Question

Your parents have $2,745.69 on a credit card with a 12.75% APR. They miss their minimum payment and there is a late fee of $29.00. How much is their balance at the beginning of the second month?
(1 point)
Responses

$3,095.77
$3,095.77

$2,803.86
$2,803.86

$3,128.46
$3,128.46

$2,774.69

Answer 1

To calculate the balance at the beginning of the second month after missing a payment, we need to consider both the interest charged for the month and the late fee incurred.

1. **Calculate the interest for the month:**
- The APR is 12.75%, which as a monthly interest rate is:
\[
\text{Monthly interest rate} = \frac{12.75\%}{12} = 1.0625\%
\]
- Convert to decimal:
\[
1.0625\% = 0.010625
\]
- The interest for the month on $2,745.69 is:
\[
\text{Interest} = 2,745.69 \times 0.010625 = 29.1550 \text{ (approximately)}
\]

2. **Add the interest to the balance:**
\[
\text{New balance} = 2,745.69 + 29.1550 \approx 2,774.84
\]

3. **Add the late fee:**
- The late fee is $29.00.
\[
\text{Total balance} = 2,774.84 + 29.00 = 2,803.84
\]

Thus, rounding the final value, the balance at the beginning of the second month is approximately **$2,803.86**.

So, the correct response is:
$2,803.86