E5.1
Su+o! /u u! m+$"! $!1i3! u d+"io d &2(500 "u cu! d m$c!do d di$o. Si "! cu! +!! !cu!1m 1 0.7% >"K( " co$$co( mo" d1 '%Q( 4cu1 "$ 1 "!1do d 1! cu! d"+u" d u !o?
DEPOSITO INTERES SALDO DESPUES DE UN AÑO ???
E5.2
S/2,517.50
2500 0.70%
Si Bob y Judy combi! "u" !#o$$o" d &'(2)0 y &*75( $"+c,-!m( y d+o"i! " moo u! cu! /u +!! 1 2% d i$" !u!1( c!+i!1i3!do m"u!1m( 4cu1 "$ 1 "!1do d 1! cu! d"+u" d 6 !o"?
BOB JUD8 INTS. ANUAL DESPUES DE 6 AÑOS
VFn=VP*(1+(i/m))^n.m
'2)0 *75 2% ??
2420.99
E1 "!1do "$! !1 9!1 d 6 !o" :
E5.3 !b$i11 !c!b! d !!$ &2.5 mi11o" 1! 1o$K! "!!1. L d! 1! o+ci d $cibi$ u o!1 d &'. mi11o" !#o$! o u +!o d &'00(000 !1 9!1 d c!d! !o du$! 1o" +$Fimo" 25 !o". Si !b$i11 +ud !!$ 1 5% !u!1 "ob$ "u" i-$"io"( d"d u +uo d -i"! "$ic!m comico( 4+o$ /u o+ci db ic1i!$"?
;o$m ;o$mu1 u1!! d1 d1 -!1o -!1o$$ +$" +$" d u! u! !u!1 !u!1id id!d !d o$d o$di i!$ !$i! i!
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VPn= (FE/i) * (1-(1+i)^n))
VPn: >'
[email protected] >'G@>'0.05C25 $
1,409,394.457
: Db$K! ic1i!$" +o$ 1! !u!1id!d o$di!$i!( " dci$ d $cibi$ '00000 & !1 9!1 d c!d! !o du$! 1o" +$Fimo" 25 !o" "iui". E5.4
Su m+$"! , 1! o+ci d $!1i3!$ u! i-$"i u u-o "o!$ /u cu"! &'0(000 !cu!1" y /u( " 1o" c1cu1o"( $!$ 1o" !#o$$o" idic!do" 1! "iui !b1! du$! "u -id! d 5 !o"< OA 6 OA OA 2 OA 5 OA 2 Ao A#o$$o" ",m!do" ' &5(000 2 50(000 50(0 00 65(000 6 25(000 5 '5(000 '5( 000 4L! m+$"! db$K! $!1i3!$ $!1i 3!$ "! i-$"i "i $/ui$ u $dimio !u!1 mKimo d1 *% "ob$ od!" "u" i-$"io"?
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=P:
=P: >5000@>'0.0*C': =P: >50000@>'0.0*C2: =P: >65000@>'0.0*C: =P: >25000@>'0.0*C6: =P: >'5000@>'0.0*C5:
=; = ; >'iC
2''0.0* 6206.00 676.2) '77'0.) *76.*7 136401.95
VP=
E5.5
Jo"+# " "u !mio.Ti muc#o di$o(+$o +oco coocimio 9!ci$o.E1 9!c i$o.E1 $cibio u $!1o d & '2.000 +o$ "u $!du!cio y "! bu"c!do u b!co +!$! d+o"i!$ 1o" Modo"( +!$$V" +!$$V " S!-i" B! oM$c u! cu! co u! !"! d i$" !u!1 d1 % com+u"! "m"$!1m( !o /u S1iV" oM$c u! cu! co u! !"! d i$" !u!1 d1 2.75% com+u"! d m!$! co,u!. W!1cu1 1 -!1o$ d 1!" do" cu!" !1 $mio d u !o y $comid ! Jo"+# 1! cu! /u db 1i$. 1i$.
Cai!a"i#ai%n &n'na
Cai!a"i#ai%n m!a"
=;: >=P >CFi =;: >'2000>2.7'%C0.0' =;: >'2000 '.006567 12365.46
=;: >=P >CFi =;: >'2000>'0.0'5C2 =;: >'2000 12002.70
'.0002250
= S " &mina &mina a & "i "a n!a ai!a"i#ai&n &n'na, &n'na, a &'n n a"& !& ma& " &!ni& &n a"i &!a nia ai!a"i#ai&n. E5.6
J!c y Ji11 !c!b! d $ ! "u +$im$ #io.Si " "+$! ! /u 1! ui-$"id!d cu" &'50.000 !u!1" d$o d ' !o"( 4Wuo db$i! m+3!$ ! d+o"i!$ !u!1m( !1 9 d c!d! !o( co 1 +$o+o"io d !cumu1!$ "u9ci" Modo" +!$! +!!$ 1o" co"o" d1 +$im$ !o d "udio" !1 iicio d1 !o '*? Su+o! /u +ud! !!$ u! !"! d1 $dimio !u!1 d1 )% "ob$ "u i-$"io.
;E:=;@>>'iCG'@i
;E:'50000 @
>H>'0.0)C'*G' 0.0)
;E: '5000 @ > >'iC'*G' i
;E:'50000 @ >H>'0.0)C'*G' 0.0) = ia m#a a &i!a $ 4444.44 a" n aa a8& a na !aa ana" " 6 aa
E5.1
;E:'50000 @
> H.25G' 0.0)
;E:'50000 @
2.025 0.0)
;E:'50000 @
$
.75
4,444.44
U"o d u! 1K! d ,m+o E1 !dmii"$!do$ 9!ci$o d S!$buc Idu"$i" -!1! $!1i3!$ u! i-$"i /u $/ui$ u d"mbo1"o iici!1 d &25(000 y d 1! cu!1 "+$! ob$ $!d!" d Mc,-o d &(000 !1 9!1 d1 !o '( &)(000( !1 9!1 d 1o" !o" 2 y ( &'0(000 !1 9!1 d1 !o 6( &(000 !1 9!1 d1 !o 5( y &7(000 !1 9!1 d1 !o ).
