Question
Kunkle Company wishes to earn 20% annually on its investments. If Kunkle makes an investment that equals or exceeds that rate, it considers it a
Kunkle Company wishes to earn 20% annually on its investments. If Kunkle makes an investment that equals or exceeds that rate, it considers it a success. Assume that Kunkle invests $2 million and gets $500,000 in return at the end of each year for X years. Assume that Kunkle can't invest for fractional parts of a year. What is the minimum value of X (number of years) for which Kunkle will consider the investment a success?
Table 1 Future value of $1 FV = $1(1+i)n
n/i | 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% | 10.0% | 11.0% | 12.0% | 20.0% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1.01000 | 1.01500 | 1.02000 | 1.02500 | 1.03000 | 1.03500 | 1.04000 | 1.04500 | 1.05000 | 1.05500 | 1.06000 | 1.07000 | 1.08000 | 1.09000 | 1.10000 | 1.11000 | 1.12000 | 1.20000 |
2 | 1.02010 | 1.03022 | 1.04040 | 1.05063 | 1.06090 | 1.07123 | 1.08160 | 1.09203 | 1.10250 | 1.11303 | 1.12360 | 1.14490 | 1.16640 | 1.18810 | 1.21000 | 1.23210 | 1.25440 | 1.44000 |
3 | 1.03030 | 1.04568 | 1.06121 | 1.07689 | 1.09273 | 1.10872 | 1.12486 | 1.14117 | 1.15763 | 1.17424 | 1.19102 | 1.22504 | 1.25971 | 1.29503 | 1.33100 | 1.36763 | 1.40493 | 1.72800 |
4 | 1.04060 | 1.06136 | 1.08243 | 1.10381 | 1.12551 | 1.14752 | 1.16986 | 1.19252 | 1.21551 | 1.23882 | 1.26248 | 1.31080 | 1.36049 | 1.41158 | 1.46410 | 1.51807 | 1.57352 | 2.07360 |
5 | 1.05101 | 1.07728 | 1.10408 | 1.13141 | 1.15927 | 1.18769 | 1.21665 | 1.24618 | 1.27628 | 1.30696 | 1.33823 | 1.40255 | 1.46933 | 1.53862 | 1.61051 | 1.68506 | 1.76234 | 2.48832 |
6 | 1.06152 | 1.09344 | 1.12616 | 1.15969 | 1.19405 | 1.22926 | 1.26532 | 1.30226 | 1.34010 | 1.37884 | 1.41852 | 1.50073 | 1.58687 | 1.67710 | 1.77156 | 1.87041 | 1.97382 | 2.98598 |
7 | 1.07214 | 1.10984 | 1.14869 | 1.18869 | 1.22987 | 1.27228 | 1.31593 | 1.36086 | 1.40710 | 1.45468 | 1.50363 | 1.60578 | 1.71382 | 1.82804 | 1.94872 | 2.07616 | 2.21068 | 3.58318 |
8 | 1.08286 | 1.12649 | 1.17166 | 1.21840 | 1.26677 | 1.31681 | 1.36857 | 1.42210 | 1.47746 | 1.53469 | 1.59385 | 1.71819 | 1.85093 | 1.99256 | 2.14359 | 2.30454 | 2.47596 | 4.29982 |
9 | 1.09369 | 1.14339 | 1.19509 | 1.24886 | 1.30477 | 1.36290 | 1.42331 | 1.48610 | 1.55133 | 1.61909 | 1.68948 | 1.83846 | 1.99900 | 2.17189 | 2.35795 | 2.55804 | 2.77308 | 5.15978 |
10 | 1.10462 | 1.16054 | 1.21899 | 1.28008 | 1.34392 | 1.41060 | 1.48024 | 1.55297 | 1.62889 | 1.70814 | 1.79085 | 1.96715 | 2.15892 | 2.36736 | 2.59374 | 2.83942 | 3.10585 | 6.19174 |
