def calcPrice(self):
if self.par != None and self.cr != None and self.cy != None:
self.pr = (self.par*self.cr)/self.cy
elif self.par != None and self.cr != None and self.ytm != None:
self.pr = -1*np.pv(0.5*self.ytm, 2.0*self.mat, 0.5*self.par*self.cr, self.par)
print "Bond price = $%.2f" % self.pr
def calculate_bond_price(self):
present_value = np.pv(
rate=self.annual_required_return / self.annual_payment_frequency,
nper=self.term_to_maturity * self.annual_payment_frequency,
pmt=self.semi_annual_coupon_payment,
fv=self.face_value
)
return -0.1 * present_value
def _calc(self):
# shortcut if the portfolio is 0...some of the math
# below doesn't like 0s.
if self.portfolio.value == 0:
return Decimal(0)
amount = pmt(self.rate, self.final_age - self.current_age, self.portfolio.value)
desired_pmt = self.desired_payment * self.cumulative_inflation
desired_value = pv(float(self.rate), self.final_age - self.current_age, float(-desired_pmt), when='begin')
desired_value = Decimal(desired_value)
tilt = (self.portfolio.value / desired_value) ** self.tilt
return amount * tilt
def getFitForN(N):
a = []
for i in range(1, N + 1):
row = []
for j in range(N - 1, -1, -1):
row.append(pow(i, j))
a.append(row)
a = na(a)
b = na([sequence(i) for i in range(1, N + 1)])
coeffs = solve(a, b)
fit = pv(coeffs, N + 1)
return fit
def levelize_costs(self):
if hasattr(self, 'is_levelized'):
inflation = float(cfg.cfgfile.get('case', 'inflation_rate'))
rate = self.cost_of_capital - inflation
if self.is_levelized == 0:
self.values_level = - np.pmt(rate, self.book_life, 1, 0, 'end') * self.values
util.convert_age(self, vintages=self.vintages, years=self.years, attr_from='values_level', attr_to='values_level', reverse=False)
else:
self.values_level = self.values.copy()
util.convert_age(self, vintages=self.vintages, years=self.years, attr_from='values_level', attr_to='values_level', reverse=False)
self.values = np.pv(rate, self.book_life, -1, 0, 'end') * self.values
else:
util.convert_age(self, vintages=self.vintages, years=self.years, reverse=False)
def levelize_costs(self):
if hasattr(self, 'is_levelized'):
inflation = float(cfg.cfgfile.get('case', 'inflation_rate'))
rate = self.cost_of_capital - inflation
if self.is_levelized == 0:
self.values_level = - np.pmt(rate, self.book_life, 1, 0, 'end') * self.values
util.convert_age(self, vintages=self.vintages, years=self.years, attr_from='values_level', attr_to='values_level', reverse=False)
else:
self.values_level = self.values.copy()
util.convert_age(self, vintages=self.vintages, years=self.years, attr_from='values_level', attr_to='values_level', reverse=False)
self.values = np.pv(rate, self.book_life, -1, 0, 'end') * self.values
else:
raise ValueError('Supply Technology id %s needs to indicate whether costs are levelized ' %self.id)
def calc_compounding ( _rate, _periods, _principal, _contribution, _delta, _inflation ) :
in_rate = 0.01 * _rate
in_delta = 0.01 * _delta
in_contrib = -1* _contribution
in_princ = -1* _principal
in_inflation = 0.01* inflation
print("rate %g, periods %g, principal %g, contribution %g, delta %g, inflation %g" %( _rate, _periods, in_princ, in_contrib, _delta, _inflation))
cf1 = np.array([round(np.fv(in_rate, i, in_contrib, in_princ, when='end'),2) for i in range(1,periods+1)])
cf2 = np.array([round(np.fv((in_rate-in_delta), i, in_contrib, in_princ, when='end'),2) for i in range(1,periods+1)])
if _inflation == 0:
return(np.subtract(cf1,cf2))
else:
diff = np.subtract(cf1,cf2)
return np.array([round(np.pv(in_inflation, i, 0, (-1*diff[i])),2) for i in range(_periods)])
def harvest(self):
amount = yield
while True:
# In order to get rid of the memory effect, the parameters to PV
# have to independent of *when* you retire. But they can use current information
# This is just our life expectancy.
nper = max(5, 100 - self.current_age)
#nper = mortality.life_expectancy(self.current_age, None)
# But let's also subtract out however many years worth of bonds
# we currently have. This assumes that bonds keep up with inflation
# which is a dubious proposition...
#nper -= int(self.portfolio.bonds / amount)
# Set a minimum years worth of stock. Pretty arbitrarily chosen...
portfolio_goal = Decimal(-numpy.pv(float(self.rate), nper, float(amount), when='beginning'))
if self.portfolio.stocks >= portfolio_goal:
#import pdb;pdb.set_trace()
#harvest_amount = self.portfolio.stocks - portfolio_goal
harvest_amount = self.portfolio.stocks / 4
self.portfolio.sell_stocks(harvest_amount)
self.portfolio.buy_bonds(harvest_amount)
#print(self.current_age, " ", harvest_amount.to_integral_value(), " ", self.portfolio.stocks.to_integral_value(), "{%d}" % amount)
else:
#print(self.current_age, "[", portfolio_goal.to_integral_value(), "]", self.portfolio.stocks.to_integral_value(), "{%d}" % amount)
pass
amount = min(amount, self.portfolio.value)
amount_bonds = min(amount, self.portfolio.bonds)
amount_stocks = amount - amount_bonds
self.portfolio.sell_bonds(amount_bonds)
self.portfolio.sell_stocks(amount_stocks)
amount = yield self.portfolio.empty_cash()
self.current_age += 1
def test_when(self):
# begin
assert_almost_equal(np.rate(10, 20, -3500, 10000, 1), np.rate(10, 20, -3500, 10000, "begin"), 4)
# end
assert_almost_equal(np.rate(10, 20, -3500, 10000), np.rate(10, 20, -3500, 10000, "end"), 4)
assert_almost_equal(np.rate(10, 20, -3500, 10000, 0), np.rate(10, 20, -3500, 10000, "end"), 4)
# begin
assert_almost_equal(np.pv(0.07, 20, 12000, 0, 1), np.pv(0.07, 20, 12000, 0, "begin"), 2)
# end
assert_almost_equal(np.pv(0.07, 20, 12000, 0), np.pv(0.07, 20, 12000, 0, "end"), 2)
assert_almost_equal(np.pv(0.07, 20, 12000, 0, 0), np.pv(0.07, 20, 12000, 0, "end"), 2)
# begin
assert_almost_equal(np.fv(0.075, 20, -2000, 0, 1), np.fv(0.075, 20, -2000, 0, "begin"), 4)
# end
assert_almost_equal(np.fv(0.075, 20, -2000, 0), np.fv(0.075, 20, -2000, 0, "end"), 4)
assert_almost_equal(np.fv(0.075, 20, -2000, 0, 0), np.fv(0.075, 20, -2000, 0, "end"), 4)
# begin
assert_almost_equal(np.pmt(0.08 / 12, 5 * 12, 15000.0, 0, 1), np.pmt(0.08 / 12, 5 * 12, 15000.0, 0, "begin"), 4)
# end
assert_almost_equal(np.pmt(0.08 / 12, 5 * 12, 15000.0, 0), np.pmt(0.08 / 12, 5 * 12, 15000.0, 0, "end"), 4)
assert_almost_equal(np.pmt(0.08 / 12, 5 * 12, 15000.0, 0, 0), np.pmt(0.08 / 12, 5 * 12, 15000.0, 0, "end"), 4)
# begin
assert_almost_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 1), np.ppmt(0.1 / 12, 1, 60, 55000, 0, "begin"), 4)
# end
assert_almost_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0), np.ppmt(0.1 / 12, 1, 60, 55000, 0, "end"), 4)
