A 40-year-old man in the U.S. has a 0.244% risk of dying during the next year . An insurance company charges $280 per year for a life-insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance? Round your answer to the nearest dollar

To determine the expected value for the person buying the life insurance, we need to consider the probabilities of the two possible outcomes: the person survives the year, or the person dies during the year. We'll calculate the expected monetary outcome for each scenario and then find the overall expected value.

### Given:
- Probability of dying within the next year: $ 0.244\% = 0.00244 $
- Probability of surviving the next year: $ 1 - 0.00244 = 0.99756 $
- Cost of the insurance policy: $ \$280 $
- Death benefit if the person dies: $ \$100,000 $

### Calculating the Expected Value (EV):

1. **Expected value if the person dies:**
   - The person receives the death benefit, but we need to subtract the cost of the policy:
   \[
   \text{EV}_{\text{die}} = 0.00244 \times (\$100,000 - \$280)
   \]
   \[
   \text{EV}_{\text{die}} = 0.00244 \times \$99,720 = \$243.37
   \]

2. **Expected value if the person survives:**
   - The person only pays the premium with no benefit received:
   \[
   \text{EV}_{\text{survive}} = 0.99756 \times -\$280 = -\$279.32
   \]

### Total Expected Value:
\[
\text{EV} = \text{EV}_{\text{die}} + \text{EV}_{\text{survive}}
\]
\[
\text{EV} = \$243.37 - \$279.32 = -\$35.95
\]

Rounding to the nearest dollar, the expected value for the person buying the insurance is **$-\$36$**.

This negative expected value suggests that, on average, the person will lose $36 per year by purchasing this insurance policy.

Would you like more details or have any questions?

Here are five related questions to consider:
1. How would the expected value change if the death benefit increased to $120,000?
2. What is the break-even cost for the insurance premium that makes the expected value zero?
3. How does the expected value differ for someone with a higher risk of death, such as 0.5%?
4. If the premium increased to $350 per year, what would the expected value be?
5. How does the insurance company's expected profit compare to the policyholder's expected loss?

**Tip:** When evaluating insurance, consider not only the expected value but also the potential financial protection it provides against significant risks.

Explore how to calculate the expected value (EV) for a life insurance policy with a $100,000 death benefit. Understand the probabilities of survival and death, the cost of the insurance policy ($280 per year), and the implications of these factors on financial outcomes. Learn with a detailed example and find out how the expected value affects decision-making. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation