Question

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?
(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**.