assert_almost_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 0), np.ppmt(0.1 / 12, 1, 60, 55000, 0, "end"), 4)
# begin
assert_almost_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 1), np.ipmt(0.1 / 12, 1, 24, 2000, 0, "begin"), 4)
# end
assert_almost_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0), np.ipmt(0.1 / 12, 1, 24, 2000, 0, "end"), 4)
assert_almost_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 0), np.ipmt(0.1 / 12, 1, 24, 2000, 0, "end"), 4)
# begin
assert_almost_equal(np.nper(0.075, -2000, 0, 100000.0, 1), np.nper(0.075, -2000, 0, 100000.0, "begin"), 4)
# end
assert_almost_equal(np.nper(0.075, -2000, 0, 100000.0), np.nper(0.075, -2000, 0, 100000.0, "end"), 4)
assert_almost_equal(np.nper(0.075, -2000, 0, 100000.0, 0), np.nper(0.075, -2000, 0, 100000.0, "end"), 4)
def test_when(self):
# begin
assert_equal(np.rate(10, 20, -3500, 10000, 1),
np.rate(10, 20, -3500, 10000, 'begin'))
# end
assert_equal(np.rate(10, 20, -3500, 10000),
np.rate(10, 20, -3500, 10000, 'end'))
assert_equal(np.rate(10, 20, -3500, 10000, 0),
np.rate(10, 20, -3500, 10000, 'end'))
# begin
assert_equal(np.pv(0.07, 20, 12000, 0, 1),
np.pv(0.07, 20, 12000, 0, 'begin'))
# end
assert_equal(np.pv(0.07, 20, 12000, 0), np.pv(0.07, 20, 12000, 0,
'end'))
assert_equal(np.pv(0.07, 20, 12000, 0, 0),
np.pv(0.07, 20, 12000, 0, 'end'))
# begin
assert_equal(np.fv(0.075, 20, -2000, 0, 1),
np.fv(0.075, 20, -2000, 0, 'begin'))
# end
assert_equal(np.fv(0.075, 20, -2000, 0),
np.fv(0.075, 20, -2000, 0, 'end'))
assert_equal(np.fv(0.075, 20, -2000, 0, 0),
np.fv(0.075, 20, -2000, 0, 'end'))
# begin
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0, 1),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'begin'))
# end
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'end'))
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0, 0),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'end'))
# begin
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 1),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'begin'))
# end
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'end'))
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 0),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'end'))
# begin
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 1),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'begin'))
# end
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'end'))
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 0),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'end'))
# begin
assert_equal(np.nper(0.075, -2000, 0, 100000., 1),
np.nper(0.075, -2000, 0, 100000., 'begin'))
# end
assert_equal(np.nper(0.075, -2000, 0, 100000.),
np.nper(0.075, -2000, 0, 100000., 'end'))
assert_equal(np.nper(0.075, -2000, 0, 100000., 0),
np.nper(0.075, -2000, 0, 100000., 'end'))
def npv_cost(inflation, num_years, cost):
npv = np.pv(inflation, num_years, -cost)
return npv
print("3: The company's current price is", "${:,.2f}".format(PV))
#4
PV = 90
R = 0.1
Dyield = 0.5 * R #the total return on the stock is evenly divided between a capital gains yield and a dividend yield
D1 = PV * Dyield #dividend for next year is the stock price times dividend yield
D0 = D1 / (1 + Dyield) #dividend this year
print("4: The current dividend is", "${:,.2f}".format(D0))
#5
import numpy as np
D = -25 #dividend as pmt
N = 7
I = 0.1
PV = np.pv(rate=I, nper=N, pmt=D)
print("5: The current stock price is", "${:,.2f}".format(PV))
#6
D1 = 1.4
G = 0.06
Ired = 0.089 #the require rate of return for Red company
Iyellow = 0.119 #the require rate of return for Yellow company
Iblue = 0.153 #the require rate of return for Blue company
#a
PRed = D1 / (Ired - G)
print("6a: The stock price for Red Inc., is", "${:,.2f}".format(PRed))
#b
PYellow = D1 / (Iyellow - G)
print("6b: The stock price for Yellow Inc., is", "${:,.2f}".format(PYellow))
#c
import numpy as np print "Present value", np.pv(0.03/4, 5 * 4, -10, 1376.09633204)
def assets_required(self):
rate = self.financial_planning.real_gain()
return numpy.pv(rate, self.duration_of_usufruct,
-self.remain_patrimony * 12)
import numpy as np print(np.fv(0.02, 20 * 12, -100, -100)) print(np.pv(0.02, 20 * 12, -100, 586032.549)) print(np.npv(0.281, [-100, 823, 59, 55, 20])) print(np.pmt(0.02 / 12, 20 * 12, 1000000)) print(np.ppmt(0.02 / 12, -100, 20 * 12, 1000000)) print(np.ipmt(0.02 / 12, 0.001, 20 * 12, 200000)) print(round(np.irr([-5, 10.5, 1, -8, 1]), 5)) print(np.mirr([-100, 823, 59, 55, 20], -100, -150)) print(np.nper(0.02, -1e7, 1e8)) print(np.rate(0.7, -1e8, 200000, 0))
def test_decimal_with_when(self):
"""Test that decimals are still supported if the when argument is passed"""
# begin
assert_equal(
np.rate(
Decimal("10"),
Decimal("20"),
Decimal("-3500"),
Decimal("10000"),
Decimal("1"),
),
np.rate(
Decimal("10"),
Decimal("20"),
Decimal("-3500"),
Decimal("10000"),
"begin",
),
)
# end
assert_equal(
np.rate(Decimal("10"), Decimal("20"), Decimal("-3500"),
Decimal("10000")),
np.rate(Decimal("10"), Decimal("20"), Decimal("-3500"),
Decimal("10000"), "end"),
)
assert_equal(
np.rate(
Decimal("10"),
Decimal("20"),
Decimal("-3500"),
Decimal("10000"),
Decimal("0"),
),
np.rate(Decimal("10"), Decimal("20"), Decimal("-3500"),
Decimal("10000"), "end"),
)
# begin
assert_equal(
np.pv(
Decimal("0.07"),
Decimal("20"),
Decimal("12000"),
Decimal("0"),
Decimal("1"),
),
np.pv(Decimal("0.07"), Decimal("20"), Decimal("12000"),
Decimal("0"), "begin"),
)
# end
assert_equal(
np.pv(Decimal("0.07"), Decimal("20"), Decimal("12000"),
Decimal("0")),
np.pv(Decimal("0.07"), Decimal("20"), Decimal("12000"),
Decimal("0"), "end"),
)
assert_equal(
np.pv(
Decimal("0.07"),
Decimal("20"),
Decimal("12000"),
Decimal("0"),
Decimal("0"),
),
np.pv(Decimal("0.07"), Decimal("20"), Decimal("12000"),
Decimal("0"), "end"),
)
# begin
assert_equal(
np.fv(
Decimal("0.075"),
Decimal("20"),
Decimal("-2000"),
Decimal("0"),
Decimal("1"),
),
np.fv(Decimal("0.075"), Decimal("20"), Decimal("-2000"),
Decimal("0"), "begin"),
)
# end
assert_equal(
np.fv(Decimal("0.075"), Decimal("20"), Decimal("-2000"),
Decimal("0")),
np.fv(Decimal("0.075"), Decimal("20"), Decimal("-2000"),
Decimal("0"), "end"),
)
assert_equal(
np.fv(
Decimal("0.075"),
Decimal("20"),
Decimal("-2000"),
Decimal("0"),
Decimal("0"),
),
np.fv(Decimal("0.075"), Decimal("20"), Decimal("-2000"),
Decimal("0"), "end"),
)
# begin
assert_equal(
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
Decimal("1"),
),
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
"begin",
),
