How to calculate the monthly fee on a loan?
Given is:
a: an amount to loan.
b: the loan period (number of months).
c: the interest rate p.a. (interests is calculated and added every month, 1/12 of the interest is added. So if the interest is on 12%, 1% interest is added every month).
d: the amount of money owed after the end of the period.
This problem is a bit different than the usual since, the goal is not to have the loan payed after the loan period has ended, but to still owe an amount that is given. I have been able to find an algorithm so solve the problem if I wanted to pay the entire amount, but it will of course not work for this problem where the goal is to end up owing a given amount rather than not owing anything.
I managed to make a solution to this problem by starting with an guess and then keep on improving that guess until it was close enough. I wondered however, if there is a better way to simply calculate this, rather than just guessing.
Edit: Here's how I'm doing it now.
def find_payment(start, end, months, interest):
difference = start
guess = int(start / months * interest)
while True:
total = start
for month in range(1, months + 1):
ascribe = total * interest / 12
total = total + ascribe - guess
difference = total - end
# See if the guess was good enough.
if abs(difference) > start * 0.001:
if difference < 0:
if abs(difference) < guess:
print "payment is %s" % guess
return evolution(start, guess, interest, months)
else:
mod = int(abs(difference) / start * guess)
if mod == 0:
mod = 1
guess -= mod
else:
mod = int(difference / start * guess)
if mod == 0:
mod = 1
guess += mod
else:
print "payment is %s" % guess
return evolution(start, guess, interest, months)
evolution is just a function that displays how the loan would look like payment for payment and interest for interest, summing up total amount of interest paid etc.
An example would be if I wanted to find out the monthly payments for a loan starting with $100k and ending at $50k with an interest of 8% and a duration of 70 months, calling
>>> find_payment(100000, 50000, 70, 0.08)
payment is 1363
In the above case I would end up owing 49935, and I went through the loop 5 times. The amount of times needed to go through the loop depends on how close I want to get to the amount and it varies a bit.
This is a basically a mortgage repayment calculation.
Assuming that start is greater than end, and that interest is between 0 and 1 (i.e. 0.1 for 10% interest)
First consider the part of the payment you want to pay off.
Principal = start - end
The monthly payment is given by:
pay_a = (interest / 12) / (1 - (1+interest/12) ^ (-months))) * Principal
You then need to consider the extra interest. Which is just equal to the remaining principal times the monthly interest
pay_b = interest / 12 * end
So the total payment is
payment = (interest / 12) * (1 / (1 - (1+interest/12) ^ (-months))) * Principal + end)
On the example you gave of
Start: 100000
End: 50000
Months: 70
Interest: 8%
pay_a = 896.20
pay_b = 333.33
Payment = 1229.54
When I tested these values in Excel, after 70 payments the remaing loan was 50,000. This is assuming you pay the interest on the notional before the payment is made each month.
Perhaps the easiest way to think about this is to split the loan in two parts, one part which is to be repaid in full and another part where you don't pay off anything. You have already computed the monthly fee for the first part.
You can keep paying the interest of every month; then, you will alway owe the same amont.
