Ejercios de Diapositiva de Ecuaciones

 

 

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WA_NA NHN_MLMLF Y_FY^N]WF] NM^AMLFKN] NQ^LTABNKWN]

BLMNKMLAGA88 @NKLA F_GFÑN] BLMNKMLAGA

KFCO_N8 BN]BLK MA_FBLKA MA_LA] TA_NBA

M^NKWA8 ?9?9149991?

A]LJKAW^_A8 CNWFGF] M^AKWLWAWLTF] NK DLKAKXA] L

 

1) ^ka ncprnsa tlnkn bas sljulnktns gnugas8 ^k gfmucnktf pfr 15>,999 mfk nb ??% gn lktnrìs slcpbn akuab, dlrcagf eamn ?7 cnsns y qun gnon makmnbarsn gnktrf gn 1? cnsns0 y ftrf pfr =>9,999 mfk uka tasa gnb >.>9% trlcnstrab slcpbn, dlrcagf a =9 cnsns pbazf y qun gnonrá pajarsn gnktrf gn ?4 cnsns. Ba ncprnsa tlnkn prfobncas para mucpblr mfk bf pamtagf nk bas gnugas aktnrlfrns pfr bf qun sn prnsnkta mfk su amrnngfr y bn plgn sustltulr ìstfs pajfs gn ftra dfrca qun sn gntabba gntab ba a mfktlkuamlýk8 prfpfkn rnablzar trns pajfs ljuabns a makmnbarsn gnktrf gn 1?, ?7 y =4 cnsns rnspnmtlvacnktn0 nb amrnngfr amnpta nstn mfkvnklf slncprn y muakgf ba kunva tasa gn lktnrìs mfkvnklga sna gnb >% olcnstrab slcpbn. Gntnrclkn nb vabfr gn ìstfs kunvfs pajfs (utlblzar mfcf dnmea dfmab nb tlncpf nk qun sn ndnmtøa nb snjukgf pajf, ns gnmlr bfs ?7 cnsns).

9

1? 15>,999.99

?7

??% tta asa akuab ?7+1?3=4 =9:199.99 pasf ? C3M*(1+(l*kl))

dnmea dfmab

=4

>.>9% tta asa trl =9 > 7?>99.99

lktnrns slcpbn

15>, 999.99 ??% tasa akuab ?7+1?3=4 pbazf 15>,999*(1+(??%*(=4/1?)) =9:199.99 pasf = tasa M3 C3

?4 =>9, 999.99

=>9,999.99 >.>9% tasa trlcn =9 pbazf =>9,99*(1+(>.>9%(=9/=)) >7?>99.99

>% Olcnstrab slcpbn C/(1+lk) M*(1+(l*k)) gnugas amtuabns

mapltab tasa pbazf

kunva dfrca gn pajf

=9:199.99 >% (?7-1?)/? 4 =9:199*(1+(>%*4)) =7?>99.99 >% (?4-?7)/? 1 >7?>99/(1+(>%*1)) >14444.4:

mapltab

5%*4)) 1.=999 U 1U

?

?) ]l uka ncprnsa gnon makmnbar uka snrln gn gnugas asã8 gnktrf gn = cnsns $19,9990 gnktrf gn : cnsns $ 1?,999 y gnktrf gn 19 cnsns $1>,999. ¶Muáktf glknrf gnon gnpfsltar nb gãa gn efy para mrnar uk dfkgf qun bn pnrclta eamnr nsfs pajfs sl sn mfkslgnra uk lktnrìs gnb :.>% sncnstrab slcpbn6

9 EF\ dnmea dfmab

WA]A

= 19,999.99

: 1?,999.99

19 CN]N] 1>,999.99

:.>9%

LKTN_MLFK U U U U3

YAJF] D^W^_F] 19,999.99 1?, 999.99 ((1+(:.>9%*(=/4))) ((1+(:.>9%*(:/4))) > 119=7.75 =7994.=: ba ncprnsa tlnkn qun lkvnrtlr efy =7994.=:

