What type of accounting recognizes revenues when they are earned regardless of cash exchange?

Accrual accounting is the correct choice because it is based on the principle that revenues are recognized when they are earned, regardless of the timing of cash transactions. This means that even if cash has not yet been received, revenue is recorded in the accounting period when the goods or services are delivered. This approach provides a more accurate reflection of a company's financial position and performance during an accounting period, as it matches revenues with their associated expenses.

In contrast, cash accounting recognizes revenues and expenses only when cash is exchanged. This method can result in a misleading view of a business's financial health, particularly for companies that extend credit to customers or incur expenses that will not be paid until a later date. Historical accounting refers to the recording of past transactions and does not center on current earnings or cash flow. Modified cash accounting combines elements of both cash and accrual accounting but only partially represents the timing of revenues and expenses, hence not fully aligning with the concept of recognizing revenues when they are earned.