Americans are bracing for a wave of higher inflation over the next year, amid projections of big increases in home prices, rent, food, gasoline and medical costs, the May New York Fed Survey of Consumer Expectations reported Monday.

One year from now, the public expects inflation to hit 4%, a series high for the New York Fed report, from the projected 3.4% increase reported in April. Three years from now, survey respondents said they expected to see inflation at 3.6%, the second highest reading for the survey, up from April’s 3.1%.

The jump in inflation expectations came as respondents to the survey project major increases in home prices and for other things critical to daily life. One year from now, food and rent prices are expected to rise by 8% and 9.7%, respectively, both carving out series highs. Meanwhile, the expected rise in gasoline and medical care costs also increased, with both readings just short of 10%.

Home prices are expected to rise by 6.2% a year from now, a series high, and up from April’s 5.5% reading, the survey said.

The New York Fed expected inflation readings arrived just as the Federal Reserve is scheduled to hold over Tuesday and Wednesday a pivotal meeting on monetary policy. Central bankers will gather as economic activity surges and the coronavirus pandemic abates. That has opened the door to an active debate as to whether it is time for central bankers to dial back the aggressive levels of stimulus they are now providing the U.S. economy.

Economists do not expect the Fed to raise the near-zero percent short-term interest rate target that has been in place since March 2020, nor do they see central bankers dialing down what are now $120 billion a month in long-term bond purchases. But many do see central bankers starting a debate on whether to slow those purchases.

The debate over dialing back stimulus is driven by many factors, but one of them is a looming fear that aggressive Fed aid coupled with historic levels of broader government support for the economy have raised the risk inflation could surge from years of moribund readings. Fed officials have argued for some time now they expect inflation to jump as the economy surges back to life but they also expect those pressures to subside as bottlenecks and other dislocations get worked out.

To some extent, the New York Fed report tracks that outlook given that expected inflation a year from now is higher than the projected level of price increases three years from now. The New York Fed also noted in the May report that those who reported the highest inflation expectations were those over 60, who presumably recall and were most scarred by the high inflation of the 1970s, and those with a high school education or less.

Fed officials believe inflation expectations are critical because they believe that where inflation is expected to go exerts a powerful influence on where it is today. In recent comments, Fed officials have welcomed rising inflation expectations as a sign their effort to get inflation sustainably back to 2% after years of weakness is working, and they have also said gains in expected inflation have returned to those levels seen in the early part of the last decade.

Other surveys have also flagged a jump in expected inflation. University of Michigan consumer sentiment survey director Richard Curtin said in a report in late May he doesn’t expect the public to move toward expectations of big and persistent inflation gains. But he added for the Fed, “early preventive actions are much less costly,” adding that hinting at a rate increase “could easily douse an incipient inflationary psychology.”

Meanwhile, market expectations of future inflation have been easing over recent days as bond yields have fallen, despite the government reporting last week that consumer-level inflation in May booked its highest reading in 13 years.

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Write to Michael S. Derby at michael.derby@wsj.com