The table given below lists a few ages and probabilities of death at those ages
ID: 3172223 • Letter: T
Question
The table given below lists a few ages and probabilities of death at those ages for a certain segment of the population.
Age
60
61
62
63
64
P(death at this age)
0.00756
0.00825
0.00896
0.00965
0.01035
a. Suppose an insurance company offers a $50,000 term (fixed pay-out) life insurance policy to a person in this demographic to cover the five years listed. What is the expected cost (loss) to the company for a death during this five-year period? (10)
b. If the company wants to make a profit of $550 above its expected total cost, what premium should it charge? (4)
Age
60
61
62
63
64
P(death at this age)
0.00756
0.00825
0.00896
0.00965
0.01035
Explanation / Answer
a. Expected loss = 50000[0.00756+ (1-0.00756)*0.00825+(1-0.00756)*(1-0.00825)*0.00896 + (1-0.00756)*(1-0.00825)*(1-0.00896 )*(0.00965)+(1-0.00756)*(1-0.00825)*(1-0.00896 )*(1-0.00965)*0.01035 ]
=2198.88883771
b. It should charge 2198.88883771 + 550 = 2748.88883771
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