Python Bisection Search Logic Error- Returning Inaccurate Results

Question

I am trying to solve the third problem on this MIT OCW assignment. It requires that you calculate the monthly payment needed to clear a given debt in one year using the bisection search method. I am getting the expected output types but very inaccurate results. Can someone point out where I am going wrong? Thank you

# Problem Set 1("C")
# Time Spent: xx hours

def payInOne_BisectionSearch (balance,annualRate):
    #initialize variables
    initialBalance = balance
    monthlyRate = float(annualRate/12.0)
    minMonthly = float(balance/12.0)
    maxMonthly = float((balance * (1 + monthlyRate ** 12.0 ))/12.0)
    monthlyPayment = float((minMonthly + maxMonthly)/2)
    numMonths = 1
    #define function to check balance after 12 months       
    def balanceAfterYear (balance, monthlyRate, monthlyPayment):
        for numMonths in range (1,13):
            interest = balance * monthlyRate
            balance += interest - monthlyPayment
            if balance <= 0:
                  break
        return [balance, numMonths]

    while maxMonthly - minMonthly >= .005:
        balance = initialBalance
        monthlyPayment = float((minMonthly + maxMonthly)/2)
        if balanceAfterYear(balance,monthlyRate,monthlyPayment)[0] < 0:#paying too much
            maxMonthly = monthlyPayment
        elif balanceAfterYear(balance,monthlyRate,monthlyPayment)[0] > 0:#paying too little
            minMonthly = monthlyPayment
        else:
            break
    print "Monthly payment to pay off debt in 1 year:", round(monthlyPayment,2)
    print "Number of months needed:", round(balanceAfterYear(balance,monthlyRate,monthlyPayment)[1], 2) 
    print "Balance:", round(balanceAfterYear(balance,monthlyRate,monthlyPayment)[0], 2) 

payInOne_BisectionSearch (float(raw_input("Enter the outstanding balance")),float(raw_input("Enter annual rate as a decimal")))


    '''Test Case Expected:
       Enter the outstanding balance on your credit card: 320000
       Enter the annual credit card interest rate as a decimal: .2
       RESULT
       Monthly payment to pay off debt in 1 year: 29643.05
       Number of months needed: 12
       Balance: -0.1

       Test Case Actual Output:
       Enter the outstanding balance320000
       Enter annual rate as a decimal.2
       Monthly payment to pay off debt in 1 year: 26666.67
       Number of months needed: 12.0
       Balance: 39179.43'''

Answer 1

Your problem is in your initial maxMonthly value. I think what you'd actually like is for it to be defined as

maxMonthly = float((balance * ((1 + monthlyRate) ** 12.0 ))/12.0)

Otherwise monthlyRate**12 will just evaluate to a near-zero number (for monthlyRates between 0 and 1), which would make maxMonthly evaluate to balance/12.0 the same as your minMonthly, which would make it so that the while-loop at the end never even starts.