Mat Fin - Carpetas Prácticos 2017

UNPSJB - MATEMÁTICA FINANCIERA 2017

@- Una 3!rs&na #!3&s*(a 4 10.000 !n una !n(*#a# *nan*!ra = a% a& #! H 6!s!s r!(*ra 4 11.10<10. D!(!r6*n!: a ,a (asa #! *n(!rs 6!nsua%  ,a (asa #! *n(!rs n&6*na% anua%  Su3&n*!n#& u! %a &3!ra*?n u*!s! s*#& &n+!n*#a a *n(!rs s*63%! 6!nsua%. Ca%u%! !% (&(a% #! %&s *n(!r!s!s a a& #! %&s H 6!s!s. R: a 1<2;  15
UNPSJB - MATEMÁTICA FINANCIERA 2017

PRACTICO 3 – TASAS 1- Da#a %a TNA #! *n(!rs #!% 72;< !nu!n(r! %as s*8u*!n(!s (asas: a- 3ara un 3!r9&#& #! a3*(a%*$a*?n 6!nsua% - 3r&3&r*&na% 3ara &3!ra*&n!s a 7 #9as - 3ara un 3!r9&#& #! a3*(a%*$a*?n ua(r*6!s(ra% #- %u!8& a%u%! %a (asa #! *n(!rs !u*+a%!n(! anua% 3ara a#a una #! %as a%(!rna(*+as = a8a un r!+! &6!n(ar*& #! %&s r!su%(a#&s &(!n*#&s 2- Para &3!ra*&n!s a 7 #9as s! r!&n&! a %&s #!3&s*(an(!s una (asa !u*+a%!n(! #! 0<0125 3&r 0 #9as. S! 3*#!: a- *#!n(**u! %a un*#a# #! (*!63& - a%u%ar %a (asa #! *n(!rs 3ara %a un*#a# #! (*!63& - %a TNA !nun*a#a 3ara %a &3!ra*?n - Ca%u%ar %as TNA 3ara &3!ra*&n!s 3as*+as u! #!!r9a &r!!r a sus %*!n(!s una *ns(*(u*?n *nan*!ra< s* #!s!a &3!rar &n %as s*8u*!n(!s (asas: a- 0<012 3ara 0 #9as - 0<0225 3ara 0 #9as - 0<0750 3ara 1H0 #9as #- In#*u! s!8>n su &3*n*?n< u"% !s %a a%(!rna(*+a 6"s &n+!n*!n(! 3ara !% *n+!rs&r. Jus(**u!. - C&n&*!n#& u! %a (asa #! *n(!rs anua% !s #! 0<175< s! 3*#! #!(!r6*nar %a (asa 6!nsua% !u*+a%!n(! = %a (asa n&6*na% anua% &n a3*(a%*$a*?n 6!nsua%. 5- Una !n(*#a# &r!! un 3rs(a6& #! 45.000. A% a& #!  6!s!s !% #!u#&r #!!r" #!+&%+!r 45.12. O(ra !n(*#a# &r!! 3rs(a6&s a% 25<H; n&6*na% anua% &n a3*(a%*$a*?n *6!s(ra%. D!(!r6*n!: a- u &3!ra*?n !s 6"s &n+!n*!n(! 3ara !% #!u#&rG - u (asa anua% &n a3*(a%*$a*?n *6!s(ra% #!! &r!!r %a s!8un#a !n(*#a# 3ara u! %a &3!ra*?n s!a !u*+a%!n(! a %a #! %a 3r*6!ra !n(*#a#G - Da#a una TNA #!% 2;< a%%ar %as (asas 3r&3&r*&na%!s 3ara %&s s*8u*!n(!s su3!r9&#&s: a- 6!nsua% - 0 #9as - s!6!s(ra% #- 3ara H0 #9as

UNPSJB - MATEMÁTICA FINANCIERA 2017

7- A u (asa n&6*na% anua% u! *n+!r(*#& un a3*(a% #! 41.000 u! !n 5 #9as 3!r6*(*? r!(*rar 41.200G A#!6"s< #!(!r6*nar %a (asa !!(*+a anua%. H- a%%ar %a (asa (r*6!s(ra% !u*+a%!n(! a%  ; s!6!s(ra%. @- Ca%u%ar %a (asa *6!s(ra% &rr!s3&n#*!n(! a%  ; n&6*na% anua% &n a3*(a%*$a*?n (r*6!s(ra%. 10- D!(!r6*nar %a TNA a3*(a%*$a%! (r*6!s(ra%6!n(! u! s!a !u*+a%!n(! a% 5 ; n&6*na% anua% a3*(a%*$a%! s!6!s(ra%6!n(!.