)
# end
assert_equal(
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
),
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
"end",
),
)
assert_equal(
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
Decimal("0"),
),
np.pmt(
Decimal("0.08") / Decimal("12"),
Decimal("5") * Decimal("12"),
Decimal("15000."),
Decimal("0"),
"end",
),
)
# begin
assert_equal(
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
Decimal("1"),
),
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
"begin",
),
)
# end
assert_equal(
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
),
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
"end",
),
)
assert_equal(
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
Decimal("0"),
),
np.ppmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("60"),
Decimal("55000"),
Decimal("0"),
"end",
),
)
# begin
assert_equal(
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
Decimal("1"),
).flat[0],
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
"begin",
).flat[0],
)
# end
assert_equal(
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
).flat[0],
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
"end",
).flat[0],
)
assert_equal(
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
Decimal("0"),
).flat[0],
np.ipmt(
Decimal("0.1") / Decimal("12"),
Decimal("1"),
Decimal("24"),
Decimal("2000"),
Decimal("0"),
"end",
).flat[0],
)
def _calc_mrtg(self, annual_housing_budget, mrtg_int):
pmt = annual_housing_budget / 12
return np.pv(mrtg_int / 12, 360, -pmt)
举例：某用户去银行存款，假设年利率 3% 、每季度续存金额 10 元、存 5年以及存款 1000 ，则计算 5年后可领取多少金额。
求未来钱数
'''
print(np.fv(0.03 / 4, 5 * 4, -10, -1000))
'''
pv 函数 —— 计算现值（ present value present valuepresent value present value present value ）是指资产在当前时刻的价值。
现值有以下 4个参数决定 —— 利率、期数每支付金额以及终值
语法格式如下： 语法格式如下： 语法格式如下： numpy.fv(rate, nper , pmt , fv[, when='end’])
#参数： rate raterate：每一期的利率（ rate of interest）。
nper nper：期数。
pmt ：paymentpayment payment 。每期支付金额
fv ： future value，终值。如果是贷款终值为零
when when：{{‘begin’, 1}, {‘end’, 0}},
2举例：某用户去银行存款，假设年利率 3% 、每季度续存金额 10 元、存 5年后可领 1376.0963320，则计算 5年前存取的本金是多 少金额。
'''
print(np.pv(0.03 / 4, 5 * 4, -10, 1376.0963320407982))
'''
np.npv(rate,values)
rate:折现率
values:现金流
03.投资 100，收入39,59,55,20，折现率为28.1% 则净现值为
'''
print(np.npv(0.281, [-100, 39, 59, 55, 20]))
'''
举例：某同学房贷 20 万，准备 15 年还清，利率为 7.5% 7.5% ，则每 月需还贷多少金额？
pmt = np.pmt(0.075/12, 15*12,200000) 计算还款金额
'''
pmt = np.pmt(0.075 / 12, 15 * 12, 200000)
'''
小明房贷 70 万，年利率 4% ，准备还 20 年，
则每月供多少？
# -*- coding: utf-8 -*-
"""
Created on Wed May 19 20:11:05 2021
@author: Dell Wang
"""
import numpy as np
c=np.array(c)
r=np.array(r)
if when==1:
n=np.arange(1,n+1)
else:
n=np.arange(0,n)
pv=c/(1+r)**n
return pv.sum()
pv1=pv_f(c,r,n,when=1)
print("普通年金现值（年末）：%.2f"% pv1)
pv2=pv_f(c,r,n,when=0)
print("预付年金现值（年初）：%.2f" % pv2)
import numpy as np
print("numpy自带公式计算（年末）：{:.2f}".format(np.pv(r,5,-c),when=0))
print("numpy自带公式计算（年初）：{:.2f}".format(np.pv(r,5,-c,when=1)))
initial = 1500000
interest = .043
time = 10
compounded = 1
#calculate compound interest
fv = initial * (1 + interest / compounded)**(compounded * time)
print('your future of {} value is {}'.format(initial, fv))
# #reverse compound interest, also for inflation
iv = initial / (1 + interest / compounded)**(compounded * time)
print('your initial value was {}'.format(iv))
investment_1 = np.pv(rate=interest, nper=time, pmt=0,
fv=initial) #calculate inflation
print("Investment 1 is worth " + str(round(-investment_1, 2)) +
" in today's dollars")
print('............')
print('............')
home_value = 159375000
loan = 127500000
monthly_payment = 1310401
anual_payment = monthly_payment * 12
duration = 20
total_paid = anual_payment * duration
print(
'loan of {} with monthly payment of 1.310.401 for 20 years for total {}\n which is'
' {:.2f} times what you got'.format(loan, total_paid, total_paid / loan))
# Python # > numpy.pv(rate, nper, pmt, fv=0.0, when='end') # # ## 引数 # * rate (必須): 利率 # * nper (必須): 複利計算期間数 (支払回数) # * pmt (必須): 毎回の支払額 # * fv : 将来価値 (返済の場合: 0, 貯蓄の場合: 積立目標額) # * when: 支払期日、いつ支払いが行われるか。 (end/0: 各期の期末, start/1: 各期の機種) # # ## 利用例 # 年利 5% で 10 年間、毎月 100 ドル支払い、15692.93 ドル積み立て目標での現在価値。 # In[4]: print(np.pv(0.05 / 12, 10 * 12, -100, 15692.93)) # # 正味現在価値 (純現在価値, NPV: Net Present Value) # `np.npv()` にて、正味現在価値を算出します。 # Excel には、NPV 関数として実装されています。 # # ## 使い方 # > numpy.npv(rate, values) # # ## 引数 # * rate (必須): 割引率 # * values (必須): 一連のキャッシュフロー額 # # ## 利用例 # 割引率 28.1% に対して、100 万円の投資と毎年、39, 59, 55, 20 万円の収益が得られた場合の正味現在価値
# Print the results at each period
print("Period " + str(i) + ": Current Investment Balance: " + \
str(round(investment_portfolio[i], 2)) + \
" | Savings Account: " + str(round(cumulative_savings_new[i], 2)) + \
" | Net Worth: " + str(round(net_worth[i], 2)) \
)
# Plot your forecasted cumulative savings vs investments and net worth
plt.figure()
plt.plot(investment_portfolio, color='red', label='investment portfolio')
plt.plot(cumulative_savings_new, color='blue', label='cumulative savings new')
plt.plot(net_worth, color='green', label='net worth')
plt.legend(loc=2)
plt.show()
# Set your future net worth
future_net_worth = 900000
# Set the annual inflation rate to 2.5%
annual_inflation = 0.025
# Calculate the present value of your terminal wealth over 15 years
inflation_adjusted_net_worth = np.pv(rate=annual_inflation,
nper=15,
pmt=0,
fv=-1 * future_net_worth)
print("Your inflation-adjusted net worth: $" +
str(round(inflation_adjusted_net_worth, 2)))
#plt.close('all')
def test_pv_decimal(self):
assert_equal(
np.pv(Decimal("0.07"), Decimal("20"), Decimal("12000"),
Decimal("0")),
Decimal("-127128.1709461939327295222005"),
)
def test_pv(self):
assert_almost_equal(np.pv(0.07, 20, 12000, 0), -127128.17, 2)
@author: ESAccount24
"""
# -*- coding: utf-8 -*-
"""
Created on Sat Sep 26 11:34:21 2015
@author: ESAccount24
"""
#financial institutions
import numpy as np
import scipy.optimize as sp
def myfnc(x):
return np.pv(x,2,0,125.44)+100.0
futval=np.fv(0.12,2,0,-100.0)
print futval
prval=np.pv(0.12,2,0,125.44)
print prval
nperiods=np.nper(0.12,0,-100.0,125.44)
print nperiods
intrate=np.rate(2,0,-100,125.44)
print intrate
initialRateGuess=0.134
#goalseek
#find interest rate that satisfies euqation connecting pv, fv, and nper
print sp.fsolve(myfnc,initialRateGuess)
def test_pv(self):
assert_almost_equal(np.pv(.10, 12, -100, 100), 649.51, 2)
import numpy as np np.pv(0.05 / 12, 10 * 12, -100, 15692.93) a = np.array((0.05, 0.04, 0.03)) / 12 np.pv(a, 10 * 12, -100, 15692.93)
def Present_Value():
a = np.pv(eval(e1.get()), eval(e2.get()), eval(e3.get()),
