Insurance: expected gain for company on given policy

skyguy

New member
Joined
Sep 11, 2006
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I think I may have made this to simple, which scares me. Can one of you whiz kids take a look and let me know what you think?

An insurance company offers a 50 year-old woman a $100,000 one-year term insurance policy for an annual premium of$850. If the annual number of deaths per 1,000 is six for women in this age group, what is the expected gain for the insurance company from a policy of this kind? (Assume the company sells 1,000 policies of this type. )

I took the total number of policies sold (1000) and multiplied it by the premium of $850. Then, I took the number of policies cashed in (6) and multiplied it by the payout of $1000 to get $600,000. I took the total revenue of $850,000 and subtracted the payout of $600,000 to get a total net gain for the policies of $250,000, or $250/policy. Thoughts?
 
I would think the expected value would be:

\(\displaystyle 99150(\frac{6}{1000})=$594.90\)
 
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