! Dibu y d"c$ib! u! 1K! d ,m+o /u $+$" 1o" uo" d Mc,-o $1!cio!do" co 1! i-$"i +$o+u"! d S!$buc Idu"$i". b U,1ic c#!" +!$! dmo"$!$( 1! 1K! d ,m+o d1 ici"o !( cmo 1! c!+i!1i3!ci +!$! c!1cu1!$ 1 -!1o$ Muu$o +ud u,1i3!$" co 1! 9!1id!d d mdi$ odo" 1o" uo" d Mc,-o !1 $mio d1 !o ). c U,1ic c#!" +!$! dmo"$!$( 1! 1K! d ,m+o d1 ici"o b( cmo 1 d"cuo +!$! c!1cu1!$ 1 -!1o$ +$" +ud u,1i3!$" co 1! 9!1id!d d mdi$ odo" 1o" uo" d Mc,-o 1 ,m+o c$o. d 4E cu1 d 1o" modo" >-!1o$ Muu$o o -!1o$ +$" " b!"! co m!yo$ M$cuci! 1o" $" 9!ci$o" +!$! om!$ dci"io"? 4Po$ /u?
a)
uo uo d Mc Mc,,-o o !o"
G&25 G&25(0 (000 00.0 .00 0 & 0
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7(00 7(000. 0.00 00 )
+$im$ d"mbo1"o
) :'"i ;a aa m&!a, m&!a, n "a "
min& " a8& 6. -!1o$ Muu$o G&25(000.00 &
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7(000.00
0 ' 2 c!+i!1i3!cio odo db d c!+i!1i3!$" +!$! u "o1o +$iodo( 1 c!"o !1 )o !o
6
5
) -!1o$ Muu$o
) :'"i ;a aa m&!a, n "a "
(000.00 & '
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& n! nani& aan mG n " a"& n! n " a"& !&, a "n a ii&n an! " inii& n &!&, n " m&mn!& &, &m& "& a " G""& " a"& a!a".
= )
2. Ca""& " a"& F!& D Sin ' "i#a "a !a"a & "a ni&n &amaa a""a&a nania '"i "a &m"a aia aa " a"& !& n!& &n "a !aa in! aa , i, " nm& i&&, n, aa a""a " a!& in! " a"& !& n aa n& "& a& n!an n "a !a"a iin!. C&ma " a"& a""a& &n " a"& &&i&na n "a !a"a ?-1 " ?ni ?
E5.2
C?S@ A B W D
A?S? E BAEES, i m& i&&, n '2.00% ).00% *.00% .00%
Ca""& F&m"a Va"& Aa"a '.2566 '.'*'0 '.'' '.'255
2 2 6
'.25 '.'* '.'* '.'
!aD & a"& "!a& a"ia "a &m"a &n ia" a "& &&i&na "a !a"a. E5.3
=!1o$ Muu$o( U"d , &'00 +!$! i-$,$. Si u"d +ud !!$ 1 '2% d i$"( 4cuo ,m+o !+$oFim!d!m !$d!$ "u i-$"i d &'00 +!$! co-$,$" &200? A#o$! "u+o! /u 1! !"! d i$" " F!c!m 1! mi!d< )%. Wo 1! mi!d d 1! !"! d i$"( 41 #c#o d du+1ic!$ "u di$o !$d!$ 1 dob1 d ,m+o? 4Po$ /u? 4Wuo ,m+o !$d!$?
C?S@ ? I:'2%( =P:G'00 =;: 200 = 6.12 ?@S
C?S@ ? I:)%( =P:G'00 =;: 200 = 11.90 ?@S
= S !aa && mn& & mG " &" a"&. :na "a a#&n aa a mG &!a n " a& H a mG <&& an! "& & "a ai!a"i#ai%n.
Va"& !&, E c!d! uo d 1o" c!"o" mo"$!do" 1! "iui !b1!( c!1cu1 1 -!1o$ Muu$o d1 uo d Mc,-o ico( d+o"i!do 1 dK! d #oy( !1 $mio d1 +$iodo d d+"io "i 1 i $" "
E5.4
c!+i!1i3! !u!1m ! 1! !"! "+ci9c!d!.
S@:CB@D Ca&
=;:200 F >'0.0520:&50 !
"& '& Ini Aaa in!> 200 5% 6500 % '0000 *% 25000 '0% 7000 ''% 60000 '2%
A B W D E ;
=;:6500 F >'0.057: & 7(7'2.2' b =;:'0(000 F >'0.05'0: & 2()7.76 c =;:25(000 F >'0.05'2: & 7(6)0.7'
PE 20 7 '0 '2 5 *
VF S/530.66 S/7,712.21 S/23,673.64 S/7J,460.71 S/62,347.15 S/110,923.15
d =;:7(000 F >'0.055: & )2(67.'5 =;:60(000 F >'0.05*: S ''0(*2.'5 M
P5.5
=!1o$ 1 ,m+o( U"d cu! co &'(500 +!$! i-$,$ #oy !1 7% d i$" com+u"o !u!1m.
a) Ca"" Gn!& aG am"a& n "a n!a a" !>min& D 1. 3 a8&, 2. 6 a8&, 3. 9 a8& ? "& im& 3 a8& i= 7 n= 3 a8& VP= 1500 VF3= VF3=
? "& im& 6 a8&
0.07 '500 '500 F ' 0.07C 1J37.56
? "& im& 9 a8& 0.07 ) '500 '500 F >' 0.07C) 2251.10
i= 7 n= 6 a8& VP= 1500 VF6= VF6=
i= 7 n= 9 a8& VP= 1500 VF9= VF9=
0.07 * '500 '500 F >' 0.07C) 2757.69
) :'"i "& "!a& &!& n " ini & a) aa a""a " m&n!& " in!> ana& nD 1. "& 3 im& a8& (a8& 1 a 3), 2. "& 3 a8& ii n! (a8& 4 a 6), 3. "& I"'m& 3 a8& (a8& 7 a 9). ' I$" !!do ! 1o" +$im$o" !o"
VF3 - VP = VF3 - VP =
'7.5) 337.56
'500
VF6 - VP = VF6 - VP =
225'.'0 751.10
'500
VF9 - VP = VF9 - VP =
2757.)* 1257.69
'500
) C&ma "& "!a& &!& n " in i& ). EK"i & > " m&n!& " in!> ana& amn!a n aa i&& i& 3 a8&.
