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To solve this step by step:

### Given:
- **Home Price**: $228,000
- **Down Payment**: 20% of the home price
- **Loan Interest Rate**: 6.15% (annual)
- **Loan Term**: 30 years (360 months)

---

### **a) Loan Amount Calculation:**

The loan amount is the remaining cost after paying the down payment.

\[
\text{Down Payment} = 20\% \times 228,000 = 0.20 \times 228,000 = 45,600
\]

\[
\text{Loan Amount} = \text{Home Price} - \text{Down Payment} = 228,000 - 45,600 = 182,400
\]

This matches the given amount in part (a): **$182,400**.

---

### **b) Monthly Payment Calculation:**

The formula for monthly payments on a loan is given by the amortization formula:

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

Where:
- $ M $ = Monthly payment
- $ P $ = Loan amount = $182,400
- $ r $ = Monthly interest rate = $\frac{6.15\%}{12} = \frac{0.0615}{12} = 0.005125$
- $ n $ = Number of payments = 30 years $\times$ 12 months/year = 360

Now, plugging the values into the formula:

\[
M = \frac{182,400 \times 0.005125 \times (1 + 0.005125)^{360}}{(1 + 0.005125)^{360} - 1}
\]

I will compute this step by step.

The monthly payment (b) is approximately **$1,111.23**.

---

### **c) Total Interest Calculation:**

The total interest paid over the life of the loan is the difference between the total amount paid and the loan amount.

- Total amount paid over 30 years:

\[
\text{Total Payments} = M \times n = 1,111.23 \times 360 = 400,042.78
\]

- Total interest:

\[
\text{Total Interest} = \text{Total Payments} - \text{Loan Amount} = 400,042.78 - 182,400 = 217,642.78
\]

So, the total interest paid is approximately **$217,642.78**.

---

Do you want any further clarifications? Here are 5 related questions for deeper understanding:

1. What happens to monthly payments if the interest rate decreases?
2. How would a shorter loan term (e.g., 15 years) affect total interest paid?
3. What are the advantages of making a larger down payment?
4. How is the total loan cost affected by making extra monthly payments?
5. Can a variable interest rate mortgage change these calculations?

**Tip**: Making additional payments toward your mortgage principal can significantly reduce the total interest paid over time.

You want to buy a $228,000 home. You plan to pay 20% as a down payment, and take out a 30-year loan at 6.15% interest for the rest. How much is the loan amount? What will your monthly payments be? How much total interest do you pay?

Learn how to calculate the loan amount, monthly payments, and total interest for a $228,000 home with 20% down and a 30-year loan at 6.15% interest. Detailed step-by-step solution included.

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