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Prévia do material em texto

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A u t o r i a : L e o n a r d o Ta k a m a s a O t s u k a
Te m a 0 3
V a l o r P r e s e n t e e V a l o r F u t u r o ( J u r o s C o m p o s t o s )
7 H P D � � �
V a l o r P r e s e n t e e V a l o r F u t u r o ( J u r o s C o m p o s t o s )
A u t o r i a : L e o n a r d o Ta k a m a s a O t s u k a
C o m o c i t a r e s s e d o c u m e n t o :
O T S U K A , L e o n a r d o T a k a m a s a . M a t e m á t i c a F i n a n c e i r a : V a l o r P r e s e n t e e V a l o r F u t u r o ( J u r o s C o m p o s t o s ) . C a d e r n o d e A t i v i d a d e s . A n h a n g u e r a P u b l i -
c a ç õ e s : V a l i n h o s , 2 0 1 4 .
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& R P R � M i � Y L P R V � Q R � W H P D � � � � D � P D W H P i W L F D � ¿ Q D Q F H L U D � H V W X G D � R � Y D O R U � G R � G L Q K H L U R � Q R � W H P S R � � 3 R U W D Q W R � H [ L V W H � D � Q H F H V V L G D G H �
G H � F R Q K H F H U P R V � T X D L V � V m R � R V � Y D O R U H V � � W D Q W R � Q R � P R P H Q W R � S U H V H Q W H � � 3 9 � � � F R P R � Q R � I X W X U R � � ) 9 � � H � V X D V � Y D U L i Y H L V � � W H P S R �
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¿ Q D Q F H L U D V � M i � S U R J U D P D G D V � Q D � P H P y U L D � G D � F D O F X O D G R U D �
3 D U D � R V � D O X Q R V � T X H � R S W D U H P � S R U � Q m R � D G T X L U L U � D � + 3 � � � & � R X � T X H � S U H W H Q G H P � I D ] H U � X P � F R Q F X U V R � S ~ E O L F R � � S R U � H [ H P S O R � � V H U i �
Q H F H V V i U L R � H I H W X D U � R V � F i O F X O R V � S H O D � I y U P X O D � � 0 D V � S D U D � I D F L O L W D U � R � D S U H Q G L ] D G R � V H U i � Q H F H V V i U L R � � Q R � P t Q L P R � � R � X V R � G H � X P D �
F D O F X O D G R U D � F L H Q W t ¿ F D � � S R L V � Y m R � H [ L V W L U � F i O F X O R V � X P � S R X F R � P D L V � F R P S O H [ R V � � F R P R � S R U � H [ H P S O R � � U D G L F L D o m R � H � O R J D U L W P R V � �
0 D V � ¿ T X H � W U D Q T X L O R � � S R L V � T X H P � Y D L � H I H W X D U � R V � F i O F X O R V � p � D � F D O F X O D G R U D � � Y R F r � G H Y H U i � V R P H Q W H � O D Q o D U � R V � Y D O R U H V � � 1 H V W H �
F D V R � � Y D P R V � D G R W D U � F R P R � H [ H P S O R � R � P R G H O R � G D � F D O F X O D G R U D � F L H Q W t ¿ F D � � P D U F D � & D V L R � � P R G H O R � f x - 8 2 m s � ¿ J X U D � � � � � � � $ R V �
T X H � R S W D U H P � S R U � R X W U R � P R G H O R � F R Q V X O W H P � R � P D Q X D O � S D U D � D V � R S H U D o } H V � � S R L V � S R G H � Y D U L D U � G H � D F R U G R � F R P � R � P R G H O R � H �
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C O N V I T E À L E I T U R A
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9 D O R U H V � S H U F H Q W X D L V � F R P R � � � � � D R � P r V � Q m R � S R G H P � V H U � L Q V H U L G R V � Q D V � I y U P X O D V � � V H U i � Q H F H V V i U L R � G H L [ D U � Q R � I R U P D W R �
