According to the PMBOK® Guide, a project is defined as a temporary endeavor undertaken to create a unique product, service, or result. The " temporary " nature of a project indicates that it has a definite beginning and end.

The end of a project is reached when one or more of the following conditions are met:

Objectives Met: The primary condition for completion is that the project objectives have been achieved. This means the specific goals, results, or products defined in the project charter and scope statement have been delivered and accepted.

Objectives Cannot Be Met: The project is also considered ended if it is determined that the objectives cannot be met (e.g., due to lack of funding, technical impossibility, or shifting organizational strategy).

Need No Longer Exists: If the original reason for the project is no longer valid (e.g., the market changed, or a competitor released a superior product first), the project is terminated.

Termination for Cause: The project may be ended for legal or convenience reasons before the objectives are reached.

Why other options are incorrect:

Option A: When the planned time duration is completed: Reaching the end date of a schedule does not mean the project is " completed " if the deliverables have not been produced. If time runs out but work remains, the project is considered behind schedule, not finished.

Option C: When the project manager has left the team: The presence or absence of a specific individual does not define the status of the project. A project manager may be replaced, but the project continues until its objectives are met or it is formally closed.

Option D: When the project team decides to stop the work: The project team does not have the unilateral authority to declare a project completed. Completion is a formal status determined by the achievement of objectives and the formal sign-off from the project sponsor or customer.