Ejercicios para Desarrollar (Resueltos)

 

FOFU@K@KJP SUJSVFP]JP 1) Pk mfp mfpjsk jsktai taijs js gjy $ 133.3 133.333, 33, mfb mfbtrj trj mf 4 ifs ifsfs fs $ 63. 63.33 333 3 y = ifsf ifsfs s mfsp mfspuë uës s mf rfalkzamj fl abtfrkjr mfpðsktj, $ 533.333, º@uábtj sf tfbmrá a`uiulamj 1; ifsfs mfspuës mf fdf`tuamj fl prkifr mfpðsktj sk sf rf`jbj`f fl 0% ifbsual: D9 63;.>01,;0 S9 133.333 k9 0% ifbsual b9 1; ifsfs

DJUIVLA TALJU DV]VUJ    D 9 S ( 1+ k ) b

Mfpjsktaijs gjy $ 133.333, mfbtrj mf 4 ifsfs $ 63.333?   D 9133.333 ( 1+ 3,30 )4911;.=36,55;> + 63.333914;.=36,55;> = ifsfs mfspuës mf rfalkzamj fl abtfrkjr mfpðsktj, $ 533.333? =  D 914;.=36,55;> ( 1+ 3,30 ) 91;3.44>,3>7= + 533.333 90;3.44>,3>7= º@uábtj sf tfbmrá a`uiulamj 1; ifsfs mfspuës mf fdf`tuamj fl prkifr mfpðsktj sk sf rf`jbj`f fl 0% ifbsual:?  D 90;3.44>,3>7= ( 1 + 3,30 ) ;963;.>01,;0 SFUKJMJ

0%

3 PALMJ KB]FUFP AEJBJ 1 $ 133.333,33 $ 0.333,33 5 $ 130.333,33 $ 0.3;3,33

UF]KUJ

@ASK]AL @ASK]AL MFPSVFP MF AEJBAU $ 130.333,33 $ 134.3;3,33

0 $ 134.3;3,33 $ 0.175,>3 = $ 13;.5>5,>3 $ 0.5>7,17

$ 13;.5>5,>3 $ 115.663,77

6 $ 115.663,77 $ 0.0>4,60

$ 116.;5>,=1

4 $ 116.;5>,=1 $ 0.=>>,75 $ 63.333,33

$ 11;.=36,50 $

> $ 14;.=36,50 $ 6.375,14 7 $ 1>=.=7>,0; $ 6.50=,45

$ 1>=.=7>,0; $ 1>;.>55,31

; $ 1>;.>55,31 $ 6.0;1,44

$ 176.110,4>

13 $ 176.110,4> $ 6.660,=1 $ 533.333,33 11 $ 0;3.44>,37 $ 11.>53,31

$ 1;3.44>,37 $ $ =35.07>,3;

15 $ =35.07>,3; $ 15.3>1,41 10 $ =1=.=67,>3 $ 15.=00,>4

$ =1=.=67,>3 $ =54.7;5,=4

1= $ =54.7;5,=4 $ 15.734,>>

$ =0;.4;;,5=

16 $ =0;.4;;,5= $ 10.1;3,;7

$ =65.7;3,55

14 $ =65.7;3,55 $ 10.674,>1

$ =44.=>4,;5

1> $ =44.=>4,;5 $ 10.;;=,01

$ =73.=>1,50

17 $ =73.=>1,50 $ 1=.=1=,1= 1; $ =;=.776,0> $ 1=.7=4,64

$ =;=.776,0> $ 63;.>01,;0 $

14;.=36,50

0;3.44>,37

63;.>01,;0

 

5) Ga` Ga`f f 11 ifs ifsfs fs mfpj mfpjskt sktë ë $ 633.3 633.333 33 y, = if ifsfs sfs mfs mfspuë puës s rftkrë $ 563.3 563.333. 33. º@u º@uábt ábtj j tfbm tfbmrë rë a` a`ui uiul ulam amj j gj gjy y sk ga ga`f `f tr trfs fs if ifsf sfs s mf mfpj pjsk sktë të $ 03 033. 3.33 333 3 y fl kbtf kbtfrë rës s qu quf f rf`jbj`f fs mfl 64,=% @apktalkzaelfs ekifstral: D9 6.5=5.5==,61 S9 633.333 k9 64,=% ekifstral b9 11 ifsfs

  DJUIVLA TALJU DV]VUJ    D 9 S ( 1+ k )   b

DJUIVLA ]APA F. EKIFP]UAP A IFBPVAL ∕1 ]FI 9( 1 + ]FE ) mkasifsfs

mkasekifstrf

 