Lin!a " <&& ini%n a ma&, !ami>n G ma& "a an'a !&!a" in! &a&, n& a"& ina& a "a ma& an'a 'm& "a ma inia" $ 1,500 in'a. E" n!& mG im&!an! " in!> aii&na" &!ni& & 3 a8& " <&& amn!a n aa <&& iin! 3 a8&. E" in!> !&!a" aa "& 3 im& a8& $ 337.56, in ma&, aa " n& <&& 3 a8& ( 3 a 6 a8&) " in!> aii&na" " !aa& $ 751.10. Paa " ! <&& 3 a8& ( 6 a 9 a8&), " in!> inmn!a" $ 1257.69. E! in! ami& n "& in! ana& a "a &m&ii%n, "a &!ni%n in! & "& in! ana& an!i&. Can!& ma& " in!> i& ana&, ma& G " ima!& " in!> &m!&.
P5.7
Va"& !& 'm&. :! &i!a $ 10,000 n na n!a aa 9 in! ana" a a & & Ka!amn! n!& 10 a8& MCGn!& aa ana& a" na" "& 40 a8& i i a & " &i!& iniia" n& n!& 10 a8&N
Aaa =A 2
9 '0000 '0 !o" 60 !o"
VF $314,094.20
!aD ?" na" " a8& 40 am& ana& $ 314,094.20 i &i!am& $10,000 " ia &
P5.11
Va"& Pn! aa aa n& "& a& m!an n "a !a"a iin! , a"" " a"& n! " ;& '&, &n!an& a "a !aa aa &nin& " '& i a" na" " i&& inia&.
F:@ E EFECABV@ :BC@
C?S@ A B W D E
P5.12
A?S? E ESC:EA@
7000 2000 '0000 '50000 65000
FB? E PEB@@ (?@S)
'2% % '6% ''% 20%
V?@ ?CA:? 6 20 '2 )
S@. 6(66.) S@. )(007.5 S@. 2(075.5* S@. 0('*).' S@. '0(6)5.5)
C&n!& " a"& n!D &na "a iin! n!a
a.M O Bni&n nia a &, na in! ana" 12 a"a $ 6,000 a" na" " a8& 6 Aaa VF n=
'2% )000 ) !o"
$3,039.79
. MCa" " a"& n! $ 6,000 in a" na" 6 a8& i "a !aa n!& 12 N Aaa n= VF
'2% ) !o" )000
$3,039.79
. MCGn!& "& ma aaia & & na &ma "iia $ 6,000 a" na" 6 a8& i &!& &&!nia 12N V?= VF= = Aaa
)000 ) '2% Wo"o d O+o$uid!d
$3,039.79
3039.79
!aD a &n"i&n n "a ! n!a ia " Va"& n! n "& 3 a& " mim& a n!a " in& a in' a&a &n "a mima !aa " mim& i&& 6 ?8& P5.13
Va"& n!. ? im an " a &i& n a& !& $500 a 3 a8& a a' &. Si &!& &&!nia 7 ai!a"i#a& ana"mn!, MO> a"& aa & aa &ma ! a&Na" & a a &&!niaN MCGn!& "& m a
VF ABELP@ BAEES
&500 AÑOS 7%
V? P5.14
&60.'5
Va& " in& n " 'm&. :n &n& a&& " !a& B&a &n' n $100 a nimin!& a 6 a8& a a' &ma.Paa "& &n& !a!a" an &m''& &n "& &n& a&& !a& :ni&, "& a" aan " J in! ana" (&m!& ana"mn!) M? i& " !a& n &n&N Sna n& a"i#an a& n '& & "& &n& a&& an! m&"&.
i!m 1 2
P5.15
F:@ :BC@
A?S? SCA@
FB? E PEB@@
V?@ PESEAE
VF
TASA
NPER
VA
.0%
)
'00.00
S@.).02
Va"& " in& n " 'm& !aa n!&. :. ?aa ana n mi& n "a "&!ia &m! aa" $1,000.000 Ka!amn! n!& 10 a8&. P!& " a& $1,000,000 "& aan'#a " !a& &n ! i, Kin!n &&!nia n " & & a ami& n a& ni& inmia!& n '&.
a) Ca" " m&n!& ma a& a" nia & i ia ana "a iin! !aa in! & ini&n i& imi"a an! " i&& 10 a8&.
1 2 3
F:@ :BC@
A?S? SCA@
FB? E PEB@@
VF
TASA
NPER
).0% *.0% '2.0%
'0 '0 '0
'(000(000.00 '(000(000.00 '(000(000.00
V?@ PESEAE VA
[email protected](*6.7 [email protected](6'0.' S/.321,973.24
) i!a " a""& " ini& a) &nin& " a& $1,000,000 iia n 15 a8& n& n 10.
