Final answer:
The correct insurance premium for a $75,000 policy for a 30-year-old male with a 10-year term requires additional information, such as mortality risk and insurance company pricing models. An actuarially fair premium would simply cover the expected payouts but insurance companies usually add additional charges.
Step-by-step explanation:
The question inquires about the premium for a $75,000 life insurance policy for a 30-year-old male with a 10-year term. To provide an answer, one would normally need more information such as the insurance company's rates, the individual's health condition, lifestyle, and other risk factors that affect insurance premiums. However, when looking closer, it seems the question might be related to actuarially fair premiums and how they are calculated using probability and expected payout.
Calculations of Actuarial Fair Premiums
An actuarially fair premium is a theoretical premium that, on average, just covers the expected payouts for insurance claims. To calculate this, actuaries use a combination of mortality tables and the insured amount to determine the risk and the fair premium. As an example, the scenario provided details a situation involving two groups of 50-year-old men, their family history with cancer, and their respective mortality risks.
Using the information provided in a similar situation, but for a 30-year-old individual, the calculations would involve estimating the probability of death within the term of the policy and multiplying that by the payout amount, then dividing it accordingly to determine the annual premium. The steps to calculate this include:
- Determining the probability of the event (death) within the policy term.
- Calculating the expected payout by multiplying the probability by the amount of insurance coverage.
- Dividing the expected payout by the term of the policy to get the annual premium.
Unfortunately, without the specific death probability data for a 30-year-old male, and without particulars about the insurance company's charges and profit margins, we cannot calculate the exact premium for the given policy. It's also not possible to identify which among the provided answers (a) $1415.25, (b) $286.50, (c) $1500, or (d) $587.25) is the correct one based on the question alone.