Random Variables

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 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
--------------------------------------…
1 0.00051
2 0.00052
3 0.00054
4 0.00056
5 0.00059
--------------------------------------

compute...
[A]over the full 5 years, what is the expected premium income in terms of P?
[B] over the full 5 years, what is the expected death payment?

Find the value of p that makes [A]-[B] = 1000.