Question

Last year, 20% of all claims were for weather-related damage (excluding floods), with an average weather-related damage claim being $6,500. What is the expected value (loss or gain) per weather-related claim to Acasa for every customer who chooses plan B? Acasa Insurance Company offers several plans for home insurance. Plan A has a $700 yearly premium with a $3,000 deductible. Plan B has a $1,200 yearly premium with a $1,000 deductible.

Options:
A. $200 gain
B. $100 gain
C. $180 loss
D. $1,180 loss

Answer 1

By subtracting the likely weather-related claims (20% chance of a $6,500 claim minus a $1,000 deductible) from the premium of $1,200 for Plan B, we find an expected gain of $100 per weather-related claim.

Step-by-step explanation:

To calculate the expected value (loss or gain) per weather-related claim for Acasa Insurance Company's Plan B, we'll use the given information: 20% of claims are for weather-related damage (excluding floods) averaging $6,500 per claim, Plan B has a $1,200 yearly premium with a $1,000 deductible.

The expected value for a weather-related claim (E) can be calculated as:

• E = Premium - (Probability of claim × (Average claim amount - Deductible))

Where:

• Premium for Plan B: $1,200
• Probability of claim: 20% or 0.20
• Average claim amount: $6,500
• Deductible for Plan B: $1,000

So the formula becomes:

E = $1,200 - (0.20 × ($6,500 - $1,000))

Doing the math:

E = $1,200 - (0.20 × $5,500)

E = $1,200 - $1,100

E = $100

Therefore, the expected gain for Acasa per weather-related claim under Plan B is $100.