To solve this problem, we need to calculate the interest paid in the first month and then determine how much of the first payment went toward reducing the loan balance.

Step 1: Calculate the Interest Paid in Month 1

The formula for calculating the interest portion of a monthly payment is:

$\text{Interest} = \left( \frac{r}{12} \right) \times P$

where:

• $r$ is the annual interest rate (4% or 0.04),
• $P$ is the loan balance ($117,000),
• The division by 12 is to convert the annual interest rate to a monthly rate.

Substituting the values:

$\text{Interest} = \left( \frac{0.04}{12} \right) \times 117,000$

Let's calculate the interest.

The interest paid in the first month is $390.00.

Step 2: Calculate the Amount Toward Reducing the Loan Balance

To find the amount that goes toward reducing the principal, we subtract the interest from the total monthly payment:

$\text{Principal Payment} = \text{Monthly Payment} - \text{Interest}$

The total monthly payment is $865.43, and the interest for the first month is $390.00. Let's calculate the principal reduction.

$\text{Principal Payment} = 865.43 - 390.00$

Let's compute that.The amount that goes toward reducing the loan balance in the first month is $475.43.

Summary:

• Interest paid in month 1: $390.00
• Principal reduction in month 1: $475.43

Would you like any further details or explanations?

Here are 5 related questions to explore:

1. How does the principal reduction change over time with each payment?
2. How much total interest will be paid over the life of the loan?
3. What would the monthly payment be if the interest rate was lower, say 3%?
4. How much will the balance be after 5 years of payments?
5. What happens to the total interest if extra payments are made?

Tip: The proportion of each payment that goes toward the principal increases over time, as the interest is calculated on the remaining balance.