The housing boom led to a record homeownership rate of nearly 70 percent, but some homeowners now face problems making their mortgage payments and can’t refinance their loans. Over the last few years, lenders invented new types of mortgages to help families buy their first homes and refinance their existing mortgages. Many of these mortgages helped families without cash for a down payment, or with less-than-perfect credit, qualify for loans known as “subprime” loans.