Which document is written by an account holder directing the bank to pay out money from an account?

The correct answer is a check, which is a financial instrument that an account holder writes to instruct a bank to pay a specified amount of money from their account to another party, typically the name indicated on the check. When the bank receives the check, it processes the payment by debiting the amount from the account holder's account and crediting it to the account of the person or entity to whom the check is made out. Checks serve as a secure and convenient way to transfer funds and can be used for various transactions, such as paying bills or purchasing goods and services.

The other options do not fulfill the same role as a check. A purchase order is typically used in business transactions to authorize the purchase of goods or services before payment is made but does not involve directly authorizing the bank to release funds. A withdrawal slip is a form used to request the withdrawal of cash from a bank account, but it is not considered a payment instrument like a check; rather, it facilitates cash transactions at a bank branch. A bill, on the other hand, is an itemized statement of charges for services or products provided, which represents a debt rather than a mechanism for instructing a bank to pay out money.