A.9-1
Table A.9
Present Value of an n Year $1 Annuityn
PV = å i=1(1-r)-i
Interest Rate, r
n .0025 .005 .0075 .01 .0125 .015 .0175 .02
1 0.9975 0.9950 0.9926 0.9901 0.9877 0.9852 0.9828 0.9804
2 1.9925 1.9851 1.9777 1.9704 1.9631 1.9559 1.9487 1.9416
3 2.9851 2.9702 2.9556 2.9410 2.9265 2.9122 2.8980 2.8839
4 3.9751 3.9505 3.9261 3.9020 3.8781 3.8544 3.8309 3.8077
5 4.9627 4.9259 4.8894 4.8534 4.8178 4.7826 4.7479 4.7135
6 5.9478 5.8964 5.8456 5.7955 5.7460 5.6972 5.6490 5.6014
7 6.9305 6.8621 6.7946 6.7282 6.6627 6.5982 6.5346 6.4720
8 7.9107 7.8230 7.7366 7.6517 7.5681 7.4859 7.4051 7.3255
9 8.8885 8.7791 8.6716 8.5660 8.4623 8.3605 8.2605 8.1622
10 9.8639 9.7304 9.5996 9.4713 9.3455 9.2222 9.1012 8.9826
11 10.8368 10.6770 10.5207 10.3676 10.2178 10.0711 9.9275 9.7869
12 11.8073 11.6189 11.4349 11.2551 11.0793 10.9075 10.7395 10.5753
13 12.7753 12.5562 12.3423 12.1337 11.9302 11.7315 11.5376 11.3484
14 13.7410 13.4887 13.2430 13.0037 12.7705 12.5434 12.3220 12.1063
15 14.7042 14.4166 14.1370 13.8651 13.6005 13.3432 13.0929 12.8493
16 15.6650 15.3399 15.0243 14.7179 14.4203 14.1313 13.8505 13.5777
17 16.6235 16.2586 15.9050 15.5623 15.2299 14.9077 14.5951 14.2919
18 17.5795 17.1728 16.7792 16.3983 16.0295 15.6726 15.3269 14.9920
19 18.5332 18.0824 17.6468 17.2260 16.8193 16.4262 16.0460 15.6785
20 19.4845 18.9874 18.5080 18.0456 17.5993 17.1686 16.7529 16.3514
21 20.4334 19.8880 19.3628 18.8570 18.3697 17.9001 17.4475 17.0112
22 21.3800 20.7841 20.2112 19.6604 19.1305 18.6208 18.1303 17.6581
23 22.3241 21.6757 21.0533 20.4558 19.8820 19.3309 18.8012 18.2922
24 23.2660 22.5629 21.8891 21.2434 20.6242 20.0304 19.4607 18.9139
25 24.2055 23.4456 22.7187 22.0232 21.3572 20.7196 20.1088 19.5235
26 25.1426 24.3240 23.5422 22.7952 22.0812 21.3986 20.7457 20.1210
27 26.0774 25.1980 24.3595 23.5596 22.7963 22.0676 21.3717 20.7069
28 27.0099 26.0677 25.1707 24.3164 23.5025 22.7267 21.9869 21.2813
29 27.9400 26.9330 25.9759 25.0658 24.2000 23.3761 22.5916 21.8444
30 28.8679 27.7941 26.7751 25.8077 24.8889 24.0159 23.1858 22.3965
31 29.7934 28.6508 27.5683 26.5423 25.5693 24.6462 23.7699 22.9377
32 30.7166 29.5033 28.3556 27.2696 26.2412 25.2672 24.3438 23.4684
33 31.6375 30.3515 29.1371 27.9897 26.9049 25.8790 24.9080 23.9886
34 32.5561 31.1956 29.9127 28.7027 27.5604 26.4818 25.4624 24.4986
35 33.4724 32.0354 30.6826 29.4086 28.2078 27.0756 26.0072 24.9986
36 34.3865 32.8710 31.4468 30.1075 28.8472 27.6607 26.5427 25.4889
37 35.2982 33.7025 32.2052 30.7995 29.4787 28.2372 27.0690 25.9695
38 36.2077 34.5299 32.9580 31.4847 30.1025 28.8051 27.5863 26.4407
39 37.1149 35.3531 33.7052 32.1630 30.7185 29.3646 28.0946 26.9026
40 38.0198 36.1722 34.4469 32.8347 31.3269 29.9159 28.5942 27.3555
A.9-2
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .0225 .025 .0275 .03 .0325 .035 .0375 .04
1 0.9780 0.9756 0.9732 0.9709 0.9685 0.9662 0.9639 0.9615
2 1.9345 1.9274 1.9204 1.9135 1.9066 1.8997 1.8929 1.8861
3 2.8699 2.8560 2.8423 2.8286 2.8151 2.8016 2.7883 2.7751
4 3.7847 3.7620 3.7394 3.7171 3.6950 3.6731 3.6514 3.6299
5 4.6795 4.6458 4.6126 4.5797 4.5472 4.5151 4.4833 4.4518
6 5.5545 5.5081 5.4624 5.4172 5.3726 5.3286 5.2851 5.2421
7 6.4102 6.3494 6.2894 6.2303 6.1720 6.1145 6.0579 6.0021
8 7.2472 7.1701 7.0943 7.0197 6.9462 6.8740 6.8028 6.7327
9 8.0657 7.9709 7.8777 7.7861 7.6961 7.6077 7.5208 7.4353
10 8.8662 8.7521 8.6401 8.5302 8.4224 8.3166 8.2128 8.1109
11 9.6491 9.5142 9.3821 9.2526 9.1258 9.0016 8.8798 8.7605
12 10.4148 10.2578 10.1042 9.9540 9.8071 9.6633 9.5227 9.3851
13 11.1636 10.9832 10.8070 10.6350 10.4669 10.3027 10.1424 9.9857
14 11.8959 11.6909 11.4910 11.2961 11.1060 10.9205 10.7396 10.5631
15 12.6122 12.3814 12.1567 11.9379 11.7249 11.5174 11.3153 11.1184
16 13.3126 13.0550 12.8046 12.5611 12.3244 12.0941 11.8702 11.6523
17 13.9977 13.7122 13.4351 13.1661 12.9049 12.6513 12.4050 12.1657
18 14.6677 14.3534 14.0488 13.7535 13.4673 13.1897 12.9205 12.6593
19 15.3229 14.9789 14.6460 14.3238 14.0119 13.7098 13.4173 13.1339
20 15.9637 15.5892 15.2272 14.8775 14.5393 14.2124 13.8962 13.5903
21 16.5904 16.1846 15.7929 15.4150 15.0502 14.6980 14.3578 14.0292
22 17.2033 16.7654 16.3435 15.9369 15.5450 15.1671 14.8027 14.4511
23 17.8028 17.3321 16.8793 16.4436 16.0242 15.6204 15.2315 14.8568
24 18.3890 17.8850 17.4008 16.9355 16.4883 16.0584 15.6448 15.2470
25 18.9624 18.4244 17.9083 17.4131 16.9379 16.4815 16.0432 15.6221
26 19.5231 18.9506 18.4023 17.8768 17.3732 16.8904 16.4272 15.9828
27 20.0715 19.4640 18.8830 18.3270 17.7949 17.2854 16.7973 16.3296
28 20.6078 19.9649 19.3508 18.7641 18.2033 17.6670 17.1540 16.6631
29 21.1323 20.4536 19.8062 19.1885 18.5988 18.0358 17.4978 16.9837
30 21.6453 20.9303 20.2493 19.6004 18.9819 18.3921 17.8292 17.2920
