Purchased branch on top of tree (6)

I believe the answer is:

bought

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'purchased' is the definition.
('buy' can be a synonym of 'purchase')

'branch on top of tree' is the wordplay.
'branch' becomes 'bough' (bough is a kind of branch).
'on top of tree' becomes 't' (I can't justify this - if you can you should believe this answer much more).
'bough'+'t'='BOUGHT'

Can you help me to learn more?

(Other definitions for bought that I've seen before include "Purchased" , "paid for" , "Puchased" , "Obtained" .)

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