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Let's break down the problem from the image you've uploaded.

You want to buy a home for **$277,000** and plan to pay **10%** as a down payment. The loan is for **30 years**. You are asked to calculate:

### a) Loan amount:
The loan amount is the total price minus the down payment.

- Home price = $277,000
- Down payment = 10% of $277,000 = $277,000 × 0.10 = $27,700
- Loan amount = $277,000 - $27,700 = **$249,300**

### b) Monthly payment with a 3.25% annual interest rate, compounded monthly:
To find the monthly payment, we use the **loan amortization formula**:

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

Where:
- $ M $ is the monthly payment.
- $ P $ is the loan amount, which is **$249,300**.
- $ r $ is the monthly interest rate = annual interest rate / 12 = $ \frac{3.25\%}{12} = 0.002708 $.
- $ n $ is the number of payments = 30 years × 12 months = **360**.

Substitute the values:

\[
M = 249300 \times \frac{0.002708(1+0.002708)^{360}}{(1+0.002708)^{360} - 1}
\]

Calculating this gives **$1,085.35** as the monthly payment for 3.25% interest.

### c) Monthly payment with a 4.25% annual interest rate, compounded monthly:
Similarly, for a 4.25% annual interest rate:

- Monthly interest rate = $ \frac{4.25\%}{12} = 0.003542 $
- Number of payments = **360**

\[
M = 249300 \times \frac{0.003542(1+0.003542)^{360}}{(1+0.003542)^{360} - 1}
\]

Calculating this gives **$1,226.31** as the monthly payment for 4.25% interest.

---

### Summary:
- **Loan amount**: $249,300
- **Monthly payment (3.25%)**: $1,085.35
- **Monthly payment (4.25%)**: $1,226.31

Do you have any questions or need further clarifications?

---

**Related Questions**:
1. What would be the total interest paid over the life of the loan at 3.25%?
2. How does the total interest compare between 3.25% and 4.25% interest rates?
3. What is the impact of increasing the down payment to 20% on monthly payments?
4. What happens if the loan term is shortened to 15 years at the same interest rates?
5. How would bi-weekly payments affect the loan payoff time?

**Tip**: The longer the loan term, the more interest you'll pay overall, even if the monthly payments are lower.

You want to buy a $277,000 home. You plan to pay 10% as a down payment, and take out a 30-year loan for the rest. (Enter numeric answers to 2 decimal places.)
a) How much is the loan amount going to be?
b) What will your monthly payments be if the annual interest rate is 3.25%, compounded monthly?
c) What will your monthly payments be if the annual interest rate is 4.25%, compounded monthly?

Learn how to calculate the loan amount and monthly payments for a $277,000 home with 10% down payment over 30 years. The solution includes detailed steps for calculating monthly payments at 3.25% and 4.25% annual interest rates, compounded monthly.

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