James has a mortgage of $92,500 at 8% for 15 years. The property taxes are $3,900 per year, and the hazard insurance premium is $754.50 per year. Find the monthly PITI payment (in $). (Round your answer to the nearest cent. Use this table as needed.)

To find the monthly PITI (Principal, Interest, Taxes, and Insurance) payment for James' mortgage, we need to calculate each component separately and then sum them up. Here’s the step-by-step process:

### 1. Principal and Interest (PI)
The principal and interest component is calculated using the formula for the monthly mortgage payment:

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

where:
- $ M $ is the monthly mortgage payment.
- $ P $ is the loan amount ($92,500).
- $ r $ is the monthly interest rate (annual rate divided by 12).
- $ n $ is the number of payments (loan term in years multiplied by 12).

Given:
- $ P = 92,500 $
- Annual interest rate = 8%, so the monthly interest rate $ r = \frac{8\%}{12} = \frac{0.08}{12} = 0.0066667 $
- Loan term = 15 years, so $ n = 15 \times 12 = 180 $ months

Plugging these values into the formula:

\[ M = 92,500 \frac{0.0066667 (1 + 0.0066667)^{180}}{(1 + 0.0066667)^{180} - 1} \]

### 2. Taxes (T)
The annual property taxes are $3,900. To find the monthly payment, divide this amount by 12:

\[ T = \frac{3,900}{12} = 325 \]

### 3. Insurance (I)
The annual hazard insurance premium is $754.50. To find the monthly payment, divide this amount by 12:

\[ I = \frac{754.50}{12} = 62.875 \]

### 4. Total Monthly PITI Payment
Sum up the monthly PI, T, and I to get the total monthly PITI payment.

#### Calculating the Monthly Mortgage Payment (PI):

Using a financial calculator or software to compute the exact monthly mortgage payment:

\[ M \approx 882.74 \]

#### Now summing up all components:

\[ \text{Total PITI} = \text{PI} + \text{T} + \text{I} \]
\[ \text{Total PITI} = 882.74 + 325 + 62.875 \]
\[ \text{Total PITI} \approx 1270.62 \]

Thus, the monthly PITI payment is approximately $1270.62.

Would you like more details or have any questions about this calculation?

Here are 5 questions you might ask:
1. How do I derive the formula for the monthly mortgage payment?
2. Can you explain how to compute the monthly interest rate?
3. What factors influence property taxes?
4. How is hazard insurance premium determined?
5. Can you show a detailed breakdown of the PITI calculation?

**Tip:** When calculating mortgage payments, always ensure you correctly convert the annual interest rate to a monthly rate and the loan term to months.

Learn how to calculate the monthly PITI payment for a $92,500 mortgage at 8% interest over 15 years. This problem covers mortgage finance concepts, including principal and interest calculations, property taxes, and hazard insurance premiums.

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