To determine Ernest's monthly PMI payment, we need to follow these steps:
1. Calculate the loan amount: This is the difference between the home price and the down payment.
2. Determine the loan-to-value (LTV) ratio: This is the loan amount divided by the home price.
3. Find the appropriate PMI rate: Using the LTV ratio, look up the rate in the given PMI rate table.
4. Calculate the annual PMI payment: Multiply the loan amount by the PMI rate.
5. Calculate the monthly PMI payment: Divide the annual PMI payment by 12.
Let's break it down step-by-step:
### Step 1: Calculate the loan amount
Ernest is purchasing a home for [tex]\( \$175,000 \)[/tex] and is making a [tex]\( \$15,000 \)[/tex] down payment.
[tex]\[
\text{Loan amount} = \text{Home price} - \text{Down payment} = 175,000 - 15,000 = \$160,000
\][/tex]
### Step 2: Determine the loan-to-value (LTV) ratio
The LTV ratio is calculated as:
[tex]\[
\text{LTV ratio} = \frac{\text{Loan amount}}{\text{Home price}} = \frac{160,000}{175,000}
\][/tex]
First, simplify the fraction:
[tex]\[
\text{LTV ratio} = \frac{160,000}{175,000} = 0.9142857
\][/tex]
Convert this to a percentage:
[tex]\[
\text{LTV ratio} = 0.9142857 \times 100 \approx 91.43\%
\][/tex]
### Step 3: Find the appropriate PMI rate
Using the given table, we know that Ernest's LTV ratio (91.43%) falls within the range [tex]\(90.01\% \text{ to } 95\%\)[/tex]. The PMI rate for a [tex]\(30\)[/tex]-year fixed mortgage in this range is [tex]\(0.90\%\)[/tex], or [tex]\(0.009\)[/tex] as a decimal.
### Step 4: Calculate the annual PMI payment
Now we calculate the annual PMI by multiplying the loan amount by the PMI rate:
[tex]\[
\text{Annual PMI payment} = \text{Loan amount} \times \text{PMI rate} = 160,000 \times 0.009 = \$1,440
\][/tex]
### Step 5: Calculate the monthly PMI payment
Finally, divide the annual PMI payment by 12 to get the monthly PMI payment:
[tex]\[
\text{Monthly PMI payment} = \frac{\text{Annual PMI payment}}{12} = \frac{1,440}{12} = \$120.00
\][/tex]
Thus, Ernest's monthly PMI payment is [tex]\(\$120.00\)[/tex]. Looking at the provided answer options, none match this computation exactly. Therefore, if the options are considered, this result might not be present.
However, according to the detailed step-by-step correct calculation, the monthly PMI payment is:
[tex]\[
\boxed{120.00}
\][/tex]