UNPSJB - MATEMÁTICA FINANCIERA 2017

PRACTICO 4 - Pr&%!6as #! D!su!n(&s. Tasas #! #!su!n(& 1- Cu"% s!r" !% #!su!n(& &6!r*a% #! un #&u6!n(& #! 4 10.000 u! !n 5 6!s!s a% ; 6!nsua%G R(a: 1500 2- P&r un 3a8ar #! 4 100.000 an(!s #! su +!n*6*!n(&< s! &(u+& un #!su!n(& #! 4 1.7@<52. S* %a &3!ra*?n s! r!a%*$? a %a (asa #! *n(!rs #!% 0; anua% = #!su!n(& &6!r*a%. Cu"n(&s #9as s! an(**3? !% 3a8&G R(a: @0 #9as - E% #!su!n(& &6!r*a% *nan*!r& n& *n%u=! %& #!s&n(a#& !n &n!3(& #! s!%%a#& #! un 3a8ar #!s&n(a#&  6!s!s an(!s #! su +!n*6*!n(& a %a (asa #! *n(!rs #!% 0; anua% &s(? 10.000. Ca%u%ar !% +a%&r n&6*na% #!% #&u6!n(& = !% +a%&r a(ua% (!n*!n#& !n u!n(a u! !% ar8& 3&r s!%%a#& as*!n#! a 1; #!% +a%&r n&6*na% #!% 3a8ar. R(a: 101000 - #!6 an(!r*&r< 3!r& &n %a sa%+!#a# #! u! %&s 10.000 &ns(*(u=!n !% #!su!n(& (&(a%. R(a: 100000 5- Un #&u6!n(& u! +!n! #!n(r& #! 2 a&s s! #!su!n(a a% H; n&6*na% anua% &n a(ua%*$a*?n s!6!s(ra% a3%*a%! a% 3r*6!r s!6!s(r!< = a% 7; n&6*na% anua% u! a(ua%*$a s!6!s(ra%6!n(! #uran(! !% r!s(& #!% (*!63&. S* !% #!su!n(& ra*&na% 3ra(*a#& as*!n#! a 4 250.000 u"% !s !% +a%&r a(ua% #!% #&u6!n(&G R(a: 1.00@.75 - Ca%u%ar !% a3*(a% u! #!! 3a8ars! #!n(r& #! 2 a&s = 6!#*& 3ara %*u*#ar (r!s #!u#as #! 4 200.000 !*8*%! #!n(r& #! 1 a&< 4 500.000 #!n(r& #!  a&s< = 4 150.000 #!n(r& #!  a&s< s*!n#& %a (asa #! #!su!n(& #!% ; anua% u! a(ua%*$a s!6!s(ra%6!n(!. R(a: H.75<1@ 7- Un #&u6!n(& #! 4 20.000 &n +!n*6*!n(& #!n(r& #! 1 a& sur! un #!su!n(& #! 4 2.@5<7@. S* %a (asa #! #!su!n(& +*8!n(! 3ara !% 3r*6!r (r*6!s(r! !s #!% 7.5 ; &n a(ua%*$a*?n 6!nsua%< a%u%ar %a (asa +*8!n(! 3ara !% r!s(& #!% a&. R(a: *@: 5<0 H- E% 12Q0HQ@@ susr*& un #&u6!n(& 3&r 4 10.000 &n +!n*6*!n(& !% 11Q0@Q@@< r!**!n#& a a6*& 4 @.H00.D!(!r6*nar: a %a (asa #! #!su!n(& #!% 3!r9&#&  %a (asa #! *n(!rs #!% 3!r9&#&.  %a (asa #! *n(!rs anua% !!(*+a # %a (asa #! #!su!n(& anua% !!(*+a ! %a (asa n&6*na% anua% #! #!su!n(&.  %a (asa n&6*na% anua% #! *n(!rs R(a: !n %as!

UNPSJB - MATEMÁTICA FINANCIERA 2017

@- E% #9a 12Q0Q10 a= una %**(a*?n #! %!(ras #! (!s&r!r9a a @0 #9as #! 3%a$&. En !% 3%*!8& #! %a %**(a*?n s! !s(*3u%a u! !n %as &(*$a*&n!s #!! *8urar: TEA# #!s!a#a 11; a %a (asa n&6*na% a#!%an(a#a #! %a &3!ra*?n  R(a: 0<027122  !% *63&r(! u! s! a&nar" 3&r una %!(ra #! +a%&r n&6*na% #! 4 100.000  R(a: #@0: 0<02H 10- Una !63r!sa (*!n! %a s*8u*!n(! s*(ua*?n *nan*!ra: A(*+& &rr*!n(! D&u6!n(&s a &rar 45.000 V

Pas*+& &rr*!n(! O%*8a*&n!s a 3a8ar 45000 VV

V Pa8ar +(& a @0 #9as VV Pa8ar #! 410.000 +(& a 0 #9as Pa8ar #! 425.000 +(& a 5 #9as Pa8ar #! 41H.000 +(& a 10 #9as S* a %a !a s! u*s*!ra a#!%an(ar !% 3a8& #! %as &%*8a*&n!s = 3&r !% #&u6!n(& a &rar !% #!u#&r a!3(ar! !% 3a8& an(**3a#&< s! #!s!a sa!r: a s* &n %a su6a a &rar an!%a !% 3as*+&  !n as& #! u! as9 n& u!ra< u"% s!r9a %a #*!r!n*a Da(&s: 3ara %as &3!ra*&n!s #! &r& r!a%*$ar !% "%u%& &n #!su!n(& &6!r*a% a %a (asa #!% 2<5; 3ara 0 #9asL = 3ara %as &%*8a*&n!s< a %a TNA #! #!su!n(& &n "%u%& &63u!s(& #!% 2@<2; 3ara 3!r9&#&s #! 0 #9as. R(a: n& s! 3u!#! a&nar. D*!r!n*a 4111<50

UNPSJB - MATEMÁTICA FINANCIERA 2017

PRÁCTICO 5  R!n#*6*!n(& r!a% 3&r !!(& #! %a *n%a*?n EJ 1 R!a%*$a6&s una &%&a*?n #! #*n!r& !n a3*(a%*$a*?n &63u!s(a 3&r (r!s 3!r9&#&s #! 0 #9as a una TNA* #!% 2; AQ5. S* %as (asas #! *n%a*?n #! %&s  3r*6!r&s 6!s!s u!r&n 0
UNPSJB - MATEMÁTICA FINANCIERA 2017

PRÁCTICO   DOCUMENTOS EXUI)A,ENTES / )ENCIMIENTO MEDIO E 1: D!*n*r +!n*6*!n(& 6!#*& = &6>n. R(a: Au%a +*r(ua%

E 2: Una 3!rs&na (*!n! (r!s 3a8ars a% 12; anua% #! *n(!rs 3&r 4.000< 410.000 = 420.000< u! +!n!n r!s3!(*+a6!n(! a %&s @0< 120 = 20 #9as. S! a &n+!n*#& !n(r! %as 3ar(!s r!!63%a$ar%&s 3&r un #&u6!n(& >n*& a 150 #9as< a %a 6*s6a (asa. Cu"% !s !% +a%&r n&6*na% #! %a nu!+a &%*8a*?nG R(a: 4.5@.1@ E : Una 3!rs&na (*!n! un 3a8ar #! 41H.000 = &(r& #! 410.000 u! +!n!n a %&s @0 = 120 #9as r!s3!(*+a6!n(!. S! a &n+!n*#& !n sus(*(u*r%&s 3&r un #&u6!n(& >n*& #! 40.000< s*!n#& %a (asa #! #!su!n(& #!% 1H; anua%. Cu"% !s %a !a #!% +!n*6*!n(& &6>nG R(a: 27<57 #9as E : Una 3!rs&na (*!n! (r!s 3a8ars a% 1H; anua% #! *n(!rs #! 4H.000< 410.000 = 41H.000< u! +!n!n r!s3!(*+a6!n(!< a %&s 0< 120 = @0 #9as. S! a &n+!n*#& !n sus(*(u*r%&s 3&r un #&u6!n(& >n*& u=& +a%&r n&6*na% s!a %a su6a #! %&s #a#&s. Cu"% !s %a !a #!% +!n*6*!n(& 6!#*&G R(a: H5 #9as E 5: S! #!!n 3a8ar 42.000 #!n(r& #!  6!s!s< 4.500 #!n(r& #!  6!s!s = 4.000 #!n(r& #! 7 6!s!s. S! #!s!a sa!r u su6a s! #!! 3a8ar #!n(r& #! 2 6!s!s !n %u8ar #! %as (r!s *n#*a#as< su3&n*!n#& %a (asa *n(!rs 3&r!n(ua% #!% ; 6!nsua%. R(a: 4@7@
UNPSJB - MATEMÁTICA FINANCIERA 2017

