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0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 200 212 "Uva\236ujme n\433jakou p
\557j\415ku, kterou chceme dlouhodob\433 spl\341cet. Sou\415asn\341 ho
dnota v\232ech spl\341tek p\531i smluven\351 \372rokov\351 m\355\531e \+
je rovna sou\415asn\351 hodnot\433 p\557j\415ky:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 122 "restart;\nA := subs(N = 12*PocetLet, simplify(sum(x*
(1+xi)^(-1/12*t), t = 1 .. N)));\nDluh := unapply(A, x, xi, PocetLet);
" }}{PARA 0 "" 0 "" {TEXT 200 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
\"AG6\",$*(,&),&\"\"\"F*I#xiGF$F*,$I)PocetLetGF$!\"\"F*F*F.F*I\"xGF$F*
,&F*F.*$)F)#F*\"#7F*F*F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 ">I%DluhG6
\"f*6%I\"xGF$I#xiGF$I)PocetLetGF$F$6$I)operatorGF$I&arrowGF$F$,$*(,&),
&\"\"\"F2F(F2,$F)!\"\"F2F2F4F2F'F2,&F2F4*$)F1#F2\"#7F2F2F4F4F$F$F$" }}
}{EXCHG {PARA 205 "" 0 "" {XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:
-mi(\"Současn\"), Typesetting:-mi(\"á\"), Typesetting:-m
o(\"⁢\", form = \"infix\", fence = \"false\", separator
 = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false\"
, symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", larg
eop = \"false\", movablelimits = \"false\", accent = \"false\", font_s
tyle_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", back
ground = \"[255,255,255]\"), Typesetting:-mi(\"hodnota\"), Typesetting
:-mo(\"⁢\", form = \"infix\", fence = \"false\", separa
tor = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"fals
e\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", l
argeop = \"false\", movablelimits = \"false\", accent = \"false\", fon
t_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", b
ackground = \"[255,255,255]\"), Typesetting:-mi(\"splátek\"), T
ypesetting:-mo(\"⁢\", form = \"infix\", fence = \"false
\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretch
y = \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize \+
= \"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fa
lse\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0
,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"při
\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+
\"false\", separator = \"false\", lspace = \"0em\", rspace = \"0em\", \+
stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", m
insize = \"1\", largeop = \"false\", movablelimits = \"false\", accent
 = \"false\", font_style_name = \"2D Math\", size = \"12\", foreground
 = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"&ua
cute;rokové\"), Typesetting:-mo(\"⁢\", form = \"
infix\", fence = \"false\", separator = \"false\", lspace = \"0em\", r
space = \"0em\", stretchy = \"false\", symmetric = \"false\", maxsize \+
= \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \+
\"false\", accent = \"false\", font_style_name = \"2D Math\", size = \+
\"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typ
esetting:-mi(\"míře\"), Typesetting:-mo(\"&InvisibleTime
s;\", form = \"infix\", fence = \"false\", separator = \"false\", lspa
