Why doesn't my bisection algorithm work? Python

Question

I'm writing a credit card payment calculator for my Python class. The assignment is to write a definition for a calculator that figures out the monthly payment necessary to bring your balance to zero in x number of months.

The definition takes 3 parameters: initialBalance, apr, months.

As much as I can figure, the point of the assignment is to get us to use bisection method to find our answer, and I have written two other definitions that aid the assignment:

1) newBalance() - which determines the new balance after a payment is made; 2) balances() - which returns a list of balances after the payments were made;

In that light, balances()[-1] returns the final balance, so my plan of action has been to evaluate the last item in the list as equal to 0 (or at least within 0.005 of 0!) and if so, return the payment that got me there.

if the final balance is negative (I've paid too much!): payment = payment - (payment / 2); if the balance is positive (I haven't paid enough!): payment = payment + (payment / 2);

As best as I can figure it, my algorithm should eventually conclude, but it NEVER finds a close enough answer...

Here is my code, (and the Prof's testing def at the end):

def newBalance(prevBalance, apr, payment):
    """
    - prevBalance: the balance on the credit card statement.
    - apr: the annual percentage rate (15.9 here means 15.9%).
    - payment: the amount paid this month to the credit card company.
    - returns: the new balance that will be owed on the credit card
      (assumes no purchases are made). 
    """
    interestCharge = float(((apr / 12.0) / 100) * prevBalance)
    return float((interestCharge + prevBalance) - payment)




def balances(initialBalance, apr, payments):
    """
    - initialBalance: the initial balance on the credit card.
    - apr: the annual percentage rate (15.9 here means 15.9%).
    - payments: a list of monthly payments made on the credit card.
    - returns: a list giving the balance on the credit card each
      month. The first number in the list is the initial
      balance, the next number is the balance after the first
      payment is made, and so on. Note that the length of the returned
      list is len(payments) + 1.
      """
    balancelist = []
    balancelist.append(initialBalance)
    for x in range(0, len(payments)):
        balancelist.append(newBalance(balancelist[x], apr, payments[x]))
    return balancelist




def findMonthlyPayment(initialBalance, apr, months):
    """
    - initialBalance: the starting balance on the card.
    - apr: the APR.
    - months: the number of equal monthly payments you wish to
      make in order to reduce the balance to zero.
    - returns: the monthly payment amount needed to reduce the
      balance to zero (well, "zero" to within $0.005, anyway)
      in the given number of months.
    """
    guess = float(initialBalance / months)
    listo = months*[guess]

    while True:

        if abs(float(balances(initialBalance, apr, listo)[-1]) - initialBalance) < 0.006:
            print "BINGO", guess  ##for debugging
            print balances(initialBalance, apr, listo)[-1]
            return guess

        else:
            if float(balances(initialBalance, apr, listo)[-1]) < -0.005:
                guess = guess - (guess / 2)

                print "BOO", guess ##for debugging
                print balances(initialBalance, apr, listo)[-1]

            else:
                guess = guess + (guess / 2)
                print "NAY", guess  ##for debugging
                print balances(initialBalance, apr, listo)[-1]

        listo = months*[guess]



def testFindMonthlyPayment():
    answer = findMonthlyPayment(1000, 18.9, 60)
    print
    myString = "Monthly payment to pay off $%.2f in %d months at %.2f%% APR:"
    print myString % (1000, 60, 18.9)
    print "$%.2f" % answer
    # Output should look approximately like this:
    """
    iteration: 1 guess: 500.0 final bal: -46777.3384635
    iteration: 2   guess: 250.0   final balance: -22111.7016729
    iteration: 3   guess: 125.0   final balance: -9778.88327752
    iteration: 4   guess: 62.5   final balance: -3612.47407985
    iteration: 5   guess: 31.25   final balance: -529.269481021
    iteration: 6   guess: 15.625   final balance: 1012.3328184
    iteration: 7   guess: 23.4375   final balance: 241.531668687
    iteration: 8   guess: 27.34375   final balance: -143.868906167
    iteration: 9   guess: 25.390625   final balance: 48.83138126
    iteration: 10   guess: 26.3671875   final balance: -47.5187624535
    iteration: 11   guess: 25.87890625   final balance: 0.656309403241
    iteration: 12   guess: 26.123046875   final balance: -23.4312265251
    iteration: 13   guess: 26.0009765625   final balance: -11.387458561
    iteration: 14   guess: 25.9399414062   final balance: -5.36557457885
    iteration: 15   guess: 25.9094238281   final balance: -2.35463258781
    iteration: 16   guess: 25.8941650391   final balance: -0.849161592282
    iteration: 17   guess: 25.8865356445   final balance: -0.0964260945206
    iteration: 18   guess: 25.8827209473   final balance: 0.27994165436
    iteration: 19   guess: 25.8846282959   final balance: 0.0917577799204
    iteration: 20   guess: 25.8855819702   final balance: -0.00233415730086

    Monthly payment to pay off $1000.00 in 60 months at 18.90 APR:
    $25.89
    """

Thanks for the help. Probably wouldn't have joined compsci unless everything I ever googled was on stackoverflow.

Answer 1

This isn't how you bisect

guess = guess - (guess / 2)

Normally you keep a low_guess and a high_guess. You try

guess = (low_guess+high_guess)/2

and then based on the result, you either set

low_guess = guess

or

high_guess = guess

and repeat

Note: In Python2, / is integer divison if the denominator and numerator are both ints, so it's best to just make sure the initial guess is a float

Answer 2

def findMonthlyPayment(initialBalance, apr, months):
    """
    - initialBalance: the starting balance on the card.
    - apr: the APR.
    - months: the number of equal monthly payments you wish to
      make in order to reduce the balance to zero.
    - returns: the monthly payment amount needed to reduce the
      balance to zero (well, "zero" to within $0.005, anyway)
      in the given number of months.
    """
    low_guess = 0
    high_guess = initialBalance
    guess = float((low_guess + high_guess) / 2)
    listo = months*[guess]

    while True:

        if abs(float(balances(initialBalance, apr, listo)[-1])) < 0.006:
            print "BINGO", guess  ##for debugging
            print balances(initialBalance, apr, listo)[-1]
            return guess

        elif float(balances(initialBalance, apr, listo)[-1]) < -0.005:
            high_guess = guess
            print "BOO", guess ##for debugging
            print balances(initialBalance, apr, listo)[-1]

        else:
            low_guess = guess
            print "NAY", guess  ##for debugging
            print balances(initialBalance, apr, listo)[-1]
        guess = float((low_guess + high_guess) / 2)
        listo = months*[guess]