Question

You make a purchase of $1,987.54 using a rewards credit card that gives you 2% cash back. If the credit card has a 17.75% APR and you do not make a payment the first month, how much is the difference between the first month's interest and the reward?
(1 point)
Responses

$10.35
$10.35

$19.48
$19.48

$29.40
$29.40

$28.81

Answer 1

To calculate the difference between the first month's interest and the reward you receive from the purchase, follow these steps:

1. **Calculate the cash back reward:**
Cash back = Purchase amount × Cash back rate
Cash back = $1,987.54 × 0.02
Cash back = $39.75

2. **Calculate the monthly interest:**
First, you'll need to calculate the monthly interest rate from the APR:
Monthly interest rate = APR / 12
Monthly interest rate = 17.75% / 12
Monthly interest rate = 1.479167% (approximately)

Now, calculate the interest on the amount:
Interest = Purchase amount × Monthly interest rate
Interest = $1,987.54 × 0.01479167
Interest ≈ $29.40

3. **Calculate the difference between interest and cash back:**
Difference = Interest - Cash back
Difference = $29.40 - $39.75
Difference = -$10.35

Since the value is negative, it indicates that the cash back reward is greater than the interest charged.

Thus, the absolute difference is:

**$10.35**

The correct answer is $10.35.