Desconto_Racional_por_Dentro

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2 Hierarchical Index 3

2.1 Class Hierarchy . . . . 3

3 Class Index 5 3.1 Class List . . . . 5

4 File Index 7 4.1 File List . . . . 7

5 Namespace Documentation 9 5.1 _02f_rational Namespace Reference . . . . 9

5.1.1 Detailed Description . . . 10

5.1.2 Function Documentation . . . 12

5.1.2.1 futureValue() . . . 12

5.1.2.2 getDownPayment() . . . 12

5.1.2.3 getInterest() . . . 13

5.1.2.4 getInterest2() . . . 14

5.1.2.5 main() . . . 15

5.1.2.6 presentValue() . . . 16

5.1.2.7 priceTable() . . . 16

5.1.2.8 printRow() . . . 17

5.1.2.9 printTable() . . . 17

5.1.2.10 rational_discount() . . . 18

5.1.2.11 setDownPayment() . . . 18

5.1.2.12 setEncodingUTF8() . . . 18

5.1.3 Variable Documentation . . . 19

5.1.3.1 CF . . . 19

5.2 calcTest Namespace Reference . . . 19

5.2.1 Detailed Description . . . 20

6 Class Documentation 21 6.1 calcTest.CalcTest Class Reference . . . 21

6.1.1 Detailed Description . . . 22

6.1.2 Member Function Documentation . . . 22

6.1.2.1 setUp() . . . 22

6.1.2.2 testPriceTable() . . . 22

6.1.2.3 testTaxa() . . . 22

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7 File Documentation 23

7.1 _02f_rational.py File Reference . . . 23 7.2 calcTest.py File Reference . . . 24

Index 25

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Namespace Index

1.1 Namespace List

Here is a list of all namespaces with brief descriptions:

_02f_rational

Desconto Racional por Dentro . . . . 9 calcTest

Class for testing the Calculator . . . . 19

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2 Namespace Index

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Hierarchical Index

2.1 Class Hierarchy

This inheritance list is sorted roughly, but not completely, alphabetically:

TestCase

calcTest.CalcTest . . . . 21

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4 Hierarchical Index

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Class Index

3.1 Class List

Here are the classes, structs, unions and interfaces with brief descriptions:

calcTest.CalcTest

Class for testing certain aspects of the behavior of the calculator . . . . 21

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6 Class Index

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File Index

4.1 File List

Here is a list of all files with brief descriptions:

_02f_rational.py . . . . 23

calcTest.py . . . . 24

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8 File Index

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Namespace Documentation

5.1 _02f_rational Namespace Reference

Desconto Racional por Dentro.

Functions

• def setDownPayment (dp=True) Set a down payment.

• def getDownPayment () Get the down payment.

• def setEncodingUTF8 () Set default enconding to UTF8.

• def getInterest (x, y, p)

Acha a taxa que produz o preço à vista pelo método de Newton:

• def getInterest2 (x, y, p)

Acha a taxa que produz o preço à vista pelo método de Newton:

• def presentValue (x, p, t)

Retorna o fator para atualizar o preço no instante da compra.

• def futureValue (y, p, t)

Retorna o fator para atualizar o preço no final da compra.

• def rational_discount (p, t, x, y, option=True) Desconto Racional por Dentro.

• def priceTable (np, pv, t, pmt)

Retorna a Tabela Price, também chamado de sistema francês de amortização.

• def printRow (pt, fmt='o')

Print a single row of the Price Table.

• def printTable (pt) Print the Price Table.

• def main (argv=None)

Programa principal para testes.

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10 Namespace Documentation

Variables

• CF = lambda i,n: float(i) / (1-(1+i) ∗∗ -n)

Coeficiente de financiamento CDC (Crédito Direto ao Consumidor).

5.1.1 Detailed Description

Desconto Racional por Dentro.

A fórmula para atualizar o preço no instante da compra, levando em conta a remuneração aplicada a cada prestação, R = ^x _p , é:

x atualizado = A = x p

(1 + t) ^p − 1

t(1 + t) ^(p−1) = x × (1 + t)

(p ∗ CF ) , CF = t 1 − (1 + t) ^−p .

