Question

An insurance policy sells for $1000. Based on past data, an average of 1 in 50 policyholders will file a $20,000 claim, an average of 1 in 200 policyholders will file a $30,000 claim, and an average of 1 in 400 policyholders will file a $60,000 claim. a. Find the expected value (to the company) per policy sold.

Answer 1

The expected value (to the company) per policy sold is $630 and the expected profit is $6,300,000.

Expected value

a. Expected value of the claim:

Expected value=20,000 (1/200)+30,000(1/200)+60,000(1/500)

Expected value=100+150+120

Expected value=370

Expected value of the company profit:

Expected value=1,000-370

Expected value=630

b. If the company sells 10,000 policies the expected profit is:

Expected profit=10,000×630

Expected profit=$6,300,000

Therefore the expected value (to the company) per policy sold is $630 and the expected profit is $6,300,000.

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The complete question is:

An insurance policy sells for $1000. Based on past data, an average of 1 in 50 policyholders will file a $20,000 claim, an average of 1 in 200 policyholders will file a $30,000 claim, and an average of 1 in 400 policyholders will file a $60,000 claim.

a. Find the expected value (to the company) per policy sold.

b. If the company sells 10,000 policies, what is the expected total profit or loss for the company?