11 | 1.11567 | 1.17795 | 1.24337 | 131209 | 1.38423 | 1.45997 | 1.53945 | 1.62285 | 1.71034 | 1.80209 | 1.89830 | 2.10485 | 2.33164 | 2.58043 | 2.85312 | 3.15176 | 3.47855 | 7.43008 |
12 | 1.12683 | 1.19562 | 1.26824 | 1.34489 | 1.42576 | 1.51107 | 1.60103 | 1.69588 | 1.79586 | 1.90121 | 2.01220 | 2.25219 | 2.51817 | 2.81266 | 3.13843 | 3.49845 | 3.89598 | 8.91610 |
13 | 1.13809 | 1.21355 | 1.29361 | 1.37851 | 1.46853 | 1.56396 | 1.66507 | 1.77220 | 1.88565 | 2.00577 | 2.13293 | 2.40985 | 2.71962 | 3.06580 | 3.45227 | 3.88328 | 4.36349 | 10.69932 |
14 | 1.14947 | 1.23176 | 1.31948 | 1.41297 | 1.51259 | 1.61869 | 1.73168 | 1.85194 | 1.97993 | 2.11609 | 2.26090 | 2.57853 | 2.93719 | 3.34173 | 3.79750 | 4.31044 | 4.88711 | 12.83918 |
15 | 1.16097 | 1.25023 | 1.34587 | 1.44830 | 1.55797 | 1.67535 | 1.80094 | 1.93528 | 2.07893 | 2.23248 | 2.39656 | 2.75903 | 3.17217 | 3.64248 | 4.17725 | 4.78459 | 5.47357 | 15.40702 |
16 | 1.17258 | 1.26899 | 1.37279 | 1.48451 | 1.60471 | 1.73399 | 1.87298 | 2.02237 | 2.18287 | 2.35526 | 2.54035 | 2.95216 | 3.42594 | 3.97031 | 4.59497 | 5.31089 | 6.13039 | 18.48843 |
17 | 1.18430 | 1.28802 | 1.40024 | 1.52162 | 1.65285 | 1.79468 | 1.94790 | 2.11338 | 2.29202 | 2.48480 | 2.69277 | 3.15882 | 3.70002 | 4.32763 | 5.05447 | 5.89509 | 6.86604 | 22.18611 |
18 | 1.19615 | 1.30734 | 1.42825 | 1.55966 | 1.70243 | 1.85749 | 2.02582 | 2.20848 | 2.40662 | 2.62147 | 2.85434 | 3.37993 | 3.99602 | 4.71712 | 5.55992 | 6.54355 | 7.68997 | 26.62333 |
19 | 1.20811 | 1.32695 | 1.45681 | 1.59865 | 1.75351 | 1.92250 | 2.10685 | 2.30786 | 2.52695 | 2.76565 | 3.02560 | 3.61653 | 4.31570 | 5.14166 | 6.11591 | 7.26334 | 8.61276 | 31.94800 |
20 | 1.22019 | 1.34686 | 1.48595 | 1.63862 | 1.80611 | 1.98979 | 2.19112 | 2.41171 | 2.65330 | 2.91776 | 3.20714 | 3.86968 | 4.66096 | 5.60441 | 6.72750 | 8.06231 | 9.64629 | 38.33760 |
21 | 1.23239 | 1.36706 | 1.51567 | 1.67958 | 1.86029 | 2.05943 | 2.27877 | 2.52024 | 2.78596 | 3.07823 | 3.39956 | 4.14056 | 5.03383 | 6.10881 | 7.40025 | 8.94917 | 10.80385 | 46.00512 |
25 | 1.28243 | 1.45095 | 1.64061 | 1.85394 | 2.09378 | 2.36324 | 2.66584 | 3.00543 | 3.38635 | 3.81339 | 4.29187 | 5.42743 | 6.84848 | 8.62308 | 10.83471 | 13.58546 | 17.00006 | 95.39622 |
30 | 1.34785 | 1.56308 | 1.81136 | 2.09757 | 2.42726 | 2.80679 | 3.24340 | 3.74532 | 4.32194 | 4.98395 | 5.74349 | 7.61226 | 10.06266 | 13.26768 | 17.44940 | 22.89230 | 29.95992 | 237.37631 |
40 | 1.48886 | 1.81402 | 2.20804 | 2.68506 | 3.26204 | 3.95926 | 4.80102 | 5.81636 | 7.03999 | 8.51331 | 10.28572 | 14.97446 | 21.72452 | 31.40942 | 45.25926 | 65.00087 | 93.05097 | 1469.77160 |
TABLE 2 Present value of $1 PV = $1/(1 + i)n
