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.
Your friend pays you $200 at the end of the first month.
How much goes towards the principal? Round to the nearest penny

Answer 1

To calculate how much of your friend's payment goes towards the principal, we need to first determine how much interest accumulates on the loan for that first month, based on the interest rate you are charging.

1. **Convert the APR to a monthly interest rate**:
The monthly interest rate can be calculated by taking the APR and dividing it by 12 (the number of months in a year).

\[
\text{Monthly interest rate} = \frac{3.6\%}{12} = \frac{0.036}{12} \approx 0.003
\]

2. **Calculate the interest for the first month**:
Now we can calculate the interest that accrues on the amount borrowed ($1,137.45) for one month.

\[
\text{Interest for the first month} = \text{Loan Amount} \times \text{Monthly interest rate}
\]

\[
\text{Interest for the first month} = 1,137.45 \times 0.003 \approx 3.41235
\]

Rounding this to the nearest penny, the interest is approximately **$3.41**.

3. **Determine how much of the $200 payment goes towards the principal**:
Now subtract the interest from the total payment to find how much of that payment reduces the principal.

\[
\text{Payment} = 200
\]

\[
\text{Amount towards principal} = \text{Payment} - \text{Interest}
\]

\[
\text{Amount towards principal} = 200 - 3.41 = 196.59
\]

Therefore, the amount that goes towards the principal is **$196.59**.