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"01;8FO 4 @0DV:8 =040==O V ?>25@=5==O :@548BC B0 =0@0EC20==O ?@>F5=B=8E ?;0B56V2, B8A. 3@=. ! 7/?>:07=8:8'0A>2V :20@B0;8 3>A?>40@AL:>W 4VO;L=>ABV ?V4?@8T<AB20#AL>3>1234567891011121@0DV: =040==O :@548BC1901661153953055612@>F5=B=V =0@0EC20==O 70 :@548B13121,4526242,939364,452485,865607,278728,791850,1104971,6118093109959120954,5131950,81106037,67272,25514544,521816,752908936361,2543633,53@0DV: ?>30H5==O :@548B=>3> 1>@3C146200159361305561#AL>3>13121,4526242,939364,459758,0580151,7100545,45120939141332,85307926,5109959120954,5291311,81411598,6>:07=8:8 B01;8FV @>7@0E>20=V 2V4?>2V4=> 4> B0:8E ?>;>65=L: :@548B8 =040NBLAO 70<>2=8:>2V ?@>5:BC ?5@H>3> G8A;0 2V4?>2V4=>3> :20@B0;C, 0 ?>25@B0NBLAO 2 >AB0==V9 45=L :20@B0;C. >7@0EC=:8 ?@>F5=B=8E ?;0B56V2 74V9A=NNBLAO 70 D>@<C;>N  EMBED Equation.3 , 45   AC<0 ?@>F5=B=8E =0@0EC20=L 2V4?>2V4=>3> ?5@V>4C;  EMBED Equation.3   =5?>25@=5=0 AC<0 =040=>3> :@548BC;  EMBED Equation.3   @VG=0 ?@>F5=B=0 AB02:0 70 :@548B C 4>;OE >48=8FV;  EMBED Equation.3   B5@<V= G0AC 2V4 =040==O :@548BC 4> 40B8 =0@0EC20==O ?@>F5=B=8E ?;0B56V2. /: ?>:07CNBL @>7@0EC=:8 B01;8FV 4, 70 :@548B C AC<V 305561 B8A. 3@=. ?@8 @VG=V9 AB02FV 28%, 73V4=> 7 C:070=>N AE5<>N =040==O B0 A?;0B8 ?>78:8 V=25AB>@ 7>1>2 O70=89 A?;0B8B8 ?@>F5=B8 2 >1AO7V 1106037,6 B8A. 3@=, B>1B> AC<C 3@>H>28E 70A>1V2, I> 2 3,6 @07C ?5@528ICT AC<C =040=>3> :@548BC. &5 ?>2 O70=> 7 B@820;8< B5@<V=>< G0AC ?>25@=5==O ?>78:8 B0 28A>:>N @VG=>N ?@>F5=B=>N AB02:>N 70 :@548B. >73;O=CB0 AE5<0 =040==O V A?;0B8 ?>78:8 T DV=0=A>2> >1 T:B82=>N 4;O V=25AB>@0 B0 @878:>2>N 4;O :@548B=>-10=:V2AL:>W CAB0=>28 V =5 <>65 22060B8AO >?B8<0;L=>N. @8 28:>@8AB0==V A:;04=>W AB02:8 ?@>F5=B0 2AO AC<0 :@548B=C >1AO3>< 305561 B8A. 3@=. =040TBLAO 70<>2=8:C =0 ?>G0B:C ?5@V>4C @50;V70FVW V=25AB8FV9=>3> ?@>5:BC. 1A;C3>2C20==O ?>78:8 (28?;0B0 ?@>F5=B=8E ?;0B56V2 B0 A?;0B0 >A=>2=>W AC<8 1>@3C) ?@>2>48BLAO 70 AE5<>N 0<>@B870FV9=>3> 3@0DV:0 I>:20@B0;L=8<8 0=CWB5B=8<8 2=5A:0<8 3@>H>28E 70A>1V2 ?@>BO3>< 3-E @>:V2 (12 - B8 G0A>28E :20@B0;V2). !C<0 0=CWB5B=8E 2=5A:V2 =0 >1A;C3>2C20==O :@548B=C 287=0G0TBLAO B0::  EMBED Equation.3  45   @V2=>25;8:89 0=CWB5B=89 ?;0BV6 =0 >1A;C3>2C20==O :@548BC;  EMBED Equation.3   AC<0 ?>78:8 =0 @50;V70FVN V=25AB8FV9=>3> ?@>5:BC;  EMBED Equation.3   :>5DVFVT=B ?@82545==O 0=CWB5B=8E ?;0B56V2 4> C<>2 ?>B>G=>3> G0AC. ;O C<>2 ?@8:;04C :>5DVFVT=B ?@82545==O 0=CWB5BC <0T 283;O4  EMBED Equation.3 & 7%, 12n, 45 7%  :20@B0;L=0 ?@>F5=B=0 AB02:0 70 :@548B (28%/4 = 7%); ? 