Why Two Different Minimums Matter
A policy can have a minimum premium even when its exposure-based calculation produces only a small charge. It can also have a minimum-earned premium that affects how much the insurer retains if coverage ends early. These provisions address different questions: the first concerns the premium charged for the policy, while the second concerns the amount retained at cancellation.
The distinction matters when a policy is audited, changed midterm, or cancelled. The exposure-based premium may change as the coverage changes, and the earned amount depends on when each portion of coverage was in force. A minimum-earned provision can then set a floor on the cancellation retention. The calculations below use hypothetical policy terms; actual contract wording determines how a particular minimum applies. This treatment is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
A minimum premium is not automatically an extra charge added on top of the exposure-based premium. It is normally a floor: charge the greater of the calculated premium and the applicable minimum. Similarly, a minimum-earned premium does not necessarily replace the ordinary earned-premium calculation. When the cancellation provision defines the retention as the greater of pro rata earned premium and the minimum-earned amount, the insurer retains the larger amount.
| Provision | Question it answers | Typical calculation |
|---|---|---|
| Minimum premium | What is the lowest premium charge for the specified policy or coverage? | Greater of calculated premium and minimum premium |
| Minimum-earned premium | What is the least the insurer retains if coverage ends early? | Greater of pro rata earned premium and minimum-earned amount, if the contract says so |
Calculating the Premium Floor
Let \(P_{\mathrm{calc}}\) be the premium calculated from the applicable rating basis and let \(P_{\min}\) be the applicable minimum premium. Under a provision that applies the minimum to the final premium for the policy, the charged premium is
The order of operations is important. First determine the premium using the relevant exposure and rate; then apply the minimum as specified by the policy. If an audit or endorsement changes exposure, recalculate the premium for the changed policy before deciding whether the floor still binds. Contract terms may apply minimums per policy, coverage, or transaction, so do not assume that the same minimum is applied separately to every adjustment.
Worked Example: Applying a Minimum After an Exposure Audit
A hypothetical annual policy charges $1.50 per $100 of audited payroll and has a $750 minimum premium. The initial payroll estimate is $40,000. At audit, payroll is determined to be $52,000. Calculate the initial charge, the final premium, and the additional amount due. Assume the minimum applies to the final policy premium.
Method: calculate the exposure-based premium at each stage, then apply the policy-level floor. The initial calculated premium is
Because $600 is below the $750 minimum, the initial charge is
At audit, the revised exposure-based premium is
The revised premium exceeds the minimum, so the final premium is $780. If $750 was already charged, the additional amount due is \(\$780-\$750=\$30\). The final check is that the revised premium is at least the minimum and agrees with the audited exposure calculation.
Common mistake avoided: Adding the $750 minimum to the $780 exposure-based premium would incorrectly produce $1,530. The minimum is a floor, not an extra charge, and it is applied to the recalculated final premium under the stated policy terms.
Minimum-Earned Premium at Cancellation
For a policy that earns premium pro rata over time, let \(P\) be the applicable premium for the full policy term, and let \(f\) be the fraction of the term that has elapsed while the relevant coverage was in force. The pro rata earned amount is \(Pf\). If the cancellation clause sets a minimum-earned amount \(M\) and requires the greater of the two amounts to be retained, then
If the full premium has been paid and there are no separate fees or adjustments, the return premium is \(P-P_{\mathrm{retained}}\). This calculation does not include a short-rate penalty unless the contract separately provides for one. A minimum-earned clause is not a license to assume a particular percentage: use the amount or formula specified in the policy.
Worked Example: A Minimum-Earned Amount Exceeds Pro Rata Earning
A hypothetical one-year policy has a premium of $1,200 and a minimum-earned provision of $300. It is cancelled after 60 days. Assume pro rata earning on a 365-day basis, no short-rate penalty, no fees, and that the full premium has been paid. Find the amount retained and the return premium.
Method: compare ordinary pro rata earned premium with the stated minimum-earned amount. The elapsed fraction is \(60/365\), so ordinary earned premium is
The minimum-earned amount is $300, which is greater than $197.2602. Therefore the insurer retains $300. The return premium is
To the nearest cent, the retained amount is $300.00 and the return premium is $900.00. The check is that the two amounts sum to the premium paid: \(\$300+\$900=\$1{,}200\).
Common mistake avoided: Returning \(\$1{,}200-\$197.26=\$1{,}002.74\) would ignore the minimum-earned provision. That return would leave only $197.26 retained, less than the contractual $300 floor.
Coverage Changes During the Term
When coverage or exposure changes midterm, separate the premium associated with each coverage segment and identify how long that segment was in force. For a simple pro rata calculation, each segment’s premium contribution is its full-term premium multiplied by the fraction of the policy term for which that segment applied. Add the contributions to obtain the earned amount before applying any minimum-earned clause.
