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 don't pay. So even if you pay credit card payments on time, interest is still accruing on the outstanding balance.
Say you've made a $5,000 purchase on a credit card with an 18% annual interest rate and a 2% minimum monthly payment rate. If you only pay the minimum monthly amount for a year, how much is the remaining balance?
You can think about this in the following way.
At the beginning of month 0 (when the credit card statement arrives), assume you owe an amount we will call (b for balance; subscript 0 to indicate this is the balance at month 0).
Any payment you make during that month is deducted from the balance. Let's call the payment you make in month 0, . Thus, your unpaid balance for month 0, , is equal to .
At the beginning of month 1, the credit card company will charge you interest on your unpaid balance. So if your annual interest rate is , then at the beginning of month 1, your new balance is your previous unpaid balance , plus the interest on this unpaid balance for the month. In algebra, this new balance would be
In month 1, we will make another payment, . That payment has to cover some of the interest costs, so it does not completely go towards paying off the original charge. The balance at the beginning of month 2, , can be calculated by first calculating the unpaid balance after paying , then by adding the interest accrued:

For Comp Science/programming, try using stackoverflow for help

To calculate the remaining balance after making the minimum monthly payments for a year, we can use the information given.

Let's break down the steps:

1. Convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, divide the annual interest rate by 12. In this case, the monthly interest rate would be 18% / 12 = 1.5%.

2. Calculate the remaining balance for each month.

- Month 0:
The initial balance, b0, is $5,000.
The minimum monthly payment, p0, is 2% of $5,000 = $100.
The unpaid balance after making the minimum payment is b0 - p0 = $5,000 - $100 = $4,900.

- Month 1:
The interest on the unpaid balance for the month, interest1, is 1.5% of $4,900 = $73.50.
The next minimum monthly payment, p1, is also 2% of $4,900 = $98.
The remaining balance at the beginning of month 2 is b1 = (b0 - p0) + interest1 = $4,900 + $73.50 = $4,973.50.

- Repeat this process for each subsequent month until month 12.

3. Calculate the remaining balance after 12 months.

After calculating the remaining balance for each month, the remaining balance at the end of month 12 will be the final answer.

So, follow the steps above to calculate the remaining balance after making the minimum monthly payments for a year.