eval(e4.get()))
a = 0 - a
v1.set(a)
def loanCal(self):
nPeriod12 = self.durationCal() * 12 #loan duration in months
return abs(np.pv(0.02/12, nPeriod12, self.pmtCal(), fv=0, when = 'end'))
# The purpose of this program is to evaluate the best decision between three options
# The decision considers a 5 year term with a $10,000 residual future state value
# Option 1: Purchase a car outright using an interest rate pegged to a mortage rate
# Option 2: Use a novated lease for a one year term
# Option 3: Use a novated lease for a two year term
# import appropriate packages
import numpy as np
# Key parameters
purchase_price_GST = 40000 # inclusive of GST
residual_value = 10000 # value of vehicle after 10 years (estimated)
lease_price_NOGST = 36000
mortgate_int = 0.05 / 12
periods = 5 * 12
lease_costs_1 = np.array([350, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
lease_costs_2 = np.array(
[350, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
# Calculate the NPV of purchasing the car outright
option_1 = np.pv(rate=mortgate_int, nper=periods, pmt=0, fv=residual_value)
print("Option 1 is worth " + str(round(-option_1, 2)) + " in today's dollars")
def do_proforma(proposal, proposal_component):
p = proposal
c = proposal_component
max_periods = max_periods_of_sale + asscalar(p['sales_start_period'])
revenues = zeros(max_periods)
costs = zeros(max_periods)
#cash_flow = zeros(max_periods)
construction_loan_balance = p['construction_cost'] * construction_loan_size
perm_loan_size = 0
perm_loan_interest_payment = 0
perm_loan_repayment = 0
perm_loan_proceeds = 0.0
full_rent_periods = 0
sold_for_rent = 0
component_sales_revenue = c['sales_revenue'].copy()
component_rent_revenue = c['rent_revenue_per_period'].copy()
component_leases_revenue = c['leases_revenue_per_period'].copy()
construction_periods = p['sales_start_period'] - p['construction_start_period']
for period in arange(max_periods):
if period == 1:
land_equity = p['land_cost']
costs[period] += land_equity
elif component_rent_revenue.sum() >= c['rent_revenue'].sum() and \
component_leases_revenue.sum() >= c['leases_revenue'].sum():
full_rent_periods += 1
if period < p['sales_start_period']:
#revenues
public_contribution = 0 if p['public_contribution'] == 0 \
else p['public_contribution'] / \
float(construction_periods)
sales_revenue = 0
rent_revenue = 0
leases_revenue = 0
revenues[period] += public_contribution
#costs
operating_cost = 0
vacancy = 0
tax = p['property_tax'] * p['land_cost']
construction_equity = p['construction_cost'] * (1 - construction_loan_size) \
/ (p['sales_start_period'] - 1)
construction_loan_interest_payment = construction_loan_balance * construction_loan_rate
construction_loan_repayment = revenues[period] \
if construction_loan_balance > revenues[period] \
else construction_loan_balance
costs[period] += tax + construction_equity + \
construction_loan_interest_payment + construction_loan_repayment
construction_loan_balance -= construction_loan_repayment
else:
if any(component_sales_revenue):
# TODO this would not work when we do proforma on multiple proposals at once
sales_revenue = np.min(column_stack((c['sales_absorption'],
component_sales_revenue)),
axis=1
).sum()
component_sales_revenue -= c['sales_absorption']
np.clip(component_sales_revenue,
0, component_sales_revenue.max(),
out=component_sales_revenue)
else:
sales_revenue = 0
if sales_revenue < 0: sales_revenue = 0
# before reaching full occupancy for rent property
if not sold_for_rent and any(component_rent_revenue <= c['rent_revenue']):
rent_revenue = np.min(column_stack((c['rent_revenue'],
component_rent_revenue)),
axis=1
)
operating_cost = (rent_revenue * c['operating_cost']).sum()
vacancy = (rent_revenue * c['vacancy_rates']).sum()
rent_revenue = rent_revenue.sum()
component_rent_revenue += c['rent_revenue_per_period']
np.clip(component_rent_revenue,
0, c['rent_revenue'],
out=component_rent_revenue)
if not sold_for_rent and any(component_leases_revenue <= c['leases_revenue']):
leases_revenue = np.min(column_stack((c['leases_revenue'],
component_leases_revenue)),
axis=1
)
operating_cost += (leases_revenue * c['operating_cost']).sum()
vacancy += (leases_revenue * c['vacancy_rates']).sum()
leases_revenue = leases_revenue.sum()
component_leases_revenue += c['leases_revenue_per_period']
np.clip(component_leases_revenue,
0, c['leases_revenue'],
out=component_leases_revenue)
#revenues
if not sold_for_rent:
revenues[period] += sales_revenue + rent_revenue + leases_revenue
else:
revenues[period] = sales_revenue
if revenues[period] == 0:
break
#costs
taxable_proportion = p['rent_sqft'] / p['total_sqft'].astype(float32)
tax = p['property_tax'] * (p['land_cost'] + p['construction_cost']) * taxable_proportion
insurance = p['rent_sqft'] * property_insurance
construction_equity = 0
construction_loan_interest_payment = construction_loan_balance * construction_loan_rate
construction_loan_repayment = revenues[period] \
if construction_loan_balance > revenues[period] \
else construction_loan_balance
#adjustment to revenues/costs
for_rent_noi = rent_revenue + leases_revenue - tax - insurance - operating_cost - vacancy
meets_perm_load_occupancy_threshold = rent_revenue + leases_revenue > \
( p['rent_revenue'] + p['leases_revenue']) * \
perm_load_occupancy_threshold
if perm_loan_size == 0 and \
for_rent_noi > 0 and \
meets_perm_load_occupancy_threshold:
perm_loan_size = min((for_rent_noi / cap_rate) * ltv_max,
-np.pv(perm_loan_rate,
perm_loan_term,
for_rent_noi / dcr_max)
)
perm_loan_proceeds = perm_loan_size
revenues[period] += perm_loan_proceeds
if perm_loan_size > 0:
perm_loan_interest_payment = -np.pmt(perm_loan_rate, perm_loan_term, perm_loan_size)
if not sold_for_rent:
costs[period] += tax + insurance + operating_cost + vacancy + \
construction_loan_interest_payment + construction_loan_repayment + \
perm_loan_interest_payment
else:
costs[period] = 0
construction_loan_balance -= construction_loan_repayment
if DEBUG: print period, sales_revenue, full_rent_periods, for_rent_seasoning_threshold
if full_rent_periods > for_rent_seasoning_threshold+1 and \
sales_revenue <= 0 and \
not sold_for_rent:
#sell_for_rent = 1
perm_loan_repayment = perm_loan_size
for_rent_sale = for_rent_noi / cap_rate
revenues[period] += for_rent_sale
costs[period] += perm_loan_repayment
sold_for_rent = 1
#break
if DEBUG: print "REVENUES:", revenues
costs = costs * (1.0-p['costdiscount'])
if DEBUG: print "COSTS:", costs
cash_flow = (revenues - costs)[1:period]
npv = np.npv(discount_rate, cash_flow)
