The result is a record figure for an Obama letter, an increase of 23.6% on the previous $7,000 record set in 2010.
Obama sent the unique item of political memorabilia, written on White House headed notepaper, in response to a 2009 fax from Virginia resident Tim Mullin, which complained about bonuses handed out by financial services group AIG.
Tim's fax, which he fired off in hope rather than expectation to the White House, was titled: "TO ANYONE WITH ANY COMMON SENSE".
A week later he received a handwritten note, which read: "Tim, Thanks for your letter. I share your sentiments, and we are moving as quickly as we can to restore some common sense to the financial system. Barack Obama."
Speaking of his surprise at obtaining a reply, Tim commented: "This is a very rare letter as it is handwritten on the White House stationary.
"It's well documented the president reads about 10 letters a day from folks like me, and rarely will he actually reply to them so personally."
Mullin sold the letter to a New York collector in 2009 who brought it to the August 17 auction.
A similar Obama note written on White House paper sold for $7,000 in a private sale in 2010.
Replying to a Michigan mother's lament at the difficulties in the job market and medical bills, Obama promised: "Things will keep getting better".
An iconic Change poster designed by contemporary artist Shepard Fairey, in support of Obama's 2008 presidential campaign, sold for £4,560 in 2011 at Bonhams in London.