I'm creating a simple model which calculates the minimum fixed monthly payment required to pay off a credit card balance within 12 months.
My code:
balance = 3329 # starting balance
annualInterestRate = 0.2 # yearly interest rate
minFixedPayment = 0 # initiate a minimum monthly payment of 0
while balance > 0:
minFixedPayment = minFixedPayment + 10
for i in range(1,13,1):
unpaidBalance = balance - minFixedPayment
balance = unpaidBalance + ((annualInterestRate/12) * unpaidBalance)
i=i+1
print(round(minFixedPayment,2))
I added the "minFixedPayment" increment BEORE the for loop so that it keeps incrementing until it finds a value where balance is <= 0 at the end of month 12. I know this is wrong since it will compute the first iteration with minFixedPayment = 10, not 0. Is there a better way to arrange this?
I've tried adding the
minFixedPayment = minFixedPayment + 10
statement to the end of the loop, like this:
while balance > 0:
for i in range(1,13,1):
unpaidBalance = balance - minFixedPayment
balance = unpaidBalance + ((annualInterestRate/12) * unpaidBalance)
i=i+1
minFixedPayment = minFixedPayment + 10 # moved this to after the loop
print(round(minFixedPayment,2))
but that makes the while loop run forever (why?).
Is there a better way to approach this? Thank you for your time.
Some issues:
i
with i=i+1
. That is already taken care of with the for
loop. Here is the suggested code:
loan = balance = 3329 # starting balance, use two names so you can restart
annualInterestRate = 0.2 # yearly interest rate
minFixedPayment = -10 # initiate a minimum monthly payment
monthlyInterestRate = annualInterestRate/12 # avoid doing this repeatedly
while balance > 0:
minFixedPayment = minFixedPayment + 10
balance = loan # start from scratch
for i in range(1,13):
unpaidBalance = balance - minFixedPayment
balance = unpaidBalance + monthlyInterestRate * unpaidBalance
print(round(minFixedPayment,2))
For your interest, here is a more sophisticated solver:
from functools import partial
from math import ceil
def diff(fn, x, h=0.001):
"""
Numerically differentiate fn at x
"""
return (fn(x + h) - fn(x)) / h
def newton_solver(fn, target_y, initial_x, max_reps=100, max_err=0.01):
"""
Find a value for x such that fn(x) == target_y (+/- max_err)
"""
x = initial_x
for _ in range(max_reps):
err = fn(x) - target_y
if abs(err) <= max_err:
# found a good enough solution
return x
else:
# first-order correction to reduce error
x -= err / diff(fn, x)
raise ValueError("solver failed to converge")
def final_balance(fixed_payment, initial_balance, period_rate, num_periods):
"""
Calculate the final balance on a fixed payment plan
"""
balance = initial_balance
for _ in range(num_periods):
balance = (balance - fixed_payment) * (1. + period_rate)
return balance
def round_up_to_next_cent(amt):
return ceil(amt * 100.) / 100.
def main():
initial_balance = 3329.
annual_interest = 0.2
# bind arguments to create a single-argument function to pass to newton_solver
my_final_balance = partial(final_balance, initial_balance = initial_balance, period_rate = annual_interest / 12, num_periods = 12)
# initial guess - in total you will pay about half a year's interest
monthly_payment_guess = initial_balance * (1. + annual_interest * 0.5) / 12
# solve to find accurate value
monthly_payment = newton_solver(my_final_balance, 0., monthly_payment_guess)
monthly_payment = round_up_to_next_cent(monthly_payment)
# and report the result
print("A fixed monthly payment of ${:0.2f} results in a final balance of ${:0.2f}".format(monthly_payment, my_final_balance(monthly_payment)))
if __name__ == "__main__":
main()
which produces
A fixed monthly payment of $303.33 results in a final balance of $-0.07
add a flag variable to control if balance is changed. Another way could be to check if balance is changed. ( if balance != original_balance: ...
) eg
balance = 3329 # starting balance
annualInterestRate = 0.2 # yearly interest rate
minFixedPayment = 0 # initiate a minimum monthly payment of 0
change_flag = 0
while balance > 0:
if change_flag: minFixedPayment = minFixedPayment + 10
change_flag = 1
for i in range(1,13,1):
unpaidBalance = balance - minFixedPayment
balance = unpaidBalance + ((annualInterestRate/12) * unpaidBalance)
i=i+1
print(round(minFixedPayment,2))
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