if DEBUG: print "CASHFLOW:", cash_flow
if DEBUG: print "NPV:", npv
irr = np.irr(cash_flow)
return asarray(npv)
print("\n0.PV\n1.FV\n2.Rate\n3.N\n4.PMT")
choice = input("\nChoose what solve to for: ")
if(choice=="0"):
print("\nEnter values as prompted")
print("Enter interest rate as decimal")
n = input("\nEnter times compounded: ")
rate = input("\nEnter rate as decimal: ")
fv = input("\nEnter FV: ")
pmt = input("\nEnter Pmt: ")
time_range = input("\nEnter number of years: ")
if(float(time_range)==0 or float(time_range)<0):
print("\nError: Must be a minimum of 1 year")
else:
pv=np.pv(float(rate)/float(n), float(time_range)*float(n), float(pmt), float(fv))
print("PV: "+str(pv))
elif(choice=="1"):
print("\nEnter values as prompted")
print("Enter interest rate as decimal")
n = input("\nEnter times compounded: ")
rate = input("\nEnter rate as decimal: ")
pv = input("\nEnter PV: ")
pmt = input("\nEnter Pmt: ")
time_range = input("\nEnter number of years: ")
if(float(time_range)==0 or float(time_range)<0):
print("\nError: Must be a minimum of 1 year")
else:
fv=np.fv(float(rate)/float(n), float(time_range)*float(n), float(pmt), float(pv))
print("FV: "+str(fv))
import numpy as np # 终值 = np.fv(利率, 期数, 每期支付, 现值) # 将1000元以1%的年利率存入银行5年，每年加存100元， # 到期后本息合计多少钱？ fv = np.fv(0.01, 5, -00, -1000000) print(round(fv, 2)) # 现值 = np.pv(利率, 期数, 每期支付, 终值) # 将多少钱以1%的年利率存入银行5年，每年加存100元， # 到期后本息合计fv元？ pv = np.pv(0.01, 5, -100, fv) print(pv) # 净现值 = np.npv(利率, 现金流) # 将1000元以1%的年利率存入银行5年，每年加存100元， # 相当于一次性存入多少钱？ npv = np.npv(0.01, [-1000, -100, -100, -100, -100, -100]) print(round(npv, 2)) fv = np.fv(0.01, 5, 0, npv) print(round(fv, 2)) # 内部收益率 = np.irr(现金流) # 将1000元存入银行5年，以后逐年提现100元、200元、 # 300元、400元、500元，银行利率达到多少，可在最后 # 一次提现后偿清全部本息，即净现值为0元？ irr = np.irr([-1000, 100, 200, 300, 400, 500]) print(round(irr, 2)) npv = np.npv(irr, [-1000, 100, 200, 300, 400, 500]) print(npv) # 每期支付 = np.pmt(利率, 期数, 现值) # 以1%的年利率从银行贷款1000元，分5年还清， # 平均每年还多少钱？ pmt = np.pmt(0.01, 5, 1000000) print(round(pmt, 2))
Näide 2
Kui suur peab olema investeeringu hetkeväärtus, et 10 aasta päras oleks
kogunenud 14485.09€, kui aastane intressimäär on 3.5% ning me lisame
investeeringule iga kuu 100€? Kui suur peab olema alginvesteering, et selline
summa koguneks 5, 6, 7, 8 või 9 aastaga?
------------------------------------------------------------------------------
"""
print("\nNäide 2\n-------\n")
RATE = 0.035 / 12 # 3.5% aastas, 3.5%/12 perioodis
PERIOD = 10*12 # 10 aastat
PAYMENT = -100 # maksame 100€ kuus, '-' tähendab raha väljavoolu
FV = 14485.09 # soovitud tulemus
PRESENT_VALUE = np.pv(RATE, PERIOD, PAYMENT, FV, when='end')
print("Et toota {0}€, peaks investeeringu hetkeväärtus olema {1:.2f}€."
.format(FV, -PRESENT_VALUE) # '-' tähistab väljaminekut
)
PERIODS = np.array([5, 6, 7, 8, 9])
PRESENT_VALUES = np.pv(RATE, PERIODS*12, PAYMENT, FV, when='end')
for period, pv in zip(PERIODS, PRESENT_VALUES):
print("{0} aasta korral peaks investeeringu hetkeväärtus olema {1:.2f}€."
.format(period, -pv) # '-' tähistab väljaminekut
)
"""
------------------------------------------------------------------------------
nper (net present value) -- perioodiliste maksete arvu arvutamine
nper(rate, pmt, pv, fv=0, when='end')
def test_pv(self):
assert_almost_equal(np.pv(.10,12,-100,100), 649.51, 2)
def get_required_portfolio(self):
amount = self.current_rate * self.portfolio.value
pv = numpy.pv(float(self.get_rate()), self.get_life_expectancy(), float(-amount), when='beginning')
return Decimal(pv)
def tvmm(pval=None,
fval=None,
pmt=None,
nrate=None,
nper=None,
due=0,
pyr=1,
noprint=True):
"""Computes the missing argument (set to ``None``) in a model relating the
present value, the future value, the periodic payment, the number of
compounding periods and the nominal interest rate in a cashflow.
Args:
pval (float, list): Present value.
fval (float, list): Future value.
pmt (float, list): Periodic payment.
nrate (float, list): Nominal interest rate per year.
nper (int, list): Number of compounding periods.
due (int): When payments are due.
pyr (int, list): number of periods per year.
noprint (bool): prints enhanced output
Returns:
Argument set to None in the function call.
**Details**
The ``tvmmm`` function computes and returns the missing value (``pmt``, ``fval``,
``pval``, ``nper``, ``nrate``) in a model relating a finite sequence of payments
made at the beginning or at the end of each period, a present value, a future value,
and a nominal interest rate. The time intervals between consecutive payments are
assumed to be equal. For internal computations, the effective interest rate per
period is calculated as ``nrate / pyr``.
**Examples**
This example shows how to find different values for a loan of 5000, with a
monthly payment of 130 at the end of the month, a life of 48 periods, and a
interest rate of 0.94 per month (equivalent to a nominal interest
rate of 11.32%). For a loan, the future value is 0.
* Monthly payments: Note that the parameter ``pmt`` is set to ``None``.
>>> tvmm(pval=5000, nrate=11.32, nper=48, fval=0, pyr=12) # doctest: +ELLIPSIS
-130.00...
When the parameter ``noprint`` is set to ``False``, a user friendly table with
the data computed by the function is print.
>>> tvmm(pval=5000, nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) # doctest: +ELLIPSIS
Present Value: ....... 5000.00
Future Value: ........ 0.00
Payment: ............. -130.01
Due: ................. END
No. of Periods: ...... 48.00
Compoundings per Year: 12
Nominal Rate: ....... 11.32
Effective Rate: ..... 11.93
Periodic Rate: ...... 0.94
* Future value:
>>> tvmm(pval=5000, nrate=11.32, nper=48, pmt=pmt, fval=None, pyr=12) # doctest: +ELLIPSIS
-0.0...
* Present value:
>>> tvmm(nrate=11.32, nper=48, pmt=pmt, fval = 0.0, pval=None, pyr=12) # doctest: +ELLIPSIS
5000...
All the arguments support lists as inputs. When a argument is a list and the
``noprint`` is set to ``False``, a table with the data is print.
>>> tvmm(pval=[5, 500, 5], nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) # doctest: +ELLIPSIS
# pval fval pmt nper nrate erate prate due
------------------------------------------------------
0 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
1 500.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
2 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
* Interest rate:
>>> tvmm(pval=5000, nper=48, pmt=pmt, fval = 0.0, pyr=12) # doctest: +ELLIPSIS
11.32...
* Number of periods:
>>> tvmm(pval=5000, nrate=11.32/12, pmt=pmt, fval=0.0) # doctest: +ELLIPSIS
48.0...