O preço atualizado, A , voltando cada parcela, R , para o tempo inicial, é a soma de uma P.G. de razão q = _(1+t) ¹ e cujo primeiro termo é q:

A = R[(1 + t) ⁻¹ + (1 + t) ⁻² + ... + (1 + t) ⁻ⁿ ] A = Rq (1 − q ⁿ )

1 − q ,

A = Rq

(1 − _(1+t) ¹

n

) (1 − _(1+t) ¹ )

= Rq ((1 + t) ⁿ − 1) (1 + t) ⁿ

(1 + t) t A = R (1 + t) ⁿ − 1

t(1 + t) ⁿ

= R (1 − (1 + t) ⁻ⁿ )

t ⇒

R = A t

(1 − (1 + t) ⁻ⁿ )

= A × CF onde R = ^x _p é o valor de cada parcela.

Como, neste exercício, a primeira parcela é paga no ato da compra, na realidade, n = p − 1 e deve-se somar R = ^x _p (a entrada):

A = R(1 + q(1 − q ^(p−1) ) (1 − q) ).

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q (1 − _(1+t) ¹ ) = q

(1 + t) ^(p−1) t 1

(1 + t) ((1 + t) ^(p−1) − 1) (1 + t)

t(1 + t) ^(p−1) = (1 + t) ^(p−1) − 1

t(1 + t) ^(p−1) ⇒ (somando 1) 1 + (1 + t) ^(p−1) − 1

t(1 + t) ^(p−1) = t(1 + t) ^(p−1) + (1 + t) ^(p−1) − 1 t(1 + t) ^(p−1)

(t + 1)(1 + t) ^(p−1) − 1

t(1 + t) ^(p−1) = (1 + t) ^p − 1

t(1 + t) ^(p−1) = (1 + t) − (1 + t) ^−(p−1)

t ⇒ (recolocando R) R(1 + t) (1 − (1 + t) ^−p )

t = R (1 + t)

CF

Nota: Achar a taxa "t" que produz o preço à vista "y" requer o método de Newton:

x n+1 = x n − f (x _n ) f ' (x n )

y = x

p (c − 1)

tb , f (t) = ytb − x

p (c − 1) f ' (t) = y(b + t(p − 1)a) − xb

onde a = (1 + t) ^(p−2) , b = (1 + t) ^(p−1) , c = (1 + t) ^p e o problema é equivalente a encontrar um zero da função f t n+1 = t n − f (t)

f ' (t) , t o = x y

A função é decrescente e converge para t quando n →∞ .

Author

Paulo Roma

Since

02/11/2012

http://pessoal.sercomtel.com.br/matematica/financeira/curso/curso.htm https://calculador.com.br/calculo/financiamento-price

https://dicascarrosusados.com/financiar-carro-por-cdc/

https://edisciplinas.usp.br/pluginfile.php/4647782/mod_resource/content/1/ ← -

ENS%20-%20MTF%20191S%20-%20Aula%2007%20C%20Financiamentos.pdf

https://mundoeducacao.uol.com.br/matematica/calculo-financiamento.htm http://www.urca.br/itec/images/pdfs/mod.%20vi%20-%20anal.%20econ.financ. ← -

e%20invest.pdf

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12 Namespace Documentation

5.1.2 Function Documentation

5.1.2.1 futureValue()

def _02f_rational.futureValue ( y,

p, t )

Retorna o fator para atualizar o preço no final da compra.

Parameters

y preço à vista.

p número de parcelas.

t taxa.

Returns

fator para atualizar o preço e o valor futuro.

Definition at line 184 of file _02f_rational.py.

References CF, and getDownPayment().

5.1.2.2 getDownPayment()

def _02f_rational.getDownPayment ( )

Get the down payment.

Definition at line 73 of file _02f_rational.py.

Referenced by futureValue(), getInterest(), main(), and presentValue().

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def _02f_rational.getInterest ( x,

y, p )

Acha a taxa que produz o preço à vista pelo método de Newton:

t n+1 = t n − f (t n ) f ' (t n )

A função é decrescente e converge para t = lim _n→∞ t n+1 . Nota: se não houve entrada, retorna getInterest2 ( x, y, p )

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14 Namespace Documentation

Parameters

x preço a prazo.

y preço à vista.

p número de parcelas.

Returns

taxa, número de iterações.

Definition at line 116 of file _02f_rational.py.

References getDownPayment().