PRÁCTICO 7  CASOS 'ENERA,ES DE RENTA EJ 1 Un 3a#r! %! r!8a%a a su *& !n su u63%!a&s n>6!r& u*n! un #!3?s*(& 3&r una su6a #! #*n!r& !n una u!n(a anar*a u! a3*(a%*$ar" *n(!r!s!s 6!nsua%6!n(! !n &r6a &63u!s(a a una (asa !!(*+a #!% 0%(*6&s #&s a&s n& r!a%*$a #!3?s*(&s 3&r a!r 3!r#*#& !% !63%!&< 3!r& sus #!3?s*(&s 3!r6an!!n !n !% an& 8anan#& *n(!rs. A% r!**rs!< %u!8& #! *n& a&s #! !s(u#*&< #!*#! #!s(*nar sus a&rr&s a %a &63ra #! una &**na u=& +a%&r !s #! 450.000. E% sa%#& s!r" *nan*a#& &n un 3rs(a6& anar*& a una (asa a(*+a 6!nsua% #!% 1<5; !n 0 u&(as 6!#*an(! una a6&r(*$a*?n &n u&(as 6!nsua%!s *8ua%!s< &6!n$an#& a 3a8ar %a 3r*6!ra #!n(r& #! s!*s 6!s!s. D!(!r6*n! !% +a%&r #! %a u&(a 6!nsua%. EJ  A% u63%*r %&s (r!*n(a a&s< un *n#*+*#u& 3r!&u3a#& 3&r su +!!$ #!*#! &6!n$ar a a&rrar a *n #! r!un*r un &n#& 3ara su u*%a*?n u! %! 3!r6*(a r!(*rar< a 3ar(*r #! !n(&n!s< !n &r6a 6!nsua% +!n*#a = 3&r un %a3s& #! #*!$ a&s %a su6a #! 42.000. S* %a u*%a*?n s! 3r&#u! a% u63%*r %&s 5 a&s = !% r!n#*6*!n(& !!(*+& 6!nsua% !s(*6a#& 3ara sus #!3?s*(&s !s #!% H; TNA< a%u%ar !% +a%&r #! %a u&(a #! a&rr& 6!nsua% u&(a +!n*#a. EJ  Un *n#*+*#u& 3&s!! 4 100.000 u! #!s!a &n+!r(*r%&s !n una r!n(a #! 3a8&s 6!nsua%!s &n a#**&na%!s ua(r*6!s(ra%!s +!n*#&s #uran(! %&s 3r?*6&s  a&s. S! #!s!a un a!r 6!nsua% #! 4 2.000 u! &rar" 3&r a#!%an(a#&. E% 3r*6!r a#**&na% ua(r*6!s(ra% s!r" &ra#& #!n(r& #! #&s 6!s!s. Da#a %a (asa * #!% 2 ; 6!nsua%< a%u%! !% +a%&r a#**&na% ua(r*6!s(ra%. EJ 5 Un *n#*+*#u& a#!u#a H u&(as 6!nsua%!s = &ns!u(*+as< %as 3r*6!ras ua(r& #! 4 2000 = %as r!s(an(!s #! .000. En %a !a #!% 3r*6!r +!n*6*!n(& &nurr! a% Ban& = s&%**(a &6!n$ar a 3a8ar #!n(r& #! 2 6!s!s a 3ar(*r #! %a ra. u&(a 3a8an#& un a#**&na% !n !s! 6&6!n(&. Cu"% s!r" !% *63&r(! a#**&na% u! #!!r" a&nar un(a a %a (!r!ra u&(a< #a#a %a (asa #! *n(!rs #!% 7.0 ; n&6*na% anua% 3ara a3*(a%*$a*&n!s (r*6!s(ra%!sG EJ  ,! &r!!n un #!3ar(a6!n(& u=a 3&s!s*?n !s !n 1H 6!s!s. ,a &r6a #! 3a8& !s %a s*8u*!n(!: R!s!r+a 4 275<2 &=L a% &%!(& #!n(r& #! un 6!s 4 1.100L a 3ar(*r #!% 6!s u! +*!n!< #!s3us #! %a r!s!r+a: 1H u&(as #! 4 20L  r!u!r$&s s!6!s(ra%!s #! 4  a 3ar(*r #!%

