Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

You have a credit card with a balance of $1,367.90 at a 9.5% APR. You pay $400.00 each month on the
due date until the card is paid off. How many months does it take to pay off the card, and what is the total
amount paid including interest?
Be sure to include in your response: answer and steps

Answer 1

Explanation:

The solution to this problem involves calculating the monthly interest and reducing the balance accordingly each month until the balance reaches zero. Here are the steps:

Calculate the monthly interest: First, we need to calculate the monthly interest rate. We can do this by dividing the APR by 12. The monthly interest rate is 9.5% / 12 = 0.7917%.

Calculate the interest charge for the first month: The interest charge for the first month is the balance multiplied by the monthly interest rate. In this case, the interest charge is $1,367.90 x 0.7917% = $10.87.

Calculate the new balance: Next, we need to subtract the payment from the balance and add the interest charge to determine the new balance. The new balance after the first payment is $1,367.90 - $400.00 + $10.87 = $978.87.

Repeat the steps for subsequent months: Repeat the process of calculating the monthly interest charge and the new balance for each subsequent month until the balance reaches zero.

Keep track of the number of months: As we repeat the steps, keep track of the number of months it takes to pay off the card.

Here is a summary of the calculations:

Month Balance Interest Payment New Balance

1 $1,367.90 $10.87 $400.00 $978.87

2 $978.87 $7.74 $400.00 $586.61

3 $586.61 $4.62 $400.00 $191.23

4 $191.23 $1.50 $400.00 $-208.27

It takes 4 months to pay off the card, and the total amount paid including interest is $1,367.90 + $10.87 + $7.74 + $4.62 + $1.50 = $1392.73.