"Over the past 14 years, rents have grown at twice the pace of income due to weak income growth, burgeoning rental demand, and insufficient growth in the supply of rental housing," said Zillow Chief Economist Stan Humphries. "Next year, we expect rents to rise even faster than home values, meaning that another increase in total rent paid similar to that seen this year isn't out of the question. In fact, it's probable."
Read MoreHome prices and supply map
Jamille Ackerman has no desire to rent. A financial analyst in Washington, D.C., she is closing on a home in suburban Maryland in about two weeks.
"I don't believe in making someone else rich," said Ackerman, who is single and plans to move her father in with her.
This is not the first time the 32-year-old has invested in the housing market. She bought in 2007, at the height of the housing boom and then lost her home to foreclosure in 2011. Even after going through all the stress of rebuilding her credit, she still believes in home ownership.
"I prefer at my age to put my money towards a better investment. A home is an asset; an apartment, there is really not much in it for me as far as benefits," Ackerman said.
One of the biggest barriers to home ownership today is that so many renters are paying so much to their landlords, they are unable to save for a down payment. That will only get worse in 2015. While developers in 2014 started the largest number of new rental units in 25 years, there is still a short supply of rental housing, both single and multifamily, and that means rents will continue to rise.
"As we prepare for New Year's and the next home shopping season, we expect soaring rents to entice more people to the relative stability of home ownership, particularly younger potential buyers," said Zillow's Humphries.
Enticing is one thing; affording is another. Builders have not been active in the entry-level market lately, preferring the higher-margin move-up and luxury homes. Price gains are easing in the existing home market, but they are still rising, and the expectation is that mortgage rates will rise, as well.
Read MoreWhat to expect from housing in 2015