Owe_1 = a
Int_2 = Owe_1*(InterestRate/12)
Pay_2 = Int_2
Owe_2 = Owe_1 + Int_2 - Pay_2 # ==> Owe_1 + Int_2 - Int_2 = Owe_1
Int_3 = Owe_2*(InterestRate/12)
Pay_3 = Int_3
Owe_3 = Owe_2 + Int_3 - Pay_3 # ==> Owe_2 + Int_3 - Int_3 = Owe_2 = Owe_1
python code to calculate emi
class EMI_CALCULATOR(object):
# Data attributes
# Helps to calculate EMI
Loan_amount = None # assigning none values
Month_Payment = None # assigning none values
Interest_rate = None #assigning none values
Payment_period = None #assigning none values
def get_loan_amount(self):
#get the value of loan amount
self.Loan_amount = input("Enter The Loan amount(in rupees) :")
pass
def get_interest_rate(self):
# get the value of interest rate
self.Interest_rate = input("Enter The Interest rate(in percentage(%)) : ")
pass
def get_payment_period(self):
# get the payment period"
self.Payment_period = input("Enter The Payment period (in month): ")
pass
def calc_interest_rate(self):
# To calculate the interest rate"
self.get_interest_rate()
if self.Interest_rate > 1:
self.Interest_rate = (self.Interest_rate /100.0)
else:
print "You have not entered The interest rate correctly ,please try again "
pass
def calc_emi(self):
# To calculate the EMI"
try:
self.get_loan_amount() #input loan amount
self.get_payment_period() #input payment period
self.calc_interest_rate() #input interest rate and calculate the interest rate
except NameError:
print "You have not entered Loan amount (OR) payment period (OR) interest rate correctly,Please enter and try again. "
try:
self.Month_Payment = (self.Loan_amount*pow((self.Interest_rate/12)+1,
(self.Payment_period))*self.Interest_rate/12)/(pow(self.Interest_rate/12+1,
(self.Payment_period)) - 1)
except ZeroDivisionError:
print "ERROR!! ZERO DIVISION ERROR , Please enter The Interest rate correctly and Try again."
else:
print "Monthly Payment is : %r"%self.Month_Payment
pass
if __name__ == '__main__':# main method
Init = EMI_CALCULATOR() # creating instances
Init.calc_emi() #to calculate EMI
for more info visit : https://emilgeorgejames.wordpress.com/2015/07/29/python-emi-equated-monthly-installment-calculator/
This rather a detailed way but will give the whole payment as well
# Mortgage Loan that gives the balance and total payment per year
# Function that gives the monthly payment
def f1 (principle,annual_interest_rate,duration):
r = annual_interest_rate/1200
n = duration*12
a=principle*r*((1+r)**n)
b= (((1+r)**n)- 1)
if r > 0 :
MonthlyPayment = (a/b)
else :
MonthlyPayment = principle/n
return MonthlyPayment
# Function that gives the balance
def f2 (principle,annual_interest_rate,duration,number_of_payments):
r = annual_interest_rate/1200
n = duration*12
a= ((1+r)**n)
b= ((1+r)**number_of_payments)
c= (((1+r)**n)-1)
if r > 0 :
RemainingLoanBalance = principle*((a-b)/c)
else :
RemainingLoanBalance = principle*(1-(number_of_payments/n))
return RemainingLoanBalance
# Entering the required values
principle=float(input("Enter loan amount: "))
annual_interest_rate=float(input("Enter annual interest rate (percent): "))
duration=int(input("Enter loan duration in years: "))
# Output that returns all useful data needed
print ("LOAN AMOUNT:",principle,"INTEREST RATE (PERCENT):",annual_interest_rate)
print ("DURATION (YEARS):",duration,"MONTHLY PAYMENT:",int(f1(principle,annual_interest_rate,duration)))
k=duration+1
BALANCE=principle
total=0
for i in range (1,k):
TOTALPAYMENT= f1(BALANCE,annual_interest_rate,k-i)*12
total+= TOTALPAYMENT
BALANCE= f2(principle,annual_interest_rate,duration,12*i)
print("YEAR:",i,"BALANCE:",int(BALANCE),"TOTAL PAYMENT",int(total))
How about this?
def EMI_calc(principle, rate, time, frequency):
return (principle / ((1-((1+(rate/frequency))**(-1*(time*frequency))))/(rate/frequency)))
print("""
----- Welcome to EMI programe for Python -----
""")
print("\n You have chosen to know the EMI for Loan.\n")
input('\nTo Continue Press ENTER --- to ABORT Press ctrl+c > \n')
print("\nPlease Enter amount of Loan to be taken: >\n")
principle = int(input())
print("\nEnter rate of interst (%): >\n")
rate = float(input())/100
print("\nEnter Term (Years): >\n")
time = float(input())
print("\nPlease enter the frequency of installments) : >\n")
frequency = int(input())
EMI = round(EMI_calc(principle, rate, time, frequency),0)
print("""
---------------------------------------------------------------------
""")
print(f"""
The EMI for Loan of Rs.{principle};
at interest rate of {rate*100} % for {time} years;
would be: Rs.""", EMI)
print("""
---------------------------------------------------------------------
""")
Here is a code snippet using numpy functions. This shows you the payment, principal, interest, instalment and total_amount each month. Run it and see the output. You can also check the syntax for Excel "IPMT()" and "PPMT()" functions for more explanation of the arguments.
https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.pmt.html#numpy.pmt
import math
import numpy as np
rate = 0.08
start_amount = 100000.0
end_amount = 50000.0
diff_amount = start_amount - end_amount
# nr_years = 4
payment_frequency = int (12)
nr_months = 70 # = nr_years * payment_frequency
per_np = np.arange (nr_months) + 1 # +1 because index starts with 1 here
pay_b = rate / payment_frequency * end_amount
ipmt_np = np.ipmt (rate / payment_frequency, per_np, nr_months, diff_amount) - pay_b
ppmt_np = np.ppmt (rate / payment_frequency, per_np, nr_months, diff_amount)
for payment in per_np:
idx = payment - 1
principal = math.fabs (ppmt_np [idx])
start_amount = start_amount - principal
interest = math.fabs (ipmt_np [idx])
instalment = principal + interest
print payment, "\t", principal, "\t", interest, "\t\t", instalment, "\t\t", start_amount
print np.sum (ipmt_np)
Related
This program is meant to get input from the user, initial investment and apy and is meant to return the number of years it takes for the investment to double. I've been testing 100 for the principal and .05 for the apy but the result I'm getting is over 14,000 years. This value should calculate to a little over 15 years. I can seem to find the issue and could use some pointers.
def main():
print("This program calculates the amount of time it takes for an investment to double")
principal = eval(input("What is the initial investment amount? "))
apy = eval(input("What is the annual interest rate? "))
years = 0
while principal < (2 * principal):
principal = principal * (1 + apy)
years = years + 1
print("It will take", years, "years for your investment to double." )
main()
when you increase the pricipal in every loop you also increase 2 times principal
as x+1 < (x+1)* 2
And you have your infinite loop in at least theory
But python stops at ∞ < 2 * ∞ and that is correct as 2 * ∞ Is ∞ and makes the equation false and ends the loop
Add another variable.
def main():
print("This program calculates the amount of time it takes for an investment to double")
principal = eval(input("What is the initial investment amount? "))
apy = eval(input("What is the annual interest rate? "))
years = 0
resultinv = principal
while resultinv < (2 * principal):
resultinv = resultinv * (1 + apy)
years = years + 1
print("It will take", years, "years for your investment to double." )
main()
I'm new to programming, so any experienced programmer will probably be able to answer this question easily.
I am trying to write a Python function which will tell me what percentage compound interest is necessary to end up with a specific sum. For example, if I deposited $100, and after 17 years of compound interest I have $155, the function will tell me what percentage interest was I receiving. I wrote the following function, with 'start' being the original sum deposited, 'finish' the sum I ended up with, and 'years' the number of years it accrued interest. I designed it to give a result in decimal points, for example for 1.5% it will show 0.015.
Here's the code I wrote:
def calculate(start, finish, years):
num = start
percentage = 0
while num < finish:
percentage += 0.000001
for year in range(years):
num += num * percentage
return percentage
print(calculate(12000, 55000, 100))
It's giving an output of 0.00017499999999999962 (i.e. 0.017499999999999962%), which is totally wrong.
I can't understand where I've gone wrong.
You need to reset the num=start after every time you guess a percentage.
def calculate(start, finish, years):
num = start
percentage = 0
while num < finish:
num = start
percentage += 0.000001
for year in range(years):
num += num * percentage
return percentage
print(calculate(12000, 55000, 100))
However, you'd probably be better off solving this problem by simply re-arranging the compound interest formula:
A=P*(1+r/n)^(nt)
(where A = Final balance, P = Initial balance, r = Interest rate, n = number of times interest applied per time period, and t = number of time periods elapsed.)
