Ejercicios Propuestos - Matematicas Financieras
February 2, 2023 | Author: Anonymous | Category: N/A
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HKHVJOJOAZ RVARXHZPAZ-OLPHVHZ ZOERDH
Laefrh; Idhxi ^ovoili Zidizir @hvoi Zhehstrh 9-Hsphjoidozijoúl hl Ghrhljoi `h Rrayhjtas
9) Yuï olthrïs olthrïs ghlhril ghlhril $ =82.222 =82.222 hl > e ehshs hshs id 6,=% ehlsuid ehlsuid1 1 V/. $ 906.=22 906.=22
O 5 Rol
O5 1 R5 $ =82.222 l5> ehshs o56,=% ehlsuid
O 5=82.222∗2,26=∗> O 5 $ 906.=22
6) Xl J@P `h `h $ 9.822.222 9.822.222 pigi pigi hd 98% shehstrid shehstrid33 ±juélta ±juélta pra`ujh pra`ujh `h olthrhshs olthrhshs id jifa `h ul ul iùa1 V/. $ 082.222 O51 o598% shehstrid l56 shehstrhs O 5 Rol O 59.82 9.822 2 .222∗2,98∗6 O 5 $ 082.222
:) Hl juélta juélta hepa hepa uli olvhrsoú olvhrsoúl l `h $ 6.222 6.222.222 .222 pra`ujh pra`ujh olthrhs olthrhshs hs `h $ 722.222, 722.222, so hd jipotid sh olvorú id 6,8% ehlsuid. V/. 90 ehshs
l51
(5 ∖ ) N
l
R5 $ 6.222.222 N5 $ 6.722.222 o; 6,8% ehlsuid
9
R
o
l
( 5
l5
6.722.222 6.222.222
∖9
)
2,268
( 9,:8 ∖9 ) 2,268
l 590 ehshs
0) Xl olvhrsoa olvhrsoalosti losti i`quo i`quoroú roú 9.222 9.222 ijjoa ijjoalhs lhs i $ :.622 :.622 ji`i uli, uli, i das = ehshs ehshs rhjofoú rhjofoú $ =?>.222 `h `ovo`hl`as. ±Juéd hs di rhltifodo`i` ehlsuid y iluid `h di olvhrsoúl1 V/. :,8% ehlsuid, 06% iluid. R59.222*:.6225 $ :.622.222 l5= ehshs
O5$ =?>.222
N5$ :.622.222+=?>.2225 $ 0.2?>.222 o51
o
(5 ∖ )
o
( 5
N
9
R
l
0.2?> 0.2 ?> .222 .222 :.622 :.6 22 .222 .222
∖9
)
=
( 9,6=∖9 ) o5
=
52,2:8
o 5:,8% ehlsuid o 5:,8%∗96 506 % Iluid
8) Hl ul prïstie prïstiea a `h $ =.222.222 =.222.222 i : iùas iùas sh pijti pijti ul olthrïs olthrïs `hd 7,8% 7,8% troehstrid troehstrid piri piri hd proehr iùa y `hd 96% shehstrid piri das `as iùas soguohlths. ±Juélta sh hsphri `h olthrhshs hl ta`a hd pdiza1. V/. $ 7.:?6.222
R5=.222.222 o5 7,8% troehstrid o5 96% Zhehstrid
Rroehr iùa @as iùas soguohlths
Iùa 9 N 5 R ( 9 + ± ) N 5=.2 =.222 22 .222 .222 ( 9 + 2,278∗0 ) N 5=.2 =.222 22 .222 .222 ( 9 + 2,: ) N 5=.2 =.222 22 .222 .222 ( 9,: ) N 5 $ 92.022.222
O 5 N ∖ R
O 5 $ 92.022.222 ∖ $ =.22 =.222 2 .222 O 9 5$ 6.02 6.022 2 .222
@as iùas soguohlths N 5 R ( 9 + ± ) N 5=.2 =.222 22 .222 .222 ( 9 + 2,96∗0 ) N 5=.2 =.222 22 .222 .222 ( 9 + 2,0= ) N 5=.2 =.222 22 .222 .222 ( 9,0= ) N 5 $99.=02.222
O 5 $ 99.= 99.=02 02 .222∖ $ =.22 =.222 2 .222 O 6 5$ :.=0 :.=02 2 .222
O 5 O 9 + O 6
O 5 $ 6.02 6.022 2 .222+ $ :.=0 :.=02 2 .222 O 5 $ >.60 >.602 2 .222
>) Middir Middir hd olthrïs olthrïs rijoalid rijoalid y hd jaehrjoi jaehrjoidd `h $ 082.222 082.222 hl hd ehs ehs `h Kuloa, Kuloa, id 62%. 62%. V/. $ 7.:?7,6> y $ 7.822
R5 $ 082.222