d a t a x a u n i t á r i a � � $ � W D [ D � X Q L W i U L D � G H � � � � � p � V R P H Q W H � G L Y L G L U � S R U � F H P � � R X � V H M D � � � � � � � � � � � W D [ D � X Q L W i U L D � �
P V ( P r e s e n t e V a l u e ) : 6 L J Q L ¿ F D � 9 D O R U � 3 U H V H Q W H � � R X � V H M D � � p � R � Y D O R U � L Q L F L D O � G D � R S H U D o m R � � Q R � P R P H Q W R � � W H P S R � � L J X D O � D � ] H U R � �
3 R G H � W D P E p P � V H U � F K D P D G D � G H � 3 U L Q F L S D O � � 3 � � � 9 D O R U � $ W X D O � R X � & D S L W D O � � & � � � 3 H U F H E D P � T X H � H [ L V W H P � Y i U L D V � W H U P L Q R O R J L D V � H �
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F V ( F u t u r e V a l u e ) : 6 L J Q L ¿ F D � 9 D O R U � ) X W X U R � � R X � V H M D � � p � R � Y D O R U � G D � R S H U D o m R � D S y V � D � L Q F L G r Q F L D � G H � M X U R V � � Y D O R U � D � V H U � U H V J D W D G R � �
3 R G H � V H U � F K D P D G R � W D P E p P � M o n t a n t e ( M ) � R X � 6 D O G R � ) X W X U R � 6 � � � ' H V W D � P D Q H L U D � W H P R V � D � S U L P H L U D � I y U P X O D � � F V = P V + J 
� 9 D O R U � ) X W X U R � p � D � V R P D � G R � 9 D O R U � 3 U H V H Q W H � F R P � R V � - X U R V � �
J – J u r o s : � U H S U H V H Q W D P � D � U H P X Q H U D o m R � G R � 9 D O R U � 3 U H V H Q W H � � 3 9 � � H P S U H J D G R � H P � D O J X P D � D W L Y L G D G H � S U R G X W L Y D � � R $ .
i ( i n t e r e s t r a t e ) � � V L J Q L ¿ F D � 7 D [ D � G H � M X U R V � � $ � W D [ D � G H � M X U R V � L Q G L F D � T X D O � U H P X Q H U D o m R � V H U i � S D J D � D R � G L Q K H L U R � H P S U H V W D G R � � S D U D �
X P � G H W H U P L Q D G R � S H U t R G R � � E x : 1 , 5 % a o m ê s .
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2 � R E M H W L Y R � G H V W H � W H P D � p � H V W X G D U � R V � F i O F X O R V � G D � I y U P X O D � G R V � M X U R V � F R P S R V W R V �
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n � � S U D ] R � � W H P S R �
i � � W D [ D � G H � M X U R V � � � � �
P o t e n c i a ç ã o � � G H V D ¿ R � P D W H P i W L F R �
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& R Q ¿ J X U D o m R � G R � 3 R Q W R � H � Y t U J X O D �
P a d r ã o B r a s i l e i r o : 1 . 2 3 5 , 5 0 .
P a d r ã o A m e r i c a n o : 1 , 2 3 5 . 5 0 .
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E x e m p l o 1 :
9 R F r � W R P R X � H P S U H V W D G R � G H � X P � E D Q F R � R � Y D O R U � G H � 5 � � � � � � � � � � H � T X H � V H U m R � S D J R V � H P � V H L V � P H V H V � � $ � W D [ D � G H � M X U R V �
F R P S R V W R V � F R E U D G D � S H O R � E D Q F R � p � G H � � � � � � D R � P r V � � � & D O F X O H � R � P R Q W D Q W H � D � V H U � S D J R � D R � E D Q F R �
P O R D E N T R O D O T E M A
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V H X V � U H V S H F W L Y R V � Y D O R U H V � �
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Q � � � P H V H V �
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) 9 "
2 º P a s s o : � $ S y V � D � F R O H W D � G H � G D G R V � G H Y H P R V � H I H W X D U � X P D � S H U J X Q W D � G H � Y H U L ¿ F D o m R � �
* O “ n ” e d o “ i ” e s t ã o n o m e s m o p e r í o d o d e t e m p o ?