31 22.1470 21.3954 20.6806 20.0004 19.3529 18.7363 18.1487 17.5885
32 22.6377 21.8492 21.1003 20.3888 19.7123 19.0689 18.4565 17.8736
33 23.1175 22.2919 21.5088 20.7658 20.0603 19.3902 18.7533 18.1477
34 23.5868 22.7238 21.9064 21.1318 20.3974 19.7007 19.0393 18.4112
35 24.0458 23.1452 22.2933 21.4872 20.7239 20.0007 19.3150 18.6646
36 24.4947 23.5563 22.6699 21.8323 21.0401 20.2905 19.5807 18.9083
37 24.9336 23.9573 23.0364 22.1672 21.3463 20.5705 19.8369 19.1426
38 25.3630 24.3486 23.3931 22.4925 21.6429 20.8411 20.0837 19.3679
39 25.7829 24.7304 23.7402 22.8082 21.9302 21.1025 20.3217 19.5845
40 26.1935 25.1028 24.0781 23.1148 22.2084 21.3551 20.5510 19.7928
A.9-3
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .0425 .045 .0475 .05 .0525 .055 .0575 .06
1 0.9592 0.9569 0.9547 0.9524 0.9501 0.9479 0.9456 0.9434
2 1.8794 1.8727 1.8660 1.8594 1.8528 1.8463 1.8398 1.8334
3 2.7620 2.7490 2.7361 2.7232 2.7105 2.6979 2.6854 2.6730
4 3.6086 3.5875 3.5666 3.5460 3.5255 3.5052 3.4850 3.4651
5 4.4207 4.3900 4.3596 4.3295 4.2997 4.2703 4.2412 4.2124
6 5.1997 5.1579 5.1165 5.0757 5.0354 4.9955 4.9562 4.9173
7 5.9470 5.8927 5.8392 5.7864 5.7343 5.6830 5.6323 5.5824
8 6.6638 6.5959 6.5290 6.4632 6.3984 6.3346 6.2717 6.2098
9 7.3513 7.2688 7.1876 7.1078 7.0294 6.9522 6.8763 6.8017
10 8.0109 7.9127 7.8163 7.7217 7.6288 7.5376 7.4481 7.3601
11 8.6435 8.5289 8.4166 8.3064 8.1984 8.0925 7.9887 7.8869
12 9.2504 9.1186 8.9896 8.8633 8.7396 8.6185 8.5000 8.3838
13 9.8325 9.6829 9.5366 9.3936 9.2538 9.1171 8.9834 8.8527
14 10.3909 10.2228 10.0588 9.8986 9.7423 9.5897 9.4406 9.2950
15 10.9265 10.7395 10.5573 10.3797 10.2065 10.0376 9.8729 9.7122
16 11.4403 11.2340 11.0332 10.8378 10.6475 10.4622 10.2817 10.1059
17 11.9331 11.7072 11.4876 11.2741 11.0665 10.8646 10.6683 10.4773
18 12.4059 12.1600 11.9213 11.6896 11.4646 11.2461 11.0338 10.8276
19 12.8594 12.5933 12.3354 12.0853 11.8428 11.6077 11.3795 11.1581
20 13.2944 13.0079 12.7307 12.4622 12.2022 11.9504 11.7064 11.4699
21 13.7116 13.4047 13.1080 12.8212 12.5437 12.2753 12.0155 11.7641
22 14.1119 13.7844 13.4683 13.1630 12.8681 12.5832 12.3078 12.0416
23 14.4958 14.1478 13.8122 13.4886 13.1763 12.8751 12.5842 12.3034
24 14.8641 14.4955 14.1405 13.7987 13.4692 13.1517 12.8456 12.5504
25 15.2173 14.8282 14.4540 14.0940 13.7475 13.4139 13.0927 12.7833
26 15.5562 15.1466 14.7532 14.3752 14.0118 13.6625 13.3265 13.0032
27 15.8812 15.4513 15.0388 14.6430 14.2630 13.8981 13.5475 13.2105
28 16.1930 15.7429 15.3116 14.8981 14.5017 14.1214 13.7565 13.4062
29 16.4921 16.0219 15.5719 15.1411 14.7285 14.3331 13.9541 13.5907
30 16.7790 16.2889 15.8204 15.3725 14.9439 14.5338 14.1410 13.7648
31 17.0542 16.5444 16.0577 15.5928 15.1486 14.7239 14.3178 13.9291
32 17.3182 16.7889 16.2842 15.8027 15.3431 14.9042 14.4849 14.0840
33 17.5714 17.0229 16.5004 16.0026 15.5279 15.0751 14.6429 14.2302
34 17.8143 17.2468 16.7068 16.1929 15.7034 15.2370 14.7923 14.3681
35 18.0473 17.4610 16.9039 16.3742 15.8703 15.3906 14.9337 14.4982
36 18.2708 17.6660 17.0920 16.5469 16.0287 15.5361 15.0673 14.6210
37 18.4852 17.8622 17.2716 16.7113 16.1793 15.6740 15.1937 14.7368
38 18.6908 18.0500 17.4431 16.8679 16.3224 15.8048 15.3131 14.8460
39 18.8881 18.2297 17.6068 17.0171 16.4583 15.9287 15.4261 14.9491
40 19.0773 18.4016 17.7630 17.1591 16.5875 16.0461 15.5330 15.0463
A.9-4
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .0625 .065 .0675 .07 .0725 .075 .0775 .08
1 0.9412 0.9390 0.9368 0.9346 0.9324 0.9302 0.9281 0.9259
2 1.8270 1.8206 1.8143 1.8080 1.8018 1.7956 1.7894 1.7833
3 2.6607 2.6485 2.6363 2.6243 2.6124 2.6005 2.5888 2.5771
4 3.4454 3.4258 3.4064 3.3872 3.3682 3.3493 3.3306 3.3121
5 4.1839 4.1557 4.1278 4.1002 4.0729 4.0459 4.0192 3.9927
6 4.8789 4.8410 4.8036 4.7665 4.7300 4.6938 4.6582 4.6229
7 5.5331 5.4845 5.4366 5.3893 5.3426 5.2966 5.2512 5.2064
8 6.1488 6.0887 6.0296 5.9713 5.9139 5.8573 5.8016 5.7466
9 6.7283 6.6561 6.5851 6.5152 6.4465 6.3789 6.3124 6.2469
10 7.2737 7.1888 7.1055 7.0236 6.9431 6.8641 6.7864 6.7101
11 7.7870 7.6890 7.5929 7.4987 7.4062 7.3154 7.2264 7.1390
12 8.2701 8.1587 8.0496 7.9427 7.8379 7.7353 7.6347 7.5361
13 8.7248 8.5997 8.4774 8.3577 8.2405 8.1258 8.0136 7.9038
14 9.1528 9.0138 8.8781 8.7455 8.6158 8.4892 8.3653 8.2442
15 9.5555 9.4027 9.2535 9.1079 8.9658 8.8271 8.6917 8.5595
16 9.9346 9.7678 9.6051 9.4467 9.2921 9.1415 8.9946 8.8514
17 10.2914 10.1106 9.9346 9.7632 9.5964 9.4340 9.2757 9.1216
18 10.6272 10.4325 10.2432 10.0591 9.8801 9.7060 9.5367 9.3719
19 10.9433 10.7347 10.5322 10.3356 10.1446 9.9591 9.7788 9.6036
20 11.2407 11.0185 10.8030 10.5940 10.3913 10.1945 10.0035 9.8182
21 11.5207 11.2850 11.0567 10.8355 10.6212 10.4135 10.2121 10.0168
