People who are in the market for a new home have been benefiting from historically low mortgage rates, allowing them to direct more of their mortgage payment toward the loan's principal. However, respondents in a recent survey said home prices and availability were more significant factors than a possible rate increase when considering their ability to buy a home.

The survey, issued by real estate site Trulia, collected responses from 2,034 adults in the United States between June 7 and 9. The results were published shortly before a meeting of the Federal Reserve to decide whether to increase U.S. interest rates. The Fed decided against raising rates for the fourth consecutive meeting, and said any increases in the future will proceed at a cautious pace.

Only 20 percent of respondents said they would be worried that rates would increase before they could buy a home. This share was down from 24 percent in a survey issued in September 2015. Among Millennials, defined as ages 18 to 34, the share of respondents concerned about rate increases fell 3 percentage points to 23 percent.

Respondents were most concerned about being able to find a home they liked, with 30 percent saying this would be a top concern if they were to buy a home this year. Thirty-seven percent of Millennials said this was a key concern.

Buyers also worried that home prices would go up before they were ready to make a purchase. Twenty-three percent cited this as a major concern, including 32 percent of Millennial respondents.

Less common concerns cited by respondents included the inability to get a mortgage (24 percent), competition with other buyers (15 percent), a drop in home prices after a purchase (14 percent), and having to make a quick decision on purchasing a home (12 percent). Millennials were more likely to say they were worried by each of these factors, with 34 percent saying they were concerned about being able to get a mortgage, 20 percent about competition or dropping prices, and 17 percent about having to make a quick decision.

"Consumers are increasingly worried about tight inventory when finding a home, and rightly so," said Ralph McLaughlin, chief economist at Trulia. "Low inventory has been, and will continue to be, a strong headwind for house hunters, and impacts their ability to buy a home much more than increases in mortgage rates."

Trulia's last quarterly inventory report determined that the number of starter homes on the market fell by 43.6 percent in the past four years. The inventory of trade-up homes shrank by 41 percent in the same period.

That report estimated that mortgage rates would have to rise to 7 to 10 percent to strain the financial advantages of homeownership over renting in most markets. Average rates have remained under 4 percent for many months. According to Freddie Mac, the average commitment rate for a 30-year fixed rate conventional mortgage was 3.85 percent in 2015 and 3.6 percent in May.

Forty percent of the respondents in the Trulia survey said they believe interest rates will change in the next six months. Thirty-seven percent said they think rates will increase, while only 2 percent said they think they will decrease.

Despite the small percentage of respondents who said they were concerned about rising rates, a significant number said they would be discouraged from buying a home if rates increased. Nineteen percent said they would be discouraged if rates rose to 5 percent, while another 19 percent said they would be discouraged if rates increased to 6 percent.

Sixty-one percent said they would be discouraged if rates increased to 7 percent. Twenty-eight percent said they will never consider buying a home, and 15 percent said they consider current rates to be too high.

David Weidner, summarizing the survey's results for Trulia, says current rates are much lower than what was common in recent decades. He says "historically low" rates used to be about 6 percent. Mortgage rates were at least 7 percent between 1971 and 2001 and sometimes exceeded 10 percent.