For-sale signs are posted in front of condominiums for sale in July in Los Angeles. A new analysis from the Center for Responsible Lending finds that the average renter household now needs 16 years to save for a down payment and closing costs. Justin Sullivan/Getty Images hide caption

Justin Sullivan/Getty Images

Mortgage rates topping 7% is the latest sign of how hard it has gotten to buy a first house, with aspiring owners already facing sky-high prices. A new analysis out Thursday shines a light on yet another growing obstacle: the amount needed to close a home loan.

"Over the last seven years, the time to save up that down payment and closing costs has doubled," said Mike Calhoun, president of the Center for Responsible Lending, a research nonprofit that promotes economic opportunity.…