Lasting Inc. has a defined benefit pension plan. One of its employees has vested benefits under the plan. During the current year, the employee earned an annual retirement benefit of $1,500. The employee has just reached the age of 45. Annual retirement payments will begin on the day the employee retires at the age of 65 and based on standard mortality tables the employee's life expectancy is 80, meaning the payments are expected to continue for 16 years after retirement. The implicit interest rates under the plan is 9%.

a. What will be the present value of the pension obligation at the time of the employee's retirement?

b. How much would the company have to contribute today in order to pay the pension benefits earned this year (the payments will begin in 20 years)?

TABLE 2 Present Value of $1 $1 PV = (1 + i)" wi 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 7.0% 8.0% 9.0% 0.0% 11.0% 12.0% 20.0% 10.99010 0.98522 0.98039 0.97561 0.97087 0.96618 0.96154 0.95694 0.95238 0.94787 0.94340 0.93458 0.92593 0.91743 0.909090 .90090 0.89286 0.83333 2 0.98030 0.97066 0.96117 0.95181 0.94260 0.93351 0.92456 0.91573 0.90703 0.89845 0.89000 0.87344 0.85734 0.84168 0.82645 0.81162 0.79719 0.69444 3 0.97059 0.95632 0.94232 0.92860 0.91514 0.90194 0.88900 0.87630 0.86384 0.85161 0.83962 0.81630 0.79383 0.77218 0.75131 0.73119 0.71178 0.57870 4 0.96098 0.94218 0.92385 0.90595 0.88849 0.87144 0.85480 0.83856 0.82270 0.80722 0.79209 0.76290 0.73503 0.70843 0.68301 0.65873 0.63552 0.48225 5 0.95147 0.92826 0.90573 0.88385 0.86261 0.84197 0.82193 0.80245 0.78353 0.76513 0.74726 0.71299 0.68058 0.64993 0.62092 0.59345 0.56743 0.40188 6 0.94205 0.91454 0.88797 0.86230 0.83748 0.81350 0.79031 0.76790 0.74622 0.72525 0.70496 0.66634 0.63017 0.59627 0.56447 0.53464 0.50663 0.33490 7 0.93272 0.90103 0.87056 0.84127 0.81309 0.78599 0.75992 0.73483 0.71068 0.68744 0.66506 0.62275 0.58349 0.54703 0.51316 0.48166 0.45235 0.27908 8 0.92348 0.88771 0.85349 0.82075 0.78941 0.75941 0.73069 0.70319 0.67684 0.65160 0.62741 0.58201 0.54027 0.50187 0.46651 0.43393 0.40388 0.23257 9 0.91434 0.87459 0.83676 0.80073 0.76642 0.73373 0.70259 0.67290 0.64461 0.61763 0.59190 0.54393 0.50025 0.46043 0.42410 0.39092 0.36061 0.19381 10 0.90529 0.86167 0.82035 0.78120 0.74409 0.70892 0.67556 0.64393 0.61391 0.58543 0.55839 0.50835 0.46319 0.42241 0.38554 0.35218 0.32197 0.16151 11 0.89632 0.84893 0.80426 0.76214 0.72242 12 0.88745 0.83639 0.78849 0.74356 0.70138 13 0.87866 0.82403 0.77303 0.72542 0.68095 14 0.86996 0.81185 0.75788 0.70773 0.66112 15 0.86135 0.79985 0.74301 0.69047 0.64186 0.68495 0.64958 0.66178 0.62460 0.63940 0.60057 0.61778 0.57748 0.59689 0.55526 0.61620 0.58468 0.55491 0.52679 0.47509 0.42888 0.38753 0.35049 0.31728 0.28748 0.58966 0.55684 0.52598 0.49697 0.44401 0.39711 0.35553 0.31863 0.28584 0.25668 0.56427 0.53032 0.49856 0.46884 0.41496 0.36770 