{VERSION 5 0 "IBM INTEL NT" "5.0" }
{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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 
1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 1 }{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 "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times
" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }
{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 
2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 
5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 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 "List It
em" -1 14 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 3 3 1 0 1 0 2 2 14 5 }{PSTYLE "Bullet Item" -1 15 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 3 3 1 0 1 0 
2 2 15 2 }{PSTYLE "Dash Item" -1 16 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 3 3 1 0 1 0 2 2 16 3 }{PSTYLE "Head
ing 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 1 
1 1 }1 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 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 
2 2 0 1 }}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Cvi\350en\355 z Finan\350n\355 ma
tematiky" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 82 "1. cvi\350en\355: pro
gam Maple, pr\371m\354rn\341 inflace a re\341ln\341 hodnota p\370i bez
\371ro\350n\351m spo\370en\355" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "
rovnost, p\370i\370azen\355 a desetin\341 te\350ka " }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 12 "evalf(2*Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
1 " " }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Pr\371m\354rn\341 m\355r
a inflace" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Pou\236ijte rad\354ji
 " }{HYPERLNK 17 "solve" 2 "solve" "" }{TEXT -1 6 " ne\236  " }
{HYPERLNK 17 "fsolve" 2 "fsolve" "usage" }{TEXT -1 42 " , ale mezi rov
nice dejte tak\351 mnerovnici " }{XPPEDIT 18 0 " iota>0:" "6#2\"\"!%%i
otaG" }{TEXT -1 46 ", nebo\235 n\341s zaj\355maj\355 jen kladn\351 re
\341ln\351 ko\370eny." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 418 "r
estart;\nrovnice:=product((1+iota[i])^(-1),i=1..n)=simplify(product((1
+iota)^(-1),i=1..n));\nn:=4;\ndig:=Digits:\nDigits:=2: #Glob\341pn\355
 prom\354n\341 Digits ur\350uje po\350et platn\375ch cifer.\nprint(`do
sazten\355 hodnot za`,iota[i],`:`);\nfor p from 1 to n do\niota[p]:=ev
alf(abs(0.01*trunc(100*sin(.9+6.2832*p))/100))\nod;\nDigits:=dig: \nso
lve(rovnice,iota);\nsolve(\{rovnice,iota>0\},iota);\nfsolve(rovnice,io
ta);\nfsolve(\{rovnice,iota>0\},iota);" }}}}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 75 "2. cvi\350en\355: sou\350asn\341 hodnota \372ro\350en\351
 \350\341stky, \350len\354n\355 textu prost\370edky Maple" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 38 "Najd\354te
 p\370edpis pro funkci cela \350\341st (" }{HYPERLNK 17 "truncating" 
2 "trunc" "examples" }{TEXT -1 146 "). Namalujte jej\355 graf. Najd
\354te p\370edpis pro funkci, kter\341 ka\236d\351mu \350\355slu p\370
i\370ad\355 \350\355slo, o ktere je dane cislo vetsi nez nejblizsi men
si cele cislo." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "funkce trunc vyh
ovuje na\232\355 definici cel\351 \350\341sti jen napravo od nuly" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "plot(trunc(x),x=-5..5,discont=true
);\nf:=x->x-trunc(x);\nf(3.1415); f(-3.1415);\nplot(f(t),t=-3..5,scali
ng=CONSTRAINED,discont=true);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 172 
"Nalevo od nuly vyhovuje funkce x->trunc(x)-1. Vytvo\370te svou funkci
 CelaCast pomoc\355 v\354tven\355. Pak zkontrolujte hodnoty v cel\375c
h z\341porn\375ch \350\355slech a funkci p\370\355padn\354 upravtre. \+
" }}{PARA 0 "" 0 "" {TEXT -1 1 "`" }{HYPERLNK 17 "if" 2 "if" "usage" }
{TEXT -1 95 "`(podm\355nka,v\375raz je-li podm. spln\354na, v\375raz n
en\355-li podm. spln\354na)\nNezam\354\361te p\370i tom apostrofy." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 25 "\330e\232en\355 je v\355ce, uv\341d\355m 2:" }}{PARA 0 "> " 0 "
" {XPPEDIT 19 1 "CelaCast:=x->`if`(x>0,trunc(x),\n`if`(x=trunc(x),trun
c(x),trunc(x-1))):\n" "6#>%)CelaCastGf*6#%\"xG7\"6$%)operatorG%&arrowG
6\"-%#ifG6%2\"\"!F'-%&truncG6#F'-F.6%/F'-F36#F'-F36#F'-F36#,&F'\"\"\"F
?!\"\"F,F,F," }{MPLTEXT 1 0 2 " \n" }{XPPEDIT 19 1 "CelaCast:=x->trunc
(x+trunc(abs(x))+1)-trunc(abs(x))-1:" "6#>%)CelaCastGf*6#%\"xG7\"6$%)o
peratorG%&arrowG6\",(-%&truncG6#,(F'\"\"\"-F/6#-%$absG6#F'F2F2F2F2-F/6
