(adds further details from minutes, background)
By Howard Schneider, Michael Flaherty and Jonathan Spicer
WASHINGTON, July 9 (Reuters) - The Federal Reserve has begun detailing how it plans to ease the U.S. economy out of an era of loose monetary policy, indicating it will end its asset purchases in October and appearing near agreement on a plan to manage interest rates in the future, according to minutes of the last Fed policy meeting.
The minutes from the June 17-18 meeting indicate the Fed envisions using overnight repurchase agreements in tandem with the interest it pays banks on excess reserves to set a ceiling and floor for its target interest rate.
Though no decisions have been announced, the discussion has become detailed enough for Fed officials to contemplate the proper spread between the two - mentioned in the minutes as 20 basis points.
The minutes showed the Fed participants also "generally agreed" that monthly bond purchases would end in October, with a final reduction of $15 billion in monthly purchases of U.S. Treasuries and mortgage-backed securities.
Fed officials expressed overall confidence that moderate economic growth will continue and unemployment and inflation will gradually move towards the central bank's targets. If anything, there was concern recent low volatility in financial markets showed investors "were not factoring in sufficient uncertainty."
Analysts found little in the minutes to suggest the Fed will move forward its first interest rate increase, currently expected in the middle of next year.
But there was ample discussion about how the central bank should exit from policies put in place to fight the 2007-2009 financial crisis.
According to the minutes, there continues to be division over when the Fed should stop reinvesting proceeds of the $4.2 trillion in assets it purchased to support financial markets.
Ending reinvestment will put the central bank's balance sheet on a declining path, and some members argue that should not take place until interest rates have been increased.
In addition, the minutes indicated the reinvestment decision may not be an all-or-nothing choice: the central bank may try to "smooth the decline in the balance sheet," perhaps by letting some maturities expire each month and reinvesting the proceeds of others.
The Fed's exit strategy is complicated because its stimulus programs flooded the financial system with $2.6 trillion that has ended up back at the Fed as excess bank reserves. With that much money on hand, banks have little need to borrow from each other in the federal funds market - stifling an important interest rate tool.
The New York branch of the U.S. central bank has been testing the reverse repo facility since September as a way to help control short-term interest rates, and has seen strong demand from money market funds and other bidders.
In reverse repos, the Fed borrows funds overnight from banks, large money market mutual funds and others. The tool is designed to mop up excess cash in the financial system which could keep market rates too low if left in circulation. (Reporting by Howard Schneider; Additional reporting by Richard Leong in New York; Editing by Paul Simao)