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8.8: Appendix: Present Value Tables

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    1801
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    Per-iods Rate per Period
      5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 18% 20% 25% 30%
    0 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 .9524 .9434 .9346 .9259 .9174 .9091 .9009 .8929 .8850 .8772 .8696 .8475 .8333 .8000 .7692
    2 .9070 .8900 .8734 .8573 .8417 .8264 .8116 .7972 .7831 .7695 .7561 .7182 .6944 .6400 .5917
    3 .8638 .8396 .8163 .7938 .7722 .7513 .7312 .7118 .6931 .6750 .6575 .6086 .5787 .5120 .4552
    4 .8227 .7921 .7629 .7350 .7084 .6830 .6587 .6355 .6133 .5921 .5718 .5158 .4823 .4086 .3501
    5 .7835 .7473 .7130 .6806 .6499 .6209 .5935 .5674 .5428 .5194 .4972 .4371 .4019 .3277 .2693
    6 .7462 .7050 .6663 .6302 .5963 .5645 .5346 .5066 .4803 .4556 .4323 .3704 .3349 .2621 .2072
    7 .7107 .6651 .6227 .5835 .5470 .5132 .4817 .4523 .4251 .3996 .3759 .3139 .2791 .2097 .1594
    8 .6768 .6274 .5820 .5403 .5019 .4665 .4339 .4039 .3762 .3506 .3269 .2660 .2326 .1678 .1226
    9 .6446 .5919 .5439 .5002 .4604 .4241 .3909 .3606 .3329 .3075 .2843 .2255 .1938 .1342 .0943
    10 .6139 .5584 .5083 .4632 .4224 .3855 .3522 .3220 .2946 .2697 .2472 .1991 .1615 .1074 .0725
    11 .5847 .5268 .4751 .4289 .3875 .3555 .3173 .2875 .2607 .2366 .2149 .1619 .1346 .0859 .0558
    12 .5568 .4970 .4440 .3971 .3555 .3186 .2858 .2567 .2307 .2076 .1869 .1372 .1122 .0687 .0429
    13 .5303 .4688 .4150 .3677 .3262 .2897 .2575 .2292 .2042 .1821 .1625 .1163 .0935 .0550 .0330
    14 .5051 .4423 .3878 .3405 .2992 .2633 .2320 .2046 .1807 .1597 .1413 .0985 .0779 .0440 .0254
    15 .4810 .4173 .3624 .3152 .2745 .2394 .2090 .1827 .1599 .1401 .1229 .0835 .0649 .0352 .0195
    16 .4581 .3936 .3387 .2919 .2519 .2176 .1883 .1631 .1415 .1229 .1069 .0708 .0541 .0281 .0150
    17 .4363 .3714 .3166 .2703 .2311 .1978 .1696 .1456 .1252 .1078 .0929 .0600 .0451 .0225 .0116
    18 .4155 .3503 .2959 .2502 .2120 .1799 .1528 .1300 .1108 .0946 .0808 .0508 .0376 .0180 .0089
    19 .3957 .3305 .2765 .2317 .1945 .1635 .1377 .1161 .0981 .0829 .0703 .0431 .0313 .0144 .0068
    20 .3769 .3118 .2584 .2145 .1784 .1486 .1240 .1037 .0868 .0728 .0611 .0365 .0261 .0115 .0053
    21 .3589 .2942 .2415 .1987 .1637 .1351 .1117 .0926 .0768 .0638 .0531 .0309 .0217 .0092 .0040
    22 .3418 .2775 .2257 .1839 .1502 .1128 .1007 .0826 .0680 .0560 .0462 .0262 .0181 .0074 .0031
    23 .3256 .2618 .2109 .1703 .1378 .1117 .0907 .0738 .0601 .0491 .0402 .0222 .0151 .0059 .0024
    24 .3101 .2470 .1971 .1577 .1264 .1015 .0817 .0659 .0532 .0431 .0349 .0188 .0126 .0047 .0018
    25 .2953 .2330 .1842 .1460 01160 .0923 .0736 .0588 .0471 .0378 .0304 .0160 .0105 .0038 .0014
    26 .2812 .2198 .1722 1352 .1064 .0839 .0663 .0525 .0417 .0331 .0264 .0135 .0087 .0030 .0011
    27 .2678 .2074 .1609 .1252 .0976 .0763 .0597 .0469 .0369 .0291 .0230 .0115 .0073 .0024 .0008
    28 .2551 .1956 .1504 .1159 .0895 .0693 .0538 .0419 .0326 .0255 .0200 .0097 .0061 .0019 .0006
    29 .2429 .1846 .1406 .1073 .0822 .0630 .0485 .0374 .0289 .0224 .0174 .0082 .0051 .0015 .0005
    30 .2314 .1741 .1314 .0994 .0754 .0573 .0437 .0334 .0256 .0196 .0151 .0070 .0042 .0012 .0004

