Final answer:
The actuarially fair premium for a life insurance policy is calculated based on a policyholder's risk profile, which includes factors like family history of cancer. For the hypothetical scenario of these 50-year-old men, it would be $2,000 for those with a family history of cancer and $500 for those without. The overall group's fair premium would be $700. Unfortunately, in Blake's case, his beneficiaries will likely receive no death benefit if his coverage was terminated and no individual conversion was made.
Step-by-step explanation:
When an insurance company sells life insurance, it assesses the risk of each policyholder to determine an actuarially fair premium, which is the premium that would be enough to cover the expected losses from the policy. The actuarially fair premium varies depending on the risk profile of the group or individual. In Blake's case, life insurance coverage was terminated 20 days prior to his death, and he did not apply for individual coverage.
If we refer back to the hypothetical life insurance scenario, the actuarially fair premium for each group would be calculated as follows:
- For men with a family history of cancer (20% of 1,000, or 200 men), each with a 1/50 chance of dying, the fair premium would be the probability of death (1/50) multiplied by the death benefit ($100,000), giving $2,000.
- For men without a family history of cancer (80% of 1,000, or 800 men), each with a 1/200 chance of dying, the fair premium would be the probability of death (1/200) multiplied by the death benefit ($100,000), giving $500.
If the insurance company could not differentiate between the two groups, the actuarially fair premium for the entire group would be the weighted average of both premiums:
[(200 men * $2,000) + (800 men * $500)] / 1,000 men = $700 per person.
When considering Blake's situation, without further details on the policy terms and conditions, such as a provision for a grace period after termination, we cannot definitively state what the beneficiaries will receive. Typically, no benefit is due if coverage has lapsed due to non-payment or termination without conversion to individual coverage.