Crossword Genius

Bitter or caustic when an account's only half paid (4)

Ross

I believe the answer is:

acid

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'bitter' is the definition.
(acid can mean bitter-tasting)

'account's only half paid' is the wordplay.
'account' becomes 'ac' (abbreviation for account).
'only half' means to take half the letters.
'paid' with half the letters taken is 'id'.
'ac'+'id'='ACID'

'or caustic when an' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for acid that I've seen before include "Tart, sour" , "something sharp" , "Sour - sharp" , "Sarcastic (could be sulphuric?)" , "Polluted precipitation" .)

I've seen this clue in the Evening Standard.
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