x=balance

m=annualInterestRate/12
x1=balance / 12
x2=(balance * (1 + m)**12)/12
updatedBalance = balance

while abs(x1-x2)>0.0001:
    x=(x1+x2)/2
    updatedBalance = balance
    for _ in xrange(12):
        updatedBalance = (updatedBalance - x) * (1 + m)
    if  updatedBalance>0:
        x1=x
    elif updatedBalance<0:
        x2=x

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