For a 30-year house mortgage of $300,000 at 5.5% interest, find the following. (Round your final answers to two decimal places.)(a) the amount of the first monthly payment that goes to repay principal

To calculate the amount of the first monthly payment that goes toward repaying the principal, we need to first calculate the monthly mortgage payment using the formula for the monthly payment on a fixed-rate mortgage:

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

Where:
- $ M $ is the monthly mortgage payment
- $ P $ is the principal loan amount (\$300,000)
- $ r $ is the monthly interest rate (annual interest rate divided by 12), which is $ \frac{5.5\%}{12} = \frac{0.055}{12} = 0.00458333 $
- $ n $ is the total number of payments (for a 30-year mortgage with monthly payments, $ n = 30 \times 12 = 360 $)

Once we calculate $ M $, we can find how much of the first payment goes toward the interest and the principal. The amount that goes to interest in the first month is calculated as:

\[
\text{Interest for first month} = P \times r
\]

Then, the portion that goes toward the principal is:

\[
\text{Principal payment} = M - \text{Interest for first month}
\]

Let's calculate this.The monthly mortgage payment is approximately \$1,703.37, and the amount of the first payment that goes toward repaying the principal is approximately \$328.37.

Would you like any further clarification or details on this calculation?

Here are 5 related questions for further exploration:
1. How does the principal repayment change over time in a mortgage?
2. How is the total interest paid over the life of the mortgage calculated?
3. How does changing the interest rate affect the monthly payment?
4. What happens if additional payments are made toward the principal?
5. How does a shorter loan term affect the monthly payment and total interest?

**Tip:** The amount of each payment going toward the principal increases as the mortgage progresses, while the interest portion decreases.

For a 30-year house mortgage of $300,000 at 5.5% interest, find the following. (Round your final answers to two decimal places.) (a) the amount of the first monthly payment that goes to repay principal

Learn how to calculate the first monthly payment's principal repayment for a $300,000 30-year mortgage at 5.5% interest. This step-by-step guide explains key finance concepts, including the mortgage payment formula, amortization schedule, and interest calculations. Suitable for advanced high school or college-level students.

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