Most millennials have saved virtually nothing for a down payment on a home, according to a new study, suggesting many will face steep obstacles to homeownership in the years ahead.

Nearly 70% of young people ages 18 to 34 years old said they have saved less than $1,000 for a down payment, according to a survey by Apartment List, a rental listing company, expected to be released Friday. About 40% said they aren’t saving anything on a monthly basis.

Even senior members of the group are falling short. Nearly 40% of older millennials, those age 25 to 34, who by historical measures should already own or be a few years away from homeownership, said they are saving nothing for a down payment each month.

The study helps illuminate a tension at the heart of the housing market. The vast majority—some 80%—of millennials said they eventually plan to buy a home. But 72% said the primary obstacle is that they can’t afford it.

“It’s encouraging that millennials do want to buy homes. It suggests that they are delaying forming households but they’re not giving it up,” said Andrew Woo, director of data science and growth at Apartment List. “The biggest reason [they aren’t buying] is because of affordability.”