# 8.9: Appendix- Present Value Tables

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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

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