Brief Exercise 6-1

Leon Spear invested $16,800 today in a fund that earns 8% compounded annually. Click here to view factor tables To what amount will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund earns 8% annual interest compounded semiannually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment at 8% annual interest	$
Investment at 8% annual interest, compounded semiannually	$

Brief Exercise 6-2

Henry Bautista needs $28,800 in 4 years. Click here to view factor tables What amount must he invest today if his investment earns 8% compounded annually? What amount must he invest if his investment earns 8% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment at 8% annual interest	$
Investment at 8% annual interest, compounded quarterly	$

Brief Exercise 6-3

Cindy Willis will invest $24,900 today. She needs $63,826 in 24 years. Click here to view factor tables What annual interest rate must she earn? (Round answer to 0 decimal places, e.g. 7%.)

Interest rate

%

Brief Exercise 6-4

Steve Newman will invest $10,470 today in a fund that earns 12% annual interest. Click here to view factor tables How many years will it take for the fund to grow to $45,686?

Years

Brief Exercise 6-5

Julia Medavoy will invest $7,780 a year for 16 years in a fund that will earn 5% annual interest. Click here to view factor tables If the first payment into the fund occurs today, what amount will be in the fund in 16 years? If the first payment occurs at year-end, what amount will be in the fund in 16 years? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

First payment today	$
First payment at year-end	$

Brief Exercise 6-6

John Madison needs $327,000 in 10 years. Click here to view factor tables How much must he invest at the end of each year, at 6% interest, to meet his needs? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment amount

$

Brief Exercise 6-7

Adams Fillmore?s lifelong dream is to own his own fishing boat to use in his retirement. Adams has recently come into an inheritance of $428,900. He estimates that the boat he wants will cost $341,100 when he retires in 6 years. Click here to view factor tables How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment amount

$

Brief Exercise 6-8

Morgan Fillmore?s lifelong dream is to own his own fishing boat to use in his retirement. Morgan has recently come into an inheritance of $449,600. He estimates that the boat he wants will cost $324,000 when he retires in 5 years. Click here to view factor tables Assuming quarterly compounding of amounts invested at 8%, how much of Morgan Fillmore?s inheritance must be invested to have enough at retirement to buy the boat? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.)

Investment amount

$

Brief Exercise 6-9

Newman Freeman is investing $8,590 at the end of each year in a fund that earns 9% interest. Click here to view factor tables In how many years will the fund be at $197,170? (Round answer to 0 decimal places, e.g. 45.)