#-F66#F'!\"\"F2F " 0 "" {MPLTEXT 1 0 96 "
plot(CelaCast(x),x=-5..5,discont=true);\nCelaCast(0.1); CelaCast(0); C
elaCast(-0.1);CelaCast(-1);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 1 {PARA 256 "" 0 "" {TEXT -1 195 "Napi\232te funkce, ktere po
\350\355taj\355 hodnotu diskr\351tn\355ho, exponenci\341ln\355ho a sm
\355\232en\351ho, po \350\341stech konstantn\355ho a po \350\341astech
 afiin\355ho jednoduch\351ho a slo\236en\351ho \372ro\350en\355 v \350
ase t a namalujte jejich grafy." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 
"Zde jsou n\354kter\351 z nich (ostatn\355 zkuste sami):" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 149 "Phi[1]:=(x0,xi,t)->x0*(1+xi)^(CelaCast(t));
\n\nPhi[2]:=(x0,xi,t)->x0*(1+xi)^(CelaCast(t))*(1+xi*(t-CelaCast(t)));
\n\nPhi[3]:=(x0,xi,t)->x0*(1+xi)^(t);\n\n\n" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 74 "Dosad\355me do vzore\350k\371 za po\350\341te\350n\355 \+
kapit\341l 10 a za \372rokovou m\355ru 1,9 (190%)" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 125 "Arg:=(10,1.9,t);\nplot(\{\nPhi[1](Arg),\nPhi[2](Ar
g),\nPhi[3](Arg)\},\nt=0..5,\nthickness=3,\ncolor=[coral,gold,maroon],
discont=true);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "Napi\232te fun
kci, kter\341 po\350\355t\341 stav \372\350tu v \350ase t p\370i zadan
\351m efektivn\355m ro\350n\355m \372roku a slo\236en\351m \372ro\350e
n\355, pokud \372roky po cel\375 dn z\372st\341vaj\355 konstantn\355.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 148 "Napi\232te funkci, kter\341 po\350\355t\341 stav \+
\372\350tu v \350ase t p\370i zadan\351m efektivn\355m ro\350n\355m \+
\372roku a slo\236en\351m \372ro\350en\355, pokud \372roky po cel\375 \+
dn z\372st\341vaj\355 konstantn\355." }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 124 "Urcete rozdily hodnot jednotlivych uroceni v zavislosti \+
na case a uroku. Urcete, kdy je jejich rozdil rovren polovine vkladu" 
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Pomocn\375 obr\341zek a v\375po
\350et (z\341visl\375 na p\370ede\232l\375ch definic\355ch)" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 37 "plot(Phi[2](Arg)-Phi[3](Arg),t=0..5);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "T:=solve(Phi[2](Arg)-Phi[3]
(Arg)=5,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "evalf(subs(t
=T,Phi[2](Arg)));\nevalf(subs(t=T,Phi[3](Arg)));" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 224 "Na
piste funkci, ktera z nominalniho uroku vypocita efektivni urok v zada
nem case, se zadanym intervalem pripisovani uroku a funkci, ktera z ef
ektivniho uroku vypocita nominalni urok. Slozte prvni z nich s funkci \+
pro uroceni." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 55 "3. cvi\350en
\355: Nomin\341ln\355 a efektivn\355 \372rok, spojit\351 \372ro\350en
\355" }}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 181 "Jak velk\341 mus\355 b
\375t m\355ra efektivn\355ho \372roku, aby se vklad zdvojn\341sobil po
jendom \372rokov\351m obdob\355? Po dvoui? Po t\370ech?. . . Napi\232t
e vztah z\341vislosti \372rokov\351 m\355ry na po\350tu t\354chto obdo
b\355." }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 144 "Jak velk\375 mus\355 \+
b\375t vklad, aby po dvan\341ct\355 \372rokov\375ch obdob\355ch byl st
av \372\350tu 1000000, je-li \372rokov\341 m\355ra v i-t\351m z nich 0
.1+trunc(100*sin(i))/1000" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 227 "P
\370edpokl\341dejme, \236e je zn\341m nomin\341ln\355 \372rok eta za d
obu 1 a \236e se p\370ipisuje v \350ase  1/n, n je p\370irozen\351 (te
dy efektivn\355 \372rok v \350ase 1/n je eta/n). Jak\375 je efektivn
\355 \372rok v \350ase 1? A jak\341 je jeho limita pro n  jdouc\355 do
 nekone\350na." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Limita  se po
\350\355t\341 p\370\355kazem " }{HYPERLNK 17 "limit" 2 "limit" "" }
{TEXT -1 25 ", viz n\341sleduj\355c\355 p\370\355klad" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 72 "Theta:=(2*n+1)/(3*n-1);\nLimit(Theta,n=infinity)
=limit(Theta,n=infinity);" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 118 "P
orovnejte rozd\355ly ve velikosti p\370ipsan\375ch \372rok\372 p\370i \+
tomt\351\236 nomin\341ln\355m \372roku a r\371zn\375ch intervalech p
\370ipisov\341n\355 \372rok\371. " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
102 "Zvolte si nomin\341ln\355 hodnotu \372roku a velikost po\350\341t
e\350n\355ho kapit\341lu. Ur\350ete soui\350asnou hodnotu kapit\341lu.
