ejercicios_grado_3_contabilidad_y_administraci_n.doc

MATEMÁTICA TERCERO CONTABILIDAD Y ADMINISTRACIÓN PROFESOR: RAMÓN V. QUIMÍ ESCALANTE. 2013 – 2014 A)

EPONENTES /

3   1. !" !"##$ ##$ $# %$& %$&'( '( '* '*+, +,-( -( $ $    2a − b   2     2. !" !"##$ ##$ $# $# ,,-'( '( '* '*+, +,-( -( $ $ (1 + 2 x )  3. S,+ S,+#, #,, ,$ :

4 3n

 $%:

2n

3

 2m + 3 ⋅ 4m + 2n    m − 2 2 n + 4      / ⋅ 4   4. C"#5#$:

    2  6  2  32 32  3 3                    

2

 7

( −  x ) 3

− 2 −2 −2 2 − 2( 2) 2

0

3

2

( − /) − 3 1

−2

 1  

   − ( − 3)  3   2a −1

1

−2

 x

2

+ a0

( − 3a ) ⋅ 3a 3

−2

a b

2

c2 3n +

3

 a b b   ÷  ÷ − 4 − 2       c a b  

2

2 3

1



  − 1   ( x )   x 3         −3 8 1 3   2     − 2     x          x          

− 3n +1

1   6 3 2    2   3     x 3   x       1        x 4             

7

+ y −1

1

− 2 −3

3( 3n −1 )  x −1

−

−

( 2a ) ⋅ a 3

4

 x −1

2

 1  −3  2  −2   4  −1     +    +      8    11     3  

a −2 2a + a 2 .

2

1

⋅ x ( x ) 2  . −2

 x −2

−  y −2  x −1 +  y −1

2

8. R$%$#9" #9": / x + 2

B)

− / x = 126 7

4n − 4n −1 = 24 7 / x − / x −1 − 14 = 0

 x + 4

3

= 2:2 x −1

RADICALES

6. S,+ S,+#, #,, ,$: 8

/1a b

6

− a 6b 8

1

4

⋅8

a 3b 8 20

300

33 16

1

a b

+

1010 a 11

ab 2

20

+ 23

−3

− 43

84

+2

48

10/ + 2 /0

/1 − 23 24

2 1/0 + 2 40 − 3 800 + 4 8000 3

4

+2

18 a

b

+

b

43 8

a

8

3

−

3

−b

1

3

7

88 a 4

13

8

+

ab

60

1

+

+3

18

3+

6

3−

6

−3 3 +3

2 3

2

2

2

2 3 +: 2

a 2b 2

b

+1 2 −1

2

8 3−4 2

− 23 138 + 36 1600 − 183

1 28

+ 1/ −

:2

80 /

b

43

2 x 3 y 2

+  x 3 3

1/  x 2 y 2

−23  y

 x + 1 +

xy 12

/

 x +  x 2

+ 1  x − +  x −  x 2 − 1  x +

−1  7  x 2 + 1

+

 x 2

x −1

+ 200 32 − / 80

: 480

−4

+3 2 − /0

320

20

/0

−8

/00

8

. R$%$#9":  x − 4 = 4 3

6 x − 3 1

8x + 2

+

1 +  x

−

 x

+

4

=8

 x

C)

=3

 x

 x

+

1+ x

=4

N;MEROS COMPLE
/. E-5$-'*$ #(% 9"#(*$% $  x =  y $- #" $5"5,>-: ?& @ 3)  ,?= – 1)  2, . S,+#,,$: ?4  2,)  ?3 – 2,)  ?/ – 3,

 4 − 3 i  −  1 i  − ( − 2i ) +  − 1 + 2i              8    4     2   ( 4 + i )( 4 − i )( 8 + 6i )

6 + 3i 2+i 1/ + i 2 + 3i

7 7

2

3 + 2i 2−i

1+ i

−

1− i

7

6   C +isen48C ) ] [ 3( 5(% 48

2−i

4( 5(% :8C +isen:8C )

7

2 + 2i

2( 5(% 48C +isen48C )

( 2 − 3i ) 3

i

( 3 + 4i ) 4

(1 + i )21 (1 + i ) 28 (1 + i )2

2

 4 + 2i        2 + i  

1+ i

(1 − i ) 4 + ( 3 + i )

(1 + i ) 1− i

(1 + i )





+

−i i −1

1:

1− i

1+ i

+

(1 + i )

1+

1− i

1:

10. !"##$ #" (*+" '*,(-(+'*,5" $# -+$*( 5(+#$( 11. !"##$ $# +>#( $ 2 (1 + i )( 2 + i )( 3 + i ) + 24 + 3i

3

+

1+ i

2

i

1+ 1:

28

i

1+



13

13

+

21

i 1+ i

+i

D) ECUACIONES EPONENCIALES Y LOGARÍTMICAS 12. R$%$#9": 2 x

 x +1

4

1   =       2  

 x +1

2

=4

 x 2 − x

8

 x

x−2

 x 2 − 2 x

2

1

2

=

4 x

 x

4

−3

2

= ( 64)

 x 2 3

2 x

#(D   x

= 16

−

− 3x1 3 = −2

=−

#(D x / =

1

2 x −1

3

2

3 − x 1

− 2 x +1 − / = 0

x 1

− / x = 126

4n

− 4n −1 = 24

/ x

− / x −1 − 14 = 0

3

2 x

13. !"##$ $# 9"#(* $ & $-: #(D 2 4 x

+ 2 x+1 = /0

/ x + 2

( x 2 +  x + 4 )3 4 = /

= 2:

