Future value and present value with compounding

FIND A SOLUTION AT Academic Writers Bay

Appendix: Formula Sheet
Future value and present value with compounding
Future value of an ordinary annuity and an annuity due
x
x x
Present value of an ordinary annuity and an annuity due
x
x x
Present value of a perpetuity and a growing perpetuity
Compounding other than annual
x
Effective annual rate
Deposits needed to accumulate a future sum
Loan amortization
Bond valuations
+ + … + +
x +
Current/coupon yield = coupon interest / price
Stock valuations
+ + + …
+ + … +
CAPM
Weighted Average Cost of Capital (WACC)
TABLE 1: Present value interest factor of $1 per period at r% for n periods, PVIF (r,n).
Present value interest factor of $1 per period at i% for n periods, PVIF(r,n).
Per
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
1
0.990
0.980
0.971
0.962
0.952
0.943
0.935
0.926
0.917
0.909
0.901
0.893
0.885
0.877
0.870
0.862
0.855
0.847
0.840
0.833
2
0.980
0.961
0.943
0.925
0.907
0.890
0.873
0.857
0.842
0.826
0.812
0.797
0.783
0.769
0.756
0.743
0.731
0.718
0.706
0.694
3
0.971
0.942
0.915
0.889
0.864
0.840
0.816
0.794
0.772
0.751
0.731
0.712
0.693
0.675
0.658
0.641
0.624
0.609
0.593
0.579
4
0.961
0.924
0.888
0.855
0.823
0.792
0.763
0.735
0.708
0.683
0.659
0.636
0.613
0.592
0.572
0.552
0.534
0.516
0.499
0.482
5
0.951
0.906
0.863
0.822
0.784
0.747
0.713
0.681
0.650
0.621
0.593
0.567
0.543
0.519
0.497
0.476
0.456
0.437
0.419
0.402
6
0.942
0.888
0.837
0.790
0.746
0.705
0.666
0.630
0.596
0.564
0.535
0.507
0.480
0.456
0.432
0.410
0.390
0.370
0.352
0.335
7
0.933
0.871
0.813
0.760
0.711
0.665
0.623
0.583
0.547
0.513
0.482
0.452
0.425
0.400
0.376
0.354
0.333
0.314
0.296
0.279
8
0.923
0.853
0.789
0.731
0.677
0.627
0.582
0.540
0.502
0.467
0.434
0.404
0.376
0.351
0.327
0.305
0.285
0.266
0.249
0.233
9
0.914
0.837
0.766
0.703
0.645
0.592
0.544
0.500
0.460
0.424
0.391
0.361
0.333
0.308
0.284
0.263
0.243
0.225
0.209
0.194
10
0.905
0.820
0.744
0.676
0.614
0.558
0.508
0.463
0.422
0.386
0.352
0.322
0.295
0.270
0.247
0.227
0.208
0.191
0.176
0.162
11
0.896
0.804
0.722
0.650
0.585
0.527
0.475
0.429
0.388
0.350
0.317
0.287
0.261
0.237
0.215
0.195
0.178
0.162
0.148
0.135
12
0.887
0.788
0.701
0.625
0.557
0.497
0.444
0.397
0.356
0.319
0.286
0.257
0.231
0.208
0.187
0.168
0.152
0.137
0.124
0.112
13
0.879
0.773
0.681
0.601
0.530
0.469
0.415
0.368
0.326
0.290
0.258
0.229
0.204
0.182
0.163
0.145
0.130
0.116
0.104
0.093
14
0.870
0.758
0.661
0.577
0.505
0.442
0.388
0.340
0.299
0.263
0.232
0.205
0.181
0.160
0.141
0.125
0.111
0.099
0.088
0.078
15
0.861
0.743
0.642
0.555
0.481
0.417
0.362
0.315
0.275
0.239
0.209
0.183
0.160
0.140
0.123
0.108
0.095
0.084
0.074
0.065
16
0.853
0.728
0.623
0.534
0.458
0.394
0.339
0.292
0.252
0.218
0.188
0.163
0.141
0.123
0.107
0.093
0.081
0.071
0.062
0.054
17
0.844
0.714
0.605
0.513
0.436
0.371
0.317
0.270
0.231
0.198
0.170
0.146
0.125
0.108
0.093
0.080
0.069