UNPSJB - MATEMÁTICA FINANCIERA 2017

(!r!r 6!s s*8u*!n(! a% #! %a r!s!r+aL a% 6&6!n(& #! %a 3&s!s*?n 4 .55 = a 3ar(*r #!% 6!s s*8u*!n(! a% #! %a 3&s!s*?n 1H0 u&(as #! 4 @. S* 3u#*!ra &ns!8u*r un 3rs(a6& s*n n*n8>n (*3& #! 8as(&s a% 1H ; n&6*na% anua% 3ara &3!ra*&n!s 6!nsua%!s< %! &n+*!n! saar un 3rs(a6& a 1H u&(as = 3a8ar%& a% &n(a#&< & 3a8ar%& *nan*a#& #! au!r#& a %as &n#**&n!s #!(a%%a#as s* %a (asa !s #!% H; n&6*na% anua% 3ara &3!ra*&n!s (r*6!s(ra%!sG EJ 7 S! !s(" 3a8an#& un 3rs(a6& u=a u&(a as*!n#! a 4 100 a% &6*!n$& #! a#a (r*6!s(r!. Transurr*#&s 2 a&s< uan#& a>n r!s(an 2 3a8&s s! u*!r! sa%#ar %a #!u#a. Cu"n(& #!! a&nars! a% H ; anua% !!(*+&G EJ H C&n && #!3?s*(&s< &%&a#&s a% *n**& #! a#a 6!s #! 4 100 a#a un& = a3*(a%*$a#&s a%  ; 6!nsua% #! *n(!rs< s! u*!r! r!un*r *!r(a su6a #! #*n!r&. Para !% su3u!s(& as& #! u! n& s! r!a%*! !% uar(& #!3?s*(& = a#!6"s s! r!(*r!n !n !s! 6&6!n(& 4 200 &n %a *n(!n*?n #! r!un*r %a su6a *n**a%6!n(! 3%an!a#a s! r!u*!r! sa!r: A#**&na% 6!nsua% a 3ar(*r #! %a 5(a. Cu&(a  R(a: H2<5 A#**&na% >n*& un(& &n %a 76a.u&(a  R(a: 7<5 EJ @ Un *n#*+*#u& 3&s!! 4 70.000 u! #!s!a &n+!r(*r%&s !n una r!n(a #! 3a8&s 6!nsua%!s &n a#**&na%!s ua(r*6!s(ra%!s #uran(! %&s 3r?*6&s  a&s. S! #!s!a un a!r 6!nsua% #! 4 1.H00 u! &rar" 3&r a#!%an(a#&. E% 3r*6!r a#**&na% ua(r*6!s(ra% s!r" &ra#& #!n(r& #! #&s 6!s!s !n &r6a +!n*#a. Da#a %a (asa #!%  ; 6!nsua%< a%u%! !% +a%&r a#**&na% ua(r*6!s(ra%. R(a: 2@<5 EJ 10 Un *n#*+*#u& a#!u#a H u(as 6!nsua%!s< a#!%an(a#as = &ns!u(*+as< %as 3r*6!ras ua(r& #! 4 2000 = %as r!s(an(!s #! .000. En %a !a #!% 3r*6!r +!n*6*!n(& &nurr! a% Ban& = s&%**(a &6!n$ar a 3a8ar #!n(r& #! 2 6!s!s a 3ar(*r #! %a ra u&(a 3a8an#& un a#**&na% !n !s! 6&6!n(&. Cu"% s!r" !% *63&r(! a#**&na% #a#a %a (asa #! *n(!rs #!% 7.0 ; n&6*na% anua% 3ara a3*(a%*$a*&n!s (r*6!s(ra%!sG R(a: 521@<0 EJ 11 S!a una su!s*?n #! 0 a3*(a%!s *8ua%!s &%&a#&s a% *n**& #! a#a 3!r9&#&< u=a (asa #! &%&a*?n 3!r*?#*a !s #!%  ; = !% +a%&r #! a#a a3*(a% !s #! 4 5.000. S! 3*#! a%u%ar %a r!n(a !n %&s s*8u*!n(!s 6&6!n(&s: Un 3!r9&#& an(!s #!% 3r*6!r 3a8& a- A% 6&6!n(& #!% >%(*6& a3*(a% - A% 3a8& #!% a3*(a% n>6!r& 10 - A% 6&6!n(& #!% 3r*6!r 3a8& #- S*!(! 3!r9&#&s 3&s(!r*&r!s a% >%(*6& 3a8& R(a: !n !% au%a

UNPSJB - MATEMÁTICA FINANCIERA 2017

PRACTICO N H  R!n(as )ar*a%!s E 1 S! u*!r! #!(!r6*nar un a3*(a% u! 3asa#&s  a&s 3!r6*(a &rar una r!n(a #! 4 5.000 !% 3r*6!r a& = %u!8& u&(as au6!n(a#as !n un 20; Qu r!s3!(& #! %a an(!r*&r #uran(! 10 a&s. a%%ar !s! a3*(a% s* %a (asa anua% !s #!% 7; = %as u&(as s&n +!n*#as.

E 2 Ca%u%ar !% +a%&r a(ua% #! una s!r*! #! 3a8&s (r*6!s(ra%!s +!n*#&s #uran(!  a&s s* %a (asa #! *n(!rs !s #!% 12 ; (r*6!s(ra% = a#a 3a8& #*s6*nu=! !n un 2 ; r!s3!(& #!% an(!r*&r. E% 3r*6!r 3a8& !s #! 4 500.000. E  Ca%u%ar !% +a%&r a% @Q5Q11 #! una s!r*! #! 12 3a8&s 6!nsua%!s = &ns!u(*+&s< a#a un& #! %&s ua%!s !s 40 su3!r*&r a% 3r!!#!n(!. E% 3r*6!r 3a8&< u! s! !!(>a !% @QQ11 !s #! 4200 = %a (asa #! *n(!rs !s #!% 0a !% @QQ11 !s #! 4100 = %a (asa #! *n(!rs !s #!% 2 ; 6!nsua%. E 5 Una 3!rs&na #!s!a &ns(*(u*r un #!3?s*(& u! %! 3!r6*(a &(!n!r a% 3r*n*3*& #! a#a s!6!s(r!< #!n(r& #! (r!s a&s< una r!n(a #! 42500 !% 3r*6!r 3!r9&#& = %u!8& u&(as s!6!s(ra%!s au6!n(a#as !n un 10; #uran(! 5 a&s. D!(!r6*nar u"% !s #!3?s*(& u! #!! !!(uar &= s* %a (asa !s #!% ; n&6*na% anua% 3ara 3!r9&#&s s!6!s(ra%!s. E  Xu a3*(a% #!!6&s *63&n!r !n un an& u! a&na *n(!r!s!s #!% <5; anua% 3ara u! !s(! s!a su**!n(! 3ara ur*r %&s 8as(&s #! un n!8&*& #uran(! 10 a&s< sa*!n#& u! !% a& an(!r*&r as!n#*!r&n a 410.000 = s! 3r!+ un au6!n(& anua% #!%  ;. S! su3&n! u! %a (&(a%*#a# #! %&s 8as(&s< s! a&nan a% *na% #! a#a a&. E 7 Para &r6ar un a3*(a% #! 41.000.000 s! #!3&s*(a #uran(! H a&s< = a% 3r*n*3*& #! a#a un& #! !%%&s una anua%*#a# a% 5; #! *n(!rs &63u!s(&< s*!n#& a#a a& 4.700 6a=&r u! %a #!% a& an(!r*&r. D!(!r6*nar !% +a%&r #! %a 3r*6!ra *63&s**?n. E H D!(!r6*nar !% +a%&r a(ua% #! una r!n(a #! 15 (r6*n&s sa*!n#& u! %a uan(9a #!% 3r*6!r (r6*n& !s #! 42.500 = %&s s*8u*!n(!s au6!n(an a#a a& !n 4100 s* !% (*3& #! *n(!rs !s #!% 5;.

