The bank's net profit fell to 2,232 crore for its fiscal first quarter to June 30.
Top Indian private sector lender ICICI Bank, which owns nearly 68 percent of the insurer, is selling up to 181.34 million shares in the IPO.
With their weak metrics and high bad loans, India's state-run banks have not been investor favourites
The stress in the banking sector, which mirrors the stress in the corporate sector, has to be dealt with in order to revive credit growth.
Here is some background on the candidates seen as potential successors to Rajan at the RBI
As the clean-up has taken hold, loan growth slipped to 10.7 per cent in the last fiscal
The RBI is not statutorily independent from the government but has long enjoyed wide latitude
Bankers and government officials told Reuters Rajan's successor may be less aggressive in fighting bad loans, but the general direction will remain the same
Finance Minister Arun Jaitley said in a Twitter post that the government appreciated all of Rajan's good work and respected his decision
Rajan said the central bank has used up all its "space available" to cut interest rates
These cash shortages increase banks' funding costs, making it harder for them to lower lending rates
The prospect of further falls in remittances is a hindrance for the Reserve Bank of India, as it seeks to bullet-proof the economy against sudden capital outflows
The ratings agency currently rates India at Baa3
In 2013, India suffered its worst currency crisis in more than two decades but has regained the confidence of foreign investors in part after its current account deficit has narrowed sharply and its foreign exchange reserves hit a record high
Indian banks would have to make higher provisions for lending to large corporate borrowers above a certain level from next financial year, according to proposals published by the Reserve Bank of India (RBI) on Thursday.
State-owned banks account for more than two-thirds of the sector's assets and about 85 percent of bad debts
India's $121 billion troubled debt pile, over $100 billion of which is on the books of state-owned banks, has come under close scrutiny from prosecutors, the media and politicians
Digibank will offer only savings deposits initially, but will expand to include investments and lending in the coming months.
The surge is a stark turnaround from 2013 when the country's current account gap hit a record high due to outflows on expectations the US Fed would rein in its stimulus programme
The lenders, led by State Bank of India (SBI), are due to inform the Supreme Court of their decision on the offer at a hearing on Thursday.