0.060
0.052
0.045
18
0.836
0.700
0.587
0.494
0.416
0.350
0.296
0.250
0.212
0.180
0.153
0.130
0.111
0.095
0.081
0.069
0.059
0.051
0.044
0.038
19
0.828
0.686
0.570
0.475
0.396
0.331
0.277
0.232
0.194
0.164
0.138
0.116
0.098
0.083
0.070
0.060
0.051
0.043
0.037
0.031
20
0.820
0.673
0.554
0.456
0.377
0.312
0.258
0.215
0.178
0.149
0.124
0.104
0.087
0.073
0.061
0.051
0.043
0.037
0.031
0.026
25
0.780
0.610
0.478
0.375
0.295
0.233
0.184
0.146
0.116
0.092
0.074
0.059
0.047
0.038
0.030
0.024
0.020
0.016
0.013
0.010
30
0.742
0.552
0.412
0.308
0.231
0.174
0.131
0.099
0.075
0.057
0.044
0.033
0.026
0.020
0.015
0.012
0.009
0.007
0.005
0.004
35
0.706
0.500
0.355
0.253
0.181
0.130
0.094
0.068
0.049
0.036
0.026
0.019
0.014
0.010
0.008
0.006
0.004
0.003
0.002
0.002
40
0.672
0.453
0.307
0.208
0.142
0.097
0.067
0.046
0.032
0.022
0.015
0.011
0.008
0.005
0.004
0.003
0.002
0.001
0.001
0.001
50
0.608
0.372
0.228
0.141
0.087
0.054
0.034
0.021
0.013
0.009
0.005
0.003
0.002
0.001
0.001
0.001
0.000
0.000
0.000
0.000
TABLE 2:Present value interest factor of an (ordinary) annuity of $1 per period at r% for n periods, PVIFA (r,n).
Present value interest factor of an (ordinary) annuity of $1 per period at i% for n periods, PVIFA(r,n).
Per
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
1
0.990
0.980
0.971
0.962
0.952
0.943
0.935
0.926
0.917
0.909
0.901
0.893
0.885
0.877
0.870
0.862
0.855
0.847
0.840
0.833
2
1.970
1.942
1.913
1.886
1.859
1.833
1.808
1.783
1.759
1.736
1.713
1.690
1.668
1.647
1.626
1.605
1.585
1.566
1.547
1.528
3
2.941
2.884
2.829
2.775
2.723
2.673
2.624
2.577
2.531
2.487
2.444
2.402
2.361
2.322
2.283
2.246
2.210
2.174
2.140
2.106
4
3.902
3.808
3.717
3.630
3.546
3.465
3.387
3.312
3.240
3.170
3.102
3.037
2.974
2.914
2.855
2.798
2.743
2.690
2.639
2.589
5
4.853
4.713
4.580
4.452
4.329
4.212
4.100
3.993
3.890
3.791
3.696
3.605
3.517
3.433
3.352
3.274
3.199
3.127
3.058
2.991
6
5.795
5.601
5.417
5.242
5.076
4.917
4.767
4.623
4.486
4.355
4.231
4.111
3.998
3.889
3.784
3.685
3.589
3.498
3.410
3.326
7
6.728
6.472
6.230
6.002
5.786
5.582
5.389
5.206
5.033
4.868
4.712
4.564
4.423
4.288
4.160
4.039
3.922
3.812
3.706
3.605
8
7.652
7.325
7.020
6.733
6.463
6.210
5.971
5.747
5.535
5.335
5.146
4.968
4.799
4.639
4.487
4.344
4.207
4.078
3.954
3.837
9
8.566
8.162
7.786
7.435
7.108
6.802
6.515
6.247
5.995
5.759
5.537
5.328
5.132
4.946
4.772
4.607
4.451
4.303
4.163
4.031
10
9.471
8.983
8.530
8.111
7.722
7.360
7.024
6.710
6.418
6.145
5.889
5.650
5.426
5.216
5.019
4.833
4.659
4.494
4.339
4.192
11
10.368
9.787
9.253
8.760
8.306
7.887
7.499
7.139
6.805
6.495
6.207
5.938
5.687
5.453
5.234
5.029
4.836
4.656
4.486
4.327
12
11.255
10.575
9.954
9.385
8.863
8.384
7.943
7.536
7.161
6.814
6.492
6.194
5.918
5.660
5.421
5.197
4.988
4.793
4.611
4.439
13
12.134
11.348
10.635
9.986
9.394
8.853
8.358
7.904
7.487
7.103
6.750
6.424
6.122
5.842
5.583
5.342
5.118
4.910
4.715
4.533
14
13.004
12.106
11.296
10.563