5.1.2.4 getInterest2()

def _02f_rational.getInterest2 ( x,

y, p )

Acha a taxa que produz o preço à vista pelo método de Newton:

t n+1 = t n − f (t n ) f ' (t n )

A função é decrescente e converge para t = lim _n→∞ t n+1 . Nota: assume-se que não houve entrada.

Parameters

x preço a prazo.

y preço à vista.

p número de parcelas.

Returns

taxa, número de iterações.

Definition at line 148 of file _02f_rational.py.

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def _02f_rational.main ( argv = None )

Programa principal para testes.

Parameters

argv command line arguments:

• h help

• n número de parcelas.

• t taxa mensal.

• x valor da compra a prazo.

• y valor da compra à vista.

• e indica uma entrada.

• v verbose mode

Usage:

• _02f_rational.py -n10 -t1 -x500 -y450 -e

• _02f_rational.py -n18 -t0 -x3297.60 -y1999

• _02f_rational.py -n10 -t0 -x1190 -y1094.80

• _02f_rational.py -n 88 -t 4.55 -x 111064.80 -y 23000

• _02f_rational.py -n 96 -t 0 -x 134788.8 -y 63816.24

• _02f_rational.py -n 4 -t 3.0 -x 1076.11 -y 1000

• _02f_rational.py –parcelas=88 –taxa=4.55 –valorP=111064.80 –valorV=23000 -v or

• _02f_rational.py –help

https://mkaz.blog/code/python-string-format-cookbook/

https://www.w3schools.com/python/ref_string_format.asp https://pyformat.info

Definition at line 344 of file _02f_rational.py.

References CF, getDownPayment(), priceTable(), printTable(), and setDownPayment().

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16 Namespace Documentation

5.1.2.6 presentValue()

def _02f_rational.presentValue ( x,

p, t )

Retorna o fator para atualizar o preço no instante da compra.

Parameters

x preço a prazo.

p número de parcelas.

t taxa.

Returns

fator para atualizar o preço e o valor presente.

Definition at line 171 of file _02f_rational.py.

References CF, and getDownPayment().

5.1.2.7 priceTable()

def _02f_rational.priceTable ( np,

pv, t, pmt )

Retorna a Tabela Price, também chamado de sistema francês de amortização.

É um método usado em amortização de empréstimos cuja principal característica é apresentar prestações (ou parcelas) iguais.

O método foi apresentado em 1771 por Richard Price em sua obra "Observações sobre Pagamentos Remissivos".

Parameters

np número de prestações.

pv valor do empréstimo.

t taxa de juros.

pmt pagamento mensal.

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Definition at line 254 of file _02f_rational.py.

Referenced by main(), and calcTest.CalcTest.testPriceTable().

5.1.2.8 printRow()

def _02f_rational.printRow ( pt,

fmt = 'o' )

Print a single row of the Price Table.

Parameters pt given row.

fmt selector:

• 'f': f-string (python 3.6+),

• 'o': new format or

• '%': the old % style.

Definition at line 277 of file _02f_rational.py.

5.1.2.9 printTable()

def _02f_rational.printTable ( pt )

Print the Price Table.

Definition at line 292 of file _02f_rational.py.

Referenced by main().

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18 Namespace Documentation

5.1.2.10 rational_discount()

def _02f_rational.rational_discount ( p,

t, x, y,

option = True )

Desconto Racional por Dentro.

Parameters

p número de prestações.

t taxa de juros mensal.

x preço a prazo.

y preço à vista.

option seleciona o que será impresso.

Definition at line 205 of file _02f_rational.py.

5.1.2.11 setDownPayment()

def _02f_rational.setDownPayment ( dp = True )

Set a down payment.

Definition at line 68 of file _02f_rational.py.

Referenced by main(), and calcTest.CalcTest.setUp().

5.1.2.12 setEncodingUTF8()

def _02f_rational.setEncodingUTF8 ( )

Set default enconding to UTF8.

Needed for python 2 CGI.

• Either use python 3, import pango or this dirty hack.

Rationale:

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But CGI with defaultencoding ascii does not accept the latter.

>>> len(’Mês’.encode())

Traceback (most recent call last):

File "<stdin>", line 1, in <module>

UnicodeDecodeError: ’ascii’ codec can’t decode byte 0xc3 in position 1: ordinal not in range(128)

Returns

sys.getdefaultencoding()

http://jonathansoma.com/tutorials//international-data/python-and-utf-8/

Definition at line 96 of file _02f_rational.py.

