Future Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
The future value of an ordinary annuity is the accumulated value of each annuity payment
excluding interest as of the date of the final payment.
Multiple Choice Questions
21.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Interest may be defined as:
22.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
If we want to know the value of present-day assets at a future date, we can use:
23.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Which interest rate column would you use from a present value or future value table for
8% interest compounded quarterly?
24.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
A company is considering investing in a project that is expected to return $350,000 four
years from now. How much is the company willing to pay for this investment if the
company requires a 12% return compounded annually?
25.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Jason has a loan that requires a single payment of $4,000 at the end of 3 years. The loan’s
interest rate is 6%, compounded semiannually. How much did Jason borrow?
26.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Patricia wants to invest a sum of money today that will yield $10,000 at the end of 6
years. Assuming she can earn an interest rate of 6% compounded annually, how much
must she invest today?
27.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Marshall has received an inheritance and wants to invest a sum of money today that will
yield $5,000 at the end of each of the next 10 years. Assuming he can earn an interest rate
of 5% compounded annually, how much of his inheritance must he invest today?
28.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Cody invests $1,800 per year from his summer wages at a 4% annual interest rate. He
plans to take a European vacation at the end of 4 years when he graduates from college.
How much will he have available to spend on his vacation?
29.
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
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2149
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.4399
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.7507
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.1533
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.6540
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.2598
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
11.9780
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
13.8164
14.4866
15.1929
15.9374
17.5487
Jessica received a gift of $7,500 at the time of her high school graduation. She invests it in
an account that yields 10% compounded semi-annually. What will the value of Jessica’s
investment be at the end of 5 years?
30.
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