Brief Exercise 61 Leon Spear invested $16,800 today in a fund that earns 8% compounded annually. Click here to view factor tables To what amount will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund earns 8% annual interest compounded semiannually? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ Investment at 8% annual interest $ Investment at 8% annual interest, compounded semiannually Brief Exercise 62 Henry Bautista needs $28,800 in 4 years. Click here to view factor tables What amount must he invest today if his investment earns 8% compounded annually? What amount must he invest if his investment earns 8% annual interest compounded quarterly? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ Investment at 8% annual interest $ Investment at 8% annual interest, compounded quarterly Brief Exercise 63 Cindy Willis will invest $24,900 today. She needs $63,826 in 24 years. Click here to view factor tables What annual interest rate must she earn? (Round answer to 0 decimal places, e.g. 7%.) Interest rate % Brief Exercise 6-4 Steve Newman will invest $10,470 today in a fund that earns 12% annual interest. Click here to view factor tables How many years will it take for the fund to grow to $45,686? Years Brief Exercise 6-5 Julia Medavoy will invest $7,780 a year for 16 years in a fund that will earn 5% annual interest. Click here to view factor tables If the first payment into the fund occurs today, what amount will be in the fund in 16 years? If the first payment occurs at year-end, what amount will be in the fund in 16 years? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ First payment today $ First payment at year-end Brief Exercise 6-6 John Madison needs $327,000 in 10 years. Click here to view factor tables How much must he invest at the end of each year, at 6% interest, to meet his needs? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ Investment amount Brief Exercise 6-7 Adams Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. Adams has recently come into an inheritance of $428,900. He estimates that the boat he wants will cost $341,100 when he retires in 6 years. Click here to view factor tables How much of his inheritance must he invest at an annual rate of 8% (compounded annually) to buy the boat at retirement? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ Investment amount Brief Exercise 6-8 Morgan Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. Morgan has recently come into an inheritance of $449,600. He estimates that the boat he wants will cost $324,000 when he retires in 5 years. Click here to view factor tables Assuming quarterly compounding of amounts invested at 8%, how much of Morgan Fillmore's inheritance must be invested to have enough at retirement to buy the boat? (Round factor values to 5 decimal places, e.g. 1.25124 and final answers to 0 decimal places, e.g. 458,581.) $ Investment amount Brief Exercise 69 Newman Freeman is investing $8,590 at the end of each year in a fund that earns 9% interest. Click here to view factor tables In how many years will the fund be at $197,170? (Round answer to 0 decimal places, e.g. 45.) Years 1.FUTURE VALUE OF 1 TABLE. Contains the amounts to which 1 will accumulate if deposited now at a specified rate and left for a specified number of periods (Table 6.1). Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 1.06000 2 1.0404 1.0506 1.0609 1.0816 1.10250 0 3 0 0 1.12360 Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 1.06000 3 1.0612 1.0768 1.0927 1.1248 1.15763 1 9 3 6 1.19102 4 1.0824 1.1038 1.1255 1.1698 1.21551 3 1 1 6 1.26248 5 1.1040 1.1314 1.1592 1.2166 1.27628 8 1 7 5 1.33823 6 1.1261 1.1596 1.1940 1.2653 1.34010 6 9 5 2 1.41852 7 1.1486 1.1886 1.2298 1.3159 1.40710 9 9 7 3 1.50363 8 1.1716 1.2184 1.2667 1.3685 1.47746 6 0 7 7 1.59385 9 1.1950 1.2488 1.3047 1.4233 1.55133 9 6 7 1 1.68948 10 1.2189 1.2800 1.3439 1.4802 1.62889 9 8 2 4 1.79085 11 1.2433 1.3120 1.3842 1.5394 1.71034 7 9 3 5 1.89830 12 1.2682 1.3448 1.4257 1.6010 1.79586 4 9 6 3 2.01220 13 1.2936 1.3785 1.4685 1.6650 1.88565 1 1 3 7 2.13293 14 1.3194 1.4129 1.5125 1.7316 1.97993 8 7 9 8 2.26090 15 1.3458 1.4483 1.5579 1.8009 2.07893 7 0 7 4 2.39656 16 1.3727 1.4845 1.6047 1.8729 2.18287 9 1 1 8 2.54035 17 1.4002 1.5216 1.6528 1.9479 2.29202 4 2 5 0 2.69277 18 1.4282 1.5596 1.7024 2.0258 2.40662 5 6 3 2 2.85434 Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 1.06000 19 1.4568 1.5986 1.7535 2.1068 2.52695 1 5 1 5 3.02560 20 1.4859 1.6386 1.8061 2.1911 2.65330 5 2 1 2 3.20714 21 1.5156 1.6795 1.8602 2.2787 2.78596 7 8 9 7 3.39956 22 1.5459 1.7215 1.9161 2.3699 2.92526 8 7 0 2 3.60354 23 1.5769 1.7646 1.9735 2.4647 3.07152 0 1 9 2 3.81975 24 1.6084 1.8087 2.0327 2.5633 3.22510 4 3 9 0 4.04893 25 1.6406 1.8539 2.0937 2.6658 3.38635 1 4 8 4 4.29187 26 1.6734 1.9002 2.1565 2.7724 3.55567 2 9 9 7 4.54938 27 1.7068 1.9478 2.2212 2.8833 3.73346 9 0 9 7 4.82235 28 1.7410 1.9965 2.2879 2.9987 3.92013 2 0 3 0 5.11169 29 1.7758 2.0464 2.3565 3.1186 4.11614 4 1 7 5 5.41839 30 1.8113 2.0975 2.4272 3.2434 4.32194 6 7 6 0 5.74349 31 1.8475 2.1500 2.5000 3.3731 4.53804 9 1 8 3 6.08810 32 1.8845 2.2037 2.5750 3.5080 4.76494 4 6 8 6 6.45339 33 1.9222 2.2588 2.6523 3.6483 5.00319 3 5 4 8 6.84059 34 1.9606 2.3153 2.7319 3.7943 5.25335 8 2 1 2 7.25103 Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 1.06000 35 1.9998 2.3732 2.8138 3.9460 5.51602 9 1 6 9 7.68609 36 2.0398 2.4325 2.8982 4.1039 5.79182 9 4 8 3 8.14725 37 2.0806 2.4933 2.9852 4.2680 6.08141 9 5 3 9 8.63609 38 2.1223 2.5556 3.0747 4.4388 6.38548 0 8 8 1 9.15425 39 2.1647 2.6195 3.1670 4.6163 6.70475 4 7 3 7 9.70351 40 2.2080 2.6850 3.2620 4.8010 7.03999 4 6 4 2 10.2857 2 8% 9% 10% 11% 12% 15% (n) Periods 1.08000 1.0900 1.1000 1.1100 1.1200 1.15000 0 0 0 0 1 1.16640 1.1881 1.2100 1.2321 1.2544 1.32250 0 0 0 0 2 1.25971 1.2950 1.3310 1.3676 1.4049 1.52088 3 0 3 3 3 1.36049 1.4115 1.4641 1.5180 1.5735 1.74901 8 0 7 2 4 1.46933 1.5386 1.6105 1.6850 1.7623 2.01136 2 1 6 4 5 1.58687 1.6771 1.7715 1.8704 1.9738 2.31306 0 6 1 2 6 1.71382 1.8280 1.9487 2.0761 2.2106 2.66002 4 2 6 8 7 1.85093 1.9925 2.1435 2.3045 2.4759 3.05902 6 9 4 6 8 1.99900 2.1718 2.3579 2.5580 2.7730 3.51788 9 5 3 8 9 Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 1 2% 2% 3% 4% 5% 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 6% 1.06000 2.15892 2.3673 2.5937 2.8394 3.1058 4.04556 6 4 2 5 10 2.33164 2.5804 2.8531 3.1517 3.4785 4.65239 3 2 6 5 11 2.51817 2.8126 3.1384 3.4984 3.8959 5.35025 7 3 5 8 12 2.71962 3.0658 3.4522 3.8832 4.3634 6.15279 1 7 8 9 13 2.93719 3.3417 3.7975 4.3104 4.8871 7.07571 3 0 4 1 14 3.17217 3.6424 4.1772 4.7845 5.4735 8.13706 8 5 9 7 15 3.42594 3.9703 4.5949 5.3108 6.1303 9.35762 1 7 9 9 16 3.70002 4.3276 5.0544 5.8950 6.8660 10.7612 3 7 9 4 6 17 3.99602 4.7171 5.5599 6.5435 7.6899 12.3754 2 2 5 7 5 18 4.31570 5.1416 6.1159 7.2633 8.6127 14.2317 6 1 4 6 7 19 4.66096 5.6044 6.7275 8.0623 9.6462 16.3665 1 0 1 9 4 20 5.03383 6.1088 7.4002 8.9491 10.803 18.8215 1 5 7 85 2 21 5.43654 6.6586 8.1402 9.9335 12.100 21.6447 0 8 7 31 5 22 5.87146 7.2578 8.9543 11.026 13.552 24.8914 7 0 27 35 6 23 6.34118 7.9110 9.8497 12.239 15.178 28.6251 8 3 16 63 8 24 6.84847 8.6230 10.834 13.585 17.000 32.9189 8 71 46 00 5 25 Table6.1FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) FVFn,i=(1+i)n (n) Periods 1 2% 2% 3% 4% 5% 1.0200 1.0250 1.0300 1.0400 1.05000 0 0 0 0 6% 1.06000 7.39635 9.3991 11.918 15.079 19.040 37.8568 6 18 86 07 0 26 7.98806 10.245 13.109 16.738 21.324 43.5353 08 99 65 88 2 27 8.62711 11.167 14.420 18.579 23.883 50.0656 14 99 90 87 1 28 9.31727 12.172 15.863 20.623 26.749 57.5754 18 09 69 93 5 29 10.0626 13.267 17.449 22.892 29.959 66.2117 6 68 40 30 92 7 30 10.8676 14.461 19.194 25.410 33.555 76.1435 7 77 34 45 11 4 31 11.7370 15.763 21.113 28.205 37.581 87.5650 8 33 78 60 73 7 32 12.6760 17.182 23.225 31.308 42.091 100.699 5 03 15 21 53 83 33 13.6901 18.728 25.547 34.752 47.142 115.804 3 41 67 12 52 80 34 14.7853 20.413 28.102 38.574 52.799 133.175 4 97 44 85 62 52 35 15.9681 22.251 30.912 42.818 59.135 153.151 7 23 68 08 57 85 36 17.2456 24.253 34.003 47.528 66.231 176.124 3 84 95 07 84 63 37 18.6252 26.436 37.404 52.756 74.179 202.543 8 68 34 16 66 32 38 20.1153 28.815 41.144 58.559 83.081 232.924 0 98 79 34 22 82 39 21.7245 31.409 45.259 65.000 93.050 267.863 2 42 26 87 97 55 40 2.PRESENT VALUE OF 1 TABLE. Contains the amounts that must be deposited now at a specified rate of interest to equal 1 at the end of a specified number of periods (Table 6.2). Table6.2PRESENT VALUE OF 1 (PRESENT VALUE OF A SINGLE SUM) PVFn,i=1(1+i)n=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 . . . . . 98039 97561 97087 96154 95238 .94340 2 . . . . . 