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "restart;\nTh
eta:=n->x[0]*(1+eta/n)^n;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
85 "Theta(1);Theta(2);\neta:=.2; x[0]:=1;\nplot(Theta(x),x=0..10);\npl
ot(Theta(x),x=0..0.1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L
imit(Theta(n),n=0)=limit(Theta(n),n=0);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "Limit(Theta(n),n=infinity)=limit(Theta(n),n=infinity)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "x[0]:=`'x[0]';\neta:='
eta';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Limit(Theta(n),n=i
nfinity)=limit(Theta(n),n=infinity);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 113 "Jak\375 j
e efektivn\355 \372rok za 144 dn\355, je-li nomin\341ln\355 \372rok za
 225 dn\355 0.09 a pokud se p\370ipisuj\355 \372roky ka\236d\375ch 7 d
n\355?" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 114 "Jak\375 je nomin\341l
n\355  \372rok za 144 dn\355, je-li efektivn\355 \372rok za 225 dn\355
 0.09 a pokud se p\370ipisij\355 \372roky ka\236d\375ch 7 dn\355?" }}}
}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 19 "4. cvi\350en\355: \372ro\350en
\355" }}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 61 " \332rok je 0.1, da\361 j
e 0.15, inflace v p-t\351m obdobi ma miru je " }{XPPEDIT 18 0 "iota[p]
:=abs(0.01*trunc(100*sin(.9+6.28*p))/100" "6#>&%%iotaG6#%\"pG-%$absG6#
*(-%&FloatG6$\"\"\"!\"#F/-%&truncG6#*&\"$+\"F/-%$sinG6#,&-F-6$\"\"*!\"
\"F/*&-F-6$\"$G'F0F/F'F/F/F/F/F5F=" }{TEXT -1 109 ", \372rokov\341 a z
da\361ovac\355 obdob\355 jsou stejn\341, \372ro\350en\355 je slo\236en
\351. Jak\341 je m\355ra inflace v p-t\351m obdob\355? Jak\375 bude " 
}{TEXT 256 12 "\350ist\375 re\341ln\375" }{TEXT -1 87 " stav \371\350t
u po 10 \372rokov\375ch obdob\355ch, pokud jedin\375 vklad \350i v\375
b\354r byl u\350in\354n na po\350\341tku?" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "iota:= p-> abs(.01*trunc(100*sin(.9+6.28*p))/100);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%iotaGf*6#%\"pG6\"6$%)operatorG%&ar
rowGF(-%$absG6#,$-%&truncG6#,$-%$sinG6#,&$\"\"*!\"\"\"\"\"*&$\"$G'!\"#
F;9$F;F;\"$+\"$\"+++++5!#8F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "x:=(xi,delta,iota)->x0*(1+xi*(1-delta))^10/product(1+
iota(p),p=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGf*6%%#xiG%&
deltaG%%iotaG6\"6$%)operatorG%&arrowGF**(%#x0G\"\"\",&F0F0*&9$F0,&F0F0
9%!\"\"F0F0\"#5-%(productG6$,&F0F0-9&6#%\"pGF0/F?;F0F7F6F*F*F*" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "V\375sledek p\370\355kladu:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "x(.1,.15,iota);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$%#x0G$\"+.Fm%4#!\"*" }}}{EXCHG {PARA 11 "" 1 "" 
{TEXT -1 0 "" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 81 " Jak\375 by byl
 v\375nos v prvn\355m p\370\355klad\354, kdybychom neplatili dan\354 a
 inflace byla 0? " }{MPLTEXT 1 0 0 "" }{TEXT -1 104 " Byl by v\375nos \+
v prvn\355m p\370\355klad\354 v\354t\232\355, kdybychom pouze neplatil
i dan\354, nebo kdyby pouze inflace byla 0?\n" }}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 26 "Bez dan\354 by stav \372\350tu byl:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "x(.1,0,iota);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$
%#x0G$\"+cN%HS#!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Bez inflac
e, \350ili nomin\341ln\355 stav \372\350tu by byl:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "x(.1,.15,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%
#x0G$\"+UM)4E#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 0 {PARA 0 "" 0 "" {TEXT -1 118 "Jak\341 by musela b\375t obdob
\355 p\370ipisov\341n\355 \372rok\371 aby efektivn\355 \372rokov\341 s
azba byla 1,1 n\341sobkem nomin\341ln\355 \372rokov\351 sazby 1/2?" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "restart;\nrce1:=(1+eta/n)^n=
1+xi;\nrce2:=xi=1.1*eta;\neta:=1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%%rce1G/),&\"\"\"F(*&%$etaGF(%\"nG!\"\"F(F+,&F(F(%#xiGF(" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%rce2G/%#xiG,$%$etaG$\"#6!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$etaG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 21 "rce:=subs(rce2,rce1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$rceG/),&\"\"\"F(*&#F(\"\"#F(%\"nG!\"\"F(F,$\"++++]:!
\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(rce,n);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$$\"+bYF\">#\"\"$$\"+*>;#)p\"!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 0 "" 0 "
" {TEXT -1 194 "Jak\375 mus\355 b\375t \372rok xi, aby \350ist\375 re
\341ln\375 stav \372\350tu z\371stal v \350ase t in N konstatn\355, kd
y\236 na n\354j ulo\236\355me v \350ase 0 \350\341stku 108K\350 a d
\341le ji\236 nic? Inflace je iota  a da\361 delta za ka\236d\351 obdo
b\355 d\351lky 1. " }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 55 "5. cvi
\350en\355: spo\370en\355, vypl\341cen\355 d\371chod\371 a spl\341cen
\355 dluh\371" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "Stavebn\355 spo
\370en\355: " }}{PARA 16 "" 0 "" {TEXT -1 169 "Vstupn\355 poplatek je \+
.01 n\341sobek c\355lov\351 \350\341stky.  C\355lov\341 \350\341stka j
e minim\341ln\354 20000 a maxim\341ln\354 1500000K\350, je celo\350
\355seln\375m n\341sobkem 1000K\350 a je v\354t\232\355, ne\236 naspo
\370en\341 \350\341stka." }}{PARA 16 "" 0 "" {TEXT -1 35 "M\355ra efek
tivn\355ho \372roku je 0.03p. a." }}{PARA 16 "" 0 "" {TEXT -1 86 "Za v
eden\355 \372\350tu se vyb\355r\341 poplatek posledn\355 den 3. 6. 9. \+
 a 12.  m\354s\355ce a jeho v\375\232e je " }{XPPEDIT 18 0 "20+5*trunc
(1.26^(Cas))" "6#,&\"#?\"\"\"*&\"\"&F%-%&truncG6#)-%&FloatG6$\"$E\"!\"
#%$CasGF%F%" }{TEXT -1 85 " korun, kde Cas je doba v roc\355ch od  1. \+
1. 2000, do okam\236iku, kdy se poplatek \372\350tuje." }}{PARA 16 "" 
0 "" {TEXT -1 83 "Poplatek se \372ro\350\355 od okam\236iku, kdy se \+
\372\350tuje. \332lo\236ky se \372ro\350\355 od n\341sleduj\355c\355ho
 dne." }}{PARA 16 "" 0 "" {TEXT -1 224 "P\370edpokl\341dejme, \236e st
\341tn\355 podpora se p\370ipisuje ka\236d\375 rok 12. 5. a od tohoto \+
data se \372ro\350\355. St\341tn\355 podpora se po\350\355t\341 z nasp
o\370en\351 \350\341stky za posledn\355 rok,  tj. z p\370\355sp\354vk
\371 klienta (minus poplatky), a z \372rok\371 ze z\371statku. je to \+
" }{XPPEDIT 18 0 "min(4500,NasporenaCastka/4)" "6#-%$minG6$\"%+X*&%0Na
sporenaCastkaG\"\"\"\"\"%!\"\"" }}{PARA 15 "" 0 "" {TEXT -1 88 "Kolik \+
naspo\370\355me, pokud za\350neme spo\370it 1. 1. 2001 a ulo\236\355me
: 1. 1.2001 vstupn\355 poplatek a" }}{PARA 16 "" 0 "" {TEXT -1 22 "17.