1>, 999.99 ((1+(:.>9%*(19/4))) 1====.==

=) ]l uka ncprnsa gnon makmnbar uka snrln gn gnugas asã8 gnktrf gn > cnsns $1,?990 gnktrf gn 1? cnsns $ 1,799 y gnktrf gn 14 cnsns $1,>99. ¶Muáktf glknrf gnon gnpfsltar nb gãa gn efy para mrnar uk dfkgf qun bn pnrclta eamnr nsfs pajfs sl sn mfkslgnra uk lktnrìs gnb 7.?>% sncnstrab slcpbn6

1 >% (=4-?7)/? 4 1/(1+(>%*4)) 9.:4%

1? 1,799.99

14 cnsns 1, >99.99

]NCN]W_AB ]LCYBN

LKTN_MLFK U U U U3

YAJF] D^W^_F] 1,?99.99 ((1+(7.?>%(>/4))) 11>5. =:5

1, 799.99 ((1+(7.?>%*(1?/4))) 1?99.99 ((1+(7.?>%*(14/4))) 1=7:.=1

7) ^ka ncprnsa tlnkn bas sljulnktns gnugas8 ^k gfmucnktf pfr 1?>,999 mfk nb ??.>9% gn lktnrìs slcpbn akuab dlrcagf eamn 15 cnsns y qun gnon makmnbarsn gnktrf gn 4 cnsns0 y f trf pfr ?>9,999 mfk uka tasa gnb 4.>9% trlcnstrab slcpbn dlrcagf a =4 cnsns pbazf y qun gnon pajarsn gnktrf gn 1? cnsns. Ba ncprnsa mfkvlnkn mfk su amrnngfr, nk sustltulr nstfs pajfs gn ba sljulnktn caknra8 trns pajfs gn dfrca dfrc a qun nb snjukgf sna ba cltag gn ba suca gnb prlcnrf y nb tnrmnrf0 y nb tnrmnrf sna nb trlpbn gnb prlcnrf0 a makmnbarsn gnktrf gn 5, 14 y ?7 cnsns cn sns rnspnmtlvacnktn0 nb amrnngfr amnpta nstn mfkvnklf sln slncprn cprn y muakgf ba tasa gn lktnrìs mfkvnklga sna gnb 5% sncnstrab nk gnsmunktf oakmarlf. Muáb ns nb vabfr gn nstfs pajfs (utlblzar mfcf dnmea dfmab nb tlncpf amtuab f prnsnktn). pasf 1 9

dnmea dfmab

4 1?>,999.99 ??.>9% 15+43?7 151? >9 1U

5

1? ?>9,999.99 4.>9% =4 77 >999 ?U

14

?7 tlncpf pfr vnkmnr

cnsns

=U

pasf ? C3M*(1+(l*k)) lktnrns slcpbn 1?>,999*(1+(??.>9%*(?7/1?)) ?>9,999*(1+(4.>9%*(=4/1?)) 151?>9 77> 999 pasf = tasa

5% sn s ncnstrab nk gnsmunktf oakmarlf gnugas frljlkabns 151 ?>9 5% ?7-1534/4 31 144 :>9

cfktf tasa pbazf mapltab

K^NTA N]W_^MW^_A GN YAJF mapltab 1U ?U tasa 5% 5% pbazf (5/4) (14/4)

77> 999 5% =4-?731?/43? =:= 599 >79> >9

cfktf 1*(1-(5%*5/4)) 9.5:===== =

>79> >9 7.>944444:

7.>9444444: 11)LMCA, ] gn _. B., tlnkn bas b as sljulnktns gnugas8 :>,999 mfk nb ??.?>% gn lktnrìs slcpbn akuab, dlrcagf a 15 cnsn pbazf y a makmnbarsn gnktrf gn 5 cnsns0 y ftra gn 1?>,>99 mfk uka tasa gnb .>9% akuab nk gnsmunktf oakmarlf. Muáb ns nb vabfr gn nstfs pajfs (utlblzar mfcf dnmea dfmab nb tlncpf amtuab f prnsnktn)

9 dnmea df d fmab

5 :>,?9?9.9?.>9% 9 15 1999=1.?> U 9.> (1/=*(9.>+1)

1= 1?>,>99.549 1*1/?