l5:2 `åis
Ehs `h Kuloa
O 5 Rol
Olthrïs Vijoalid
o;62% Iluid
( )
O 5 082.222∗2,62∗
:2
:>8
O 5 082.222∗2,62∗2,2=69 O 5 $ 7.:?7,6>
Olthrïs Jaehrjoid
O 5 Rol
( )∗
O 5 082.222∗
2,62 :>2
:2
( )∗
O 5 082.222∗
2,62 :>2
:2
O 5 082.222∗2,2228>∗:2 O 5 $ 7.822
7) Jidjudh Jidjudh hd olthrïs olthrïs jaehrjoid jaehrjoid y h hxijta xijta `h `h ul prïstiea prïstiea `h $ 8.222.22 8.222.222 2 id 6=%, `hd 98 `h ifrod ifrod `hd 6227 id 9: `h igasta `hd eosea iùa. V/. $ 0>>.>>>,>7 y $ 0>2.67:,?7
R 5 8.222.222
o5 6=% Iluid l5 962 `åis
O 5 Rol
Olthrïs Jaehrjoid O 58.2 8.222 22 .222 .222∗2,6=∗(
962 :>2
)
O 58.2 8.222 22 .222 .222∗2,6=∗2,:::: O 5 $ 0>>.>>>,>7
O 5 Rol
Olthrïs Hxijta a Vhid O 58.2 8.222 22 .222 .222∗2,6=∗(
962 :>8
)
O 58.22 8.222 2 .222∗2,6=∗2,:6=7 O 5 $ 0>2.67:,?7
=) Afthlgi Afthlgi hd olthrïs olthrïs soepdh soepdh ar`oliro ar`oliroa a y rhid `h 68.222 68.222 `údirhs `údirhs,, `hd 6 `h hlhra hlhra `h 622= (iùa (iùa fosohsta) id 9 `h igasta `hd eosea iùa. Di tisi `h olthrïs hs `h >,8%. V/. $ ?8>,?0 y $ ?09,6>
R5 $ 68.222
l5696 `åis o5>,8% Iluid
Olthrïs Ar`oliroa O 568.222∗2,2>8∗(
O 5 Rol
696 :>2
)
O 568.222∗2,2>8∗ 2,8=== O 5 $ ?8>,?0
Olthrïs Vhid O 5 Rol O 568.222∗2,2>8∗(
696 :>>
)
O 568.222∗2,2>8∗2,87?6 O 5 $ ?09,6>
?) ±Juélta ±Juélta `olhra `olhra `hfa `hpasotir `hpasotir may may 68 `h ifrod hl uli uli juhlti quh quh pigi hd 6:% soepdh soepdh rhid piri quh hd 6= `h kudoa puh`i rhrir $ >2.222. V/. 8>.>00,77
R5 1
R5
R5
o5 6:% soepdh rhid
N
( 9+ ±)
>2.222
( 9+ 2,6:∗(
?0 :>8
R5
>2.222 ( 9+ 2,6:∗2,6878 )
R5
>2.222
R5
))
( 9+ 2,2> )
>2.222
( 9,2> )
R5 $ 8>.>00,77
l5?0 `åis N5 $>2.222
99) Xli heprhsi `hshi `hpasotir `hpasotir $ 0.:82.222 i ul pdiza `h 622 `åis, `åis, y `hfhré `hjo`or so `hpasoti hd `olhra hl hd Filja ], quh pigi hd h d 62% `h olthrïs jaehrjoid, a hl h hdd Filja _, quh pigi hd 69% `h olthrïs rhid. ±Hl quï Filja dh jalvohlh `hpasotir1 V/. Jalvohlh `hpasotir hl hd Filja _
R5 $ 0.:82.222
l5622 `åis
Filja ] O 5 Rol O 5 0.:82.222∗2,62∗(
622 :>2
)
O 5 0.:82.222∗2,62∗2,8888 O 5 $ 0=:.:::
Filja _ O 5 Rol O 5 0.:82.222∗2,69∗(
622 :>8
)
O 5 0.:82.222∗2,69∗2,807? O 5 $ 822.80=
V// Dh jalvohlh `hpasotir hl hd Filja —_― parquh afhlh afhlh eiyar rhl`oeohlta 96) Jidjudh hd ealta a vidar nutura `h u ul l prïstiea `h $6.222.222 id :2% `h olthrïs soep soepdh dh y 92 ehshs `h pdiza. V/. $ 6.822.222 N51
R5 $ 6.222.222 o5 :2% soepdh l592 ehshs
N 5 R ( 9 + ± )
( ))
N 56.2 6.222 22 .222 .222 ( 9 + 2,:2∗
92 96
N 56.2 6.222 22 .222 .222 ( 9 + 2,:2∗2,=::: )
N 56.2 6.222 22 .222 .222 ( 9 + 2,68 ) N 5 $ 6.822.222
9:) ±Juélta pigiré ul jaehrjoilth par ul jrï`ota quh dh jaljh`oú uli néfroji par di sue suei i `h $ ?9=.:22 i 68 `åis, so dh ipdojil uli tisi `h olthrïs `h :% ehlsuid1 V/. $ ?09.687,8