96117 95181 94260 92456 90703 .89000 3 . . . . . 94232 92860 91514 88900 86384 .83962 4 . . . . . 92385 90595 88849 85480 82270 .79209 5 . . . . . 90573 88385 86261 82193 78353 .74726 6 . . . . . 88797 86230 83748 79031 74622 .70496 7 . . . . . 87056 84127 81309 75992 71068 .66506 8 . . . . . 85349 82075 78941 73069 67684 .62741 9 . . . . . 83676 80073 76642 70259 64461 .59190 10 . . . . . 82035 78120 74409 67556 61391 .55839 11 . . . . . 80426 76214 72242 64958 58468 .52679 12 . . . . . 78849 74356 70138 62460 55684 .49697 13 . . . . . 77303 72542 68095 60057 53032 .46884 14 . . . . . 75788 70773 66112 57748 50507 .44230 15 . . . . . 74301 69047 64186 55526 48102 .41727 16 . . . . . 72845 67362 62317 53391 45811 .39365 17 . . . . . 71416 65720 60502 51337 43630 .37136 Table6.2PRESENT VALUE OF 1 (PRESENT VALUE OF A SINGLE SUM) PVFn,i=1(1+i)n=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 . . . . . 98039 97561 97087 96154 95238 .94340 18 . . . . . 70016 64117 58739 49363 41552 .35034 19 . . . . . 68643 62553 57029 47464 39573 .33051 20 . . . . . 67297 61027 55368 45639 37689 .31180 21 . . . . . 65978 59539 53755 43883 35894 .29416 22 . . . . . 64684 58086 52189 42196 34185 .27751 23 . . . . . 63416 56670 50669 40573 32557 .26180 24 . . . . . 62172 55288 49193 39012 31007 .24698 25 . . . . . 60953 53939 47761 37512 29530 .23300 26 . . . . . 59758 52623 46369 36069 28124 .21981 27 . . . . . 58586 51340 45019 34682 26785 .20737 28 . . . . . 57437 50088 43708 33348 25509 .19563 29 . . . . . 56311 48866 42435 32065 24295 .18456 30 . . . . . 55207 47674 41199 30832 23138 .17411 31 . . . . . 54125 46511 39999 29646 22036 .16425 32 . . . . . 53063 45377 38834 28506 20987 .15496 33 . . . . . 52023 44270 37703 27409 19987 .14619 Table6.2PRESENT VALUE OF 1 (PRESENT VALUE OF A SINGLE SUM) PVFn,i=1(1+i)n=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 . . . . . 98039 97561 97087 96154 95238 .94340 34 . . . . . 51003 43191 36604 26355 19035 .13791 35 . . . . . 50003 42137 35538 25342 18129 .13011 36 . . . . . 49022 41109 34503 24367 17266 .12274 37 . . . . . 48061 40107 33498 23430 16444 .11579 38 . . . . . 47119 39128 32523 22529 15661 .10924 39 . . . . . 46195 38174 31575 21662 14915 .10306 40 . . . . . 45289 37243 30656 20829 14205 .09722 8% 9% 10% 11% 12% 15% (n) Periods .92593 . . . . . 91743 90909 90090 89286 86957 1 .85734 . . . . . 84168 82645 81162 79719 75614 2 .79383 . . . . . 77218 75132 73119 71178 65752 3 .73503 . . . . . 70843 68301 65873 63552 57175 4 .68058 . . . . . 64993 62092 59345 56743 49718 5 .63017 . . . . . 59627 56447 53464 50663 43233 6 .58349 . . . . . 54703 51316 48166 45235 37594 7 .54027 . . . . . 50187 46651 43393 40388 32690 8 Table6.2PRESENT VALUE OF 1 (PRESENT VALUE OF A SINGLE SUM) PVFn,i=1(1+i)n=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 . . . . . 98039 97561 97087 96154 95238 .94340 .50025 . . . . . 46043 42410 39092 36061 28426 9 .46319 . . . . . 42241 38554 35218 32197 24719 10 .42888 . . . . . 38753 35049 31728 28748 21494 11 .39711 . . . . . 35554 31863 28584 25668 18691 12 .36770 . . . . . 32618 28966 25751 22917 16253 13 .34046 . . . . . 29925 26333 23199 20462 14133 14 .31524 . . . . . 27454 23939 20900 18270 12289 15 .29189 . . . . . 25187 21763 18829 16312 10687 16 .27027 . . . . . 23107 19785 16963 14564 09293 17 .25025 . . . . . 21199 17986 15282 13004 08081 18 .23171 . . . . . 19449 16351 13768 11611 07027 19 .21455 . . . . . 17843 14864 12403 10367 06110 20 .19866 . . . . . 16370 13513 11174 09256 05313 21 .18394 . . . . . 15018 12285 10067 08264 04620 22 .17032 . . . . . 13778 11168 09069 07379 04017 23 .15770 . . . . . 12641 10153 08170 06588 03493 24 Table6.2PRESENT VALUE OF 1 (PRESENT VALUE OF A SINGLE SUM) PVFn,i=1(1+i)n=(1+i)n (n) Periods 2% 2% 3% 4% 5% 6% 1 . . . . . 98039 97561 97087 96154 95238 .94340 .14602 . . . . . 11597 09230 07361 05882 03038 25 .13520 . . . . . 10639 08391 06631 05252 02642 26 .12519 . . . . . 09761 07628 05974 04689 02297 27 .11591 . . . . . 08955 06934 05382 04187 01997 28 .10733 . . . . . 08216 06304 04849 03738 01737 29 .09938 . . . . . 07537 05731 04368 03338 01510 30 .09202 . . . . . 06915 05210 03935 02980 01313 31 .08520 . . . . . 06344 04736 03545 02661 01142 32 .07889 . . . . . 05820 04306 03194 02376 00993 33 .07305 . . . . . 05340 03914 02878 02121 00864 34 .06763 . . . . . 