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The problem in the image asks how much of the first monthly payment will go towards the principal balance for a $15,000 loan over 3 years at an annual interest rate of 5.4%. 

Here’s how to calculate it:

### Step 1: Determine the monthly payment amount using the formula for an amortizing loan:
\[
M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $ M $ is the monthly payment,
- $ P $ is the loan amount ($15,000),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the number of payments (loan term in months).

The annual interest rate is 5.4%, so the monthly interest rate is:
\[
r = \frac{5.4\%}{12} = \frac{0.054}{12} = 0.0045
\]
The loan term is 3 years, so the number of months is:
\[
n = 3 \times 12 = 36
\]

Substituting these into the formula:
\[
M = \frac{15,000 \times 0.0045 \times (1 + 0.0045)^{36}}{(1 + 0.0045)^{36} - 1}
\]

I will calculate this now.The monthly payment amount for the loan is approximately **$452.26**.

### Step 2: Calculate how much goes toward interest in the first payment:
The first payment's interest is calculated as:
\[
\text{Interest} = P \times r = 15,000 \times 0.0045 = 67.50
\]

### Step 3: Calculate how much goes toward the principal:
The amount going toward the principal in the first payment is the total monthly payment minus the interest:
\[
\text{Principal} = M - \text{Interest} = 452.26 - 67.50 = 384.76
\]

Therefore, **$384.76** of the first payment goes toward the principal.

Let me know if you'd like further details or have any questions!

Here are some related questions:
1. How does the interest portion change over time with each payment?
2. How do you calculate the total interest paid over the life of the loan?
3. What is the impact of making additional payments on the loan principal?
4. How would changing the loan term (e.g., to 5 years) affect the monthly payment?
5. How is the loan's amortization schedule structured?

**Tip:** To reduce interest payments, consider making extra payments toward the principal when possible. This lowers the total amount of interest paid over time!

If you take out a $15,000 loan for a period of 3 years at a 5.4% annual interest rate, how much of your first monthly payment will go toward the principal balance?

Learn how to calculate the amount that goes toward the principal in the first monthly payment of a $15,000 loan over 3 years at 5.4% interest. This problem demonstrates loan amortization, including interest and principal payment calculations.

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