22 11.7842 11.5352 11.2943 11.0612 10.8356 10.6172 10.4057 10.2008
23 12.0322 11.7701 11.5169 11.2722 11.0356 10.8067 10.5853 10.3711
24 12.2656 11.9907 11.7255 11.4693 11.2220 10.9830 10.7520 10.5288
25 12.4852 12.1979 11.9208 11.6536 11.3958 11.1469 10.9067 10.6748
26 12.6920 12.3924 12.1038 11.8258 11.5578 11.2995 11.0503 10.8100
27 12.8866 12.5750 12.2752 11.9867 11.7089 11.4414 11.1836 10.9352
28 13.0697 12.7465 12.4358 12.1371 11.8498 11.5734 11.3073 11.0511
29 13.2421 12.9075 12.5862 12.2777 11.9812 11.6962 11.4221 11.1584
30 13.4043 13.0587 12.7272 12.4090 12.1037 11.8104 11.5286 11.2578
31 13.5570 13.2006 12.8592 12.5318 12.2179 11.9166 11.6275 11.3498
32 13.7007 13.3339 12.9828 12.6466 12.3244 12.0155 11.7192 11.4350
33 13.8360 13.4591 13.0987 12.7538 12.4236 12.1074 11.8044 11.5139
34 13.9633 13.5766 13.2072 12.8540 12.5162 12.1929 11.8834 11.5869
35 14.0831 13.6869 13.3088 12.9477 12.6025 12.2725 11.9568 11.6546
36 14.1958 13.7906 13.4041 13.0352 12.6830 12.3465 12.0249 11.7172
37 14.3020 13.8879 13.4933 13.1170 12.7581 12.4154 12.0880 11.7752
38 14.4018 13.9792 13.5768 13.1935 12.8280 12.4794 12.1467 11.8289
39 14.4958 14.0650 13.6551 13.2649 12.8933 12.5390 12.2011 11.8786
40 14.5843 14.1455 13.7284 13.3317 12.9541 12.5944 12.2516 11.9246
A.9-5
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .0825 .085 .0875 .09 .0925 .095 .0975 .10
1 0.9238 0.9217 0.9195 0.9174 0.9153 0.9132 0.9112 0.9091
2 1.7772 1.7711 1.7651 1.7591 1.7532 1.7473 1.7414 1.7355
3 2.5655 2.5540 2.5426 2.5313 2.5201 2.5089 2.4978 2.4869
4 3.2938 3.2756 3.2576 3.2397 3.2220 3.2045 3.1871 3.1699
5 3.9665 3.9406 3.9150 3.8897 3.8646 3.8397 3.8151 3.7908
6 4.5880 4.5536 4.5196 4.4859 4.4527 4.4198 4.3874 4.3553
7 5.1622 5.1185 5.0755 5.0330 4.9910 4.9496 4.9088 4.8684
8 5.6925 5.6392 5.5866 5.5348 5.4838 5.4334 5.3838 5.3349
9 6.1825 6.1191 6.0567 5.9952 5.9348 5.8753 5.8167 5.7590
10 6.6351 6.5613 6.4889 6.4177 6.3476 6.2788 6.2111 6.1446
11 7.0532 6.9690 6.8863 6.8052 6.7255 6.6473 6.5705 6.4951
12 7.4394 7.3447 7.2518 7.1607 7.0714 6.9838 6.8979 6.8137
13 7.7962 7.6910 7.5879 7.4869 7.3880 7.2912 7.1963 7.1034
14 8.1259 8.0101 7.8969 7.7861 7.6778 7.5719 7.4682 7.3667
15 8.4304 8.3042 8.1810 8.0607 7.9431 7.8282 7.7159 7.6061
16 8.7116 8.5753 8.4423 8.3126 8.1859 8.0623 7.9416 7.8237
17 8.9715 8.8252 8.6826 8.5436 8.4081 8.2760 8.1472 8.0216
18 9.2115 9.0555 8.9036 8.7556 8.6116 8.4713 8.3346 8.2014
19 9.4333 9.2677 9.1067 8.9501 8.7978 8.6496 8.5053 8.3649
20 9.6381 9.4633 9.2935 9.1285 8.9682 8.8124 8.6609 8.5136
21 9.8274 9.6436 9.4653 9.2922 9.1242 8.9611 8.8026 8.6487
22 10.0022 9.8098 9.6233 9.4424 9.2670 9.0969 8.9318 8.7715
23 10.1637 9.9629 9.7685 9.5802 9.3977 9.2209 9.0495 8.8832
24 10.3129 10.1041 9.9021 9.7066 9.5174 9.3341 9.1567 8.9847
25 10.4507 10.2342 10.0249 9.8226 9.6269 9.4376 9.2544 9.0770
26 10.5780 10.3541 10.1379 9.9290 9.7271 9.5320 9.3434 9.1609
27 10.6956 10.4646 10.2417 10.0266 9.8189 9.6183 9.4245 9.2372
28 10.8043 10.5664 10.3372 10.1161 9.9029 9.6971 9.4984 9.3066
29 10.9046 10.6603 10.4250 10.1983 9.9797 9.7690 9.5658 9.3696
30 10.9974 10.7468 10.5058 10.2736 10.0501 9.8347 9.6271 9.4269
31 11.0830 10.8266 10.5800 10.3428 10.1145 9.8947 9.6830 9.4790
32 11.1621 10.9001 10.6483 10.4062 10.1735 9.9495 9.7340 9.5264
33 11.2352 10.9678 10.7111 10.4644 10.2274 9.9996 9.7804 9.5694
34 11.3028 11.0302 10.7688 10.5178 10.2768 10.0453 9.8227 9.6086
35 11.3651 11.0878 10.8219 10.5668 10.3220 10.0870 9.8612 9.6442
36 11.4228 11.1408 10.8707 10.6118 10.3634 10.1251 9.8963 9.6765
37 11.4760 11.1897 10.9156 10.6530 10.4013 10.1599 9.9283 9.7059
38 11.5252 11.2347 10.9569 10.6908 10.4360 10.1917 9.9574 9.7327
39 11.5706 11.2763 10.9948 10.7255 10.4677 10.2207 9.9840 9.7570
40 11.6125 11.3145 11.0297 10.7574 10.4968 10.2472 10.0082 9.7791
A.9-6
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .1025 .105 .1075 .11 .1125 .115 .1175 .12
1 0.9070 0.9050 0.9029 0.9009 0.8989 0.8969 0.8949 0.8929
2 1.7297 1.7240 1.7182 1.7125 1.7069 1.7012 1.6956 1.6901
3 2.4759 2.4651 2.4544 2.4437 2.4331 2.4226 2.4122 2.4018
4 3.1528 3.1359 3.1191 3.1024 3.0860 3.0696 3.0534 3.0373
5 3.7667 3.7429 3.7193 3.6959 3.6728 3.6499 3.6272 3.6048
6 4.3235 4.2922 4.2612 4.2305 4.2002 4.1703 4.1407 4.1114
7 4.8286 4.7893 4.7505 4.7122 4.6744 4.6370 4.6002 4.5638
8 5.2867 5.2392 5.1923 5.1461 5.1006 5.0556 5.0113 4.9676
9 5.7022 5.6463 5.5913 5.5370 5.4837 5.4311 5.3793 5.3283
10 6.0791 6.0148 5.9515 5.8892 5.8280 5.7678 5.7085 5.6502
11 6.4210 6.3482 6.2767 6.2065 6.1375 6.0698 6.0031 5.9377
12 6.7310 6.6500 6.5704 6.4924 6.4158 6.3406 6.2668 6.1944
13 7.0123 6.9230 6.8356 6.7499 6.6659 6.5835 6.5027 6.4235
14 7.2674 7.1702 7.0750 6.9819 6.8907 6.8013 6.7139 6.6282
