The probability that a 30-year old white male will live another year is .99842. What premium would
an insurance company charge to break even on a 1-year $1 million dollar term life insurance policy?
To calculate the premium an insurance company would charge to break even on a 1-year $1 million term life insurance policy, we need to consider the concept of "expected value." The expected value of an event is the average outcome weighted by its probabilities.
In this case, we can calculate the premium as follows:
1. Determine the probability of surviving the year: Since the given probability is the likelihood that a 30-year-old white male will live another year, the probability of surviving the year is 0.99842.
2. Calculate the amount the insurer would pay out if the insured person dies: In this case, the coverage amount is $1 million.
3. Multiply the coverage amount by the probability of surviving: Multiply $1 million by 0.99842 to get the expected payout if the person survives for the year.
Expected payout = $1,000,000 * 0.99842
4. Deduct the expected payout from the full coverage amount: Subtract the expected payout from the coverage amount to find the expected cost to the insurance company.
Expected cost = $1,000,000 - (1,000,000 * 0.99842)
5. The premium charged by the insurance company should be equal to the expected cost: Therefore, the premium charged to break even would be the same as the expected cost.
Premium = Expected cost
By following these steps, you can calculate the premium an insurance company would charge to break even on a 1-year $1 million term life insurance policy based on the provided probability.
To calculate the premium charged by an insurance company to break even on a 1-year $1 million dollar term life insurance policy, we need to consider the concept of expected value.
The expected value is calculated by multiplying the possible outcomes by their probabilities and summing them up. In this case, we need to find the premium that would result in an expected value of zero for the insurance company.
Let's break down the steps to find the premium:
Step 1: Calculate the probability of survival
The problem states that the probability that a 30-year old white male will live another year is 0.99842. Therefore, the probability of death within a year is 1 - 0.99842 = 0.00158.
Step 2: Calculate the payouts
The insurance policy payout is $1 million in the event of the insured person's death within the year. If the person survives, there is no payout.
Step 3: Calculate the expected value
To break even, the expected value should be zero. We can set up the equation:
Expected Value = (Probability of Death * Payout) - (Probability of Survival * Premium) = 0
0.00158 * $1,000,000 - (0.99842 * Premium) = 0
Step 4: Solve for the premium
Rearranging the equation:
0.00158 * $1,000,000 = 0.99842 * Premium
Premium = (0.00158 * $1,000,000) / 0.99842
After calculating the value, you will find that the premium required for the insurance company to break even on a 1-year $1 million term life insurance policy for a 30-year old white male is the result of dividing (0.00158 * $1,000,000) by 0.99842.
Note: The calculation provided is based on the given probability of survival and assumption of no other costs or factors involved in determining the premium. Actual insurance premiums may vary based on a variety of factors considered by insurance companies, such as medical history, lifestyle, and other risk factors.