INDICE
AMORTIZACIÓN............ AMORTIZACIÓN.................... ................. .................. .................. .................. .................. .......................... ......................................3 .....................3 DEFINICIÓN............. DEFINICIÓN...................... .................. .................. .................. ................. ................. .................. .................. ...................................3 ..........................3 SISTEMA DE AMORTIZACIÓN.................................................................................3 COMPOSICION DE LOS PAGOS.............................................................................3 TABLA DE AMORTIZACION......................................................................................4 CALCULO DEL SALDO ABSOLUTO........... ABSOLUTO................... ................. .................. .................. ...................................4 ..........................4 SISTEMAS DE AMORTIZACIÓN......... AMORTIZACIÓN................. ................. .................. .................. .................. ..................................4 .........................4 AMORTIZACIÓN MEDIANTE MEDIANTE ABONO ABONO CONSTANTE CONSTANTE A CAPITAL.......... CAPITAL................... ..................5 .........5 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES............... UNIFORMES........................ ................. ................. .................. ...............7 ......7 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS PACTA PACTADAS. DAS. 9 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS PUNTUALES PACTADAS................................................................................................................9 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS PERIÓDICAS PACTADAS..............................................................................................................11 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS NO PACTADAS..............................................................................................................14 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS NO PACTADAS AFECTANDO EL VALOR DE LAS CUOTAS UNIFORMES................14 AMORTIZACIÓN CON CUOTA CUOTAS S UNIFORMES Y CUOTAS CUOTAS EXTRAS NO PACTADAS AFECTANDO EL NÚMERO DE CUOTAS UNIFORMES....................17 AMORTIZACIÓN CON PERODOS PERODOS DE GRACIA.............. GRACIA...................... ........................ .............................1! .............1! AMORTIZACIÓN CON PERODOS PERODOS DE GRACIA MUERTOS................................19 MUERTOS................................19 AMORTIZACIÓN CON PERODOS PERODOS DE GRACIA CON CUOTAS CUOTAS REDUCIDAS...."" REDUCIDAS... .""
1
CONCLUSION........................................................................................................."4
AMORTIZACIÓN DEFINICIÓN L# #$%&'()#*(+, -/ 0-0- - 2,'% 0- ('# (,#,*(-&%/ - 2&%*-% 0- 2#6% 0- ,# 0-0# 0-0# (,'-&- (,'-&-- - $-0(#,'$-0(#,'- ,# -&(- 0- *%'# *%'# 82-&(+ 82-&(+0(* 0(*# # % ,%/ -, , '(-$2% 0-'-&$(,#0%. L# #$%&'()#*(+, - - 2&%*-% :- $#'# ,# 0-0#. SISTEMA DE AMORTIZACIÓN A MORTIZACIÓN C#, C#,0% 0% - #0: #0:((-&&- ,# ,# %;( %;(6# 6#*( *(+, +,// 2#6% 2#6% - 2#*' 2#*'# # *%, *%, ,# ,# -&( -&(- 0*%,0(* *%,0(*(%, (%,- - $<,($# $<,($# :- 0-'-&$( 0-'-&$(,#, ,#, - *%$2%&' *%$2%&'#$( #$(-,' -,'% % :- 0-;0-;- #$(& #$(& - 0-0%&. E ,-*-#&(% *%,%*-& *#'&% 0#'% ;=(*%. • • •
V#%& V#%& 0- # D-0# P#)% 0&#,'- - *# -'#&= (6-,'- # %;(6#*(+,. C%'% (,#,*(-&% :- 0-;- #$(& - 0-0%& -, # *#,*-#*(+, 0- # 0-0#. E'E'- *%'% *%'% (,# (,#,* ,*((-&% &% - # '## '## 0- (,'(,'-&> &> *%;&# *%;�# 0# -, # %2-&# %2-&#*( *(+, +,
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(,#,*(-&#. E 2#'&+, 0- 2#6% 0- *&>0('%. S- 0-;- -2-*((*#& # %&$# 0- 2#6% 0- # *%'#.