"""
#pylint: disable=too-many-arguments
#pylint: disable=too-many-branches
numnone = 0
numnone += 1 if pval is None else 0
numnone += 1 if fval is None else 0
numnone += 1 if nper is None else 0
numnone += 1 if pmt is None else 0
numnone += 1 if nrate is None else 0
if numnone > 1:
raise ValueError('One of the params must be set to None')
if numnone == 0:
pmt = None
if pmt == 0.0:
pmt = 0.0000001
nrate = numpy.array(nrate)
if pval is None:
result = numpy.pv(rate=nrate / 100 / pyr,
nper=nper,
fv=fval,
pmt=pmt,
when=due)
elif fval is None:
result = numpy.fv(rate=nrate / 100 / pyr,
nper=nper,
pv=pval,
pmt=pmt,
when=due)
elif nper is None:
result = numpy.nper(rate=nrate / 100 / pyr,
pv=pval,
fv=fval,
pmt=pmt,
when=due)
elif pmt is None:
result = numpy.pmt(rate=nrate / 100 / pyr,
nper=nper,
pv=pval,
fv=fval,
when=due)
else:
result = numpy.rate(pv=pval, nper=nper, fv=fval, pmt=pmt,
when=due) * 100 * pyr
if noprint is True:
if isinstance(result, numpy.ndarray):
return result.tolist()
return result
nrate = nrate.tolist()
if pval is None:
pval = result
elif fval is None:
fval = result
elif nper is None:
nper = result
elif pmt is None:
pmt = result
else:
nrate = result
params = _vars2list([pval, fval, nper, pmt, nrate])
pval = params[0]
fval = params[1]
nper = params[2]
pmt = params[3]
nrate = params[4]
# raise ValueError(nrate.__repr__())
erate, prate = iconv(nrate=nrate, pyr=pyr)
if len(pval) == 1:
if pval is not None:
print('Present Value: ....... {:8.2f}'.format(pval[0]))
if fval is not None:
print('Future Value: ........ {:8.2f}'.format(fval[0]))
if pmt is not None:
print('Payment: ............. {:8.2f}'.format(pmt[0]))
if due is not None:
print('Due: ................. {:s}'.format('END' if due ==
0 else 'BEG'))
print('No. of Periods: ...... {:8.2f}'.format(nper[0]))
print('Compoundings per Year: {:>5d}'.format(pyr))
print('Nominal Rate: ....... {:8.2f}'.format(nrate[0]))
print('Effective Rate: ..... {:8.2f}'.format(erate))
print('Periodic Rate: ...... {:8.2f}'.format(prate))
else:
if due == 0:
sdue = 'END'
txtpmt = []
for item, _ in enumerate(pval):
txtpmt.append(pmt[item][-1])
else:
sdue = 'BEG'
txtpmt = []
for item, _ in enumerate(pval):
txtpmt.append(pmt[item][0])
maxlen = 5
for value1, value2, value3, value4 in zip(pval, fval, txtpmt, nper):
maxlen = max(maxlen, len('{:1.2f}'.format(value1)))
maxlen = max(maxlen, len('{:1.2f}'.format(value2)))
maxlen = max(maxlen, len('{:1.2f}'.format(value3)))
maxlen = max(maxlen, len('{:1.2f}'.format(value4)))
len_aux = len('{:d}'.format(len(pval)))
fmt_num = ' {:' + '{:d}'.format(maxlen) + '.2f}'
fmt_num = '{:<' + '{:d}'.format(
len_aux) + 'd}' + fmt_num * 7 + ' {:3s}'
# fmt_shr = '{:' + '{:d}'.format(len_aux) + 's}'
fmt_hdr = ' {:>' + '{:d}'.format(maxlen) + 's}'
fmt_hdr = '{:' + '{:d}'.format(len_aux) + 's}' + fmt_hdr * 7 + ' due'
txt = fmt_hdr.format('#', 'pval', 'fval', 'pmt', 'nper', 'nrate',
'erate', 'prate')
print(txt)
print('-' * len_aux + '-' * maxlen * 7 + '-' * 7 + '----')
for item, _ in enumerate(pval):
print(
fmt_num.format(item, pval[item], fval[item], txtpmt[item],
nper[item], nrate[item], erate[item],
prate[item], sdue))
def main():
# Sweep over
# (cost per flight w/ 1st stage reuse)
# / (cost per flight of all-expendable launch vehicle)
# [units: dimensionless].
# Figure format switch - paper or presentation?
fig_format = 'presentation'
if fig_format == 'presentation':
fontsize = 14
if fig_format == 'paper':
fontsize = 17
cpf_ratio = np.linspace(0, 1)
# Launch rate [units: year**-1].
launch_rates = [1, 5, 10, 20, 40]
# Discount rate (per year)
discount_rate_annual = 0.20
# Horizon [units: year].
horizon = 20
# Present value of savings from reuse
# [units: multiples of (cost per flight of all-expendable launch vehicle)]
pres_val = np.zeros(len(cpf_ratio))
plt.figure(figsize=(8, 6))
for launch_rate in launch_rates:
# Discount rate per "payment period", i.e. per
# interval between launches.
discount_rate_per_period = discount_rate_annual / launch_rate
for i in range(len(cpf_ratio)):
pres_val[i] = np.pv(
rate=discount_rate_per_period,
nper=launch_rate * horizon,
pmt=cpf_ratio[i] - 1,
when='begin',
)
plt.plot(cpf_ratio, pres_val, label='{:.0f}'.format(launch_rate))
# Highlight credible range of cpf ratio
# These ranges were computed by lvreuse.analysis.combined.cost_ratio.py,
# https://github.mit.edu/mvernacc/1st-stage-return/blob/1d0a2a4421405421b4fb6cac9cb14ff232de4fd0/lvreuse/analysis/combined/cost_ratio.py
# For downrange propulsive landing, LEO mission, kerosene technology.
# For medium-heavy launch vehicles (10 to 100 Mg payload to LEO)
plt.axvspan(xmin=0.39, xmax=0.68, color='green', alpha=0.1)
# For small lauch vehicles (100 kg to LEO)
plt.axvspan(xmin=0.80, xmax=0.96, color='green', alpha=0.1)
# Highlight credible range of dev costs
# e.g. for a eelv-size vehicle, cpf is likely $50M, and
# reusability development probably costs $400M to $3B
# so credible range is 8 to 60
# Sources:
# Low bound on dev cost: https://www.nasa.gov/sites/default/files/files/Section403(b)CommercialMarketAssessmentReportFinal.pdf
