Ernest is purchasing a \[tex]$175,000 home with a 30-year mortgage. He will make a \$[/tex]15,000 down payment. Use the table below to find his monthly PMI payment.

\begin{tabular}{|c|c|c|c|}
\hline
Loan-to-Value (\%) & \begin{tabular}{l}
Fixed-Rate Loan \\
30 yrs. & 15 yrs.
\end{tabular} & \begin{tabular}{l}
ARM (2\%+1) \\
30 yrs.
\end{tabular} & \begin{tabular}{l}
1 Year Cap \\
15 yrs.
\end{tabular} \\
\hline
95.01\% to 97\% & 0.90\% \quad 0.79\% & n/a & n/a \\
\hline
90.01\% to 95\% & 0.78\% \quad 0.26\% & 0.92\% & 0.81\% \\
\hline
85.01\% to 90\% & 0.52\% \quad 0.23\% & 0.65\% & 0.54\% \\
\hline
85\% and Under & 0.32\% \quad 0.19\% & 0.37\% & 0.26\% \\
\hline
\end{tabular}

A. \$97.50

B. \$1248

C. \$1170

D. \$104.00



Answer :

To determine Ernest's monthly PMI (Private Mortgage Insurance) payment for his home mortgage, we need to follow these steps:

1. Calculate the Loan Amount:
- The home price is \$175,000.
- Ernest's down payment is \$15,000.
- The loan amount is then calculated by subtracting the down payment from the home price:
[tex]\[ \text{Loan Amount} = \[tex]$175,000 - \$[/tex]15,000 = \$160,000
\][/tex]

2. Calculate the Loan-to-Value (LTV) Ratio:
- The LTV ratio is a measure of the loan amount compared to the value of the home.
- It is calculated as:
[tex]\[ \text{LTV Ratio} = \left( \frac{\text{Loan Amount}}{\text{Home Price}} \right) \times 100 \][/tex]
- Plugging in the values:
[tex]\[ \text{LTV Ratio} = \left( \frac{\[tex]$160,000}{\$[/tex]175,000} \right) \times 100 \approx 91.43\%
\][/tex]

3. Determine the PMI Rate based on the LTV Ratio:
- Using the table provided, we need to find the PMI rate that corresponds to Ernest's LTV ratio of approximately 91.43%.
- According to the table, for a 30-year fixed-rate loan:
- If the LTV ratio is between 90.01% and 95%, the PMI rate is 0.78%.

4. Calculate the Monthly PMI Payment:
- The annual PMI cost is calculated by multiplying the loan amount by the PMI rate.
- The monthly PMI payment is then found by dividing the annual PMI cost by 12:
[tex]\[ \text{Annual PMI Cost} = \text{Loan Amount} \times \text{PMI Rate} \][/tex]
[tex]\[ \text{Annual PMI Cost} = \[tex]$160,000 \times 0.0078 = \$[/tex]1,248
\][/tex]
[tex]\[ \text{Monthly PMI Payment} = \frac{\[tex]$1,248}{12} = \$[/tex]104.00
\][/tex]

Therefore, Ernest’s monthly PMI payment is:

D. \$104.00