0.32618 0.28966 0.25751 0.22917 0.53997 0.50507 0.47257 0.44230 0.38782 0.34046 0.29925 0.26333 0.23199 0.20462 0.51672 0.48102 0.44793 0.41727 0.36245 0.31524 0.27454 0.23939 0.20900 0.18270 0.13459 0.11216 0.09346 0.07789 0.06491 16 0.85282 0.78803 0.72845 0.67362 0.62317 0.57671 0.53391 0.49447 0.45811 0.42458 0.39365 0.33873 0.29189 0.25187 0.21763 0.18829 0.16312 0.05409 17 0.84438 0.77639 0.71416 0.65720 0.60502 0.55720 0.51337 0.47318 0.43630 0.40245 0.37136 0.31657 0.27027 0.23107 0.19784 0.16963 0.14564 0.04507 18 0.83602 0.76491 0.70016 0.64117 0.58739 0.53836 0.49363 0.45280 0.41552 0.38147 0.35034 0.29586 0.25025 0.21199 0.17986 0.15282 0.13004 0.03756 19 0.82774 0.75361 0.68643 0.62553 0.57029 0.52016 0.47464 0.43330 0.39573 0.36158 0.33051 0.27651 0.23171 0.19449 0.16351 0.13768 0.11611 0.03130 20 0.81954 0.74247 0.67297 0.61027 0.55368 0.50257 0.45639 0.41464 0.37689 0.34273 0.31180 0.25842 0.21455 0.17843 0.14864 0.12403 0.10367 0.02608 21 0.81143 0.73150 0.65978 0.59539 0.53755 0.48557 0.43883 0.39679 0.35894 0.32486 0.29416 0.24151 0.19866 0.16370 0.13513 0.11174 0.09256 0.02174 24 0.78757 0.69954 0.62172 0.55288 0.49193 0.43796 0.39012 0.34770 0.31007 0.27666 0.24698 0.19715 0.15770 0.12640 0.10153 0.08170 0.06588 0.01258 25 0.77977 0.68921 0.609530.53939 0.47761 0.42315 0.37512 0.33273 0.29530 0.26223 0.23300 0.18425 0.14602 0.11597 0.09230 0.07361 0.05882 0.01048 28 0.75684 0.65910 0.57437 0.50088 0.43708 0.38165 0.33348 0.29157 0.25509 0.22332 0.19563 0.15040 0.11591 0.08955 0.06934 0.05382 0.04187 0.00607 29 0.74934 0.64936 0.56311 0.48866 0.42435 0.36875 0.32065 0.27902 0.24295 0.21168 0.18456 0.14056 0.10733 0.08215 0.06304 0.04849 0.03738 0.00506 30 31 40 0.74192 0.63976 0.73458 0.63031 0.67165 0.55126 0.55207 0.47674 0.41199 0.54125 0.46511 0.39999 0.45289 0.37243 0.30656 0.35628 0.34423 0.25257 0.30832 0.26700 0.29646 0.25550 0.20829 0.17193 0.23138 0.20064 0.17411 0.13137 0.09938 0.07537 0.05731 0.22036 0.19018 0.16425 0.12277 0.09202 0.06915 0.05210 0.14205 0.11746 0.09722 0.06678 0.04603 0.03184 0.02209 0.04368 0.03338 0.00421 0.03935 0.02980 0.00351 0.01538 0.01075 0.00068 TABLE 1 Future Value of $1 FV = $1(1+i)" 20.0% 1.20000 1.44000 wi 1.0% 1 1.01000 2 1.02010 3 1.03030 4 1.04060 5 1.05101 1.5% 2.0% 1.01500 1.02000 1.03022 1.04040 1.04568 1.06121 1.06136 1.08243 1.07728 1.10408 2.5% 3.0% 1.02500 1.03000 1.05063 1.06090 1.07689 1.09273 1.10381 1.12551 1.13141 1.15927 3.5% 1.03500 1.07123 1.10872 1.14752 1.18769 4.0% 4.5% 5.0% 5.5% 1.04000 1.04500 1.05000 1.05500 1.08160 1.09203 1.10250 1.11303 1.12486 1.14117 1.15763 1.17424 1.16986 1.19252 1.21551 1.23882 1.21665 1.24618 1.27628 1.30696 6.0% 7.0% 1.06000 1.07000 1.12360 1.14490 1.191021.22504 1.26248 1.31080 1.33823 1.40255 8.0% 1.08000 1.16640 1.25971 1.36049 1.46933 9.0% 1.09000 1.18810 1.29503 1.41158 1.53862 10.0% 11.0% 1.10000 1.11000 1.21000 1.23210 1.33100 1.36763 1.46410 1.51807 1.610511.68506 12.0% 1.12000 1.25440 1.40493 1.57352 1.76234 1.72800 2.07360 2.48832 2.98598 3.58318 6 1.06152 7 1.07214 8 1.08286 9 1.09369 10 1.10462 1.09344 1.12616 1.10984 1.14869 1.12649 1.17166 1.14339 1.19509 1.16054 1.21899 1.15969 1.18869 1.21840 1.24886 1.28008 1.19405 1.22926 1.26532 1.30226 1.34010 1.37884 1.41852 1.22987 1.27228 1.31593 1.36086 1.40710 1.45468 1.50363 1.26677 1.31681 1.36857 1.42210 1.47746 1.53469 1.59385 1.30477 1.36290 1.42331 1.48610 1.55133 1.619091.68948 1.34392 1.41060 1.48024 1.55297 1.62889 1.70814 1.79085 1.50073 1.60578 1.71819 1.83846 1.96715 1.58687 1.67710 1.71382 1.82804 1.850931.99256 1.99900 2.17189 2.15892 2.36736 1.77156 1.87041 1.948722.07616 2.143592.30454 2.35795 2.55804 2.59374 2.83942 1.97382 2.21068 2.47596 2.77308 3.10585 4.29982 5.15978 6.19174 7.43008 8.91610 11 12 13 14 15 1.11567 1.17795 1.12683 1.19562 1.13809 1.21355 1.14947 1.23176 1.16097 1.25023 1.24337 1.26824 1.29361 1.31948 1.34587 1.31209 1.38423 1.34489 1.42576 1.37851 1.46853 1.41297 1.51259 1.44830 1.55797 1.45997 1.51107 1.56396 1.61869 1.67535 1.53945 1.60103 1.66507 1.73168 1.80094 1.62285 1.71034 1.802091.89830 1.69588 1.79586 1.90121 2.01220 1.77220 1.88565 2.00577 2.13293 1.85194 1.979932.116092.26090 1.93528 2.07893 2.23248 2.39656 2.10485 2.33164 2.25219 2.51817 2.40985 2.71962 2.57853 2.93719 2.759033.17217 2.58043 2.81266 3.06580 3.34173 3.64248 2.85312 3.13843 3.45227 3.79750 4.17725 3.15176 3.47855 3.49845 3.89598 3.88328 4.36349 4.31044 4.88711 4.784595.47357 10.69932 12.83918 15.40702 18.48843 22.18611 16 17 18 19 20 1.17258 1.18430 1.19615 1.20811 1.22019 1.26899 1.28802 1.30734 1.32695 1.34686 1.37279 1.48451 1.40024 1.52162 1.42825 1.55966 1.45681 1.59865 1.48595 1.63862 1.60471 1.73399 1.65285 1.79468 1.70243 1.85749 1.75351 192250 1.80611 1.98979 1.87298 2.02237 2.18287 2.35526 1.94790 2.11338 2.29202 2.48480 2.02582 2.20848 2.40662 2.62147 2.10685 2.30786 2.52695 2.76565 2.19112 2.41171 2.65330 2.91776 2.54035 2.69277 2.85434 3.02560 3.20714 2.95216 3.15882 3.37993 3.61653 3.86968 3.42594 3.70002 3.99602 4.31570 4.66096 3.97031 4.32763 4.71712 5.14166 5.60441 4.59497 5.05447 5.55992 6.11591 6.72750 5.310896.13039 5.895096.86604 6.54355 7.68997 7.26334 8.61276 8.06231 9.64629 26.62333 31.94800 38.33760 21 1.23239 1.36706 25 1.28243 1.45095 30 1.34785 1.56308 40 1.48886 1.81402 1.51567 1.67958 1.64061 1.85394 1.81136 2.09757 2.20804 2.68506 1.86029 2.05943 2.27877 2.52024 2.78596 3.07823 3.39956 2.09378 2.36324 2.66584 3.00543 3.38635 3.813394.29187 2.42726 2.80679 3.24340 3.74532 4.32194 4.98395 5.74349 3.26204 3.95926 4.80102 5.81636 7.03999 8.51331 10.28572 4.14056 5.03383 6.10881 7.40025 8.94917 5.427436.84848 8.62308 10.83471 13.58546 7.61226 10.06266 13.26768 17.44940 22.89230 14.97446 21.72452 31.40942 45.25926 65.00087 10.80385 17.00006 29.95992 