Question

Your parents have a credit card with a balance of $2,748.56. The interest rate is 10.5% APR. A late payment fee of $40.00 is added to the principal if they pay after 6/1. They make a payment for $300.00 on 6/1. How much interest did they pay?
(1 point)
Responses

$24.05
$24.05

$288.60
$288.60

$24.40
$24.40

$297.00

Answer 1

To calculate the interest they paid on the credit card balance, we need to determine if any interest is added before or after the payment is made. Here's a step-by-step breakdown:

1. **Determine the daily interest rate**:
The APR is 10.5%, so the daily interest rate is:
\[
\text{Daily Interest Rate} = \frac{10.5\%}{365} = \frac{0.105}{365} \approx 0.00028767
\]

2. **Calculate interest accrued before the payment**:
Since the payment is made on 6/1 and we can assume there is no late fee yet, we will calculate interest on the principal for one month (assuming 30 days of interest calculation for simplicity).

\[
\text{Interest Accrued} = \text{Principal} \times \text{Daily Interest Rate} \times \text{Number of Days}
\]
Plugging in the values:
\[
\text{Interest Accrued} = 2748.56 \times 0.00028767 \times 30 \approx 23.73
\]

3. **Total amount owed after including interest**:
\[
\text{Total Amount After Interest} = \text{Principal} + \text{Interest Accrued} = 2748.56 + 23.73 = 2772.29
\]

4. **Calculate the remaining balance after the payment**:
\[
\text{Remaining Balance} = \text{Total Amount After Interest} - \text{Payment} = 2772.29 - 300.00 = 2472.29
\]

5. **Check late fee**: Since they paid on 6/1, there is no late fee, so we only concern ourselves with the interest calculated before the payment.

From the calculations, it appears the total interest paid prior to the payment was about $23.73, which is closer to $24.05 when rounding effects or variations due to the exact days considered.

Since $24.05 is a listed option, this is the closest answer. Therefore, the interest they paid is:

**$24.05**