3

4 x

2

= 64

2

= 2: 2 x−4

 x 2 + 2 x

= 28

 x 2 − x

+2

+ 3 x +1 = 4

3 3 x +1

3

2

= 64

= 82 x+1

#(D / 2 + #(D / 4

=  x

=2

14. R$%$#9" #"% $5"5,(-$%: #(D? x 2

− 3x) = 1

#(D 3 ( x + 2) + #(D 3 ( 2 x + : )

#(D( x

− 3x ) = 1

#(D? x

2

#(D 2 ? x + 1) + #(D 2 ? x − 1) #(D( 2 x − 1)

− #(D( x ) = 2

=3

2

− 1) − #(D? x + 1) = 2

#(D( x − 2)

#(D  x

=

=3

1 2

+ #(D( x + 2) = #(D( 30x) − 1 #(D 16 −

1 3

#(D / + 1

3

#(D?8 x − 6) #(D x

E)

( #(D x 3) #(D 3 + #(D 3 = 0

=2

 x 3

MATRICES Y DETERMINANTES

18. !"##$ $#$ 9"#(* $ u = v $-:  3 u     3 3v − :          =  4    v 4    u − 1  

 2   :

  1 − 42  16. D$+$%'*$ $ A   6 x 20 0 1   +"'*,H %,+'*,5". 1. D$+$%'*$ $ A  b   c − 12 −  3  2 b − 18 a + b − 16   3a − 12 16   

 y

− 3 x     1   $% -" 30    

    c − 2/   $% "-',%,+'*,5". 0       a − 16  

 1 x − :  1/. D$+$%'*$ $ A   3  2  y + /  8

  :   $% -" 4 w + /     :   1

 z  − 6  

+"'*,H -#".

  n  1. D$+$%'*$ $: A   31 + m   p +    $% -" +"'*,H %,+'*,5"

 m − 13  20. D$+$%'*$ $ A   n − 6  6−n  

11 − m

1: −  p  

m

2: + n  

13 − n

 p + 4

18 − m 2n − 12

$% -" +"'*,H ,$-',". 21. R$%$#9" :

  3   − 6

 :

2

−1

4

0

1

  2 − 3

F)

x /1

 1      2   4       3     0    2      

  1   0 8     − 2   4  

6  

  4   3    

  2 − : − 1  18    a            − 1 − 1 2   4   =  b    − 1 8 − 1  /    c              IDENTIDADES TRIGONOMTRICAS

 

 p

   

    0     m − 1  :   0

3 4

 1 − 1     4 −      :  

 − 2 − 3        8  +  − 8 − 4   7    /      − : − /   2  

 − 1    2  − 6  3  8       4

  4   A = : 8 − 3  

1  

0  

2  

 1    1  − 3 0  :      1

  0    

1  

0    − 3 2    0 1    a  2 1 0 − 1  4        =   3 − 4 2 8   1 − 3 − 1    d   3 8 − 2       22. !"##$ $# $'$*+,-"-'$ $ #" +"'*,H: − 3     :       − 12 6  

 1  1 6  

2

3  

0

0  

b e

c  

 

  f     

 

8    

:

 4 − 3 2      23. L" $'$*+,-"-'$ $  8 m − :   $% 1/. !"##$  4 − 1 4       $# 9"#(* $ m  $%:  11 24. D$ #" ($*"5,>-    8

14 12

  6      :    16

13  

    4   $% 10     /

"#%( $: ? ) L" +"'*,H *$%#'"-'$ $% $ (*$- 2 ? ) L" $'$*+,-"-'$ $% @8300 ? ) L" %+" $ #(% $#$+$-'(% $ #" +"'*,H *$%#'"-'$ $% 10/2 ? ) T("% #"% "-'$*,(*$% %(- 9$*"$*"% ? ) N. A. 28. C"#5#$

  3   0  −1   − 2

$#

$'$*+,-"-'$

4

−:

4

0

2

2

1

0

$

#"

+"'*,H

    0   7 $%: − 3     − 2     /

4

DEMUESTRA LAS SIGUIENTES IDENTIDADES: 26. ( senx − 5(% x ) 2 + ( senx + 5(% x ) 2 = 2 2. %$5 x −  senx '"- x = 5(% x 2/. (1 − 5(% 2  x )(1 + 5(' 2 x ) = 1 2. ( 5%5 x − 1)( 5%5 x + 1) = 5(' 2 x

3/. 3. 40.

%$5 θ  + 1

= 1 + 5(% θ  %$5 θ  − 1 1 − 5(% θ 

1 − 5(' 2 θ  1 + 5('

2

=  sen 2θ  − 5(% 2 θ 

θ 

30. %$52  x + 5%52  x = %$52  x 5%52 x 31. ( '"-  x + 5('  x ) 2 = %$5 2  x 5%5 2 x 32. %$5  x + '"-  x = 33. 34. 38.

5(% x 1 + 5(% x

=

5(% x 1 −  senx

 senx + '"-  x

 sen 2 x + 2 5(% 2  x  senx. 5(% x

'"-  x + 5('  x %$5 x

G)

 senx 5(% x

42.

 senx

= '"-  x + 2 5(' x

= 5%5 x

2 36. ( 5%5 x + 5('  x ) =

3.

41.

1 + 5(% x 1 − 5(% x

+ 5(% x = 5%5 x. %$5 x

43. 44.

5%5 2 α  − 1 %$5

2

α 

−1

1 1 +  senα  %$5 β  + 1 '"- β 

= 5(' 4 α 

+

=

5('  y 5%5  y

1 1 − senα 

= 2 %$5 2 α 

'"- β  %$5 β  − 1 1

=

%$5  y − 5(%  y

48. 5%5 4 θ  − 5(' 4 θ  = 5%5 2 θ  + 5(' 2 θ  46. '"- 3  x +  senx %$5 x −  senx 5(% x %$5 x − 5(% x

= '"-  x %$5 x +  senx

 senx

ECUACIONES TRIGONOMTRICAS

RESUELVE Y ENCUENTRA TODAS LAS SOLUCIONES DESDE 0 !ASTA 2π   . 4. 2 '"- x + 3 = 0 4/. 4 senx − 1 = 0

84. 2 5(% 2  x + 3 5(% x = −1

4.

88. 5(%2  x + 2 5(% x = 3

80.

2 senx +

3

=0

3 '"-  x + 1 = 0

81. 4 sen  x − 1 = 0 2

86. 2 sen 2 x − sen = 3 8. 2 sen 2 x + :  senx = 4 8/. 2 sen 2 x − 8  senx + 2 = 0

82. 2 5(% 2  x = 1

8. 2 sen 2 x + senx = 0

83. 2 sen 2 x +  senx = 1

60. 6 5(%2  x + 8 5(% x + 1 = 0

8

64. 2 5(% x '"-  x − 1 = 0 61. 4 5(%  x = 3 − 4 5(% x 2

62. 2 5(% x = 5(' x

68. 3 5(% 2  x + sen 2 x = 3

63.

66. 5(% 2  x =

5%5  x

=

%$5 x

3   ?1 − senx) 2

!) RECTA 6. C"#5#$: L" ,%'"-5," $# -'( P?@87@6) "# $$ = E# J*$" = #(% J-#(% ,-'$*-(% $# '*,J-#( $ ',$-$ 5(+( 9*',5$ #(% -'(% A?@273)7 B?671) = C?@278) E# -'( P $ (*$-"" 10 $ $%'J %(K*$ #" *$5'" 5=" $-,$-'$ $% 3 = $ "%" (* $# -'( A?7@2) ( − 673)  =  B ( 47: )

L" $5"5,>- $ #" *$5'" $ "%" (* #(% -'(%

 A

L" $5"5,>- $ #" *$5'" $ "%" (* $# -'(

( − 67 −3)  = ',$-$ 5(+( $-,$-'$ −

L" $5"5,>- $ #" *$5'" 5=" $-,$-'$

%$: 

 A

1 4

 = ',$-$ 5(+( (*$-"" "# (*,$- @8

L" $5"5,>- $ #" *$5'" 5="% ,-'$*%$55,(-$% 5(- #(% $$% $ #" & $ = %(- @ = 117 *$%$5',9"+$-'$ L" $5"5,>- $-$*"# $ #" *$5'" $ "%" (* $# -'( ?@27@3)  x + y − 1 = 0 I)

= $% "*"#$#" " #" *$5'" "" (* 

PORCENTA
 U- '*"$ +"*5"K"  180 "-'$% $ #"% *$K""%. E- #" (5" $ *$K""% $# +,%+( '*"$ 5(%'"K"  120. ") Q *$K"" -(% ,5,$*(- ?$- )  K) S, -(% *$K""%$- $# 18 5J-'( -(% 5(%'"*" 5) S, #(%  120 %(- %,- IVA = $# IVA $% $# 12 5J-'( -(% 5(%'"*J $# '*"$. S(#: ") 20 K) 1278 5) 13474 E# *$5,( $ 9"*,(% "*'5#(% %,- IVA $% $  28 =  176. A9$*," 5J# $% $# *$5,( ,-"# %"K,$-( $ 5(- $# IVA %K$- - 16. S(#:  2  20742. S, "# 5"K( $ 9"*,(% "(% $# *$5,( $ -" +$*5"-5" %$ " +#',#,5"( (* 2723. CJ# " %,( $# "+$-'( $&*$%"( $- . S(#: 123. U- 9$-$(* *$5,K$ - 6 $ #(% K$-$,5,(% $ 5"" 9$-'" $ *$"#,H". V$-$ - ,%( (*  /0.000. S, #$ "-> - 10. Q 5"-'," 5(**$%(-$ "# 9$-$(*. S(#:  4/0. U- 5"+$%,-( (%$$ 110 $5'J*$"% $ +(-'$ = $5,$ #"-'"* - 20 5(- ,-(%7 - 28 $ "K$'(%7 - 38 $ *(K#$ = $# *$%'( $ 5"%'"(%7 '$-,$-( $- 5$-'" $ - 8 #( '9( $ $,5"*  6

" 5"+,-(%. Q %$*,5,$ #"-'> $ 5"" ',( $ J*K(#$% Q (*5$-'"$ #"-'> $ 5"%'"(%. S(#: ") 22 !" $ ,-(%7 278 !" $ "K$'(%7 3/78 !" $ *(K#$ = 1678 !" $ 5"%'"(%. K) E# 18 E- - 5(#$,( $ 1.800 "#+-(% $# 40 %(- 5,5"% = $# *$%'( 5,5(%. Q (*5$-'"$ $ 5,5(% "= CJ-'"% 5,5"% "= Y 5,5(%. S(#: 60 600 5,5"%7 00 5,5(%. E# 20 $ #(% "#+-(% $ 1 $ BAC ,5,$*(- +"# - $&"+$-. S, $# *( $%'J (*+"( (* 48 "#+-(%. CJ-'(% 5(-'$%'"*(- 5(**$5'"+$-'$. S(#: 36. A# 5(+*"* -" K,5,5#$'" $ 5(%'"K"  80 +$ "5$- - $%5$-'( $# /. CJ-'( ,-$*( +$ *$K""*(- CJ-'( '$-( $ ""*. S(#: R$K""-  4  P""*  46. U- 5(+$*5,"-'$ 5(+*" -" K,5,5#$'" $-  40 = #" 9$-$ $- 60. Q '"-'( (* 5,$-'( %$ "->. S(#: 80 E- -" 5#"%$ $ 80 "#+-(% "= 30 5,5"% = 20 5,5(%7 $ #(% 80 "#+-(% - 10 %(*$$',(*$% = $ $%'(% $# 20 %(- 5,5"%. ") Q (*5$-'"$ *$*$%$-'"- #(% 5,5(% $-'*( $ #" 5#"%$ Y #"% 5,5"%  K) CJ-'(% 5,5(% *$,'$- 5*%( 5) S, "= 8 5,5"% *K,"%  (*5$-'"$ *$*$%$-'"- $-'*( $ #"% 5,5"% Y $-'*( $ #" 5#"%$ S(#: ") 407 60 K) 4 5) 16767 10

 ) INTERS SIMPLE 6. R$%$#9$: D$'$*+,-" $# 5",'"# ,-"# $,9"#$-'$ "  6000.000 +$,"-'$ 5",'"#,H"5,>- %,+#$ $-'*( $ (% "(% = +$,( %"K,$-( $ $# ',( $ ,-'$*% %,+#$ "-"# $% $# 8. Solución: $ 6.750 000. C"#5#" $# 5",'"# $ ,+$%'( "# 3 $ ,-'$*% %,+#$ "-"# %$ " 5(-9$*',( $- 4 +$%$% $-  1.000. Solución: $ 990. CJ#$% %(- #(% ,-'$*$%$% *(5,(% (* - 5",'"# $  3000 *$%'"( " - ,-'$*% %,+#$ "-"# $# 278  *"-'$ (% '*,+$%'*$% ? 1 "( ',$-$ 4 '*,+$%'*$%) Solución: $ 37,5. U- 5(+$*5,"-'$ $ $K$*J $-'*$"* $-'*( $ 3 "(% -" 5"-'," $  4207 ,$*$ %"K$* $  5",'"# " $ ,%(-$* (= %, $%$*" $# +,%+( - *$-,+,$-'( $# 4728 "-"# " ,-'$*% %,+#$. Solución: 68665,18. C"#5#" #(% ,-'$*$%$% *$%#'"-'$% $ -" ($*"5,>- $- #" $ " "*',* $ - 5",'"# $ 12/30 %$ (K',$-$ 5",'"# ,-"# $,9"#$-'$ " - 128  $# 5",'"# ,-,5,"#. Solución: $ 31957,5 CJ-'( ',$+( '"*"*J - 5",'"# C ,-9$*',( "# 10 $ ,-'$*% %,+#$ "-"# $- *(5,* - 5",'"# ,-"# ,"# "# (K#$ $# +,%+( Solución: n = 10 año. CJ# $ $# ',( $ ,-'$*% %,+#$ "-"# $ $*+,',> $ (* - 5",'"# $ 22444078 %$ (K'9,$*"648 $ ,-'$*$%$% $-  "(% Solución: !,1"# i%l& anual Q ',$+( $%'9( ,-9$*',( - 5",'"# $ 22.000 UF "# 2 $ ,-'$*% %,+#$ "-"#7 %, #(% ,-'$*$%$% $*($  4400 Solución: 10 año CJ# %$*J $# 5",'"# ,-"# *$%#'"-'$ $ #" ,-9$*%,>- $ - 5",'"# $  1216 "# 6 $ ,-'$*% %,+#$ "-"# *"-'$: ") 4 5"'*,+$%'*$% K) 1 +$%$% 5) 120 "% ?"( (*,-"*,( = "( K"-5"*,() Solución: a' 76913 (' 77"769 c' 7"6"0 )año o*+ina*io' 7".6!0 )año (anca*io'



Q ,-'$*$%$% $-$*"*J - 5",'"# $ 12000 US " - 6728 %,+#$ "-"# *"-'$ 42 "% ?"( K"-5"*,( = "( (*,-"*,() Solución: 87,50 S$ )año (anca*io' 86,30 S$ )año o*+ina*io' Q ',( $ ,-'$*% $% $# $ ,H( $ - 5",'"# $  8243 ,-9$*',( *"-'$ 3 "% $-$*"%$ -" ,$*$-5," $-'*$ #(% ,-'$*$%$% 5"#5#"(% K"-5"*,( = (*,-"*,( $ 1/4 Solución: 8,8# )-ilia -o+o lo +&cial& %a*a &l c/lculo' A  ',( $ ,-'$*% %$ *$%'> - 5",'"# $  2280 %, " *(5,( -(% ,-'$*$%$% +$,"-'$7 5",'"#,H"5,>%,+#$ $  18 $- 8 "% U',#,H"* "( K"-5"*,(. Solución: i = 3," # anual. C"#5#" #(% ,-'$*$%$% *(5,(% (* - 5",'"# $ US 8000 $- 0 "% " - ',( $ ,-'$*% %,+#$ $# 10 "-"# ',#,H"-(7 $# "( K"-5"*,(. Solución: $ 1"5. CJ-'( ',$+( '"*"*" - 5",'"# 5(#(5"( "# / $ ,-'$*% %,+#$ "-"# $- '*"-%(*+"*%$ $- $# '*,#$ $# +,%+( Solución: n = "5 año. T$-( -(% "(**(% 5(#(5"(% $ #" %,,$-'$ +"-$*":   20000 "# 2 $ ,-'$*% %,+#$ '*,+$%'*"#   30000 "# 1 $ ,-'$*% %,+#$ +$-%"#   8000 "# 478 $ ,-'$*% %,+#$ %$+$%'*"# ¿Cuál es el capital fnal si mis ahorros están colocados durante un año y medio? Solución: $ 62.575.

) INTERS COMPUESTO 0. R$%$#9$:

D$'$*+,-"* #(% ,-'$*$%$% = $# 5",'"# ,-"# *(5,( (*  80000 "# 18 $ ,-'$*% 5(+$%'( "-"#7 *"-'$ 1 "(. Solución: C.F 8800. I-'$*$%$%: .800. D$'$*+,-"* #(% ,-'$*$%$% $-$*"(% (* - 5",'"# $  300007 *"-'$ 8 +$%$%7 "# 18 $ ,-'$*% "-"#. Solución: 16. T$-$+(% -" (K#,"5,>- (*  120007 " %$* #,,"( $-'*( $ 10 "(%. CJ-'( ,-9$*',*$+(% (= "#  "-"#7 5(- $# (K$'( $ ($* 5+#,* 5(- $# "( $ #" $" Solución: 80673 . U-" $+*$%" $- *(5$%( $ #,,"5,>-7 ',$-$ $- "5',9(% (K#,"5,(-$% " 4 "(% (*  420007 $9$-"- $# 12 5",'"#,H"-( "-"#+$-'$. C"#5#"* $# 9"#(* "5'"# "# 187 5(- 5",'"#,H"5,>"-"#. Solución: 3/872. U-" $+*$%" $(%,'"  00000.@ " -" '"%" $ ,-'$*% 5(+$%'( "-"# $# 247 5",'"#,H"K#$ +$-%"#+$-'$7 5J# %$*J $# +(-'( "5+#"( $- 4 "(% Solución:  1/104. U%'$ $(%,'"  1200000.@ "# B"-5( *"-'$ 260 "% " -" '"%" $ ,-'$*% 5(+$%'( "-"# $# 7 5",'"#,H"K#$ +$-%"#+$-'$7 CJ-'( ,-$*( *$',*"*" "# '*+,-( $ #(% 260 "% Solución:  126162. D$'$*+,-$ #" '"%" $ ,-'$*% "-"#7 " #" $ $K$- ,-9$*',*%$ 3230000.@ "*" $ $-  "(% %$ (K'$-" - 5",'"# ,-"# $  4234/0.@ Solución: 374. D$'$*+,-$ $# +(-'( = #(% ,-'$*$%$% (K'$-,(% "# ,-9$*',*  860000.@ "# 8 $ ,-'$*% "-"#7 *"-'$ / "(% $- *,+$- $ 5",'"#,H"5,>- 5(+$%'". Solución: C.F /238. I-'$*$%$%: 2638. /

U- 5",'"# $  18007 5(#(5"( "# 6 $ ,-'$*% 5(+$%'( "-"#7 "%5,$-$ "  284000.@ D$'$*+,-$ $# ',$+( $ $%'9( ,+$%'( Solución: 6,35 año U- 5",'"# $  12000007 5(#(5"( "# 12 $ ,-'$*% 5(+$%'( "-"#7 "%5,$-$ "  1880000.@ D$'$*+,-$ $# ',$+( $ $%'9( ,+$%'( Solución: ","5 año #) ANUALIDADES VENCIDAS 1. R$%$#9$:

!"##"* $# +(-'( $ -" %$*,$ $ 5"'*( "(% $ S. 86000 "# ,-"# $ 5"" "(7 5(#(5"( "# 20 $ ,-'$*% 5(+$%'( 5(- 5",'"#,H"5,>- "-"#. R'": S. 30060/ CJ# %$*J $# 5",'"# "5+#"( "# 5"K( $ 10 "(%7 +$,"-'$ "(% "# ,-"# $ 5"" %$+$%'*$ $ S. 23800 " #" '"%" $ ,-'$*% 5(+$%'( $# 18 "-"# 5(- 5",'"#,H"5,>- %$+$%'*"# R'": S. 101660 U-" $*%(-" $%$*" *$5,K,*7 (*,-"*,"+$-'$7 *"-'$ #(% *>&,+(% / "(% #" 5"-'," $ S. 12000 -$9(% %(#$% "-"#$%7 (* 5(-5$'( $ ,9,$-(% $ -" $+*$%" #$ "$" $*( -$%'*(  $*%(-"$ $%$" -$(5,"* "5'"#+$-'$ ,5" *$-'" "# 1/ "-"# $ ,-'$*% 5(+$%'(. D$'$*+,-"* " 5J-'( "%5,$-$ #" 5"-'," " *$5,K,*. R'": S. 4/307 C"#5#"* $# 9"#(* *$%$-'$ $ -" %$*,$ $ "(% $ S. /000 5"" -(7 $$5'"(% (*,-"*,"+$-'$ = $- (*+" %$+$%'*"# *"-'$ 8 "(% = 6 +$%$% "# 13  "-"# 5(- 5",'"#,H"5,>- %$+$%'*"#. S$ $%$" %"K$* $# 9"#(* $ #" 5('"7 "*" "5+#"* S. 2000 $- (5( $-'*$"% (*,-"*,"% "-"#$%7 5",'"#,H"K#$ "-"#+$-'$ "# 28 $ ,-'$*% "-"#. R'": S.136076 S$ $%$" %"K$* 5J# %$*J $# 9"#(* $ #" 5('" (*,-"*," %$+$%'*"# "*" "5+#"* #" 5"-'," $ S. 101660 $- - $*(( $ 10 "(%7 " -" '"%" $ ,-'$*% 5(+$%'( $# 18 "-"# 5(5",'"#,H"5,>- %$+$%'*"#. R'": S. 23800 S(-"+(% $ %'$7 (K',$-$ - *%'"+( $ S. 10000 "# 16 $ ,-'$*% 5(+$%'( "-"# "*" %$* $9$#'( $- 10 "(% "# ,-"# $ 5"" "(. CJ-'( $K$*J "K(-"* $- 5"" "( R'": S. 206 CJ-'(% "(% %$+$%'*"#$% $ S. 600 $K$*J- "5$*%$ "*" 5"-5$#"* -" $" $ S.4800 "#  "-"# 5(- 5",'"#,H"5,>- %$+$%'*"# R'": 474288 "(% $,9"#$-'$ " /7/83 $*((% %$+$%'*"#$%. U-" $*%(-" $%$" %"K$* " 5J-'( "%5$-$*J $# +(-'( $ %% $>%,'(% $ 5"" ,- $ "( $ S. 1400 "-"#$% *"-'$ 8 "(%7 "# 1/ "-"# 5(- 5",'"#,H"5,>- K,+$%'*"#. R'": S. 6660878/ CJ-'( $K$*J $(%,'"*%$ '*,+$%'*"#+$-'$ $- -" 5$-'" $ "(**(%7 $ "" $# 16 5(-9$*',K#$ '*,+$%'*"#+$-'$7 *"-'$ 3 "(% "*" 5(+*"* - "'(+>9,# $ 5$%'" US /000 "# ',( $ 5"+K,( $ S. 27/8. C"#5#"* $# 9"#(* *$%$-'$ $ -" %$*,$ $ $>%,'(% $ S.800700 -$9(% %(#$% +$-%"#$%7 *"-'$ 3 "(%7 " #" '"%" $# 2 +$-%"#. U- *%'"+( $ S. 8000 $K$ 5"-5$#"*%$ $- - #"H( $ - "(7 5(- 5('"% (*,-"*,"% +$-%"#$% "# 36 "-"# 5",'"#,H"K#$ +$-%"#+$-'$. C"#5#"* $# 9"#(* $ 5"" 5('". CJ-'"% 5('"% (*,-"*,"% $ S. 1680 %$*J- -$5$%"*,"% "*" 5"-5$#"* - *%'"+( $ S. /8007 "# 24 "-"# 5(- 5",'"#,H"5,>- +$-%"#. 

U- 5(+$*5,"-'$ $%% $ 20 "(% $%% $ "K$* $(%,'"( $- - K"-5( #" 5"-'," $ S. 1000 "# ,-"# $ 5"" "(7 $%$" *$',*"* '('"#+$-'$ % ,-$*( "*" ,-9$*',*#( $- - -$(5,( %, $#  K"-5( "" $# 22 "-"# 5",'"#,H"K#$ '*,+$%'*"#+$-'$. A 5J-'( "%5$-$*J $# +(-'( " *$5,K,* +) ANUALIDADES ANTICIPADAS 2. R$%$#9$:

U-" 5(+"" $(%,'" " *,-5,,( $ 5"" "( S. 20000 $- -" 5$-'" $ "(**(% $ "" $# 12 $ ,-'$*% 5(+$%'( "-"#. A 5J-'( "%5$-$*J #(% $>%,'(% "# 5"K( $ 8 "(% R'": S. 1423037/ CJ# %$*J $# +(-'( $ -" %$*,$ $ -,(*+$ $ "(% $ S. 2000 "# ,-,5,( $ 5"" %$+$%'*$ *"-'$ 3 "(% "# 16 "-"# 5(- 5",'"#,H"5,>- %$+$%'*"# R'": S. 18/48760 U-" $+*$%" $%$*"7 "#,#" - $,,5,( "*" $# -5,(-"+,$-'( $ %% (,5,-"% "+,-,%'*"',9"%  (* S. 4000 -$9(% %(#$% +$-%"#$% = *((-$ "# *(,$'"*,( ""* $# "#,#$* $- (*+" "-"# =  (* "$#"-'"(7 %, #" '"%" $ ,-'$*% 5(+$%'( $% $# 12 "-"# 5(- 5",'"#,H"5,>- +$-%"#. CJ-'( ""*J #" $+*$%" "-"#+$-'$ R'": S. 4840781 !"##"* $# 9"#(* $ #" 5('" "-',5,"" $ -(% $*+,'" "5+#"* S. 2000 $- / $-'*$"% "-"#$%7 ,+$%'"% "# 28 $ ,-'$*% 5(+$%'( "-"#. R'": S. 10//761 S$ $%$" %"K$* 5J# %$*J $# 9"#(* $ #" 5('" "-',5,"" %$+$%'*"#7 "*" "5+#"* #" 5"-'," $ S. 101660 $- - $*(( $ 10 "(% " -" '"%" $ ,-'$*% 5(+$%'( $# 18 "-"# 5(5",'"#,H"5,>- %$+$%'*"#. R'": S. 21/60746 S(-"+(% $ %'$7 (K',$-$ - *%'"+( $ S. 10000 "# 16  $ ,-'$*% 5(+$%'( "-"# "*" %$* $9$#'( $- 10 "(% "# *,-5,,( $ 5"" "(. CJ-'( $K$*J "K(-"* $- 5"" "( R'": S. 1/3763 U-" $+*$%" (K',$-$ - *%'"+( $ S. /80000 = $%$" %"K$* $# 9"#(* $ #" 5('" "-',5,"" '*,+$%'*"# $ #$ $*+,'" #,,"* ,5( *%'"+( $- 8 "(%7 %, #" '"%" $ ,-'$*% $% $# 22 "-"# 5(- 5",'"#,H"5,>- '*,+$%'*"#. R'": S. 641736 U-" $*%(-" $(%,'" $- -" 5$-'" $ "(**(% US 180 "# *,-5,,( $ 5"" +$%. S, #" 5$-'" #$  "" - 3 +$-%"# $ ,-'$*%. CJ-'( "K*J "(**"( *"-'$ $# *,+$* "( C"-'( '$-*J $ $(%,'"* +$-%"#+$-'$ *"-'$ - "( $+$H"-( (= "*" -'"* S. 300 %, %$ 5(-%,$*" -" '"H" ,-'$*% $ 3 5",'"#,H"K#$ +$-%"#+$-'$. S$ (K'9( - +(-'( $ US 30./0 $- "(% +$-%"#$% $ US 80700 *"-'$ - "( Q '"%" $ ,-'$*% %$ "#,5> -) AMORTIWACIÓN 3. R$%$#9$:

