Wednesday, December 11, 2013

Health insurance policy math -- post number one.

Question:   A health plan has a $3,000 deductible, a coinsurance rate of 20%, and a maximum allowable out-of-pocket expense limit of $9,000.   What level of total health expenditures will result in the insurance company paying all further covered health care expenses during the year?

First some definitions:

Deductible — A deductible is the specified amount of money that an insured must pay prior to an insurance company paying a claim.

Coinsurance rate — the share of health expenses paid by the insured for expenses over the deductible but lower than the maximum allowable out-of-pocket expense limit.

The out-of-pocket expense limit — The maximum amount of covered claims that the insured is responsible for under a policy.   After the out-of-pocket expense limit is reached the insurance company pays all covered expenses.

The answer:

Will denote total health expenditures EXPT and out of pocket expenditures OUTP.  

Out of pocket expenditures under the plan are the minimum of $9,000 (the limit under the plan) and the amount stipulated by the benefit formula.  

When EXPT is less than $3,000 the OUTP is equal to EXPT.

When EXPT is greater than $3,000 the OUTP is give by equation below.

OUTP=Min($9,000,$3000+0.20 x (EXPT- $3000))

When OUTP=$9,000 the insurance firm must pay all additional expenditures.

This occurs when

$9000 = $3000 + 0.20 X (EXPT - $3000)

($6000 + 0.20 X  $3,000)/0.2  = OUTP = $33,000.

Note that when EXPT= $33,000 the OUTP = $3,000  + 0.20 x ($33,000- $3,000)

or OUTP = $9,000.

Happiness — Answer appears to check today.


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