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?

Question

(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