Business Mathematics: Insurance - Major Medical Insurance

Most major medical insurance policies have both an annual deductible and a coinsurance clause. Unlike property insurance, the major medical deductible accumulates. It is not applied separately to each medical visit. Once satisfied, the annual deductible will not apply for the remainder of the year.

Since your health has no real monetary value, coinsurance works differently from property insurance. It serves to limit the amount of money an insurance company will pay to a fixed percentage of the claim.

Suppose that a policy has an 80% coinsurance clause. After applying any deductibles that may be applicable, the insurance company will pay 80% of the claim and the patient will be responsible for the difference. Because the patient pays 20% of the claim, this amount is called a 20% copayment.


Example
Jennifer has a health insurance policy which has a $250 deductible and a 20% copayment. Jennifer goes skiing and breaks a leg and incurs $3,000 worth of medical bills.

Her insurance company will pay 80% of the amount in excess of the deductible.

The insurance company will pay $2,200 and Jennifer will have to pay $800.

After the deductible is satisfied, the insured pays 20% of the medical bill. This amount is known as an “out-of-pocket expense.”

Many insurance policies have an upper limit on the out-of-pocket expenses an insured is required to pay. After your deductible has been satisfied and your out-of-pocket maximum has been reached, the insurance company pays 100% of the claim.


Example
Suppose that Harold Weiss had $68,000 worth of medical expenses last year. His insurance policy has a $300 deductible, a 20% copayment, and an out-of-pocket maximum of $1,500.

To compute Mr. Weiss’ insurance benefit, we first apply the deductible to his medical bill:
$68,000–$300 = $67,700

Then we apply the coinsurance to compute the benefit:
80% of $67,700 = 0.8 × $67,700 = $54,160   

The difference, $67,700–$54,160 = $13,540, is his out-of-pocket expense. Since the maximum out-of-pocket expense under this policy is $1,500, Harold is entitled to an additional reimbursement of
$13,540–$1,500 = $12,040   

The total benefit under the policy is then $54,160 + $12,040 = $66,200.

To avoid excessive and unrealistic claims, major medical insurance companies use reasonable and customary benefit schedules.

These represent average fees doctors charge for medical procedures performed in a certain locality. These schedules determine the maximum benefits that can be considered, regardless of actual charges, before any benefit calculation is performed.


Example
Mrs. White needs hip surgery. Her orthopedic surgeon wants to charge her $20,000 for the operation. Her major medical policy has a $500 deductible and a 20% copayment. Reasonable and customary charges for the procedure she requires are $17,500 for the city she lives in.
We shall assume that Mrs. White had no other insurance claims that year. (Deductibles are cumulative within a calendar year, for all insurance claims that year.)

Even though her surgeon is charging her $20,000, the maximum fee the insurance company will allow is $17,500.

After subtracting the deductible, the insurance company will pay 80% of the difference:
$17,500–$500 = $17,000
80% × $17,000 = $13,600

The insurance company will pay $13,600 and Mrs. White will have to pay the difference, $6,400.


Example
Suppose that Mrs. White’s policy (see Example 9) stipulates that her maximum out-of-pocket expense is $1,000. How much additional will the insurance company allow?
The only part of the medical bill that qualifies as out-of-pocket expense is the 20% of the $17,000 that the insurance company did not pay:
20% × $17,000 = $3,400
Since her maximum out-of-pocket expense is $1,000, the insurance company will pay an additional $2,400.

Solved Problems

10.10  Julio received medical treatment totaling $2,700 in 2000. His insurance policy has a $250 deductible and a 20% copayment. His out-of-pocket maximum is $1,000. How much will Julio receive from his insurance company?
 

Solution

Since his out-of-pocket expenses are $2,450 – $1,960 = $490, Julio has not reached his out-of-pocket maximum. He will receive $1,960.

10.11  Jeremy Jenkins fell and broke his collarbone. His medical bills totaled $17,000. How much of the bill is he personally responsible for if his major medical policy has a $750 deductible, a 20% copayment, and a $2,000 maximum out-of-pocket expense?
 

Solution
Since this exceeds $2,000 he is responsible for only
$2,000 (out of pocket) + $750 (deductible) = $2,750

10.12  Marty had a medical procedure performed, for which his physician charged $3,000. His insurance policy has a $250 deductible and a 20% copayment. He received, however, only $1,560 from his insurance company. What were the reasonable and customary charges allowed for his procedure?
 

Solution
Let x represent the reasonable and customary charges after the deductible is applied:

The allowed charge was $1,950 + $250 = $2,200.

10.13  In 2000, Steve had a series of medical procedures performed:

His major medical policy has a $750 deductible and a 20% copayment with $1,500 maximum out-of-pocket expense. How much will Steve collect from his insurance company?
 

Solution
For each procedure, Steve will collect the smaller of (a) the actual cost or (b) reasonable and customary charges. Thus the insurance company will consider
$75 + $250 + $1,100 + $12,000 + $2,000 + $4,000 = $19,425

From this we subtract the deductible: $19,425–$750 = $18,675

Next we apply coinsurance: 80% of $18,675 = $14,940. The difference, $18,675 – $14,940 = $3,735, is Steve’s out-of-pocket expense. Since the maximum out-of-pocket expense under Steve’s policy is $1,500, the insurance company will pay an additional $3,735–$1,500 = $2,235. Steve's total benefit under his policy is $14,940 + $2,235 = $17,175.