Marcel Thiessen purchased a home for $203,500 and obtained a 15-year, fixed-rate mortgage at 8% after paying a down payment of 10%. Of the first month's mortgage payment, how much is interest and how much is applied to the principal?

To calculate how much of the first month's mortgage payment goes toward interest and how much goes toward the principal, let's break it down step by step.

### 1. Down Payment
Marcel Thiessen made a down payment of 10% on a home priced at \$203,500.
\[
\text{Down Payment} = 10\% \times 203,500 = 0.10 \times 203,500 = 20,350
\]
The loan amount is the home's price minus the down payment:
\[
\text{Loan Amount} = 203,500 - 20,350 = 183,150
\]

### 2. Monthly Mortgage Payment
Next, we calculate the monthly mortgage payment using the loan amount, interest rate, and loan term. The formula for the monthly payment is:

\[
M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]
Where:
- $M$ is the monthly payment.
- $P$ is the loan amount (\$183,150).
- $r$ is the monthly interest rate (annual rate of 8% divided by 12).
- $n$ is the total number of payments (15 years × 12 months = 180 months).

First, calculate the monthly interest rate:
\[
r = \frac{8\%}{12} = \frac{0.08}{12} = 0.006667
\]
Now, plug the values into the formula to get the monthly payment. I'll compute this.The monthly mortgage payment is approximately \$1,750.28.

### 3. Interest for the First Month
The interest portion of the first month's payment is calculated by multiplying the loan balance by the monthly interest rate:
\[
\text{Interest} = 183,150 \times 0.006667 = 1,221
\]

### 4. Principal Payment for the First Month
The amount applied to the principal is the total monthly payment minus the interest:
\[
\text{Principal} = 1,750.28 - 1,221 = 529.28
\]

### Summary:
- **Interest for the first month:** \$1,221.00
- **Principal payment for the first month:** \$529.28

Would you like further details or explanations?

Here are some related questions to explore:
1. How does the interest change over time during the loan?
2. What would happen if the down payment percentage increased?
3. How would a lower interest rate affect the monthly payment?
4. What is the impact of extending the loan to 30 years instead of 15 years?
5. How can extra payments reduce the total interest paid?

**Tip:** The interest portion of your payment decreases with time, while the principal portion increases as you pay down the loan!

Marcel Thiessen purchased a home for $203,500 and obtained a 15-year, fixed-rate mortgage at 8% after paying a down payment of 10%. Of the first month's mortgage payment, how much is interest and how much is applied to the principal?

Explore how to calculate the interest and principal portions of a mortgage payment for a $203,500 home with a 15-year term and 8% interest rate. Learn the step-by-step process to determine how much of the first month's payment is interest and how much goes toward the principal. Ideal for students and anyone interested in finance.

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