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'? = CFo +  EMBED Equation.3  = 0. =25AB8FV9=89 ?@>5:B 22060TBLAO DV=0=A>2> 5D5:B82=8<, O:I> 9>3> 2=CB@VH=O =>@<0 ?@81CB:C ?5@528ICT 7=0G5==O 20@B>ABV :0?VB0;C V=25AB8FV9=>3> ?@>5:BC. ;O 287=0G5==O ?>:07=8:V2 DV=0=A>2>-5:>=><VG=>W 5D5:B82=>ABV V=25AB8FV9=>3> ?@>5:BC =5>1EV4=> ?>?5@54=L> 74V9A=8B8 ?@>3=>7=V @>7@0EC=:8 >GV:C20=8E 7=0G5=L G8AB>3> 3@>H>2>3> ?>B>:C 2 ?>ABV=25AB8FV9=89 ?5@V>4 4VO;L=>ABV ?V4?@8T<AB20. 8EV4=8<8 40=8<8 B0:8E @>7@0EC=:V2 T ?@89=OB0 B@820;VABL ?>ABV=25AB8FV9=>3> ?5@V>4C A5@54=L>@VG=V B5<?8 7@>AB0==O ?>:07=8:V2, WE 01A>;NB=89 @V25=L =0 7025@H5==O V=25AB8FV9=>W D078 ?@>5:BC. >2=0 B@820;VABL ?5@V>4C ?>ABV=25AB8FV9=>W 4VO;L=>ABV ?V4?@8T<AB20, O: ?@028;>, 287=0G0TBLAO B@820;VABN 0<>@B870FVW 0:B82=>W G0AB8=8 >A=>2=8E 70A>1V2, I> 22>4OBLAO 2 5:A?;C0B0FVN, 70 @57C;LB0B0<8 @50;V70FVW V=25AB8FV9=>3> ?@>5:BC V <>65 A:;040B8 10,12,15 @>:V2. # @>7@0EC=:0E 7=0G5=L ?>:07=8:V2 G8AB>3> 3@>H>2>3> ?>B>:C B@820;VABL ?@>3=>7=>3> ?5@V>4C ?@89<0TBLAO =0 @V2=V G0AB8=8 ?>ABV=25AB8FV9=>3> ?5@V>4C 4VO;L=>ABV ?V4?@8T<AB20, O:5 =5 <>65 1CB8 <5=H5 =V6 5 @>:V2. @8 >1@C=BC20==V B5<?V2 7@>AB0==O ?>:07=8:V2 3@>H>2>3> ?>B>:C <>6CBL @>73;O40B8AO 45:V;L:0 AF5=0@VW2 3>A?>40@AL:>W 4VO;L=>ABV ?V4?@8T<AB20: >?B8<VAB8G=89 (B5<?8 7@>AB0==O 28IV, =V6 C ?5@54V=25AB8FV9=89 ?5@V>4); ?><V@:>20=89 (B5<?8 7@>AB0==O, 265 4>AO3=CBV 2 ?5@54V=25AB8FV9=89 ?5@V>4); ?5A8<VAB8G=89 (B5<?8 7@>AB0==O =86GV, =V6 C ?5@54V=25AB8FV9=89 ?5@V>4). 3V4=> 7 28:;045=8<8 ?>;>65==O<8 2 B01;8FV 6 =02545=V @57C;LB0B8 ?@>3=>7=8E @>7@0EC=:V2 7=0G5=L G8AB>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20, I> @>73;O40TBLAO 2 ?@8:;04V <5B>48G=8E 2:07V2>: 4> :C@A>2>W @>1>B8. 8EV4=V 40=V ?@>3=>7=8E @>7@0EC=:V2: B@820;VABL ?@>3=>7=>-@>7@0EC=:>2>3> ?5@V>4C  10 @>:V2; A5@54=L>@VG=V B5<?8 7@>AB0==O G8AB>3> ?@81CB:C  35%; A5@54=L>@VG=V B5<?8 7@>AB0==O 0<>@B870FV9=8E 2V4@0EC20=L  1%. # @>7@0EC=:0E ?>:07=8:V2 DV=0=A>2>-5:>=><VG=>W 5D5:B82=>ABV V=25AB8FV9=>3> ?@>5:BC 4C65 206;828< V 2V4?>2V40;L=8< T ?@89=OBBO V=AB@C<5=BV2 C@0EC20==O DV=0=A>28E @878:V2 ?@>5:BC, 7>:@5<0 @878:C >B@8<0==O 2 <091CB=VE ?5@V>40E ?@>3=>7>20=8E 7=0G5=L G8AB>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20. /: :0B53>@VN =5287=0G5=>ABV @878:8, WE :>=:@5B=89 7<VAB V <0AHB018 WE ?@>O2C, ?>2=VABN ?5@5410G8B8 =5<>6;82>. 030;L=0 B5=45=FVO ?@8 FL><C B0:0: G8< B@820;VH89 ?5@V>4 ?@>3=>7C20==O, B8< 28I89 @V25=L =5287=0G5=>ABV AB0=C V 2V4?>2V4=> B8< 28I89 @V25=L @878:C >B@8<0==O 2 <091CB=VE ?5@V>40E ?