"If the economy  progresses about as the [Fed] expects, warranting reductions in  the pace of purchases at each upcoming meeting, this final  reduction would occur following the October meeting,"  according to Wednesday press release of June 17-18 Minutes of the Federal  Open Market Committee.

Monthly bond purchases are already cut from a peak of $85 billion  to $35 billion following the results of the June meeting.
The Fed plans to successively reduce purchases at its next three  policy meetings, cutting them in October from $15 billion to  zero.
After five years of recession the US economy started to show  positive results, indicating recovery.
Last month, the unemployment rate had fallen to 6.1 percent, the  lowest since September 2008, according to US Bureau of Labor  Statistics. A level that Fed officials didn’t expect to see  before the end of the year was led by 288,000 extra jobs. June  resumed a five month 200,000-plus job gains chain which is an  almost 15-year growth record.

After GDP shrank by 2.9% from January to March, mostly due to a  brutal winter, the US economy is expected to stabilize and grow  at a healthy 3 percent for the rest of the year.
Meanwhile the US inflation rate of 2.1 percent is also  approaching the Fed’s 2 percent target.
Since January the Federal Open Markets Committee (FOMC) has been   reducing the volume of Treasury bond and  mortgage-backed securities purchases, known as quantitative  easing (QE), but did not set an end date for the scheme.
The policy also known as ‘easy money’ was mostly used to buy debt  and junk financial instruments from the market like Treasury  bonds and mortgage-backed assets to provide the financial system  with plentiful cheap cash. It was also aimed to stimulate  investors to back stocks or corporate debt and to keep long-term  interest rates down in order to boost the economy.

Since being introduced in 2009 during the financial crisis, QE  became the largest financial aid scheme in history, as it  provided the US financial markets with the estimated $4 trillion. Critics of ‘easy money’ in Congress and elsewhere have warned  that the program will lead to another financial bubble or  excessive inflation.
Potential Republican presidential candidate Senator Rand Paul is  a long-time critic of QE, and has worried that the recovery of  the US economy is “illusory”, says the Guardian.
Andrew Hussar a former manager of the Fed’s mortgage-backed  security purchase program and a senior fellow at Rutgers Business  School said in the Wall Street Journal that QE had  helped Wall Street far more than Main Street.