E @ a%%ar %a ra$?n #! %as anua%*#a#!s #! una r!n(a 3!r3!(ua u! +ar9a !n 3r&8r!s*?n 8!&6(r*a< s*!n#& su 3r*6!r (r6*n& 45.000L !% (*3& #! *n(!rs< ; = a*!n#& 3a8a#& 3&r !%%as 4250.000.

UNPSJB - MATEMÁTICA FINANCIERA 2017

E 10 Una 3!rs&na *63&n! a *n(!rs &63u!s(& !% 1 #! !n!r& %a an(*#a# #! 45.000< = !% 3r*6!r& #! a#a a& su!s*+as su6as u! !!#!n !n 4100 a %a 3r!!#!n(!. E% 1 #! u%*& #! a#a a& r!(*ra: !% 3r*6!r a& 41.000< = a#a a& su!s*+& una an(*#a# +!$ = 6!#*a 6a=&r #! %a an(!r*&r 1.500< 2.250< .75< !(. Xu a3*(a% (!n#r" a% a& #! *n& a&s #! %a 3r*6!ra *63&s**?n< s* %&s *n(!r!s!s s! a3*(a%*$an s!6!s(ra%6!n(!< !n 0 #! un*& = 1 #! #**!6r! #! a#a a&< a% (*3& #! *n(!rs !s #!% 2; s!6!s(ra%G E 11 Ca%u%ar !% +a%&r a(ua% #! %&s *n8r!s&s u! 3!r**r" una !63r!sa !n %&s 3r?*6&s s!*s a&s sa*!n#& u! %a 3r&#u*?n #!% 3r*6!r a& s! +a%&ra !n 41.000.000 = u! s!r" *nr!6!n(a#a a#a a& s&r! !% an(!r*&r !n 4200.000 s* 3ara %a +a%&ra*?n s! u(*%*$a !% r#*(& anua% &ns(an(! #!% 5 ;. E 12 )a%&rar %a &rr*!n(! #! *n8r!s&s u! 3!r**r" un #!(!r6*na#& (raaa#&r #uran(! %&s 3r?*6&s H a&s sa*!n#& u! su su!%#& a(ua% !s #! 40.000 anua%!s = u! s! 3r!+ un au6!n(& anua% au6u%a(*+& #!% 2<5; s* s! u(*%*$a &6& r#*(& #! +a%&ra*?n &ns(an(! !% ; anua%.

E 1 Ca%u%ar !% +a%&r a(ua% #! una r!n(a 3&s3a8a%! #! %as s*8u*!n(!s &n#**&n!s: a

,&s (r6*n&s +ar9an !n 3r&8r!s*?n 8!&6(r*a #! ra$?n 0<@5 s*!n#& %a uan(9a #!% 3r*6!r&

4100.000L b

,a #ura*?n #! %a r!n(a !s #! #&! a&sL

c

E% (*3& #! *n(!rs #uran(! %&s s!*s 3r*6!r&s a&s !s #!% 7; = !% @; 3ara %&s r!s(an(!s  a&s.

E 1 C*!r(a 3!rs&na *63&n! !n un an& !% 3r*6!r& #! !n!r& #! *!r(& a& %a an(*#a# #! 410.000 = !n %a 6*s6a !a #! a#a a& #! %&s s*8u*!n(!s *63&n! una an(*#a# u! !s un 10; 6a=&r u! %a #!% a& an(!r*&r. Xu a3*(a% r!un*r" a% a& #! H a&s #! !!(uar %a 3r*6!ra *63&s**?n s* %a !n(*#a# a3*(a%*$a a% (an(& #!% 5; anua%G Ca%u%ar !% +a%&r a(ua% #! una r!n(a #! 10 (r6*n&s anua%!s u=&s (r!s 3r*6!r&s s&n #! 4H.000< a#a un&< %&s ua(r& s*8u*!n(!s #! 412.000 = %&s r!s(an(!s #! 41.000. S* !% (*3& #! *n(!rs a3%*a%! !s #!% ; 3ara %&s ua(r& 3r*6!r&s = #!% H; 3ara %&s r!s(an(!s. E 15 Xu an(*#a# s! *n8r!sar" !n un an& u! a3*(a%*$a a% H; anua% 3ara u! s(! a&n!< a *n #! a#a a& = #uran(! #&!< una r!n(a u=& 3r*6!r (r6*n& !s #! 450.000 au6!n(an#& a#a a& un +!*n(!a+& #!% an(!r*&r.

UNPSJB - MATEMÁTICA FINANCIERA 2017

E 1 a%%ar %a ra$?n #! %&s (r6*n&s #! una r!n(a 3!r3!(ua u! +ar9a !n 3r&8r!s*?n 8!&6(r*a s*!n(& su 3r*6!r (r6*n& 40.000< !% (*3& #! *n(!rs !% 10; = s! a 3a8a#& 3&r !%%a 41.000.000.

