Why Coinsurance Shares Get Reversed
A coinsurance percentage describes a division of a covered loss, but the percentage may be stated as the insurer’s share or the insured’s share. Those are complementary percentages, not interchangeable labels. Applying the stated percentage to the wrong party reverses the allocation: the two payments may still add to the covered loss, so a simple total check alone will not reveal the error.
There is no safe rule that a bare phrase such as “80% coinsurance” always identifies the same party across all policy contexts. Read the wording that defines the percentage. Does it say the insurer pays 80%, or that the insured is responsible for 80%? If the wording does not identify the party, the information is insufficient to determine the allocation without clarification.
The key exam habit is to identify both the percentage and its owner before multiplying. A percentage without its owner is not yet a complete payment instruction. Also distinguish the amount subject to the coinsurance split from a larger bill or loss amount: use the eligible covered amount specified by the problem, not automatically the total submitted amount.
A Short Justification: The Shares Must Reconcile
Suppose the insurer’s contractual share is \(c\), where \(0\leq c\leq 1\). The remaining fraction of the eligible loss is \(1-c\), because the full loss represents 100% of the allocation. Multiplying each fraction by \(L\) gives the two payments. Their sum must recover the full amount being divided:
If instead the wording gives the insured’s share \(q\), then the insurer receives the complementary fraction \(1-q\). Thus \(qL+(1-q)L=L\) as well. This conservation check confirms that the amounts account for the entire eligible loss; it does not determine which party owns the stated percentage. That must come from the contract wording.
Read the Wording Before Calculating
Use a consistent sequence rather than relying on familiarity with a particular product. First identify the amount to which the coinsurance percentage applies. Next underline who is said to pay, bear, or be responsible for that percentage. Then calculate the named party’s share and obtain the other party’s share as the complement. Finally, reconcile the two amounts to the eligible covered loss.
Use the amount expressly subject to the coinsurance split. If a problem separately identifies excluded or ineligible amounts, do not include them in this split.
Translate the wording into “insurer share” or “insured share.” Do not infer the owner from the word “coinsurance” alone.
If one party’s fraction is \(r\), the other party’s fraction is \(1-r\).
Add the insurer and insured payments. They should equal the amount being divided under the stated assumptions.
Worked Example: The Insurer Pays the Stated Percentage
A hypothetical policy states, “The insurer pays 70% of the eligible covered loss, and the insured is responsible for the balance.” A submitted bill is $17,000, of which $2,400 is expressly excluded. Find each party’s amount for this coinsurance allocation. Assume there are no other adjustments to the eligible amount.
Method. Identify the eligible amount first, then apply the insurer’s stated percentage. The 70% belongs to the insurer because the clause explicitly says the insurer pays it.
The eligible covered amount is:
The insurer pays:
The insured is responsible for the balance, which is 30%:
Check. The payments reconcile to the eligible amount: \(\$10{,}220+\$4{,}380=\$14{,}600\). The excluded $2,400 is not part of this split. A common mistake is to treat the insurer’s 70% as the insured’s share; that would incorrectly assign $10,220 to the insured and $4,380 to the insurer, reversing the parties’ payments.
Worked Example: The Insured Bears the Stated Percentage
A hypothetical plan defines its coinsurance as “the member pays 15% of the allowable covered expense; the plan pays the remainder.” For one claim, the allowable covered expense is $28,500. Calculate the member’s responsibility and the plan payment.
Method. Translate the clause before calculating. The 15% is the insured’s share, not the plan’s share.
The member pays:
The plan pays the remaining 85%:
Check. \(\$4{,}275+\$24{,}225=\$28{,}500\), the allowable covered expense. The common reversal is to pay the plan 15% and assign 85% to the member. That calculation still sums to $28,500, but it contradicts the sentence specifying that the member pays 15%.
Worked Example: Resolving a Worksheet That Reversed the Share
A hypothetical claim has an eligible covered loss of $12,600. The policy wording states, “The insured bears 20% of each eligible covered loss; the insurer pays the remainder.” A draft worksheet assigns $2,520 to the insurer and $10,080 to the insured. Determine whether the worksheet is correct and give the correct allocation.
Method. Compare the worksheet’s amounts with the party named in the contract. The stated 20% belongs to the insured, so the insurer’s share is \(1-0.20=0.80\).
The insured’s correct amount is:
The insurer’s correct payment is:
The draft worksheet is reversed: its two dollar amounts are individually the correct shares, but they are assigned to the wrong parties. Check. The corrected insurer payment and insured responsibility sum to \(\$10{,}080+\$2{,}520=\$12{,}600\). This example shows why both checks matter: reconcile the total, and confirm that each amount is assigned to the party named by the policy.
Common Mistake and Exam Check
The most tempting error is to memorize a convention and apply it before reading the clause. For instance, seeing “20% coinsurance” and automatically multiplying the loss by 20% for the insurer may be wrong if the contract says the insured pays 20%. Conversely, treating every stated percentage as the insured’s share is also unsafe. The text controls.
A reliable scratch-paper setup labels the terms before substituting values:
Fill in the first two labels from the policy sentence, not from a remembered product convention. Then multiply each share by the correct eligible amount. If the question gives only a percentage but never says whose share it is, state that the allocation cannot be determined uniquely from the information given.
This distinction matters whenever claim payments are calculated: a reversed share can produce a substantial transfer between the parties while passing a superficial arithmetic check. Keep the scope narrow when performing the calculation. The coinsurance split allocates the amount specified for the split; it does not by itself determine whether a separate exclusion, deductible, or limit changes that amount. This treatment of coinsurance shares is aligned with the SOA Exam FAM (Fundamentals of Actuarial Mathematics) syllabus.
Check Your Understanding
For each problem, identify whose percentage is stated, calculate both amounts, and check the allocation.
- A hypothetical policy says the insurer pays 65% of an eligible covered loss of $7,400. How much does each party pay or bear? (Answer: Insurer $4,810; insured $2,590.)
- A hypothetical plan states that the insured pays 12% of an allowable covered expense of $23,750. Find the insured’s amount and the plan’s payment. (Answer: Insured $2,850; plan $20,900.)
- A hypothetical claim has a submitted amount of $21,000, including $1,800 expressly excluded. The policy says the insurer pays 75% of the eligible covered amount. Find both shares. (Answer: Eligible amount $19,200; insurer $14,400; insured $4,800.)
- A policy says the insured is responsible for 35% of an eligible covered loss of $36,500. A worksheet assigns $12,775 to the insurer. Is that assignment correct? State the correct allocation. (Answer: No; insured $12,775 and insurer $23,725.)
- Two hypothetical claims have different wording. For Claim A, the insurer pays 80% of an eligible loss of $6,250. For Claim B, the insured bears 20% of an eligible loss of $11,400. Find each claim’s allocation and the combined insurer and insured totals. (Answer: Claim A—insurer $5,000, insured $1,250; Claim B—insurer $9,120, insured $2,280; combined insurer $14,120 and insured $3,530.)