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Sagot :
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
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
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