04899 03558 02592 01894 00751 35 .06262 . . . . . 04494 03235 02335 01691 00653 36 .05799 . . . . . 04123 02941 02104 01510 00568 37 .05369 . . . . . 03783 02674 01896 01348 00494 38 .04971 . . . . . 03470 02430 01708 01204 00429 39 .04603 . . . . . 03184 02210 01538 01075 00373 40 3.FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 TABLE. Contains the amounts to which periodic rents of 1 will accumulate if the payments (rents) are invested at the end of each period at a specified rate of interest for a specified number of periods (Table 6.3). Table6.3FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 FVF-OAn,i=(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 2.02000 2.02500 2.03000 2.04000 2.05000 2.06000 3 3.06040 3.07563 3.09090 3.12160 3.15250 3.18360 4 4.12161 4.15252 4.18363 4.24646 4.31013 4.37462 5 5.20404 5.25633 5.30914 5.41632 5.52563 5.63709 6 6.30812 6.38774 6.46841 6.63298 6.80191 6.97532 7 7.43428 7.54743 7.66246 7.89829 8.14201 8.39384 8 8.58297 8.73612 8.89234 9.21423 9.54911 9.89747 9 9.75463 9.95452 10.1591 10.5828 1 0 11.0265 6 11.4913 2 10 10.9497 11.2033 11.4633 12.0061 2 8 8 1 12.5778 9 13.1807 9 11 12.1687 12.4834 12.8078 13.4863 2 7 0 5 14.2067 9 14.9716 4 12 13.4120 13.7955 14.1920 15.0258 9 5 3 1 15.9171 3 16.8699 4 13 14.6803 15.1404 15.6177 16.6268 3 4 9 4 17.7129 8 18.8821 4 14 15.9739 16.5189 17.0863 18.2919 4 5 2 1 19.5986 3 21.0150 7 15 17.2934 17.9319 18.5989 20.0235 2 3 1 9 21.5785 6 23.2759 7 16 18.6392 19.3802 20.1568 21.8245 9 2 8 3 23.6574 9 25.6725 3 17 20.0120 20.8647 21.7615 23.6975 7 3 9 1 25.8403 7 28.2128 8 18 21.4123 22.3863 23.4144 25.6454 1 5 4 1 28.1323 8 30.9056 5 19 22.8405 23.9460 25.1168 27.6712 6 1 7 3 30.5390 0 33.7599 9 Table6.3FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 FVF-OAn,i=(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 20 24.2973 25.5446 26.8703 29.7780 7 6 7 8 33.0659 5 36.7855 9 21 25.7833 27.1832 28.6764 31.9692 2 7 9 0 35.7192 5 39.9927 3 22 27.2989 28.8628 30.5367 34.2479 8 6 8 7 38.5052 1 43.3922 9 23 28.8449 30.5844 32.4528 36.6178 6 3 8 9 41.4304 8 46.9958 3 24 30.4218 32.3490 34.4264 39.0826 6 4 7 0 44.5020 0 50.8155 8 25 32.0303 34.1577 36.4592 41.6459 0 6 6 1 47.7271 0 54.8645 1 26 33.6709 36.0117 38.5530 44.3117 1 1 4 4 51.1134 5 59.1563 8 27 35.3443 37.9120 40.7096 47.0842 2 0 3 1 54.6691 3 63.7057 7 28 37.0512 39.8598 42.9309 49.9675 1 0 2 8 58.4025 8 68.5281 1 29 38.7922 41.8563 45.2188 52.9662 3 0 5 9 62.3227 1 73.6398 0 30 40.5680 43.9027 47.5754 56.0849 8 0 2 4 66.4388 5 79.0581 9 31 42.3794 46.0002 50.0026 59.3283 4 7 8 4 70.7607 9 84.8016 8 32 44.2270 48.1502 52.5027 62.7014 3 8 6 7 75.2988 3 90.8897 8 33 46.1115 50.3540 55.0778 66.2095 7 3 4 3 80.0637 7 97.3431 6 34 48.0338 52.6128 57.7301 69.8579 0 9 8 1 85.0669 6 104.183 76 35 49.9944 54.9282 60.4620 73.6522 8 1 8 2 90.3203 1 111.434 78 36 51.9943 57.3014 63.2759 77.5983 7 1 4 1 95.8363 2 119.120 87 Table6.3FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 FVF-OAn,i=(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 37 54.0342 59.7339 66.1742 81.7022 5 5 2 5 101.628 14 127.268 12 38 56.1149 62.2273 69.1594 85.9703 4 0 5 4 107.709 55 135.904 21 39 58.2372 64.7829 72.2342 90.4091 4 8 3 5 114.095 02 145.058 46 40 60.4019 67.4025 75.4012 95.0255 8 5 6 2 120.799 77 154.761 97 8% 9% 10% 11% 12% 15% (n) Periods 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1 2.08000 2.09000 2.10000 2.11000 2.12000 2.15000 2 3.24640 3.27810 3.31000 3.34210 3.37440 3.47250 3 4.50611 4.57313 4.64100 4.70973 4.77933 4.99338 4 5.86660 5.98471 6.10510 6.22780 6.35285 6.74238 5 7.33592 7.52334 7.71561 7.91286 8.11519 8.75374 6 8.92280 9.20044 9.48717 9.78327 10.0890 1 11.0668 0 7 10.6366 11.0284 11.4358 11.8594 12.2996 3 7 9 3 9 13.7268 2 8 12.4875 13.0210 13.5794 14.1639 14.7756 6 4 8 7 6 16.7858 4 9 14.4865 15.1929 15.9374 16.7220 17.5487 6 3 3 1 4 20.3037 2 10 16.6454 17.5602 18.5311 19.5614 20.6545 9 9 7 3 8 24.3492 8 11 18.9771 20.1407 21.3842 22.7131 24.1331 3 2 8 9 3 29.0016 7 12 21.4953 22.9533 24.5227 26.2116 28.0291 0 9 1 4 1 34.3519 2 13 24.2149 26.0191 27.9749 30.0949 32.3926 2 9 8 2 0 40.5047 1 14 Table6.3FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 FVF-OAn,i=(1+i)n1i (n) Periods 1 2% 2% 3% 4% 5% 6% 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 27.1521 29.3609 31.7724 34.4053 37.2797 1 2 8 6 2 47.5804 