Your parents make a purchase of $2,975.34 using a popular reward credit card that gives you 1% cash back. If the credit card has a 13.5% APR and you do not make a payment the first month, how much is the difference between the interest and reward?

Question

(1 point)
Responses

$29.75
$29.75

$371.92
$371.92

$3.72
$3.72

$33.47

Answer 1

To find the difference between the interest and the reward, we first need to calculate both.

1. Calculate the Reward: The cash back reward is 1% of the purchase amount.

   \[ \text{Reward} = 0.01 \times 2975.34 = 29.7534 \approx 29.75 \]

2. Calculate the Interest: The interest for the first month can be calculated using the formula:

   \[ \text{Interest} = \text{Principal} \times \left(\frac{\text{APR}}{12}\right) \]

   where:

   • Principal = $2,975.34
   • APR = 13.5% = 0.135

   \[ \text{Interest} = 2975.34 \times \left(\frac{0.135}{12}\right) \]

   \[ \text{Interest} = 2975.34 \times 0.01125 \approx 33.47 \]

3. Calculate the Difference: Now, we find the difference between the interest and the reward.

   \[ \text{Difference} = \text{Interest} - \text{Reward} \]

   \[ \text{Difference} = 33.47 - 29.75 = 3.72 \]

Thus, the answer is $3.72.