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.

Question

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.