Effect of a personal cost (10)

I believe the answer is:

perpetrate

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'effect' is the definition.
(thesaurus)

'a personal cost' is the wordplay.
'a' becomes 'per' (eg 'one a day' means 'one per day').
'personal' becomes 'pet' (I can't justify this - if you can you should believe this answer much more).
'cost' becomes 'rate' (rate is a kind of cost).
'per'+'pet'+'rate'='PERPETRATE'

'of' acts as a link.

Can you help me to learn more?

(Other definitions for perpetrate that I've seen before include "perform" , "Act" , "Be responsible for" , "Commit (a bad action)" , "Commit (crime)" .)

I've seen this clue in The Telegraph.

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