Q � � � m e s e s �
L � � � � � � � � D R � P r V �
5 H V S R V W D � � 1 H V W H � F D V R � V L P � � R � ³ Q ´ � H V W i � H P � P H V H V � H � R � ³ L ´ � D R � P r V � � S R U W D Q W R � Q H Q K X P D � D O W H U D o m R � V H U i � Q H F H V V i U L D � �
3 º P a s s o : � $ W H Q o m R � � 3 D V V R � R E U L J D W y U L R � V R P H Q W H � Q D � U H V R O X o m R � S H O D � I y U P X O D � � � ' H Y H P R V � D O W H U D U � D � W D [ D � G H � M X U R V � � L � � S D U D �
I R U P D � X Q L W i U L D � � R X � V H M D � � G L Y L G L U � D � W D [ D � S R U � � � � �
L � � � � � � � � � � � � � � � � � � � � � � R � Y D O R U � G H � � � � � � � G H Y H U i � V H U � O D Q o D G R � Q D � I y U P X O D � �
4 º P a s s o : 5 H V R O X o m R � G D � I y U P X O D � � � 1 H V W H � F D V R � H V F U H Y D � D � I y U P X O D � H � O D Q F H � R V � Y D O R U H V � T X H � H V W m R � U H O D F L R Q D G R V � Q D � F R O H W D �
G H � G D G R V � � 5 D V F X Q K R � � � 8 W L O L ] H � Q R � P t Q L P R � � � F D V D V � G H F L P D L V � Q D � U H V R O X o m R � H � Q D � U H V S R V W D � ¿ Q D O � S R G H � V H U � H P � � � F D V D V �
d e c i m a i s .
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0 p W R G R � � � 5 H V R O X o m R � S H O D � + 3 � � � & �
1 º P a s s o : ( I H W X D U � D � F R O H W D � G R V � G D G R V � Q R � H Q X Q F L D G R � H � P R Q W D U � X P � ³ 5 D V F X Q K R ´ � � & R O R F D U � D V � W H U P L Q R O R J L D V � � V L J O D V � � F R P � R V �
V H X V � U H V S H F W L Y R V � Y D O R U H V � �
3 9 � � � � � � � � � Y D O R U � S U H V H Q W H � �
Q � � � P H V H V �
L � � � � � � � � D R � P r V �
) 9 "
P O R D E N T R O D O T E M A
� �
2 º P a s s o : $ S y V � D � F R O H W D � G H � G D G R V � G H Y H P R V � H I H W X D U � X P D � S H U J X Q W D � G H � Y H U L ¿ F D o m R � �
* O “ n ” e d o “ i ” e s t ã o n o m e s m o p e r í o d o d e t e m p o ?
