TABLE B.1 Present Value of 1 p=1/(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0.9901 0.9803 0.9706 0.9610 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.9804 0.9709 0.9615 0.9612 0.9426 0.9246 0.9423 0.9151 0.8890 0.9238 0.8885 0.8548 0.9057 0.8626 0.8219 0.8880 0.8375 0.7903 0.8706 0.8131 0.7599 0.8535 0.7894 0.7307 0.8368 0.7664 0.7026 0.82030.7441 0.6756 0.8043 0.7224 0.6496 0.7885 0.7014 0.6246 0.7730 0.7720 0 0.6810 0.6006 0.75790.6611 0.5775 0.7430 0.64190 .5553 0.7284 0.6232 0.5339 0.7142 0.6050 0.5134 0.7002 0.5874 0.4936 0.6864 0.5703 0.4746 0.6730 0.5537 0.4564 0.6095 0.4776 0.3751 0.5521 0.4120 0.3083 0.5000 0.3554 0.2534 0.4529 0.3066 0.2083 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2330 0.1741 0.1301 0.0972 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.1842 0.1314 0.0937 0.0668 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 .3152 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1160 0.0754 0.0490 0.0318 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.0923 0.0573 0.0356 0.0221 0.8929 0.8696 0.7972 0.7561 0.7118 0.6575 0.6355 0.5718 0.5674 0.4972 0.5066 0.4323 0.4523 0.3759 0.40390.3269 0.3606 0.2843 0.3220 0.2472 0.2875 0.2149 0.2567 0.1869 0.2292 0.1625 0.2046 0.1413 0.1827 0.1229 0.1631 0.1069 0.1456 0.0929 0.13000.0808 0.1161 0.0703 0.1037 0.0611 0.0588 0.0304 0.0334 0.0151 0.0189 0.0075 0.0107 0.0037 13 14 0 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.7798 0.7419 0.7059 0.6717 0.3769 0.2953 0.2314 0.1813 0.1420 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 *Used to compute the present value of a known future amount. For example: How much would you need to invest today at 10% compounded semiannually to accumulate $5,000 in 6 years from today? Using the factors of n= 12 and i=5% (12 semiannual periods and a semiannual rate of 5%), the factor is 0.5568. You would need to invest $2,784 today ($5.000 x 0.5568). TABLE B.2 Future Value of 1 f= (1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.0721 1.1487 1.2299 1.3159 1.4071 1 .5036 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.1046 1.21901.3439 1.4802 1.6289 1.7908 1.1157 1.2434 1.3842 1.5395 1.71031.8983 1.1268 1.2682 1.4258 1.6010 1.79592.0122 1.1381 1.2936 1.4685 1.66511.8856 2.1329 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 1.16101.34591.5580 1.8009 2.0789 2.3966 1.1726 1.3728 1.60471.8730 2.1829 2.5404 1.1843 1.40021.6528 1.9479 2.2920 2.6928 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 1.3478 1.8114 2.4273 3.2434 4.3219 5.7435 1.4166 1.99992.8139 3.9461 5.5160 7.6861 1.4889 2.2080 3.2620 4.8010 7.0400 10.2857 1.0000 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 5.4274 7.6123 10.6766 14.9745 1.0000 1.0000 1.0800 1.0900 1.1664 1.1881 1.25971.2950 1.3605 1.4116 1.4693 1.5386 1.5869 1.6771 1.7138 1.8280 1.8509 1.9926 1.9990 2.1719 2.1589 2.3674 2.3316 2.5804 2.5182 2.8127 2.7196 3.0658 2.9372 3.3417 3.1722 3.6425 3.4259 3.9703 3.7000 4.3276 3.9960 4.7171 4.3157 5.1417 4.6610 5.6044 6.8485 8.6231 10.0627 13.2677 14.7853 20.4140 21.7245 31.4094 1.0000 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 1 0.8347 17.4494 28.1024 45.2593 1.0000 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 17.0001 29.9599 52.7996 93.0510 1.0000 1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.1755 267.8635 35 *Used to compute the future value of a known present amount. For example: What is the accumulated value of $3,000 invested today at 8% compounded quarterly for 5 years? Using the factors of n= 20 and i= 2% (20 quarterly periods and a quarterly interest rate of 2%), the factor is 1.4859. The accumulated value is $4,457.70 ($3,000 x 1.4859). p=[i-a + ] TABLE B.3 Present Value of an Annuity of 1 Rate Periods 1% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% O co vo 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 32.8347 0.9804 0.9709 0.9615 1.9416 1.9135 1.8861 2.8839 2.8286 2.7751 3.8077 3.7171 3.6299 4.71354.5797 4.4518 5.6014 5.41725.2421 6.4720 6.23036.0021 7.3255 7.0197 8.1622 7.7861 7.4353 8.9826 8.53028.1109 9.7868 9.2526 8.7605 10.5753 9.9540 9.3851 11.3484 10.6350 9.9856 12.1062 11.2961 