Srkifr pfrkjmj 5 ekifstrfs y rftkrj $ 563.333.    D 9633.333 ( 1+ 3,64= )591.55 1.550 0 .3=7∕563.333 9;>0.3=7  

Pfnubmj pfrkjmj 5 ekifstrfs y mfpðsktj $ 033.333    D 9;>0.3=7 ( 1 + 3,64= )5 95.073.147,75 + 033.333 95.47 5.473 3 .147,75 .147,75    

A`uiulamj gjy sk ga`f 0 ifsfs mfpjsktf 033.333 ekifstrf y ifmkj 1,6  D 95.473 .147,75 ( 1 + 3,64= ) 96.5=5 .5==,61

SFUKJMJ 3 PALMJ 1 5 0 = 6 4 > 7 ; 13 11

$ $ $ $

633.333,33 456.5;;,;0 >75.333,33 ;>>.;4;,3;

$ ;>0.3=7,33 $ 1.514.7;0,4; $ 1.651.7=>,3> $ 1.;30.551,>0 $ 5.473.147,75 $ 0.061.717,> ,>= = $ =.1;1.>7=,3=

56,3433% ]APAFDF@]KTAIFBPVAL KB]FUFP AEJBJ UF]KUJ $ $ $ $

156.5;;,;0 6.5;;,;0 164.>33,3> 4.>33,3> 1;6.;4;,3; 6.;4;,3; 5=6.3>7,;1

$ 5=0.7=6,4; 0.7=6,4; $ 03=.;60,07 =.;60,07 $ 071.0>=,44 1.0>=,44 $ =>4.;=>,3; $ 033.333,33 $ 4>1.4=;,;5 1.4=;,;5 $ 70;.;46,5; ;.;46,5; $ 1.363.=43,=7

@ASK]AL

@ASK]AL MFPSVFP MF AEJBAUJUF]KUA

$ $ $ $ 563.333,33 $

456.5;;,;0 >75.333,33 ;>>.;4;,3; 1.550.3=7,33 $

$ $ $ $ $ $ $

1.514.7;0,4; 1.514.7;0 1.651.7=> 1.651. 7=>,3> 1.;30.551 1.;30. 551,>0 5.073.147,75 $ 0.061.717 0.061. 717,>= =.1;1.>7= =.1;1. >7=,3= 6.5=5.5==,61 $

;>0.3=7,33

5.473.147,75

6.5=5.5==,61

0) Vba pfrs pfrsjba jba rf` rf`kekð kekð uba gf gfrfb`k rfb`ka a mf $ 1.633.3 1.633.333 33 y qukfrf kbvfrtkr kbvfrtkr uba pa partf rtf mf fstf mkbfrj fb ub djbmj mf mf ouekla`kðb. Skfbsa oueklarsf mfb mfbtrj trj mf 16 añjs y para fb fbtjb`fs tjb`fs mfsfa tfbfr $ 03.333.333 fb fl djbmj. ºQuë partf mf la gfrfb`ka mfefrá kbvfrtkr agjra sk fl mkbfrj fstará kbvfrtkmj a uba tasa mfl 5% ifbsual: D9 03.333.333 S9 7=;.06>,10 k9 5% ifbsual b9 173 ifsfs / 16 añjs  

DJUIVLA TALJU DV]VUJ 

 D 9 S

 

DJUIVA TALJU SUFPFB]F 

 S9

( 1+ k )  D  b

( 1+k )

b

 

ºQuë partf mf la gfrfb`ka mfefrá kbvfrtkr agjra sk fl mkbfrj fstará kbvfrtkmj a uba tasa mfl 5% ifbsual:  S9

03.333.333

( 1 + 3,35 )173

 9

7=;.06>,10

=) Vb pamr pamrf f mf daikl daiklka ka prjif prjiftf tf a `ama ub ubj j mf sus mjs gk gkojs, ojs, quf a all tfrikba tfrikbarr la `arrfra lf fbtrfnará a `ama ubj $ =.333.333 para quf rfalk`fb ub vkaof. Pk al prkifrj lf daltab 5 añjs para tfrikbar y al sfnubmj 0 añjs. º@uábtj mfef kbvfrtkr gjy fb ub djbmj quf pana fl 5,6% ifbsual a dkb mf pjmfrlfs `uiplkr la prjifsa: D9 =333.333 S9 0.766.7>4,01 k9 5,6% ifbsual b9 0 añjs

