A 40-year-old man in the U.S. has a $$ 0.243 \% $$ risk of dying during the next year. An insurance company charges $$ \$ 250 $$ 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. Expected Value: $$ \$ $$

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Let $$ p = 0.00243 $$ be the probability of dying during the next year. The policy costs $$\$250$$ regardless of the outcome. If death occurs, the benefit is $$\$100{,}000$$, so the net gain (benefit minus premium) is

$$
\text{Net gain if death occurs} = 100{,}000 - 250 = 99{,}750.
$$

If the individual survives, the net change is simply the loss of the premium:

$$
\text{Net gain if survival} = -250.
$$

Thus, the expected value (EV) for the insurance buyer is given by

$$
\text{EV} = p \times 99{,}750 + (1-p) \times (-250).
$$

Substitute $$ p = 0.00243 $$:

$$
\text{EV} = 0.00243 \times 99{,}750 + 0.99757 \times (-250).
$$

First, compute the contribution from the death scenario:

$$
0.00243 \times 99{,}750 \approx 242.39.
$$

Next, compute the contribution from the survival scenario:

$$
0.99757 \times (-250) \approx -249.39.
$$

Now, add these values:

$$
\text{EV} \approx 242.39 - 249.39 = -7.
$$

Thus, the expected value for the person buying the insurance is

$$
\boxed{-\$7}.
$$
The expected value for the person buying the insurance is **-\$7**.

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

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