93.05097 46.00512 95.39622 237.37631 1469.77160 TABLE 5 Future Value of an Annuity Due of $1 FVAD = m (1 + i)" - 11 x (1+i) w 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 7.0% 8.0% 0.0% 10.0% 11.0% 12.0% 20.0% 1 2 3 4 5 1.0100 2.0301 3.0604 4.1010 5.1520 1.0150 2.0452 3.0909 4.1523 5.2296 1.0200 2.0604 3.1216 4.2040 5.3081 1.0250 2.0756 3.1525 4.2563 5.3877 1.0300 1.0350 1.0400 2.0909 2.1062 2.1216 3.1836 3.21493.2465 4.30914.3625 4.4163 5.4684 5.5502 5.6330 10450 1.0500 2.1370 2.1525 3.2782 3.3101 4.4707 4.5256 5.71695.8019 1.0550 2.1680 3.3423 4.5811 5.8881 1.0600 2.1836 3.3746 4.6371 5.9753 1.0700 1.0800 1.0900 2.2149 2.2464 2.2781 3.4399 3.5061 3.5731 4.7507 4.8666 4.9847 6.15336.33596.5233 1.1000 2.3100 3.6410 5.1051 6.7156 1.1100 1.1200 2.3421 2.3744 3.7097 3.7793 5.2278 5.3528 6.91297.1152 1.2000 2.6400 4.3680 6.4416 89299 11.9159 6 7 8 9 10 6.21356.3230 6.43436.5474 7.2857 7.4328 7.5830 7.7361 8.3685 8.5593 8.75468.9545 9.4622 9.7027 9.9497 10.2034 10.5668 10.8633 11.1687 11.4835 6.6625 6.77946.89837.01927.1420 7.26697.3938 7.89238.0517 8.2142 8.3800 8.5491 8.7216 8.8975 9.1591 9.36859.5828 9.8021 10.0266 10.2563 10.4913 10.4639 10.7314 11.0061 11.2882 11.577911.8754 12.1808 11.8078 12. 1420 12.4864 12.8412 13.2068 13.5835 13.9716 7.6540 9.2598 10.9780 12.8164 14.7836 7.9228 8.2004 9.6366 10.0285 11.4876 12.0210 13.4866 14.1929 15.6455 16.5603 8.4872 10.4359 12.5795 14.9374 17.5312 8.7833 10.8594 13.1640 15.7220 18.5614 9.0890 11.2997 13.7757 16.5487 19.6546 15.4991 19.7989 24.9587 31.1504 11 11.6825 12.0412 12.4121 12.7956 13.1920 12 12.8093 13.2368 13.6803 14.1404 14.6178 13 139474 14.4504 14.9739 15.5190 16.0863 14 15.0969 15.6821 16.2934 16.9319 17.5989 15 16.2579 16.9324 17.6393 18.3802 19.1569 13.6020 14.0258 14.4640 15.1130 15.6268 16.1599 16.6770 17.291917.9321 18.2957 19.0236 19.7841 19.9710 20.824521.7193 14.9171 15.3856 16.7130 17.2868 18.5986 19.2926 20.5786 21.4087 22.657523.6411 15.8699 17.8821 20.0151 22.2760 24.6725 16.8885 19.1406 21.5505 24.1290 26.8881 17.9771 19.140720.3843 20.495321.9534 23.5227 23.2149 25.0192 26 9750 26.1521 28.3609 30.7725 29.3243 32.0034 34.9497 21.713223.1331 25.2116 27.0291 29.0949 31.3926 33.4054 36.2797 38.1899 41.7533 38.5805 47.4966 58.1959 71.0351 8 6.4421 16 17.4304 18.2014 19.0121 17 18.6147 19.4894 20.4123 18 19.8109 20.7967 21.8406 19 21.0190 22.1237 23.2974 20 22.2392 23.4705 24.7833 19.8647 20.7616 21.7050 22.6975 21.3863 22.4144 23.4997 24.6454 22.9460 24.1169 25.3572 26.6712 24.5447 25.8704 27.2797 28.7781 26.1833 27.6765 29.2695 30.9692 23.7417 25.8551 28.0636 30.3714 32.7831 24.8404 27.1324 29.5390 32.0660 34.7193 25.9964 27.2129 28.4812 29.9057 31.102732.7600 33.8683 35.7856 36.7861 38.9927 29.840232.7502 35.9737 39.5447 32.9990 36.4502 40.301344.5992 36.3790 40.446345.0185 50.1591 39.9955 44.762050.1601 56.2750 43.8652 49.4229 55.7645 63.0025 43.5008 