You want to buy a $153,000 home. You plan to pay 10% as a down payment, and take out a 30 year loan at 3.65% interest for the rest.

a) How much is the loan amount going to be?

b) What will your monthly payments be?

c) How much of the first payment is interest?

Let's break down the problem step by step.

### a) Loan amount

The down payment is 10% of the home's price, so the loan will cover the remaining 90%.

\[
\text{Loan amount} = \text{Home price} - \text{Down payment}
\]

The down payment is:
\[
\text{Down payment} = 10\% \times 153,000 = 0.10 \times 153,000 = 15,300
\]

So, the loan amount is:
\[
\text{Loan amount} = 153,000 - 15,300 = 137,700
\]

### b) Monthly payment

To calculate the monthly payment for a fixed-rate mortgage, we use the formula:

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

Where:
- $M$ is the monthly payment,
- $P$ is the loan amount ($137,700),
- $r$ is the monthly interest rate (annual interest rate divided by 12),
- $n$ is the total number of payments (loan term in years multiplied by 12).

First, let's calculate $r$ and $n$:
\[
r = \frac{3.65\%}{12} = \frac{0.0365}{12} = 0.00304167
\]
\[
n = 30 \times 12 = 360 \text{ months}
\]

Now, substituting these values into the formula:

\[
M = 137,700 \times \frac{0.00304167(1 + 0.00304167)^{360}}{(1 + 0.00304167)^{360} - 1}
\]

I will calculate the monthly payment next.

### c) Interest in the first payment

The interest portion of the first payment is calculated as:

\[
\text{Interest in first payment} = \text{Loan amount} \times \text{Monthly interest rate}
\]
\[
\text{Interest in first payment} = 137,700 \times 0.00304167
\]

Let's calculate both the monthly payment and the interest in the first payment.### Results:

**a) Loan amount:**
\[
\text{Loan amount} = 137,700
\]

**b) Monthly payment:**
\[
\text{Monthly payment} \approx 629.92
\]

**c) Interest in the first payment:**
\[
\text{Interest in first payment} \approx 418.84
\]

Would you like further details or have any questions?

### 5 Related Questions:
1. How does the monthly payment change if the interest rate increases to 4%?
2. What would happen if you reduced the loan term to 15 years?
3. How much total interest will you pay over the life of the loan?
4. What is the principal paid in the first monthly payment?
5. How would additional payments toward the principal affect the loan duration?

**Tip:** Making extra payments toward your principal early can significantly reduce the overall interest paid on a mortgage.

Learn how to calculate the loan amount, monthly payments, and interest for a $153,000 home with 10% down payment and a 30-year loan at 3.65% interest. This detailed solution breaks down loan calculations, fixed-rate mortgage formulas, and interest components. Suitable for high school students or anyone learning loan basics.

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