Suppose that Brittney has an income of $80,000 per year and that there is a 1 in
ID: 2439528 • Letter: S
Question
Suppose that Brittney has an income of $80,000 per year and that there is a 1 in 5 (20%) chance that she will get sick in a given year. Let’s suppose that the cost of the illness (in terms of lost work time and medical bills) is $60,000 which leaves her with an income of only $20,000 in that particular year.What is the actuarially fair premium for Brittney’s situation?
(a)$68,000
(b)$16,000
(c)$12,000
(d)$8,000
(e)There is no possibility of an actuarially fair premium being calculated in Brittney’s case.
Explanation / Answer
The actuarially fair premium by definition is the premium that allows insurance company to exactly break even (i.e., make zero profits):
Profits = revenues-costs = premium-expected cost = 0.
Therefore actuarially fair premium is equal to expected costs(EC), which are calculated as :
EC = p*(loss of income if sick) + (1-p)(loss of income when healthy), where P is the probability of getting sick i.e, 20% in this case, it means p = 0.20
EC = 0.20*(60,000)+0.80*(0)= $12,000
Actuarial fair premium = $12,000.
So correct option is C) $12,000.
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