The rearrangement gives:
r=n((A/P)^(1/nt)-1)
and putting this into python gives us:
def calculate(start, finish, years):
num = ((finish / start)**(1/years))-1
return num
print(calculate(12000.0, 55000.0, 100.0))
which gives the expected results.
You can do a one-liner if you understand how compound interest works
def calculate(start, finish, years):
return (finish/start)**(1/years) - 1
print(calculate(12000, 55000, 100) * 100, '%')
I've written a solution for an EdX course homework problem using iteration.
The code takes a credit card balance and annual interest rate to calculate the minimum monthly payment required to pay off the balance (plus any interest) in 12 months.
Here is my iterative code:
def minimum_payment_iter(ann_interest, balance):
month_int = ann_interest/12
remaining = balance
payment = 10
months = 1
while remaining > 0:
months = 1
payment += 10
remaining = balance
while months < 13:
remaining -= payment
remaining += remaining*month_int
months += 1
return payment
I've taken a stab at doing the recursive version, but I've exceeded the maximum recursion depth:
def minimum_payment_recur(ann_interest, balance, payment = 10):
month_int = ann_interest/12
remaining = balance
month = 1
if remaining <= 0:
return payment
else:
remaining -= payment
remaining += remaining*month_int
month += 1
return minimum_payment_recur(ann_interest, balance, payment + 10)
I just did this one. You need to add a counter in the recursion, which is what you would do in a loop.
So, something like:
def function(a,b,counter=12):
"""
Docstring goes here
"""
if counter == 1:
return a+b
else:
return function(a,b,counter-1)
I find it tough to get real help in these online courses on edX as well because the courses are so strict on what you can post, and I never got an offer to speak with an individual outside of the "Discussion". I'd pay a premium if I could get 1 on 1 help from edX courses, honestly.
Anyway, hope that helps you.
I'm struggling with a problem that calculates the minimum fixed monthly payment needed in order pay off a credit card balance within 12 months. By a fixed monthly payment, I mean a single number which does not change each month, but instead is a constant amount, multiple of 10 and the same for all months, that will be paid each month. ( it is possible for the balance to become negative using this payment scheme, which is OK)
So as input I have
original_balance = 3329
annualInterestRate = 0.2
From this I'm calculating the followings :
after_12_months_interest = original_balance
monthlyInterestRate = round(annualInterestRate/12.0,2)
monthly_payment = 10
total_paid = 0
for i in range(0,12):
after_12_months_interest = after_12_months_interest + (annualInterestRate/12.0)*after_12_months_interest
while total_paid < after_12_months_interest:
new_balance = 0
unpaid_balance = original_balance - monthly_payment
total_paid = 0
for i in range(0, 13):
total_paid = total_paid + monthly_payment
if total_paid < after_12_months_interest:
monthly_payment = monthly_payment + 10
print "Lowest Payment: ", monthly_payment
My problem I have is that I end up having a monthly_payment just a little more than I should have it. In this case the return for the monthly_payment is 320 instead of 310. For all use cases I've tried the monthly_payment it's slightly more than it should be.
Anyone can give me a hint or an idea on what I'm doing wrong please. Thank you
Mandatory one-liner
from itertools import count
print(next(payment for payment in count(0, 10)
if sum(payment*(1+monthly)**i for i in range(12)) > original_balance*(1+annual)))
What this does:
next takes the first element of an iterator.
count tries values from 0 to infinity (only each time next is called, and only until a value is returned)
sum(payment*(1+monthly)**i for i in range(12)) That's the combined value of the payments. Each payment is worth itself plus all the saved interests (the earlier you repay, the less interest you'll owe later)
original_balance*(1+annual) is indeed the total value if nothing is repayed.