1 15 30.3242 33.0034 35.9497 39.1899 42.7532 8 0 3 5 8 55.7174 7 16 33.7502 36.9737 40.5447 44.5008 48.8836 3 1 0 4 7 65.0750 9 17 37.4502 41.3013 45.5991 50.3959 55.7497 4 4 7 3 2 75.8363 6 18 41.4462 46.0184 51.1590 56.9394 63.4396 6 6 9 9 8 88.2118 1 19 45.7619 51.1601 57.2750 64.2028 72.0524 6 2 0 3 4 102.443 58 20 50.4229 56.7645 64.0025 72.2651 81.6987 2 3 0 4 4 118.810 12 21 55.4567 62.8733 71.4027 81.2143 92.5025 6 4 5 1 8 137.631 64 22 60.8933 69.5319 79.5430 91.1478 104.602 0 4 2 8 89 159.276 38 23 66.7647 76.7898 88.4973 102.174 118.155 6 1 3 15 24 184.167 84 24 73.1059 84.7009 98.3470 114.413 133.333 4 0 6 31 87 212.793 02 25 79.9544 93.3239 109.181 127.998 150.333 2 8 77 77 93 245.711 97 26 87.3507 102.723 121.099 143.078 169.374 7 14 94 64 01 283.568 77 27 95.3388 112.968 134.209 159.817 190.698 3 22 94 29 89 327.104 08 28 103.965 124.135 148.630 178.397 214.582 94 36 93 19 75 377.169 69 29 113.283 136.307 164.494 199.020 241.332 21 54 02 88 68 434.745 15 30 123.345 149.575 181.943 221.913 271.292 87 22 43 17 61 500.956 92 31 Table6.3FUTURE VALUE OF AN ORDINARY ANNUITY OF 1 FVF-OAn,i=(1+i)n1i (n) Periods 1 2% 2% 3% 4% 5% 6% 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 134.213 164.036 201.137 247.323 304.847 54 99 77 62 72 577.100 46 32 145.950 179.800 222.251 275.529 342.429 62 32 54 22 45 644.665 53 33 158.626 196.982 245.476 306.837 384.520 67 34 70 44 98 765.365 35 34 172.316 215.710 271.024 341.589 431.663 80 76 37 55 50 881.170 16 35 187.102 236.124 299.126 380.164 484.463 15 72 81 41 12 1014.34 568 36 203.070 258.375 330.039 422.982 543.598 32 95 49 49 69 1167.49 753 37 220.315 282.629 364.043 470.510 609.830 95 78 43 56 53 1343.62 216 38 238.941 309.066 401.447 523.266 684.010 22 46 78 73 20 1546.16 549 39 259.056 337.882 442.592 581.826 767.091 52 45 56 07 42 1779.09 031 40 4.PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 TABLE. Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the end of regular periodic intervals for the specified number of periods (Table 6.4). Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 2% 2% 3% 4% 5% 6% 1 .98039 .97561 .97087 .96154 .95238 .94340 2 1.9415 1.9274 1.9134 1.8860 1.8594 6 2 7 9 1 1.83339 3 2.8838 2.8560 2.8286 2.7750 2.7232 8 2 1 9 5 2.67301 4 3.8077 3.7619 3.7171 3.6299 3.5459 3 7 0 0 5 3.46511 5 4.7134 4.6458 4.5797 4.4518 4.3294 4.21236 Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 1 2% 2% 3% 4% 5% 6% .98039 .97561 .97087 .96154 .95238 6 3 1 2 .94340 8 6 5.6014 5.5081 5.4171 5.2421 5.0756 3 3 9 4 9 4.91732 7 6.4719 6.3493 6.2302 6.0020 5.7863 9 9 8 5 7 5.58238 8 7.3254 7.1701 7.0196 6.7327 6.4632 8 4 9 4 1 6.20979 9 8.1622 7.9708 7.7861 7.4353 7.1078 4 7 1 3 2 6.80169 10 8.9825 8.7520 8.5302 8.1109 7.7217 9 6 0 0 3 7.36009 11 9.7868 9.5142 9.2526 8.7604 8.3064 5 1 2 8 1 7.88687 12 10.575 10.257 9.9540 9.3850 8.8632 34 76 0 7 5 8.38384 13 11.348 10.983 10.634 9.9856 9.3935 37 19 96 5 7 8.85268 14 12.106 11.690 11.296 10.563 9.8986 25 91 07 12 4 9.29498 15 12.849 12.381 11.937 11.118 10.379 26 38 94 39 66 9.71225 16 13.577 13.055 12.561 11.652 10.837 71 00 10 30 77 10.1059 0 17 14.291 13.712 13.166 12.165 11.274 87 20 12 67 07 10.4772 6 18 14.992 14.353 13.753 12.659 11.689 03 36 51 30 59 10.8276 0 19 15.678 14.978 14.323 13.133 12.085 46 89 80 94 32 11.1581 2 20 16.351 15.589 14.877 13.590 12.462 43 16 47 33 21 11.4699 2 21 17.011 16.184 15.415 14.029 12.821 21 55 02 16 15 11.7640 8 22 17.658 16.765 15.936 14.451 13.163 12.0415 Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 1 2% 2% 3% 4% 5% .98039 .97561 .97087 .96154 .95238 05 41 92 12 6% .94340 00 8 23 18.292 17.332 16.443 14.856 13.488 20 11 61 84 57 12.3033 8 24 18.913 17.884 16.935 15.246 13.798 93 99 54 96 64 12.5503 6 25 19.523 18.424 17.413 15.622 14.093 46 38 15 08 94 12.7833 6 26 20.121 18.950 17.876 15.982 14.375 04 61 84 77 19 13.0031 7 27 20.706 19.464 18.327 16.329 14.643 90 01 03 59 03 13.2105 3 28 21.281 19.964 18.764 16.663 14.898 27 89 11 06 13 13.4061 6 29 21.844 20.453 19.188 16.983 15.141 38 55 45 71 07 13.5907 2 30 22.396 20.930 19.600 17.292 15.372 46 29 44 03 45 13.7648 3 31 22.937 21.395 20.000 17.588 15.592 70 41 43 49 81 13.9290 9 32 23.468 21.849 20.388 17.873 15.802 33 18 77 55 68 14.0840 4 33 23.988 22.291 20.765 18.147 16.002 56 88 79 65 55 14.2302 3 34 24.498 22.723 21.131 18.411 16.192 59 79 84 20 90 