Even renters can't escape the housing crisis. Prices just spiked at the fastest rate in 16 years.

• Stifling home prices are pushing buyers into the rental market and sparking a new affordability crisis.
• US rent prices rose in June at the fastest pace since at least 2005, CoreLogic said Tuesday.
• The bounce is largely driven by the housing shortage and risks trapping millennials in the rental market.

Renters beware. People who thought they wanted to buy a home - but balked at skyrocketing prices - are coming for the rental market. It's already sparking a new affordability crisis.

Single-family rent prices rose 7.5% year-over-year in June, property analytics firm CoreLogic said in a Tuesday report. That's up from 6.6% growth in May and marks the fastest price growth since at least 2005. Prices grew the most for higher-priced rentals, with year-over-year inflation hitting 9.6% in June. Lower-priced units saw prices rise 5.3% from the year-ago period.

The surge in rent prices is largely a result of the red-hot housing market. Home prices surged at record pace throughout much of 2021 as supply shortages powered frenetic bidding wars. Home sales have since cooled as buyers balk at high prices. But left with few alternatives, those buyers are now fueling massive demand for rentals.

"For would-be homebuyers who have been either priced out of the market or unable to find a home in today's supply-constrained market, detached rentals are overwhelmingly preferred and remain in high demand," Molly Boesel, principal economist at CoreLogic, said in a statement.

Detached rentals are those which stand on their own, while attached units share walls with other rentals. Detached units have outperformed attached rentals throughout the pandemic. Price growth for the standalone rentals fell far less in early 2020 and is now more than double that for attached units.

Prices leaped the most in Phoenix, Las Vegas, and Tucson, according to the report. Prices grew the least in Washington, DC, and Philadelphia, and rents declined year-over-year in Chicago and Boston. The disparities match up with migration data that shows Americans leaving urban centers throughout the pandemic for exurban areas and Sun Belt cities in Texas, Arizona, and Nevada.

The surge in rent prices signals the housing crisis will only get worse in the months ahead. Affordability was already evaporating as Americans snapped up homes at a historic rate. Rental properties offered a safe haven for those unable to buy homes, but stronger inflation risks pushing Americans out of that market as well.

The price rally also comes at a precarious time for both markets. Millennials are expected to bring unprecedented demand to the housing market as the generation enjoys its peak homebuying years in 2022 and 2023. Buying a home has, for decades, marked a significant achievement, as homes allow people to build equity instead of paying rent to a landlord. With homes already in such short supply, millennials are in danger of not making that crucial step and staying trapped in an already strained rental market.