@>3=>7>20=8E 7=0G5=L ?>:07=8:V2. "01;8FO 6 @>3=>7=V 7=0G5==O ?>:07=8:V2 G8AB>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20 2 ?>ABV=25AB8FV9=89 ?5@V>4 9>3> 4VO;L=>ABV, B8A. 3@=. ! 7/?>:07=8:8 >:8 ?>ABV=25AB8FV9=>3> ?5@V>4C123456789101'8AB89 ?@81CB>:6137648285811118584151010020386212752138371538650157716771291914124320?VB0;V7>20=89 G8AB89 ?@81CB>: :=15%92064124287167787226515305793412821557308752365101563313711863<>@B870FV9=V 2V4@0EC20==O1730001753601784001802001821501838001856001875001893001913004'8AB89 728G09=89 3@>H>289 ?>BV:26600029988634618640671548794359662174290893986512049331562486 # :C@A>2V9 @>1>BV @V25=L DV=0=A>28E @878:V2 C@0E>2CTBLAO 25;8G8=0<8 :>5DVFVT=BV2 48A:>=BC20==O G8AB>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20: 25;8G8=8 :>5DVFVT=BV2 48A:>=BC20==O 7@>AB0NBL ?@>?>@FV9=> B@820;>ABV @>:V2 ?@>3=>7=>3> ?5@V>4C. 57C;LB0B8 ?@>3=>7=8E @>7@0EC=:V2 G8AB>3> 48A:>=B>20=>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20 =02545=V 2 B01;8FV 7. "01;8FO 7 @>3=>7=V 7=0G5==O G8AB>3> 48A:>=B>20=>3> 3@>H>2>3> ?>B>:C 2 ?>ABV=25AB8FV9=89 ?5@V>4 4VO;L=>ABV ?V4?@8T<AB20, B8A. 3@=. ! 7/?>:07=8:8 >:8 ?>ABV=25AB8FV9=>3> ?5@V>4C123456789101=25AB8FV9=V 28B@0B8 (-500000 B8A. 3@=)228G09=89 G8AB89 3@>H>289 ?>BV:26600029983634612640671548794359662174297893686512049331562486@>4>265==O B01;. 73 V25=L @878:C ?@>5:BC  :>5DVFVT=B8 48A:>=BC20==O5%7%10%12%15%20%24%24%28%28%4=0G5==O :>5DVFVT=BV2 48A:>=BC20==O0,95240,87340,75130,63530,49720,33490,22180,17890,10840,084758A:>=B>20=89 G8AB89 3@>H>289 ?>BV:2533382618762600442584672426051998081647921681591233851323426!C:C?=89 ?@82545=89 G8AB89 3@>H>289 ?>BV:-246662+152142752585337257763309761381140930130908914324741564816 8:>@8AB>2CNG8 40=V B01;8FV 7, ?@>2545<> @>7@0ECT<> ?>:07=8:8 DV=0=A>2>-5:>=><VG=>W 5D5:B82=>ABV V=25AB8FV9=>3> ?@>5:BC. "@820;VABL ?5@V>4C >:C?=>ABV V=25AB8FV9=8E 28B@0B AC<0<8 48A:>=B>20=>3> 3@>H>2>3> ?>B>:C ?V4?@8T<AB20. 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3 >5DVFVT=B8 =0@>I5==O 0=CWB5BV2 kV,n=[(1+VA)n-1]/VAn1%2%3%4%5%6%7%8%9%10%12%15%20%24%28%32%36%11,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,00001,000022,01002,02002,03002,04002,05002,06002,07002,08002,09002,100099,00002,15002,20002,24002,283,32002,360033,03013,06043,09093,12163,15253,18363,21493,24643,27813,31003,37443,47253,643,77763,91844,06244,209644,06044,12164,18364,24654,31014,37464,43994,50614,57314,64104,77934,99345,3685,68426,01566,36246,725155,10105,20405,30915,41635,52565,63715,75075,86665,98476,10516,35286,74247,44168,04848,69999,398310,146066,1520 