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The first year's commission paid to a producer for the sale of a long-term care policy is limited to:

a) 50% of the annual premium
b) 100% of the annual premium
c) 25% of the annual premium
d) No commission is paid in the first year

1 Answer

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Final answer:

Calculating actuarially fair premiums for life insurance requires estimating the risk of payout and assigning it evenly among policyholders. The actuarially fair premium for men with a family history of cancer is higher at $2,000, while it's lower for those without at $500. When the entire group is considered, the premium averages out to $800, but this could lead to adverse selection and potential financial losses for the insurer.

Step-by-step explanation:

Actuarially Fair Premium Calculation

Calculating an actuarially fair premium for life insurance involves estimating the expected payouts and distributing the cost among policyholders. Consider a group of 1,000 50-year-old men.

Separate Group Premiums

Group with Family History of Cancer:

20% of 1,000 men = 200 men

Probability of dying in the next year = 1/50

Expected payout per person = 1/50 * $100,000 = $2,000
Total expected payout for group = 200 men * $2,000 = $400,000

The actuarially fair premium per person = $400,000 / 200 = $2,000.

Group without Family History of Cancer:

80% of 1,000 men = 800 men

Probability of dying in the next year = 1/200

Expected payout per person = 1/200 * $100,000 = $500

Total expected payout for group = 800 men * $500 = $400,000

The actuarially fair premium per person = $400,000 / 800 = $500.

Group as a Whole Premium

When combining both groups without knowledge of cancer history:

Expected payout per person = (200/1,000 * $2,000) + (800/1,000 * $500) = $800

The actuarially fair premium per person for the entire group = $800.

Implications for Insurance Company

If the insurance company charges the actuarially fair premium for the group as a whole, they face the risk of adverse selection. Healthier individuals from the group without a family history of cancer might opt out due to the higher premium, leaving a disproportionate number of higher-risk individuals, which could result in financial losses for the company.

User Adam Venezia
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