14

?7 U

9.>

1

=U 5% (?7/4)

?.97

 

pasf ? M*(1 M*(1+( +(l* l*k) k))) lk lktn tnrn rnss sl slcp cpbn bn :>,999*(1+(??.?>%*15/1?)) 1999=1.?>

pasf = Wasa M3

1?>,>99*(1+( 549

1>.>9% akuab C*(1-(k*g)) gnugas frljlkabns 1999=1.?> 1>.>9% (5/1?39.4444

cfktf tasa pbazf mapl maplta tabb

kunva nstrumtura gn pajfs 9.> 9.> 1 1>.>9% 1>.>9% 1>.>9% (5/1?)39.444 (14/1?)31.= (?7/1?)3?

?1> 549 1>.>9% (1=/1?)31.95==

=:>= =:>=:>* :>*(1 (1-( -(1>. 1>.>9 >9%*( %*(5/1 5/1?) ?))) )) = =59 59*(1 *(1-( -(1> 1>.> .>9% 9%*( *(1=/ 1=/1? 1?)) )))) 9.>* 9.>*(1 (1-(1 -(1>. >.>9 >9%( %(5/ 5/1?) 1?))) 5=>

U

1:>77>.95 WN_MN_ YAJF 5::??.>7 5::??. >7 Y_LCN_ Y_LCN_F F \ ]NKJ^KGF ]NKJ^KGF

4) ^ka daclbla pbakna vlahar a Austrabla gnktrf gn ? añfs y para nbbf knmnslta glspfknr gn $?9,999 qun sfk bfs jastfs nstlcagfs qun muorn pasahns gn avlýk, nstagãa, mfclga, ntm. para mfktar mfk nsn glknrf pbakna a pfrtar a uk dfkgf gn lkv lkvnrslfkns nrslfkns qun jnknra nb 9.:>% slcpbn cnksuab, bas sljulnktns sucas8 $>,999 efy0 $ 5,999 gnktrf gn 1? cnsns y ftra maktlgag a bfs ?9 cnsns. Gn muaktf gnon snr nb gnpfsltf qun gnon rnablzar a bfs ?9 cnsns para qun huktf mfk bfs gfs gnpýsltfs cás (ab lklmlf y 1? cnsns) bn pnrcltak amucubar ba maktlgag gnsnaga gn $?9,9996

9 EF\ >999.99 9.:>% ?9 Yasf 1

1? 5,999.99 9.:>% slcpbn cn cnksuab 1?

M*(1+lk) >9 >999 99*( *(1+ 1+(9 (9..:> :>%* %*?9 ?9)) )) >:>9.99

?9 6

M*(1+lk) 5999 5999*( *(1+ 1+(9 (9.: .:>% >%*1 *1?) ?))) 5,:?9.99 17,7:9.99 >,>=9.99

:) . ^ka ncprnsa tlnkn bas b as sljulnktns gnugas8 ^k gfmucnktf pfr 1?>,999 mfk nb ??.>9% gn lktnrìs slcpbn akuab dlrcagf eamn 15 cnsns y qun sn makmnbará gnktrf gn 4 cnsns0 y ftrf pfr ?>9,999 mfk uka tasa gnb 4.>9% trlcnstrab slcpbn dlrcagf dl rcagf a =4 cnsns pbazf y a pajarsn gnktrf gn 1? cnsns. Ba ncprnsa mfkvlnkn mfk su amrnngfr sustltulr nstfs pajfs gn ba sljulnktn c caknra8 aknra8 trns pajfs gn dfrca qun nb snjukgf sna ba cltag gn ba suca gnb prlcnrf y nb tnrmnrf0 y nb tnrmnrf sna nb trlpbn gnb prlcnrf, a makmnbarsn gnktrf gn 5, 14 y ?7 cnsns rnspnmtlvacnktn0 nb amrnngfr amnpta nstn mfkvnklf slncprn y muakgf ba kunva tasa gn lktnrìs mfkvnklga sna gnb 5% sncnstrab nk gnsmunktf oakmarlf. Muáb ns nb vabfr gn nstfs pajfs (utlblzar mfcf dnmea dfmab nb tlncpf amtuab f prnsnktn)

