When Amazon announced in January that Nashville had made the list of 20 finalists being considered for its second North American headquarters, city leaders cheered. They saw the project as the next step in Nashville’s transformation from country-music capital into a regional and even national economic force.

To some locals, Amazon represented something else: more people, more traffic and, most of all, higher rents in a city where a rising share of residents were already struggling to afford housing.

“With the onslaught of new people, with the onslaught of higher-income earners, I just think it’s going to further exacerbate what’s already a crisis situation,” said Paulette Coleman, a local affordable-housing advocate.

Coleman has reason to worry. A new analysis from the real estate site Zillow estimates that rents in Nashville would rise 3.3 percent per year if the Tennessee capital landed the Amazon campus, almost four times as fast as currently projected. After a decade, that could translate into Nashville residents paying $400 more per month in extra rent.

Other cities could also see big increases if Amazon picks them. Monthly rents in Boston and Los Angeles could jump by even larger amounts in dollar terms — albeit from a higher starting point — reflecting a shortfall in rental housing construction. Denver — like Nashville, a midsize city that has seen brisk population growth in recent years — could see its already rapid rate of rent increases hit nearly 6 percent per year, triple the overall rate of inflation.

“I definitely think it has the possibility of pushing us over the tipping point,” said Felicia Griffin, executive director of United for a New Economy, a Colorado nonprofit that has opposed the Amazon project.

Some potential locations would be less severely affected. Atlanta and Chicago, big cities that have made it relatively easy to build new housing in recent decades, would see only a small rent increase if they won the Amazon project.

And Indianapolis, where population growth has been slow and housing is plentiful, would see no effect on its rents, according to Zillow’s model. Even in those cities, however, neighborhoods near the Amazon campus would most likely see significant rent increases. (The study did not look at the effect on prices of owner-occupied homes.)

Amazon has provided few details about what it plans for the new campus, known as HQ2, other than that it could eventually be a base for up to 50,000 employees earning an average of about $100,000. The company has not said whether it prefers to build downtown, as it has at its current headquarters in Seattle, or will opt instead for a suburban office park — a decision that could have significant implications for the project’s effect on local housing costs. Though it mentioned the issue only in passing in its request for proposals last fall, Amazon said it will take such costs into account, and has met with affordable-housing groups in several of the finalist cities.

Zillow cautions that its estimates are rough, based on a simple model that looks at how rents in each city have responded to past influxes of workers. If the cities respond differently to Amazon’s arrival — for example, by building more housing — the effect on rents could be smaller.

But there are also reasons to think Zillow’s analysis could understate Amazon’s potential effect. The model looks only at the effect of the jobs that the new campus is expected to create. If Amazon’s presence draws other businesses to the area, rents could rise even faster.

Whichever city wins the HQ2 sweepstakes will enjoy one big advantage over Seattle: advance warning. Aaron Terrazas, a Zillow economist who led the rent analysis, said Amazon’s growth caught Seattle by surprise, and the city struggled to build enough housing to accommodate the influx of young, affluent tech workers. Whichever city is chosen, Terrazas said, needs to move quickly to build.

“What’s so important is once a city is selected that they start to get ahead of the curve,” Terrazas said.

In Nashville, the debate over HQ2 has gotten caught up in a broader discussion of gentrification, race and the consequences of growth. Residents long described Nashville as a small town disguised as a big city. But during the last decade, the city’s tourism industry has taken off, and some of those tourists liked Nashville enough to stay. For years, the Nashville metropolitan area grew by more than 100 residents per day, with many moving into new downtown apartment complexes.

The growth has led to tensions. Longtime residents, many of them black, have been displaced, and the city’s homeless population has grown. A recent study commissioned by the mayor’s office found that the city had lost 18,000 affordable-housing units since 2000. That gap could grow to 31,000 units by 2025 if current trends continue — without taking Amazon into account.

Adriane Harris, who leads housing policy for the Nashville mayor’s office, said concerns about gentrification were legitimate. But she said there were two sides to the affordability equation: housing costs and income.

“If we’re only addressing housing, then I don’t think we’re getting to the root of the issue,” Harris said. “Wage growth is critical in this conversation.”