14.3681 4 35 24.998 23.145 21.487 18.664 16.374 62 16 22 61 19 14.4982 5 36 25.488 23.556 21.832 18.908 16.546 84 25 25 28 85 14.6209 9 37 25.969 23.957 22.167 19.142 16.711 45 32 24 58 29 14.7367 8 38 26.440 24.348 22.492 19.367 16.867 64 60 46 86 89 14.8460 2 39 26.902 24.730 22.808 19.584 17.017 14.9490 Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 1 2% 8% 3% 4% 5% .98039 .97561 .97087 .96154 .95238 59 40 2% 7 27.355 25.102 23.114 19.792 17.159 48 78 77 77 09 15.0463 0 10% 22 11% 48 .94340 04 9% 34 6% 12% 15% (n) Periods .92593 .91743 .90909 .90090 .89286 .86957 1 1.78326 1.7591 1.7355 1.7125 1.6900 1.6257 1 4 2 5 1 2 2.57710 2.5313 2.4868 2.4437 2.4018 2.2832 0 5 1 3 3 3 3.31213 3.2397 3.1698 3.1024 3.0373 2.8549 2 6 5 5 8 4 3.99271 3.8896 3.7907 3.6959 3.6047 3.3521 5 9 0 8 6 5 4.62288 4.4859 4.3552 4.2305 4.1114 3.7844 2 6 4 1 8 6 5.20637 5.0329 4.8684 4.7122 4.5637 4.1604 5 2 0 6 2 7 5.74664 5.5348 5.3349 5.1461 4.9676 4.4873 2 3 2 4 2 8 6.24689 5.9952 5.7590 5.5370 5.3282 4.7715 5 2 5 5 8 9 6.71008 6.4176 6.1445 5.8892 5.6502 5.0187 6 7 3 2 7 10 7.13896 6.8051 6.4950 6.2065 5.9377 5.2337 9 6 2 0 1 11 7.53608 7.1607 6.8136 6.4923 6.1943 5.4206 3 9 6 7 2 12 7.90378 7.4869 7.1033 6.7498 6.4235 5.5831 0 6 7 5 5 13 8.24424 7.7861 7.3666 6.9818 6.6281 5.7244 5 9 7 7 8 14 8.55948 8.0606 7.6060 7.1908 6.8108 5.8473 9 8 7 6 7 15 Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 1 2% 2% 3% 4% 5% .98039 .97561 .97087 .96154 .95238 6% .94340 8.85137 8.3125 7.8237 7.3791 6.9739 5.9542 6 1 6 9 4 16 9.12164 8.5436 8.0215 7.5487 7.1196 6.0471 3 5 9 3 6 17 9.37189 8.7556 8.2014 7.7016 7.2496 6.1279 3 1 2 7 7 18 9.60360 8.9501 8.3649 7.8392 7.3657 6.1982 2 2 9 8 3 19 9.81815 9.1285 8.5135 7.9633 7.4694 6.2593 5 6 3 4 3 20 10.0168 9.2922 8.6486 8.0750 7.5620 6.3124 0 4 9 7 0 6 21 10.2007 9.4424 8.7715 8.1757 7.6446 6.3586 4 3 4 4 5 6 22 10.3710 9.5802 8.8832 8.2664 7.7184 6.3988 6 1 2 3 3 4 23 10.5287 9.7066 8.9847 8.3481 7.7843 6.4337 6 1 4 4 2 7 24 10.6747 9.8225 9.0770 8.4217 7.8431 6.4641 8 8 4 4 4 5 25 10.8099 9.9289 9.1609 8.4880 7.8956 6.4905 8 7 5 6 6 6 26 10.9351 10.026 9.2372 8.5478 7.9425 6.5135 6 58 2 0 5 3 27 11.0510 10.116 9.3065 8.6016 7.9844 6.5335 8 13 7 2 2 1 28 11.1584 10.198 9.3696 8.6501 8.0218 6.5508 1 28 1 1 1 8 29 11.2577 10.273 9.4269 8.6937 8.0551 6.5659 8 65 1 9 8 8 30 11.3498 10.342 9.4790 8.7331 8.0849 6.5791 0 80 1 5 9 1 31 11.4350 10.406 9.5263 8.7686 8.1115 6.5905 0 24 8 0 9 3 32 Table6.4PRESENT VALUE OF AN ORDINARY ANNUITY OF 1 PVF-OAn,i=11(1+i)ni (n) Periods 1 2% 2% 3% 4% 5% 6% .98039 .97561 .97087 .96154 .95238 .94340 11.5138 10.464 9.5694 8.8005 8.1353 6.6004 9 44 3 4 5 6 33 11.5869 10.517 9.6085 8.8293 8.1565 6.6091 3 84 8 2 6 0 34 11.6545 10.566 9.6441 8.8552 8.1755 6.6166 7 82 6 4 0 1 35 11.7171 10.611 9.6765 8.8785 8.1924 6.6231 9 76 1 9 1 4 36 11.7751 10.652 9.7059 8.8996 8.2075 6.6288 8 99 2 3 1 2 37 11.8288 10.690 9.7326 8.9185 8.2209 6.6337 7 82 5 9 9 5 38 11.8785 10.725 9.7569 8.9356 8.2330 6.6380 8 52 7 7 3 5 39 11.9246 10.757 9.7790 8.9510 8.2437 6.6417 1 36 5 5 8 8 40 5.PRESENT VALUE OF AN ANNUITY DUE OF 1 TABLE. Contains the amounts that must be deposited now at a specified rate of interest to permit withdrawals of 1 at the beginning of regular periodic intervals for the specified number of periods (Table 6.5). Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 1.00000 2 1.9803 1.9756 1.9708 1.9615 1.9523 9 1 7 4 8 1.94340 3 2.9415 2.9274 2.9134 2.8860 2.8594 6 2 7 9 1 2.83339 4 3.8838 3.8560 3.8286 3.7750 3.7232 8 2 1 9 5 3.67301 5 4.8077 4.7619 4.7171 4.6299 4.5459 3 7 0 0 5 4.46511 Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 1.00000 6 5.7134 5.6458 5.5797 5.4518 5.3294 6 3 1 2 8 5.21236 7 6.6014 6.5081 6.4171 6.2421 6.0756 3 3 9 4 9 5.91732 8 7.4719 7.3493 7.2302 7.0020 6.7863 9 9 8 5 7 6.58238 9 8.3254 8.1701 8.0196 7.7327 7.4632 8 4 9 4 1 7.20979 10 9.1622 8.9708 8.7861 8.4353 8.1078 4 7 1 3 2 7.80169 11 9.9825 9.7520 9.5302 9.1109 8.7217 9 6 0 0 3 8.36009 12 10.786 10.514 10.252 9.7604 9.3064 85 21 62 8 1 8.88687 13 11.575 11.257 10.954 10.385 9.8632 34 76 00 07 5 9.38384 14 12.348 11.983 11.634 10.985 10.393 37 19 96 65 57 9.85268 15 13.106 12.690 12.296 11.563 10.898 25 91 07 12 64 10.2949 8 16 13.849 13.381 12.937 12.118 11.379 26 38 94 39 66 10.7122 5 17 14.577 14.055 13.561 12.652 11.837 71 00 10 30 77 11.1059 0 