6,30816,46846,63306,80196,97537,15337,33597,52337,71568,11528,75379,929910,980012,13613,40614,79977,21357,43437,66257,89838,14208,39388,65408,92289,20049,487210,08911,06712,91614,61516,53418,69621,12688,28578,58308,89239,21429,54919,897510,26010,63711,02811,43612,30013,72716,49919,12322,16325,67829,73299,36859,754610,15910,58311,02711,49111,97812,48813,02113,57914,77616,78620,79924,71229,36934,89541,4351010,46210,95011,46412,00612,57813,18113,81614,48715,19315,93717,54920,30425,95931,64338,59347,06257,3521111,56712,16912,80813,48614,20714,97215,78416,64517,5618,53120,65524,34932,15040,23850,39863,12278,9981212,68313,41214,19215,02615,91716,8717,88818,97720,14121,38424,13329,00239,58150,89565,5184,320108,4401313,80914,68015,61816,62717,71318,88220,14121,49522,95324,52328,02934,35248,49764,11084,853112,30148,471414,94715,97417,08618,29219,59921,01522,55024,21526,01927,97532,39340,50559,19680,496109,61149,24202,931516,09717,29318,59920,02421,57923,27625,12927,15229,36131,77237,28047,58072,035100,820141,3198,00276,981617,25818,63920,15721,82523,65725,67327,88830,32433,00335,95042,75355,71787,442126,010181,87262,36377,691718,43020,01221,76223,69825,84028,21330,84033,75036,97440,54548,88465,075105,93157,25233,79347,31514,661819,61521,41223,41425,64528,13230,90633,99937,45041,30145,59955,75075,836128,12195,99300,25459,45700,941920,81122,84125,11727,67130,53933,7637,37941,44646,01851,15963,44088,212154,74244,03385,32607,47954,282022,01924,29726,8729,77833,06636,78640,99545,72651,16057,27572,052102,440186,69303,60494,21802,861298,802123,23925,78328,67631,96935,71939,99344,00650,42356,76564,00281,699118,810225,03377,46633,591060,81767,42224,47227,29930,53734,24838,50543,39249,00655,45762,87371,40392,503137,630271,03469,06812,001401,22404,72325,71628,84532,45336,61841,43046,99653,43660,89369,53279,543104,60159,28326,24582,631040,401850,63271,32426,97330,42234,42639,08344,50250,81658,17766,76576,79088,497118,16184,17392,48723,461332,702443,84450,02528,24332,0336,45941,64647,72754,86563,24973,10684,70198,347133,33212,79471,98898,091706,803226,86053,02629,52633,67138,55344,31251,11359,15668,67679,95493,324109,18150,33245,71567,381114,62185,74260,48233,12730,82135,34440,71047,08454,66963,70674,48487,351102,72121,10169,37283,57681,851383,12798,75624,8111982832,12937,05142,93149,96858,40368,52880,69895,339112,97134,21190,70327,10819,221716,13583,37425,7152302933,45038,79245,21952,96662,32373,6487,347103,97124,14148,63214,58377,17984,072129,04587,79802,9207143034,78540,56847,57556,08566,43979,05894,461113,28136,31164,49241,33434,751181,902640,95873,212941281724048,88660,40275,40195,026120,80154,76199,64259,06337,88442,59767,091779,107343,9022 