Question

You have a credit card with a balance of $1,187.92 and the interest is 12.25% APR. A late fee of $30.00 is charged for payments after the due date. You missed your payment due date, but plan to make a payment of $125.00 on the next due date. What will be the new principal after that payment?
(1 point)
Responses

$1,242.39
$1,242.39

$1,105.05
$1,105.05

$1,117.61
$1,117.61

$1,062.92

Answer 1

To calculate the new principal after making a payment of $125.00 on the next due date, we need to consider the following steps:

1. **Determine the interest for the period since the last payment was due.**
- The APR (Annual Percentage Rate) is 12.25%. This means the monthly interest rate is:
\[
\text{Monthly interest rate} = \frac{12.25\%}{12} = 1.0208333\% \approx 0.010208333
\]

2. **Calculate the interest amount on the current balance.**
- Current balance: $1,187.92
- Monthly interest:
\[
\text{Interest} = \text{Current balance} \times \text{Monthly interest rate} = 1,187.92 \times 0.010208333 \approx 12.12
\]

3. **Add the interest and the late fee to the current balance.**
- After adding the late fee of $30.00 and the calculated interest of approximately $12.12, the new balance will be:
\[
\text{New balance} = \text{Current balance} + \text{Interest} + \text{Late fee} = 1,187.92 + 12.12 + 30.00 \approx 1,230.04
\]

4. **Make the payment and find the new principal.**
- Now, subtract the payment of $125.00 from this new balance:
\[
\text{New principal} = 1,230.04 - 125.00 \approx 1,105.04
\]

Thus, after rounding slightly, the new principal after the payment will be **$1,105.05**.

The correct answer is: **$1,105.05**.