Let's go through the solution for Matthew's PMI (Private Mortgage Insurance) payment step-by-step:
1. Home Price and Down Payment:
- Home price: \[tex]$165,000
- Down payment: \$[/tex]15,000
2. Loan Amount Calculation:
- The loan amount is the difference between the home price and the down payment.
[tex]\[
\text{Loan Amount} = \text{Home Price} - \text{Down Payment} = 165,000 - 15,000 = 150,000
\][/tex]
3. Base-to-Loan Percentage Calculation:
- The base-to-loan percentage is calculated as follows:
[tex]\[
\text{Base-to-Loan Percentage} = \left(\frac{\text{Loan Amount}}{\text{Home Price}}\right) \times 100 = \left(\frac{150,000}{165,000}\right) \times 100 \approx 90.91\%
\][/tex]
4. PMI Rate Determination:
- According to the given table, we find the PMI rate for a base-to-loan percentage of approximately 90.91%. This percentage falls in the range of "90.01% to 95%".
- The corresponding PMI rate for a 30-year fixed-rate loan is:
[tex]\[
\text{PMI Rate} = 0.78\%
\][/tex]
5. Annual PMI Payment Calculation:
- To calculate the annual PMI payment, we use the loan amount and the PMI rate:
[tex]\[
\text{Annual PMI} = \text{Loan Amount} \times \text{PMI Rate} = 150,000 \times 0.0078 = 1,170.00
\][/tex]
6. Monthly PMI Payment Calculation:
- To determine the monthly PMI payment, we divide the annual PMI payment by 12:
[tex]\[
\text{Monthly PMI} = \frac{\text{Annual PMI}}{12} = \frac{1,170.00}{12} \approx 97.50
\][/tex]
Therefore, the monthly PMI payment for Matthew is [tex]\(\$97.50\)[/tex], which corresponds to option C.
So, the correct answer is:
[tex]\[
\boxed{C. \$97.50}
\][/tex]
