
13.33
14.73
16.28
17.99
19.89
3.00
3.10
3.20
3.30
3.40
20.09
22.20
24.53
27.11
29.96
20.29
22.42
24.78
27.39
30.27
20.49
22.65
25.03
27.66
30.57
20.70
22.87
25.28
27.94
30.88
20.91
23.10
25.53
28.22
31.19
21.12
23.34
25.79
28.50
31.50
21.33
23.57
26.05
28.79
31.82
21.54
23.81
26.31
29.08
32.14
21.76
24.05
26.58
29.37
32.46
21.98
24.29
26.84
29.67
32.79
3.50
3.60
3.70
3.80
3.90
33.12
36.60
40.45
44.70
49.40
33.45
36.97
40.85
45.15
49.90
33.78
37.34
41.26
45.60
50.40
34.12
37.71
41.68
46.06
50.91
34.47
38.09
42.10
46.53
51.42
34.81
38.47
42.52
46.99
51.94
35.16
38.86
42.95
47.47
52.46
35.52
39.25
43.38
47.94
52.98
35.87
39.65
43.82
48.42
53.52
36.23
40.04
44.26
48.91
54.05
Note: For example, if the continuously compounded interest rate is 10% per year, the investment of $1 today will be worth $1.105 at year 1 and $1.221 at year 2.
bre30735_app_wA-wA5.indd Sec1:3
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A-4
Present Value Tables
APPENDIX TABLE 5
Present value of $1 per year received in a continuous stream for each of t years (discounted at an annually compounded rate r) ⫽ {1 ⫺ 1/(1 ⫹ r)t}/
{ln(1 ⫹ r)}.
Interest Rate per Year
Note: For example, if the interest rate is 10% per year, a continuous cash flow of $1 a year for each of 5 years is worth $3.977. A continuous flow of $1 in year 5 only
is worth $3.977 ⫺ $3.326 ⫽ $.651.
bre30735_app_wA-wA5.indd Sec1:4
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confirming pages
A-5
Present Value Tables
APPENDIX TABLE 6
Cumulative probability [N(d )] that a normally distributed variable will be less than d standard deviations above the mean.
d
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0
0.1
0.2
0.3
0.4
.5000
.5398
.5793
.6179
.6554
.5040
.5438
.5832
.6217
.6591
.5080
.5478
.5871
.6255
.6628
.5120
.5517
.5910
.6293
.6664
.5160
.5557
.5948
.6331
.6700
.5199
.5596
.5987
.6368
.6736
.5239
.5636
.6026
.6406
.6772
.5279
.5675
.6064
.6443
.6808
.5319
.5714
.6103
.6480
.6844
.5359
.5753
.6141
.6517
.6879
0.5
0.6
0.7
0.8
0.9
.6915
.7257
.7580
.7881
.8159
.6950
.7291
.7611
.7910
.8186
.6985
.7324
.7642
.7939
.8212
.7019
.7357
.7673
.7967
.8238
.7054
.7389
.7704
.7995
.8264
.7088
.7422
.7734
.8023
.8289
.7123
.7454
.7764
.8051
.8315
.7157
.7486
.7794
.8078
.8340
.7190
.7517
.7823
.8106
.8365
.7224
.7549
.7852
.8133
.8389
1
1.1
1.2
1.3
1.4
.8413
.8643
.8849
.9032
.9192
.8438
.8665
.8869
.9049
.9207
.8461
.8686
.8888
.9066
.9222
.8485
.8708
.8907
.9082
.9236
.8508
.8729
.8925
.9099
.9251
.8531
.8749
.8944
.9115
.9265
.8554
.8770
.8962
.9131
.9279
.8577
.8790
.8980
.9147
.9292
.8599
.8810
.8997
.9162
.9306
.8621
.8830
.9015
.9177
.9319
1.5
1.6
1.7
1.8
1.9
.9332
.9452
.9554
.9641
.9713
.9345
.9463
.9564
.9649
.9719
.9357
.9474
.9573
.9656
.9726
.9370
.9484
.9582
.9664
.9732
.9382
.9495
.9591
.9671
.9738
.9394
.9505
.9599
.9678
.9744
.9406
.9515
.9608
.9686
.9750
.9418
.9525
.9616
.9693
.9756
.9429
.9535
.9625
.9699
.9761
.9441
.9545
.9633
.9706
.9767
2
2.1
2.2
2.3
2.4
.9772
.9821
.9861
.9893
.9918
.9778
.9826
.9864
.9896
.9920
.9783
.9830
.9868
.9898
.9922
.9788
.9834
.9871
.9901
.9925
.9793
.9838
.9875
.9904
.9927
.9798
.9842
.9878
.9906
.9929
.9803
.9846
.9881
.9909
.9931
.9808
.9850
.9884
.9911
.9932
.9812
.9854
.9887
.9913
.9934
.9817
.9857
.9890
.9916
.9936
2.5
.9938
.9940
.9941
.9943
.9945
.9946
.9948
.9949
.9951
.9952
Note: For example, if d ⫽ .22, N(d ) ⫽ .5871 (i.e., there is a .5871 probability that a normally distributed variable will be less than .22 standard deviations above the mean).