 11. 2001 10 000K\350," }}{PARA 16 "" 0 "" {TEXT -1 22 "13. 11. 2002 1
2 000K\350," }}{PARA 16 "" 0 "" {TEXT -1 20 "1. 12. 2003 15 000K\350" 
}}{PARA 16 "" 0 "" {TEXT -1 21 "10. 10. 2004 15 000K\350" }}{PARA 16 "
" 0 "" {TEXT -1 20 "21. 10 2005 18 000K\350" }}{PARA 0 "" 0 "" {TEXT 
-1 104 "do 12. 3. 2006, co\236 je doba, kdy n\341m spo\370itelna vypla
t\355 pen\355ze z \372\350tu, kter\375 jsme vypov\354d\354li 12. 1. 20
06" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 18 "pozn\341mky k \370e\232en
\355:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 198 "for rok from 2001 \+
to 2005 do\n   for mesic from 3 by 3 to 12 do\n       Cas:= rok-2000+m
esic/12:\n       print(`poplatek dne 31.`,\n             mesic,`.`, ro
k,`je`,20+5*trunc(1.26^Cas),`K\350`);\n   od\nod;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 290 "PocetDniVMesici[1]:=31:\nPocetDniVMesici[2]
:=28:\nPocetDniVMesici[3]:=31:\nPocetDniVMesici[4]:=30:\nPocetDniVMesi
ci[5]:=31:\nPocetDniVMesici[6]:=30:\nPocetDniVMesici[7]:=31:\nPocetDni
VMesici[8]:=31:\nPocetDniVMesici[9]:=30:\nPocetDniVMesici[10]:=31:\nPo
cetDniVMesici[11]:=30:\nPocetDniVMesici[12]:=31:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 84 "PocetDniDoKonceRoku:=(d,m)->\nPocetDniVMesici
[m]-d+sum(PocetDniVMesici[i],i=m+1..12);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 196 "`Pro kontrolu:`;\nPocetDniDoKonceRoku(31,12);\nPocet
DniDoKonceRoku(1,12);\nPocetDniDoKonceRoku(1,11);\nPocetDniDoKonceRoku
(1,1);\n`mimochodem:`;\nPocetDniDoKonceRoku(32,11)=PocetDniDoKonceRoku
(2,12);\n;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "`doba, po \+
kterou se \372ro\350\355 \372lo\236ky:`;\nPocetDniDoKonceRoku(7,11);\n
PocetDniDoKonceRoku(13,11);\nPocetDniDoKonceRoku(1,12);\nPocetDniDoKon
ceRoku(10,10);\nPocetDniDoKonceRoku(21,10);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 169 "`doba, po kterou se \372ro\350\355 poplatky za ve
den\355 \372\350tu:`;\nPocetDniDoKonceRoku(31,3)+1;\nPocetDniDoKonceRo
ku(31,6)+1;\nPocetDniDoKonceRoku(31,9)+1;\nPocetDniDoKonceRoku(31,12)+
1;" }}}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 123 "Porovnejte naspo\370enpu \350\341stku ze stavebn\355ho s
po\370en\355, pokud spo\370\355te 750K\350 m\354s\355\350n\354 s \350
\341stkou, kterou naspo\370\355te, pokud spo\370\355te " }{XPPEDIT 18 
0 "12*750" "6#*&\"#7\"\"\"\"$](F%" }{TEXT -1 16 "K\350 na konci roku" 
}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 332 "Ur\350ete, jak\351 \350ist\351 ro\350n\355 \372rokov\351
 m\355\370e slo\236en\351ho spo\370en\355 odpov\355d\341 zhodnocen\355
 stavebn\355ho spo\370en\355 za p\354t let, pokud spo\370\355te m\354s
\355\350n\355 \372lo\236ky, kter\351 jsou dostate\350n\354 mal\351, ta
k\236e je vypl\341cena jako st\341tn\355 podpora v\236dy \350tvrtina n
aspo\370en\351 \350\341stky. (Stavebn\355 spo\370en\355 je osvobozeno \+
od dan\355, p\370i nestavebn\355m spo\370en\355 uva\236ujte da\361 15%
 \372roku za rok)." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 "Spo\370en
\355, teoretick\375 z\341klad" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 55 "
Spo\370en\355 p\370i slo\236en\351m \372ro\350en\355 a ekvidistantn
\355ch \372lo\236k\341ch" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Obecn
\375 vzorec" }}{PARA 0 "" 0 "" {TEXT -1 93 "P\370edpokl\341dejme, \236
e ukl\341d\341me v ekvidistantn\355ch okam\236ic\355ch, kter\351 jsou \+
od sebe v \350ase vzd\341leny " }{XPPEDIT 18 0 "tau" "6#%$tauG" }
{TEXT -1 37 ", \236e prvn\355 \372lo\236ka se d\354je v okam\236iku " 
}{XPPEDIT 18 0 "epsilon;" "6#%(epsilonG" }{TEXT -1 19 ", druh\341 v ok
am\236iku " }{XPPEDIT 18 0 "epsilon+tau;" "6#,&%(epsilonG\"\"\"%$tauGF
%" }{TEXT -1 20 ", t\370et\355 v okam\236iku  " }{XPPEDIT 18 0 "epsilo
n+2*tau;" "6#,&%(epsilonG\"\"\"*&\"\"#F%%$tauGF%F%" }{TEXT -1 23 " a p
osledn\355 v okam\236iku " }{XPPEDIT 18 0 "epsilon+T;" "6#,&%(epsilonG
\"\"\"%\"TGF%" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Ukl\341d\341me v
