You want to buy a $244,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 5.05% 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 this down step by step:

### Part (a): Loan Amount
You plan to pay 5% as a down payment, which means the remaining 95% will be the loan amount.

- **Home price** = $244,000
- **Down payment** = 5% of $244,000 = $ 0.05 \times 244,000 $
  
\[
\text{Down payment} = 12,200
\]

So, the **loan amount** is:

\[
\text{Loan amount} = 244,000 - 12,200 = 231,800
\]

### Part (b): Monthly Payment
We use the formula for monthly mortgage payment $ M $:

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

Where:
- $ P $ = loan amount = 231,800
- $ r $ = monthly interest rate = $ \frac{5.05\%}{12} = \frac{0.0505}{12} $
- $ n $ = total number of payments = $ 30 \times 12 = 360 $

Let's calculate the monthly payment next.

### Part (c): First Payment Interest
The interest portion of the first payment is calculated as:

\[
\text{First payment interest} = \text{Loan amount} \times r
\]

I will calculate both the monthly payment and the first payment's interest next.### Part (b): Monthly Payment
Your monthly mortgage payment will be approximately **$1,251.45**.

### Part (c): First Payment Interest
The interest portion of your first payment will be approximately **$975.49**.

Would you like more details or have any further questions?

Here are five related questions:
1. How does the loan amount change with a higher down payment?
2. What happens to the monthly payments if the interest rate decreases?
3. How much total interest will you pay over the 30 years?
4. How does the length of the loan term affect the monthly payments?
5. What is the principal portion of the first payment?

**Tip:** Making extra payments on your loan early can significantly reduce the total interest paid over the loan term.

You want to buy a $244,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan at 5.05% 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?

Learn how to calculate the loan amount, monthly mortgage payments, and first payment interest for a $244,000 home with a 5% down payment and 5.05% interest rate. This problem demonstrates loan and interest rate calculations, suitable for high school students in Grades 10-12.

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