A health insurance company charges policyholders a $2400 annual premium for heal

Question

A health insurance company charges policyholders a $2400 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $2750. Furthermore, they have estimated that 85% of patients will not be hospitalized, 10% 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 80,000 policyholders?

Explanation / Answer

a) here insurance company’s expected profit per policyholder =Premium-expected cost of being hospitalized once a year -expected cost of being hospitalized twice a year

=2400-0.1*2750-0.05*(2*2750)=1850

b) expected profit if they enroll 80,000 policyholders =80000*1850=$1.48*108

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