15 7.4988 7.3938 7.2912 7.1909 7.0927 6.9967 6.9028 6.8109
16 7.7086 7.5962 7.4864 7.3792 7.2744 7.1719 7.0718 6.9740
17 7.8990 7.7794 7.6627 7.5488 7.4376 7.3291 7.2231 7.1196
18 8.0716 7.9451 7.8218 7.7016 7.5844 7.4700 7.3585 7.2497
19 8.2282 8.0952 7.9655 7.8393 7.7163 7.5964 7.4796 7.3658
20 8.3703 8.2309 8.0953 7.9633 7.8349 7.7098 7.5880 7.4694
21 8.4991 8.3538 8.2125 8.0751 7.9415 7.8115 7.6851 7.5620
22 8.6160 8.4649 8.3183 8.1757 8.0373 7.9027 7.7719 7.6446
23 8.7220 8.5656 8.4138 8.2664 8.1234 7.9845 7.8495 7.7184
24 8.8181 8.6566 8.5000 8.3481 8.2008 8.0578 7.9191 7.7843
25 8.9053 8.7390 8.5779 8.4217 8.2704 8.1236 7.9813 7.8431
26 8.9844 8.8136 8.6482 8.4881 8.3329 8.1826 8.0369 7.8957
27 9.0562 8.8811 8.7117 8.5478 8.3892 8.2355 8.0867 7.9426
28 9.1212 8.9422 8.7690 8.6016 8.4397 8.2830 8.1313 7.9844
29 9.1803 8.9974 8.8208 8.6501 8.4851 8.3255 8.1712 8.0218
30 9.2338 9.0474 8.8675 8.6938 8.5259 8.3637 8.2069 8.0552
31 9.2824 9.0927 8.9097 8.7331 8.5626 8.3980 8.2388 8.0850
32 9.3264 9.1337 8.9478 8.7686 8.5956 8.4287 8.2674 8.1116
33 9.3664 9.1707 8.9823 8.8005 8.6253 8.4562 8.2930 8.1354
34 9.4026 9.2043 9.0133 8.8293 8.6520 8.4809 8.3159 8.1566
35 9.4355 9.2347 9.0414 8.8552 8.6759 8.5030 8.3363 8.1755
36 9.4653 9.2621 9.0667 8.8786 8.6974 8.5229 8.3547 8.1924
37 9.4923 9.2870 9.0896 8.8996 8.7168 8.5407 8.3711 8.2075
38 9.5168 9.3095 9.1102 8.9186 8.7342 8.5567 8.3857 8.2210
39 9.5391 9.3299 9.1289 8.9357 8.7499 8.5710 8.3989 8.2330
40 9.5593 9.3483 9.1457 8.9511 8.7639 8.5839 8.4106 8.2438
A.9-7
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .1225 .125 .1275 .13 .1325 .135 .1375 .14
1 0.8909 0.8889 0.8869 0.8850 0.8830 0.8811 0.8791 0.8772
2 1.6845 1.6790 1.6735 1.6681 1.6627 1.6573 1.6520 1.6467
3 2.3916 2.3813 2.3712 2.3612 2.3512 2.3413 2.3314 2.3216
4 3.0214 3.0056 2.9900 2.9745 2.9591 2.9438 2.9287 2.9137
5 3.5826 3.5606 3.5388 3.5172 3.4959 3.4747 3.4538 3.4331
6 4.0825 4.0538 4.0255 3.9976 3.9699 3.9425 3.9154 3.8887
7 4.5278 4.4923 4.4572 4.4226 4.3884 4.3546 4.3213 4.2883
8 4.9245 4.8820 4.8401 4.7988 4.7580 4.7177 4.6780 4.6389
9 5.2780 5.2285 5.1797 5.1317 5.0843 5.0377 4.9917 4.9464
10 5.5929 5.5364 5.4809 5.4262 5.3725 5.3195 5.2674 5.2161
11 5.8734 5.8102 5.7480 5.6869 5.6269 5.5679 5.5098 5.4527
12 6.1233 6.0535 5.9849 5.9176 5.8516 5.7867 5.7229 5.6603
13 6.3459 6.2698 6.1951 6.1218 6.0499 5.9794 5.9103 5.8424
14 6.5442 6.4620 6.3814 6.3025 6.2251 6.1493 6.0749 6.0021
15 6.7209 6.6329 6.5467 6.4624 6.3798 6.2989 6.2197 6.1422
16 6.8783 6.7848 6.6933 6.6039 6.5164 6.4308 6.3470 6.2651
17 7.0186 6.9198 6.8234 6.7291 6.6370 6.5469 6.4589 6.3729
18 7.1435 7.0398 6.9387 6.8399 6.7435 6.6493 6.5573 6.4674
19 7.2548 7.1465 7.0410 6.9380 6.8375 6.7395 6.6438 6.5504
20 7.3539 7.2414 7.1317 7.0248 6.9205 6.8189 6.7198 6.6231
21 7.4422 7.3256 7.2121 7.1016 6.9938 6.8889 6.7866 6.6870
22 7.5209 7.4006 7.2835 7.1695 7.0586 6.9506 6.8454 6.7429
23 7.5910 7.4672 7.3468 7.2297 7.1157 7.0049 6.8971 6.7921
24 7.6535 7.5264 7.4029 7.2829 7.1662 7.0528 6.9425 6.8351
25 7.7091 7.5790 7.4527 7.3300 7.2108 7.0950 6.9824 6.8729
26 7.7587 7.6258 7.4968 7.3717 7.2502 7.1321 7.0175 6.9061
27 7.8028 7.6674 7.5360 7.4086 7.2849 7.1649 7.0483 6.9352
28 7.8422 7.7043 7.5707 7.4412 7.3156 7.1937 7.0755 6.9607
29 7.8772 7.7372 7.6015 7.4701 7.3427 7.2191 7.0993 6.9830
30 7.9084 7.7664 7.6289 7.4957 7.3666 7.2415 7.1203 7.0027
31 7.9362 7.7923 7.6531 7.5183 7.3877 7.2613 7.1387 7.0199
32 7.9610 7.8154 7.6746 7.5383 7.4064 7.2786 7.1549 7.0350
33 7.9831 7.8359 7.6936 7.5560 7.4229 7.2940 7.1691 7.0482
34 8.0028 7.8542 7.7105 7.5717 7.4374 7.3075 7.1817 7.0599
35 8.0203 7.8704 7.7255 7.5856 7.4502 7.3193 7.1927 7.0700
36 8.0359 7.8848 7.7388 7.5979 7.4616 7.3298 7.2024 7.0790
37 8.0498 7.8976 7.7506 7.6087 7.4716 7.3390 7.2109 7.0868
38 8.0622 7.9089 7.7611 7.6183 7.4804 7.3472 7.2183 7.0937
39 8.0732 7.9191 7.7704 7.6268 7.4883 7.3543 7.2249 7.0997
40 8.0830 7.9281 7.7786 7.6344 7.4951 7.3607 7.2307 7.1050
A.9-8
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .1425 .145 .1475 .15 .1525 .155 .1575 .16
1 0.8753 0.8734 0.8715 0.8696 0.8677 0.8658 0.8639 0.8621
2 1.6414 1.6361 1.6309 1.6257 1.6205 1.6154 1.6103 1.6052
3 2.3119 2.3023 2.2927 2.2832 2.2738 2.2644 2.2551 2.2459
4 2.8988 2.8841 2.8695 2.8550 2.8406 2.8263 2.8122 2.7982
5 3.4126 3.3922 3.3721 3.3522 3.3324 3.3129 3.2935 3.2743
6 3.8622 3.8360 3.8101 3.7845 3.7591 3.7341 3.7093 3.6847
7 4.2557 4.2236 4.1918 4.1604 4.1294 4.0988 4.0685 4.0386
8 4.6002 4.5621 4.5245 4.4873 4.4507 4.4145 4.3788 4.3436
9 4.9017 4.8577 4.8143 4.7716 4.7294 4.6879 4.6469 4.6065
10 5.1656 5.1159 5.0670 5.0188 4.9713 4.9246 4.8786 4.8332
11 5.3966 5.3414 5.2871 5.2337 5.1812 5.1295 5.0787 5.0286
