Michael is purchasing a \[tex]$142,000 home with a 30-year mortgage. He will put down a \$[/tex]17,000 down payment. Use the table below to find his monthly PMI payment.

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

A. \$650

B. \$54.17

C. \$52.90

D. \$56.23



Answer :

Let's break this problem down step-by-step to find Michael's monthly Private Mortgage Insurance (PMI) payment.

1. Determine the Loan Amount:
Michael is purchasing a home costing \[tex]$142,000 and making a down payment of \$[/tex]17,000.
[tex]\[ \text{Loan Amount} = \text{Home Cost} - \text{Down Payment} = 142,000 - 17,000 = 125,000 \][/tex]

2. Calculate the Loan-to-Value (LTV) Ratio:
The Loan-to-Value ratio is calculated as the loan amount divided by the home cost, multiplied by 100 to get a percentage.
[tex]\[ \text{LTV Ratio} = \left( \frac{\text{Loan Amount}}{\text{Home Cost}} \right) \times 100 = \left( \frac{125,000}{142,000} \right) \times 100 \approx 88.03\% \][/tex]

3. Determine the PMI Rate:
Using the table provided, we look up the PMI rate based on the LTV ratio:
- 85.01% to 90% corresponds to a PMI rate of 0.52%.

4. Calculate the Annual PMI Payment:
The annual PMI payment is calculated as the loan amount multiplied by the PMI rate.
[tex]\[ \text{Annual PMI Payment} = \text{Loan Amount} \times \text{PMI Rate} = 125,000 \times 0.0052 = 650 \][/tex]

5. Calculate the Monthly PMI Payment:
The monthly PMI payment is the annual PMI payment divided by 12.
[tex]\[ \text{Monthly PMI Payment} = \frac{\text{Annual PMI Payment}}{12} = \frac{650}{12} \approx 54.17 \][/tex]

To summarize, based on the calculations, Michael's monthly PMI payment is:
[tex]\[ \boxed{54.17} \][/tex]