9.899
9.295
8.745
8.244
7.786
7.367
6.982
6.628
6.302
6.002
5.724
5.468
5.229
5.008
4.802
4.611
15
13.865
12.849
11.938
11.118
10.380
9.712
9.108
8.559
8.061
7.606
7.191
6.811
6.462
6.142
5.847
5.575
5.324
5.092
4.876
4.675
16
14.718
13.578
12.561
11.652
10.838
10.106
9.447
8.851
8.313
7.824
7.379
6.974
6.604
6.265
5.954
5.668
5.405
5.162
4.938
4.730
17
15.562
14.292
13.166
12.166
11.274
10.477
9.763
9.122
8.544
8.022
7.549
7.120
6.729
6.373
6.047
5.749
5.475
5.222
4.990
4.775
18
16.398
14.992
13.754
12.659
11.690
10.828
10.059
9.372
8.756
8.201
7.702
7.250
6.840
6.467
6.128
5.818
5.534
5.273
5.033
4.812
19
17.226
15.678
14.324
13.134
12.085
11.158
10.336
9.604
8.950
8.365
7.839
7.366
6.938
6.550
6.198
5.877
5.584
5.316
5.070
4.843
20
18.046
16.351
14.877
13.590
12.462
11.470
10.594
9.818
9.129
8.514
7.963
7.469
7.025
6.623
6.259
5.929
5.628
5.353
5.101
4.870
25
22.023
19.523
17.413
15.622
14.094
12.783
11.654
10.675
9.823
9.077
8.422
7.843
7.330
6.873
6.464
6.097
5.766
5.467
5.195
4.948
30
25.808
22.396
19.600
17.292
15.372
13.765
12.409
11.258
10.274
9.427
8.694
8.055
7.496
7.003
6.566
6.177
5.829
5.517
5.235
4.979
35
29.409
24.999
21.487
18.665
16.374
14.498
12.948
11.655
10.567
9.644
8.855
8.176
7.586
7.070
6.617
6.215
5.858
5.539
5.251
4.992
40
32.835
27.355
23.115
19.793
17.159
15.046
13.332
11.925
10.757
9.779
8.951
8.244
7.634
7.105
6.642
6.233
5.871
5.548
5.258
4.997
50
39.196
31.424
25.730
21.482
18.256
15.762
13.801
12.233
10.962
9.915
9.042
8.304
7.675
7.133
6.661
6.246
5.880
5.554
5.262
4.999
TABLE 3: Future value interest factor of $1 per period at r% for n periods, FVIF (r,n).
Per
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
1
1.010
1.020
1.030
1.040
1.050
1.060
1.070
1.080
1.090
1.100
1.110
1.120
1.130
1.140
1.150
1.160
1.170
1.180
1.190
1.200
2
1.020
1.040
1.061
1.082
1.103
1.124
1.145
1.166
1.188
1.210
1.232
1.254
1.277
1.300
1.323
1.346
1.369
1.392
1.416
1.440
3
1.030
1.061
1.093
1.125
1.158
1.191
1.225
1.260
1.295
1.331
1.368
1.405
1.443
1.482
1.521
1.561
1.602
1.643
1.685
1.728
4
1.041
1.082
1.126
1.170
1.216
1.262
1.311
1.360
1.412
1.464
1.518
1.574
1.630
1.689
1.749
1.811
1.874
1.939
2.005
2.074
5
1.051
1.104
1.159
1.217
1.276
1.338
1.403
1.469
1.539
1.611
1.685
1.762
1.842
1.925
2.011
2.100
2.192
2.288
2.386
2.488
6
1.062
1.126
1.194
1.265
1.340
1.419
1.501
1.587
1.677
1.772
1.870
1.974
2.082
2.195
2.313
2.436
2.565
2.700
2.840
2.986
7
1.072
1.149
1.230
1.316
1.407
1.504
1.606
1.714
1.828
1.949
2.076
2.211
2.353
2.502
2.660
2.826
3.001
3.185
3.379
3.583
8
1.083
1.172
1.267
1.369
1.477
1.594
1.718
1.851
1.993
2.144
2.305
2.476
2.658
2.853
3.059
3.278
3.511
3.759
4.021
4.300
9
1.094
1.195
1.305
1.423
1.551
1.689
1.838
1.999
2.172
2.358
2.558
2.773
3.004
3.252
3.518
3.803
4.108
4.435
4.785
5.160
10
1.105
1.219
1.344
1.480
1.629
1.791
1.967
2.159
2.367
2.594
2.839
3.106
3.395
3.707
4.046
4.411
4.807
5.234
5.695
6.192
11
