Your home loan has an initial principal balance of $292,000, monthly payments over the next 30 years, and an annualized interest rate of 5.0%. What is the interest component of payment #24? Enter your answer as a positive number (in dollars), and round to the nearest dollar.

To determine the interest component of the 24th payment for the home loan, we'll follow these steps:

### Step 1: Identify the details of the loan
- **Principal (P)**: $292,000
- **Annual interest rate (r)**: 5.0% (0.05 in decimal form)
- **Monthly interest rate (i)**: $ \frac{5.0\%}{12} = \frac{0.05}{12} = 0.004167 $
- **Loan term**: 30 years (which is 360 months)

### Step 2: Use the formula for the monthly payment
The formula for the monthly mortgage payment is:

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

Where:
- $ M $ is the monthly payment
- $ P $ is the principal loan amount
- $ i $ is the monthly interest rate
- $ n $ is the number of payments (360 months for a 30-year loan)

Let's calculate the monthly payment.

### Step 3: Calculate the loan balance after 23 payments
To find the interest component of the 24th payment, we need to know the remaining balance after 23 payments. The formula for the remaining loan balance after $ k $ payments is:

\[
B_k = P \times \frac{(1 + i)^n - (1 + i)^k}{(1 + i)^n - 1}
\]

Where $ B_k $ is the balance after $ k $ payments.

### Step 4: Calculate the interest portion of payment #24
Once we have the balance after 23 payments, the interest portion of the 24th payment is simply:

\[
\text{Interest component} = B_{23} \times i
\]

Now, let's compute the interest portion of payment #24 using the provided data.The interest component of payment #24 is **$1,181**.

Would you like more details or have any questions? Here are 5 related questions for further exploration:

1. How much of the 24th payment goes toward the principal?
2. What will the total interest paid be after 24 payments?
3. How does the loan balance change after each payment?
4. What is the total interest paid over the life of the loan?
5. How would an extra payment impact the loan balance and interest?

**Tip:** Making extra payments early in the loan significantly reduces the total interest paid.

Learn how to calculate the interest component of the 24th payment for a home loan of $292,000 over 30 years with a 5% annual interest rate. This solution explains the loan amortization process and uses key formulas such as the monthly payment formula and the remaining balance formula. Ideal for college-level students studying finance or economics.

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