Q � � � m e s e s �
L � � � � � � � � D R � m ê s �
5 H V S R V W D � � 1 H V W H � F D V R � V L P � � R � ³ Q ´ � H V W i � H P � P H V H V � H � R � ³ L ´ � D R � P r V � � S R U W D Q W R � Q H Q K X P D � D O W H U D o m R � V H U i � Q H F H V V i U L D �
� ž � 3 D V V R � � / D Q o D U � Y D O R U H V � Q D � + 3 � � � &
2 � Y D O R U � Q H J D W L Y R � T X H � D � + 3 � � � F � P R V W U D � p � V R P H Q W H � X P D � L Q G L F D o m R � G H � V D t G D � G H � G L Q K H L U R � G R � À X [ R � G H � F D L [ D � � R X � V H M D � � V H �
Y R F r � O D Q o R X � R � Y D O R U � S U H V H Q W H � S R V L W L Y R � � D � + 3 � � � & � W H � U H W R U Q D � R � I D Y R U � I X W X U R � Q H J D W L Y R � H � Y L F H � Y H U V D � � 1 m R � T X H U � G L ] H U � T X H � R �
Y D O R U � H V W i � H U U D G R � � p � V R P H Q W H � R � V L V W H P D � G D � F D O F X O D G R U D �
E x e m p l o 2 :
9 R F r � W R P R X � H P S U H V W D G R � G H � X P � E D Q F R � R � Y D O R U � G H � 5 � � � � � � � � � � H � T X H � V H U m R � S D J R V � H P � W U r V � D Q R V � � $ � W D [ D � G H � M X U R V �
F R P S R V W R V � F R E U D G D � S H O R � E D Q F R � p � G H � � � � � � D R � P r V � � � & D O F X O H � R � P R Q W D Q W H � D � V H U � S D J R � D R � E D Q F R �
P O R D E N T R O D O T E M A
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P O R D E N T R O D O T E M A
0 p W R G R � � � 5 H V R O X o m R � S H O D � I y U P X O D �
1 º P a s s o : � ( I H W X D U � D � F R O H W D � G R V � G D G R V � Q R � H Q X Q F L D G R � H � P R Q W D U � X P � ³ 5 D V F X Q K R ´ � � & R O R F D U � D V � W H U P L Q R O R J L D V � � V L J O D V � � F R P � R V �
V H X V � U H V S H F W L Y R V � Y D O R U H V � �
3 9 � � � � � � � � � Y D O R U � S U H V H Q W H � �
Q � � � D Q R V �
L � � � � � � � � D R � P r V �
) 9 "
2 º P a s s o : � $ S y V � D � F R O H W D � G H � G D G R V � G H Y H P R V � H I H W X D U � X P D � S H U J X Q W D � G H � Y H U L ¿ F D o m R � �
* O “ n ” e d o “ i ” e s t ã o n o m e s m o p e r í o d o d e t e m p o ?
Q � � � a n o s �
L � � � � � � � � D R � m ê s �
5 H V S R V W D � � 1 H V W H � F D V R � n ã o � � R � ³ Q ´ � H V W i � H P � D Q R V � H � R � ³ L ´ � D R � P r V � � S R U W D Q W R � D � D O W H U D o m R � G D � P H G L G D � G H � W H P S R � V H U i �
Q H F H V V i U L D � � ' L F D � � Q R V � M X U R V � F R P S R V W R V � Q m R � U H F R P H Q G R � D � D O W H U D o m R � G R � ³ L ´ � � S R L V � V H U i � Q H F H V V i U L R � X W L O L ] D U � R X W U R � F R Q F H L W R �
� R X W U D � I y U P X O D � G D � W D [ D � H T X L Y D O H Q W H � F R P S R V W D � � T X H � Q m R � I R L � H Q V L Q D G R � D L Q G D � � S R U W D Q W R � D O W H U H � R � ³ Q ´ �
Q � � � D Q R V � [ � � � � � � � � P H V H V � � Y D P R V � W U D Q V I R U P D U � R � S H U t R G R � G H � D Q R V � S D U D � P H V H V � � F R P � R � R E M H W L Y R � G H � G H L [ D U � Q R � P H V P R �
S H U t R G R � G H � W H P S R � � 9 D P R V � P X O W L S O L F D U � S R U � � � � � S R L V � � � D Q R � S R V V X L � � � � P H V H V � �
L � � � � � � � � D R � m ê s
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3 º P a s s o : $ W H Q o m R � � 3 D V V R � R E U L J D W y U L R � V R P H Q W H � Q D � U H V R O X o m R � S H O D � I y U P X O D � � � ' H Y H P R V � D O W H U D U � D � W D [ D � G H � M X U R V � � L � �
S D U D � I R U P D � X Q L W i U L D � � R X � V H M D � � G L Y L G L U � D � W D [ D � SR U � � � � �
L � � � � � � � � � � � � � � � � � � � � � � R � Y D O R U � G H � � � � � � � G H Y H U i � V H U � O D Q o D G R � Q D � I y U P X O D � �
4 º P a s s o : � 5 H V R O X o m R � G D � I y U P X O D � � � 1 H V W H � F D V R � H V F U H Y D � D � I y U P X O D � H � O D Q F H � R V � Y D O R U H V � T X H � H V W m R � U H O D F L R Q D G R V � Q D � F R O H W D �
G H � G D G R V � � 5 D V F X Q K R � �
0 p W R G R � � � 5 H V R O X o m R � S H O D � + 3 � � � & �
1 º P a s s o : ( I H W X D U � D � F R O H W D � G R V � G D G R V � Q R � H Q X Q F L D G R � H � P R Q W D U � X P � ³ 5 D V F X Q K R ´ � � & R O R F D U � D V � W H U P L Q R O R J L D V � � V L J O D V � � F R P � R V �
V H X V � U H V S H F W L Y R V � Y D O R U H V � �
3 9 � � � � � � � � � Y D O R U � S U H V H Q W H � �
Q � � � D Q R V �
L � � � � � � � � D R � P r V �
) 9 "
P O R D E N T R O D O T E M A
� �
2 º P a s s o : � $ S y V � D � F R O H W D � G H � G D G R V � G H Y H P R V � H I H W X D U � X P D � S H U J X Q W D � G H � Y H U L ¿ F D o m R � �
* O “ n ” e d o “ i ” e s t ã o n o m e s m o p e r í o d o d e t e m p o ?
Q � � � a n o s �
L � � � � � � � � D R � m ê s �
R e s p o s t a : 1 H V W H � F D V R � n ã o � � R � ³ Q ´ � H V W i � H P � D Q R V � H � R � ³ L ´ � D R � P r V � � S R U W D Q W R � D � D O W H U D o m R � G D � P H G L G D � G H � W H P S R � V H U i �
Q H F H V V i U L D � S D U D � G H L [ D U � S D G U m R � � ' L F D � � Q R V � M X U R V � F R P S R V W R V � Q m R � U H F R P H Q G R � D � D O W H U D o m R � G R � ³ L ´ � � S R L V � V H U i � Q H F H V V i U L R �
X W L O L ] D U � X P � F R Q F H L W R � � R X W U D � I y U P X O D � G D � W D [ D � H T X L Y D O H Q W H � F R P S R V W D � � T X H � Q m R � I R L � H Q V L Q D G R � D L Q G D � � S R U W D Q W R � D O W H U H � R � ³ Q ´ � � 
Q � � � D Q R V � [ � � � � � � � � P H V H V � � Y D P R V � W U D Q V I R U P D U � R � S H U t R G R � G H � D Q R V � S D U D � P H V H V � � F R P � R � R E M H W L Y R � G H � G H L [ D U � Q R � P H V P R �
S H U t R G R � G H � W H P S R � � � 9 D P R V � P X O W L S O L F D U � S R U � � � � � S R L V � � � D Q R � S R V V X L � � � � P H V H V � �
i = 2 , 5 % a o m ê s .
