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]
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]
