balance = 320000
annualInterestRate = 0.2
monthlyInterestRate = (annualInterestRate)/12
lowerBound = balance/12
upperBound = (balance*(1+monthlyInterestRate)**12)/12
payment = (upperBound + lowerBound)/2
newBalance = balance
epsilon = 0.01

while abs(upperBound-lowerBound) > .01:
    for month in range(1, 13):


        balance = (balance - payment)*(1 + monthlyInterestRate)

        if (balance) > 0.01:
            lowerBound = payment
            balance = newBalance
            payment = (upperBound + lowerBound)/2.0
        else:
            upperBound = payment
            balance = newBalance
            payment = (upperBound + lowerBound)/2.0


print 'Lowest Payment: ' + str(round(payment,2))