1.116
1.243
1.384
1.539
1.710
1.898
2.105
2.332
2.580
2.853
3.152
3.479
3.836
4.226
4.652
5.117
5.624
6.176
6.777
7.430
12
1.127
1.268
1.426
1.601
1.796
2.012
2.252
2.518
2.813
3.138
3.498
3.896
4.335
4.818
5.350
5.936
6.580
7.288
8.064
8.916
13
1.138
1.294
1.469
1.665
1.886
2.133
2.410
2.720
3.066
3.452
3.883
4.363
4.898
5.492
6.153
6.886
7.699
8.599
9.596
10.699
14
1.149
1.319
1.513
1.732
1.980
2.261
2.579
2.937
3.342
3.797
4.310
4.887
5.535
6.261
7.076
7.988
9.007
10.147
11.420
12.839
15
1.161
1.346
1.558
1.801
2.079
2.397
2.759
3.172
3.642
4.177
4.785
5.474
6.254
7.138
8.137
9.266
10.539
11.974
13.590
15.407
16
1.173
1.373
1.605
1.873
2.183
2.540
2.952
3.426
3.970
4.595
5.311
6.130
7.067
8.137
9.358
10.748
12.330
14.129
16.172
18.488
17
1.184
1.400
1.653
1.948
2.292
2.693
3.159
3.700
4.328
5.054
5.895
6.866
7.986
9.276
10.761
12.468
14.426
16.672
19.244
22.186
18
1.196
1.428
1.702
2.026
2.407
2.854
3.380
3.996
4.717
5.560
6.544
7.690
9.024
10.575
12.375
14.463
16.879
19.673
22.901
26.623
19
1.208
1.457
1.754
2.107
2.527
3.026
3.617
4.316
5.142
6.116
7.263
8.613
10.197
12.056
14.232
16.777
19.748
23.214
27.252
31.948
20
1.220
1.486
1.806
2.191
2.653
3.207
3.870
4.661
5.604
6.727
8.062
9.646
11.523
13.743
16.367
19.461
23.106
27.393
32.429
38.338
25
1.282
1.641
2.094
2.666
3.386
4.292
5.427
6.848
8.623
10.835
13.585
17.000
21.231
26.462
32.919
40.874
50.658
62.669
77.388
95.396
30
1.348
1.811
2.427
3.243
4.322
5.743
7.612
10.063
13.268
17.449
22.892
29.960
39.116
50.950
66.212
85.850
111.065
143.371
184.675
237.376
35
1.417
2.000
2.814
3.946
5.516
7.686
10.677
14.785
20.414
28.102
38.575
52.800
72.069
98.100
133.176
180.314
243.503
327.997
440.701
590.668
40
1.489
2.208
3.262
4.801
7.040
10.286
14.974
21.725
31.409
45.259
65.001
93.051
132.782
188.884
267.864
378.721
533.869
750.378
1,051.668
1,469.772
50
1.645
2.692
4.384
7.107
11.467
18.420
29.457
46.902
74.358
117.391
184.565
289.002
450.736
700.233
1,083.657
1,670.704
2,566.215
3,927.357
5,988.914
9,100.438
TABLE 4: Future value interest factor of an ordinary annuity of $1 per period at r% for n
Per
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
1
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
2
2.010
2.020
2.030
2.040
2.050
2.060
2.070
2.080
2.090
2.100
2.110
2.120
2.130
2.140
2.150
2.160
2.170
2.180
2.190
2.200
3
3.030
3.060
3.091
3.122
3.153
3.184
3.215
3.246
3.278
3.310
3.342
3.374
3.407
3.440
3.473
3.506
3.539
3.572
3.606
3.640
4
4.060
4.122
4.184
4.246
4.310
4.375
4.440
4.506
4.573
4.641
4.710
4.779
4.850
4.921
4.993
5.066
5.141
5.215
5.291
5.368
5
5.101
5.204
5.309
5.416
5.526
5.637
5.751
5.867
5.985
6.105
6.228
6.353
6.480
6.610
6.742
6.877
7.014
7.154
7.297
7.442
6
6.152
6.308
6.468
6.633
6.802
6.975
7.153
7.336
7.523
7.716
7.913
8.115
8.323
8.536
8.754
8.977
9.207
9.442
9.683
9.930
7
7.214
7.434
7.662
7.898
8.142
8.394
8.654
8.923
9.200
9.487
9.783
10.089
10.405
10.730
