Question

A 53-year old woman paid a yearly premium of $387.00 for a life insurance policy. If she dies within the next year, the life insurance company will pay the death benefit of $100,000 to her beneficiary. If she lives throughout the year, she receives nothing from the company. An actuarial life table from the Social Security Administration website indicates that the probability of a random 53-year old female dying within the next year is 0.003852 . What is the expected value for the woman's life insurance policy ?

Answer 1

Given that the probability of dying is 0.003852, the probability of living will be

$\begin{gathered} P(living\text{) =1-P(dying)=1-0.}003852=0.996148 \\ P(living\text{)=0.996148} \end{gathered}$

Annual insurance charge=387.

Thus, the gain or loss from death will be

$100000-387=99613$

The gain or loss from when alive will be -387, since she does not get the death benefit when alive instead she pays the annual insurance charge.

Thus, the Expected value of insurance policy is evaluated as

$((\text{profit or loss from death)}\times P(dying))+((\text{profit or loss from living)}\times P(\text{living))}$

This is calculated to be

$\begin{gathered} (\text{0}.996148\times(-387))+(0.003852\times99613)=-385.509276+383.709276 \\ =-1.8 \end{gathered}$

Thus, the expected value is $ 1.8