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A life insurance company sells a $150,000 five-year term policy to a 30 year old man. If at the beginning of each year the man

A life insurance company sells a $150,000 five-year term policy to a 30 year old man. If at the beginning of each year the man is alive, the insurance company collects a premium of $P. The probability that the man dies and the company pays the $150,000 is 0.00051 at year 1; 0.00052 at year 2; 0.00053 at year 3; 0.00055 at year 4; and 0.00058 at year 5. Thus, for example, in year 4, the insurance company loses $150,000 - $P with probability 0.00055 and gains $P with probability 1-0.00055=0.99945. If the insurance company expects to earn $2000 on this policy. What should P be?

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