40-year-old man in the U.S. has a $$ 0.243 \% $$ risk of dying during the next year. An insurance company charges $$ \$ 260 $$ per ear for a life-insurance policy that pays a $$ \$ 100,000 $$ death benefit. What is the expected value for the person buying the nsurance? Round your answer to the nearest dollar. Expected Value: $$ \$-37.00 \quad $$ for the year

Question

UpStudy AI · Accepted Answer

Let 
$$
p = 0.243\% = 0.00243
$$
be the probability of death during the next year.

If the policyholder dies during the year, he receives a death benefit of $$\$100,\!000$$ but has paid a $$\$260$$ premium. Thus, his net gain if death occurs is
$$
\text{Net gain upon death} = \$100,\!000 - \$260 = \$99,\!740.
$$

If he survives the year, he receives no benefit but still pays the $$\$260$$ premium, resulting in a net outcome of 
$$
\text{Net outcome if alive} = -\$260.
$$

The expected value (EV) for the policyholder is computed by weighing these outcomes by their probabilities:
$$
\begin{aligned}
\text{EV} &= p \times (\$99,\!740) + (1-p) \times (-\$260) \
          &= 0.00243 \times 99,\!740 + 0.99757 \times (-260).
\end{aligned}
$$

Performing the calculations:
$$
0.00243 \times 99,\!740 \approx \$242.42,
$$
$$
0.99757 \times 260 \approx \$259.37.
$$

Thus,
$$
\text{EV} \approx \$242.42 - \$259.37 = -\$16.95.
$$

Rounded to the nearest dollar, the expected value is 
$$
-\$17.
$$
The expected value for the person buying the insurance is approximately \$-17 for the year.

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

Upstudy AI Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Economics Questions

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