U-" $" $  6800.00 %$ $K$ "+(*',H"* $- - "( 5(- "(% +$-%"#$% ,"#$% 5(- $# 24 %(K*$ %"#(% ,-%(#'(%. !"##"* $# 9"#(* $ 5"" "( = "5$* #" '"K#" $ "+(*',H"5,>-. U-" $" $  30000.00 5(- ,-'$*$%$% "# 2/ 5",'"#,H"K#$ '*,+$%'*"#+$-'$7 $K$ %$* "+(*',H"" 5(- "(% $  421.33 (* '*,+$%'*$ 9$-5,(. !"5$* #" '"K#" $ "+(*',H"5,>-. 10

U- "'(+>9,# 5=( *$5,( $ 5(-'"( $% $  4830.00 %$ 9$-$ 5(- - $-"-5$ $# 10 $#  *$5,( $ 5(-'"( = $# %"#( $- "(% ,-5$-"#$% " 3 +$%$% $ #"H(7 5(- - ,-'$*% $# 33.64/ 5",'"#,H"K#$ 5"" ,-5$-". E#"K(*"* #" '"K#" $ "+(*',H"5,>-. U-" $*%(-" %(#,5,'" - *%'"+( $  /8000.00 "*" %$* "+(*',H"( $- "(% +$-%"#$% *"-'$ 2 "(% 5(- ,-'$*$%$% $# 2.8 +$-%"# 5",'"#,H"K#$ 5"" +$%. !"##"* #" ,%'*,K5,>- $# "( -+$*( 12 "% 5(+( $# %"#( ,-%(#'( $%% $ "K$* $$5'"( ,5( "(. G#(*," 5(+*> -" 5(+'"(*" " 5*,'( #" 5"# '$-" - *$5,( $ 5(-'"( $  340.00. L" 5(+*" $ %,- $-"-5$ = " - #"H( $ 1/ +$%$% "*" ""*7 5(- -" '"%" $ ,-'$*% $# 34.0/ 5(+$%'( +$-%"#+$-'$. D$'$*+,-$ #" 5"-'," $ G#(*," $K$*J ""* %, "# 5"K( $ 10 +$%$% $%$" #,,"* $# '('"# $ #" $". S$ 5(+*> - "'(+>9,# -$9( 5=( 9"#(* $% $  3000.007 " - #"H( $ 20 "(% '*,+$%'*"#$%7 %,- $-"-5$ = 5(- -" '"%" $ ,-'$*% $# 26 5",'"#,H"K#$ 5"" '*,+$%'*$. C"#5#"* #" 5"-'," "+(*',H"" = $# %"#( ,-%(#'( $%% $ '*"-%5**,(% 3 "(%. E# %$(* R,9$*" 5(+*> - $"*'"+$-'( " 10 "(% 5(- "(% +$-%"#$% $  3112.10. S, #" '"%" $ ,-'$*% $% $# 2/ 5",'"#,H"K#$ 5"" +$%7 5"#5#$ #" 5"-'," $ "= $ ""* "*" %"#"* #" $" "# 5"K( $  "(%. Q 5"-'," $ ,-'$*$%$% %$ "- ""( $- $%'(%  "(% U- *%'"+( (*  80000.00 %$ "+(*',H"*J +$,"-'$ 8 "(% 5"'*,+$%'*"#$% ,"#$% = -'( 5(- $# ,-'( "( %$ $-'*$"*J  18000.00. S, #" '"%" $ ,-'$*% $% $# 32.04 5",'"#,H"K#$ 5"" 4 +$%$%7 $-5(-'*"* $# "( 5"'*,+$%'*"# = $#"K(*"* #" '"K#" $ "+(*',H"5,>-. U-" "*$" $ *$5,- 5"%"(% 5(+*" - $"*'"+$-'( $  8000.00 ""-(  18000.00 $ $-"-5$ = (* $# %"#( ",$*$- - 5*,'( ,('$5"*,( " 12 "(% 5(- -" '"%" $ ,-'$*% $# 2 5",'"#,H"K#$ 5"" +$%. ") C"#5#$ $# "( +$-%"#.  K) Q 5"-'," $# "( -+$*( 2 %$ $%',-" " ,-'$*$%$% =  5"-'," %$ "#,5" " *$5,* #" $" 5) Q 5"-'," %$ $K$ ,-+$,"'"+$-'$ $%% $ $$5'"( $# "( -+$*( 2 C(- *$%$5'( "# $$*5,5,( "-'$*,(*7 %>-"%$ $ " #(% (5(% "% $ $$5'"( $# "( -+$*( 88 #" '"%" $ ,-'$*% K"" "# 227 5",'"#,H"K#$ 5"" +$%. CJ# %$*J $# 9"#(* $# -$9( "( +$-%"# E# %$(* S"#,-"% 5(+*" " 5*,'( - "'(+>9,# $ 9"#$  837000.00. L"% 5(-,5,(-$% $ "( %(- #"% %,,$-'$%:  / $ $-"-5$  6 "(% +$-%"#$% ,"#$%   107000.00 $ %$ $-'*$"*J- -'( 5(- $# #',+( "( S, #" '"%" $ ,-'$*% $% $# 32 5",'"#,H"K#$ +$-%"#+$-'$: ") C"#5#$%$ $# 9"#(* $# "( +$-%"#.  K) E#"K>*$%$ #" '"K#" $ "+(*',H"5,>-. C=-'," ",$*$ - +$K#$ $-  37260.00 = "5$*" ""* $%" 5"-'," +$,"-'$ "K(-(% +$-%"#$% $  83.00. S, $# ,-'$*% %$ 5(K*" " *"H>- $# 30.68 5",'"#,H"K#$ 5"" +$%7 5J-'(% "(% %$ "*J- E#"K(*$ #" '"K#" $ "+(*',H"5,>- $ #" $".