ce = \"0em\", rspace = \"0em\", stretchy = \"false\", symmetric = \"fa
lse\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", m
ovablelimits = \"false\", accent = \"false\", font_style_name = \"2D M
ath\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,25
5,255]\"), Typesetting:-mn(\"0.04\"), Typesetting:-mo(\"&InvisibleTime
s;\", form = \"infix\", fence = \"false\", separator = \"false\", lspa
ce = \"thickmathspace\", rspace = \"thickmathspace\", stretchy = \"fal
se\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", \+
largeop = \"false\", movablelimits = \"false\", accent = \"false\", fo
nt_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", \+
background = \"[255,255,255]\"), Typesetting:-mi(\"a\"), Typesetting:-
mo(\"⁢\", form = \"infix\", fence = \"false\", separato
r = \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspace
\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity
\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", font_style_name = \"2D Math\", size = \"12\", foreg
round = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(
\"při\"), Typesetting:-mo(\"⁢\", form = \"infix
\", fence = \"false\", separator = \"false\", lspace = \"thickmathspac
e\", rspace = \"thickmathspace\", stretchy = \"false\", symmetric = \"
false\", maxsize = \"infinity\", minsize = \"1\", largeop = \"false\",
 movablelimits = \"false\", accent = \"false\", font_style_name = \"2D
 Math\", size = \"12\", foreground = \"[0,0,0]\", background = \"[255,
255,255]\"), Typesetting:-mi(\"splátkách\"), Typesetting
:-mo(\"⁢\", form = \"infix\", fence = \"false\", separa
tor = \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspac
e\", stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity
\", minsize = \"1\", largeop = \"false\", movablelimits = \"false\", a
ccent = \"false\", font_style_name = \"2D Math\", size = \"12\", foreg
round = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(
\"na\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence
 = \"false\", separator = \"false\", lspace = \"thickmathspace\", rspa
ce = \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", \+
maxsize = \"infinity\", minsize = \"1\", largeop = \"false\", movablel
imits = \"false\", accent = \"false\", font_style_name = \"2D Math\", \+
size = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]
\"), Typesetting:-mi(\"dobu\"), Typesetting:-mo(\"⁢\", \+
form = \"infix\", fence = \"false\", separator = \"false\", lspace = \+
\"thickmathspace\", rspace = \"thickmathspace\", stretchy = \"false\",
 symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", large
op = \"false\", movablelimits = \"false\", accent = \"false\", font_st
yle_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", backg
round = \"[255,255,255]\"), Typesetting:-mn(\"20\"), Typesetting:-mo(
\"⁢\", form = \"infix\", fence = \"false\", separator =
 \"false\", lspace = \"thickmathspace\", rspace = \"thickmathspace\", \+
stretchy = \"false\", symmetric = \"false\", maxsize = \"infinity\", m
insize = \"1\", largeop = \"false\", movablelimits = \"false\", accent