47.8837 49.395954.7497 55.9395 62.4397 63.2028 71.0524 71.2651 80.6987 104.9306 127.1167 153.7400 185.6880 224.0256 21 23.4716 24.8376 26.2990 27.8629 29.5368 31.3289 33.2480 25 28.5256 30.5140 32.670935.0117 37.5530 40.3131 43.3117 30 35.1327 38.1018 41.379445.0003 49.0027 53.4295 58.3283 40 49.3752 55.0819 61.6100 69.0876 77.6633 87.5095 98.8265 35.3034 46.5706 63.7524 111.8467 37.5052 50.1135 69.7608 126.8398 39.8643 53.9660 76.4194 144. 1189 42.3923 48.0057 58.1564 67.6765 83.8017 101.0730 164.0477 213.6096 54.4568 78.9544 122.3459 279.7810 61.8733 92.3240 148.5752 368.2919 70.4027 80.2143 91.5026 108.1818 126.9988 149.3339 180.9434 220.9132 270.2926 486.8518 645.8269 859.1424 270.0307 566.3773 1418.2579 8812.6294 TABLE 3 Future Value of an Ordinary Annuity of $1 FVA - (1+1)" - 1 wi 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 7.0% 8.0% 0.0% 10.0% 11.0% 12.0% 20.0% 1.0000 2.2000 1 2 3 4 5 1.0000 2.0100 3.0301 4.0604 5.1010 1.0000 1.0000 2.0150 2.0200 3.0452 3.0604 4.09094.1216 5.1523 5.2040 1.0000 2.0250 3.0756 4.1525 5.2563 1.0000 2.0300 3.0909 4.1836 5.3091 1.0000 1.0000 1.0000 10000 1.0000 1.0000 2.0350 2.0400 2.0450 2.0500 2.0550 2.0600 3.1062 3.1216 3.1370 3.1525 3.16803.1836 4.21494.2465 4.2782 4.3101434234.3746 5.3625 5.41635.47075.5256 5.5811 5.6371 1.000 1.0000 2.0700 2.0800 3.21493.2464 4.4399 4.5061 5.75075.8666 1.0000 2.0900 3.2781 4.5731 59847 1.0000 2.1000 3.3100 4.6410 0.1051 10000 2.1100 3.3421 4.7097 6.2278 1.0000 2.1200 3.3744 4.7793 6.3528 3.6400 5.3680 7.4416 8.1152 6 7 8 9 10 6.1520 6.2296 6.3081 7.21357.3230 7.4343 8.2857 8.4328 8.5830 9.3685 9.55939.7546 10.4622 10.7027 10.9497 6.3877 7.5474 8.7361 9.9545 11.2034 6.4684 6.5502 7.6625 7.7794 8.89239.0517 10.1591 10.3685 11.4639 11.7314 6.6330 6.7169 7.89838.0192 9.2142 9.3800 10.5828 10.8021 12.0061 12.2882 8.1420 9.5491 11.0266 12.5779 6.8881 6.9753 7.1533 8.26698 .3938 8.6540 9.7216 9.8975 10.2598 11.2563 11.491311.9780 12.8754 13.1808 13.8164 7.33597.5233 8.9228 9.2004 10.6366 11.0285 12.4876 13.0210 14.4866 15.1929 7.7156 79129 9.4872 9.7833 11.435911.8594 13.5795 14.1640 15.9374 16.7220 10.0890 12.2997 14.7757 17.5487 9.9299 12.9159 16.4991 20.7989 25.9587 11 12 13 14 15 11.5668 11.8633 12.6825 13.0412 13.8093 14.2368 14.9474 15.4504 16.0969 16.6821 12.1687 13.4121 14.6803 15.9739 17.2934 12.4835 12.8078 13.1420 13.4864 13.8412 13.7956 14.1920 14.6020 15.0258 15.4640 15.1404 15.6178 16.1130 16.6268 17.1599 16.5190 17.0863 17.6770 18.291918.9321 17.9319 18.5989 19.2957 20.0236 20.7841 14.2068 15.9171 17.7130 19.5986 21.5786 14.5835 16.3856 18.2868 20.2926 22.4087 14.9716 16.8699 18.8821 21.0151 23.2760 15.7836 17.8885 20.1406 22.5505 25.1290 16.6455 18.9771 21.4953 24.2149 27.1521 17.5603 18.5312 20.1407 21.3843 22.9534 24.5227 26.0192 27.9750 29.360931.7725 19.5614 22.7132 26.2116 30.0949 34.4054 20.6546 32.1504 24.1331 39.5805 28.0291 