n/i | 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% | 10.0% | 11.0% | 12.0% | 20.0% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.99010 | 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 | 0.90909 | 0.90090 | 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 | 0.68495 | 0.64958 | 0.61620 | 0.58468 | 0.55491 | 0.52679 | 0.47509 | 0.42888 | 0.38753 | 0.35049 | 0.31728 | 0.28748 | 0.13459 |
12 | 0.88745 | 0.83639 | 0.78849 | 0.74356 | 0.70138 | 0.66178 | 0.62460 | 0.58966 | 0.55684 | 0.52598 | 0.49697 | 0.44401 | 0.39711 | 0.35553 | 0.31863 | 0.28584 | 0.25668 | 0.11216 |
13 | 0.87866 | 0.82403 | 0.77303 | 0.72542 | 0.68095 | 0.63940 | 0.60057 | 0.56427 | 0.53032 | 0.49856 | 0.46884 | 0.41496 | 0.36770 | 0.32618 | 0.28966 | 0.25751 | 0.22917 | 0.09346 |
14 | 0.86996 | 0.81185 | 0.75788 | 0.70773 | 0.66112 | 0.61778 | 0.57748 | 0.53997 | 0.50507 | 0.47257 | 0.44230 | 0.38782 | 0.34046 | 0.29925 | 0.26333 | 0.23199 | 0.20462 | 0.07789 |
15 | 0.86135 | 0.79985 | 0.74301 | 0.69047 | 0.64186 | 0.59689 | 0.55526 | 0.51672 | 0.48102 | 0.44793 | 0.41727 | 0.36245 | 0.31524 | 0.27454 | 0.23939 | 0.20900 | 0.18270 | 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 | 0.60953 | 0.53939 | 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 | 0.74192 | 0.63976 | 0.55207 | 0.47674 | 0.41199 | 0.35628 | 0.30832 | 0.26700 | 0.23138 | 0.20064 | 0.17411 | 0.13137 | 0.09938 | 0.07537 | 0.05731 | 0.04368 | 0.03338 | 0.00421 |
31 | 0.73458 | 0.63031 | 0.54125 | 0.46511 | 0.39999 | 0.34423 | 0.29646 | 0.25550 | 0.22036 | 0.19018 | 0.16425 | 0.12277 | 0.09202 | 0.06915 | 0.05210 | 0.03935 | 0.02980 | 0.00351 |
40 | 0.67165 | 0.55126 | 0.45289 | 0.37243 | 0.30656 | 0.25257 | 0.20829 | 0.17193 | 0.14205 | 0.11746 | 0.09722 | 0.06678 | 0.04603 | 0.03184 | 0.02209 | 0.01538 | 0.01075 | 0.00068 |
Table 3 Future Value of an Ordinary Annuity of $1 FVA = ((1+i)n 1)/i
n/i | 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% | 10.0% | 11.0% | 12.0% | 20.0% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
2 | 2.0100 | 2.0150 | 2.0200 | 2.0250 | 2.0300 | 2.0350 | 2.0400 | 2.0450 | 2.0500 | 2.0550 | 2.0600 | 2.0700 | 2.0800 | 2.0900 | 2.1000 | 2.1100 | 2.1200 | 2.2000 |
3 | 3.0301 | 3.0452 | 3.0604 | 3.0756 | 3.0909 | 3.1062 | 3.1216 | 3.1370 | 3.1525 | 3.1680 | 3.1836 | 3.2149 | 3.2464 | 3.2781 | 3.3100 | 3.3421 | 3.3744 | 3.6400 |
4 | 4.0604 | 4.0909 | 4.1216 | 4.1525 | 4.1836 | 4.2149 | 4.2465 | 4.2782 | 4.3101 | 4.3423 | 4.3746 | 4.4399 | 4.5061 | 4.5731 | 4.6410 | 4.7097 | 4.7793 | 5.3680 |
5 | 5.1010 | 5.1523 | 5.2040 | 5.2563 | 5.3091 | 5.3625 | 5.4163 | 5.4707 | 5.5256 | 5.5811 | 5.6371 | 5.7507 | 5.8666 | 5.9847 | 6.1051 | 6.2278 | 6.3528 | 7.4416 |
