Let's solve the problem step by step.
1. Calculate the Loan Amount:
- Home price: \[tex]$142,000
- Down payment: \$[/tex]17,000
- Loan amount = Home price - Down payment
- Loan amount = \[tex]$142,000 - \$[/tex]17,000 = \[tex]$125,000
2. Determine the Loan-to-Value (LTV) Ratio:
- LTV ratio = (Loan amount / Home price) * 100
- LTV ratio = (\$[/tex]125,000 / \[tex]$142,000) * 100 ≈ 88.03%
3. Using the Table to Find the PMI Rate:
- Looking at the provided PMI rate table:
\[
\begin{tabular}{|c|c|}
\hline \\
Loan-to-Value (\%) & PMI Rate (30-year Fixed-Rate Loan) \\
\hline 95.01\% to 97\% & 0.90\% \\
90.01\% to 95\% & 0.78\% \\
85.01\% to 90\% & 0.52\% \\
85\% and Under & 0.32\% \\
\hline
\end{tabular}
\]
- The LTV ratio of 88.03% falls in the "85.01% to 90%" range.
- The corresponding PMI rate for this range and a 30-year fixed-rate loan is 0.52%.
4. Calculate the Monthly PMI Payment:
- Annual PMI payment = Loan amount * PMI rate
- Annual PMI payment = \$[/tex]125,000 * 0.0052 = \[tex]$650
- Monthly PMI payment = Annual PMI payment / 12
- Monthly PMI payment = \$[/tex]650 / 12 ≈ \[tex]$54.17
5. Find the Closest Answer Choice:
- The closest answer to the calculated monthly PMI payment of \$[/tex]54.17 is option D: \[tex]$54.17.
Therefore, Michael's monthly PMI payment is:
D. \$[/tex]54.17
