Appendix B Applying Present and Future Values Answer Key
True / False Questions
1.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
Interest is the borrower’s payment to the owner of an asset for its use.
2.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
From the perspective of an account holder, a savings account is a liability with interest.
3.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
An interest rate is also called a discount rate.
4.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
Present and future value computations enable companies to measure or estimate the
interest component of holding assets or liabilities over time.
5.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
The number of periods in a present value calculation may only be expressed in years.
6.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
The present value factor for determining the present value of $6,300 to be received three
years from today at 10% interest compounded semiannually is 0.7462.
7.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
The present value of 1 formula is often useful when a borrowed asset must be repaid in
full at a later date and the borrower wants to know the worth of the asset at the future
date.
8.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
In a present value or future value table, the length of one time period may be interpreted
as one year, one month, or any other length of time.
9.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
4%
5%
6%
7%
8%
10%
12%
3
3.1216
3.1525
3.1836
3.2149
3.2464
3.3100
3.3744
4
4.2465
4.3101
4.3746
4.4399
4.5061
4.6410
4.7793
5
5.4163
5.5256
5.6371
5.7507
5.8666
6.1051
6.3528
6
6.6330
6.8019
6.9753
7.1533
7.3359
7.7156
8.1152
7
7.8983
8.1420
8.3938
8.6540
8.9228
9.4872
10.0890
8
9.2142
9.5491
9.8975
10.2598
10.6366
11.4359
12.2997
9
10.5828
11.0266
11.4913
11.9780
12.4876
13.5795
14.7757
10
12.0061
12.5779
13.1808
13.8164
14.4866
15.9374
17.5487
The present value of $2,000 to be received nine years from today at 8% interest
compounded annually is $1,000.
10.
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502