6 | 6.1520 | 6.2296 | 6.3081 | 6.3877 | 6.4684 | 6.5502 | 6.6330 | 6.7169 | 6.8019 | 6.8881 | 6.9753 | 7.1533 | 7.3359 | 7.5233 | 7.7156 | 7.9129 | 8.1152 | 9.9299 |
7 | 7.2135 | 7.3230 | 7.4343 | 7.5474 | 7.6625 | 7.7794 | 7.8983 | 8.0192 | 8.1420 | 8.2669 | 8.3938 | 8.6540 | 8.9228 | 9.2004 | 9.4872 | 9.7833 | 10.0890 | 12.9159 |
8 | 8.2857 | 8.4328 | 8.5830 | 8.7361 | 8.8923 | 9.0517 | 9.2142 | 9.3800 | 9.5491 | 9.7216 | 9.8975 | 10.2598 | 10.6366 | 11.0285 | 11.4359 | 11.8594 | 12.2997 | 16.4991 |
9 | 9.3685 | 9.5593 | 9.7546 | 9.9545 | 10.1591 | 10.3685 | 10.5828 | 10.8021 | 11.0266 | 11.2563 | 11.4913 | 11.9780 | 12.4876 | 13.0210 | 13.5795 | 14.1640 | 14.7757 | 20.7989 |
10 | 10.4622 | 10.7027 | 10.9497 | 11.2034 | 11.4639 | 11.7314 | 12.0061 | 12.2882 | 12.5779 | 12.8754 | 13.1808 | 13.8164 | 14.4866 | 15.1929 | 15.9374 | 16.7220 | 17.5487 | 25.9587 |
11 | 11.5668 | 11.8633 | 12.1687 | 12.4835 | 12.8078 | 13.1420 | 13.4864 | 13.8412 | 14.2068 | 14.5835 | 14.9716 | 15.7836 | 16.6455 | 17.5603 | 18.5312 | 19.5614 | 20.6546 | 32.1504 |
12 | 12.6825 | 13.0412 | 13.4121 | 13.7956 | 14.1920 | 14.6020 | 15.0258 | 15.4640 | 15.9171 | 16.3856 | 16.8699 | 17.8885 | 18.9771 | 20.1407 | 21.3843 | 22.7132 | 24.1331 | 39.5805 |
13 | 13.8093 | 14.2368 | 14.6803 | 15.1404 | 15.6178 | 16.1130 | 16.6268 | 17.1599 | 17.7130 | 18.2868 | 18.8821 | 20.1406 | 21.4953 | 22.9534 | 24.5227 | 26.2116 | 28.0291 | 48.4966 |
14 | 14.9474 | 15.4504 | 15.9739 | 16.5190 | 17.0863 | 17.6770 | 18.2919 | 18.9321 | 19.5986 | 20.2926 | 21.0151 | 22.5505 | 24.2149 | 26.0192 | 27.9750 | 30.0949 | 32.3926 | 59.1959 |
15 | 16.0969 | 16.6821 | 17.2934 | 17.9319 | 18.5989 | 19.2957 | 20.0236 | 20.7841 | 21.5786 | 22.4087 | 23.2760 | 25.1290 | 27.1521 | 29.3609 | 31.7725 | 34.4054 | 37.2797 | 72.0351 |
16 | 17.2579 | 17.9324 | 18.6393 | 19.3802 | 20.1569 | 20.9710 | 21.8245 | 22.7193 | 23.6575 | 24.6411 | 25.6725 | 27.8881 | 30.3243 | 33.0034 | 35.9497 | 39.1899 | 42.7533 | 87.4421 |
17 | 18.4304 | 19.2014 | 20.0121 | 20.8647 | 21.7616 | 22.7050 | 23.6975 | 24.7417 | 25.8404 | 26.9964 | 28.2129 | 30.8402 | 33.7502 | 36.9737 | 40.5447 | 44.5008 | 48.8837 | 105.9306 |
18 | 19.6147 | 20.4894 | 21.4123 | 22.3863 | 23.4144 | 24.4997 | 25.6454 | 26.8551 | 28.1324 | 29.4812 | 30.9057 | 33.9990 | 37.4502 | 41.3013 | 45.5992 | 50.3959 | 55.7497 | 128.1167 |
19 | 20.8109 | 21.7967 | 22.8406 | 23.9460 | 25.1169 | 26.3572 | 27.6712 | 29.0636 | 30.5390 | 32.1027 | 33.7600 | 37.3790 | 41.4463 | 46.0185 | 51.1591 | 56.9395 | 63.4397 | 154.7400 |
20 | 22.0190 | 23.1237 | 24.2974 | 25.5447 | 26.8704 | 28.2797 | 29.7781 | 31.3714 | 33.0660 | 34.8683 | 36.7856 | 40.9955 | 45.7620 | 51.1601 | 57.2750 | 64.2028 | 72.0524 | 186.6880 |