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T(+J% ',$-$ -" $" $  17800.00 #" 5"# 9" " "+(*',H"* $$5'"-( "(% $  280.00 "# ,-"# $ 5"" '*,+$%'*$. ") D$'$*+,-$ $# -+$*( $ "(% 5(+#$'(% $ %$*J- -$5$%"*,(%7 %, #" '"%" $ ,-'$*% $% $# 21.36 5(+$%'( 5"" '*,+$%'*$.  K) E#"K(*$ #" '"K#" $ "+(*',H"5,>-. 5) D$'$*+,-$ $# 9"#(* $# "( ,-"#7 %, %'$ %$ *$"#,H" - '*,+$%'*$ $%% $ *$"#,H"( $# #',+(  "( 5(+#$'( S$ #,," -" $" +$,"-'$ 8 "(% +$-%"#$% $  17800.00 5"" -(7 #(% 5"#$% ,-5#=$,-'$*$%$% $# 36 "-"# 5",'"#,H"K#$ 5"" +$%. E-5$-'*$ $# 9"#(* (*,,-"# $ #" $" = $#"K(*$ #" '"K#" $ "+(*',H"5,>-.

() FONDO DE AMORTIWACIÓN 4. R$%$#9$:

U-" $*%(-" $%$" *$-,* 1380.00 "*" 5(+*"* -" 5J+"*" ('(*J,5" $-'*( $ 3 +$%$%. CJ-'( $K$*J $(%,'"* 5"" ,-5$-" $- -" 5$-'" K"-5"*," $ "" $# 20 $ ,-'$*% 5",'"#,H"K#$ ,-5$-"#+$-'$ E#"K(*$ #" '"K#" $ 5",'"#,H"5,>-. U-" $*%(-" $%$" *$-,*  30000.00 $- 3 "(%7 "5,$-( $>%,'(% 5"'*,+$%'*"#$% $- -" 5$-'" $ "(**(% $ "" $# 1/ 5",'"#,H"K#$ 5"'*,+$%'*"#+$-'$. D$%% $ - "( $# K"-5( $#$9> #" '"%" $ ,-'$*% "# 22. S, #(% $>%,'(% 5(-',-"*(- ,"#7 5J# %$*J $# +(-'( "# ,-"# $ 3 "(% E#"K(*$ #" '"K#" $ 5",'"#,H"5,>-. A*"5$#, ,$  8800.00 *$%'"(% (* 6 +$%$% "# 32 5(+$%'( 5"" '*,+$%'*$. A*"5$#, ,$-%" $%'"K#$5$* - (-( $ "+(*',H"5,>- "*" %"#"* #" $" "# ,-"# $ #(% 6 +$%$%. S, $# (-( "" - ,-'$*% $# 26 5(+$%'( 5"" +$%7 5J# %$*J $# 9"#(* $# $>%,'( +$-%"# E#"K>*$%$ #" '"K#" $ 5",'"#,H"5,>-. A*,"-" $%$" "(**"*  67380.00 5(- $# ,- $ 5(+*"* -" +,5*(5(+'"(*". S, $$ "(**"*  1000.00 5"" +$% = $$ ,-9$*',* $%" 5"-'," "# 28 5",'"#,H"K#$ +$-%"#+$-'$7 5J-'(% $>%,'(% 5(+#$'(% "*J = 5J# %$*J $# 9"#(* $# $>%,'( ,-"# E#"K(*$ #" '"K#" $ 5",'"#,H"5,>-.

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