� ž � 3 D V V R � � / D Q o D U � Y D O R U H V � Q D � + 3 � � � & �
3 9 � � � � � � � � � Y D O R U � S U H V H Q W H � �
Q � � � D Q R V � � � � � P H V H V �
L � � � � � � � � D R � P r V �
) 9 "
P O R D E N T R O D O T E M A
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P O R D E N T R O D O T E M A
C á l c u l o d o V a l o r P r e s e n t e ( P V )
1 R � S U y [ L P R � H [ H P S O R � Y H U H P R V � R � P p W R G R � G H � F i O F X O R � G R � 9 D O R U � 3 U H V H Q W H � � 3 9 � �
E x e m p l o 3 :
6 H X � L U P m R � O K H � H P S U H V W R X � F H U W D � T X D Q W L D � K i � � � P H V H V � � 6 H � D � W D [ D � F R Q W U D W D G D � I R L � G H � � � � � � D � P � � � T X D O � R � Y D O R U � S U H V H Q W H � G H V V H �
H P S U p V W L P R � V H � K R M H � Y R F r � G H Y H � � � � � � � � � � " � � * , 0 ( 1 ( 6 � � � � � � � � S � � � � �
5 H V R O X o m R � S H O D � ) y U P X O D
1 º P a s s o : 2 º P a s s o : $ S y V � D � F R O H W D � G H � G D G R V � G H Y H P R V � H I H W X D U � X P D � S H U J X Q W D � G H � Y H U L ¿ F D o m R � �
* O “ n ” e d o “ i ” e s t ã o n o m e s m o p e r í o d o d e t e m p o ?
Q � � � m e s e s �
L � � � � � � � � D R � m ê s �
5 H V S R V W D � � 1 H V W H � F D V R � V L P � � R � ³ Q ´ � H V W i � H P � P H V H V � H � R � ³ L ´ � D R � P r V � � S R U W D Q W R � Q H Q K X P D � D O W H U D o m R � V H U i � Q H F H V V i U L D � �
� �
3 º P a s s o : $ W H Q o m R � � 3 D V V R � R E U L J D W y U L R � V R P H Q W H � Q D � U H V R O X o m R � S H O D � I y U P X O D � � � ' H Y H P R V � D O W H U D U � D � W D [ D � G H � M X U R V � � L � �
S D U D � I R U P D � X Q L W i U L D � � R X � V H M D � � G L Y L G L U � D � W D [ D � S R U � � � � �
L � � � � � � � � � � � � � � � � � � � � � � R � Y D O R U � G H � � � � � � � G H Y H U i � V H U � O D Q o D G R � Q D � I y U P X O D �
4 º P a s s o : � 5 H V R O X o m R � G D � I y U P X O D � � � 1 H V W H � F D V R � H V F U H Y D � D � I y U P X O D � H � O D Q F H � R V � Y D O R U H V � T X H � H V W m R � U H O D F L R Q D G R V � Q D � F R O H W D �
G H � G D G R V � � 5 D V F X Q K R � � � 8 W L O L ] H � Q R � P t Q L P R � � � F D V D V � G H F L P D L V � Q D � U H V R O X o m R � H � Q D � U H V S R V W D � ¿ Q D O � S R G H � V H U � H P � � � F D V D V �
G H F L P D L V �
0 p W R G R � � � 5 H V R O X o m R � S H O D � + 3 � � � & �
P O R D E N T R O D O T E M A
� �
P O R D E N T R O D O T E M A
2 E V H U Y D o m R � � $ � G L I H U H Q o D � G H � X P � F H Q W D Y R � I R L � G H Y L G R � D R � D U U H G R Q G D P H Q W R � � S R U � V H U � V R P H Q W H � � � F H Q W D Y R � � Q m R � V H U i �
c o n s i d e r a d o e r r a d o .
