Answer :
Let's break down the problem step-by-step to determine the new annual premium rate per [tex]$100 of home value that would result in an annual out-of-pocket expense about the same as Stephanie's current plan.
1. Determine the current annual premium:
- Stephanie's home value is $[/tex]355,000.
- The premium rate is [tex]$0.42 per $[/tex]100 of home value.
The formula to calculate the current annual premium is:
[tex]\[ \text{Current Premium} = \left(\frac{\$355,000}{100}\right) \cdot 0.42 = \$1,491.00 \][/tex]
2. Calculate the total annual out-of-pocket expense under her current plan:
- Deductible is [tex]$500. - Total annual out-of-pocket expense is given by: \[ \$[/tex]1,491.00 + \[tex]$500 = \$[/tex]1,991.00
\]
3. Stephanie wants to increase her deductible to [tex]$1,000 and maintain the same total annual out-of-pocket expense of $[/tex]1,991.00.
4. Calculate the new premium that would correspond to the new desired deductible:
- Desired total out-of-pocket expense = [tex]$1,991.00. - New deductible = $[/tex]1,000.
- The new annual premium can be calculated by subtracting the new deductible from the target out-of-pocket expense:
[tex]\[ \text{New Premium} = \$1,991.00 - \$1,000 = \$991.00 \][/tex]
5. Determine the new annual premium rate per [tex]$100 of home value: - The new premium is $[/tex]991.00.
- Home value remains [tex]$355,000. - Using the formula for premium rate: \[ \text{New Premium Rate} = \left(\frac{\text{New Premium}}{\text{Home Value}}\right) \cdot 100 = \left(\frac{991}{355,000}\right) \cdot 100 \approx 0.2792 \] 6. Select the closest matching rate from the given options: - The calculated premium rate is approximately 0.2792. - The closest matching rate from the provided choices is: \[ b. \$[/tex]0.28 \text{ per } \$100 \text{ of value}
\]
Therefore, the best answer from the choices provided is:
B
- The premium rate is [tex]$0.42 per $[/tex]100 of home value.
The formula to calculate the current annual premium is:
[tex]\[ \text{Current Premium} = \left(\frac{\$355,000}{100}\right) \cdot 0.42 = \$1,491.00 \][/tex]
2. Calculate the total annual out-of-pocket expense under her current plan:
- Deductible is [tex]$500. - Total annual out-of-pocket expense is given by: \[ \$[/tex]1,491.00 + \[tex]$500 = \$[/tex]1,991.00
\]
3. Stephanie wants to increase her deductible to [tex]$1,000 and maintain the same total annual out-of-pocket expense of $[/tex]1,991.00.
4. Calculate the new premium that would correspond to the new desired deductible:
- Desired total out-of-pocket expense = [tex]$1,991.00. - New deductible = $[/tex]1,000.
- The new annual premium can be calculated by subtracting the new deductible from the target out-of-pocket expense:
[tex]\[ \text{New Premium} = \$1,991.00 - \$1,000 = \$991.00 \][/tex]
5. Determine the new annual premium rate per [tex]$100 of home value: - The new premium is $[/tex]991.00.
- Home value remains [tex]$355,000. - Using the formula for premium rate: \[ \text{New Premium Rate} = \left(\frac{\text{New Premium}}{\text{Home Value}}\right) \cdot 100 = \left(\frac{991}{355,000}\right) \cdot 100 \approx 0.2792 \] 6. Select the closest matching rate from the given options: - The calculated premium rate is approximately 0.2792. - The closest matching rate from the provided choices is: \[ b. \$[/tex]0.28 \text{ per } \$100 \text{ of value}
\]
Therefore, the best answer from the choices provided is:
B
