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
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
