To calculate the interest your friend saves by taking a loan from you instead of paying the credit card interest, we first need to find the interest amounts for both the credit card and the loan after one month.
Step 1: Calculate the Credit Card Interest for One Month
The credit card has an APR of 16.65%. To find the monthly interest rate, we divide the APR by 12 months:
\[ \text{Monthly interest rate} = \frac{16.65%}{12} = 1.3875% \]
Convert this percentage to decimal for the calculation:
\[ 1.3875% = 0.013875 \]
Now, calculate the interest on the credit card balance of $880.00:
\[ \text{Credit card interest} = 880.00 \times 0.013875 = 12.195 \]
Rounding to the nearest penny:
\[ \text{Credit card interest} \approx 12.20 \]
Step 2: Calculate Your Loan Interest for One Month
The loan has an APR of 3.25%. Again, we'll find the monthly interest rate:
\[ \text{Monthly interest rate} = \frac{3.25%}{12} = 0.2708333% \]
Convert this percentage to decimal:
\[ 0.2708333% = 0.002708333 \]
Calculate the interest on the loan amount of $880.00:
\[ \text{Loan interest} = 880.00 \times 0.002708333 \approx 2.384 \]
Rounding to the nearest penny:
\[ \text{Loan interest} \approx 2.38 \]
Step 3: Calculate Savings
Now we'll find the difference between the interest from the credit card and the interest from the loan:
\[ \text{Savings} = \text{Credit card interest} - \text{Loan interest} = 12.20 - 2.38 \]
\[ \text{Savings} = 9.82 \]
Final Answer
Your friend saves approximately $9.82 at the end of the first month by paying you instead of the credit card.