 = \"false\", font_style_name = \"2D Math\", size = \"12\", foreground
 = \"[0,0,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"let
\"), Typesetting:-mo(\"⁢\", form = \"infix\", fence = \+
\"false\", separator = \"false\", lspace = \"thickmathspace\", rspace \+
= \"thickmathspace\", stretchy = \"false\", symmetric = \"false\", max
size = \"infinity\", minsize = \"1\", largeop = \"false\", movablelimi
ts = \"false\", accent = \"false\", font_style_name = \"2D Math\", siz
e = \"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"),
 Typesetting:-mo(\"⁢\", form = \"infix\", fence = \"fal
se\", separator = \"false\", lspace = \"thickmathspace\", rspace = \"t
hickmathspace\", stretchy = \"false\", symmetric = \"false\", maxsize \+
= \"infinity\", minsize = \"1\", largeop = \"false\", movablelimits = \+
\"false\", accent = \"false\", font_style_name = \"2D Math\", size = \+
\"12\", foreground = \"[0,0,0]\", background = \"[255,255,255]\"), Typ
esetting:-mi(\"je\"));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_s
yslibGF'6A-I#miGF$6#Q/SoučasnF'-F,6#Q)áF'-I#moGF$63Q1&In
visibleTimes;F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF;/%'ls
paceGQ$0emF'/%'rspaceGF@/%)stretchyGF;/%*symmetricGF;/%(maxsizeGQ)infi
nityF'/%(minsizeGQ\"1F'/%(largeopGF;/%.movablelimitsGF;/%'accentGF;/%0
font_style_nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+b
ackgroundGQ.[255,255,255]F'-F,6#Q(hodnotaF'F2-F,6#Q/splátekF'F2
-F,6#Q+přiF'F2-F,6#Q6úrokovéF'F2-F,6#Q3mí&
rcaron;eF'F2-I#mnGF$6#Q%0.04F'-F363F5F6F9F " 0 "" {XPPEDIT 19 1 "z[1] \+
:= Dluh(x, 0.4000000000e-1, 20.); 1;" "C$>&I\"zG6\"6#\"\"\"-I%DluhGF&6
%I\"xGF&$\"+++++S!#6$\"#?\"\"!F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I
\"zG6\"6#\"\"\",$*&$\"+Yg_g;!\"(F'I\"xGF%F'F'" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT 200 33 "tj. m\557\236eme si p\557j\415it " }}{PARA 0 "> " 0 "
" {XPPEDIT 19 1 "subs(z[1] = 1, xxx); 1;" "C$-I%subsG%*protectedG6$/&I
\"zG6\"6#\"\"\"F,I$xxxGF*F," }}{PARA 11 "" 1 "" {XPPMATH 20 "I$xxxG6\"
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 58 "n\341sobek toho, co budeme m
\433s\355\415n\433 spl\341cet." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 
186 "Pokud n\341m n\433kdo jin\375 nab\355dne p\557j\415it pen\355ze s
 \372rokovou m\355rou 0.025, bude sou\415asn\341 hodnota v\232ech spl
\341tek, \415ili to, co si m\557\236eme p\557j\415it" }}}{EXCHG {PARA 
0 "> " 0 "" {XPPEDIT 19 1 "z[2] := Dluh(x, 0.2500000000e-1, 20.); 1;" 
"C$>&I\"zG6\"6#\"\"#-I%DluhGF&6%I\"xGF&$\"+++++D!#6$\"#?\"\"!\"\"\"" }
}{PARA 11 "" 1 "" {XPPMATH 20 ">&I\"zG6\"6#\"\"#,$*&$\"+b#R?*=!\"(\"\"
\"I\"xGF%F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 9 "co\236 je" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "xi := (z[2]-z[1])/z[2]; 1;" "C
$>I#xiG6\"*&,&&I\"zGF%6#\"\"#\"\"\"&F)6#F,!\"\"F,F(F/F," }}{PARA 11 ""
 1 "" {XPPMATH 20 ">I#xiG6\"$\"+mthB7!#5" }}}{EXCHG {PARA 0 "" 0 "" 
{XPPEDIT 2 0 "Typesetting:-mrow(Typesetting:-mi(\"krát\"), Type
setting:-mo(\"⁢\", form = \"infix\", fence = \"false\",