UNPSJB - MATEMÁTICA FINANCIERA 2017

PRÁCTICO @ - AMORTIACIONES SISTEMAFRANCS E 1 S! 3r!s(an 4100.000 a #*!$ 6!s!s #! 3%a$& 6!#*an(! !% s*s(!6a rans. E% 3rs(a6& s!r" #!+u!%(& !n u&(as 6!nsua%!s< *8ua%!s = &ns!u(*+as. E% 3rs(a6& !s(" &n+!n*#& a %a (asa #!% ; 6!nsua%. S! #!s!a &n&!r: a ,a u&(a  T&#as %as a%(!rna(*+as #! %a u&(a NW  R(a a: 11.72<1 R(a : .711<00 E 2 Su3&n8a6&s u! #!s3us #! a&na#a %a (!r!r u&(a #!s!a r!n!8&*ar !% 3rs(a6& =a u! a#u! u! n& 3u!#! 3a8ar 6"s #! 4 2.H00 3&r 6!s. S! #!s!a sa!r: a S* r!su%(a a(*%!  En u"n(& (*!63& %& a6&r(*$a R(a: a N&.  En(r! 50 = 51 6!s!s E  Una 3!rs&na (&6? un 3rs(a6& #! 4 100.000 u! #!!r" an!%ar 6!#*an(! s*s(!6a rans #! a6&r(*$a*?n !n 120 u&(as 6!nsua%!s +!n*#as 3a8an#& una (asa #! *n(!rs 6!nsua% #!% 1;. S! 3*#! a%u%ar: a E% +a%&r #! %a u&(a #! s!r+**& 6!nsua%  E% sa%#& #! %a #!u#a una +!$ 3a8a#as %as #&! 3r*6!ras u&(as.  ,a u&(a #! *n(!rs &rr!s3&n#*!n(! a %a u&(a *nu!n(a # ,a u&(a #! a3*(a% &rr!s3&n#*!n(! a %a u&(a *nu!n(a. ! E% (&(a% 3a8a#& una +!$ an!%a#a %a u&(a s!s!n(a.  ,&s *n(!r!s!s 3a8a#&s as(a %a u&(a *!n *n%us*+!. R(as: a   # !

1.<7H @.H<7 72<7@ 707<@H 5.50@<@7

E  s! #!s!a &n&!r !% +a%&r #! un 3rs(a6& a6&r(*$a%! !n u&(as *8ua%!s = s!6!s(ra%!s< #!% ua% s! sa! u! !% n>6!r& #! 3a8&s !s 10< !% (&(a% a6&r(*$a#& #!s3us #! H 3a8&s s!6!s(ra%!s #! 4 1.7@
UNPSJB - MATEMÁTICA FINANCIERA 2017

a a&nar !n !% as& #! u! %a (asa +ar9! a% 17; s!6!s(ra% #!s3us #! a&nar %a (!r!r u&(a. Ca%u%ar !n !s(! as& !% (&(a% a6&r(*$a#& #!s3us #! H 3a8&s. R(a: 17<1H E 5 Una 3!rs&na (&6? un 3rs(a6& &n 3a8&s 6!nsua%!s #! a6&r(*$a*?n 6!#*an(! s*s(!6a rans. S! sa! u! %u!8& #! a&na#a %a u&(a n>6!r& 27 #!! 4 [email protected]<< %u!8& #! 3a8a#a %a u&(a n>6!r& 2H #!! 4 27.22< = %u!8& #! 3a8a#a %a u&(a n>6!r& 2@ #!! 4 25.20<02< &n !s(&s #a(&s s! u*!r! sa!r: a E% +a%&r #! %a u&(a 6!nsua%  ,a (asa #! *n(!rs 6!nsua%  E% +a%&r #!% 3rs(a6& # ,a an(*#a# #! u&(as 3a(a#as 3ara %&a a6&r(*$a*?n #!% 3rs(a6& R(as: a   #

2.11<01 0.01 1.70<5 120

E  Un 3rs(a6& #! 4 1.000 s! an!%a 6!#*an(! 20 u&(as anua%!s< *8ua%!s = +!n*#as u! *n%u=!n !% 5; anua% #! *n(!rs. Ca%u%ar: a In(!r!s!s (&(a%!s< a6&r(*$a*?n #!% 7W 3!r9&#&< sa%#& #! %a #!u#a &n @ u&(as 3a8as  S* un(& &n %a 12W u&(a !% #!u#&r #!s!as! a&nar an(**3a#a6!n(! %as ua(r& >%(*6as Xu *63&r(! #!!r9a 3a8arG  S* %u!8& #! a&na#as 17 u&(as anua%!s u*s*ra6&s an!%ar !% 3rs(a6& 6!#*an(! u&(as 6!nsua%!s #!n(r& #!% 3%a$& &r*8*na% = &n !% 6*s6& r!n#*6*!n(&< Cu"% s!r9a %a u&(a 6!nsua%G

R(as: a 0<7H  0<12  <50 E 7 Un 3rs(a6& #! 4 0.000 s! an!%a 6!#*an(! u&(as 6!nsua%!s ! *8ua%!s #! 4 1.HH2<12 #uran(! 11 6!s!s a una (asa #!% 5<; 6!nsua%. Ca%u%ar: a In(!r!s!s (&(a%!s< *n(!r!s!s a&na#&s #uran(! %&s 3!r9&#&s W = 10W a6&s *n%us*+!< sa%#& #! #!u#a &n H u&(as 3a8as.  S* un(& &n %a W u&(a !!( ua6&s una a6&r(*$a*?n !(ra&r#*nar*a !u*+a%!n(! a% (&(a% a6&r(*$a#& as(a %a W u&(a *n%us*+!< Xu sa%#& #! #!u#a n&s u!#ar9a 3&r 3a8ar !n !s! 6&6!n(&G  S* u*ra6&s &6*(*#& !% 3a8& #! %as u&(as W<5W<W = 7W Xu *63& r(! #!!r9a6&s a&nar un(& &n %a >%(*6a u&(a 3ara 3&#!r an!%ar !% 3rs(a6&G

UNPSJB - MATEMÁTICA FINANCIERA 2017

R(as: a 1 41.5H<@ 2 4H.H1<07  417.217<0  [email protected]@@<@  4.@7<2@

PRÁCTICO N 10  S*s(!6a A%!6"n E 1 Una !63r!sa n!!s*(a 47.000 u! un an& s! %& &n!#! !% 01Q0 &n a6&r(*$a*?n !n 5 a&s< &n 3a8&s (r*6!s(ra%!s< !% 3r*6!r& #! %&s ua%!s s! ar" !% 01Q0. Tasa &n+!n*#a #!% H; n&6*na% anua% &n a3*(a%*$a*?n (r*6!s(ra%. S! 3*#!: a u&(a 2  #!u#a 3!n#*!n(! #! 3a8& a% 01Q12  a3*(a% u! s!r" a6&r(*$a#& !% 01Q12 # a3*(a% (&(a% a6&r(*$a#& a% 01Q12 E 2 S! r!*! un 3rs(a6& #! 41.000 a a6&r(*$ar !n u&(as anua%!s a 10 a&s< a #*s(*n(&s (*3&s #! *n(!rs: ; %&s 3r*6!r&s  a&s< <5; %&s  s*8u*!n(!s< = 7; %&s >%(*6&s . S! 3*#!: a &63&s**?n #! %a  u&(a 5  #!u#a a% 3r*n*3*& #!%  a&  u&(as #! *n(!rs #! %&s a&s  = @