9 dnmea dfmab

YA]F 1

4 1?>,999.99 ??.>9% akuab 15+ 43 ?7 151 ?>9 M*(1+(l*k)) lktnrns slcpbn 1?>,999*(1+(??.>9%*?7/1?)) 151 ?>9

5 1U

1? ?>9,999.99 4.>9% =4 77 >999

14

?7

?U

=U

M*(1+(l*k)) ?>9,999*(1+(4.>9%*=4/=)) 77 >999

9.4<

 

pasf = tasa M3

5% gn gnsunktf oakmarlf C*(1-(k*g) GN^GA] F_LJLKABN] 151 ?>9 5% 1 151?>9*(1-(5%*1)) 144 :>9

CFKWF WA]A YBAXF MAYLWAB

77> 999 5% ? 77>999*(1-(5%*?)) =:= 599

>79> >9 7.>944444:

K^NTA N]W_^MW^_A GN YAJF mapltab 1U ?U tasa 9.95 pbazf (5/4) (14/4) cfktf

=U 9.95

1*(1-(5%*5/4)) 9.5:===== =

7.>9444444:

119,99 999* 9*(1 (1+(= +(=>% >%*7 *7/1? /1?)) )) 14: >99

pasf = M3 tasa cfktf tasa pbazf mapltab

? 1>9 999 =>% s akuab 14: >99

C/(1+(k*l)) 17% muatrcnstrab ?59 999 17%

14: >99 17% ?/739.>

7/731

1U 17% 1 mapltab

?7>417.97

9.5::14>7?.94 79?1>4.9< 9.5::1

kunva nstrumtura gn pajf C/(1+l*k) cfktf 1 tasa >% pbazf 19 >7?>99 mapltab 9.5

5>:< ?> ?.7444444:

1 >% ?9 9.44444 4:

?.74444444: =7:59:.7=

1?) ]abvagfr Kasrabba, tlnkn bas sljulnktns gnugas8 gfs bntras gn macolf, uka pfr B 49,999 a makmnbarsn gnktrf gn : cnsns y 14 gãas, gã as, y ftra pfr B :>,999 a pajarsn gnktrf gn 1= qulkmnkas. agncás gnon uk prìstacf pfr ba maktlgag gn =>9,999 ab :.>% trlcnstrab slcpbn, mfkmngl mfkmnglgf gf eamn uk añf y qun gnon makmnbarsn gnktrf gn 15 cnsns. Kasrabba mfkvlnkn mfk su amrnngfr sustltulr nstfs pajfs pfr ftra nstrumtura, asã8 eará ? pajfs, gn dfrca qun nb prlcnrf sna uk =>% gnb vabfr gnb snjukgf pajf, a pajarsn gnktrf gn 1 y ? añfs rnspnmtlvacnktn, nb amrnngfr amnpta slncprn y muakgf ba tasa gn lktnrìs mfkvnklga sna gnb 1>% slcpbn sncnstrab. Muab ns nb vabfr gn nstfs pajfs (utlblzar mfcf dnmea dfmab nb prlcnr añf)

??4 49,999.99

1 :>,999.99

=49 dnmea dfmab

>79 =>9,999.99 :.>9% trlcnstrab

:?9

1?+153=9 41?>99

pasf ?

M*(1+(l*k) =>9,999*(1+(:.>9%*=9/=)) 41?>99

pasf = tasa

1>% sl slcpbn sncnstrab

mapltab tasa pbazf cfktf

gnugas frljlkabns M*(1+(l*k)) C/(1+(l*k)) 49,999.99 :>,999.99 ma m apltab 1>% 1>% tasa 1=7 14> pbazf 44 :99 5>=1?.> mapltab 4574?1.?9 1.1?

kunva nstrumtura gn pajf 41?,>99.99 1>% 159 >=?495.:9

tasa pbazf cfktf mapltab

1>% ? 1 1/(1+(1>%*?)) 9.:4