You want to buy a $219,000 home. You plan to pay 20% 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 6%? S c) What will your monthly payments be if the interest rate is 7%?

To break down the problem:

### Part a) Loan Amount:
The down payment is 20%, and you are financing the remaining 80%. 

- **Home price**: $219,000
- **Down payment**: $ 20\% \times 219,000 = 0.20 \times 219,000 = 43,800 $
- **Loan amount**: $ 219,000 - 43,800 = 175,200 $

So, the loan amount will be **$175,200**.

---

### Part b) Monthly Payments at 6% Interest:
For a 30-year mortgage (360 months), the monthly payment can be calculated using the **loan payment formula**:

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

Where:
- $ M $ = monthly payment
- $ P $ = loan amount = 175,200
- $ r $ = monthly interest rate = $ \frac{6\%}{12} = \frac{0.06}{12} = 0.005 $
- $ n $ = total number of payments = 30 years $ \times $ 12 months/year = 360

Let me calculate this.

The monthly payment with a 6% interest rate would be **$1,050.41**.

---

### Part c) Monthly Payments at 7% Interest:
For a 7% interest rate, we follow the same formula. The monthly interest rate will now be:

\[
r = \frac{7\%}{12} = \frac{0.07}{12} = 0.005833
\]

Let me calculate this.The monthly payment with a 7% interest rate would be **$1,165.61**.

---

### Summary:
a) Loan amount: **$175,200**  
b) Monthly payment at 6% interest: **$1,050.41**  
c) Monthly payment at 7% interest: **$1,165.61**

Would you like any further details or clarifications?

### Related Questions:
1. How does the loan term (e.g., 15 years vs. 30 years) affect the monthly payments?
2. What is the total interest paid over the life of the loan for both interest rates?
3. How would additional principal payments affect the total loan amount?
4. How do different down payment percentages impact the overall loan costs?
5. What is the effect of points or loan fees on the total cost of the mortgage?

### Tip:
Even small changes in the interest rate can significantly affect monthly payments and total interest over time. Consider locking in a favorable rate when interest rates are low.

You want to buy a $219,000 home. You plan to pay 20% 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 6%? c) What will your monthly payments be if the interest rate is 7%?

Learn how to calculate the loan amount and monthly payments for a $219,000 home with a 20% down payment. Explore detailed solutions for interest rates of 6% and 7% using loan amortization formulas. Suitable for students and homeowners looking to understand mortgage calculations.

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