Question

gertrude took out a 30-year loan for $95,000 at 8.4% interest, compounded monthly. if her monthly payment on he loan is $723.75,
how much of her first payment went toward note reduction?

$60.80
$665.00
$58.75
$723.75

Answer 1

To determine how much of Gertrude's first payment went toward note reduction (the principal), we can first calculate the amount of interest charged on the loan for the first month and subtract that from the total payment.

1. **Determine the monthly interest rate:**
The annual interest rate is 8.4%, so the monthly interest rate (as a decimal) is:
\[
\text{Monthly interest rate} = \frac{8.4\%}{12} = \frac{0.084}{12} = 0.007
\]

2. **Calculate the interest for the first month:**
The interest for the first month can be calculated using the formula:
\[
\text{Interest} = \text{Loan amount} \times \text{Monthly interest rate}
\]
\[
\text{Interest} = 95,000 \times 0.007 = 665
\]

3. **Determine the principal reduction:**
The total monthly payment is $723.75. The amount that goes toward reducing the principal is:
\[
\text{Principal reduction} = \text{Total payment} - \text{Interest}
\]
\[
\text{Principal reduction} = 723.75 - 665 = 58.75
\]

Therefore, the amount of Gertrude's first payment that went toward note reduction is **$58.75**.

The correct answer is **$58.75**.