{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 256 14 "HYPOTE\310N\315 \332V\314R" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 54 "Spl\341c en\355 \372v\354ru stejn\375mi spl\341tkami - konstantn\355 anuita " } {TEXT -1 2 "\n\n" }{TEXT 258 9 "\332LOHA 1: " }{TEXT -1 849 "Mlad\375 \+ man\236elsk\375 p\341r s dosta\350uj\355c\355mi p\370\355jmy (tzn. na \+ z\355sk\341n\355 hypot\351\350n\355ho \372v\354ru) se rozhodl postavi t si men\232\355 rodinn\375 domek. Podle p\370edb\354\236n\351 kalkula ce k realizaci sv\375ch pl\341n\371 pot\370ebuje 3 100 000,- K?. Posl \351ze zjist\355, \236e rodi\350e jsou jim ochotni v\354novat \350\341 stku 600 000,- K\350. Banka jim nab\355dne \372rokovou sazbu ve v\375 \232i 4,9% ro\350n\354 a dobu splatnosti 20 let. Ur\350ete\na) v\375 \232i ro\350n\355 polh\371tn\355 anuitn\355 spl\341tky a sestavte umo \370ovac\355 pl\341n,\nb) v\375\232i m\354s\355\350n\355 polh\371tn \355 anuitn\355 spl\341tky (uva\236ujme m\354s\355\350n\355 p\370ipiso v\341n\355 \372rok\371),\nc) ro\350n\355 m\355ru zisku banky, jestli \236e v\355te, \236e za schv\341len\355 \372v\354ru si banka \372\350t uje 0,90 % ze zap\371j\350en\351 \350\341stky (minim\341ln\354 9 000,- K\350, maxim\341ln\354 30 000,- K\350) a za veden\355 \372\350tu 150, -K\350 m\354s\355\350n\354.\nPozn\341mka: V p\370\355pad\354 hypot\351 \350n\355ch \372v\354r\371 banky ned\341vaj\355 klient\371m RPSN ( ro \350n\355 procentn\355 sazba n\341klad\371), ud\341vaj\355 pouze na p \370\341n\355 klienta celkov\351 n\341klady na \372v\354r.\n" }}{PARA 0 "" 0 "" {TEXT 259 12 "\330e\232en\355 ad a)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "eqDl:=Dl=factor(a*v*(sum(v^i, i = 0 .. n-1)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqDlG/%#DlG**%\"aG\"\"\"%\"vGF),&)F*%\"nGF)F)!\" \"F),&F*F)F)F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=solv e(eqDl,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG**%#DlG\"\"\",&%\" vGF'F'!\"\"F'F)F*,&)F)%\"nGF'F'F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "v:=i->1/(1+i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"vGf*6#%\"iG6\"6$%)operatorG%&arrowGF(*&\"\"\"F-,&F-F-9$F-!\"\"F(F(F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ani:=(n,i)->(1-v(i)^n)/ i;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$aniGf*6$%\"nG%\"iG6\"6$%)oper atorG%&arrowGF)*&,&\"\"\"F/)-%\"vG6#9%9$!\"\"F/F4F6F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "an:=unapply(simplify(eval(a,\{v=v(i )\})),Dl,i,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#anGf*6%%#DlG%\"iG %\"nG6\"6$%)operatorG%&arrowGF*,$*(9$\"\"\"9%F1,&)*&F1F1,&F1F1F2F1!\" \"9&F1F1F7F7F7F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Dl: =2500000; n:=20; i:=0.049;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DlG\" (++]#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#?" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"iG$\"#\\!