You want to buy a $216,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for the rest. What will your monthly payments be if the interest rate is 7%

To determine the monthly payments for a 30-year mortgage with a 7% annual interest rate, we'll use the following formula for the monthly payment of a fixed-rate mortgage:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the loan principal (the amount of the loan),
- $ r $ is the monthly interest rate,
- $ n $ is the number of monthly payments.

### Step-by-Step Calculation:

1. **Determine the down payment and loan amount:**
   - Down payment: $ 20\% $ of $ \$216,000 $
   \[ \text{Down payment} = 0.20 \times 216,000 = \$43,200 \]
   - Loan amount (principal): $ \$216,000 - \$43,200 = \$172,800 $

2. **Convert the annual interest rate to a monthly interest rate:**
   \[ r = \frac{7\%}{12} = \frac{0.07}{12} \approx 0.0058333 \]

3. **Determine the total number of monthly payments:**
   \[ n = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ months} \]

4. **Plug the values into the mortgage formula:**
   \[ M = 172,800 \times \frac{0.0058333(1 + 0.0058333)^{360}}{(1 + 0.0058333)^{360} - 1} \]

### Calculating Monthly Payment:

Now, let's perform the calculation:

\[ M = 172,800 \times \frac{0.0058333 \times (1.0058333)^{360}}{(1.0058333)^{360} - 1} \]

Using a calculator, we find:

\[ (1.0058333)^{360} \approx 10.677 \]

\[ M = 172,800 \times \frac{0.0058333 \times 10.677}{10.677 - 1} \]

\[ M = 172,800 \times \frac{0.062296}{9.677} \]

\[ M = 172,800 \times 0.006437 \]

\[ M \approx 1,111.46 \]

### Monthly Payment:

The monthly payment for the loan will be approximately $ \$1,111.46 $.

Would you like any more details or have any questions?

Here are 5 numbered questions for you to ask:
1. How can I calculate the total interest paid over the life of the loan?
2. What is the impact of making additional payments on the mortgage?
3. How do different interest rates affect monthly mortgage payments?
4. What are the benefits of a larger down payment?
5. How can I calculate the mortgage amortization schedule?

**Tip:** Always review and compare mortgage offers from multiple lenders to find the best interest rates and terms for your financial situation.

Learn how to calculate monthly mortgage payments for a $216,000 home with a 20% down payment and a 30-year loan at 7% interest rate. Detailed step-by-step solution provided. Explore impact of down payments and interest rates.

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