According to an American experience mortality table, the probability that a 25-year-old man will survive one year is 0.992 , and that he will die within a year is 0.008 . An insurance company offers to sell such a man a $1000 one year term life insurance policy for a premium of $10 . what is the company's expected gain?
2007-04-02 04:31:47 · 5 answers · asked by Geek 2 in Science & Mathematics ➔ Mathematics
Gain = 10*.992 - 990*.008 = 2
2007-04-02 04:37:24 · answer #1 · answered by fcas80 7 · 0⤊ 1⤋
There is a 99.2% chance the insurance company keeps the $10, and a 0.8% chance the company loses $990 (i.e. $1000 payout after collecting the $10. So, the expectation is:
.992 * 10 + .008 * (-990) = 9.92 - 7.92. The expected gain is $2.00.
The posters above do have a simpler way to calculate this, at least in terms of the numbers you have to deal with - the odds of collecting $10 is 100%, while the odds of paying out $1000 is 0.8%. So, you again get $2: 10 * 1 - 1000 * .008 = 10 - 8 = 2. Use whichever approach makes more sense to you.
2007-04-02 11:56:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
paid out expected per person = 0.008 * 1000=8
fixexd income =10 thus 2 gain.
2007-04-02 11:41:04 · answer #3 · answered by gjmb1960 7 · 0⤊ 0⤋
$10 is the most they can gain from selling such a policy and they expect that to be realized due to the statistical data provided.
2007-04-02 12:09:17 · answer #4 · answered by amirT 3 · 0⤊ 0⤋
$2 on that one person. So per person, they get $2. :]
2007-04-02 11:38:34 · answer #5 · answered by Anonymous · 0⤊ 0⤋