Final answer:
The 'b' in the life insurance premium formula stands for the Benefit factor. The Benefit factor directly affects the premium, with higher benefits requiring higher premiums. Calculating an actuarially fair premium requires considering individual risks, such as family medical history.
Step-by-step explanation:
The b in the formula for calculating life insurance annual premium p = 2rb stands for the Benefit factor. This factor is crucial in determining the annual premium that must be paid for a life insurance policy. It takes into account the amount of benefit or coverage provided by the policy. The formula showcases the direct relationship between the benefit factor and the premium — as the benefit increases, the premium cost also tends to increase.
To understand how life insurance premiums are calculated in practice, let's consider a scenario:
- For the group with a family history of cancer (20% chance), the actuarially fair premium would account for the higher likelihood of a payout due to increased risk.
- For the group without a family history of cancer (80% chance), the premium would be lower due to a reduced risk of a payout.
- If the insurance company cannot differentiate between the two groups, they would need to calculate a premium that covers the risk present within the entire population pool.
If the insurance company tries to charge the actuarially fair premium to the entire group without accounting for individual risk factors (such as family history of cancer), it could lead to issues with adverse selection where people with higher risks are more likely to buy insurance, while those with lower risks opt out, potentially making the premium insufficient to cover the payouts.