Paying Off Credit Card Debt

Each month, a credit card statement will come with the option for you to pay a minimum amount of your charge, usually 2% of the balance due. However, the credit card company earns money by charging interest on the balance that you dont pay. So even if you pay credit card payments on time, interest is still accruing on the outstanding balance.

Say youve made a $5,000 purchase on a credit card with 18% annual interest rate and 2% minimum monthly payment rate. After a year, how much is the remaining balance? Use the following equations.

Minimum monthly payment = Minimum monthly payment rate x Balance (Minimum monthly payment gets split into interest paid and principal paid)

Interest Paid = Annual interest rate / 12 months x Balance

Principal paid = Minimum monthly payment Interest paid

Remaining balance = Balance Principal paid

For month 1, we can compute the minimum monthly payment by taking 2% of the balance:

Minimum monthly payment = 0.02 x $5000.0 = $100.0

We cant simply deduct this from the balance because there is compounding interest. Of this $100 monthly payment, compute how much will go to paying off interest and how much will go to paying off the principal. Remember that its the annual interest rate that is given, so we need to divide it by 12 to get the monthly interest rate.

Interest paid = 0.18/12.0 x $5000.0 = $75.0

Principal paid = $100.0 $75.0 = $25.0

The remaining balance at the end of the first month will be the principal paid this month subtracted from the balance at the start of the month.

Remaining balance = $5000.0 $25.0 = $4975.0

For month 2, we repeat the same steps:

Minimum monthly payment = 0.02 x $4975.0 = $99.50

Interest Paid = 0.18/12.0 x $4975.0 = $74.63

Principal Paid = $99.50 $74.63 = $24.87

Remaining Balance = $4975.0 $24.87 = $4950.13

After 12 months, the total amount paid is $1167.55, leaving an outstanding balance of $4708.10. Pretty depressing!

question

Write a program that uses these bounds and bisection search (for more info check out the Wikipedia page here) 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.