Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement where the interest (12.5% APR) is waived for the first 12 months provided you make the required monthly payments; otherwise the interest is accrued from the date of purchase. You miss the first payment due date. The late fee is $35.00. How much is the interest?

Question

(1 point)
Responses

$103.13
$103.13

$110.34
$110.34

$8.59
$8.59

$9.20

Answer 1

To calculate the total interest accrued after missing the first payment due date, we start with the original purchase price and calculate the sales tax before determining the interest.

1. Calculate the total purchase price including sales tax:

   • Original purchase price: $825.00
   • Sales tax (7%): \( 825.00 \times 0.07 = 57.75 \)
   • Total purchase price: \( 825.00 + 57.75 = 882.75 \)

2. Determine the interest rate and time period:

   • The APR is 12.5%, which means the monthly interest rate is \( \frac{12.5%}{12} = \frac{0.125}{12} \approx 0.01041667 \) (or about 1.041667% per month).
   • Since you missed the first payment, the interest will be calculated for 1 month.

3. Calculate the interest for 1 month:

   • Interest for 1 month: \( 882.75 \times 0.01041667 \approx 9.20 \)

Therefore, if you missed the first payment, the interest accrued would be $9.20.

The correct response is: $9.20