In the given question, a word is specified followed by three sentences. Identify the statement(s) in which the word has been used in a contextually and grammatically correct manner.

PRINCIPAL
(A) The school principal announced a new policy regarding student attendance during the assembly.
(B) She refused to compromise her core ethical principals even under intense pressure.
(C) A significant portion of the loan payment goes toward reducing the principal balance of the debt.

The correct option is Both (A) and (C).

Let us analyze the given statements for the usage of the word PRINCIPAL:

• Statement (A): "The school principal announced a new policy regarding student attendance during the assembly."
In this sentence, principal is used as a noun referring to the head of an educational institution. This is grammatically and contextually correct.

• Statement (B): "She refused to compromise her core ethical principals even under intense pressure."
In this sentence, the word principals is incorrectly used instead of principles (which refers to fundamental truths, rules of conduct, or moral beliefs). Thus, this statement is incorrect.

• Statement (C): "A significant portion of the loan payment goes toward reducing the principal balance of the debt."
In this sentence, principal is used to denote the original sum of money lent or borrowed, as distinguished from interest. This is grammatically and contextually correct.

Therefore, the word is used correctly in statements (A) and (C).