 \350ase " }{XPPEDIT 18 0 "n*tau+epsilon,n = 0 .. T;" "6$,&*&%\"nG\"\"
\"%$tauGF&F&%(epsilonGF&/F%;\"\"!%\"TG" }{TEXT -1 24 "\nKolik je \372l
o\236ek v \350ase " }{XPPEDIT 18 0 "t < T+epsilon;" "6#2%\"tG,&%\"TG\"
\"\"%(epsilonGF'" }{TEXT -1 1 "?" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "p
ocetA:=CelaCast((t-epsilon)/tau)+1:" "6#>%'pocetAG,&-%)CelaCastG6#*&,&
%\"tG\"\"\"%(epsilonG!\"\"F,%$tauGF.F,F,F," }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 10 "a v \350ase  " }{XPPEDIT 18 0 "t > T+epsilon;" "6#2,&%\"T
G\"\"\"%(epsilonGF&%\"tG" }{TEXT -1 2 "? " }{XPPEDIT 19 1 "pocetB:=T/t
au+1;" "6#>%'pocetBG,&*&%\"TG\"\"\"%$tauG!\"\"F(F(F(" }{TEXT -1 20 ", \+
co\236 je cel\351 \350\355slo." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Tedy obecn\354, ukl\341d\341me-
li v \350ase " }{XPPEDIT 18 0 "n*tau+epsilon,n = 0 .. T;" "6$,&*&%\"nG
\"\"\"%$tauGF&F&%(epsilonGF&/F%;\"\"!%\"TG" }{TEXT -1 13 "\nm\240me v \+
\350ase " }{XPPEDIT 18 0 "t" "6#%\"tG" }}{PARA 0 "> " 0 "" {XPPEDIT 
19 1 "pocet:=min(pocetA,pocetB); #pocet:=K;" "6#>%&pocetG-%$minG6$%'po
cetAG%'pocetBG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "\372lo\236ek. V
e kter\351m okam\236iku se ukl\341d\341 " }{XPPEDIT 18 0 "i" "6#%\"iG
" }{TEXT -1 13 "-t\341 polo\236kla?" }}{PARA 0 "> " 0 "" {XPPEDIT 19 
1 "okamzik:=i->i*tau+epsilon;" "6#>%(okamzikGf*6#%\"iG7\"6$%)operatorG
%&arrowG6\",&*&F'\"\"\"%$tauGF/F/%(epsilonGF/F,F,F," }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 26 "Jak dlouho se do okam\236iku " }{XPPEDIT 18 0 "
t" "6#%\"tG" }{TEXT -1 7 " \372ro\350\355 " }{XPPEDIT 18 0 "i" "6#%\"i
G" }{TEXT -1 17 "-t\341 \372lo\236ka je-li " }{XPPEDIT 19 1 "okamzik(i
)<=t;" "6#1-%(okamzikG6#%\"iG%\"tG" }{TEXT -1 1 "?" }}{PARA 0 "> " 0 "
" {XPPEDIT 19 1 "doba:=i->t-okamzik(i): doba(i);" "6#C$>%%dobaGf*6#%\"
iG7\"6$%)operatorG%&arrowG6\",&%\"tG\"\"\"-%(okamzikG6#F(!\"\"F-F-F--F
%6#F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Jak\341 je hodnota  " }
{XPPEDIT 18 0 "i" "6#%\"iG" }{TEXT -1 18 "-t\351 \372lo\236ky v \350as
e " }{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT -1 18 " p\370\355 \372rokov
\351 m\355\370e " }{XPPEDIT 18 0 "xi" "6#%#xiG" }{TEXT -1 9 ",  je-li \+
" }{XPPEDIT 19 1 "okamzik(i)<=t;" "6#1-%(okamzikG6#%\"iG%\"tG" }{TEXT 
-1 57 " a pokud byla v okam\236iku ukl\341d\341n\355 jej\355 nomin\341
ln\355 hodnota " }{XPPEDIT 18 0 "z" "6#%\"zG" }{TEXT -1 1 "?" }}{PARA 
0 "> " 0 "" {XPPEDIT 19 1 "hodnota:=i->z*(1+xi)^doba(i): hodnota(i);" 
"6#C$>%(hodnotaGf*6#%\"iG7\"6$%)operatorG%&arrowG6\"*&%\"zG\"\"\"),&F0
F0%#xiGF0-%%dobaG6#F(F0F-F-F--F%6#F(" }{TEXT -1 23 " je tedy za p\370e
dpokladu" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 105 "Chceme-li se\350\355
st sou\350asn\351 hodnoty v\232ech \372lo\236ek proveden\375ch v \350a
se p\370edchg\341azej\355c\355m nobo rovn\351m  okam\236iku " }
{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT -1 16 " Dost\341v\341me \370adu " }
{XPPEDIT 18 0 "Sum(hodnota(i),i=0..pocet)" "6#-%$SumG6$-%(hodnotaG6#%
\"iG/F);\"\"!%&pocetG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Pod\355l
 i-t\351ho a i+1-n\355ho \350lenu  t\351to \370ady  nez\341vis\355 na \+
i, a m\371\236eme jej ozna\350it kvocient, nebo\235 \n" }}{PARA 0 "> \+
" 0 "" {XPPEDIT 19 1 "kvocient:=hodnota(i+1)/hodnota(i): kvocient:=sim
plify(kvocient);\n\n" "6#C$>%)kvocientG*&-%(hodnotaG6#,&%\"iG\"\"\"F,F
,F,-F(6#F+!\"\">F%-%)simplifyG6#F%" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "A tedy je
dn\341 se o geometrickou \370adu, s t\355mto kvocientem." }}}{EXCHG 
{PARA 16 "" 0 "" {TEXT -1 15 "po\350et \350len\371 je\n" }}{PARA 16 ">
 " 0 "" {XPPEDIT 19 1 "PocetClenu=pocet;" "6#/%+PocetClenuG%&pocetG" }
}}{EXCHG {PARA 16 "" 0 "" {TEXT -1 14 "nult\375 \350len je\n" }}{PARA 
16 "> " 0 "" {XPPEDIT 19 1 "NultyClen:=hodnota(0);" "6#>%*NultyClenG-%
(hodnotaG6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "tedy sou\350e
