The U.S. homeownership rate is near an all-time low and has been falling since 2004, although members of the largest generation of Americans -- millennials -- are coming of age and starting to think about buying a home and settling down. Rents are also at record highs, costing almost 50 percent of the median income in some cities. Making a monthly mortgage payment is cheaper than a monthly rent payment in all but two of the 35 largest U.S. metros^iv, but first renters need to save enough money for a down payment.

The Zillow Housing Aspirations Report, a semi-annual survey sponsored by Zillow and conducted by IPSOS, asks 10,000 renters and homeowners in 20 metros across the country about their views on homeownership and their personal housing expectations going forward.

Here are some highlights from the report:

• Over half (63 percent) of renters are confident that they will be able to afford a home someday, with 25 percent planning on buying in the next three to five years.

• Millennial renters are more confident than any other generation that they will be able to afford a home someday, with 34 percent planning on buying in three to five years. Almost a quarter (22 percent) said they plan to buy in one to two years and 2 percent of millennial renters said they never plan on buying a home.

• The majority of respondents (66 percent) believe owning a home is necessary to live The American Dream, and 72 percent believe owning a home increases your standing in the local community -- millennials believe these two statements more than any other generation.

With home values across the country at their highest point since June 2007, cobbling together a 20-percent down payment on a home costs more than two-thirds of the U.S. median household annual income^v. In pricier markets like San Jose and Los Angeles, buyers must come up with more than 180 percent of the median annual income, making a home purchase out of reach for many aspiring homeowners.

"With home values close to record highs, it's no surprise renters are concerned about coming up with enough money to buy a home," said Zillow Chief Economist Dr. Svenja Gudell. "Rising rents are also a factor -- it's extremely difficult to save when you're paying record-high rents. While it is possible to put down as little as 3 percent on a home, the trade-off is a higher interest rate and costly private mortgage insurance, a financial tradeoff that may make sense for some buyers. But with interest rates rising in 2017, it's important to remember that a lower interest rate can save buyers thousands of dollars over the life of their loan. For those trying to save for a down payment, it's important to set realistic goals and realize it may take a few years. Also, consider working with a reputable financial advisor to help set a budget that works for you."

San Jose, San Diego and Los Angeles had the greatest share of renters say affording the down payment is the number one barrier to owning, at over 72 percent. Women (72 percent) were more likely than men (62 percent) to select the down payment as the top barrier to homeownership.

One-third of buyers used more than one source of funds for their down payment, including gifts and loans from family, according to the Zillow Group Report on Consumer Housing Trends^vi. Over half of buyers saved by setting aside a little money at a time.

Mortgage rates on Zillow ended the month of March at 3.94 percent, down from a high of 4.13 percent in the middle of the month^vii. Home shoppers can use the Zillow Affordability Calculator to see how varying loan amounts and down payments will impact monthly payments and the lifetime balance of their mortgage.