� & i O F X O R � G R � 3 U D ] R � � Q �
' H Y L G R � D R � I D W R � G D � I y U P X O D � G R V � M X U R V � F R P S R V W R V � V H U � X P D � H [ S R Q H Q F L D O � � S D U D � R � F i O F X O R � G R � S U D ] R � � Q � � U H T X H U � D O J X Q V �
F R Q K H F L P H Q W R V � G H � P D W H P i W L F D � E i V L F D � � S R U p P � H [ L V W H � X P D � I y U P X O D � H V S H F t ¿ F D � � $ V � G X D V � P D Q H L U D V � V H U m R � G H P R Q V W U D G D V � D �
V H J X L U �
$ � S D U W L U � G D � I y U P X O D � D F L P D � S R G H P R V � G H G X ] L U � D � I y U P X O D � S D U D � R � F i O F X O R V � G R � ³ Q ´ �
( G I M E N E S , 2 0 1 2 , p . 8 3 - - a d a p t a d o p e l o p r o f e s s o r )
o u
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( [ H P S O R � � �
( P � T X D Q W R � W H P S R � X P D � D S O L F D o m R � G H � � � � � � � � � J H U D � X P � P R Q W D Q W H � G H � 5 � � � � � � � " � & R Q V L G H U H � T X H � H V V D � D S O L F D o m R � I R L �
U H P X Q H U D G D � D � � � � � � D � P � � � * , 0 ( 1 ( 6 � � � � � � � � S � � � �
5 H V R O X o m R � S H O D � ) y U P X O D � � S D U D � R V � D O X Q R V � T X H � S R V V X H P � D � + 3 � � & � � S X O H P � S D U D � D � U H V R O X o m R � S H O D � F D O F X O D G R U D � �
1 º P a s s o : C o l e t a d o s d a d o s e a c e r t o d a t a x a ( d i v i s ã o p o r 1 0 0 ) :
3 9 � � � � � �
) 9 � � � � � �
L � � � � � � � � D R � m ê s � � � � � � � � � � � � � � � W D [ D � X Q L W i U L D � �
Q � " � � D � W D [ D � G H � M X U R V � H V W i � H P � P H V H V � � S R U W D Q W R � D � U H V S R V W D � V H � G D U i � H P � m e s e s � � �
P O R D E N T R O D O T E M A
� �
P O R D E N T R O D O T E M A
5 H V R O X o m R � G R � H [ H P S O R � � � S H O D � I y U P X O D � G R V � M X U R V � F R P S R V W R V �
e � S R V V t Y H O � U H V R O Y H U � R � F i O F X O R � G R � ³ Q ´ � X W L O L ] D Q G R � D � I y U P X O D � L Q L F L D O � � P D V � X W L O L ] D Q G R � X P D � S U R S U L H G D G H � G H � O R J D U L W P R �
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P O R D E N T R O D O T E M A
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P O R D E N T R O D O T E M A
0 p W R G R � � � 5 H V R O X o m R � S H O D � + 3 � � � & �
3 D U D � R � F i O F X O R � G R � S U D ] R � F R P � Y D O R U H V � T X H E U D G R V � � F R P R � R � H [ H P S O R � � � � D � + 3 � � � & � Q m R � p � U H F R P H Q G D G D � � S R L V � R � U H V X O W D G R � S H O D �
+ 3 � � � & � V H U i � D U U H G R Q G D G R � S D U D � F L P D �
� �
C á l c u l o d a T a x a d e J u r o s ( i )
$ � U H V R O X o m R � S H O D � I y U P X O D � p � P D L V � V L P S O H V � S D U D � D � W D [ D � G H � M X U R V � H � P D L V � F R P S O H [ D � V H � S H J DU � D � I y U P X O D � R U L J L Q D O � S H O R V � M X U R V �
F R P S R V W R V � �
2 � G H V D ¿ R � P D W H P i W L F R � F R Q W L Q X D � S D U D � R � F i O F X O R � G D � W D [ D � G H � M X U R V � � ' H Y H P R V � X W L O L ] D U � D V � S U R S U L H G D G H V � G H � U D G L F L D o m R � � F R P R �
Y H U H P R V � D � V H J X L U �
( [ H P S O R � � �
2 � V D O G R � ¿ Q D O � G H � X P D � D S O L F D o m R � G H � � � � � � � � � p � G H � � � � � � � � � � � D S y V � � � P H V H V � � & D O F X O H � D � W D [ D � G H � M X U R V � G H V V D � D S O L F D o m R �
� * , 0 ( 1 ( 6 � � � � � � � � S � � � � � � �
5 H V R O X o m R � S H O D � ) y U P X O D �
1 º P a s s o : C o l e t a d o s d a d o s e a c e r t o d a t a x a :
3 9 � � � � � �
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