# High bound on dev cost: guess at Blue Origin dev. spending based on J. Bezos'
# sales of Amazon stock.
plt.axhspan(ymin=8, ymax=60, color='grey', alpha=0.2)
plt.xlim([0, 1])
plt.ylim([0, 100])
plt.xticks(fontsize=0.8 * fontsize)
plt.yticks(fontsize=0.8 * fontsize)
plt.xlabel('Cost p.f. w/ 1st stage reuse / cost p.f. expendable [-]',
fontsize=fontsize)
plt.ylabel('Present value of savings / cost p.f. expendable [-]',
fontsize=fontsize)
plt.title('Present value of reuse cost per flight savings' +
'\n {:.0f} %/year discount rate, {:.0f} year horizon'.format(
discount_rate_annual * 100, horizon),
fontsize=fontsize)
plt.tight_layout()
plt.savefig(os.path.join('plots', 'reuse_npv.png'), dpi=200)
plt.legend(title='Launch rate / year', fontsize=0.8 * fontsize)
plt.show()
def test_decimal_with_when(self):
"""Test that decimals are still supported if the when argument is passed"""
# begin
assert_equal(
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000'), Decimal('1')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000'), 'begin'))
# end
assert_equal(
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000'), 'end'))
assert_equal(
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000'), Decimal('0')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'),
Decimal('10000'), 'end'))
# begin
assert_equal(
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0'), Decimal('1')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0'), 'begin'))
# end
assert_equal(
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0'), 'end'))
assert_equal(
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0'), Decimal('0')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0'), 'end'))
# begin
assert_equal(
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0'), Decimal('1')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0'), 'begin'))
# end
assert_equal(
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0'), 'end'))
assert_equal(
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0'), Decimal('0')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'),
Decimal('0'), 'end'))
# begin
assert_equal(
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0'),
Decimal('1')),
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0'),
'begin'))
# end
assert_equal(
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0')),
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0'),
'end'))
assert_equal(
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0'),
Decimal('0')),
np.pmt(
Decimal('0.08') / Decimal('12'),
Decimal('5') * Decimal('12'), Decimal('15000.'), Decimal('0'),
'end'))
# begin
assert_equal(
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0'), Decimal('1')),
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0'), 'begin'))
# end
assert_equal(
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0')),
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0'), 'end'))
assert_equal(
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0'), Decimal('0')),
np.ppmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'),
Decimal('55000'), Decimal('0'), 'end'))
# begin
assert_equal(
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0'), Decimal('1')).flat[0],
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0'), 'begin').flat[0])
# end
assert_equal(
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0')).flat[0],
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0'), 'end').flat[0])
assert_equal(
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0'), Decimal('0')).flat[0],
np.ipmt(
Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'),
Decimal('2000'), Decimal('0'), 'end').flat[0])
def test_when(self):
# begin
assert_equal(np.rate(10, 20, -3500, 10000, 1),
np.rate(10, 20, -3500, 10000, 'begin'))
# end
assert_equal(np.rate(10, 20, -3500, 10000),
np.rate(10, 20, -3500, 10000, 'end'))
assert_equal(np.rate(10, 20, -3500, 10000, 0),
np.rate(10, 20, -3500, 10000, 'end'))
# begin
assert_equal(np.pv(0.07, 20, 12000, 0, 1),
np.pv(0.07, 20, 12000, 0, 'begin'))
# end
assert_equal(np.pv(0.07, 20, 12000, 0),
np.pv(0.07, 20, 12000, 0, 'end'))
assert_equal(np.pv(0.07, 20, 12000, 0, 0),
np.pv(0.07, 20, 12000, 0, 'end'))
# begin
assert_equal(np.fv(0.075, 20, -2000, 0, 1),
np.fv(0.075, 20, -2000, 0, 'begin'))
# end
assert_equal(np.fv(0.075, 20, -2000, 0),
np.fv(0.075, 20, -2000, 0, 'end'))
assert_equal(np.fv(0.075, 20, -2000, 0, 0),
np.fv(0.075, 20, -2000, 0, 'end'))
# begin
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0, 1),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'begin'))
# end
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'end'))
assert_equal(np.pmt(0.08 / 12, 5 * 12, 15000., 0, 0),
np.pmt(0.08 / 12, 5 * 12, 15000., 0, 'end'))
# begin
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 1),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'begin'))
# end
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'end'))
assert_equal(np.ppmt(0.1 / 12, 1, 60, 55000, 0, 0),
np.ppmt(0.1 / 12, 1, 60, 55000, 0, 'end'))
# begin
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 1),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'begin'))
# end
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'end'))
assert_equal(np.ipmt(0.1 / 12, 1, 24, 2000, 0, 0),
np.ipmt(0.1 / 12, 1, 24, 2000, 0, 'end'))
# begin
assert_equal(np.nper(0.075, -2000, 0, 100000., 1),
np.nper(0.075, -2000, 0, 100000., 'begin'))
# end
assert_equal(np.nper(0.075, -2000, 0, 100000.),
np.nper(0.075, -2000, 0, 100000., 'end'))
assert_equal(np.nper(0.075, -2000, 0, 100000., 0),
np.nper(0.075, -2000, 0, 100000., 'end'))
def test_pv_decimal(self):
assert_equal(
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'),
Decimal('0')), Decimal('-127128.1709461939327295222005'))
def test_pv_decimal(self):
assert_equal(np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0')),
Decimal('-127128.1709461939327295222005'))
def myfnc(x):
return np.pv(x,2,0,125.44)+100.0
import numpy as np
# Calculate investment_1
investment_1 = np.fv(rate=0.08, nper=10, pmt=0, pv=-10000)
print("Investment 1 will yield a total of $" + str(round(investment_1, 2)) +
" in 10 years")
# Calculate investment_2
investment_1_discounted = np.pv(rate=0.03, nper=10, pmt=0, fv=investment_1)
print("After adjusting for inflation, investment 1 is worth $" +
str(round(-investment_1_discounted, 2)) + " in today's dollars")
def desired_cash(self):
return np.pv(self.interest, self.years_in_retire,
-self.annual_spend_retire, 0)
def tvmm(pval=None,
fval=None,
pmt=None,
nrate=None,
nper=None,
due=0,
pyr=1,
noprint=True):
"""Computes present and future values, interest rate and number
of periods.
Args:
pval (float, list): Present value.
fval (float, list): Future value.
pmt (float, list): Periodic payment.
nrate (float, list): Nominal rate per year.
nper (int, list): Number of compounding periods.
due (int): When payments are due.
pyr (int, list): number of periods per year.
noprint (bool): prints enhanced output
Returns:
Argument set to None in the function call.
Effective interest rate per period is calculated as `nrate` / `pyr`.
>>> tvmm(pval=5000, nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) # doctest: +ELLIPSIS
Present Value: ....... 5000.00
Future Value: ........ 0.00
Payment: ............. -130.01
Due: ................. END
No. of Periods: ...... 48.00
Compoundings per Year: 12
Nominal Rate: ....... 11.32
Effective Rate: ..... 11.93
Periodic Rate: ...... 0.94
>>> tvmm(pval=[5, 500, 5], nrate=11.32, nper=48, fval=0, pyr=12, noprint=False) # doctest: +ELLIPSIS
# pval fval pmt nper nrate erate prate due
------------------------------------------------------
0 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
1 500.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
2 5.00 0.00 -0.13 48.00 11.32 11.93 0.94 END
"""
#pylint: disable=too-many-arguments
#pylint: disable=too-many-branches
numnone = 0
numnone += 1 if pval is None else 0
numnone += 1 if fval is None else 0
numnone += 1 if nper is None else 0
numnone += 1 if pmt is None else 0
numnone += 1 if nrate is None else 0
if numnone > 1:
raise ValueError('One of the params must be set to None')
if numnone == 0:
pmt = None
if pmt == 0.0:
pmt = 0.0000001
nrate = numpy.array(nrate)
if pval is None:
result = numpy.pv(rate=nrate / 100 / pyr,
nper=nper,
fv=fval,
pmt=pmt,
when=due)
elif fval is None:
result = numpy.fv(rate=nrate / 100 / pyr,
nper=nper,
pv=pval,
pmt=pmt,
when=due)
