## 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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