Expected value word problem: deciding whether to insure lives of those leading quest

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jmasta

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Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 91.3%. If BIC charges a premium of 5,200 silver coins and would pay a death benefit of 93,000 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC?
Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number.

How do I break this down into a solvable formula?
 
jmasta said:
Brandybuck Insurance Company (BIC) is deciding whether to insure the lives of those leading a quest to Moria. Based on past experience, the probability of surviving such a quest is 91.3%. If BIC charges a premium of 5,200 silver coins and would pay a death benefit of 93,000 silver coins if the insured were to die, what is the expected value of this insurance policy to BIC?
Round to the nearest silver coin as needed. If the expected value is a loss to BIC, enter your answer as a negative number.

How do I break this down into a solvable formula?
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What are your thoughts?

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Apologies.

The way my text book breaks it down has several variations that are a bit confusing to separate. If I am reading it correctly than

E= 5200(91.3) + 93000(8.7)= 1,283,860

At no point did I ever feel confident that this was even approaching the correct way to break this problem down, as the expected value seems far to high for this problem to make any sense.
 
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