If you take out a $15,000 loan for a period of 36 months at a 5.4% annual interest rate, how much of your first monthly payment will go toward the *balance*? Round your answer to the nearest cent as necessary and do not include the dollar sign.

To find out how much of the first monthly payment will go toward the balance, we need to break down the monthly payment into two components: interest and principal (the amount applied to the balance). 

Here’s how to calculate it:

1. **Loan amount (P)**: $15,000
2. **Annual interest rate (r)**: 5.4% or 0.054
3. **Loan term (n)**: 36 months

### Step 1: Calculate the monthly interest rate
The monthly interest rate is calculated by dividing the annual interest rate by 12.

\[
\text{Monthly interest rate} = \frac{0.054}{12} = 0.0045
\]

### Step 2: Calculate the monthly payment using the amortization formula
The formula for the monthly payment on a loan is:

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]

Where:
- $ M $ is the monthly payment
- $ P $ is the loan amount
- $ r $ is the monthly interest rate
- $ n $ is the number of months

Substituting the values into the formula:

\[
M = 15000 \times \frac{0.0045(1+0.0045)^{36}}{(1+0.0045)^{36} - 1}
\]

Let's calculate the monthly payment first, then determine how much goes toward the balance.

The monthly payment for the loan is approximately $ 452.26 $.

### Step 3: Calculate the interest portion of the first payment
The interest portion of the first payment is calculated by multiplying the loan balance by the monthly interest rate:

\[
\text{Interest} = P \times \text{monthly interest rate}
\]

\[
\text{Interest} = 15000 \times 0.0045 = 67.50
\]

### Step 4: Calculate how much of the first payment goes toward the balance
The portion of the payment that goes toward the balance is the total monthly payment minus the interest:

\[
\text{Principal payment} = \text{Monthly payment} - \text{Interest}
\]

\[
\text{Principal payment} = 452.26 - 67.50 = 384.76
\]

Therefore, $ 384.76 $ of the first monthly payment will go toward the balance.

Would you like further details on how these calculations work?

Here are five related questions:
1. What is the total interest paid over the loan's 36-month term?
2. How much is the total amount paid over the loan period?
3. How does the interest portion of the payment change over time?
4. What would happen if the loan term were reduced to 24 months?
5. How would an increased interest rate impact the monthly payment?

**Tip:** Early payments on a loan apply more toward interest, while later payments reduce the balance faster.

If you take out a $15,000 loan for a period of 36 months at a 5.4% annual interest rate, how much of your first monthly payment will go toward the balance? Round your answer to the nearest cent as necessary and do not include the dollar sign.

Learn how to calculate how much of the first monthly payment on a $15,000 loan at a 5.4% annual interest rate over 36 months will go toward the balance. Understand loan amortization, interest calculation, and principal payment breakdown.

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