t je:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "Vzorecek:=Sum(hodnota(i),i
=0..pocet-1)=simplify(sum(hodnota(i),i=0..pocet-1));" }}{PARA 0 "" 0 "
" {TEXT -1 34 "Pou\236ijeme jej k definic\355m funkc\355:\n" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 96 "Vzorecek:=simplify(op(2,Vzorecek)):\n#Vzo
recek:=subs(tau=1/k,Vzorecek);\n#limit(subs(k=K,\"),K=k);\n" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Nebo" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 76 "SoucetGeometrickeRady:=Sum(a[0]*q^i,i=0..n)=simplify(sum(a[0]*
q^i,i=0..n));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Vzorecek
2:=subs(a[0]=NultyClen,q=kvocient,n=pocet-1,SoucetGeometrickeRady):" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Vzorecek2:=op(2,Vzorecek2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "psi2:=(Tau,Epsilon,Xi,Z,TT,
cas)->subs(tau=Tau,epsilon=Epsilon,xi=Xi,z=Z,T=TT,t=cas,Vzorecek2);\np
rint(`----------`);\nsimplify(psi2(tau,epsilon,xi,z,T,t)-psi(tau,epsil
on,xi,z,T,t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Prvn\355 funkce
 ud\341v\341 hodnotu naspo\370en\351 \350\341stky, ze zadan\375ch para
matr\371:" }}{PARA 14 "" 0 "" {TEXT -1 67 "Vz\341jemn\341 zd\341kenost
 \372lo\236ek v \350ase (pro ka\236d\351 dv\354 sousedn\355 je stejn
\341)" }}{PARA 14 "" 0 "" {TEXT -1 34 "\310as v n\354m\236 je ulo\236e
na prvn\355 \372lo\236ka" }}{PARA 14 "" 0 "" {TEXT -1 25 "\332rokov
\341 m\355ra (konstantn\355)" }}{PARA 14 "" 0 "" {TEXT -1 41 "Hodnota \+
jednotliv\375ch \372l\371o\236ek (konstantn\355)" }}{PARA 14 "" 0 "" 
{TEXT -1 33 "Doba po kterou se \372lo\236ky ukl\341daj\355" }}{PARA 
14 "" 0 "" {TEXT -1 49 "okam\236ik ve kter\351m n\341s zaj\355m\341 no
min\341ln\355 stav \372\350tu." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "p
si:=(Tau,Epsilon,Xi,Z,TT,cas)->subs(tau=Tau,epsilon=Epsilon,xi=Xi,z=Z,
T=TT,t=cas,Vzorecek);" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 7 "P\370
\355klad" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Bu\357 " }{XPPEDIT 18 
0 "tau=1/3, epsilon=1/6, xi=3/4, z=5, T=2 a nebo T=1.4, t=0..2.27" "6#
%#%?G" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 70 "p2:=plot(\{psi2(1/3,1/6,3/4,5,2,t),[2+1/2,h]\},t=0
..2.75,discont=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "
p3:=plot(psi2(1/3,1/6,3/4,5,2,1.4)*(1+3/4)^(t-1.4),t=1.4..2.75,title=`
y\371statek se \372ro\350\355 d\341l. i kdy\236 u\236 neukl\341d\341me
`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "l := [[n/3+1/6,(n+1
)*5] $n=0..5]:\np1:=plot(l, x=0..2.5, style=point,symbol=circle,title=
`body zn\341zor\344uj\355 jsou sou\350et nomin\341ln\355ch hodnot ulo
\236en\375ch \350\341stek`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "with(plots):\ndisplay(p1,p2,p3);" }}}{EXCHG {PARA 12 "> " 1 "" 
{MPLTEXT 1 0 34 " evalf(psi2(1/3,1/6,1/3,5,2,0.1));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 179 "ll := [trunc(100*(n/3+1/6))/100 $n=0..5]
;\nplot(evalf(subs(tau=1/3,epsilon=1/6,T=2,t=t,pocet)),t=0..4,y=0..7,x
tickmarks=ll, title=`graf z\341vislosti po\350tu ulo\236en\375ch \350
\341stek na \350ase`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "e
valf(subs(tau=1/3,epsilon=1/6,T=2,t=.1,pocet));" }}}}}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 7 "P\370\355klad" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
187 "P\370edpokl\341dejme, \236e ukl\341d\341me 10. den ka\236d\351ho \+
m\354s\355ce 250K\350. Za\350neme v b\370eznu a sko\350\355me v kv\354
tnu o t\370i roky pozd\354ji. Jak\375 bude stav \372\350tu na konci on
oho kv\354tna, je-li \372rokov\341 m\355ra st\341le 2/50?" }}}{EXCHG 
{PARA 20 "" 0 "" {TEXT -1 0 "" }}{PARA 14 "" 0 "" {TEXT -1 45 "Od 1. b
\370ezna do 31. kv\354tna ulo\236\355me 15  \372lo\236ek" }}{PARA 14 "
" 0 "" {TEXT -1 57 "vzd\341lenost sousedn\355ch dvou v \350ase  je jed
en m\354s\355c, to je " }{XPPEDIT 18 0 "1/12" "6#*&\"\"\"F$\"#7!\"\"" 
}{TEXT -1 54 " roku (n\354kdy je to 30 dn\355, n\354kdy 31 dn\355, n
