Question

Round any decimals to the nearest penny. Your friend wants to pay off his credit card with a balance of $880.00 and an interest
rate of 16.65% APR by getting a loan from you. You agree to the loan, but insist your friend pay you interest of 3.25% APR. Your
friend agrees. How much interest does your friend save at the end of the first month by paying you instead of the credit card?

Answer 1

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.