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

while abs(newBalance) > 0.01:


    for month in range(1, 13):
        newBalance = (balance - payment) * (1 + monthlyInterestRate)

        if newBalance > 0:
            upperBound = payment


        elif newBalance < 0:
            lowerBound = payment

        else:
            break
        payment = (upperBound + lowerBound)/2
        newBalance = balance


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