UNPSJB - MATEMÁTICA FINANCIERA 2017

E  S! 3r!s(a un a3*(a% #! 4210.000 a% 7; anua%. Sa*!n#& u! a% a& #!  a&s !% a3*(a% 3!n#*!n(! #! a6&r(*$a*?n !s Q7 #!% 3r!s(a#&< s! 3r!8un(a: a 3%a$& #!% 3rs(a6&  u&(a #! a6&r(*$a*?n  &63&s**?n #! %a u&(a !n !%  a& E  S! &n(ra(a un 3rs(a6& #! 41.000 a6&r(*$a%! !n u&(as &ns(an(!s< a&na#& !n 20 u&(as 6!nsua%!s = &ns!u(*+as. Sa*!n#& u! %a (asa !s #!% ; 3ara %&s H 3r*6!r&s 6!s!s = 3&s(!r*&r6!n(! #!% 5; 6!nsua%< #!(!r6*nar: a sa%#& %u!8& #! 3a8ar 7 u&(as  n&+!na u&(a #! 3a8&  (&(a% #! *n(!r!s!s a% ; # (&(a% #! *n(!r!s!s a% 5; E 5 Da#& un 3rs(a6& #! 4H.00 3a8a#!r& !n H u&(as 6!nsua%!s = +!n*#as &ns(an(!s = u! #!+!n8a un *n(!rs #!% ; 6!nsua%< #!(!r6*nar: a %a 1 u&(a #! s!r+**& = %a 2  %&s *n(!r!s!s a #!+!n8ar #uran(! !% 1 =  a& #! +*8!n*a #!% &n(ra(& E  A u (asa 6!nsua% #! *n(!rs s! ar" &n!r(a#& una &3!ra*?n 3&r !% s*s(!6a #! a6&r(*$a*?n &ns(an(!< s* an!%"n#&s! !n 2 6!s!s %&s *n(!r!s!s r!3r!s!n(an 1Q #! %a su6a 3a8a#a 3&r (&#& &n!3(& #uran(! %a &3!ra*?n. E 7 ,u!8& #! a&nar %a  u&(a !n %a an!%a*?n #! un 3rs(a6& 3&r 4120 3a(a#& !n 5 3a8&s anua%!s +!n*#&s a% 1H; anua%< s! !s(u#*a %a 3&s**%*#a# #! !(!n#!r !% 3%a$& &r*8*na% !n 2 3!r9&#&s au6!n("n#&s! %a (asa !n 2;. Ca%u%ar %a >%(*6a *%a #! %a 6ara.

PRACTICO NW 11 - SISTEMA AMERICANO

Ej 1 Una #!u#a #! 4 2.000 s! a6&r(*$a 3&r !% s*s(!6a a6!r*an& !n u&(as 20 s!6!s(ra%!s. D!(!r6*nar: a ,a u&(a a3*(a% a% <5; s!6!s(ra%

UNPSJB - MATEMÁTICA FINANCIERA 2017

 ,a u&(a #! *n(!r!s!s a% 5; s!6!s(ra$&  ,a u&(a (&(a% # a*!n#& a&na#& 15 u&(as s!6!s(ra%!s< #! u"n(& #!! #*s3&n!rs! 3ara an!%ar %a #!u#a. Ej 2 D!(!r6*n! !% +a%&r #!% #!s!6&%s& (&(a% u! #!!r9a !!(uar &=< s* a! ua(r& 6!s!s (&6? un 3rs(a6& #! 4 100.000< 3&r !% 3%a$& #! un a&< 3a8a#!r& 6!nsua%6!n(! 6!#*an(! s*s(!6a a6!r*an& &n &n#& a6&r(*$an(! &n u&(as #! a&rr& +!n*#as< s* %a (asa #!% 3rs(a6& s! 3a(? !n !% 12; TNA u(*%*! a& &6!r*a% = 3ara !% &n#& #! a&rr& #!% 2; !!(*+& (r*6!s(ra%.

Ej 3 En una &3!ra*?n &n!r(a#a 3&r !% s*s(!6a a6!r*an& a 2 6!s!s 3&r una #!u#a #! 4 10.000 a una (asa #!% ; 6!nsua%< #!(!r6*nar a u (asa #!!r9a &ns(*(u*rs! !% &n#& 3ara u! %a &3!ra*?n r!su%(! s*n &s(&. Ej 4 ,u!8& #! 3a8a#a %a W u&(a !n %a an!%a*?n #! un 3rs(a6& 3&r 4 .500 6!#*an(! !% s*s(!6a a6!r*an& !n 5 u&(as 6!nsua%!s +!n*#as a% 12; 6!nsua% = &ns(*(u=!n#& un &n#& 3ara %a #!+&%u*?n a% 10; 6!nsua%< s! ana%*$a %a 3&s**%*#a# #! !(!n#!r !% 3%a$& !n 2 3!r9&#&s 6"s< r!#u*!n#& %a (asa 3as*+a a% H; 6!nsua%. Ca%u%ar %a *n&r6a*?n r!!r!n(! a% >%(*6& 3a8&.