5.1.3 Variable Documentation

5.1.3.1 CF

_02f_rational.CF = lambda i,n: float(i) / (1-(1+i)∗∗-n)

Coeficiente de financiamento CDC (Crédito Direto ao Consumidor).

Parameters

i taxa mensal.

n período (meses).

Definition at line 194 of file _02f_rational.py.

Referenced by futureValue(), main(), presentValue(), and calcTest.CalcTest.testPriceTable().

5.2 calcTest Namespace Reference

Class for testing the Calculator.

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20 Namespace Documentation

Classes

• class CalcTest

Class for testing certain aspects of the behavior of the calculator.

5.2.1 Detailed Description

Class for testing the Calculator.

Author

Paulo Roma

Since

23/08/2021

https://docs.python.org/2/library/unittest.html

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Class Documentation

6.1 calcTest.CalcTest Class Reference

Class for testing certain aspects of the behavior of the calculator.

Inheritance diagram for calcTest.CalcTest:

calcTest.CalcTest unittest::TestCase

Collaboration diagram for calcTest.CalcTest:

calcTest.CalcTest

unittest::TestCase

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22 Class Documentation

Public Member Functions

• def setUp (self)

setUp is called automatically before every test is executed.

• def testTaxa (self) Test getInterest.

• def testPriceTable (self) Test priceTable.

6.1.1 Detailed Description

Class for testing certain aspects of the behavior of the calculator.

Definition at line 21 of file calcTest.py.

6.1.2 Member Function Documentation

6.1.2.1 setUp()

def calcTest.CalcTest.setUp ( self )

setUp is called automatically before every test is executed.

Definition at line 25 of file calcTest.py.

References _02f_rational.setDownPayment().

6.1.2.2 testPriceTable()

def calcTest.CalcTest.testPriceTable ( self )

Test priceTable.

Definition at line 36 of file calcTest.py.

References _02f_rational.CF, and _02f_rational.priceTable().

6.1.2.3 testTaxa()

def calcTest.CalcTest.testTaxa ( self )

Test getInterest.

Definition at line 29 of file calcTest.py.

The documentation for this class was generated from the following file:

• calcTest.py

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File Documentation

7.1 _02f_rational.py File Reference

Namespaces

• _02f_rational

Desconto Racional por Dentro.

Functions

• def _02f_rational.setDownPayment (dp=True) Set a down payment.

• def _02f_rational.getDownPayment () Get the down payment.

• def _02f_rational.setEncodingUTF8 () Set default enconding to UTF8.

• def _02f_rational.getInterest (x, y, p)

Acha a taxa que produz o preço à vista pelo método de Newton:

• def _02f_rational.getInterest2 (x, y, p)

Acha a taxa que produz o preço à vista pelo método de Newton:

• def _02f_rational.presentValue (x, p, t)

Retorna o fator para atualizar o preço no instante da compra.

• def _02f_rational.futureValue (y, p, t)

Retorna o fator para atualizar o preço no final da compra.

• def _02f_rational.rational_discount (p, t, x, y, option=True) Desconto Racional por Dentro.

• def _02f_rational.priceTable (np, pv, t, pmt)

Retorna a Tabela Price, também chamado de sistema francês de amortização.

• def _02f_rational.printRow (pt, fmt='o') Print a single row of the Price Table.

• def _02f_rational.printTable (pt) Print the Price Table.

• def _02f_rational.main (argv=None)

Programa principal para testes.

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24 File Documentation

Variables

• _02f_rational.CF = lambda i,n: float(i) / (1-(1+i) ∗∗ -n)

Coeficiente de financiamento CDC (Crédito Direto ao Consumidor).

7.2 calcTest.py File Reference

Classes

• class calcTest.CalcTest

Class for testing certain aspects of the behavior of the calculator.

Namespaces

• calcTest

Class for testing the Calculator.

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CF, 19 futureValue, 12 getDownPayment, 12 getInterest, 12 getInterest2, 14 main, 14 presentValue, 15 priceTable, 16 printRow, 17 printTable, 17 rational_discount, 17 setDownPayment, 18 setEncodingUTF8, 18 _02f_rational.py, 23 calcTest, 19

calcTest.CalcTest, 21 setUp, 22 testPriceTable, 22 testTaxa, 22 calcTest.py, 24 CF