12 5.5988 5.5383 5.4790 5.4206 5.3633 5.3069 5.2515 5.1971
13 5.7757 5.7103 5.6462 5.5831 5.5213 5.4605 5.4009 5.3423
14 5.9306 5.8606 5.7919 5.7245 5.6584 5.5935 5.5299 5.4675
15 6.0662 5.9918 5.9188 5.8474 5.7773 5.7087 5.6414 5.5755
16 6.1849 6.1063 6.0295 5.9542 5.8806 5.8084 5.7377 5.6685
17 6.2887 6.2064 6.1259 6.0472 5.9701 5.8947 5.8209 5.7487
18 6.3796 6.2938 6.2099 6.1280 6.0478 5.9695 5.8928 5.8178
19 6.4592 6.3701 6.2832 6.1982 6.1152 6.0342 5.9549 5.8775
20 6.5288 6.4368 6.3470 6.2593 6.1738 6.0902 6.0086 5.9288
21 6.5898 6.4950 6.4026 6.3125 6.2245 6.1387 6.0549 5.9731
22 6.6431 6.5459 6.4511 6.3587 6.2686 6.1807 6.0950 6.0113
23 6.6898 6.5903 6.4933 6.3988 6.3068 6.2170 6.1296 6.0442
24 6.7307 6.6291 6.5301 6.4338 6.3399 6.2485 6.1594 6.0726
25 6.7665 6.6629 6.5622 6.4642 6.3687 6.2758 6.1853 6.0971
26 6.7978 6.6925 6.5901 6.4906 6.3937 6.2994 6.2076 6.1182
27 6.8252 6.7184 6.6145 6.5135 6.4153 6.3198 6.2268 6.1364
28 6.8492 6.7409 6.6357 6.5335 6.4341 6.3375 6.2435 6.1520
29 6.8702 6.7606 6.6542 6.5509 6.4504 6.3528 6.2579 6.1656
30 6.8886 6.7778 6.6704 6.5660 6.4646 6.3661 6.2703 6.1772
31 6.9047 6.7929 6.6844 6.5791 6.4769 6.3775 6.2810 6.1872
32 6.9187 6.8060 6.6967 6.5905 6.4875 6.3875 6.2903 6.1959
33 6.9311 6.8175 6.7073 6.6005 6.4968 6.3961 6.2983 6.2034
34 6.9419 6.8275 6.7166 6.6091 6.5048 6.4035 6.3053 6.2098
35 6.9513 6.8362 6.7247 6.6166 6.5117 6.4100 6.3112 6.2153
36 6.9596 6.8439 6.7318 6.6231 6.5178 6.4156 6.3164 6.2201
37 6.9668 6.8505 6.7379 6.6288 6.5230 6.4204 6.3209 6.2242
38 6.9731 6.8564 6.7433 6.6338 6.5276 6.4246 6.3247 6.2278
39 6.9787 6.8615 6.7480 6.6380 6.5315 6.4282 6.3281 6.2309
40 6.9835 6.8659 6.7520 6.6418 6.5349 6.4314 6.3309 6.2335
A.9-9
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .1625 .165 .1675 .17 .1725 .175 .1775 .18
1 0.8602 0.8584 0.8565 0.8547 0.8529 0.8511 0.8493 0.8475
2 1.6002 1.5952 1.5902 1.5852 1.5803 1.5754 1.5705 1.5656
3 2.2367 2.2276 2.2186 2.2096 2.2007 2.1918 2.1830 2.1743
4 2.7843 2.7705 2.7568 2.7432 2.7298 2.7164 2.7032 2.6901
5 3.2553 3.2365 3.2178 3.1993 3.1810 3.1629 3.1450 3.1272
6 3.6605 3.6365 3.6127 3.5892 3.5659 3.5429 3.5201 3.4976
7 4.0090 3.9798 3.9509 3.9224 3.8942 3.8663 3.8388 3.8115
8 4.3088 4.2745 4.2406 4.2072 4.1741 4.1415 4.1093 4.0776
9 4.5667 4.5275 4.4887 4.4506 4.4129 4.3758 4.3391 4.3030
10 4.7886 4.7446 4.7013 4.6586 4.6166 4.5751 4.5343 4.4941
11 4.9794 4.9310 4.8833 4.8364 4.7902 4.7448 4.7001 4.6560
12 5.1436 5.0910 5.0393 4.9884 4.9384 4.8892 4.8408 4.7932
13 5.2848 5.2283 5.1728 5.1183 5.0647 5.0121 4.9603 4.9095
14 5.4063 5.3462 5.2872 5.2293 5.1725 5.1167 5.0619 5.0081
15 5.5108 5.4474 5.3852 5.3242 5.2644 5.2057 5.1481 5.0916
16 5.6007 5.5342 5.4691 5.4053 5.3427 5.2814 5.2213 5.1624
17 5.6780 5.6088 5.5410 5.4746 5.4096 5.3459 5.2835 5.2223
18 5.7445 5.6728 5.6026 5.5339 5.4666 5.4008 5.3363 5.2732
19 5.8017 5.7277 5.6553 5.5845 5.5152 5.4475 5.3811 5.3162
20 5.8510 5.7748 5.7005 5.6278 5.5567 5.4872 5.4192 5.3527
21 5.8933 5.8153 5.7392 5.6648 5.5921 5.5210 5.4516 5.3837
22 5.9297 5.8501 5.7723 5.6964 5.6222 5.5498 5.4790 5.4099
23 5.9610 5.8799 5.8007 5.7234 5.6480 5.5743 5.5024 5.4321
24 5.9880 5.9055 5.8250 5.7465 5.6699 5.5951 5.5222 5.4510
25 6.0112 5.9274 5.8458 5.7662 5.6886 5.6129 5.5390 5.4669
26 6.0311 5.9463 5.8637 5.7831 5.7046 5.6280 5.5533 5.4804
27 6.0483 5.9625 5.8789 5.7975 5.7182 5.6408 5.5654 5.4919
28 6.0630 5.9764 5.8920 5.8099 5.7298 5.6518 5.5757 5.5016
29 6.0757 5.9883 5.9032 5.8204 5.7397 5.6611 5.5845 5.5098
30 6.0866 5.9986 5.9128 5.8294 5.7481 5.6690 5.5919 5.5168
31 6.0960 6.0073 5.9211 5.8371 5.7553 5.6758 5.5982 5.5227
32 6.1041 6.0149 5.9281 5.8437 5.7615 5.6815 5.6036 5.5277
33 6.1111 6.0214 5.9341 5.8493 5.7667 5.6864 5.6082 5.5320
34 6.1171 6.0269 5.9393 5.8541 5.7712 5.6905 5.6120 5.5356
35 6.1222 6.0317 5.9437 5.8582 5.7750 5.6941 5.6153 5.5386
36 6.1266 6.0358 5.9475 5.8617 5.7783 5.6971 5.6181 5.5412
37 6.1304 6.0393 5.9508 5.8647 5.7810 5.6996 5.6205 5.5434
38 6.1337 6.0423 5.9535 5.8673 5.7834 5.7018 5.6225 5.5452
39 6.1365 6.0449 5.9559 5.8695 5.7854 5.7037 5.6242 5.5468
40 6.1389 6.0471 5.9580 5.8713 5.7871 5.7053 5.6256 5.5482
A.9-10
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .1825 .185 .1875 .19 .1925 .195 .1975 .20
1 0.8457 0.8439 0.8421 0.8403 0.8386 0.8368 0.8351 0.8333
2 1.5608 1.5560 1.5512 1.5465 1.5418 1.5371 1.5324 1.5278
3 2.1656 2.1570 2.1484 2.1399 2.1315 2.1231 2.1148 2.1065
4 2.6770 2.6641 2.6513 2.6386 2.6260 2.6135 2.6010 2.5887
5 3.1095 3.0921 3.0748 3.0576 3.0406 3.0238 3.0071 2.9906
6 3.4753 3.4532 3.4314 3.4098 3.3884 3.3672 3.3463 3.3255
7 3.7846 3.7580 3.7317 3.7057 3.6800 3.6546 3.6294 3.6046
8 4.0462 4.0152 3.9846 3.9544 3.9245 3.8950 3.8659 3.8372
