Question

Life tables show that the probability a healthy 23-year-old man will die before his 30th birthday is 0.065. Suppose one insurance company is considering offering a life insurance policy for men who have just turned 23. The policy will pay $150,000 if the policy holder dies before his 30th birthday, nothing if he does not. The premium, which has to be paid at the time the policy is purchased, will be set at $1000. Create the table that shows the company’s net payouts and the probabilities for those payouts, and find the expected net payout per policy

Answer 1

We need to make the following assumptions to answer this question.

First instead of year by year bifurcation we will consider the entire span of 7 years i.e. between the age of 23 and 30 as one time period.

Secondly, there are no external factors such as rate of interest, tax and expenses affecting the outcome of the policy.

With the given information we have.

The sum insured is $150,000

The one time premium is $1000

The probability of policyholder death between the ages 23 and 30 is 0.065

Consequently the survival probability is = 1 - 0.065 = 0.935

So we have:

Event	Premium	Sum Assured	Probability	Net payout
Death	1000	150000	0.065	$149000
Survive	1000	150000	0.935	-$1000

From the above table we can see that there is a positive payout of $149000 in the event of policyholder death with the probability 0.065 and a negative payout of $1000 in the event the policyholder survives with the probability 0.935.

The expected net payout of the company per policy can be calculated as:

EP = 149000*0.065-1000*0.935

= $8750

Thus, the expected net payout per policy is $8750.

(This payout is such a high figure because we have considered the additional information such as rate of interest as zero).