Crossword Genius

Raj account switching deposits again into Agra's banks (1,7,2,5)

Ross

I believe the answer is:

a passage to india

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'raj account' is the definition.
I don't know anything about this answer so I can't tell whether this works.

'switching deposits again into agra's banks' is the wordplay.
'switching' is an anagram indicator (letters switch places).
'into' is an insertion indicator.
'banks' means to remove the middle letters (the sides or banks of the word).
'agra' with its centre taken out is 'aa'.
'deposits'+'again'='depositsagain'
'depositsagain' anagrammed gives 'passagetoindi'.
'passagetoindi' placed within 'aa' is 'A PASSAGE TO INDIA'.

Can you help me to learn more?

(Other definitions for a passage to india that I've seen before include "taken by hippies seeking guru?" , "Novel's" , "Book" , "E.M. Forster novel" , "a journey that ends up in the subcontinent" .)

I've seen this clue in The Times.
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