48.4966 32.3926 59.1959 37.2797 72.0351 16 17.2579 17.9324 18.6393 19.3802 20.1569 17 18.4304 19.2014 20.0121 20.8647 21.7616 18 19.6147 20.4894 21.4123 22.3863 23.4144 19 20.8109 21.7967 22.8406 23.9460 25.1169 20 22.0190 23.1237 24.2974 25.5447 26.8704 20.9710 21.8245 22.7050 23.6975 24.4997 25.6454 26.3572 27.6712 28.2797 29.7781 22.7193 24.7417 26.8551 29.0636 31.3714 23.6575 25.8404 28.1324 30.5390 33,0660 24.6411 25.6725 27.8881 26.996428.212930.8402 29.4812 30.9057 33.9990 32.1027 33.7600 37.3790 34.8683 36.7856 40.9955 30.3243 33.0034 33.7502 36.9737 37.450241.3013 41.4463 46.0185 45.7620 51.1601 35.9497 40.5447 45.5992 51.1591 57.2750 39.1899 42.7533 44.5008 48.8837 50.395955.7497 56.9395 63.4397 64.2028 72.0524 8 7.4421 105.9306 128. 1167 154.7400 186.6880 21 23.2392 24.4705 25.7833 27.1833 28.676530.2695 31.9692 33.7831 30 34.7849 37.5387 40.5681 43.9027 47.5754 51.6227 56.084961.0071 40 48.8864 54.2679 60.4020 67.4026 75.4013 84.5503 95.0255 107.0303 35.7193 66.4388 120.7998 37.7861 72.4355 136.6056 39.9927 44.8652 79.058294.4608 154.7620 199.6351 50.4229 56.7645 113.2832 136.3075 259.0565337.8824 64.0025 72.2651 81.6987 225.0256 164.4940 199.0209241.3327 1181.8816 442.5926 581.8261 767.0914 7343.8578 TABLE 4 Present Value of an Ordinary Annuity of $1 PVA = w 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 70% 8.0% 9,0% 10.0% 11.0% 12.0% 20.0% 1 2 3 4 5 0.99010 0.98522 1.97040 1.95588 2.940992.91220 3.90197 3.85438 4.85343 4.78264 0.980390.975610.97087 1.94156 1.92742 1.91347 2.88388 2.85602 2.82861 3.80773 3.76197 3.71710 4.71346 4.64583 4.57971 0.96618 0.96154 0.95694 1.899691.886091.87267 2.80164 2.77509 2.74896 3.67308 3.62990 3.58753 4.51505 4.45182 4.38998 0.95238 1.85941 2.72325 3.54595 4.32948 0.94787 1.84632 2.69793 3.50515 4.27028 0.94340 1.83339 2.67301 3.46511 4.21236 0.93458 1.80802 2.62432 3.38721 4.10020 0.92593 1.78326 2.57710 3.31213 3.99271 0.91743 0.909090.90090 0.89286 0.83333 1.75911 1.73554 1.71252 1.69005 1.52778 2.53129 2.48685 2.44371 2.40183 2.10648 3.23972 3.16987 3.10245 3.03735 2.58873 3.88965 3.79079 3.69590 3.60478 2.99061 5.79548 5.69719 5.60143 5.508135.41719 5.32855 5.24214 5.15787 5.07569 4.99553 4.91732 4.76654 4.62285 4.48592 4.35526 4.23054 4.11141 3.32551 7 6.72819 6.59821 6.47199 6.349396.23028 6.11454 6.00205 5.89270 5.78637 5.68297 5.58238 5.38929 5.20637 5.03295 4.86842 4.71220 4.56376 3.60459 8 9 10 7.65168 8.56602 9.47130 7.485937.32548 8.36052 8.16224 9.22218 8.98259 7.170147.01969 7970877.78611 8.75206 8.53020 6.87396 6.73274 7.60769743533 8.31661 8.11090 6.595896.46321 6.33457 7.26879710782 6.95220 7.91272 7.721737.53763 6.20979 5.97130 5.74664 6.801696.515236.24689 7.360097.02358 6.71008 5.53482 5.33493 5.14612 4.96764 3.83716 5.99525 5.75902 5.53705 5.32825 4.03097 6.41766 6.14457 5.88923 5.65022 4.19247 11 10.36763 12 11.25508 13 12.13374 14 13.00370 15 13.86505 