 

DJUIVLA TALJU DV]VUJ 

 

DJUIVLA TALJU SUFPFB]F 

 D 9 S

 S9

( 1+ k )

b

 D 

( 1 +k )

b

Srkifrjs 5 añjs  S9

=.333.333

( 1 + 3,356 )15 ]fr`fr añj

 S9

9

4.;>= .550,6=

( 1 + 3.356 )

5=

5.;>=.550,6= + =.333.333 9 4.;>= .550,6=

  9

0.766.7>4,01

Fl valjr prfsfbtf quf mfefrá kbvfrtkr fl pamrf fs mf 0.766.7>4,01 quf a 5 añjs tfbna 4.7>=.550,6=  para rftkrar =.333 =.333.333 .333 prj prjiftkm iftkmjs js al prkifr gkoj gkoj.. ]fbmrá ub sa salmj lmj mf 5.;>=.550,6= y ub añj iás tarmf prjmu`krá ljs =.333.333 prjiftkmjs al sfnubmj gkoj.

6) Pf mkspj mkspjbf bf gjy mf uba suia mf mkb mkbfrj frj para kbvf kbvfrtkr. rtkr. [ sf prfsfb prfsfbtab tab mjs altf altfrbatkv rbatkvas? as? la prkifra fs kbvfrtkr al 5, =5% ifbsual y la sfnubma fs kbvfrtkr al 16,56% sfifstral. º@uál mfef a`fptarsf:

DJUIVLA  D 9 S ( 1+ k ) SUKIFUA AL]FUBA]KTA b

Pf tjiab 4 ifsfs ya quf la sfnubma altfrbatkva sf fxprfsa fb sfifstrf

( 1+ 3.35=5 )491,16=0 PFNVBMA AL]FUBA]KTA 1  D 9 S ( 1+ 3,1656 ) 91,1656   º@uál mfef a`fptarsf:  D 9 S

 

U/? La prkifra jp`kðb mf 5,=5% ifbsual

 

4) Vb Vba a ek` ek`k`l k`lfta fta tkfb tkfbf f ub valj valjrr mf `jbt `jbtamj amj mf $ 5.6 5.633. 33.333 333.. A pla plazjs zjs fxk fxknfb nfb uba `uj `ujta ta kbk`kal mf $ 1.333.333 y fl rfstj dkbab`kamj para sfr `ab`flamj `jb trfs `ujtas mf $1.33 $1. 333.3 3.3338 338 $63 $633.3 3.333 33 y $1; $1;7.0 7.036, 36,03, 03, mj mjs, s, `kb `kb`j `j y buf bufvf vf ifs ifsfs fs mfs mfspuë puës s mf rf`kekma la ek`k`lfta. Fb`jbtrar fl kbtfrës mf dkbab`ka`kðb.

DJUIVLA k9

()  D   S

1 b

∕

1

Fb`jbtrar fl kbtfrës mf dkbab`ka`kðb. k9

(

 

1333.333 + 1333.333 + 633.333 + 1;7.036,03 5.633 5.6 33 .333

)

1 ;

∕

193,76 3,761>6 1>6 %

U/? fl kbtfrës mf dkbab`ka`kðb fs mf 3,761>6% >) Vb Vba a pfr pfrsjb sjba a mfpjs mfpjskta kta gjy $ =63 =63.33 .333 3 fb uba `jr `jrpjr pjra`k a`kðb ðb mf agjrr agjrrj j quf pana fl >% trki trkifs fstr tral al.. ]r ]rfs fs añ añjs js mf mfsp spuë uës s mf mfpj pjsk skta ta $ 45 453. 3.33 333, 3, ub añ añj j iá iás s tarm tarmf f mf mfpj pjsk skta ta $633.333, y mjs añjs mfspuës mf`kmf rftkrar la `uarta partf mfl tjtal a`uiulamj gasta fsf ijifbtj. Gallar fl salmj fb la `ufbta mf agjrrjs `kb`j ifsfs mfspuës mfl rftkrj.

