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?

Question

(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.