Question

If the credit card in problem #3 has an interest rate of 14.75% and you do not make a payment the first month on that $1,685.90 balance, how much is the difference between the interest and reward?

Problem 3:A credit card gives 2% cash back on purchases. You purchase $1,685.90 in items with that card. What is your reward amount?

(1 point)
Responses

$17.91
$17.91

$88.51
$88.51

$13.00
$13.00

$32.31

Answer 1

To solve this problem, we need to calculate both the rewards and the interest for the first month on a balance of $1,685.90 with an interest rate of 14.75%.

**Step 1: Calculate the reward amount.**

The credit card gives 2% cash back on purchases. To find the reward amount:

\[
\text{Reward} = \text{Total Purchase} \times \text{Cash Back Percentage}
\]

\[
\text{Reward} = 1685.90 \times 0.02 = 33.718 \text{ or } 33.72 \text{ (rounded to two decimal places)}
\]

**Step 2: Calculate the interest for the first month.**

The monthly interest rate is calculated by dividing the annual interest rate by 12:

\[
\text{Monthly Interest Rate} = \frac{14.75\%}{12} = 1.2291667\% = 0.012291667
\]

Now, we calculate the interest for the balance of $1,685.90 for one month:

\[
\text{Interest} = \text{Balance} \times \text{Monthly Interest Rate}
\]

\[
\text{Interest} = 1685.90 \times 0.012291667 \approx 20.71 \text{ (rounded to two decimal places)}
\]

**Step 3: Calculate the difference between the interest and the reward.**

Now, we find the difference between the interest accrued and the reward earned:

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

\[
\text{Difference} = 20.71 - 33.72 = -13.01
\]

Thus, the difference between the interest and the reward is approximately **-$13.01**. This means that the rewards outweigh the interest.

To summarize:
- Reward amount = $33.72
- Interest amount = $20.71
- Difference = $20.71 - $33.72 = -$13.01

The difference is negative, indicating the rewards exceeded the interest by about $13.01.