18 15.291 14.712 14.166 13.165 12.274 87 20 12 67 07 11.4772 6 19 15.992 15.353 14.753 13.659 12.689 03 36 51 30 59 11.8276 0 20 16.678 15.978 15.323 14.133 13.085 46 89 80 94 32 12.1581 2 21 17.351 16.589 15.877 14.590 13.462 43 16 47 33 21 12.4699 2 22 18.011 17.184 16.415 15.029 13.821 12.7640 Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 1 2% 2% 3% 4% 5% 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 21 55 02 16 6% 1.00000 15 8 23 18.658 17.765 16.936 15.451 14.163 05 41 92 12 00 13.0415 8 24 19.292 18.332 17.443 15.856 14.488 20 11 61 84 57 13.3033 8 25 19.913 18.884 17.935 16.246 14.798 93 99 54 96 64 13.5503 6 26 20.523 19.424 18.413 16.622 15.093 46 38 15 08 94 13.7833 6 27 21.121 19.950 18.876 16.982 15.375 04 61 84 77 19 14.0031 7 28 21.706 20.464 19.327 17.329 15.643 90 01 03 59 03 14.2105 3 29 22.281 20.964 19.764 17.663 15.898 27 89 11 06 13 14.4061 6 30 22.844 21.453 20.188 17.983 16.141 38 55 45 71 07 14.5907 2 31 23.396 21.930 20.600 18.292 16.372 46 29 44 03 45 14.7648 3 32 23.937 22.395 21.000 18.588 16.592 70 41 43 49 81 14.9290 9 33 24.468 22.849 21.388 18.873 16.802 33 18 77 55 68 15.0840 4 34 24.988 23.291 21.765 19.147 17.002 56 88 79 65 55 15.2302 3 35 25.498 23.723 22.131 19.411 17.192 59 79 84 20 90 15.3681 4 36 25.998 24.145 22.487 19.664 17.374 62 16 22 61 19 15.4982 5 37 26.488 24.556 22.832 19.908 17.546 84 25 25 28 85 15.6209 9 38 26.969 24.957 23.167 20.142 17.711 45 32 24 58 29 15.7367 8 Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 2% 2% 3% 4% 5% 6% 1 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 1.00000 39 27.440 25.348 23.492 20.367 17.867 64 60 46 86 89 15.8460 2 40 27.902 25.730 23.808 20.584 18.017 59 34 22 48 04 15.9490 7 8% 9% 10% 11% 12% 15% (n) Periods 1.00000 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 1 1.92593 1.9174 1.9090 1.9009 1.8928 1.8695 3 9 0 6 7 2 2.78326 2.7591 2.7355 2.7125 2.6900 2.6257 1 4 2 5 1 3 3.57710 3.5313 3.4868 3.4437 3.4018 3.2832 0 5 1 3 3 4 4.31213 4.2397 4.1698 4.1024 4.0373 3.8549 2 6 5 5 8 5 4.99271 4.8896 4.7907 4.6959 4.6047 4.3521 5 9 0 8 6 6 5.62288 5.4859 5.3552 5.2305 5.1114 4.7844 2 6 4 1 8 7 6.20637 6.0329 5.8684 5.7122 5.5637 5.1604 5 2 0 6 2 8 6.74664 6.5348 6.3349 6.1461 5.9676 5.4873 2 3 2 4 2 9 7.24689 6.9952 6.7590 6.5370 6.3282 5.7715 5 2 5 5 8 10 7.71008 7.4176 7.1445 6.8892 6.6502 6.0187 6 7 3 2 7 11 8.13896 7.8051 7.4950 7.2065 6.9377 6.2337 9 6 2 0 1 12 8.53608 8.1607 7.8136 7.4923 7.1943 6.4206 3 9 6 7 2 13 8.90378 8.4869 8.1033 7.7498 7.4235 6.5831 14 Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 1 2% 2% 3% 4% 5% 6% 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 0 6 7 5 1.00000 5 9.24424 8.7861 8.3666 7.9818 7.6281 6.7244 5 9 7 7 8 15 9.55948 9.0606 8.6060 8.1908 7.8108 6.8473 9 8 7 6 7 16 9.85137 9.3125 8.8237 8.3791 7.9739 6.9542 6 1 6 9 4 17 10.1216 9.5436 9.0215 8.5487 8.1196 7.0471 4 3 5 9 3 6 18 10.3718 9.7556 9.2014 8.7016 8.2496 7.1279 9 3 1 2 7 7 19 10.6036 9.9501 9.3649 8.8392 8.3657 7.1982 0 2 2 9 8 3 20 10.8181 10.128 9.5135 8.9633 8.4694 7.2593 5 55 6 3 4 3 21 11.0168 10.292 9.6486 9.0750 8.5620 7.3124 0 24 9 7 0 6 22 11.2007 10.442 9.7715 9.1757 8.6446 7.3586 4 43 4 4 5 6 23 11.3710 10.580 9.8832 9.2664 8.7184 7.3988 6. 21 2 3 3 4 24 11.5287 10.706 9.9847 9.3481 8.7843 7.4337 6 61 4 4 2 7 25 11.6747 10.822 10.077 9.4217 8.8431 7.4641 8 58 04 4 4 5 26 11.8099 10.928 10.160 9.4880 8.8956 7.4905 8 97 95 6 6 6 27 11.9351 11.026 10.237 9.5478 8.9425 7.5135 8 58 22 0 5 3 28 12.0510 11.116 10.306 9.6016 8.9844 7.5335 8 13 57 2 2 1 29 12.1584 11.198 10.369 9.6501 9.0218 7.5508 1 28 61 1 1 8 30 Table6.5PRESENT VALUE OF AN ANNUITY DUE OF 1 PVF-ADn,i=1+11(1+i)n1i (n) Periods 1 2% 2% 3% 4% 5% 1.0000 1.0000 1.0000 1.0000 1.0000 0 0 0 0 0 6% 1.00000 12.2577 11.273 10.426 9.6937 9.0551 7.5659 8 65 91 9 8 8 31 12.3498 11.342 10.479 9.7331 9.0849 7.5791 0 80 01 5 9 1 32 12.4350 11.406 10.526 9.7686 9.1115 7.5905 0 24 38 0 9 3 33 12.5138 11.464 10.569 9.8005 9.1353 7.6004 9 44 43 4 5 6 34 12.5869 11.517 10.608 9.8293 9.1565 7.6091 3 84 58 2 6 0 35 12.6545 11.566 10.644 9.8552 9.1755 7.6166 7 82 16 4 0 1 36 12.7171 11.611 10.676 9.8785 9.1924 7.6231 9 76 51 9 1 4 37 12.7751 11.652 10.705 9.8996 9.2075 7.6288 8 99 92 3 1 2 38 12.8288 11.690 10.732 9.9185 9.2209 7.6337 7 82 65 9 9 5 39 12.8785 11.725 10.756 9.9356 9.2330 7.6380 8 52 97 7 3 5 40