\354kdy 28 dn\355)" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT -1 6 "\330e\232e
n\355" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Prvn\355 (p\370ibli\236n
\351) \370e\232en\355:" }}{PARA 16 "" 0 "" {TEXT -1 43 "po\350\355t
\341me v\232echny m\354s\355ce t\370icetidenn\355 a tdy " }{XPPEDIT 
18 0 "epsilon=1/3" "6#/%(epsilonG*&\"\"\"F&\"\"$!\"\"" }}{PARA 16 "" 
0 "" {TEXT -1 19 "m\354s\355c\371 je 12 za rok" }}{PARA 16 "" 0 "" 
{TEXT -1 29 "za po\350\341tek vezmeme 1. b\370ezen." }}{PARA 16 "" 0 "
" {TEXT -1 35 "za jednotku \350asu bereme rok a tedy " }{XPPEDIT 18 0 
"t=3+3/12" "6#/%\"tG,&\"\"$\"\"\"*&F&F'\"#7!\"\"F'" }}{PARA 0 "" 0 "" 
{TEXT -1 44 "pak jde o mezilh\371tn\355 spo\370en\355 a podle vzorce:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "evalf(psi(1/12,(1/12)/3,2/50,25
0,3+3/12,3+3/12));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 25 "Druh\351 (p\370ibli\236n\351) \370e\232en
\355:" }}{PARA 16 "" 0 "" {TEXT -1 35 "za po\350\341tek vezmeme 10. 3.
   Pak je " }{XPPEDIT 18 0 "epsilon=0" "6#/%(epsilonG\"\"!" }{TEXT -1 
3 " a " }{XPPEDIT 18 0 "t=12+1/12-(1/12)/3" "6#/%\"tG,(\"#7\"\"\"*&F'F
'F&!\"\"F'*(F'F'F&F)\"\"$F)F)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "evalf(psi(1/12,0,2/50,250,3+3/12,3+
3/12-1/36));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "T\370et\355 (p
\370ibli\236n\351) \370e\232en\355:" }}{PARA 0 "" 0 "" {TEXT -1 64 "Sp
o\350\355t\341me efektivn\355 \372rok za m\354s\355c.\nza jednotku \+
\350asu bereme m\354s\355c" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "xi[me
sic]:=(1+2/50)^(1/12)-1;\nevalf(xi[mesic]);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 46 "evalf(psi(1,1/3,xi[mesic],250,3*12+3,3*12+3));" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 149 "Uveden\351 \372vahy m\372\236eme
 zobecnit a pak v\236dy vysta\350\355me se vzorcem . . .\ntedy bez eps
ilon, zejm\351na tedy nen\355 rozd\355l mezi p\370edlh\371tn\355m a po
lh\371tn\355m spo\370en\355. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 221 
"P\370esn\351 \370e\232en\355 z\341le\236\355 na tom, je-li rok p\370e
stupn\375, p\370edpokl\341dejme, \236e nen\355, nebo nen\355 a po jako
u dobu z\371st\341v\341j\355 \372roky konstantn\355, p\370edpokl\341de
jme, \236e po jeden den. Pak doby, po kterou jsou \372lo\236ky \372ro
\350eny jsou posupn\354: . . ." }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 
"" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 59 "Spo\370en\355 p\370i jedn
oduch\351m  \372ro\350en\355 a ekvidistantn\355ch \372lo\236k\341ch" }
}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Obecn\375 vzorec" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 93 "P\370edpokl\341dejme, \236e ukl\341d\341me v ekvidistantn
\355ch okam\236ic\355ch, kter\351 jsou od sebe v \350ase vzd\341leny \+
" }{XPPEDIT 18 0 "tau" "6#%$tauG" }{TEXT -1 37 ", \236e prvn\355 \372l
o\236ka se d\354je v okam\236iku " }{XPPEDIT 18 0 "epsilon;" "6#%(epsi
lonG" }{TEXT -1 19 " a posledn\355 v \350ase " }{XPPEDIT 18 0 "`T+epsi
lon`;" "6#%*T+epsilonG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "V \350ase " }{XPPEDIT 18 0 "t \+
< T+epsilon;" "6#2%\"tG,&%\"TG\"\"\"%(epsilonGF'" }{TEXT -1 6 " m\341m
e " }{XPPEDIT 19 1 "pocetA:=CelaCast((t-epsilon)/tau)+1:" "6#>%'pocetA
G,&-%)CelaCastG6#*&,&%\"tG\"\"\"%(epsilonG!\"\"F,%$tauGF.F,F,F," }
{TEXT -1 11 " a v \350ase  " }{XPPEDIT 18 0 "t > T+epsilon;" "6#2,&%\"
TG\"\"\"%(epsilonGF&%\"tG" }{TEXT -1 6 " m\341me " }{XPPEDIT 19 1 "poc
etB:=T/tau+1:" "6#>%'pocetBG,&*&%\"TG\"\"\"%$tauG!\"\"F(F(F(" }{TEXT 
-1 21 " \372lo\236ek, tedy v \350ase " }{XPPEDIT 18 0 "t>0" "6#2\"\"!%
\"tG" }{TEXT -1 7 " m\341me  " }{XPPEDIT 19 1 "pocet:=min(pocetA,pocet
B):" "6#>%&pocetG-%$minG6$%'pocetAG%'pocetBG" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "\372lo\236ek, i-t\341 \+
\372lo\236ka se ukl\341d\341 v okam\236iku " }{XPPEDIT 19 1 "okamzik:=
i->i*tau+epsilon;" "6#>%(okamzikGf*6#%\"iG7\"6$%)operatorG%&arrowG6\",