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Annuita:=an(Dl,i,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(AnnuitaG$\"+S/4*)>!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "a := an(Dl, i, n);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG$ \"+S/4*)>!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 239 "matrix([[ 'obdob\355', 'anuita', '\372rok', '\372mor', 'z\371statek'], [0, ``, ` `, ``, Dl], seq([j, a, a*(1-v(i)^(n-j+1)), a*v(i)^(n-j+1), a*ani(n-j, \+ i)], j = 1 .. n-1), [n, a, a*(1-v(i)), a*v(i), ``], [``, ``, ``, ``, ` `], [``, n*a, n*a-Dl, Dl, ``]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K% 'matrixG6#7:7'%'obdob|hyG%'anuitaG%%|ezrokG%%|ezmorG%)z|dzstatekG7'\" \"!%!GF/F/\"(++]#7'\"\"\"$\"+S/4*)>!\"%$\"++++D7F5$\"++W!4k(!\"&$\"+c4 fBC!\"$7'\"\"#F3$\"+o&fv=\"F5$\"+;(3`,)F:$\"+pyVVBF=7'\"\"$F3$\"+cXG[6 F5$\"+W)e!3%)F:$\"+!Gd$fAF=7'\"\"%F3$\"+n]326F5$\"+FP0?))F:$\"+Vn:r@F= 7'\"\"&F3$\"+/o'Q1\"F5$\"+fjB_#*F:$\"+zVjy?F=7'\"\"'F3$\"+Y3`=5F5$\"+T ff0(*F:$\"+?%y:)>F=7'\"\"(F3$\"+eUt4(*F:$\"+9q6=5F5$\"+=nwz=F=7'\"\")F 3$\"+>p&3@*F:$\"+[Z+o5F5$\"+Vi'Hx\"F=7'\"\"*F3$\"+#fMvo)F:$\"+\")pL?6F 5$\"+XD$4m\"F=7'\"#5F3$\"+s%p&Q\")F:$\"+$\\L_<\"F5$\"+'>4Ma\"F=7'\"#6F 3$\"+g]qivF:$\"+M*>GB\"F5$\"+-s7?9F=7'\"#7F3$\"+#HB'epF:$\"+6\"GKH\"F5 $\"+\"R/3H\"F=7'\"#8F3$\"+<:%\\K'F:$\"+)G'fc8F5$\"+iZ9b6F=7'\"#9F3$\"+ O$4-m&F:$\"+1&pIU\"F5$\"+7y$G,\"F=7'\"#:F3$\"+y_!H'\\F:$\"+7**z#\\\"F5 $\"+0#ybj)F57'\"#;F3$\"+@LVJUF:$\"+3r%fc\"F5$\"+'4J'pqF57'\"#TY$F:$\"+;&yEk\"F5$\"+\"e_pU&F57'\"#=F3$\"+kn?fEF:$\"+k(pJs\"F5$\"+7G y.PF57'\"#>F3$\"+zN&[\"=F:$\"+#30w!=F5$\"+Kx<'*=F57'\"#?F3$\"+()3F\"H* !\"'$\"+Jx<'*=F5F/7'F/F/F/F/F/7'F/$\"+!)3=yRF=$\"+!)3=y9F=F0F/Q(pprint 06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "matrix([['doba*spl \341cen\355', seq(j, j = 5 .. 30, 5)], ['\372rok', seq(convert(j*an(Dl , i, j)-Dl,float,20), j = 5 .. 30, 5)]]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7)*&%%dobaG\"\"\"%)spl|\\ycen|hyGF*\"\"& \"#5\"#:\"#?\"#D\"#I7)%%|ezrokG$\"*Q&3#z$!\"$$\"*u.\">sF6$\"+[lX)3\"F6 $\"+!)3=y9F6$\"+)[(=!*=F6$\"+0UQBBF6Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "plot([Dl, j*an(Dl, i, j)-Dl], j = 5 .. 35, co lor = [red, blue], legend = [\"\332v\354r\", \"\332rok\"]);" }}{PARA 13 "" 1 "" {GLPLOT2D 454 454 454 {PLOTDATA 2 "6&-%'CURVESG6%7S7$$\"\"& \"\"!$\"(++]#F*7$$\"3k*****\\i9Rl&!#fS***F0F+7$$\"3-+](=$f%G1\"!#;F+7$ $\"3$*****\\#y,\"G6FIF+7$$\"3/++Dr\"zb=\"FIF+7$$\"37++](4&G]7FIF+7$$\" 3#*****\\7nD:8FIF+7$$\"3/++]-*oyP\"FIF+7$$\"3,+]PpnsM9FIF+7$$\"3,++]si L-:FIF+7$$\"3%********Q5'f:FIF+7$$\"3*)**\\P/QBE;FIF+7$$\"35+++:o?&o\" FIF+7$$\"3?+]Pa&4*\\FIF+7$$\"31++DJ#>&)*>FIF+7$$\"3;+]P>:mk?FIF+7$$\"3()**\\i v&QA7#FIF+7$$\"3;++vtLU%=#FIF+7$$\"3%******\\Nm'[AFIF+7$$\"34++vyb^6BF IF+7$$\"3++]PMaKsBFIF+7$$\"3$)***\\7TW)RCFIF+7$$\"3z*****\\@80]#FIF+7$ $\"3)*****\\7,HlDFIF+7$$\"3()**\\P4w)Ri#FIF+7$$\"3O++]x%f\")o#FIF+7$$ \"3)***\\P/-a[FFIF+7$$\"38+](=Yb;\"GFIF+7$$\"3y****\\i@OtGFIF+7$$\"3/+ ]PfL'z$HFIF+7$$\"35+++!*>=+IFIF+7$$\"3?