Question

Stephanie has a homeowners insurance policy for her $355,000 home with an annual premium of $0.42 per $100 of value and a deductible of $500. Under this policy, in the event of a major mishap, Stephanie would have a total annual out-of-pocket expense of Left-bracket (355,000 dollars divided by 100) times 42 cents right-bracket + 500 dollars = 1,991 dollars.
Stephanie would like to lower her premium by increasing her deductible. If Stephanie wants to increase her deductible to $1000, what annual premium would result in an annual out-of-pocket expense that is about the same as her current plan?
a.
$0.16 per $100 of value
b.
$0.28 per $100 of value
c.
$0.35 per $100 of value
d.
$0.46 per $100 of value

Answer 1

To find out what annual premium would result in an annual out-of-pocket expense that is about the same as Stephanie's current plan after increasing her deductible to $1000, we first need to establish her current total annual out-of-pocket expense with the existing deductible and then solve for the new premium with the new deductible.

1. **Current Total Annual Out-of-Pocket Expense**:
- Home value: $355,000
- Premium rate: $0.42 per $100
- Current deductible: $500

**Calculating current premium**:
\[
\text{Current premium} = \frac{355,000}{100} \times 0.42 = 3550 \times 0.42 = \$1,491
\]

**Total out-of-pocket expense with current deductible**:
\[
\text{Total out-of-pocket} = \text{Current premium} + \text{deductible} = 1,491 + 500 = \$1,991
\]

2. **New Annual Out-of-Pocket Expense with the increased deductible**:
- New deductible: $1,000
- We want the total out-of-pocket expense to still be about $1,991.

**Let P be the new premium**:
\[
\text{Total out-of-pocket result with new deductible} = P + 1,000
\]

We set this equal to the current out-of-pocket expense:
\[
P + 1,000 = 1,991
\]
\[
P = 1,991 - 1,000 = 991
\]

3. **Finding the New Premium Rate**:
Now that we know the required premium is $991, we need to calculate the premium rate that corresponds to that premium amount for the $355,000 home.
\[
\text{Premium} = \frac{355,000}{100} \times \text{New Rate}
\]
\[
991 = \frac{355,000}{100} \times \text{New Rate}
\]
\[
991 = 3,550 \times \text{New Rate}
\]
\[
\text{New Rate} = \frac{991}{3550}
\]
\[
\text{New Rate} \approx 0.2794 \text{ or } 0.28 \text{ per } 100
\]

Thus, if Stephanie increases her deductible to $1,000, the resulting annual premium rate that would keep her out-of-pocket expenses approximately the same would be about **$0.28 per $100 of value**.

So, the correct answer is:
**b. $0.28 per $100 of value**.