Alternative
print(next(payment for payment in count(0, 10)
if reduce(lambda x,_:(x - payment)*(1+monthly), range(12), original_balance) <= 0))
This one computes the combined remainder of the debt by reduceing the original_balance 12 times.
I am starting to learn coding and beginning with Python. In my Python course I have a problem that is the following:
Write a program to calculate the credit card balance after one year if
a person only pays the minimum monthly payment required by the credit
card company each month.
The following variables contain values as described below:
balance - the outstanding balance on the credit card
annualInterestRate - annual interest rate as a decimal
monthlyPaymentRate - minimum monthly payment rate as a decimal
For each month, calculate statements on the monthly payment and
remaining balance, and print to screen something of the format:
Month: 1
Minimum monthly payment: 96.0
Remaining balance: 4784.0
(I've got that part alright)
Finally, print out the total amount paid that year and the remaining balance at the end of the year in the format:
Total paid: 96.0
Remaining balance: 4784.0
(It is the part of total paid that I can't resolve after many hours of trying and searching)
So here is what I need to do: add up together all the results of minimum monthly payment to get the total that was paid.
Here is my code:
def creditPayment(balance, annuelInterestRate, monthlyPaymentRate):
for month in range(1, 13):
monthlyInterestRate = annuelInterestRate/ 12.0
minimumMonthlyPayment = monthlyPaymentRate * balance
monthlyUnpaidBalance = balance - minimumMonthlyPayment
balance = monthlyUnpaidBalance + (monthlyInterestRate * monthlyUnpaidBalance)
totalPaid = sum((minimumMonthlyPayment) for _ in range(0, 13))
print 'Month: ', month
print 'Minimum monthly payment: ', round(minimumMonthlyPayment, 2)
print 'Remaining balance: ', round(balance, 2)
print ' '
print 'Total paid: ', round(totalPaid, 2)
print 'Remaining balance: ', round(balance, 2)
print creditPayment(4213, 0.2, 0.04)
Everything works fine except for the total paid that adds up 12 times only the first value of minimumMonthlyPayment. I can't make it better.
If I've correctly interpreted your question, I'm assuming that your intent is to increment totalPaid by the minimumMonthlyPayment for each month. If so:
totalPaid = 0.0
for month in range(1, 13):
#
# Other stuff you're doing in the loop
#
totalPaid += minimumMonthlyPayment
Each time through the loop, totalPaid gets incremented by the minimum payment computed for that particular month. This logic of course has to be changed/augmented if you intend to add cases in which anything other than the minimum payment is paid.
In your for loop, you have:
totalPaid = sum((minimumMonthlyPayment) for _ in range(0, 13))
This is setting totalPaid to be 13 times the minimumMonthlyPayment, as it is for that iteration of the loop, so on the last loop the value is set to 13 times the last minimum payment. You need to add one value to the totalPaid each iteration, so that the value is updated before it is added. Here is what I would change the code to:
def creditPayment(balance, annuelInterestRate, monthlyPaymentRate):
totalPaid = 0
for month in range(1, 13):
monthlyInterestRate = annuelInterestRate/ 12.0
minimumMonthlyPayment = monthlyPaymentRate * balance
monthlyUnpaidBalance = balance - minimumMonthlyPayment
balance = monthlyUnpaidBalance + (monthlyInterestRate * monthlyUnpaidBalance)
totalPaid +=minimumMonthlyPayment
print 'Month: ', month
print 'Minimum monthly payment: ', round(minimumMonthlyPayment, 2)
print 'Remaining balance: ', round(balance, 2)
print ' '
print 'Total paid: ', round(totalPaid, 2)
print 'Remaining balance: ', round(balance, 2)
print creditPayment(4213, 0.2, 0.04)
print creditPayment(4213, 0.2, 0.04)
Also, since you aren't using the actual value of your iterator in for _ in range(0, 13), it would be more readable to just use range(13). I suspect you may have meant to have it loop 12 times, since the rest of your program does.