That lack of affordability is why “attaining the American dream is becoming more challenging than ever,” Bank of America (BofA) analysts wrote in its eighth annual millennial housing survey published on Friday.  

“By almost every measure—rents, home prices, interest rates—this group expects to pay more for housing even as it already takes up one-third of their household income,” BofA analysts found. 

However, two-thirds of the survey’s respondents are still set on buying a home and say they’ll likely do so within the next two years, despite already spending around 30% of their income on housing (rent or a mortgage). Partly because the respondents expect housing costs, like rent, home prices, and mortgage rates to go up even further from here. Millennials also cited buying as a good investment. BofA’s survey respondents included over 1,000 millennials between the ages of 25 and 41, with average household incomes concentrated in the $25,000 to $75,000 range. 

“While some Millennials could feel motivated to buy a home soon to get ahead of cost increases, others may stay out of the housing market due to affordability challenges, particularly if rent moderates,” wrote the BofA analysts. (Analysts at BofA expect national home prices to flatten and rent growth to moderate over the coming year).

Millennials that said they weren’t planning to buy homes were most concerned about affordability, particularly with the jump in mortgage rates. Over the past three years, respondents have cited affordability as a concern, however, this year’s survey showed “a material jump,” wrote BofA analysts. 

Interestingly enough, 82% of the survey’s respondents reported wanting to buy older, less expensive homes and renovate them rather than buy a newly built home. As Fortune’s recently reported, millennials are paying millions of dollars to knock down homes—but of course those are rich millennials that aren’t as concerned with affordability. But this simply speaks to the generation’s creativity in home buying.  

Nonetheless, more millennials are homeowners than ever before, and each year BofA runs the survey the percentage of millennials that are homeowners has gone up. This year’s survey, 58% of respondents said they owned their home, up from 53% last year. Of those, 64% of millennials ages 31 to 41 said they owned their home. Meanwhile, only 51% of those ages 25 to 35 reported being homeowners.

From Fortune’s previous reporting, it’s clear that there’s variation among millennials and homeownership. For example, Fortune’s interviewed some high-earners, or higher than average, that are still renting because they don’t feel like they can afford to buy a home in the markets they live in. 

From a professional couple earning around $225,000 living in Los Angeles to a business owner earning over $200,000 on her own, living in Manhattan, in both cases these millennials were opting to rent, citing several barriers to home ownership.

Still, according to BofA analysts, the survey “suggests a slightly higher homeownership rate for Millennials overall than the latest Census Bureau data, which showed that 51.5% of Millennials were homeowners as of 2022, indicating that our survey respondents may not be representative of the broader U.S. Millennial population.”