10.07112 10.90751 11.73153 12.54338 13.34323 9.78685 10.57534 11.34837 12.10625 12.84926 9.51421 10.25776 10.98319 11.69091 12.38138 9.252629.00155 9.95400 9.66333 10.63496 10.30274 11.29607 10.92052 11.93794 11.51741 8.76048 9.38507 9.98565 10.56312 11.11839 8.52892 9.11858 9.68285 10.22283 10.73955 8.30641 8.86325 9.39357 9.89864 10.37966 8.09254 8.61852 9.11708 9.58965 10.03758 7.88687 8.38384 8.85268 9.29498 9.71225 7.49867 7.94269 8.35765 8.74547 9.10791 7.13896 6.80519 6.49506 6.20652 5.93770 4.32706 7.53608 7.16073 6.81369 6.49236 6.19437 4.43922 7.90378 7.486907.10336 6.74987 6.42355 4.53268 8.24424 7.78615 7.36669 6.98187 6.62817 4.61057 8.559488060697.60608 7.19087 6.81086 4.67547 16 17 14.71787 14.13126 15.56225 14.90765 13.57771 14.29187 13.05500 12.56110 13.7122013.16612 12.09412 12.65132 11.65230 12.16567 11.23402 11.70719 10.83777 10.46216 10.105909.446658.85137 11.27407 10.86461 10.47726 9.76322 9.12164 8.31256 7.82371 8.54363 8.02155 7.37916 7.54879 6.97399 7.11963 4.72956 4.77463 18 19 20 16.39827 1722601 18.04555 15.67256 16,42617 17.16864 14.99203 14.35336 15.67846 14.97889 16.35143 15.58916 13.75351 14.32380 14.87747 13.18968 13.70984 14.21240 12.65930 13.13394 13.59033 12.15999 12.59329 13.00794 11.68959 12.08532 12.46221 11.24607 11.60765 11.95038 10.82760 11.15812 11.46992 10.059099.37189 10.33560 9.60360 10.59401 9.81815 8.75563 895011 9.12855 8.20141 7.701627.24967 4.81219 8.36492 7839297.36578 4.84350 8.51356 7.96333 7.46944 4.86958 10.83553 11.65358 10.01680 10.67478 9.29224 9.82258 8.64869 9.07704 8.07507 8.42174 7.56200 7.84314 4.89132 4.94759 21 18.85698 25 22.02316 30 25.80771 40 32.83469 17.90014 17.01121 20.71961 19.52346 24.01584 22.39646 29.91585 27.35548 16.18455 18.42438 20.93029 25.10278 15.41502 17.41315 19.60044 23.11477 14.69797 14.02916 13.40472 16.48151 15.62208 14.82821 18.39205 17.29203 16.28889 21.35507 19.79277 18.40158 12.82115 14.09394 15.37245 17.15909 12.27524 13.41393 14.53375 16.04612 11.76408 12.78336 13. 15.04630 13.33171 11.92461 10.75736 9.77905 8.95105 8.24378 4.99660 TABLE 6 Present Value of an Annuity Due of $1 PVAD = X (1+i) w 1 2 3 4 1.0% 1.00000 1.99010 2.97040 3.94099 1.5% 1.00000 1.98522 2.95588 3.91220 2.0% 1.00000 1.98039 2.94156 3.88388 2.5% 3.0% 1.000001.00000 1.97561 1.97087 2.927422.91347 3.85602 3.82861 4.71710 3.5% 4.0% 4.5% 5.0% 1.00000 1.00000 1.00000 1.00000 1.96618 1.96154 1.95694 1.95238 2.899692.886092.872672.85941 3.80164 3.77509 3.74896 3.72325 4.67308 4.62990 4.58753 4.54595 5,5% 1.00000 1.94787 2.84632 3.69793 4.50515 6.0% 1.00000 1.94340 2.83339 3.67301 4.46511 70% 8.0% 0.0% 1.00000 1.00000 1.00000 1.93458 1.92593 1.91743 2.808022.78326 2.75911 3.62432 3.57710 3.53129 4.38721 4312134.23972 0.0% 11.0% 12.0% 20.0% 1.00000 1.00000 1.00000 1.00000 1.90909 1.90090 1.89286 1.83333 2.73554 2.71252 2.69005 2.52778 3.48685 3.44371 3.40183 3.10648 4.16987 4.10245 