credit bisection

balance = 999999
annualInterestRate = 0.18
startbalance = balance
monthlyinterest = annualInterestRate/12
lower = balance/12
upper = (balance*((1+monthlyinterest)**12/12))
balance = startbalance
minpayment = (upper+lower)/2.0
while True:
    for a in range(12):
        balance = balance - minpayment
        balance = balance + balance * monthlyinterest
        #balance = (balance - minpayment) * ( 1 + monthlyinterest)
        print "month: " + str(a) + " balance: " + str(balance)
    if abs(balance)<0.08:

        break;
    if balance <0:
        upper = minpayment
        print "upper minpayment has changed to: " + str(minpayment)
    else:
        lower = minpayment
        print "lower minpayment has changed to: " + str(minpayment)
    minpayment = (lower+upper)/2.0
    balance = startbalance


#ans = payYear(startbalance, balance, monthlyinterest)
print "minpayment is: " + str(round(minpayment, 2))