Prorating Midterm Endorsement Premium Changes

Why Midterm Endorsement Premiums Are Prorated

A midterm endorsement changes the coverage or another premium-determining feature of a policy while the policy is in force. The revised premium is not generally charged for the entire policy term: the change applies only to the portion of the term beginning on the endorsement’s effective date. The premium adjustment therefore depends on two items: the difference between the old and revised full-term premiums, and the fraction of the policy term affected.

This calculation is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus. It uses the same distinction between a full-term premium and premium associated with coverage over a portion of a term that appears in the earlier material on earned premium.

The Pro Rata Calculation

Use dates consistently. Represent the policy term as the interval from its start date \(s\) up to, but not including, its expiration date \(e\). If the endorsement takes effect on date \(t\), count the full term’s days from \(s\) to \(e\), and the affected remaining days from \(t\) to \(e\). Thus, a change effective on the policy’s start date affects the full term; a change effective at expiration affects no remaining coverage.

The fraction is between zero and one when \(t\) falls within the policy term. Keep the sign of \(\Delta P\): a positive result is additional premium, and a negative result is return premium. If reporting the amount of return premium as a positive dollar amount, state that it is a return rather than silently changing the calculation’s sign.

Why the Remaining-Term Fraction Applies

The method assumes the premium change is earned uniformly over time: each day in the policy term is assigned the same share of the full-term premium change. If the change is \(\Delta P\) for the whole term of \(D\) days, its share per day is \(\Delta P/D\). Over the \(R\) days to which the endorsement applies, the total change is \(R\) such daily shares:

This justifies the pro rata formula under straight-line treatment. It is not a universal rule for every contract or billing arrangement. It assumes the stated premiums are comparable full-term amounts and the endorsement change is allocated uniformly over the affected time. A contract-specific charge, minimum, or other adjustment must be handled according to its own terms rather than automatically treated as a time-based premium change.

Decreases and Day-Count Details

A decrease uses the same formula. The only change is the sign: if revised coverage has a lower full-term premium, then \(P_1<P_0\), so \(\Delta P\) is negative. The result represents a return of premium for the affected remaining period. Do not use elapsed time merely because part of the term has already passed; the endorsement changes the premium prospectively from its effective date.

Leap years require careful date counting, not an automatic extra day in every policy year. The number of days between the two specified dates controls. For example, March 1, 2024, to March 1, 2025, is 365 days: the interval starts after February 29, 2024, and ends before March 1, 2025. The presence of February 29 in the calendar year 2024 does not make this particular interval 366 days.

Keep Premium Changes Separate from Other Amounts

The pro rata calculation applies to the premium change attributable to the revised coverage or rating feature. It does not mean that every amount shown on an endorsement should be multiplied by the remaining-term fraction. For example, if a fixed policy fee is the same before and after the change, it contributes nothing to \(\Delta P\). A separate one-time charge, if applicable, should be identified and handled under its stated terms.

Also confirm what the quoted premium represents. The formula above uses full-term premiums for the same policy term. If the figures supplied are annualized rates rather than premiums for the actual term, convert them to the applicable term basis before comparing them. For a term whose day count differs from a year, do not treat an annualized amount as though it were automatically the full-term premium. Apply the basis specified in the problem or contract consistently to both old and revised premiums.

Common Exam Trap: Using the Wrong Fraction

A frequent error is to multiply the full-term premium change by the portion of the policy term that has already elapsed. That fraction answers how much of a uniformly earned full-term amount relates to the past; it does not calculate the amount attributable to a change effective now. For a midterm endorsement, use the remaining fraction unless the problem explicitly specifies a different method.

For the first worked example, the incorrect calculation would be:

The 90 days are the time from January 1 to April 1. The endorsement is effective April 1, so its change applies for the 275 days from April 1 to expiration:

A second check is directional and bounded: a premium increase should not produce a return premium under this simple method, a premium decrease should not produce additional premium, and the magnitude of the prorated change should not exceed the full-term change.