This method is not a substitute for the contract’s rating and transaction rules. A midterm change may generate an additional or return premium based on the effective date and the applicable rate. A minimum premium may apply to the revised policy premium, while a minimum-earned amount may separately affect cancellation retention. Keep those calculations distinct.
Use the applicable exposure, rate, effective dates, and minimum-premium rule to determine the premium for the coverage actually placed.
Mark when each coverage or exposure change became effective and the date coverage ended.
For each segment, multiply its full-term premium contribution by the fraction of the term that segment was in force; then sum the contributions.
Use the contractual rule to determine retention and return premium. If it specifies the greater of ordinary earned premium and a floor, compare those two amounts.
Worked Example: Added Coverage Followed by Cancellation
A hypothetical 365-day policy has an original coverage premium of $1,200 for the full term. An endorsement adds coverage with a full-term premium of $365, effective on day 100. The policy is cancelled at the end of day 200. The cancellation provision requires the insurer to retain the greater of pro rata earned premium and an $800 minimum-earned amount. Assume day fractions are measured on a 365-day basis, the full adjusted premium was paid, and there are no fees or short-rate penalties. Calculate the adjusted premium, earned premium, amount retained, and return premium.
Method: prorate the endorsement from its effective date, then calculate earned premium by coverage segment. The added coverage is in force for \(365-100=265\) days of the full term. Its additional premium is
The adjusted premium for the policy is therefore
By cancellation, the original coverage has been in force for 200 days. Its earned premium is
The added coverage has been in force from day 100 through day 200, or 100 days under the stated elapsed-day convention. Its earned premium is
Thus ordinary earned premium is \(\$657.5342\ldots+\$100=\$757.5342\ldots\), or $757.53 to the nearest cent. Compare this with the $800 minimum-earned amount: \(\max(\$757.5342\ldots,\$800)=\$800\). The insurer retains $800.00, and the return premium is
The final check is that the retained amount and return sum to the adjusted premium: \(\$800+\$665=\$1{,}465\). Ordinary earned premium is $757.53, but contractual retention is $800.00 because the minimum-earned provision binds.
Common mistake avoided: Do not count the added coverage as if it had been in force for all 200 elapsed days. It began on day 100, so it contributes only 100 days of earned premium by cancellation. Also, do not apply the minimum-earned amount before calculating the segment premiums; first find ordinary earned premium, then apply the clause.
Common Traps and Practical Checks
The calculations are manageable when each amount is tied to a clearly defined question. In particular, do not use “premium” to mean the calculated exposure premium, the charged premium, the earned premium, and the retained amount interchangeably. State which one you are calculating.
- Adding rather than applying a floor. A minimum premium generally replaces a lower calculated amount; it is not automatically added to it.
- Applying the wrong minimum. A minimum premium sets a charge floor; a minimum-earned premium sets a retention floor under its stated cancellation terms.
- Ignoring effective dates. Added coverage earns premium only for the time it was in force. Use its own effective date when determining the earned fraction.
- Using the wrong denominator. If the problem specifies 365 days, use 365 consistently. Do not silently switch to a 360-day year or a monthly approximation.
- Returning the pro rata unearned amount despite a binding floor. Under a greater-of clause, retention is the larger of ordinary earned premium and minimum earned; return is based on that retention.
- Assuming every contract has the same treatment. The wording controls whether the minimum applies per policy, coverage, or transaction and whether a percentage, fixed amount, or other formula is used.
A useful final check is to compare the amount retained with both ordinary earned premium and the minimum-earned amount, then verify that retained premium plus return premium equals the applicable premium paid. These checks catch many arithmetic and interpretation errors.
Check Your Understanding
For each hypothetical policy, follow the stated terms and round money to the nearest cent where needed.
- A policy charges $2 per $100 of exposure and has a $500 minimum premium. Final audited exposure is $18,000. What is the charged premium? (Answer: $500.00)
- A $900 one-year policy has a 20% minimum-earned provision. It is cancelled after 90 days, using a 365-day pro rata basis. The clause retains the greater of ordinary earned premium and the minimum-earned amount. Find retention and return premium. (Answer: Retained $221.92; return $678.08)
- A fully paid $1,000 policy is cancelled after 100 days of a 365-day term. Its minimum-earned amount is 40% of the policy premium, and retention is the greater of that amount and pro rata earned premium. Find retention and return premium. (Answer: Retained $400.00; return $600.00)
- A hypothetical 365-day policy has an original full-term premium of $730. Added coverage with a full-term premium of $292 takes effect on day 91. The policy is cancelled at the end of day 182. Calculate the adjusted premium and ordinary earned premium. (Answer: Adjusted premium $949.20; earned premium $436.80)
- In the policy in question 4, suppose the minimum-earned amount is $500 and the full adjusted premium has been paid. Under a clause requiring retention of the greater of ordinary earned premium and that minimum, find retention and return premium. (Answer: Retained $500.00; return $449.20)