729 69 377 **5064,46384,579112,80152,67209,35290,34406,53573,77815,081163,92400,07217,745497,00*** :V,n>999996081,670114,05163,05237,99353,58533,13813,521253,21944,83034,87471,629220***** "01;8FO 4 >5DVFVT=B8 ?@82545==O 0=CWB5BV2 0i,n=1/ic-1/[ic*(1+ic)n]n1%2%3%4%5%6%7%8%9%10%12%15%20%24%28%32%10,99010,98040,97090,96150,95240,94340,93460,92590,91740,90910,89290,86960,83330,80650,78130,757621,97041,94161,91351,88611,85941,83341,8081,78331,75911,73551,69011,62571,52781,45681,39161,3315832,9412,88392,82862,77512,72322,6732,62432,57712,53132,48692,40182,28322,10651,98131,86841,766343,9023,80773,71713,62993,5463,46513,38723,31213,23973,16993,03732,8552,58872,40432,2412,095754,85344,71354,57974,45184,32954,21244,10023,99273,88973,79083,60483,35222,99062,74542,5322,345265,79555,60145,41725,24215,07574,91734,76654,62294,48594,35534,11143,78453,32553,02052,75942,534276,72826,4726,23036,00215,78645,58245,38935,20645,0334,86844,56384,16043,60463,224232,9372,677587,65177,32557,01976,73276,46326,20985,97135,74665,53485,33494,96764,48733,83723,42123,07582,78698,5668,16227,78617,43537,10786,80176,51526,24695,99525,7595,32824,77164,0313,56553,18422,8681109,47138,98268,53028,11097,72177,36017,02366,71016,41776,14465,65025,01884,19253,68193,26892,93041110,36769,78689,25268,76058,30644,88697,49877,1396,80526,49515,93775,23374,32713,77573,33512,97761211,255110,57539,9549,38518,86338,38387,94277,53617,16076,81376,19445,42064,43923,85143,38683,01331312,133711,348410,6359,98569,39368,85278,35777,90387,48697,10346,42355,58314,53273,91243,42723,04041413,003712,106211,296110,56319,89869,2958,74558,24427,78627,36676,62825,72454,61063,96163,45873,06091513,865112,849311,937911,118410,37979,71229,10798,55958,06077,60616,81095,84744,67554,00133,48343,07641614,717913,577712,561111,652310,837810,10599,44668,85148,31267,82376,9745,95424,72964,03333,50263,08821715,562314,291913,166112,165711,274110,47739,76329,12168,54368,02167,11966,04724,77464,05913,51773,09711816,398314,99213,753512,659311,689610,827610,05919,37198,75568,20147,24976,1284,81224,07993,52943,10391917,22615,678514,323813,133912,085311,158110,33569,60368,95018,36497,36586,19824,84354,09673,53863,1092018,045616,351414,877513,590312,462211,469910,5949,81819,12858,51367,46946,25934,86964,11033,54583,11292118,85717,011215,41514