9 4.2674 4.2322 4.1975 4.1633 4.1296 4.0963 4.0634 4.0310
10 4.4544 4.4154 4.3769 4.3389 4.3015 4.2647 4.2283 4.1925
11 4.6126 4.5699 4.5279 4.4865 4.4457 4.4056 4.3660 4.3271
12 4.7464 4.7004 4.6551 4.6105 4.5666 4.5235 4.4810 4.4392
13 4.8596 4.8104 4.7622 4.7147 4.6680 4.6222 4.5771 4.5327
14 4.9552 4.9033 4.8524 4.8023 4.7531 4.7047 4.6572 4.6106
15 5.0361 4.9817 4.9283 4.8759 4.8244 4.7738 4.7242 4.6755
16 5.1045 5.0479 4.9923 4.9377 4.8842 4.8317 4.7801 4.7296
17 5.1624 5.1037 5.0461 4.9897 4.9343 4.8801 4.8268 4.7746
18 5.2113 5.1508 5.0915 5.0333 4.9764 4.9206 4.8658 4.8122
19 5.2527 5.1905 5.1296 5.0700 5.0116 4.9544 4.8984 4.8435
20 5.2877 5.2241 5.1618 5.1009 5.0412 4.9828 4.9256 4.8696
21 5.3173 5.2524 5.1889 5.1268 5.0660 5.0065 4.9483 4.8913
22 5.3423 5.2763 5.2117 5.1486 5.0868 5.0264 4.9673 4.9094
23 5.3635 5.2964 5.2309 5.1668 5.1042 5.0430 4.9831 4.9245
24 5.3814 5.3135 5.2471 5.1822 5.1188 5.0569 4.9963 4.9371
25 5.3965 5.3278 5.2607 5.1951 5.1311 5.0685 5.0074 4.9476
26 5.4093 5.3399 5.2722 5.2060 5.1414 5.0783 5.0166 4.9563
27 5.4201 5.3501 5.2818 5.2151 5.1500 5.0864 5.0243 4.9636
28 5.4293 5.3588 5.2900 5.2228 5.1572 5.0932 5.0307 4.9697
29 5.4370 5.3661 5.2968 5.2292 5.1633 5.0989 5.0361 4.9747
30 5.4436 5.3722 5.3026 5.2347 5.1684 5.1037 5.0406 4.9789
31 5.4491 5.3774 5.3074 5.2392 5.1727 5.1077 5.0443 4.9824
32 5.4538 5.3818 5.3115 5.2430 5.1762 5.1111 5.0475 4.9854
33 5.4578 5.3854 5.3150 5.2462 5.1792 5.1139 5.0501 4.9878
34 5.4611 5.3886 5.3179 5.2489 5.1817 5.1162 5.0522 4.9898
35 5.4639 5.3912 5.3203 5.2512 5.1839 5.1182 5.0541 4.9915
36 5.4663 5.3934 5.3224 5.2531 5.1856 5.1198 5.0556 4.9929
37 5.4684 5.3953 5.3241 5.2547 5.1871 5.1212 5.0569 4.9941
38 5.4701 5.3969 5.3256 5.2561 5.1883 5.1223 5.0579 4.9951
39 5.4715 5.3982 5.3268 5.2572 5.1894 5.1233 5.0588 4.9959
40 5.4727 5.3993 5.3278 5.2582 5.1903 5.1241 5.0595 4.9966
A.9-11
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .205 .21 .215 .22 .225 .23 .235 .24
1 0.8299 0.8264 0.8230 0.8197 0.8163 0.8130 0.8097 0.8065
2 1.5186 1.5095 1.5004 1.4915 1.4827 1.4740 1.4654 1.4568
3 2.0901 2.0739 2.0580 2.0422 2.0267 2.0114 1.9962 1.9813
4 2.5644 2.5404 2.5169 2.4936 2.4708 2.4483 2.4261 2.4043
5 2.9580 2.9260 2.8945 2.8636 2.8333 2.8035 2.7742 2.7454
6 3.2847 3.2446 3.2054 3.1669 3.1292 3.0923 3.0560 3.0205
7 3.5557 3.5079 3.4612 3.4155 3.3708 3.3270 3.2842 3.2423
8 3.7807 3.7256 3.6718 3.6193 3.5680 3.5179 3.4690 3.4212
9 3.9674 3.9054 3.8451 3.7863 3.7290 3.6731 3.6186 3.5655
10 4.1223 4.0541 3.9877 3.9232 3.8604 3.7993 3.7398 3.6819
11 4.2509 4.1769 4.1051 4.0354 3.9677 3.9018 3.8379 3.7757
12 4.3576 4.2784 4.2017 4.1274 4.0552 3.9852 3.9173 3.8514
13 4.4461 4.3624 4.2813 4.2028 4.1267 4.0530 3.9816 3.9124
14 4.5196 4.4317 4.3467 4.2646 4.1851 4.1082 4.0337 3.9616
15 4.5806 4.4890 4.4006 4.3152 4.2327 4.1530 4.0759 4.0013
16 4.6312 4.5364 4.4449 4.3567 4.2716 4.1894 4.1100 4.0333
17 4.6732 4.5755 4.4814 4.3908 4.3034 4.2190 4.1377 4.0591
18 4.7080 4.6079 4.5115 4.4187 4.3293 4.2431 4.1601 4.0799
19 4.7370 4.6346 4.5362 4.4415 4.3504 4.2627 4.1782 4.0967
20 4.7610 4.6567 4.5565 4.4603 4.3677 4.2786 4.1929 4.1103
21 4.7809 4.6750 4.5733 4.4756 4.3818 4.2916 4.2047 4.1212
22 4.7974 4.6900 4.5871 4.4882 4.3933 4.3021 4.2144 4.1300
23 4.8111 4.7025 4.5984 4.4985 4.4027 4.3106 4.2222 4.1371
24 4.8225 4.7128 4.6077 4.5070 4.4104 4.3176 4.2285 4.1428
25 4.8320 4.7213 4.6154 4.5139 4.4166 4.3232 4.2336 4.1474
26 4.8398 4.7284 4.6217 4.5196 4.4217 4.3278 4.2377 4.1511
27 4.8463 4.7342 4.6270 4.5243 4.4259 4.3316 4.2411 4.1542
28 4.8517 4.7390 4.6312 4.5281 4.4293 4.3346 4.2438 4.1566
29 4.8562 4.7430 4.6348 4.5312 4.4321 4.3371 4.2460 4.1585
30 4.8599 4.7463 4.6377 4.5338 4.4344 4.3391 4.2478 4.1601
31 4.8630 4.7490 4.6401 4.5359 4.4362 4.3407 4.2492 4.1614
32 4.8656 4.7512 4.6420 4.5376 4.4377 4.3421 4.2504 4.1624
33 4.8677 4.7531 4.6436 4.5390 4.4390 4.3431 4.2513 4.1632
34 4.8694 4.7546 4.6450 4.5402 4.4400 4.3440 4.2521 4.1639
35 4.8709 4.7559 4.6461 4.5411 4.4408 4.3447 4.2527 4.1644
36 4.8721 4.7569 4.6470 4.5419 4.4415 4.3453 4.2532 4.1649
37 4.8731 4.7578 4.6477 4.5426 4.4420 4.3458 4.2536 4.1652
38 4.8740 4.7585 4.6483 4.5431 4.4425 4.3462 4.2539 4.1655
39 4.8747 4.7591 4.6488 4.5435 4.4428 4.3465 4.2542 4.1657
40 4.8752 4.7596 4.6492 4.5439 4.4431 4.3467 4.2544 4.1659
A.9-12
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .245 .25 .255 .26 .265 .27 .275 .28
1 0.8032 0.8000 0.7968 0.7937 0.7905 0.7874 0.7843 0.7813
2 1.4484 1.4400 1.4317 1.4235 1.4154 1.4074 1.3995 1.3916
3 1.9666 1.9520 1.9376 1.9234 1.9094 1.8956 1.8819 1.8684
4 2.3828 2.3616 2.3407 2.3202 2.2999 2.2800 2.2603 2.2410
5 2.7171 2.6893 2.6619 2.6351 2.6087 2.5827 2.5571 2.5320