1 2 3
F:@ :BC@
A?S? SCA@
FB? E PEB@@
VF
TASA
NPER
).0% *.0% '2.0%
'5 '5 '5
'(000(000.00 '(000(000.00 '(000(000.00
V?@ PESEAE VA
[email protected]'7(2)5.0) [email protected](5.06 S/.1J2,696.26
) a& &n "& "!a& &!& n "& ini& a) ) ana"i " !& &n !an!& "a !aa in! &m& " 'm& "a i&n " a& & " a"& n! na ma !a = S &a n am& a& a na mn& !aa in! " a"& n! ma&. P5.16
C&maai&n " a"& n " 'm& m&n!& ni&. ? ami& n a& $20,000 & na ma &n&ia " mi! "i na "a a"!na'a n!a "a iin! !a"a. S &&! &&!nia " 11
a)
F:@ :BC@
A?S? SCA@
FB? E PEB@@
VF
TASA
NPER
V?@ PESEAE
? H
2(500.00 56(000.00
''.0% ''.0%
*
S/.20,J3J.95 S/.21,109.94
C
')0(000.00
''.0%
20
S/.19,J45.43
VA
a) a""a " a"& aa a"!na'a 'n a" ia & ) Aa "a a"!na'a &n a!a", i a"n 20,000 & = @. Ainn a"& i'n!& ) O a"!na'a "iia . = P& !ma a"& n! "iiaa "a &i%n H P5.17
ii&n ini&n n ;& '&. A&m ?"Kan 'n "a &!nia a"i#a a"na "a ini&n n! "a iin! !a"a. S in" " i& &ma, " m&n! "a n!a '& nia " a8& i%n " in& aa aa ini&n.MO &mnai&n &ma aia !,&nin& !&m ana " 10 & ini&n
F:@ :BC@
A?S? SCA@
FB? E PEB@@
VF
TASA
NPER
0(000.00 (000.00 '0(000.00 '5(000.00
'0.0% '0.0% '0.0% '0.0%
5 20 '0 60
? H C
V?@ PESEAE VA
PRECIO
S/.1J,627.64 S/.445.93 S/.3,J55.43 S/.331.42
Diferencia
'(000.00 )00.00 G (500.00 '(000.00 G
)27.)6 '56.07 55.6 )).5
Sob$-!1o$!do Sub -!1u!do Sob$-!1o$!do Sub -!1u!do
= C&m& H & nn!an a"a& P5.1J
Va"& !&
V? '0(000.00 6(77.0
P5.19
PE 7 6
A?S? 5% 5%
VF S@. S@. S@.
'6(07'.00 5(*2*.00 20(000.00
Va"& !& na ana"ia, Paa aa n& "& a& "a !a"a n!a a &n'nai%n, &n!! "a n!a "an!aa.
Ca& ? H C E
L!& ?na"ia 2500 500 0000 ''500 )000
Aaa Bn!.
% '2% 20% *% '6%
'0 ) 5 0
VF @B?B@ ?ABCBP?? G2552.)750)' G27*20.*02507)5 G'7*.755260767 G5)'.25*)2*)) G7550.6 G*0620.6 G'06).07*6' G''60'.0050)6'*' 2)26.0)627* 2**)6'.*6'52722
) C&ma "& G""& a"i#a& n "a & &i&n " ini& a). Si !&& "& mG man i>n'&, M> '& ana"ia (&inaia & a"an!aa) i"N EK"i & >. Vaiai&n C?S@ ?
C?S@ H 7.41 7
C?S@ C 10.71 11
C?S@ 16.67 17
J.26 J
C?S@ E 12.2J 12
a ana"ia an'iaa "!a n n ma& a"& !& n aa a&. ?" &i!a " a& n " inii& n& a" na" " a8&, 'n n a8& mG "a ai!a"i#ai%n. C&maan& "a inia &n!a" n! " a"& !& an'ia& " a"& !& &inai& , !nm& " iin! &nD a& C (17) , Ca& E ( 12 ) , Ca& H ( 11.) , Ca& ( J) na"mn! " Ca& ? ( 7) . En " a" m& "a m& ini%n a n " a& C.
P5.20
Va"& Pn! na ana"ia, Paa aa n& "& a& "a !a"a n!a a &n'nai%n, &n!! "a n!a "an!aa.
Ca& A B W D E
n'a "a ana"i '2000 55000 700 '60000 22500
Aaa in!> 7% '2% 20% 5% '0%
Pi&& (a8&)
VP @ 2206.6 66*5'.7' 5)6.6 60506.)' 52*.27
'5 * 7 5
?ACBP?@ 25.76 5065.*' )77.20 6252*.6 *2.20
) C&ma "& G""& a"i#a& n "a & &i&n " ini& a). Si !&& "& mG man i>n'&, M> '& ana"ia (&inaia & a"an!aa) i"N EK"i & >. C?S@ ? C?S@ H C?S@ C C?S@ C?S@ E 6.54 10.71 16.67 4.76 9.09 7 11 17 5 10 a ana"ia an'iaa "!a n n ma& a"& n! n aa a&. ?" &i!a " a& n " inii& n& a" na" " a8&, 'n n a8& mG "a ai!a"i#ai%n. C&maan& "a inia &n!a" n! " a"& n! an'ia& " a"& n! &inai& , !nm& " iin! &nD a& C (17) , Ca& H ( 11 ) , Ca& E ( 10) , Ca& ? ( 7) na"mn! " Ca& ( 5) . En " a" m& "a m& ini%n a n " a& C.
P5.23 20.-Va"& Pn! na ?na"ia '& n an! & !a !a!an& n na ana"ia '& inmia!&, &n na an'a nia a & " &&i&naa $12,000 aa na a8& an! "& &Kim& 25 a8& a!a"mn! ana 9 n ini&n a& i#& n &maai&n &n "a ana"ia '& MCGn!& "& ma aaia & !a ana"iaN +!o +$iodo !"!
