Modi will also need to reconcile market demands with those from forces within his own administration
India is gearing up to introduce a six-member monetary policy committee that would vote on interest rates.
Here is some background on the candidates seen as potential successors to Rajan at the RBI
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
Rajan said the central bank has used up all its "space available" to cut interest rates
A two-year extension at the helm of the RBI still looks a real possibility
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 funds, some of which have invested in the NSE for almost a decade, want the exchange to list as soon as possible so that they can exit and pay back investors in their funds
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
Mauritius and Singapore account for the bulk of the $278 billion in foreign equity investments since 2000
Now, funds from Mauritius interested in India will have to weigh paying capital gains taxes that could range from zero to as much as 20 per cent
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
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
After months of denying there was a liquidity problem, Governor Raghuram Rajan has reversed course.
Markets hope the Budget will steer spending towards infrastructure.
RBI Governor Raghuram Rajan wanted to improve training for staff, through initiatives such as sending them to other central banks for short stints.
The slowdown is especially pronounced in rural areas, which have suffered two consecutive dry years.