The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Example 13.2.1 Mary has a “deductible and coinsurance” health insurance policy
with a $250 deductible and 80/20 coinsurance. She submits claims for $650.79 of
medical expenses covered under her contract. How much will she receive from her
insurer in reimbursement for these claims?

The $250 deductible must fi rst be satisfi ed, so the insurer will cover $650.79  $250 
$400.79. This is covered at 80%, so she will be reimbursed (80%)($400.79)  $320.64.

Example 13.2.2 Suppose that later in the same year, Mary submits an additional
$708.25 in covered claims. How much will she be reimbursed for these?

She has already satisfi ed her deductible, so the entire remaining claim is covered:
(80%)($708.25)  $566.60.

Deductible and coinsurance plans often include an out-of-pocket maximum. If the total
of the insured’s share of medical costs (from the deductible and coinsurance) exceeds the
out-of-pocket maximum, the insurer covers all additional claims in full.

Example 13.2.3 Mary’s policy has a $1,000 out-of-pocket maximum. Before the
end of the year, she has some signifi cant medical expenses, and runs up claims totaling
$6,000, which she submits to the insurer. How much will the insurer pay?

Since her deductible is satisfi ed, the insurer would normally cover 80%($6,000)  $4,800.
However, the out-of-pocket maximum applies. So far this year, Mary has been left to pay
$650.79  $320.64  $330.15 on the fi rst claim and $708.25  $566.70  $141.65 on
the second, for a total of $330.15  $141.65  $471.80.

Thus, the most she can be left to pay this year is $1,000  $471.80  $528.20. Her insurer
will pay $6,000  $528.80  $5,471.80.

Indemnity policies also may have a maximum amount that the insurer will pay on the con-
tract. Unlike the deductible, which resets every year, these coverage maximums are often a
maximum over the entire lifetime of the contract. Usually this limit is quite high (a million
dollars or more), in which case it is not much of a concern. Most policies offered through
an employer have high lifetime maximums (if they have them at all). However, there are
policies sold with lower lifetime maximums, and with those policies the maximum may
be a significant issue. For example, policies sold to college students through a campus
health office often carry limits of $10,000 or $25,000 or some similar amount. This maxi-
mum is more than adequate to cover a broken leg or minor illness, but the policy could be
exhausted very quickly in the event of a more serious injury or illness.
A health insurance policy may be an individual policy covering just one single individual,
or a family policy covering an individual and his immediate family. Spouses and dependent
children (up to a certain age limit) may be covered under almost any family policy; some
policies will also cover an unmarried domestic partner. When more than one individual is
covered under a policy, a separate deductible may apply to each individual up to a certain
overall policy deductible. For example, a “$250/$500 deductible” indicates that the deduct-
ible is $250 per person, up to a maximum $500 deductible for the contract as a whole.

Example 13.2.4 Ken is a single father with three children covered under a family
health insurance policy. The policy provides 80/20 coinsurance with a $250/$500
deductible. Ken submits claims of $840 for himself, $100 for one child, and $670
for another child. He has not submitted any other claims this year. How much will his
health insurance pay?

Ken has a $250 deductible for himself, so the insurer will cover $840  $250  $590 of
his claim.

His fi rst child’s claim of $100 falls under the $250 deductible, so none of it is covered.

His second child’s $670 claim is over the deductible, so it will be covered. However, it is not
the $250 per person deductible that applies. Ken and his fi rst child have already satisfi ed

13.2 Health Insurance and Employee Benefits 539
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