Question

Suppose a life insurance company sells a ​$290 comma 000 ​one-year term life insurance policy to a 20​-year-old female for ​$280. The probability that the female survives the year is 0.999644. Compute and interpret the expected value of this policy to the insurance company.

Answer 1

Answer:

The insurance company will gain an expected value $176.66032

Explanation:

The expected value is the gain or loss of an event and is calculated each outcome by its probability.

In our case we have to consider all events as follows;

The probability of dying means the insurance company will have a loss of $290,000 and gain $280 which is the cost of the policy. The probability of this happening=(1-probability of living)=(1-0.999644)=0.000356

The probability of living means the insurance company will gain $280, and the probability of this happening=0.999644

The gain or loss from death=280-290,000=-$289,720

The gain or loss from living=$280

Expected value=(The loss from death×probability of death)+(The gain from living×probability of living)

where;

The loss from death=-$290,000

Probability of death=0.000356

The gain from living=$280

Probability of living=0.999644

replacing;

Expected value=(-290,000×0.000356)+(280×0.999644)

Expected value=(-103.24+279.90032)

Expected value=$176.66032

The insurance company will gain an expected value $176.66032