21 | 23.2392 | 24.4705 | 25.7833 | 27.1833 | 28.6765 | 30.2695 | 31.9692 | 33.7831 | 35.7193 | 37.7861 | 39.9927 | 44.8652 | 50.4229 | 56.7645 | 64.0025 | 72.2651 | 81.6987 | 225.0256 |
30 | 34.7849 | 37.5387 | 40.5681 | 43.9027 | 47.5754 | 51.6227 | 56.0849 | 61.0071 | 66.4388 | 72.4355 | 79.0582 | 94.4608 | 113.2832 | 136.3075 | 164.4940 | 199.0209 | 241.3327 | 1181.8816 |
40 | 48.8864 | 54.2679 | 60.4020 | 67.4026 | 75.4013 | 84.5503 | 95.0255 | 107.0303 | 120.7998 | 136.6056 | 154.7620 | 199.6351 | 259.0565 | 337.8824 | 442.5926 | 581.8261 | 767.0914 | 7343.8578 |
Table 4 Present Value of an Ordinary Annuity of $1 PVA = (1 - (1/(1 + i)n))/i
n/i | 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% | 10.0% | 11.0% | 12.0% | 20.0% |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.99010 | 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 | 0.90909 | 0.90090 | 0.89286 | 0.83333 |
2 | 1.97040 | 1.95588 | 1.94156 | 1.92742 | 1.91347 | 1.89969 | 1.88609 | 1.87267 | 1.85941 | 1.84632 | 1.83339 | 1.80802 | 1.78326 | 1.75911 | 1.73554 | 1.71252 | 1.69005 | 1.52778 |
3 | 2.94099 | 2.91220 | 2.88388 | 2.85602 | 2.82861 | 2.80164 | 2.77509 | 2.74896 | 2.72325 | 2.69793 | 2.67301 | 2.62432 | 2.57710 | 2.53129 | 2.48685 | 2.44371 | 2.40183 | 2.10648 |
4 | 3.90197 | 3.85438 | 3.80773 | 3.76197 | 3.71710 | 3.67308 | 3.62990 | 3.58753 | 3.54595 | 3.50515 | 3.46511 | 3.38721 | 3.31213 | 3.23972 | 3.16987 | 3.10245 | 3.03735 | 2.58873 |
5 | 4.85343 | 4.78264 | 4.71346 | 4.64583 | 4.57971 | 4.51505 | 4.45182 | 4.38998 | 4.32948 | 4.27028 | 4.21236 | 4.10020 | 3.99271 | 3.88965 | 3.79079 | 3.69590 | 3.60478 | 2.99061 |
6 | 5.79548 | 5.69719 | 5.60143 | 5.50813 | 5.41719 | 5.32855 | 5.24214 | 5.15787 | 5.07569 | 4.99553 | 4.91732 | 4.76654 | 4.62288 | 4.48592 | 4.35526 | 4.23054 | 4.11141 | 3.32551 |
7 | 6.72819 | 6.59821 | 6.47199 | 6.34939 | 6.23028 | 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 | 7.65168 | 7.48593 | 7 32548 | 7.17014 | 7.01969 | 6.87396 | 6.73274 | 6.59589 | 6.46321 | 6.33457 | 6.20979 | 5.97130 | 5.74664 | 5.53482 | 5.33493 | 5.14612 | 4.96764 | 3.83716 |
9 | 8.56602 | 8.36052 | 8.16224 | 7.97087 | 7.78611 | 7.60769 | 7.43533 | 7.26879 | 7.10782 | 6.95220 | 6.80169 | 6.51523 | 6.24689 | 5.99525 | 5.75902 | 5.53705 | 5.32825 | 4.03097 |
10 | 9.47130 | 9.22218 | 8.98259 | 8.75206 | 8.53020 | 8.31661 | 8.11090 | 7.91272 | 7.72173 | 7.53763 | 7.36009 | 7.02358 | 6.71008 | 6.41766 | 6.14457 | 5.88923 | 5.65022 | 4.19247 |
11 | 10.36763 | 10.07112 | 9.78685 | 9.51421 | 9.25262 | 9.00155 | 8.76048 | 8.52892 | 8.30641 | 8.09254 | 7.88687 | 7.49867 | 7.13896 | 6.80519 | 6.49506 | 6.20652 | 5.93770 | 4.32706 |
