def calcPay(newBal, mIR, guess):
    for x in range(12):
        newInt = ((newBal - guess) * mIR)
        newBal = (newBal - guess + newInt)
    return newBal

def othermain(balance, annualInterestRate):
    epsilon = 0.01
    mIR = annualInterestRate /12.0
    low = balance/12
    high = round(((balance*(1+mIR)**12)/12),2)
    guess = round(((high+low)/2.0),2)
    ans = round(calcPay(balance,mIR,guess),2)

    print('')
    print('lo: '+str(low)+' hi: '+str(high))
    print('')
    print('guess: ' + str(guess) + ' ans: ' + str(ans))

    while abs(balance -(guess*12)) <= epsilon:

        newbal =(ans*12)-balance

        print('')
        print('ans*12-bal: ' + str(newbal))

        if newbal < epsilon:
            high = guess
        else:
            low = guess

        print('')
        print('lo: '+str(low)+' hi: '+str(high))

        guess = round(((high+low)/2.0),2)
        ans = round(calcPay(balance,mIR, guess),2)
        print('')
        print('guess: '+str(guess)+' ans: '+str(ans))
    print('lowest payment: ' +str(guess))
othermain(320000,0.2)
othermain(999999,0.18)