DJUIVLA TALJU DV]VUJ  D 9 S ( 1+ k )   b

PALMJ AL SUKIFU MFSÐPK]J Pjb 15 pfrkjmjs ya quf fb 0 añjs gay 15 pfrkjmjs trkifstralfs  D 9=63.333

( 1 +3.3> )1591.310 .=17,55+ 453.33391.40 1.400 0 .=74,55 .=74,55

PALMJ PFNVBMJ MFSÐPK]J Pjb = pfrkjmjs ya quf fb 1 añj gay = pfrkjmjs trkifstralfs  D 91.400 1.400.=74,55 .=74,55( 1 + 3.3> )

=

5.1=1 .14>,51+ 633.33395.4=1.14>,51

9

PALMJ AL UF]KUAU LA ¼ SAU]F MFL ]J]AL A@VIVLAMJ Pjb 7 pfrkjmjs ya quf fb 5 añjs gay 7 pfrkjmjs trkifstralfs  D 95.4=1 .14>,51

( 1 + 3.3> )7 9=.607 .31>,33

1 .31>,3391.10= 1.10=.63=,5 .63=,56 6 ∞=.607 .31>,33 = =.607.31>,33 ∕1.10= .63=,56 .63=,5690.=30 .615,>6 .615,>6

Gallar fl salmj fb la `ufbta mf agjrrjs `kb`j ifsfs mfspuës mfspuës mfl rftkrj. .615,>6 ( 1 +3.3> )  D 90.=30 .615,>6

6 0

9

0.73; .>70,;0 .>70,;0

 

7) Vb Vba a fi fiprf prfsa sa amq amqukf ukfrf rf ub prëst prëstaij aij pjr $ 53. 53.333 333.33 .333 3 al 5.6 5.6% % if ifbsu bsual al y dkrið dkrið ub panarë pjr $ =7.463.>34,01. ºQuë plazj lf `jb`fmkfrjb para `ab`flar la mfuma y ljs kbtfrfsfs: D9 =7.463.>34,01 S9 53.333.333 k9 5,6% ifbsual b9 04 ifsfs

DJUIVLA BVIFUJ MF SFUKJMJP ljn b9

()  D   S

ljn ( 1 + k )

 ºQuë plazj lf `jb`fmkfrjb para `ab`flar la mfuma y ljs kbtfrfsfs: ljn b9

(

 )

=7.463 .>34,01 53.333.333

ljn ( 1 + 3,356 )

 

9

04 ifsfs

;) Mf Mfbt btrj rj mf `u `uáb ábtj tjs s tr trki kifs fstr trfs fs sf tfbm tfbmrá rá fb ub uba a `u `ufb fbta ta mf ag agjr jrrj rjs s ub sa salm lmj j mf $;13.443 saekfbmj quf gjy sf ga`f ub mfpðsktj mf $ =33.333 y lufnj rftkrjs asé? $73.333 mfbtrj mf ; ifsfs, $ 153.333 mfbtrj mf 15 ifsfs, sk la `ufbta mf agjrrjs aejba ub kbtfrës mfl ;,6% trkifstral.

 

D9 ;13.443 S9 =33.333 k9 ;,6% trkifstral b9 1= trkifstrfs

DJUIVLA TALJU DV]VUJ  D 9 S ( 1+ k ) PALMJ SUKIFU UF]KUJ b

Pjb 0 pfrkjmjs ya quf ; ifsfs fqukvalfb a 0 trkifstrfs 0

 D 9=33.333

( 1 +3.3;6 )

9

656.=4=,;6 ∕73.333 9==6.1>5,;6

PALMJ PFNVBMJ UF]KUJ 1  D 9==6.1>5,;6 ( 1 + 3.3;6 ) 9 =7>.=4=,07 ∕153.333 904>.=4=,07 Mfbtrj mf `uábtjs trkifstrfs sf tfbmrá fb uba `ufbta mf agjrrjs ub salmj mf $;13.443. ljn b9

(

  ;13.443 04>.=4=,07

ljn ( 1 + 3,3;6 )

)

  9

13 += ( mf 1 añj )91= trkifstrfs

 

13)Jetfbna fl prf`kj mf `jbtamj mf ub fqukpj mf sjbkmj pjr fl quf sf ma uba `ujta kbk`kal mfl 56% mfl valjr mf `jbtamj y sf dkria ub panarë, `jb vfb`kikfbtj a 7 ifsfs, pjr $ 1.=53.333, fl `ual kb`luyfb kbtfrfsfs al 5.7% ifbsual.

  DJUIVLA TALJU SUFPFB]F  S9

 D   B 

( 1 +k )

 

TALJU SUFPFB]F MFL >6% MFL TALJU MF @JB]AMJ  S9

1.=53 1.= 53 .333 .333

( 1 + 3,357 )

7

9

1.107.65>,5= 1.107 .65>,5=

 

SUF@KJ MF @JB]AMJ AL 133%  133  13 3% .304,05 ( 1.107 .65>,5=)   91.617 .304,05 >6 %