Due to poor spending habits, Bryant has accumulated $5,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 16.75 percent! If he pays $200 per month on the card, in total, how much interest expense does Bryant pay to the credit card company?
(5,000 * 0.1675) / 12 = $69.79 interest a month
To determine the total interest expense that Bryant will pay to the credit card company, we need to calculate the interest for each month.
Step 1: Convert the annual interest rate to a monthly rate.
The annual interest rate is 16.75%. To convert it to a monthly rate, divide it by 12 to get 1.39%.
Step 2: Calculate the interest for each month.
Bryant pays $200 per month on the card. So, for the first month, the remaining debt is $5,000. The interest for the first month is calculated by multiplying the remaining debt by the monthly interest rate:
Interest for the first month = $5,000 * 1.39% = $69.50
For the second month, the remaining debt is $5,000 - $200 = $4,800. The interest for the second month is:
Interest for the second month = $4,800 * 1.39% = $66.72
Continue this process for each subsequent month, reducing the principal amount each month by $200.
Step 3: Calculate the total interest expense.
To get the total interest expense, add up the interest for each month:
Total interest expense = Interest for the first month + Interest for the second month + ...
In this case, we need to consider how many months it will take for Bryant to pay off the entire debt. Let's assume it takes X months. Since the debt is decreasing by $200 each month, we can calculate X by dividing the initial debt by $200:
X = $5,000 / $200 = 25 months
Now that we know it will take 25 months to pay off the entire debt, we can calculate the total interest expense by summing up the interest for each month:
Total interest expense = ($69.50 + $66.72 + ...) * 25 months
Please note that the ellipsis (...) represents the interest for each remaining month of repayment.
By following these steps, you can determine the total interest expense that Bryant will pay to the credit card company. Keep in mind that this is a general explanation and the actual calculation may vary depending on the specific terms and conditions of Bryant's credit card agreement.