 separator = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy =
 \"false\", symmetric = \"false\", maxsize = \"infinity\", minsize = \+
\"1\", largeop = \"false\", movablelimits = \"false\", accent = \"fals
e\", font_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0
,0]\", background = \"[255,255,255]\"), Typesetting:-mi(\"víc\"
), Typesetting:-mo(\".\", form = \"infix\", fence = \"false\", separat
or = \"false\", lspace = \"0em\", rspace = \"0em\", stretchy = \"false
\", symmetric = \"false\", maxsize = \"infinity\", minsize = \"1\", la
rgeop = \"false\", movablelimits = \"false\", accent = \"false\", font
_style_name = \"2D Math\", size = \"12\", foreground = \"[0,0,0]\", ba
ckground = \"[255,255,255]\"));" "-I%mrowG6#/I+modulenameG6\"I,Typeset
tingGI(_syslibGF'6&-I#miGF$6#Q,krátF'-I#moGF$63Q1&InvisibleTime
s;F'/%%formGQ&infixF'/%&fenceGQ&falseF'/%*separatorGF8/%'lspaceGQ$0emF
'/%'rspaceGF=/%)stretchyGF8/%*symmetricGF8/%(maxsizeGQ)infinityF'/%(mi
nsizeGQ\"1F'/%(largeopGF8/%.movablelimitsGF8/%'accentGF8/%0font_style_
nameGQ(2D~MathF'/%%sizeGQ#12F'/%+foregroundGQ([0,0,0]F'/%+backgroundGQ
.[255,255,255]F'-F,6#Q+vícF'-F063Q\".F'F3F6F9F;F>F@FBFDFGFJFLFN
FPFSFVFY" }{TEXT 200 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 48 "n\43
3kdo by \531ekl o dvan\341ct procent v\355c." }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 200 245 "Budeme se obecn\433ji zab\375vat t\355mto probl\351me
m: jak se projev\355 zm\433na \557rokov\351 sazby na velikosti sou\415
asn\351 hodnotz n\433jak\351ho finan\415n\355ho toku, zejm\351na pokud
 je tento tok p\557j\415kou a spl\341cen\355m dluhu." }}}{EXCHG {PARA 
0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
200 14 "P\531\355klad:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "wit
h(plots); -1;" "C$-I%withG6\"6#I&plotsGF%!\"\"" }}{PARA 7 "" 1 "" 
{TEXT 202 49 "Warning, the name changecoords has been redefined" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`Změnu`*`úrokove
`*sazby*`vyjádříme`*multiplikativne*(`č&ia
cute;slem`*delta, tak*jako*`úrok`*`úrokovou`*`mír
ou`);" "*.I-ZměnuG6\"\"\"\"I/úrokoveGF$F%I&sazbyGF$F%I?v
yjádřímeGF$F%I0multiplikativneGF$F%6$*&I5č
íslemGF$F%I&deltaGF$F%*,I$takGF$F%I%jakoGF$F%I,úrokGF$F%
I0úrokovouGF$F%I-mírouGF$F%F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "*.I-ZměnuG6\"\"\"\"I/úrokoveGF$F%I&sazbyGF$
F%I?vyjádřímeGF$F%I0multiplikativneGF$F%6$*&I5&cc
aron;íslemGF$F%I&deltaGF$F%*,I$takGF$F%I%jakoGF$F%I,úrok
GF$F%I0úrokovouGF$F%I-mírouGF$F%F%" }}}{EXCHG {PARA 0 ">
 " 0 "" {XPPEDIT 19 1 "ff[1] := simplify((Dluh(1, zeta*(1+delta), T)-D
luh(1, zeta, T))/Dluh(1, zeta, T)); 1;" "C$>&I#ffG6\"6#\"\"\"-I)simpli
fyG6$%*protectedGI(_syslibGF&6#*&,&-I%DluhGF&6%F(*&I%zetaGF&F(,&F(F(I&
deltaGF&F(F(I\"TGF&F(-F26%F(F5F8!\"\"F(F9F;F(" }{XPPEDIT 19 1 "ff[2] :
= simplify((Dluh(1, zeta+delta, T)-Dluh(1, zeta, T))/Dluh(1, zeta, T))
; 1;" "C$>&I#ffG6\"6#\"\"#-I)simplifyG6$%*protectedGI(_syslibGF&6#*&,&
-I%DluhGF&6%\"\"\",&I%zetaGF&F4I&deltaGF&F4I\"TGF&F4-F26%F4F6F8!\"\"F4
F9F;F4" }{XPPEDIT 19 1 "f := ff[1]; 1;" "C$>I\"fG6\"&I#ffGF%6#\"\"\"F)
" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#ffG6\"6#\"\"\"*(,&F'!\"\"*$),(F'
F'I%zetaGF%F'*&F.F'I&deltaGF%F'F'#F'\"#7F'F'F*,.*&),&F'F'F.F'I\"TGF%F'
)F-,$F7F*F'F'*&)F6,&F7F'F1F'F'F8F'F*F;F'F'F*F+F'*&F5F'F,F'F*F',&F'F*F5
F'F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ">&I#ffG6\"6#\"\"#*(,&\"\"\"!\"\"
*$),(F*F*I%zetaGF%F*I&deltaGF%F*#F*\"#7F*F*F+,.*&),&F*F*F/F*I\"TGF%F*)
F.,$F7F+F*F**&)F6,&F7F*F1F*F*F8F*F+F;F*F*F+F,F**&F5F*F-F*F+F*,&F*F+F5F
*F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"fG6\"*(,&\"\"\"!\"\"*$),(F'F'
I%zetaGF$F'*&F,F'I&deltaGF$F'F'#F'\"#7F'F'F(,.*&),&F'F'F,F'I\"TGF$F')F
+,$F5F(F'F'*&)F4,&F5F'F/F'F'F6F'F(F9F'F'F(F)F'*&F3F'F*F'F(F',&F'F(F3F'
F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "A:=plot(subs(T=20,zet
a=0.04,f),delta=-0.5..0.5,color=red);\n" }{MPLTEXT 1 0 61 "B:=plot(sub
s(T=30,zeta=0.04,f),delta=-0.5..0.5,color=blue);\n" }{MPLTEXT 1 0 61 "
C:=plot(subs(T=20,zeta=0.05,f),delta=-0.5..0.5,color=navy);\n" }
{MPLTEXT 1 0 15 "display(A,B,C);" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I\"
AG6\"-I/INTERFACE_PLOTGF$6&-I'CURVESGF$6#7S7$$!3++++++++]!#=$\"3#\\+H1
6*\\C>F/7$$!3MLLLe%G?y%F/$\"3ilM^z8UH=F/7$$!3OmmT&esBf%F/$\"3?2-J\"R2w
u\"F/7$$!3KLL$3s%3zVF/$\"3EU'p)G+gc;F/7$$!33LL$e/$QkTF/$\"3!Q0.0_Xgc\"
F/7$$!3!pm;/\"=q]RF/$\"3#yf_PF/$\"3A&\\p2tw_R\"F
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F][l$!39_\\\")z59l;F67$Fb[l$!3mhkf\\3+I " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 459 "To n\341m d
\341v\341 prvn\355 p\531edstavu o citliovosti p\557j\415iteln\351 \415
\341tky na \557rokov\351 m\355\531e. Pro mal\351 zm\433ny \372rokov\35
1 sazby (ml\341 \1664), m\341 smysl vypo\415\355tt line\341rn\355 \415
\341st p\531\355r\557stku sou\415asn\351 hodnoty spl\341tek (tj nahrad
it k\531\355vku na obr\341zku p\531\355mkou, kter\341nt\351 k\531ivce \+
bude te\415na). Vypo\415\355t\341me tazlor\557v polynom stupn\433 1:\n
v na\232em p\531\355pad\433:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 49 "tau:=taylor(subs(T=20,zeta=0.04,f),delta=0,2); \n" }{MPLTEXT 1 
0 59 "C:=plot(convert(tau,polynom),delta=-.5..0.5,color=black);\n" }
{MPLTEXT 1 0 17 "display(\{A,C\});" }}{PARA 11 "" 1 "" {XPPMATH 20 ">I
$tauG6\"+'I&deltaGF$$!+80WkL!#5\"\"\"-I\"OG%*protectedG6#F*\"\"#" }}
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0 "" {TEXT 200 455 "To n\341m d\341v\341 prvni predstavu o citliovosti
 p\557j\415iteln\351 \415\341tky na \557rokov\351 m\355\531e. Pro mal
\351 zm\433ny \372rokov\351 sazby (ml\341 \1664), m\341 smysl vypo\415
\355tt line\341rn\355 \415\341st p\531\355r\557stku sou\415asn\351 hod
noty spl\341tek (tj nahradit k\531\355vku na obr\341zku p\531\355mkou,
 kter\341nt\351 k\531ivce bude te\415na). Vypo\415\355t\341me tazlor\5
57v polynom stupn\433 1:\n\nv na\232em p\531\355pad\433:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "tau:=taylor(subs(T=20,zeta=0.04,f),
delta=0,2); \n" }{MPLTEXT 1 0 61 "C:=plot(convert(tau,polynom),delta=-
.02..0.02,color=black);\n" }{MPLTEXT 1 0 17 "display(\{A,C\});" }}
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