Unearned premium represents the portion of a written premium that corresponds to the unexpired term of the policy. It is a liability on an insurer's balance sheet because the insurer is still obligated to provide coverage for that period. The most common method for calculating this is the pro-rata method, which evenly distributes the premium over the policy's life. The formula in option A correctly calculates this by taking the total policy premium and multiplying it by the ratio of the remaining days of coverage to the total days in the policy term. This ensures the amount recognized as unearned is directly proportional to the remaining coverage period.

B. This formula incorrectly uses "Interest premium" and "expired coverage days," which would be used to calculate earned premium, not unearned premium.

C. This formula is nonsensical, as it uses a count of "Insurance contracts" instead of a premium value and the non-standard term "Reserve coverage days."

D. This formula incorrectly specifies "Overhead premium"; the calculation should be based on the total gross or net written premium for the policy.

1. National Association of Insurance Commissioners (NAIC). (2023). Statement of Statutory Accounting Principles (SSAP) No. 53 – Property and Casualty Contracts-Premiums. In Accounting Practices and Procedures Manual. Paragraph 6 states, "Unearned premiums shall be calculated on a monthly or more frequent pro rata basis." The formula in option A is the mathematical representation of the daily pro-rata method.

2. Rejda, G. E., McNamara, M. J., & Rabel, W. H. (2017). Principles of Risk Management and Insurance (13th ed.). Pearson. In Chapter 7, "Financial Operations of Insurers," the concept of the unearned premium reserve is explained as the portion of gross premiums corresponding to the unexpired portion of the policy, calculated on a pro-rata basis.

3. Gorvett, R. (2003). An Introduction to Insurance Ratemaking and Reserving. Casualty Actuarial Society (CAS) Study Note. Section 5.2, "Unearned Premium Reserve," describes the pro-rata fraction method for calculating the unearned premium reserve, which aligns directly with the formula presented in option A. Available via the CAS website.