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Let's solve this step by step.

You want to buy a $249,000 home, paying 10% as a down payment and financing the rest with a 30-year loan. We'll address each part:

---

### Part (a): How much is the loan amount going to be?

1. **Home Price**: $249,000
2. **Down Payment (10%)**:  
   \[
   \text{Down Payment} = 0.10 \times 249,000 = 24,900
   \]
3. **Loan Amount** (Remaining after down payment):  
   \[
   \text{Loan Amount} = 249,000 - 24,900 = 224,100
   \]

So, the loan amount is **$224,100**.

---

### Part (b): What will your monthly payments be if the interest rate is 5%?

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

\[
M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}
\]
Where:
- $ M $ = monthly payment
- $ P $ = loan amount ($224,100)
- $ r $ = monthly interest rate (annual interest rate ÷ 12)
- $ n $ = total number of payments (years × 12)

For **5% interest rate**:
- Annual interest rate = 5%, so monthly interest rate $ r = \frac{0.05}{12} = 0.004167 $
- Loan term = 30 years, so $ n = 30 \times 12 = 360 $ months

Now, let's calculate the monthly payment:

\[
M = 224,100 \times \frac{0.004167(1+0.004167)^{360}}{(1+0.004167)^{360} - 1}
\]

I'll compute this next.The monthly payment for a 30-year loan at a 5% interest rate is **$1,203.02**.

---

### Part (c): What will your monthly payments be if the interest rate is 6%?

Now, we apply the same mortgage formula but with a 6% interest rate:

For **6% interest rate**:
- Annual interest rate = 6%, so monthly interest rate $ r = \frac{0.06}{12} = 0.005 $
- Loan term remains the same, $ n = 360 $ months.

Now, let me calculate the monthly payment for the 6% rate.The monthly payment for a 30-year loan at a 6% interest rate is **$1,343.59**.

---

### Summary:
1. **Loan amount**: $224,100
2. **Monthly payment at 5% interest**: $1,203.02
3. **Monthly payment at 6% interest**: $1,343.59

Would you like more details on any of these steps or calculations? 

Here are 5 related questions you might explore:
1. How does the down payment percentage affect the loan amount?
2. What is the impact of a shorter loan term on monthly payments?
3. How would an interest rate of 4% change the monthly payments?
4. What portion of the monthly payment goes toward interest vs principal over time?
5. How does increasing the down payment affect the total interest paid over the life of the loan?

**Tip:** Increasing the down payment reduces both the loan amount and total interest, resulting in lower monthly payments.

You want to buy a $249,000 home. You plan to pay 10% as a down payment, and take out a 30-year loan for the rest. a) How much is the loan amount going to be? b) What will your monthly payments be if the interest rate is 5%? c) What will your monthly payments be if the interest rate is 6%?

Learn how to calculate the loan amount and monthly payments for a $249,000 home with a 10% down payment. This problem covers key concepts like loan calculation, interest rates, and monthly payments for 30-year loans at 5% and 6% interest rates. Suitable for high school students.

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