elif nper is None:
result = numpy.nper(rate=nrate / 100 / pyr,
pv=pval,
fv=fval,
pmt=pmt,
when=due)
elif pmt is None:
result = numpy.pmt(rate=nrate / 100 / pyr,
nper=nper,
pv=pval,
fv=fval,
when=due)
else:
result = numpy.rate(pv=pval, nper=nper, fv=fval, pmt=pmt,
when=due) * 100 * pyr
if noprint is True:
if isinstance(result, numpy.ndarray):
return result.tolist()
return result
nrate = nrate.tolist()
if pval is None:
pval = result
elif fval is None:
fval = result
elif nper is None:
nper = result
elif pmt is None:
pmt = result
else:
nrate = result
params = vars2list([pval, fval, nper, pmt, nrate])
pval = params[0]
fval = params[1]
nper = params[2]
pmt = params[3]
nrate = params[4]
# raise ValueError(nrate.__repr__())
erate, prate = iconv(nrate=nrate, pyr=pyr)
if len(pval) == 1:
if pval is not None:
print('Present Value: ....... {:8.2f}'.format(pval[0]))
if fval is not None:
print('Future Value: ........ {:8.2f}'.format(fval[0]))
if pmt is not None:
print('Payment: ............. {:8.2f}'.format(pmt[0]))
if due is not None:
print('Due: ................. {:s}'.format('END' if due ==
0 else 'BEG'))
print('No. of Periods: ...... {:8.2f}'.format(nper[0]))
print('Compoundings per Year: {:>5d}'.format(pyr))
print('Nominal Rate: ....... {:8.2f}'.format(nrate[0]))
print('Effective Rate: ..... {:8.2f}'.format(erate))
print('Periodic Rate: ...... {:8.2f}'.format(prate))
else:
if due == 0:
sdue = 'END'
txtpmt = []
for item, _ in enumerate(pval):
txtpmt.append(pmt[item][-1])
else:
sdue = 'BEG'
txtpmt = []
for item, _ in enumerate(pval):
txtpmt.append(pmt[item][0])
maxlen = 5
for value1, value2, value3, value4 in zip(pval, fval, txtpmt, nper):
maxlen = max(maxlen, len('{:1.2f}'.format(value1)))
maxlen = max(maxlen, len('{:1.2f}'.format(value2)))
maxlen = max(maxlen, len('{:1.2f}'.format(value3)))
maxlen = max(maxlen, len('{:1.2f}'.format(value4)))
len_aux = len('{:d}'.format(len(pval)))
fmt_num = ' {:' + '{:d}'.format(maxlen) + '.2f}'
fmt_num = '{:<' + '{:d}'.format(
len_aux) + 'd}' + fmt_num * 7 + ' {:3s}'
# fmt_shr = '{:' + '{:d}'.format(len_aux) + 's}'
fmt_hdr = ' {:>' + '{:d}'.format(maxlen) + 's}'
fmt_hdr = '{:' + '{:d}'.format(len_aux) + 's}' + fmt_hdr * 7 + ' due'
txt = fmt_hdr.format('#', 'pval', 'fval', 'pmt', 'nper', 'nrate',
'erate', 'prate')
print(txt)
print('-' * len_aux + '-' * maxlen * 7 + '-' * 7 + '----')
for item, _ in enumerate(pval):
print(
fmt_num.format(item, pval[item], fval[item], txtpmt[item],
nper[item], nrate[item], erate[item],
prate[item], sdue))
# 时间点的价值。 # pv函数计算现值（present value），即金融资产当前的价值。 # npv函数返回的是净现值（net present value），即按折现率计算的净现金流之和。 # pmt函数根据本金和利率计算每期需支付的金额。 # irr函数计算内部收益率（internal rate of return）。内部收益率是是净现值为0时的有效利 # 率，不考虑通胀因素。 # mirr函数计算修正后内部收益率（modified internal rate of return），是内部收益率的改进 # 版本。 # nper函数计算定期付款的期数。 # rate函数计算利率（rate of interest）。 print u"终值" #fv函数参数为利率，参数，每期支付金额，现值 print "Future value",np.fv(0.03/4, 5*4,-10,1000) print u"现值" #pv函数参数为利率，参数，每期支付金额，终值 print "Present value",np.pv(0.03/4,5*4,-10,1376.09633204) #npv参数为利率和一个表示现金流的数组. cashflows = np.random.randint(100,size=5) cashflows = np.insert(cashflows,0,-100) print "Cashflows",cashflows print "Net present value",np.npv(0.03,cashflows) print u"内部收益率" print "Internal rate of return",np.irr([-100, 38, 48,90 ,17,36]) print u"分期付款" #pmt输入为利率和期数,总价，输出每期钱数 print "Payment",np.pmt(0.10/12,12*30,100000) #nper参数为贷款利率，固定的月供和贷款额，输出付款期数 print "Number of payments", np.nper(0.10/12,-100,9000) #rate参数为付款期数，每期付款资金，现值和终值计算利率 print "Interest rate",12*np.rate(167,-100,9000,0)
#%% m-기간 기준단리: FV=PV*(1+r/m*n*m) ==> PV=FV/(1+r/m*n*m)
# 년기준복리: FV=PV*(1+r)**n ==> PV=FV/(1+r)**n
# m-기간 기준복리: FV=PV*(1+r/m)*(n*m) ==> PV=FV/(1+r/m)*(n*m)
# 기존 모듈 이용
import scipy as sp
import numpy as np
help(sp.pv)
help(np.pv)
fv = 1276.2815625000003
r = 0.05
n = 5
m = 1
PV_sp = sp.pv(r, n, 0, fv) # pv(rate, nper, pmt, fv=0, when='end')
print(PV_sp)
PV_np = np.pv(r, n, 0, fv)
print(PV_np)
#%%[과제 43-2] 이자가 6개월에 한번 복리로 계산되고 년이자율이 5%인 계좌의 5년 후1000원의 현재가치는 얼마인가?
#i) 사용자 정의 함수를 사용하여 계산하여 보세요.
import numpy as np
FV = 1000
r = 0.05
n = 5
m = 2
def get_pv(Fv, r, n, m):
return FV / (1 + r / m * n * m)
def calculate_previous_balance(loan):
return np.pv((loan.rate/100)/loan.period, loan.period, -loan.payment, -loan.present_balance)
def get_pv_np(Fv, r, n, m):
return np.pv(r / m, n * m, 0, Fv)
def test_decimal_with_when(self):
"""Test that decimals are still supported if the when argument is passed"""
# begin
assert_equal(np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000'), Decimal('1')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000'), 'begin'))
# end
assert_equal(np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000'), 'end'))
assert_equal(np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000'), Decimal('0')),
np.rate(Decimal('10'), Decimal('20'), Decimal('-3500'), Decimal('10000'), 'end'))
# begin
assert_equal(np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0'), Decimal('1')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0'), 'begin'))
# end
assert_equal(np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0'), 'end'))
assert_equal(np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0'), Decimal('0')),
np.pv(Decimal('0.07'), Decimal('20'), Decimal('12000'), Decimal('0'), 'end'))
# begin
assert_equal(np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0'), Decimal('1')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0'), 'begin'))
# end
assert_equal(np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0'), 'end'))
assert_equal(np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0'), Decimal('0')),
np.fv(Decimal('0.075'), Decimal('20'), Decimal('-2000'), Decimal('0'), 'end'))
# begin
assert_equal(np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0'), Decimal('1')),
np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0'), 'begin'))
# end
assert_equal(np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0')),
np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0'), 'end'))
assert_equal(np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0'), Decimal('0')),
np.pmt(Decimal('0.08') / Decimal('12'), Decimal('5') * Decimal('12'), Decimal('15000.'),
Decimal('0'), 'end'))
# begin
assert_equal(np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0'), Decimal('1')),
np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0'), 'begin'))
# end
assert_equal(np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0')),
np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0'), 'end'))
assert_equal(np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0'), Decimal('0')),
np.ppmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('60'), Decimal('55000'),
Decimal('0'), 'end'))
# begin
assert_equal(np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0'), Decimal('1')).flat[0],
np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0'), 'begin').flat[0])
# end
assert_equal(np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0')).flat[0],
np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0'), 'end').flat[0])
assert_equal(np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0'), Decimal('0')).flat[0],
np.ipmt(Decimal('0.1') / Decimal('12'), Decimal('1'), Decimal('24'), Decimal('2000'),
Decimal('0'), 'end').flat[0])
capital=np.zeros((3, 7))
interets=np.zeros((3, 7))
# Hypothèse de mensualité fixe
mensualite=50.0
# Hypothèses de taux (source: meilleurstaux.com au 30/06/2014)
mention=('Bon', 'Très bon', 'Excellent')
duree=np.array(([7, 10, 12, 15, 20, 25, 30]))
taux=np.array(([0.0223, 0.0245, 0.0263, 0.0281, 0.0300, 0.0337, 0.0425],
[0.0205, 0.0225, 0.0243, 0.0258, 0.0274, 0.0320, 0.0370],
[0.0175, 0.0196, 0.0216, 0.0240, 0.0267, 0.0283, 0.0335]))
taux_df=pd.DataFrame(taux, index=mention, columns=duree)
for i in range(len(mention)):
for j in range(len(taux[0])):
capital[i,j]=np.pv(taux[i,j]/12, duree[j]*12, -mensualite)
interets[i,j]=mensualite*12*duree[j]-capital[i,j]
# Affichage des résultats
for i in range(len(mention)):
plt.figure('Taux '+ mention[i])
plt.title('Taux '+ mention[i])
plt.grid(color="k")
plt.xlabel('Durée')
plt.xlim(5, 31)
plt.ylabel('Montant (EUR)')
plt.plot(duree, capital[i], 'b', label='Montant financable')
plt.plot(duree, interets[i], 'r', label='Interets versés')
plt.show()
def test_pv(self):
assert_almost_equal(np.pv(0.07,20,12000,0),
-127128.17, 2)
def present_value(montly_payment,interest_rate=.05,term=30): return numpy.pv((interest_rate/12),(term*12),montly_payment) * -1