P5.25
'2000 c@9 d !o 25 !o" *% S/. 117,J70.96 "& ma &ia aa&
22.- Va"& n! na ana"ia n &maai&n &n na an'a nia. &na aaa ana "a "&!ia. P ii n mi& n &ma $40,000 a n a8& an! "& &Kim& 25 a8& ( i, $1000,000 a" !min& 25 a8&) & &m& na an'a nia $500,000 aa& inmia!&.
a. i a & ana 5 ana"mn! & ini&n an! "& &Kim& 25 a8&, in&an& im!& &!a &niai&n, MO> a"!na'a "iN . Mamiaia ii&n "a a! a i ia ana 7 n # 5 & ini&n an! "& &Kim& 25 a8&N . Qa"an& n n n'& !i!amn! &n&mi&, M&Kimaamn! a !aa '"ia ia inin! n! !& & "anN
P5.26
!.
PAO TIEXPO =; INTERES V?
60000 25 '000000 5% $563,757.7J
c.
=A TIEXPO PAO BAEES
500000 25 60000 6
23. P!iD C&ni "& a!& "a !a"a iin!
b.
P!o P$iodo =; T!"! Va
60000 25 '000000 7% $466,143.33
!aD PERPETUIDAD A B W D
P5.27
WANTIDAD ANUAL 20000 '00000 000 )0000
TASA DWTO % '0% )% 5%
a) !aD ) ;!co$ d I$" =!1o$ P$" 12.50 S/. 250,000.00 10.00 S/. 1,000,000.00 16.67 S/. 50,000.00 20.00 S/. 1,200,000.00
D$mi +!$! c!d! u! d 1!" +$+uid!d" ! E1 M!co$ d i$" d1 -!1o$ +$" !+$o+i!do b E1 -!1o$ +$"
Cai%n na nai%n, ?" !>min& & in!&i%n a "a nan#a, La"a in'% !an &m"aia &n "a an'a &n&imin!& I'" in!an!, &nni% a a, in &n K a"mn& aina& "a niia a "a ai!, aan na nai%n. a nai%n mi'
a) MO> !an an " a& Ini& iniia" " & a La"a n a a "a niia aa nania "a nai%nN = (600*3)/0.06 =
30000
) MO> m&n!& ni!a
P5.29
20000
a"& n m&n!& ni& n in& miK!&. Rina Vi!a" &nin& n n n 8& !n& & a "n& a8&. E" &ma& !a i!& a $24,000 a" i "a !anai&n & "& m&n!& n!a& n "a iin! !a"a a" inii& aa n& "& &Kim& 5 a8&. C&m& ina a&a n& ni!a " in& a"mn! "ana &i!a"& n na n!a ana " 7 in! ana". C&m& a &ma na aa a" !min& 5 a8& " i "a n!a " !n& i "i "a a"!na'a a& (a a " m&n!& ni& $24,000 & " in& miK!& a& "a iin! !a"a), &&i&n " a"& !&ma a"!& a" na" "& 5 a8&. MO a"!na'a "iiaN
F:@S ;LUJO UNIWO TASA
0 26(000.00 7% =A [email protected](6*.72
;LUJOS
1
2
3
2(000.00
6(000.00
4
)000
5 S/.33,661.24
000
'0000 =; S/.32,951.16
= E"i
Va"& in& miK!&. Ca"" " a"& n! "& in& ;& '& m!a "a iin! !a"a. S&na " &!& &&'na "a ma " 12
P5.30
F:@S A B W TASA
P5.31
0 [email protected] G S@.'0.25 S@.'0.2) '2%
=A 1 2(000.00 '0(000.00 '0(000.00
2
3
(000.00 5(000.00 '0(000.00
6(000.00 5(000.00 '0(000.00
4
5
)(000.00 5(000.00 '0(000.00
(000.00 5(000.00 '0(000.00
6 70(000.00 0(000.00
7
0(000.00
J
0(000.00
9
0(000.00
Va"& n!D Bn& miK!&( Wo"id$ 1o" i$"o" miFo" d uo" d Mc,-o /u +$"! 1! "iui !b1!.
?@ ' 2 6 5 A@A?
Bn& ;& '& ? H S@. 50(000.00 S@. '0(000.00 S@. 60(000.00 S@. 20(000.00 S@. 0(000.00 S@. 0(000.00 S@. 20(000.00 S@. 60(000.00 S@. '0(000.00 S@. 50(000.00 S/. 150,000.00 S/. 150,000.00
VP E ? 4347J.26 30245.75 19725.49 11435.06 4971.77 109J56.33
VP E H 9523.J1 1J140.59 25915.13 3290J.10 39176.31 91272.9J
'5%
S@ '0*(5).
S@*'(272.*
a) Ca"" " a"& n! aa in& an& na !aa n!& " 15
) C&ma "& a"& n! a""a& ana"<"& &nian& " & "& ;& '& n& &n!a& man n !&!a" $150,000 n aa a&. = E" ;& aa " a& ?, &n n a"& a!a" $ 109,J56.33, mG a& " ;& aa " a& H $ 91,272.9J i& a "& ;& '& mG an &n n "& im& a8& " ?, an& a"& a!a" ma&, min!a "& ;& '& mG 8& n n " !&. En " a& H !&& "& &n!ai&, "& m&n!& ma& &n n "& I"'m& a8& ;& '& inmn!a a !a> "& a8&. P5.32
=!1o$ d i$"o miFo( Y!$ Si"m" Ic. U! m+$"! M!b$ic! d /ui+o d -ii1!ci! 1c$oic!( "! co"id$!do -d$ ! u! coocid! c!d! d M$$$i!" 1o" d$c#o" +!$! com$ci!1i3!$ "u "i"m! d "u$id!d dom",co. E1 !cu$do +$o+u"o $/ui$ /u 1! c!d! d M$$$i!" +!u ! Y!$ &0.000 y &25(000 !1 $mii4o d 1o" !o" ' y 2( !dm!" d $!1i3!$ +!o" !u!1" ! 9 d !o d &'5(000 d 1o" !o" !1 *. S $!1i3!$! u +!o 9!1 ! Y!$ d &'0(000 !1 $mio d1 !o '0.
a) i!ia n na "ina 'm& "& ;& '& a'ian n "a &!a.