    Figure 8.9 - Present Value of $1 Received at the End of n Periods

    Note

    $$\text{Factor} = \frac{1}{(1 + r)^{n}}$$

    Per-iods Rate per Period
      5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 18% 20% 25% 30%
    0 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.84746 0.8333 0.8000 0.7692
    1 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.56564 1.5278 1.4400 1.3609
    2 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.17427 2.1065 1.9520 1.8161
    3 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.17427 2.1065 1.9520 1.8161
    4 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.69006 2.5887 2.3616 2.1662
    5 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.12717 2.9906 2.6893 2.4356
    6 5.0757 4.9173 4.7665 4.6229 4.4829 4.3553 4.2305 4.1114 3.9975 3.8887 3.7845 3.4976 3.3255 2.9514 2.6427
    7 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883 4.1604 3.8115 3.6046 3.1611 2.8021
    8 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873 4.0776 3.8372 3.3289 2.9247
    9 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716 4.3030 4.0310 3.4631 3.0190
    10 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 5.0188 4.4941 4.1925 3.5705 3.0915
    11 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 4.6560 4.3271 3.6564 3.1473
    12 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 4.7932 4.4392 3.7251 3.1903
    13 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 4.9095 4.5327 3.7801 3.2233
    14 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 3.0021 5.7245 5.0081 4.6106 3.8241 3.2487
    15 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.0916 4.6755 3.8593 3.2682
    16 10.38378 10.1059 9.4466 8.8514 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.1624 4.7296 3.8874 3.2832
    17 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.2223 4.7746 3.9099 3.2948
    18 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280 5.2732 4.8122 3.9279 3.3037
    19 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982 5.3162 4.8435 3.9424 3.3105
    20 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.3527 4.8696 3.9539 3.3158
    21 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 8.0751 7.5620 7.1016 6.6870 6.3125 5.3837 4.8913 3.9631 3.3198
    22 13.1630 12.0416 11.0612 10.2007 9.4424 8.7715 8.1757 7.6446 7.1695 6.7429 6.3587 5.4099 4.9094 3.9705 3.3230
    23 13.4886 12.3034 11.2722 10.3711 9.5802 8.8832 8.2664 7.7184 7.2297 6.7921 6.3988 5.4321 4.9245 3.9764 3.3254
    24 13.7986 12.5504 11.4693 10.5288 9.7066 8.9847 8.3481 7.7843 7.2829 6.8351 6.4338 5.4509 4.9371 3.9811 3.3272
    25 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 8.4217 7.8431 7.3300 6.8729 6.4641 5.4669 4.9476 3.9849 3.3286
    26 14.3752 13.0032 11.8258 10.8100 9.9290 9.1609 8.4881 7.8957 7.3717 6.9061 6.4906 5.4804 4.9563 3.9879 3.3297
    27 14.6430 13.2105 11.9867 10.9352 10.0266 9.2372 8.5478 7.9426 7.4086 6.9352 6.5135 5.4919 4.9636 3.9903 3.3305
    28 14.8981 13.4062 12.1371 11.0511 10.1161 9.3066 8.6016 7.9844 7.4412 6.9607 6.5335 5.5016 4.9697 3.9923 3.3312
    29 15.1411 13.5907 12.2777 11.1584 10.1983 9.3696 8.6501 8.0218 7.4701 6.9830 6.5509 5.5098 4.9747 3.9938 3.3317
    30 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 8.0552 7.4957 7.0027 6.5660 5.5168 4.9789 3.9950 3.3321

    Figure 8.10 - Present Value of a $1 Annuity Received at the End of Each Period for n Periods

    Note

    $$\text{Factor} = \frac{1-(1+r)^{-n}}{r}$$