A health insurance company charges policyholders a $1650 annual premium for heal

Question

A health insurance company charges policyholders a $1650 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $2700. Furthermore, they have estimated that 80% of patients will not be hospitalized, 14% will be hospitalized once a year, and no one will be hospitalized more than twice

. (a) Find the insurance company’s expected profit per policyholder.

(b) What is the expected profit if they enroll 800,000 policyholders?

Explanation / Answer

80% of patients will not be hospitalized,

14% will be hospitalized once a year

6% will be hospitalized twice a year

0% will be hospitalized e than twice a year

E(profit per policy holder) = 1650 - [(0.14*2700)+(2*0.06*2700)] = 1650-702 = $948

b)

E(profit if they enroll 800,000 policyholders) = 800000*948 = $758,400,000

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