A 2#&'(& 0- % 0#'% #,'-&(%&- - 2-0- *%,%*-& -, *#:(-& $%$-,'% - -'#0% 0- *&>0('%? V#%& 0- # *%'# 2%& 2#6#&/ *%$2%(*(+, 0- # *%'# - #0% (,%'% 0- # 0-0#. COMPOSICION DE LOS PAGOS P%& P%& % 6-,-& -,-&# #// *#0# *#0# *%' *%'# # 0- 2#6% 2#6% :- #$%&' $%&'() ()# # ,# ,# 0-0 0-0# # '(-, '(-,- 0% 0% *%$2%,-,'-/ (,'-&> #;%,% # *#2('#. E@('-, *#% -2-*(#- -, % *#- # 2&(,*(2(% 0- 2#)% 0- *&>0('%/ # *%'# ,% *;&-, - *%'% (,#,*(-&% - #0%
2
0- *&>0('% - (,*&-$-,'#/ 2%& --$2%/ % ('-$# 0- *&>0('% 0- (,#,*(#*(+, 0((-,0#. E, -'% *#% - #0% 0- # 0-0# *&-*- -, 6#& 0- ;##&. TABLA DE AMORTIZACION A 0(-#& , 2#, 0- #$%&'()#*(+, 0- ,# 0-0# - *%,'&- # '#;# #$%&'()#*(+,/ :- &-6('&# 2-&(%0% # 2-&(%0% # %&$# *%$% # -%*(%,#,0% - 2#6% 0- # 0-0#. E'# '#;# 0-;- *%,'-,-& 5 *%$,#.
P-&(%0% 0- 2#6% V#%& 0- # *%'# 2-&(+0(*# V#%& 0- (,'-&> A;%,% # C#2('# S#0% 0- # 0-0#
P#&# *%,%*-& # *%$2%(*(+, 0- # *%'# ;#'# *%, *#*#&- % (,'-&-- # *#2('# (,%'% 0- 2-&(%0% (,$-0(#'#$-,'- #,'-&(%& &-'=&-% # #%& 0- # *%'#/ 2#&# *%,%*-& :- 2#&'- *%&&-2%,0- # # #$%&'()#*(+,.
CALCULO DEL SALDO ABSOLUTO E #0% 0- ,# 0-0# - % :- - -'= 0-;(-,0% -, *#:(-& $%$-,'%/ 0-,'&% 0- 2#)%. C%,%*-& - #0% 0- ,# 0-0# - 0- $*# ($2%&'#,*(# -, # %2-&#*(%,- (,#,*(-&#/ 2%& &#)%,- 2&-2-'#-/ 2#&# #*-& 2&%-**(%,- *%,'&% (,#,*(-&%/ #*-& #;%,% 2#&*(#- # # 0-0#/ % *%,%*-&% 2#&# *#,*-#& # 0-0# '%'#. SISTEMAS DE AMORTIZACIÓN E, - 2#6% 0- *&>0('%/ *#:(-&# :- -# ,#'&#-)#/ - 0-0%& *%$2&%$-'- # *;&(& 0% &;&%? 2&($-&%/ - *%'% (,#,*(-&% 82#6% 0- (,'-&>/ :- - 2#6% 2%& - % 0- 0(,-&% '%$#0% -, 2&>'#$% 0&#,'- - 2#)% 2#*'#0%. E -6,0%/ - # &-'('*(+, 0- *#2('# &-*(;(0% -, 2&>'#$%. D- # $'(2- %&$# :- -@('-, 2#&# &-'('*(+, 0- *#2('# &-*(;(0% -, 2&>'#$%.
3
AMORTIZACIÓN MEDIANTE ABONO CONSTANTE A CAPITAL S- *%,(6&# -'- ('-$# 0- #$%&'()#*(+, *#,0% - 2#*'# - 2#6% 0- 2&>'#$% -, *%'# (6#- 0- #$%&'()#*(+, 0- *#2('#. P#&# - *#%/ # *%'# 0- *#2('# *#*# *%$% - #%& 0- 2&>'#$% 0((0(0% 2%& - ,$-&% 0- 2-&(%0% #*%&0#0% 2#&# - 2#6%.
E (,'-&> 8 Ik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olución.
Valor del préstamo N. de pagos Periodos T. de interés
$ 10,000,000.00 10 Trimestrales 11.1!
0.02"#
P#&# -#;%&#& # '#;# 0- #$%&'()#*(+, - 0-;- (,(*(#$-,'- 0-'-&$(,#& # '## 0(,'-&> --*'(# '&($-'&# # 2#&'(& 0- # '## ,%$(,# '(()#,0% # +&$#?
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'
10 000.000 =1' 000.000 Vk = 10
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AMORTIZACIÓN CON CUOTAS UNIFORMES E, -'- ('-$# 0- #$%&'()#*(+, - 2#*'# - 2#6% 0- 2&>'#$% -, *%'# (6#- .
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olución.
Valor del préstamo N. de pagos Periodos T. de interés
$ 10,000,000.00 10 Trimestrales 11.1!
0.02"#
C=*%. P#&# -#;%&#& # '#;# 0- #$%&'()#*(+, - 0-;- (,(*(#$-,'- 0-'-&$(,#& # '## 0(,'-&> --*'(# '&($-'&# # 2#&'(& 0- # '## ,%$(,# '(()#,0% # +&$#?
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0.1116 4
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0.0279 1 +¿ ¿ ¿−10 1−¿
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AMORTIZACIÓN CON CUOTAS UNIFORMES Y CUOTAS EXTRAS PACTADAS
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Amortización con cuotas uniformes y cuotas extras puntuales pactadas E'- ('-$# #2#&'- 0- # *%'# ,(%&$- 2-&(+0(*#/ - 0-0%& - *%$2&%$-'# 2#6% 0- ,# % #&(# *%'# -@'&#%&0(,#&(# -, 0(-&-,'- 2-&(%0% 0&#,'- - '(-$2% 0- #$%&'()#*(+,. E 0-*(&/ - 2#*'# - 2#6% 0- 2&>'#$% -, *%'# (6#- /
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Valor del $ préstamo 10,000,000.00 N. de pagos 12 $ C'ota. E(tra 3,000.00 Periodos mens'ales T. de interés .!
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10
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Valor préstamo N. de pagos
del
$ 10,000,000.00 2 $
C'ota. E(tra Periodos T. de interés
%00.00 mens'ales ".1!
C=*%.
11
A,'- 0- ##& # *%'# - 0-;- 0-'-&$(,#& # '## --*'(# 0- (,'-&> :- #2(*#&# # # #,#(0#0 -@'&#%&0(,#&(#/ 2#&# -% - '(()# # %&$# (6(-,'-/ '-,(-,0% -, *-,'# # '## 0- (,'-&> --*'(# $-,#/ 2#&# % *# 1 1"" ".
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¿ ¿−24
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N+'-- :- -, % $-- / 1"/ 1! "4 - 2#6% - *%$2%,- 0- # *%'# ,(%&$:- - 2#6# -, *#0# 2-&(%0% $= # *%'# -@'&#. AMORTIZACIÓN CON CUOTAS UNIFORMES Y CUOTAS EXTRAS NO PACTADAS B#% -'- ('-$#/ 0-0%& #*&--0%& #*-&0#, # *#,*-#*(+, 0- 2&>'#$% # '&#> 0- *%'# ,(%&$- *%, # 2%(;((0#0 0- &-#()#& 2#6% -@'&#%&0(,#&(%. E, *#% 0- &-#()#&- - 2#6% -@'&# -@('-, 0% 2%(;((0#0-? #-*'#& - #%& 0- # *%'# 2-&(+0(*#/ % 0($(,-,0% - ,$-&% 0- 2#6%/ # *%,'(,#*(+, - #,#()#, #$;# ('#*(%,-?
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13
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olución) V#%& 0- 2&>'#$% N. 0- 2#6% C%'#. E@'&# N% #*%&0#0# P-&(%0% T. 0- (,'-&>
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0.1116 1 +¿ '
¿
1−¿=7 269795,703 0.1116 '
A =60
¿
000.000 ¿
1
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