From the Help CenterHelp Center:
If the bounty was started by the question owner, and the question owner accepts an answer during the bounty period, and the bounty expires without an explicit award – we assume the bounty owner liked the answer they accepted and award it the full bounty amount at the time of bounty expiration.
Unless something has changed and the help center hasn't been updated, the full bounty amount, not half, should be awarded.