11.067
11.414
11.772
12.142
12.523
12.916
8
8.286
8.583
8.892
9.214
9.549
9.897
10.260
10.637
11.028
11.436
11.859
12.300
12.757
13.233
13.727
14.240
14.773
15.327
15.902
16.499
9
9.369
9.755
10.159
10.583
11.027
11.491
11.978
12.488
13.021
13.579
14.164
14.776
15.416
16.085
16.786
17.519
18.285
19.086
19.923
20.799
10
10.462
10.950
11.464
12.006
12.578
13.181
13.816
14.487
15.193
15.937
16.722
17.549
18.420
19.337
20.304
21.321
22.393
23.521
24.709
25.959
11
11.567
12.169
12.808
13.486
14.207
14.972
15.784
16.645
17.560
18.531
19.561
20.655
21.814
23.045
24.349
25.733
27.200
28.755
30.404
32.150
12
12.683
13.412
14.192
15.026
15.917
16.870
17.888
18.977
20.141
21.384
22.713
24.133
25.650
27.271
29.002
30.850
32.824
34.931
37.180
39.581
13
13.809
14.680
15.618
16.627
17.713
18.882
20.141
21.495
22.953
24.523
26.212
28.029
29.985
32.089
34.352
36.786
39.404
42.219
45.244
48.497
14
14.947
15.974
17.086
18.292
19.599
21.015
22.550
24.215
26.019
27.975
30.095
32.393
34.883
37.581
40.505
43.672
47.103
50.818
54.841
59.196
15
16.097
17.293
18.599
20.024
21.579
23.276
25.129
27.152
29.361
31.772
34.405
37.280
40.417
43.842
47.580
51.660
56.110
60.965
66.261
72.035
16
17.258
18.639
20.157
21.825
23.657
25.673
27.888
30.324
33.003
35.950
39.190
42.753
46.672
50.980
55.717
60.925
66.649
72.939
79.850
87.442
17
18.430
20.012
21.762
23.698
25.840
28.213
30.840
33.750
36.974
40.545
44.501
48.884
53.739
59.118
65.075
71.673
78.979
87.068
96.022
105.93
18
19.615
21.412
23.414
25.645
28.132
30.906
33.999
37.450
41.301
45.599
50.396
55.750
61.725
68.394
75.836
84.141
93.406
103.74
115.27
128.12
19
20.811
22.841
25.117
27.671
30.539
33.760
37.379
41.446
46.018
51.159
56.939
63.440
70.749
78.969
88.212
98.603
110.28
123.41
138.17
154.74
20
22.019
24.297
26.870
29.778
33.066
36.786
40.995
45.762
51.160
57.275
64.203
72.052
80.947
91.025
102.44
115.38
130.03
146.63
165.42
186.69
25
28.243
32.030
36.459
41.646
47.727
54.865
63.249
73.106
84.701
98.347
114.41
133.33
155.62
181.87
212.79
249.21
292.10
342.60
402.04
471.98
30
34.785
40.568
47.575
56.085
66.439
79.058
94.461
113.28
136.31
164.49
199.02
241.33
293.20
356.79
434.75
530.31
647.44
790.95
966.71
1,181.9
35
41.660
49.994
60.462
73.652
90.320
111.43
138.24
172.32
215.71
271.02
341.59
431.66
546.68
693.57
881.17
1,120.7
1,426.5
1,816.7
2,314.2
2,948.3
40
48.886
60.402
75.401
95.026
120.80
154.76
199.64
259.06
337.88
442.59
581.83
767.09
1,013.7
1,342.0
1,779.1
2,360.8
3,134.5
4,163.2
5,529.8
7,343.9
50
64.463
84.579
112.80
152.67
209.35
290.34
406.53
573.77
815.08
1,163.9
1,668.8
2,400.0
3,459.5
4,994.5
7,217.7
10,436
15,090
21,813
31,515
45,497
periods, FVIFA (r,n).

YOU MAY ALSO READ ...  MITS4002 OBJECT-ORIENTED SOFTWARE DEVELOPMENTLegal and Ethical RequirementsAssignment 2 – Managing Operations
Order from Academic Writers Bay
Best Custom Essay Writing Services

QUALITY: 100% ORIGINAL PAPERNO PLAGIARISM – CUSTOM PAPER