Question

"The insurance company gets information about gas leakage in several houses that use the same gas provider that your customer does. In light of this new information, the probabilities of total loss and 50% damage (that were originally .002 and .008, respectively) are tripled (to .006 for total loss and .024 for 50% damage). Obviously, this change in the probabilities should be reflected in the annual premium, to account for the added risk that the insurance company is taking. What should be the new annual premium (instead of $1,350), if the company wants to keep its expected gain of $750?"

Answer 1

Answer: $2550

Explanation:

Note that the probabilities of total loss and 50% damage were tripled and the probability of no fire has therefore changed to:

1 - 0006 - 0.024 = 0.97.

The company wants to keep same annual gain from the policy ($750), and the question now is, what would the new premium (N) be which will satisfy this? To get this, we need to solve the equation for:

N:750 = (N - 100,000)(0.006) + (N - 50,000)(0.024) + N(0.97)

Thus, 750 = N - 600 - 1,200, or N - 1,800. Therefore,N= 750+1,800= 2,550.

To account for the added risk which the insurance company is taking by continuing insuring the customer, the premium changes from $1,350 to $2550