Final answer:
The assertion that a balanced trial balance assures no mistakes were made is false; it merely indicates that debits equal credits, but does not rule out several possible errors.
Step-by-step explanation:
The statement that if a trial balance is in balance, the accountant is assured that no mistakes were made either in recording or posting, is False. A trial balance only confirms that the total of debits equals the total of credits after posting. However, it does not guarantee that all transactions have been recorded correctly or posted to the correct accounts. Potential errors that could occur and not be detected by a balanced trial balance include transactions not recorded, transactions recorded in the wrong account, offsetting errors, or incorrect amounts being recorded as long as they are incorrect in both debit and credit by the same amount. Therefore, while a balanced trial balance is an initial checkpoint, it is not a conclusive proof of the absence of errors.