12 | 11.25508 | 10.90751 | 10.57534 | 10.25776 | 9.95400 | 9.66333 | 9.38507 | 9.11858 | 8.86325 | 8.61852 | 8.38384 | 7.94269 | 7.53608 | 7.16073 | 6.81369 | 6.49236 | 6.19437 | 4.43922 |
13 | 12.13374 | 11.73153 | 11.34837 | 10.98319 | 10.63496 | 10.30274 | 9.98565 | 9.68285 | 9.39357 | 9.11708 | 8.85268 | 8.35765 | 7.90378 | 7.48690 | 7.10336 | 6.74987 | 6.42355 | 4.53268 |
14 | 13.00370 | 12.54338 | 12.10625 | 11.69091 | 11.29607 | 10.92052 | 10.56312 | 10.22283 | 9.89864 | 9.58965 | 9.29498 | 8.74547 | 8.24424 | 7.78615 | 7.36669 | 6.98187 | 6.62817 | 4.61057 |
15 | 13.86505 | 13.34323 | 12.84926 | 12.38138 | 11.93794 | 11.51741 | 11.11839 | 10.73955 | 10.37966 | 10.03758 | 9.71225 | 9.10791 | 8.55948 | 8.06069 | 7.60608 | 7.19087 | 6.81086 | 4.67547 |
16 | 14.71787 | 14.13126 | 13.57771 | 13.05500 | 12.56110 | 12.09412 | 11.65230 | 11.23402 | 10.83777 | 10.46216 | 10.10590 | 9.44665 | 8.85137 | 8.31256 | 7.82371 | 7.37916 | 6.97399 | 4.72956 |
17 | 15.56225 | 14.90765 | 14.29187 | 13.71220 | 13.16612 | 12.65132 | 12.16567 | 11.70719 | 11.27407 | 10.86461 | 10.47726 | 9.76322 | 9.12164 | 8.54363 | 8.02155 | 7.54879 | 7.11963 | 4.77463 |
18 | 16.39827 | 15.67256 | 14.99203 | 14.35336 | 13.75351 | 13.18968 | 12.65930 | 12.15999 | 11.68959 | 11.24607 | 10.82760 | 10.05909 | 9.37189 | 8.75563 | 8.20141 | 7.70162 | 7.24967 | 4.81219 |
19 | 17.22601 | 16.42617 | 15.67846 | 14.97889 | 14.32380 | 13.70984 | 13.13394 | 12.59329 | 12.08532 | 11.60765 | 11.15812 | 10.33560 | 9.60360 | 8.95011 | 8.36492 | 7.83929 | 7.36578 | 4.84350 |
20 | 18.04555 | 17.16864 | 16.35143 | 15.58916 | 14.87747 | 14.21240 | 13.59033 | 13.00794 | 12.46221 | 11.95038 | 11.46992 | 10.59401 | 9.81815 | 9.12855 | 8.51356 | 7.96333 | 7.46944 | 4.86958 |
21 | 18.85698 | 17.90014 | 17.01121 | 16.18455 | 15.41502 | 14.69797 | 14.02916 | 13.40472 | 12.82115 | 12.27524 | 11.76408 | 10.83553 | 10.01680 | 9.29224 | 8.64869 | 8.07507 | 7.56200 | 4.89132 |
25 | 22.02316 | 20.71961 | 19 52346 | 18.42438 | 17.41315 | 16.48151 | 15.62208 | 14.82821 | 14.09394 | 13.41393 | 12.78336 | 11.65358 | 10.67478 | 9.82258 | 9.07704 | 8.42174 | 7.84314 | 4.94759 |
30 | 25.80771 | 24.01584 | 22.39646 | 20.93029 | 19.60044 | 18.39205 | 17.29203 | 16.28889 | 15.37245 | 14.53375 | 13.76483 | 12.40904 | 11.25778 | 10.27365 | 9.42691 | 8.69379 | 8.05518 | 4.97894 |
40 | 32.83469 | 29.91585 | 27.35548 | 25.10278 | 23.11477 | 21.35507 | 19.79277 | 18.40158 | 17.15909 | 16.04612 | 15.04630 | 13.33171 | 11.92461 | 10.75736 | 9.77905 | 8.95105 | 8.24378 | 4.99660 |
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