edx demo two | Python Fiddle

from math import log, ceil

balance = 320000
annualInterestRate = 0.2

monthlyInterestRate = annualInterestRate / 12
lower = balance / 12
upper = (balance * pow(1 + monthlyInterestRate,12))/12

def paidMonth(pay):
    '''
    Given a specified monthly payment, returns the month in which the balance will be paid off.    
    '''
    mo = 0
    bal = balance
    while bal>0:
        bal = (bal - pay)*(1+monthlyInterestRate) 
        mo+=1
    #print 'mo:',mo
    return mo
    
def midpoint(a,b):
    return (a+b)/2
    
# initial guess = halfway between the bounds
payment = midpoint(upper,lower)

# for "nearest cent resolution" we need to examine all the cents between upper and lower
cents = (upper-lower)*100 + 1
#print 'cents:',cents
iters = int(ceil(log(cents,2)))
#print 'iters:',iters

for i in range(iters):
    #print 'payment:',payment
    if paidMonth(payment)<=12:
        upper = payment
        payment = midpoint(payment,lower)
    else:
        lower=payment
        payment = midpoint(payment,upper)
                
print 'Lowest Payment:',("%.2f" % payment)

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