Suppose that Annie's loss distribution is as follows:

$20,000 with probability 0.01

Loss = $1,000 with probability 0.03

$250 with probability 0.06

$0 with probability 0.90

Assume that there are no other costs than the cost of processing a claim, which equals $500. Ignoring the time value of money, the insurance price is the sum of expected claim costs and expected claim processing costs.

Question: (1) Find the fair premium of the insurance policy (with no deductibles and coinsurance).

Question: (2) Assume that the insurance has a policy of a $250 deductible and a 10% of coinsurance. Find the fair premium of the policy.