Question

A 38 year old man in the united states has a 0.224% risk of dying during the next year. an insurance company charges a premium of $362 for a life insurance policy that pays a $244,434 death benefit. what is the expected gain or loss to the man when purchasing the insurance policy?

Answer 1

The expected gain for a 38-year-old man purchasing a life insurance policy with a 0.224% risk of death and a premium of $362 is $186.44.

Step-by-step explanation:

A 38-year-old man in the United States has a 0.224% risk of dying during the next year. An insurance company charges a premium of $362 for a life insurance policy that pays a $244,434 death benefit. To calculate the expected gain or loss from purchasing the insurance policy, we must compute the expected value of the insurance policy to the man. The expected value (EV) is calculated by multiplying the probability of each outcome by the financial gain or loss that would result from that outcome and then summing these products. For the possibility of death, the man gains a benefit of $244,434, but for the possibility of staying alive, he only loses the premium ($362).

EV = (Probability of death) x (Death benefit) – (Probability of staying alive) x (Premium cost)

So, EV = (0.00224 x $244,434) - (0.99776 x $362).

Calculating this, we have:

EV = ($547.53) - ($361.09) = $186.44.

The expected gain to the man from purchasing the policy is $186.44.