R5 $ ?9=.:22
l568 `åis o5 :% ehlsuid
N 5 R ( 9 + ± ) N 5?9=.:22 ( 9 + 2,2:∗
68
)
( ) :2
N 5?9=.:22 ( 9 + 2,2:∗2,=::: ) N 5?9=.:22 ( 9 + 2,268) N 5 $ ?09.687,8
90) Hljuhltrh hd vidar prhshlth prhshlth `h $ :.=22.222 quh vhljh vhljh `hltra `h 7 ehshs, so di tisi `h olthrïs hs `hd 68%. V/. $ :.:9>.:>:,>0
R51
R5
N5 $ :.=22.222
N
( 9+ ±)
l5 7 ehshs
o5 68% Iluid
R5
:.=22.222
( 9+ 2,68∗(
R5
7 96
))
:.=22.222
( 9+ 2,68∗2,8=:: ) R5
R5
:.=22.222
( 9+ 2,908=)
:.=22 :.=2 2 .222
(9,908= )
R5:.:9> .:>:,>0
98) Xli phrsali jaeprú ul iutaeúvod p par ar hd juid pigú $ 98.722.222 98.722.222 hd proehra `h hlhra, y da vhl`oú hd proehra `h kudoa `hd iùa soguohlth hl $ 69.822.222. ±Nuh jalvhlohlth jaea olvhrsoúl di aphrijoúl rhidozi`i so di tisi `h olthrïs `hd ehrji`a hri `h :2%1 V/. La nuh jalvhlohlth di olvhrsoúl.
R5 $ 98.722.222
9 Hlhra
N5 $ 69.822.222
9 `h kudoa `hd iùa soguohlth
o5 :2% tisi `h olthrïs `hd ehrji`a O 5 N ∖ R
O 569.8 69.822 22 .222∖98.7 98.722 22 .222
O 5 $ 8.=22.222
O 5 Rol
O 598.722 98.722.222 .222∗ 2,:2∗(
9= 96
)
O 598.722 98.722.222 .222∗2,:2∗9,8
O 5 $ 7.2>8.222
V// La nuh jalvhlohlth di olvhrsoúl parquh hlh eiyar rhl`oeohlta jal di tisi `h olthrïs `h ehrji`a
9>) ±Juéd hs di tisi `h olthrïs soepdh ehlsuid ehlsuid hquovidhlth i uli tisi `hd 0=% iluid1 V/. 0% ehlsuid
o ehlsuid 5 1 o 5 0=% Iluid
o5
( )∗ 2,0= 96
922%
o 52,20∗922%
o 5 0 % ehlsuid
97) ±Juéd hs hd pa `h olthrïs ehlsuid soepdh soepdh hquovidhlth i ul uli i tisi `hd 9=% sshehstrid1 hehstrid1 V/. :% ehlsuid
o ehlsuid 5 1 o 5 9=% Zhehstrid
o5
( )∗ 2,9=
922%
>
o 52,2:∗922%
o 5: % ehlsuid
9=) ±Hl juélta hepa sh `updoji `updoji ul jipotid olvhr`a id 68% `h olthrïs iluid soep soepdh. dh. V/. 0 iùas
o 5 68% Iluid soepdh
l5
( ) N ∖9 R o
(5 ∖ ) 6
l
l5
9
9
2,68
( 6 ∖9 ) 2,68
l 50 Iùas
9?) ±Hl juélta hepa sh thl`råil $ 802.222 so sh sh `hpasotiril may $ :22.222 hl ul nal`a quh pigi hd :,6% soepdh ehlsuid1 V/. 68 ehshs
N5 $ 802.222 R 5 $ :22.222 o5 :,6% soepdh ehlsuid
(5 ∖ ) N
l
9
R
o
802.222
∖9
)
(
l 5 :22.222 2,2:6 l5
( 9,= ∖9 ) 2,2:6
l 568 Ehshs
62) ±Juéd hs hd prhjoa `h jalti`a `h ul thdïnala jhdudir jhdudir quh sh pigi `il`a `h juati olojoid hd 68% `hd prhjoa `h jalti`a y sh rei ul pigirï i : ehshs par $ 962.222 quh oljduyh uli tisi `hd 60% iluid1 V/. $ 982.?0:,0
R5
R5
N
( 9+ ±)
962.222
( 9+ 2,60∗(
R5
R5
: 96
))
962.222
( 9+ 2,60∗2,68 )
962.222
( 9+ 2,2> )
R5
962.222
( 9,2> )
R599:.627,88
Vhgdi `h trhs
99:.627,88
78%
]
68%
]5 :7.7:8,= quh jarrhspal`h id 68% Rrhjoa `h Jalti`a5 $ 99:.627, 88 + $ :7.7:8,= Rrhjoa `h Jalti`a 5 $ 982.?0:,0
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