&*&F'\"\"\"%$tauGF/F/%(epsilonGF/F,F,F," }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 14 "A do okam\236iku " }{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT 
-1 18 " se \372ro\350\355 po dobu " }{XPPEDIT 19 1 "doba:=i->t-okamzik
(i): doba(i);" "6#C$>%%dobaGf*6#%\"iG7\"6$%)operatorG%&arrowG6\",&%\"t
G\"\"\"-%(okamzikG6#F(!\"\"F-F-F--F%6#F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 24 "Jej\355 hodnota v okam\236iku " }{XPPEDIT 18 0 "t" "6#%\"
tG" }{TEXT -1 4 " je " }{XPPEDIT 19 1 "hodnota:=i->z*(1+xi*doba(i)): h
odnota(i);" "6#C$>%(hodnotaGf*6#%\"iG7\"6$%)operatorG%&arrowG6\"*&%\"z
G\"\"\",&F0F0*&%#xiGF0-%%dobaG6#F(F0F0F0F-F-F--F%6#F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 90 "M\341me se\350\355st sou\350asn\351 hodno
ty (jej\355ch p\371vodn\355 hodnoty a \372roky) v\232ech \372lo\236ek \+
a\236 do okam\236iku " }{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT -1 17 ". Ro
zd\355l hodnoty " }{XPPEDIT 18 0 "i" "6#%\"iG" }{TEXT -1 6 "-t\351 a \+
" }{XPPEDIT 18 0 "i+1" "6#,&%\"iG\"\"\"F%F%" }{TEXT -1 13 "-n\355 \372
lo\236ky je" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "diference:=simplify(
hodnota(i+1)-hodnota(i));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "A te
dy nez\341vis\355 na " }{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT -1 50 " a t
edy \370ada je aritmetick\341. Nult\375 \350len m\341 v \350ase " }
{XPPEDIT 18 0 "t" "6#%\"tG" }{TEXT -1 9 " hodnotu " }{XPPEDIT 19 1 "ho
dnota(0);" "6#-%(hodnotaG6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
28 "a posledn\355 \372lo\236ka m\341 v \350ase " }{XPPEDIT 18 0 "t" "6
#%\"tG" }{TEXT -1 20 " u\236 hodnotu hodnotu " }{XPPEDIT 19 1 "hodnota
(pocet-1);" "6#-%(hodnotaG6#,&%&pocetG\"\"\"F(!\"\"" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 15 "tedy sou\350et je:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 79 "Vzorecek:=Sum(hodnota(i),i=0..pocet-1)\n=simplify(sum
(hodnota(i),i=0..pocet-1));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Vzor
ecek:=op(2,Vzorecek);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Vzorecek2:=simplify(1/2*(hod
nota(0)+hodnota(pocet-1))*pocet);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 88 "subs(min(T/tau,-trunc((-t+epsilon)/tau))=K,\n2*simpli
fy(xxx/sum(hodnota(i),i=0..pocet)));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 72 "simplify(subs(min(trunc((t-epsilon)/tau),T/tau)=K, Vz
orecek-Vzorecek2));" }}}}}{PARA 4 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 29 "6. cvi\350en\355: vypl\341cen\355 d\371ch
od\371" }}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 120 "Jak dlouho lze vypl
\341cet z \371\350tu na kter\351m je 1000 \350\341stku 10 p\370i \372r
okov\351 m\355\370e, j\355\236 se \372ro\350\355 z\371statek \372rokem
, jeho\236 m\355ra je" }}{PARA 16 "" 0 "" {XPPEDIT 18 0 "0.01" "6#-%&F
loatG6$\"\"\"!\"#" }{TEXT -1 6 " p. a." }}{PARA 16 "" 0 "" {TEXT -1 
11 "0.05 p. a. " }}{PARA 16 "" 0 "" {TEXT -1 10 "0.10 p. a." }}{PARA 
15 "" 0 "" {TEXT -1 32 "je-li ona \350\341stka vypl\341cena ro\350n
\354" }}{PARA 15 "" 0 "" {TEXT -1 44 "je-li polovin\341 on\341 \350
\341stkz vypl\341cena p\371lro\350n\354" }}{PARA 15 "" 0 "" {TEXT -1 
50 "je-li  dvan\341ctina on\351 \350\341stky vypl\341cena ka\236d\375 \+
m\354s\355c" }}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 133 "Jak dlouho je t
\370eba spo\370it \350\341stku z (p\370i jak\351m \372rokov\351 m\355
\370e a jak\375ch \372lo\236k\341ch z), aby pak z \372spor mohl b\375t
 vypl\341cen d\371chod velikosti " }{XPPEDIT 18 0 "2*z" "6#*&\"\"#\"\"
\"%\"zGF%" }{TEXT -1 74 " po stejnou dobu, jakou trvalo spo\370en\355,
 z\372stane-li \372rokov\341 m\355ra zachov\341na?" }}}}{SECT 1 {PARA 
3 "" 0 "" {TEXT -1 10 "7. cvi\350en\355" }}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 33 "Vypracujte  komentovan\375 protokol " }}}}}{MARK "4 3" 0 
}{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }