Long Island home prices rose by more than 7 percent last month, driven by a scarce supply of listings, an influx of buyers from New York City and rising interest rates.

In Nassau County, homes sold for a median price of $475,000 in January, up 7.3 percent from a year earlier, the Multiple Listing Service of Long Island reported Monday.

Suffolk County home prices reached a median of $338,250 last month, 7.4 percent higher than a year before.

“The housing market is hot, there’s no question about it,” said Irwin Kellner, president of Kellner Economic Advisers in Port Washington.

Local brokers said a growing number of buyers are getting priced out of New York City, where home values have skyrocketed.

Those buyers are jostling for a shrinking number of homes. Across the Island, the listing service reported 10,830 homes for sale, down nearly 22 percent from a year earlier.

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Even the most eager buyers are getting frustrated with the dearth of options, real estate agents said. Many young, first-time buyers “are financially sound, they have enough money in the bank,” said Laura Corley, a real estate agent with Prime Properties Long Island in Huntington. But, she said, “there’s not enough inventory.”

The reasons for the low supply are varied. In some cases, homeowners have decided not to list their properties because prices still lag below the heights they attained 10 years ago, before the housing bubble burst. In the summer of 2007, median prices peaked at $502,500 in Nassau and $420,000 in Suffolk, listing service figures show.

In other cases, homeowners do not have enough equity to buy their next residence, blocking them from selling their existing homes. On Long Island, 4.7 percent of households with a mortgage owed more than their homes were worth, national real estate data company CoreLogic reported last month.

And in some cases, would-be sellers just can’t find the right home to move into at an appealing price.

The low supply feeds on itself, since some homeowners would like to downsize to a smaller home or condominium — or upgrade to a larger residence — but they cannot find a new home they like, said Jerry O’Neill, owner of Coldwell Banker Harbor Light in Amity Harbor.

The competition among buyers is driving up prices, O’Neill said.

“We’ve had a lot of full-price offers right off the bat, because the buyers didn’t want to miss out,” O’Neill said.

The Island’s healthy economy and Wall Street’s strong performance in recent years also are giving home prices a boost, Kellner said.

Despite rising prices, homes remain relatively affordable, “thanks in part to very low interest rates,” Kellner said.

Last week, the average interest rate for a 30-year, fixed-rate mortgage was 4.17 percent, up 0.52 percentage points from a year earlier, mortgage giant Freddie Mac reported. Home buyers should expect mortgage rates to rise modestly this year, as Federal Reserve chair Janet Yellen makes “very cautious” moves to increase short-term rates, Kellner predicted.

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If borrowing costs keep rising, said Mark Lesko, executive dean of the Wilbur F. Breslin Center for Real Estate Studies at Hofstra University, “that would slow demand, and that would result ultimately in stagnation in housing prices.”

For now, as mortgage interest costs climb, some buyers are scrambling to close deals quickly, before rates rise further, real estate agents said.

The number of closed transactions grew 4.9 percent in Nassau and 9.5 percent in Suffolk last month, compared with a year earlier. In a sign of buyers’ growing interest in Suffolk properties, the number of contract signings made annual gains of 16 percent in Suffolk last month, even as they dropped 2.7 percent in Nassau.

The lower prices in Suffolk are generating more interest among buyers, especially close to the Nassau County line. One couple started house-hunting in Seaford, but now they’re looking farther east — in Lindenhurst — despite the slightly longer commute into the city, O’Neill said.

“A few stops on the railroad is not going to make a difference,” O’Neill said, “especially if they’re saving some money on the purchase.”