To determine how much interest your friend saves at the end of the first month by paying you instead of the credit card, we need to calculate the interest for both the credit card and the loan.
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Calculate the interest on the credit card for one month:
- The APR is 17.34%, which needs to be converted to a monthly interest rate: \[ \text{Monthly Interest Rate} = \frac{17.34%}{12} = \frac{0.1734}{12} \approx 0.01445 \]
- Now, calculate the interest for the credit card balance of $689.34: \[ \text{Interest on Credit Card} = 689.34 \times 0.01445 \approx 9.951 \]
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Calculate the interest on the loan for one month:
- The APR for the loan is 4.67%, which also needs to be converted to a monthly interest rate: \[ \text{Monthly Interest Rate} = \frac{4.67%}{12} = \frac{0.0467}{12} \approx 0.00389 \]
- Now, calculate the interest for the loan amount of $689.34: \[ \text{Interest on Loan} = 689.34 \times 0.00389 \approx 2.684 \]
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Calculate the savings in interest:
- Finally, subtract the interest on the loan from the interest on the credit card: \[ \text{Interest Savings} = \text{Interest on Credit Card} - \text{Interest on Loan} \approx 9.951 - 2.684 \approx 7.267 \]
Thus, your friend saves approximately $7.27 in interest at the end of the first month by paying you instead of using the credit card.