Suppose a life insurance company sells a $50,000, five-year term policy to a twenty-five-year-old woman. At the beginning of each year the woman is alive, the company collects a premium of $P. The probability that the woman dies and the company pays the $50,000 is given in the table below. So, for example, in Year 3, the company loses $50,000 – $P with probability 0.00054 and gains $P with probability 1 – 0.00054 = 0.99946. If the company expects to make $1000 on this policy, what should P be?
Year Probability of Payoff
1 ……………………………….0.00051
2 ……………………………….0.00052
3 ……………………………….0.00054
4 ……………………………….0.00056
5 ……………………………….0.00059