,029212,821211,764110,835510,01689,29228,64877,5626,31254,89134,12123,55143,11582219,660417,65815,936914,451113,16312,041611,061210,20079,44248,77157,64466,35874,90944,133,55583,1182320,455818,292216,443614,856813,488612,303411,272210,37119,58028,88327,71846,39884,92454,13713,55923,11972421,243418,913916,935515,24713,798612,550411,469310,52889,70668,98477,78436,43384,93714,14283,56193,1212522,023219,523517,413115,622114,093912,783411,653610,67489,82269,0777,84316,46414,94764,14743,5643,1222622,795220,12117,876815,982814,375213,003211,825810,819,9299,16097,89576,49064,95634,15113,56563,12272723,559620,706918,32716,329614,64313,210511,986710,935210,02669,23727,94266,51354,96364,15423,56693,12332824,326421,281318,764116,663114,898113,406212,137111,051110,11619,30667,98446,53354,96974,15663,56793,12372925,065821,844419,188516,983715,141113,590712,277711,158410,19839,36968,02186,55094,97474,15853,56873,1243025,800722,396519,600417,29215,372513,764812,40911,257810,27379,42698,05526,5664,97894,16013,56933,12423529,408624,998621,487218,664616,374214,498212,947711,654610,56689,64428,17556,61664,99154,16443,57083,12484032,834727,355523,114819,792817,159115,046313,331711,924610,75749,77918,24386,64184,99664,16593,57123,1254536,094529,490224,518720,7217,774115,455813,605512,108410,88129,86288,28256,65434,99864,16643,57143,1255039,196131,423625,729821,482218,255915,761913,800712,233510,96179,91488,30456,66054,99954,16663,57143,125 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"   # / / 4> 28:>=0==O :C@A>2>W @>1>B8 7 48AF8?;V=8  @>5:B=5 DV=0=AC20==O  !BC45=B0 _______________________________3@C?8 _______________________ 0B0 2840GV 70240==O _____________ 0B0 740GV @>1>B8_____________________ "5<0 B5>@5B8G=>W G0AB8=8 _____________________________________________ ____________________________________________________________________ 0 <0B5@V0;0E _______________________________________________________ ABC? >74V; I 1@C=BC20==O =5>1EV4=>ABV, 20@B>ABV B0 V==>20FV9=>3> 7<VABC V=25AB8FV9=>3> ?@>5:BC @>728B:C ?V4?@8T<AB20 >74V; II @30=V70FVO DV=0=AC20==O V @50;V70FVW V=25AB8FV9=>3> ?@>5:BC >74V; III FV=:0 DV=0=A>2>-5:>=><VG=>3> B0 A>FV0;L=>3> 5D5:BC 2?@>20465==O V=25AB8FV9=>3> ?@>5:BC @>728B:C ?V4?@8T<AB20 V @53V>=C 8A=>2:8 VB5@0BC@0 >40B:8 0240==O 28402 ___________________________________________ 078=8G .. " VB5@0BC@0 0:>= #:@0W=8 @> V=25AB8FV9=C 4VO;L=VABL ! 1560-12 2V4 18 25@5A=O 1991 @. // V4><>ABV 5@E>2=>W 048.  1991.  ! 47.  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