10.5631 12.8493 11.9379 11.1184 13.5777 12.5611 11.6523 14.291913.1661 12.1657 14.9920 13.7535 12.6593 15.6785 14.3238 13.1339 16.3514 14.8775 13.5903 19.5235 17.4131 15.6221 22.3965 19.6004 17.2920 24.9986 21.4872 18.6646 27.3555 23.1148 19.7928 0.9524 0.9434 0 .9346 0.9259 1.8594 1.8334 1.8080 1.7833 2.7232 2.6730 2.62432.5771 3.5460 3.4651 3.3872 3.3121 4.3295 4.2124 4.1002 3.9927 5.0757 4.9173 4 .7665 4.6229 5.7864 5.5824 5.3893 5.2064 6.4632 6.2098 5.9713 5.7466 7.1078 6.8017 6.5152 6.2469 7.7217 7.3601 7.0236 6.7101 8.3064 7.8869 7.49877.1390 8.8633 8.3838 7.9427 7.5361 9.3936 8.8527 8.3577 7.9038 9.8986 9.2950 8.74558.2442 10.37979.71229.10798.5595 10.8378 10.1059 9.4466 8.8514 11.2741 10.4773 9.7632 9.1216 11.6896 10.8276 10.0591 9 .3719 12.0853 11.1581 10.3356 9.6036 12.4622 11.4699 10.5940 9.8181 14.093912.7834 11.6536 10.6748 15.3725 13.7648 12.4090 11.2578 16.3742 14.4982 12.9477 11.6546 17.1591 15.0463 13.3317 11.9246 0.9174 0.9091 0.8929 0.8696 1.7591 1.73551.6901 1.6257 2.5313 2.4869 2.4018 2.2832 3.2397 3.16993.0373 2.8550 3.8897 3.7908 3.6048 3.3522 4.48594.3553 4.1114 3.7845 5.0330 4.8684 4.5638 4.1604 5.5348 5.3349 4.9676 4.4873 5.9952 5.7590 5.3282 4.7716 6.4177 6.1446 5.6502 5.0188 6.8052 6.4951 5.9377 5.2337 7.1607 6.81376.1944 5.4206 7.48697.1034 6.4235 5.5831 7.78627.3667 6.6282 5.7245 8.0607 7.6061 6.81095.8474 8.3126 7.8237 6.9740 5.9542 8.5436 8.0216 7.1196 6.0472 8.7556 8.2014 7.2497 6.1280 8.9501 8.36497.3658 6.1982 9.1285 8.5136 7.4694 6.2593 9.8226 9.0770 7.8431 6.4641 10.27379.42698.0552 6.5660 10.5668 9.6442 8.1755 6.6166 10.7574 9.77918.2438 6.6418 *Used to calculate the present value of a series of equal payments made at the end of each period. For example: What is the present value of $2,000 per year for 10 years assuming an annual interest rate of 9%? For (n= 10,i=9%), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today ($2,000 X 6.4177). f=[(1 + i)" 1]/i TABLE B.4 Future Value of an Annuity of 1 Rate 7% Periods 1% 2% 3% 4% 5% 6% 8% 9% 10% 12% 15% 11 12 13 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1200 3.0301 3.0604 3.0909 3.1216 3.15253.1836 3.2149 3.2464 3.2781 3.3100 3.3744 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.7507 5 .8666 5.9847 6.1051 6.3528 6.1520 6.3081 6.4684 6.6330 6.80196.9753 7.15337.33597.52337.7156 8.1152 7.21357.4343 7.66257.89838.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 8.2857 8.5830 8.89239 .2142 9.54919.8975 10.2598 10.6366 11.0285 11.4359 12.2997 9.3685 9.7546 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.7757 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 20.6546 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.97712 0.1407 21.3843 24.1331 13.8093 14.6803 15.6178 16.6268 17.7130 18.882120.1406 21.4953 22.9534 24.5227 28.0291 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 32.3926 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.360931.7725 37.2797 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 42.7533 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 33.750236.9737 40.5447 48.8837 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.999037.450241.3013 45.5992 55.7497 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 63.4397 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 72.0524 28.243232.0303 36.4593 41.6459 47.7271 54.8645 63.2490 73.1059 84.700998.3471 133.3339 34.7849 40.5681 47.5754 56.084966.4388 79.0582 94.4608 113.2832 136.3075 164.4940 241.3327 4 1.6603 49.994560.4621 73.6522 90.3203 111.4348 138.2369 172.3168 215.7108 271.0244 431.6635 48.8864 60.4020 75.4013 95.0255 120.7998 154.7620 199.6351 259.0565 337.8824 442.5926 767.0914 1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.0668 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.4436 212.7930 434.7451 881.1702 1.779.0903 15 16 35 40 Used to calculate the future value of a series of equal payments made at the end of each period. For example: What is the future value of $4,000 per year for 6 years assuming an annual interest rate of 8%? For (n=6,1 = 8%), the FV factor is 7.3359. $4.000 per year for 6 years accumulates to $29.343.60 ($4.000 x 7.3359)