Formula for Insurer's Expected Payoff
The expected payoff for an insurance company is calculated by subtracting the expected claim from the premium charged. The expected claim is determined by multiplying the probability of the insured event, such as theft, by the value of the potential loss, such as the car's value (). The formula is:
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A company offers full insurance coverage for a smartphone valued at $1,000. Based on historical data, there is a 5% chance the phone will be stolen within the one-year policy period, resulting in a total loss. To precisely cover its anticipated average payout for this policy, what is the minimum premium the company should charge?
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A company insures a fleet of delivery drones, each valued at $2,000. Based on operational data, there is a 10% probability of a drone being lost or damaged beyond repair during a one-year policy period. The company sets the annual premium for each drone at $180, stating that this price is intentionally set $20 below the average expected cost of a claim in order to attract more customers. Is the company's statement about its pricing strategy accurate?
An insurance company offers full coverage for several different assets. Match each asset profile (value and probability of total loss over the policy period) with the minimum premium required to exactly cover the expected claim.
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An insurer provides a policy for a piece of art valued at $50,000. Historical data suggests a 0.5% probability of a total loss due to damage or theft during the one-year policy term. To exactly cover the average anticipated cost of a claim, the insurer must charge a premium of $____.
An insurance company offers two separate one-year policies for full coverage against total loss.
- Policy A is for a piece of equipment valued at $5,000 with a 4% probability of loss. The premium for Policy A is $240.
- Policy B is for an art piece valued at $20,000 with a 1% probability of loss. The premium for Policy B is $230.
Which policy has a larger 'loading charge' (the amount charged in the premium that exceeds the mathematically expected claim cost)?
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Learn After
An insurance company provides a policy for a bicycle valued at $1,000. The annual premium is $100, and the initial probability of theft is 5%. A new security initiative is launched, reducing the probability of theft to 3%. Assuming the premium and the bicycle's value remain unchanged, how does this change in probability affect the company's expected payoff per policy?
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True or False: For an insurance policy covering an asset of a specific value, a higher premium charged by the insurer guarantees a greater expected payoff for the company.
An insurance company offers a policy for a smartphone valued at $800. The annual premium for this policy is $120. If historical data suggests a 10% probability that a claim will be made against the policy in a given year, the company's expected payoff for this single policy is $____.
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Match each term related to an insurance policy with its correct description in the context of calculating an insurer's expected financial outcome.
An analyst for an insurance company is evaluating a new policy to determine if it is expected to be profitable. Arrange the following steps in the correct logical sequence to complete this evaluation.
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