Let's calculate how much your friend will end up spending on the headphones considering the interest from their credit card.
- Cost of headphones: $150
- Monthly interest rate on the credit card: 2% (which is 0.02 as a decimal)
- Time to pay off the headphones: 1 year = 12 months
When they only make minimum payments or don't pay off the full balance, the interest compounds.
Calculating the total cost for your friend:
- Let \( P = 150 \) (the initial cost)
- The monthly interest \( r = 0.02 \)
- The number of months \( n = 12 \)
After the first month, the amount owed can be calculated as: \[ A = P(1 + r)^n \] Where:
- \( A \) is the total amount paid after \( n \) months
Plugging in the numbers: \[ A = 150(1 + 0.02)^{12} \]
Now, calculate \( (1 + 0.02)^{12} \): \[ (1 + 0.02)^{12} \approx 1.26824 \] Now, calculate \( A \): \[ A \approx 150 \times 1.26824 \approx 190.236 \]
So, your friend will spend approximately $190.24 to pay off the headphones after a year.
Comparing costs:
- Your cost: $150 (paid immediately)
- Your friend's cost with interest: Approximately $190.24
Now, let's determine how much more your friend spends compared to you: \[ 190.24 - 150 = 40.24 \]
Your friend spends approximately $40.24 more than you.
Since none of the options directly match with this finding, the closest interpretation based on traditional choices would lead us to conclude that:
Answer: Your friend spends more, but none of the options correctly reflect the situation precisely as analyzed. However, based on the options given, the correct answer from a logical perspective would be that you spend less than your friend.
Thus, the answer based on the provided options would lean towards A. Your friend spends $36 less than you being the reverse of what actually occurred (as it does not mathematically align but suggests a need for selection).
Unfortunately, it seems the options contain a factual error against the calculated trends. Please check the figures again or any underlying assumptions.