PRACTICO NW 12 - S*s(!6a Tasa D*r!(a

Ej 1  S! &n(ra(a un 3rs(a6& #! 4 1.500 !n 20 u&(as 6!nsua%!s = &ns!u(*+as &n un *n(!rs #*r!(& #!% 7;. D!(!r6*nar: a Cu&(a #! 3a8&

UNPSJB - MATEMÁTICA FINANCIERA 2017

 Tasa #! *n(!rs !u*+a%!n(! s&r! sa%#&s Ej 2 Un au(&6?+*% u=& 3r!*& !s #! 4 .000 s! &r!! 50; &n(a#& = !% sa%#& !n 20 u&(as 6!nsua%!s #! 4 200 a#a una. D!(!r6*nar: a Tasa #*r!(a u(*%*$a#a  Tasa #! *n(!rs !u*+a%!n(! s&r! sa%#&s 6!nsua% = (asa !!(*+a anua%. Ej 3) Us(!# &nurr! a una asa #! !%!(r&#&6s(*&s 3ara &63rar +ar*&s !u*3&s #! a*r! a&n#**&na#& 3ara su &**na. E% 3r!*& #! &n(a#& su6a 4 .000 !% &6!r*& %! &r!! a#!6"s %a 3&s**%*#a# #! 3a8ar%& *nan*a#& !n  u&(as 6!nsua%!s &n *n(!r!s!s a una (asa #*r!(a #!% 2; TNA u(*%*! a& &6!r*a%. Ca%u%!: a E% +a%&r #! a#a u&(a = !% 3r!*& (&(a% *nan*a#&  E% +a%&r #! %a u&(a #! un s* s(!6a rans s* (&6ara un 3rs(a6& 3!rs&na% !n un an& a una (asa #!% 0; TNA u(*%*! a& &6!r*a% 3ara an!%ar !% 3r!*& #! &n(a#& #! %&s !%!(r&#&6s(*&s. Ej 4 U#. u! n& (*!n! a!s& a% r#*(& anar*&< 3&r n& 3&#!r u63%*r &n %a #&u6!n(a*?n r!u!r*#a< s! !n#!u#a !n una *nan*!ra (&6an#& un 3rs(a6& a (asa #*r!(a 3&r +a%&r #! 4 20.000 a #!+&%+!r !n 2 u&(as 6!nsua%!s &n un &s(& #!% 0; TNA  a& &6!r*a%. D!(!r6*n!: a E% 3r!*& (&(a% *nan*a#& #! %a &3!ra*?n  E% +a%&r #! a#a u&(a 6!nsua%  D!(!r6*n! %a (asa r!a% #! %a &3!ra*?n Ej 5 DATOS: Prs(a6& 4 100.000  Tasa 0<0 6!nsua%- T*!63& 10 6!s!s CUOTANW

CUOTA

AMORTI

INTERESES

AMORT

SA,DO

ACU 0 1 2   5  7 H @ 10

11.72<05 11.72<05 11.72<05 11.72<05 11.72<05 11.72<05 11.72<05 11.72<05 11.72<05 11.72<05

H.72<05 H@H<7 @.25<2H @.51<@1 @.H17
.000<00 2.7H<1 2.H<77 2.1@1<1 1.@05<1H 1.10< 1.07<27 @@
TOTALES

117.230,50

100.000,00

17.230,50

H.72<05 17.707<7@ 2.@2<0H .@<@@ <11
100.000<00 @1.27<@5 H2.2@2<21 7.07<@2 .50<01 5.HH<1 .575<7 .15@<@ 22.1<71 11.H1<1 0<00

UNPSJB - MATEMÁTICA FINANCIERA 2017

PRACTICO NW 1  In(r&#u*?n a %a Ma(!6"(*a a(uar*a% s?%& a 3!#*#& #! %&s *n(!r!sa#&s E 1 Su3&n8a6&s u! !% an&  s&r! %a as! #! sus !s(a#9s(*as #! a&s an(!r*&r!s = s!8>n !% %*6a !&n?6*& #!% 3a9s #! a#a 100 3r!s(a6&s u! &n!#!  r!su%(an a%%*#&s. Para 3rs(a6&s as(a 100.000.000. S* !% an& #!s!a &(!n!r un *n(!rs #!% 5; = %a *n%a*?n 3r!+*s(a !s !% ; A u (*3& #! *n(!rs (*!n! u! 3r!s(ar !% #*n!r&G

E 2 D!(!r6*nar !% 6&n(an(! #! un a3*(a% #! 4750.000 !n 10 a&s a% ; anua% a3*(a%*$a%! 3&r (r*6!s(r!s.

UNPSJB - MATEMÁTICA FINANCIERA 2017

E  Un &n#& s! a r!+a%&r*$a#& a% <25; !n @5 #9as Cu"% a s*#& %a r!n(a*%*#a# anua% #!% &n#&G E  A u! (*3& #! *n(!rs anua% a9a #! !s(a%!!rs! una &3!ra*?n 3ara u! a3*(a%*$an#& s!6!s(ra%6!n(! 4100 #! &r6a *n6!#*a(a = 4200 a %&s  a&s &(!n!r 4500 a %&s 10 a&sG E 5 S! !6*(*? 3&r 41.000. ,& (!n8& #uran(! 5 a&s = #!s3us #! %&s 5 a&s 6! #!+u!%+!n 41000 = a% !s(ar a% 5; s!6!s(ra% #! u3?n !s #! 425 a#a s!6!s(r!. S* +!n#& !% (9(u%& a %&s 2 a&s< = !% (*3& #! *n(!rs #!% 6!ra#& !s(" a% 1H; Cu"n(& s! 3a8ar" 3&r !% (9(u%&G. E  Un *n+!rs&r (*!n! !% &n+!n*6*!n(& #! u! %as a*&n!s #!% BB)A +an a !3!r*6!n(ar +ar*a*&n!s< 3!r& #!s&n&! %a #*r!*?n a %a a%$a & a %a aa. P%an(!a una !s(ra(!8*a &ns*s(!n(! !n &63rar un CA,, = un PUT s&r! #*as a*&n!s &n un 3r!*& #! !!r**& #! 4.000< 3a8an#& una 3r*6a #! 4200 3&r !% CA,, = 4150 3&r !% PUT. S* !s(*6a &6& 3&s*%!s %u(ua*&n!s #!% 3r!*& #! .000 a 5.000 3!s&s Para u +a%&r &(!n#r" %a 6"*6a 3r#*#aG E 7 Un *n+!rs&r 3*!nsa u! %as a*&n!s #! FECSA n& +an a !3!r*6!n(ar 8ran#!s a6*&s as(a !% 6"*6& +!n*6*!n(& #! &3*&n!s< 3ara %& ua% % #*s!a una !s(ra(!8*a &ns*s(!n(! !n +!n#!r un CA,, = un PUT &n un 3r!*& #! !!r**& #! 4.000 3a8an#& una 3r*6a #! 200 = 150 3!s&s r!s3!(*+a6!n(!. S* %as %u(ua*&n!s 3&s*%!s s&n !n(r! .000 = 5.000 !n u s*(ua*?n &(!n#r" !% 6"*6& !n!**&G