Question

Your friend wants to borrow $1,137.45 from you
to pay off a credit card that charges 14.7% APR.
You agree to the loan but require your friend to pay you
interest of 3.6% APR on the loan and your friend agrees.
How much interest does your friend save compared to the
credit card at the end of the first month?

Answer 1

To calculate how much interest your friend saves compared to the credit card at the end of the first month, we first need to determine the interest amounts for both the credit card and your loan.

1. **Calculate the interest for the credit card**:
- Principal: $1,137.45
- APR: 14.7%
- Monthly interest rate = \( \frac{14.7\%}{12} = \frac{0.147}{12} = 0.01225 \)
- Interest for the first month = Principal × Monthly interest rate
\[
\text{Interest (credit card)} = 1,137.45 \times 0.01225 \approx 13.925
\]

2. **Calculate the interest for your loan**:
- Principal: $1,137.45
- APR: 3.6%
- Monthly interest rate = \( \frac{3.6\%}{12} = \frac{0.036}{12} = 0.003 \)
- Interest for the first month = Principal × Monthly interest rate
\[
\text{Interest (your loan)} = 1,137.45 \times 0.003 \approx 3.41235
\]

3. **Calculate the savings**:
- Savings = Interest (credit card) - Interest (your loan)
\[
\text{Savings} = 13.925 - 3.41235 \approx 10.51265
\]

Therefore, your friend saves approximately **$10.51** in interest compared to the credit card at the end of the first month.