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.

I. i = 1

while i <= 12:

monthlyInterestRate = annualInterestRate/12.0

minimumMonthlyPayment = balance * monthlyPaymentRate

unpaidBalance = balance - minimumMonthlyPayment

updatedBalance = unpaidBalance + monthlyInterestRate * unpaidBalance

balance = updatedBalance

i += 1

print("The Remaining Balance is:" + " " + str(round(balance,2)))

II. monthlyInterestRate = annualInterestRate/12.0

fixedPayment = 10

def calculate(balance,monthlyInterestRate):

i = 1

while i <= 12:

unpaidBalance = balance - fixedPayment

balance = unpaidBalance + unpaidBalance * monthlyInterestRate

i += 1

return balance

while calculate(balance,monthlyInterestRate) > 0:

fixedPayment += 10

calculate(balance,monthlyInterestRate)

print("Lowest Payment is:" + " " + str(fixedPayment))

III.

initBalance = balance

monthlyInterestRate = annualInterestRate/12.0

low = balance/12.0

high = (balance * ((1.0 + monthlyInterestRate)**12))/12.0

epsilon = 0.01

minPay = (high + low)/2.0

month = 0

def calculate(month, balance, minPay, monthlyInterestRate):

while month <12:

unpaidBalance = balance - minPay

balance = unpaidBalance + (monthlyInterestRate * unpaidBalance)

month += 1

return balance

while abs(balance) >= epsilon:

balance = initBalance

month = 0

balance = calculate(month, balance, minPay, monthlyInterestRate)

if balance > 0:

low = minPay

else:

high = minPay

minPay = (high + low)/2.0

minPay = round(minPay,2)

print('Lowest Payment: ' + str(minPay))

Explanation:

I.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.

The following variables contain values as described below:

balance - the outstanding balance on the credit card

annualInterestRate - annual interest rate as a decimal

monthlyPaymentRate - minimum monthly payment rate as a decimal

For each month, calculate statements on the monthly payment and remaining balance. At the end of 12 months, print out the remaining balance. Be sure to print out no more than two decimal digits of accuracy

II.

Now 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.

In this problem, we will not be dealing with a minimum monthly payment rate.

The following variables contain values as described below:

balance - the outstanding balance on the credit card

annualInterestRate - annual interest rate as a decimal

III. In short:

Monthly interest rate = (Annual interest rate) / 12.0

Monthly payment lower bound = Balance / 12

Monthly payment upper bound = (Balance x (1 + Monthly interest rate)12) / 12.0