To determine who spends less on the purchase, let's calculate the total amount your friend pays for the headphones after a year of interest.
- Cost of headphones: $150
- Monthly interest rate on the credit card: 2%
- Total time to pay off: 1 year (12 months)
Calculating the total amount your friend pays:
The formula to calculate the total amount paid with interest over time is:
\[ A = P(1 + r)^n \]
where:
- \(A\) is the total amount after interest,
- \(P\) is the principal amount (initial cost),
- \(r\) is the interest rate per period,
- \(n\) is the number of periods.
Here:
- \(P = 150\)
- \(r = 0.02\)
- \(n = 12\)
Now we plug in the values:
\[ A = 150 \times (1 + 0.02)^{12} \]
Calculating \(A\):
\[ = 150 \times (1.02)^{12} \] \[ = 150 \times 1.2682418 \quad (\text{approximation for } (1.02)^{12}) \] \[ \approx 190.23 \]
So, your friend will pay approximately $190.23 for the headphones after one year.
Total spent:
- You (using debit card): $150
- Your friend (using credit card): approximately $190.23
Difference in spending:
To find out who spends less and by how much:
\[ 190.23 - 150 = 40.23 \]
Thus, your friend spends $40.23 more than you.
Conclusion:
You spend $40.23 less than your friend. Since this specific amount isn't among the options provided, it seems there might be a discrepancy in the choices listed. None of the given responses are correct according to the calculations. You should clarify the interest period as it significantly changes the total cost.