4.037353 6 7 8 9 5.85343 6.79548 7.72819 8.65168 5.78264 5.71346 5.64583 5.57971 5.51505 6.69719 6.60143 6.508136.417196.32855 7.59821 7.471997.349397.23028 7.11454 8.485938.32548 8.170148.01969 7.87396 5.45182 6.24214 7.00205 7.73274 5.38998 5.32948 6.157876.07569 6.892706.78637 7.595897.46321 5.27028 5.99553 6.68297 7.33457 5.21236 5.10020 4.99271 5.91732 5.766545.62288 6.58238 6.389296.20637 7.209796.97130 6.74664 4.88965 4.79079 5.48592 5.35526 6.032955.86842 6.53482 6.33493 4.69590 5.23054 5.71220 6.14612 4.60478 3.99061 5.111414 .32551 5.56376 4.60459 5.96764 4.83716 109.56602 9.36052 9.16224 8.97087 8.78611 8.607698.43533 8.26879 8.10782 7.95220 7.801697.51523 7.246896.99525 6.75902 6.53705 6.328255.03097 11 10.47130 12 11.36763 13 12.25508 14 13.13374 15 14.00370 10.22218 11.07112 11.90751 12.73153 13.54338 9.98259 10.78685 11.57534 12.34837 13.10625 9.75206 10.51421 11.25776 11.98318 12.69091 9.53020 10.25262 10.95400 11.63496 12.29607 9.31661 9.11090 8.91272 8.72173 10.00155 9.76048 9.528929.30641 10.66333 10.38507 10.11858 9.86325 11.30274 10.98565 10.68285 10.39357 11.92052 11.56312 11.22283 10.89864 8.53763 9.09254 9.61852 10.11708 10.58965 8.360098.02358 7.71008 8886878.49867 8.13896 9.38384 8.942698.53608 9.85268 9.35765 8.90378 10.29498 9.745479.24424 7.41766 7.14457 6.88923 6.650225.19247 7.80519 7.49506 7.20652 6.93770 532706 8.160737.813697 .49236 7.19437 5.43922 8.48690 8.10336 7.74987 7.42355 5.53268 8.78615 8.36669 798187 7.62817 5.61057 16 14.86505 17 15.71787 18 16.56225 1917.39827 20 18.22601 14.34323 15.13126 15.90765 16.67256 17.42617 13.84926 13.38138 14.57771 14.05500 15.29187 14.71220 15.99203 15.35336 16.67846 15.97889 12.93794 12.51741 12.11839 13.56110 13.09412 12.65230 14.16612 13.65132 13.16567 14.75351 14.18968 13.65930 15.32380 14.70984 14.13394 11.73955 11.37966 11.03758 12 23402 11.83777 11.46216 12.70719 12.27407 11.86461 13.15999 12.68959 12.24607 13.59329 13.08532 12.60765 10.71225 11.10590 11.47726 11.82760 12.15812 10.10791 10.44665 10.76322 11.05909 11.33560 9.55948 9.85137 10.12164 10.37189 10.60360 9.060698.60608 8.19087 7.81086 5.67547 9.31256 8.82371 8.37916 7.97399 5.72956 9.54363 9.02155 8.54879 8.11963 5.77463 9.95011 9.36492 8.83929 8.36578 5.84350 21 19.04555 18.16864 25 22 24339 21.03041 30 26.06579 24.37608 40 33.16303 30.36458 17.35143 16.58916 19 91393 18.88499 22.84438 21.45355 27.90259 25.73034 15.87747 15.21240 14.59033 14.00794 1793554 17.05837 16 24696 15.49548 20.18845 19.03577 17.98371 17.02189 23.80822 22.10250 20.58448 19.22966 13.46221 14.79864 16.14107 18.01704 12.95038 14.15170 15.33310 16.92866 12.46992 11.59401 13.55036 12.46933 14.59072 13.27767 15.94907 14.26493 10.81815 10.12855 11.52876 10.70661 12.15841 11.19828 12.87858 11.72552 9.51356 8.96333 8.469445.86958 998474 934814 8.78432 593710 10.36961 9.65011 9.02181 5.97472 10.75696 9.93567 9.23303599592