30,000 1
25,000 2
15,000 3
15,000 4
15,000 5
15,000 6
15,000 7
15,000 J
15,000 9
10,000 10
) SB a! " a"ia na !aa nimin!& i& " 12, MCG" " a"& n! !a i a&N
i!m 1 2 3 4 5 6 7 J 9 10
a& 30,000 25000 15000 15000 15000 15000 15000 15000 15000 10000 170,000
a8&
!aa 1 2 3 4 5 6 7 J 9 10
12 12 12 12 12 12 12 12 12 12 VP !&!a"
VP 267J5.71 19929.J5 10676.70 9532.77 J511.40 7599.47 67J5.24 605J.25 5409.15 3219.73 10450J.2J
) :na na ma &i& a Qa! n a& inmia!& ni& $100000 & "& & &mia"i#a " i!ma ia &m'&. MO> &!a ia a!a Qa!N
R: Au ido cu! /u 1! +$im$! m+$"! 1 oM$c &'70(000 >"um!do 1o" +!o" y obido u =P d &'06(50.2( 1! cu!1 " m!yo$ /u 1! c!,d!d oM$cid! d &'00(000 +o$ 1! "ud! m+$"! como +!o !1 co!do( 1! mo$ o+cio " 1! "ud! m+$"! oM$cid!( y! /u Y !$ d$! "u" !$c!" 1! "um! o!1 d &'00(000( /u " muc#o m o$ /u ob$ 1o" &'06(50.2 !1 c!bo d di3 !o".
P5.33
;u!!ci!mio d u 9ci +$"u+u"!$io. Womo +!$ d 1! 1!bo$!cio d "u +$"u+u"o +$"o!1 ud. D$mio /u c!d! uo d 1o" +$oFimo" 5 !o" d$! u d9ci
10
0(000.00
+$"u+u" !$o. o $!" +! ! $! c" !$! o" mo o" /u mu" $! ! " u ! !. ! ! ! o co$$"+o +!$! /u $!$ "u +$"u+u" o( " c$ /u +!$! /u !" $! !" "! iu!1" /u 1!" "!1id!". Ud. "+$! !!$ 1 % "ob$ "u" i-$"io" du$! 1o" +$oFimo" 5 !o" y d"! 9!ci!$ 1 d9ci+$"u+u!$io du$! " ,m+o co u moo uico
F:@S EFBCBA A?S?
0 S/.2J,000.00 J
1
F:@S EFBCBA A?S?
0 S/.19,9J1.20 12
1
2 5(000.00
3 6(000.00
2 5(000.00
)(000.00
4 '0(000.00
5 (000.00
)(000.00
4 '0(000.00
5 (000.00
3 6(000.00
= Can& "a !aa " V? aa & m"a a!a"i#ai%n P5.34
"ai&n n! a"& !& a"& n! . Bn& miK!& an& "a in&mai&n "a !a"a n!a a &n'nai&n &naD
F:@S
0 S@.'(0'7.7' 5
1
0 S@.'2(2)7.05 A?S? 7 Haaia " i& n&iai&n
1
A?S? Paaia "& 13,017.71 F:@S
P5.35
TASA
P5.36 P5.37 P5.3J P5.39 P5.40
P5.44
P5.45
5 2(000.00
'(500.00
5 2(000.00
0 S@.2(*''.0 6%
1 '0(000.00
2 5(000.00 G
3 25(*).02
4 20(000.00
5 0(000.00
;u!!ci!mio d u 9ci +$"u+u"!$io. Womo +!$ d 1! 1!bo$!cio d "u +$"u+u"o +$"o!1 ud. D$mio /u c!d! uo d 1o" +$oFimo" 5 !o" d$! u d9ci +$"u+u"!$io. E o$!" +!1!b$! c"i!$! 1o" moo" /u mu"$! 1! "iui !b1!. !1 9!1 d1 !o co$$"+odi +!$! /ui1ib$!$ "u +$"u+u"o( " dci$ /u +!$! /u 1!" $!d!" "! iu!1" /u 1!" "!1id!". Ud. "+$! !!$ 1 % "ob$ "u" i-$"io" du$! 1o" +$oFimo" 5 !o" y d"! 9!ci!$ 1 d9ci+$"u+u!$io du$! " ,m+o co u moo uico
PLAZO NPER
TASA TASA 2
'2%
XONTO =; S@.'(00.00
D+o"io" +!$! !cumu1!$ "um!" Muu$!". E c!d! uo d 1o" c!"o" +$"!do" 1!"iui !b1! d$mi 1 moo d 1o" d+o"io" !u!1" iu!1" !1 9!1 d1 !o /u " $/ui$ +!$! !cumu1!$ 1! "um! idic!d! !1 9!1 d1 +$iodo "+ci9co co"id$!do 1! !"! d i$" !u!1 "!b1cid!.
XONTO =; 5(000.00 '00(000.00 0(000.00 '5(000.00
P5.43
3 '0(000.00
4
*00.00
2 00.00
'(500.00
E E PE: @ SE :S? A?S?S @LB?ES ESE 1991 E E PE: @ SE :S? A?S?S @LB?ES ESE 1991 E E PE: @ SE :S? A?S?S @LB?ES ESE 1991 E E PE: @ SE :S? A?S?S @LB?ES ESE 1991 E E PE: @ SE :S? A?S?S @LB?ES ESE 1991
DEPOSITOS PAO '5(000.00
P5.42
3 '0(000.00
4
*00.00
"ai&n n! a"& !& a"& n! . a iin! !a"a m!a n in& miK!& ;& '&, K!& a"!a " ;& '& " a8& 3 a""a
F:@S
P5.41
2 00.00
PLAZO NPER
TASA TASA 20 '2
'2% 7% '0% %
DEPOSITOS PAO S/.1,4J1.74 S/.2,439.29 S/.2,623.32 S/.790.43
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
XONTO =; 220(000.00
PLAZO NPER
PAO 00.00
NPER
TASA TASA 62
%
DEPOSITOS PAO [email protected].'0
%
=; [email protected](*6.2
TASA 62
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
=A '5(000.00
NPER
XONTO =; 5*(20.0)
PLAZO NPER
TASA 20
)%
=; [email protected]*(20.0)
'0%
DEPOSITOS PAO S@.'0(5*.'5
TASA TASA 20
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
P?R@ PEPEA:@ )(000.00
A?S? '0%
V? PEPEA:B? V? )0(000.00
?C:L:? E F@@ V? F:A:@ VF )0(000.00 P5.46
P?@ PE
A?S? A?S? '0
'0%
C:@A? P?R@ S/.3,764.72
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
=!1o$ d 1! c!"! ! "u $,$o V? PE 200(000.00
A?S? 25
5%
VF C?S? S/.677,270.99
a& aa am"a " &n& aa &ma "a aa V? F:A:@ VF S@.)77(270.** S@.)77(270.** P5.47
A?S? A?S? 25 25
*% *%
C:@A? P?R@ S/.7,996.03 9 d m" S/.7,335.J1 iicio d m"
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
E:? V? '2(000.00 )0(000.00 75(000.00 6(000.00
P5.4J
P?@ PE
P?@ PE
A?S? % '2% '0% '5%
'0 0 5
C:@A?S P?R@ S/.4,656.40 S/.10,619.05 S/.7,955.94 S/.1,193.26
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
C?C:@ E ? C:@A? PESA?L@ V? '5(000.00
P?@ PE
A?S? A?S?
'6%
C:@A? P?R@ S/.6,460.97
PLAN DE PAOS
PEB@@ 0 ' 2
P5.49
C:@A?
BAEES
)(6)0.*7 )(6)0.*7 )(6)0.*7
?L@AB?CB@
2('00.00 '(6*.6) 7*.65
6()0.*7 6(*7'.5' 5())7.52
S?@ '5(000.00 '0()*.0 5())7.52 G
W$!cio d u Modo d ubi1!cio.P$! com+1!$ "u ubi1!cio +1!!d! F!c!m 62 !o" Ud. W!1cu1! /u c"i! !cumu1!$ &220(000 +!$! "! Mc#!. P1!! $!1i3!$ d+o"io" !u!1" iu!1" ! 9 d !o u! cu! /u +!! 1 % d i$" !u!1
C?C:@ E ? C:@A? PESA?L@ V? '0(000.00
P?@ PE
A?S? A?S?
'%
C:@A? P?R@ [email protected](25.22
PLAN DE PAOS
PEB@@ 0 ' 2
P5.52
C:@A? 6(25.22 6(25.22 6(25.22
BAEES '(600.00 '(00.07 550.57
?L@AB?CB@ 2(5.22 (22.'5 ()6.)5
S?@ '0(000.00 7(')6.7 (*2.) 267.*
52.G T!"! d $dimio Ri"#i Si# , & '(500 +!$! i-$,$. Su !""o$ i-$"io" "ui$ u! i-$"i /u o +!! i$"" "!b1cido" +$o /u $di$ &2(000 !1 9!1 d $" !o"
a. MO> !aa nimin!& ana" anaG " 8& Sin &n !a ini%nN . E" 8& Sin !G &nian& &!a ini%n, ia" i&, ana n nimin!& ana" J. MP& G" ini%n ii & >N S@:CB@D Xoo iici!1 : '500( Xoo ;i!1 :2000( P$iodo : !o"
G'
an& iD
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0.'
10
) 1JJ9.56J Si " i& ia" aa aa a&, n!&n
P5.53
Tasa de rendimien! " e#ei%n de in&ersi%n '#are aard iene $5,000 para in&erir. '!m! apenas iene 25 a!s de edad, n! #e ineresa #a d*rai%n de #a in&ersi%n, sin! #a asa de rendimien! *e anar s!re #a in&ersi%n. '!n #a a"*da de s* ases!r inanier!, '#are idenii% *ar! in&ersi!nes de i*a# ries!, ada *na de #as *a#es pr!p!ri!na *n m!n! ni! a# rmin! de #a &ida de #a in&ersi%n, !m! se m*esra en #a si*iene a#a. T!das #as in&ersi!nes re*ieren *n pa! iniia# de $5,000. a) W!1cu1( !1 $o +o$cu!1 m" c$c!o( 1! !"! d $dimio d c!d! u! d 1!" cu!$o i-$"io" /u " di"+oib1 " +!$! W1!$. Bni%n A B W D
S@ S@ S@ S@
m&n!& Ini& (600.00 '5(*00.00 7()00.00 '(000.00
ini%n n a8& 12 ) '5 6 '0
c!1cu1o
9.03 J.02 11.04 10.03
) MO> ini%n &mna
= SIn "& a!& &mnam& "a &i%n a a 10 a8& 'n na !aa in!> " 10 &G a ini%n a a "& 15 a8& &"& na na !aa in!> " J "a inia " 2 aa 5 a8& inia "& &mna" a "& 10 a8& aa &!a ini%n aa na mG in!> & in&
P5.54
54.-Ca" "a !aa nimin!& na ini%n $ 10,606.00 i "a &ma8
-!1o$ !cu!1 +!o +$iodo !"!