6 2.9856 2.9514 2.9179 2.8850 2.8527 2.8210 2.7899 2.7594
7 3.2013 3.1611 3.1218 3.0833 3.0456 3.0087 2.9725 2.9370
8 3.3745 3.3289 3.2843 3.2407 3.1981 3.1564 3.1157 3.0758
9 3.5137 3.4631 3.4138 3.3657 3.3187 3.2728 3.2280 3.1842
10 3.6254 3.5705 3.5170 3.4648 3.4140 3.3644 3.3161 3.2689
11 3.7152 3.6564 3.5992 3.5435 3.4893 3.4365 3.3851 3.3351
12 3.7873 3.7251 3.6647 3.6059 3.5489 3.4933 3.4393 3.3868
13 3.8452 3.7801 3.7169 3.6555 3.5959 3.5381 3.4818 3.4272
14 3.8918 3.8241 3.7585 3.6949 3.6331 3.5733 3.5152 3.4587
15 3.9291 3.8593 3.7916 3.7261 3.6626 3.6010 3.5413 3.4834
16 3.9591 3.8874 3.8180 3.7509 3.6858 3.6228 3.5618 3.5026
17 3.9832 3.9099 3.8391 3.7705 3.7042 3.6400 3.5779 3.5177
18 4.0026 3.9279 3.8558 3.7861 3.7187 3.6536 3.5905 3.5294
19 4.0182 3.9424 3.8692 3.7985 3.7302 3.6642 3.6004 3.5386
20 4.0306 3.9539 3.8798 3.8083 3.7393 3.6726 3.6082 3.5458
21 4.0407 3.9631 3.8883 3.8161 3.7465 3.6792 3.6142 3.5514
22 4.0487 3.9705 3.8951 3.8223 3.7522 3.6844 3.6190 3.5558
23 4.0552 3.9764 3.9005 3.8273 3.7567 3.6885 3.6228 3.5592
24 4.0604 3.9811 3.9047 3.8312 3.7602 3.6918 3.6257 3.5619
25 4.0646 3.9849 3.9082 3.8342 3.7630 3.6943 3.6280 3.5640
26 4.0679 3.9879 3.9109 3.8367 3.7652 3.6963 3.6298 3.5656
27 4.0706 3.9903 3.9131 3.8387 3.7670 3.6979 3.6312 3.5669
28 4.0728 3.9923 3.9148 3.8402 3.7684 3.6991 3.6323 3.5679
29 4.0745 3.9938 3.9162 3.8414 3.7695 3.7001 3.6332 3.5687
30 4.0759 3.9950 3.9173 3.8424 3.7703 3.7009 3.6339 3.5693
31 4.0771 3.9960 3.9181 3.8432 3.7710 3.7015 3.6344 3.5697
32 4.0780 3.9968 3.9188 3.8438 3.7715 3.7019 3.6348 3.5701
33 4.0787 3.9975 3.9194 3.8443 3.7720 3.7023 3.6352 3.5704
34 4.0793 3.9980 3.9198 3.8447 3.7723 3.7026 3.6354 3.5706
35 4.0797 3.9984 3.9202 3.8450 3.7726 3.7028 3.6356 3.5708
36 4.0801 3.9987 3.9205 3.8452 3.7728 3.7030 3.6358 3.5709
37 4.0804 3.9990 3.9207 3.8454 3.7730 3.7032 3.6359 3.5710
38 4.0806 3.9992 3.9209 3.8456 3.7731 3.7033 3.6360 3.5711
39 4.0808 3.9993 3.9210 3.8457 3.7732 3.7034 3.6361 3.5712
40 4.0810 3.9995 3.9211 3.8458 3.7733 3.7034 3.6361 3.5712
A.9-13
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .285 .29 .295 .30 .305 .31 .315 .32
1 0.7782 0.7752 0.7722 0.7692 0.7663 0.7634 0.7605 0.7576
2 1.3838 1.3761 1.3685 1.3609 1.3535 1.3461 1.3388 1.3315
3 1.8551 1.8420 1.8290 1.8161 1.8034 1.7909 1.7785 1.7663
4 2.2219 2.2031 2.1845 2.1662 2.1482 2.1305 2.1129 2.0957
5 2.5073 2.4830 2.4591 2.4356 2.4124 2.3897 2.3673 2.3452
6 2.7294 2.7000 2.6711 2.6427 2.6149 2.5875 2.5607 2.5342
7 2.9023 2.8682 2.8348 2.8021 2.7700 2.7386 2.7077 2.6775
8 3.0368 2.9986 2.9613 2.9247 2.8889 2.8539 2.8196 2.7860
9 3.1415 3.0997 3.0589 3.0190 2.9800 2.9419 2.9046 2.8681
10 3.2229 3.1781 3.1343 3.0915 3.0498 3.0091 2.9693 2.9304
11 3.2863 3.2388 3.1925 3.1473 3.1033 3.0604 3.0185 2.9776
12 3.3357 3.2859 3.2374 3.1903 3.1443 3.0995 3.0559 3.0133
13 3.3741 3.3224 3.2722 3.2233 3.1757 3.1294 3.0843 3.0404
14 3.4039 3.3507 3.2990 3.2487 3.1998 3.1522 3.1059 3.0609
15 3.4272 3.3726 3.3197 3.2682 3.2182 3.1696 3.1224 3.0764
16 3.4453 3.3896 3.3356 3.2832 3.2324 3.1829 3.1349 3.0882
17 3.4594 3.4028 3.3480 3.2948 3.2432 3.1931 3.1444 3.0971
18 3.4703 3.4130 3.3575 3.3037 3.2515 3.2008 3.1516 3.1039
19 3.4789 3.4210 3.3649 3.3105 3.2578 3.2067 3.1571 3.1090
20 3.4855 3.4271 3.3706 3.3158 3.2627 3.2112 3.1613 3.1129
21 3.4907 3.4319 3.3750 3.3198 3.2664 3.2147 3.1645 3.1158
22 3.4947 3.4356 3.3783 3.3230 3.2693 3.2173 3.1669 3.1180
23 3.4978 3.4384 3.3810 3.3254 3.2715 3.2193 3.1688 3.1197
24 3.5002 3.4406 3.3830 3.3272 3.2732 3.2209 3.1702 3.1210
25 3.5021 3.4423 3.3845 3.3286 3.2745 3.2220 3.1712 3.1220
26 3.5036 3.4437 3.3857 3.3297 3.2755 3.2229 3.1720 3.1227
27 3.5047 3.4447 3.3867 3.3305 3.2762 3.2236 3.1727 3.1233
28 3.5056 3.4455 3.3874 3.3312 3.2768 3.2241 3.1731 3.1237
29 3.5063 3.4461 3.3880 3.3317 3.2772 3.2245 3.1735 3.1240
30 3.5069 3.4466 3.3884 3.3321 3.2776 3.2248 3.1737 3.1242
31 3.5073 3.4470 3.3887 3.3324 3.2778 3.2251 3.1740 3.1244
32 3.5076 3.4473 3.3890 3.3326 3.2780 3.2252 3.1741 3.1246
33 3.5079 3.4475 3.3892 3.3328 3.2782 3.2254 3.1742 3.1247
34 3.5081 3.4477 3.3893 3.3329 3.2783 3.2255 3.1743 3.1248
35 3.5082 3.4478 3.3894 3.3330 3.2784 3.2256 3.1744 3.1248
36 3.5084 3.4479 3.3895 3.3331 3.2785 3.2256 3.1744 3.1249
37 3.5084 3.4480 3.3896 3.3331 3.2785 3.2257 3.1745 3.1249
38 3.5085 3.4481 3.3896 3.3332 3.2786 3.2257 3.1745 3.1249
39 3.5086 3.4481 3.3897 3.3332 3.2786 3.2257 3.1745 3.1249
40 3.5086 3.4481 3.3897 3.3332 3.2786 3.2257 3.1745 3.1250
A.9-14
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .325 .33 .335 .34 .345 .35 .355 .36
1 0.7547 0.7519 0.7491 0.7463 0.7435 0.7407 0.7380 0.7353
2 1.3243 1.3172 1.3102 1.3032 1.2963 1.2894 1.2827 1.2760
