"""
Problem #1
"""

balance = 42
annualInterestRate = 0.2
monthlyPaymentRate = 0.04

def cc_12mo_bal(balance, annualInterestRate, monthlyPaymentRate):
    """

    Write a program to calculate the credit card balance after
    one year if a person only pays the minimum monthly
    payment required by the credit card company each month.

    """
    Monthly_Int_Rate = annualInterestRate / 12
    Min_Monthly_Pmt = monthlyPaymentRate * balance
    Monthly_Unpaid_Bal = balance - Min_Monthly_Pmt
    Updated_bal = Monthly_Unpaid_Bal + (Monthly_Int_Rate * Monthly_Unpaid_Bal)
    if hasattr(cc_12mo_bal, "count"):
        cc_12mo_bal.count += 1
    else:
        cc_12mo_bal.count = 1
    if cc_12mo_bal.count == 12:
        return print("Remaining balance: " + str(round(Updated_bal, 2)))
    else:
        return cc_12mo_bal(Updated_bal, annualInterestRate, monthlyPaymentRate)

cc_12mo_bal(balance, annualInterestRate, monthlyPaymentRate)

"""
Problem #2
"""

def cc_12mo_payoff(balance, annualInterestRate, \
                   increment = 10, epsilon = 10, \
                   guess = 10, \
                   num_guesses = 12):
    """

    Write a program that calculates the minimum fixed monthly payment
    needed in order pay off a credit card balance within 12 months.
    By a fixed monthly payment, we mean a single number which does
    not change each month, but instead is a constant amount that will
    be paid each month.

    """

    def pmt_trial(balance, annualInterestRate, num_guesses, \
                  guess = round((balance*(1+annualInterestRate/12)**12)*.0833333,-1)):
        Monthly_Int_Rate = annualInterestRate / 12
        Monthly_Unpaid_Bal = balance - guess
        Updated_bal = Monthly_Unpaid_Bal + (Monthly_Int_Rate * Monthly_Unpaid_Bal)
        if num_guesses == 1:
            return Updated_bal
        else:
            return pmt_trial(Updated_bal, annualInterestRate, num_guesses - 1, guess)

    Updated_bal = pmt_trial(balance, annualInterestRate, num_guesses, guess)

    if Updated_bal <= 0:
        print("Lowest Payment: " + str(guess))
    else:
        return cc_12mo_payoff(balance, annualInterestRate, guess = guess + increment)

cc_12mo_payoff(balance, annualInterestRate)


"""
Problem #3
"""

def cc_12mo_payoff(balance, annualInterestRate, lower_bound = 0, \
                   upper_bound = 0, guess = 10, num_guesses = 12, epsilon = .01):
    """

    Write a program that uses these bounds and bisection search (for more info
    check out the Wikipedia page on bisection search) to find the smallest
    monthly payment to the cent (no more multiples of $10) such that we can
    pay off the debt within a year. Try it out with large inputs, and notice
    how fast it is (try the same large inputs in your solution to Problem 2 to
    compare!). Produce the same return value as you did in Problem 2.

    """
    Monthly_Int_Rate = annualInterestRate / 12

    if lower_bound == 0 and upper_bound == 0:
        lower_bound = balance / 12
        upper_bound = balance * ((1+Monthly_Int_Rate)**12)/12.0
        guess = (upper_bound + lower_bound) / 2
    else:
        guess = (upper_bound + lower_bound) / 2

    def pmt_trial(balance, annualInterestRate, num_guesses, guess):
        Monthly_Unpaid_Bal = balance - guess
        Updated_bal = Monthly_Unpaid_Bal + \
        (Monthly_Int_Rate * Monthly_Unpaid_Bal)
        if num_guesses == 1:
            return Updated_bal
        else:
            return pmt_trial(Updated_bal, annualInterestRate, \
                             num_guesses - 1, guess)

    Updated_bal = pmt_trial(balance, annualInterestRate, num_guesses, guess)

    if Updated_bal <= 0 and Updated_bal >= -0.01:
        print("Lowest Payment: " + str(round(guess,2)))
    elif Updated_bal > 0:
        return cc_12mo_payoff(balance, annualInterestRate,
                              lower_bound = guess, upper_bound = upper_bound)
    else:
        return cc_12mo_payoff(balance, annualInterestRate, \
                              lower_bound = lower_bound, upper_bound = guess)

cc_12mo_payoff(999999, 0.18)