You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts.
a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month?
b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month?
Be sure to include in your response:
the answer to the original question
the mathematical steps for solving the problem demonstrating mathematical reasoning
a. If you are putting half of the available $300.00 each month towards the credit card, that would be $150.00.
To calculate how many months it will take to pay off the credit card, we need to consider the monthly interest rate. The monthly interest rate is the annual percentage rate (APR) divided by 12.
For 13.6% APR, the monthly interest rate is 13.6% / 12 = 1.1333%.
So, the equation to calculate the balance after each month would be:
Balance = (Balance - Payment) * (1 + Monthly Interest Rate)
Plugging in the values:
$754.43 = ($754.43 - $150.00) * (1 + 0.011333)
After solving this equation iteratively, it would take approximately 6 months to pay off the credit card by putting $150.00 towards it each month.
b. If you put all of the available $300.00 each month towards the credit card, then the equation becomes:
$754.43 = ($754.43 - $300.00) * (1 + 0.011333)
After solving this equation iteratively, it would take approximately 3 months to pay off the credit card by putting $300.00 towards it each month.