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8.8: Appendix: Present Value Tables

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

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