3 1.7542 1.7423 1.7305 1.7188 1.7073 1.6959 1.6846 1.6735
4 2.0786 2.0618 2.0453 2.0290 2.0128 1.9969 1.9813 1.9658
5 2.3235 2.3021 2.2811 2.2604 2.2400 2.2200 2.2002 2.1807
6 2.5083 2.4828 2.4578 2.4331 2.4089 2.3852 2.3618 2.3388
7 2.6478 2.6187 2.5901 2.5620 2.5345 2.5075 2.4810 2.4550
8 2.7530 2.7208 2.6892 2.6582 2.6279 2.5982 2.5690 2.5404
9 2.8325 2.7976 2.7634 2.7300 2.6973 2.6653 2.6340 2.6033
10 2.8924 2.8553 2.8191 2.7836 2.7489 2.7150 2.6819 2.6495
11 2.9377 2.8987 2.8607 2.8236 2.7873 2.7519 2.7173 2.6834
12 2.9718 2.9314 2.8919 2.8534 2.8158 2.7792 2.7434 2.7084
13 2.9976 2.9559 2.9153 2.8757 2.8371 2.7994 2.7626 2.7268
14 3.0171 2.9744 2.9328 2.8923 2.8528 2.8144 2.7768 2.7403
15 3.0317 2.9883 2.9459 2.9047 2.8646 2.8255 2.7873 2.7502
16 3.0428 2.9987 2.9557 2.9140 2.8733 2.8337 2.7951 2.7575
17 3.0512 3.0065 2.9631 2.9209 2.8798 2.8398 2.8008 2.7629
18 3.0575 3.0124 2.9686 2.9260 2.8846 2.8443 2.8050 2.7668
19 3.0623 3.0169 2.9727 2.9299 2.8882 2.8476 2.8081 2.7697
20 3.0659 3.0202 2.9758 2.9327 2.8908 2.8501 2.8104 2.7719
21 3.0686 3.0227 2.9782 2.9349 2.8928 2.8519 2.8121 2.7734
22 3.0706 3.0246 2.9799 2.9365 2.8943 2.8533 2.8134 2.7746
23 3.0722 3.0260 2.9812 2.9377 2.8954 2.8543 2.8143 2.7754
24 3.0733 3.0271 2.9822 2.9386 2.8962 2.8550 2.8150 2.7760
25 3.0742 3.0279 2.9829 2.9392 2.8968 2.8556 2.8155 2.7765
26 3.0749 3.0285 2.9834 2.9397 2.8972 2.8560 2.8159 2.7768
27 3.0754 3.0289 2.9839 2.9401 2.8976 2.8563 2.8161 2.7771
28 3.0758 3.0293 2.9842 2.9404 2.8978 2.8565 2.8163 2.7773
29 3.0760 3.0295 2.9844 2.9406 2.8980 2.8567 2.8165 2.7774
30 3.0763 3.0297 2.9846 2.9407 2.8982 2.8568 2.8166 2.7775
31 3.0764 3.0299 2.9847 2.9408 2.8983 2.8569 2.8167 2.7776
32 3.0765 3.0300 2.9848 2.9409 2.8983 2.8570 2.8167 2.7776
33 3.0766 3.0301 2.9849 2.9410 2.8984 2.8570 2.8168 2.7777
34 3.0767 3.0301 2.9849 2.9410 2.8984 2.8570 2.8168 2.7777
35 3.0768 3.0302 2.9850 2.9411 2.8985 2.8571 2.8168 2.7777
36 3.0768 3.0302 2.9850 2.9411 2.8985 2.8571 2.8169 2.7777
37 3.0768 3.0302 2.9850 2.9411 2.8985 2.8571 2.8169 2.7777
38 3.0769 3.0302 2.9850 2.9411 2.8985 2.8571 2.8169 2.7778
39 3.0769 3.0303 2.9850 2.9411 2.8985 2.8571 2.8169 2.7778
40 3.0769 3.0303 2.9850 2.9412 2.8985 2.8571 2.8169 2.7778
A.9-15
Table A.9(Continued)
Present Value of an n Year $1 AnnuityInterest Rate, r
n .365 .37 .375 .38 .385 .39 .395 .40
1 0.7326 0.7299 0.7273 0.7246 0.7220 0.7194 0.7168 0.7143
2 1.2693 1.2627 1.2562 1.2497 1.2433 1.2370 1.2307 1.2245
3 1.6625 1.6516 1.6409 1.6302 1.6197 1.6093 1.5991 1.5889
4 1.9505 1.9355 1.9206 1.9060 1.8915 1.8772 1.8631 1.8492
5 2.1616 2.1427 2.1241 2.1058 2.0877 2.0699 2.0524 2.0352
6 2.3162 2.2939 2.2721 2.2506 2.2294 2.2086 2.1881 2.1680
7 2.4294 2.4043 2.3797 2.3555 2.3317 2.3083 2.2854 2.2628
8 2.5124 2.4849 2.4580 2.4315 2.4056 2.3801 2.3551 2.3306
9 2.5732 2.5437 2.5149 2.4866 2.4589 2.4317 2.4051 2.3790
10 2.6177 2.5867 2.5563 2.5265 2.4974 2.4689 2.4409 2.4136
11 2.6503 2.6180 2.5864 2.5555 2.5252 2.4956 2.4666 2.4383
12 2.6742 2.6409 2.6083 2.5764 2.5453 2.5148 2.4850 2.4559
13 2.6918 2.6576 2.6242 2.5916 2.5598 2.5286 2.4982 2.4685
14 2.7046 2.6698 2.6358 2.6026 2.5702 2.5386 2.5077 2.4775
15 2.7140 2.6787 2.6442 2.6106 2.5778 2.5457 2.5145 2.4839
16 2.7209 2.6852 2.6503 2.6164 2.5832 2.5509 2.5193 2.4885
17 2.7259 2.6899 2.6548 2.6206 2.5872 2.5546 2.5228 2.4918
18 2.7296 2.6934 2.6580 2.6236 2.5900 2.5573 2.5253 2.4941
19 2.7323 2.6959 2.6604 2.6258 2.5921 2.5592 2.5271 2.4958
20 2.7343 2.6977 2.6621 2.6274 2.5936 2.5606 2.5284 2.4970
21 2.7357 2.6991 2.6633 2.6285 2.5946 2.5616 2.5293 2.4979
22 2.7368 2.7000 2.6642 2.6294 2.5954 2.5623 2.5300 2.4985
23 2.7376 2.7008 2.6649 2.6300 2.5960 2.5628 2.5304 2.4989
24 2.7382 2.7013 2.6654 2.6304 2.5964 2.5632 2.5308 2.4992
25 2.7386 2.7017 2.6657 2.6307 2.5966 2.5634 2.5310 2.4994
26 2.7389 2.7019 2.6660 2.6310 2.5969 2.5636 2.5312 2.4996
27 2.7391 2.7022 2.6662 2.6311 2.5970 2.5637 2.5313 2.4997
28 2.7393 2.7023 2.6663 2.6313 2.5971 2.5638 2.5314 2.4998
29 2.7394 2.7024 2.6664 2.6313 2.5972 2.5639 2.5315 2.4999
30 2.7395 2.7025 2.6665 2.6314 2.5973 2.5640 2.5315 2.4999
31 2.7395 2.7025 2.6665 2.6315 2.5973 2.5640 2.5316 2.4999
32 2.7396 2.7026 2.6666 2.6315 2.5973 2.5640 2.5316 2.4999
33 2.7396 2.7026 2.6666 2.6315 2.5973 2.5641 2.5316 2.5000
34 2.7397 2.7026 2.6666 2.6315 2.5974 2.5641 2.5316 2.5000
35 2.7397 2.7027 2.6666 2.6315 2.5974 2.5641 2.5316 2.5000
36 2.7397 2.7027 2.6666 2.6316 2.5974 2.5641 2.5316 2.5000
37 2.7397 2.7027 2.6666 2.6316 2.5974 2.5641 2.5316 2.5000
38 2.7397 2.7027 2.6667 2.6316 2.5974 2.5641 2.5316 2.5000
39 2.7397 2.7027 2.6667 2.6316 2.5974 2.5641 2.5316 2.5000
40 2.7397 2.7027 2.6667 2.6316 2.5974 2.5641 2.5316 2.5000