++DE&4Q1$FIF+7$$\"3=+]P%>5p7$FI F+7$$\"3K+++bJ*[=$FIF+7$$\"3E++Dr\"[8D$FIF+7$$\"3#)******Hjy5LFIF+7$$ \"3E+]P/)fTP$FIF+7$$\"3;+]i0j\"[V$FIF+7$$\"#NF*F+-%'COLOURG6&%$RGBG$\" *++++\"!\")$F*F*F`u-%'LEGENDG6#Q%|exv|gyr6\"-F$6%7S7$F($\"3;8Ux\"Q&3#z $!#77$F.$\"3CfC[JdbEUF\\v7$F2$\"3y9jd!Gfzg%F\\v7$F5$\"3qGp\\.6jS]F\\v7 $F8$\"31GhjYi;![&F\\v7$F;$\"3=is0URe@fF\\v7$F>$\"3\\nIN.jOMjF\\v7$FA$ \"3mg47H4NlnF\\v7$FD$\"3zF!z)H$*)[@(F\\v7$FG$\"3SCz/KV$om(F\\v7$FK$\"3 ^F`(p)=rN\")F\\v7$FN$\"3ANx(z@Y?b)F\\v7$FQ$\"3v-s=\"\\yW-*F\\v7$FT$\"3 4&[6<(3#G]*F\\v7$FW$\"3A_xS!G\"Fjx7$Ffo$\"3#)3ct\"G-'G8Fjx7$Fio$\"3At M@?6Ez8Fjx7$F\\p$\"3dD;#y+5hU\"Fjx7$F_p$\"3?s?f0L*pZ\"Fjx7$Fbp$\"3B?'R iqH-`\"Fjx7$Fep$\"3))HF$G/))od\"Fjx7$Fhp$\"3re]'om3wi\"Fjx7$F[q$\"3%pg %[2SO!o\"Fjx7$F^q$\"3Z?a64FKKFjx7$F]r$\"3E'e5g%)zc *>Fjx7$F`r$\"3#H\"*o\")>&y]?Fjx7$Fcr$\"3<[Cidr%H5#Fjx7$Ffr$\"3%\\))[(* [#zd@Fjx7$Fir$\"32:S\"RoG<@#Fjx7$F\\s$\"3WLrg$zD&oAFjx7$F_s$\"3]CI%4fX NK#Fjx7$Fbs$\"3?W,cS28!Q#Fjx7$Fes$\"3Ksn#4qjlV#Fjx7$Fhs$\"3;Om4s^p)[#F jx7$F[t$\"3G'*))3c`w[DFjx7$F^t$\"3TdhOy8y-EFjx7$Fat$\"3!>UIl7r1m#Fjx7$ Fdt$\"3YTItARO;FFjx7$Fgt$\"3;%p`\")>@lx#Fjx-Fjt6&F\\uF`uF`uF]u-Fbu6#Q% |exrokFeu-%+AXESLABELSG6$%\"jGQ!Feu-%%VIEWG6$;F(Fgt%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "\332v\354r" "\332ro k" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 12 " \330e\232en\355 ad b)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "n:= 12*20; i:=0.049/12; Dl:=2500000; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"nG\"$S#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG$\"+LLL$3%!#7" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DlG\"(++]#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a:=an(Dl,i,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"aG$\"++-6O;!\"&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 12 "\330e\232en\355 ad c)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "eqDl:=Dl=a[0]+Sum(a[k]/(1+i)^(k/12),k=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqDlG/%#DlG,&&%\"aG6#\"\"!\"\"\"-%$SumG6$*&&F)6#%\"k GF,),&F,F,%\"iGF,,$*&\"#7!\"\"F3F,F,F:/F3;F,%\"nGF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "Dl:=2500000; a[0]:=0.009*2500000; n:=12*2 0; for j from 1 to n do a[j]:=16361+150 end do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DlG\"(++]#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"a G6#\"\"!$\")++]A!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"$S#" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "eqDl:=Dl=a[0]+Sum(a[k]/(1+ i)^(k/12),k=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqDlG/\"(++]# ,&$\")++]A!\"$\"\"\"-%$SumG6$*&&%\"aG6#%\"kGF+),&F+F+%\"iGF+,$*&\"#7! \"\"F3F+F+F:/F3;F+\"$S#F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "fsolve(eqDl,i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+fWwQ_!#6" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "240*a[1]+a[0]-Dl;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++9&[\"!\"$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }