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A Repo is a item of money market. Generally, Reserve Bank and Commercial Banks engage in repo transactions but not limited to these two. Individuals, banks, financial institutes can also engage in Repo. It is also know as Repurchase Agreement.
The rate at which the RBI gives money to commercial banks is called Repo Rate. This item is of monetary policy. When banks have any shortage of funds they can borrow from the RBI. So, Repo rate is interest rate which is less than Bonds as the borrowing is collateral.
A reducing in the repo rate benefits banks get money at a cheaper rate and vice versa. The repo rate in India and same as the discount rate in the US.
Reverse Repo rate is simply the rate at that the RBI borrows money from commercial banks. Banks are always happy to lend money to the RBI since their money are in safe and secure hands with a good interest. An additional, reverse repo Reserve Bank borrows money from banks by lending securities. The interest paid by Reserve Bank in this case is called reverse repo rate.