'0)0) 2000 '0 '6%
= a !aa nimin!& ia 14
P5.55 E1cci d 1! mo$ !u!1id!d R!i! Y$3i d"! 1i$ 1! mo$ d cu!$o !u!1id!d" d ubi1!ci imdi!! /u " di"+oib1" +!$! 11!. E c!d! c!"o( ! c!mbio d u! +$im! ic! #oy( $cibi$ b9cio" Mc,-o !u!1" iu!1"( ! 9 d !o( du$! u m$o "+cK9co d !o". Wo"id$! /u 1!" !u!1id!d" , 1 mi"mo $i"o y o 1 +$ocu+! 1o" diM$" ,m+o" d -id! d 1o" +1!". Su dci"i " b!"!$ ic!m 1! !"! d $dimio /u !!$ "ob$ c!d! !u!1id!d. L! "iui !b1! mu"$! 1o" $mio" +$ici+!1" d 1!" cu!$o !u!1id!d".
a) W!1cu1( !1 $o +o$cu!1 m" c$c!o( 1! !"! d $dimio d c!d! u! d 1!" cu!$o !u!1id!d" /u R!i! " co"id$!do. ?na"ia a in& ana" ia (?8&) !aa in!> A 0000 '00 20 .'*% B 25000 *00 '0 *.0% W 60000 6200 '5 ).0% D 5000 6000 '2 5.2% a) C&n "& i!i& ii%n aina !a"i%, M> ana"ia " &mna
Aaa in!> na ana"ia ?nna Ta"im "i&n% amn! n n ain! in!ia". man% a "a a! &na" " &!&% na inmni#ai%n $2,000,000. Q&, ""a a&a& ai!n a na ni%n a& &n "& a&a& n&, in ii&n na &!a iniia" $156,000 ana" an! 25 a8&. ?nna "ana &"ii!a na &n!a&!a $255,000 ana" an! 25 a8&. Aan!& "a &!a &m& "a &n!a&!a 'nn n a"& n! $2,000,000, i, " m&n!& "a inmni#ai%n, &nn a& a" na" aa a8&.
a) MO> !aa in!> !a, &naa a" n!& &n!a" mG an&, a&n "& a&a& n& n &!aN
I=(($2,000,000/$156,000)^(1/25))-(1)=
10.74
) MO> !aa in!> !a, &naa a" n!& &n!a" mG an&, &nia&n ?nna a&a& n &n!a&!aN
I=(($2,000,000/$.255,000)^(1/25))-(1)=
J.59
) ?nna !G i!a a ""a a n a& & na ana"ia im"i na !aa in!> " 9. MCG"
Vp=2,000,000/[(1+0.09)^25)] =
P5.57
231935.67
Tasas de iners de prsam!s !n 3#emmin a esad! *sand! *n prsam! para inaniar #a !mpra de *n a*!m%&i# *sad!. 4n!nr% res p!sii#idades *e pareen arai&as " desea e#eir a*e##a !n #a asa de iners ms aa. a si*iene a#a presena #a in!rmai%n disp!ni#e en re#ai%n !n ada *n! de #!s res prsam!s de $5,000.
P!am& A B W
Pinia" 5000 5000 5000
Pa& ana" '52.' '56.2' 20'0.65
P"a#& a8&
Aaa 5 6
''% *% '0%
)(7)6.05 )('72.6 )(0'.5
a) !min "a !aa in!> "ai&naa &n aa n& "& >!am&. ) MO> >!am& "i &nN = E" "i!a" " ma &nnin! a " m&n!& na" ma a& "& &!& & a" ma Gi& " !am& " m&n!& !&!a" mn&
P5.5J
7mer! de a!s para i*a#ar *n m!n! **r! E c!d! uo d 1o" c!"o" +$"!do" 1! "iui !b1!( d$mi 1 m$o d !o" /u $/u$i$ 1 d+"io iici!1 +!$! ic$m!$" #!"! iu!1!$ 1 moo Muu$o ! 1! !"! d i$" idic!d!.
;LUJO A B W D E
DEP.INIW =A 00.00 '2(000.00 *(000.00 '00.00 7(500.00
=AL ;UTURO TASA =; TASA '(000.00 '5(000.00 20(000.00 500.00 0(000.00
PLAZO NPER 7% 5% '0% *% '5%
1J 5 J 19 10
?. C&n n &i!& 300.00 a n in! 7 ia"aa a" m&n!& !& n 1J a8& H. C&n n &i!& 12,000.00 a n in! ia"aa a" m&n!& !& n 5 a8& C. C&n n &i!& 9,000.00 a n in! 10 ia"aa a" m&n!& !& n J a8& . C&n n &i!& 500.00 a n in! 9 ia"aa a" m&n!& !& n 19 a8& E. C&n n &i!& 7,500.00 a n in! 15 ia"aa a" m&n!& !& n 10 a8& P5.59
Tiemp! para a*m*#ar *na s*ma espe8ia X!u1 RKo" d"! d$mi!$ cu o ,m+o $/u$i$ u d+"io !u!1 d &'0(000 +!$! du+1ic!$".
a. Si Lan" ana " 10 ana" & " %i!&, MGn!& 'm& iG aa "ia in&N . MCGn!& 'm& iG i ana %"& " 7 in!> ana"N . MCGn!& 'm& iG i ana " 12 in!> ana"N
;LUJO
DEP.INIW =A
A B W
P5.60
=AL ;UTURO TASA =; TASA '0000 20000 '0000 20000 '0000 20000
PLAZO NPER '0% 7% '2%
7 Lan" ia 7 a8& aa "ia in& 10 Lan" ia 10 a8& aa "ia in& 6 Lan" ia 6 a8& aa "ia in&
7mer! de a!s para pr!p!ri!nar *n rendimien! espe8i! 4n ada *n! de #!s si*ienes as!s, a#*#e e# nmer! de a!s *e e# #*! de eei&! an*a# espe8i! de in de a! dee !nin*ar para !reer #a asa de rendimien! indiada s!re e# m!n! iniia# deerminad!.
;LUJO A B W D E
DEP.INIW =A
;LUJO ANUAL PAO '000 '50000 0000 )00 '7000
250 0000 '0000 275 500
TASA TASA
PERIODOS NPER ''% '5% '0% *% )%
5.56 9.92 16.J9 2.54 5.91
