(Corrects number of years for historic low in first paragraph) (Recasts lead; adds money manager, Chase comments)

By Al Yoon

NEW YORK, Jan 8 (Reuters) - The average interest rate on 30-year U.S. fixed-rate mortgages dropped to a 38-year low of 5.01 percent in the latest week, after the Federal Reserve launched its mammoth plan to lower home borrowing costs, Freddie Mac said on Thursday.

The rate for the week ended Thursday declined from 5.1 percent in the prior week and marked the 10th consecutive week of declines. It was the lowest rate recorded by Freddie Mac, the second-largest provider of funding for residential mortgages, since its survey began in 1971.

The Fed this week began its purchases of up to $500 billion in mortgage-backed securities issued by Freddie Mac, Fannie Mae and Ginnie Mae, resulting in sharply lower yields on the bonds that influence the rates that lenders can offer consumers.

Mortgage rates began to fall after the Fed announced its plans to buy mortgage-backed securities in November, and should continue to drop since the bond rally is extending, albeit at a slower rate, analysts said.

"The U.S. government has decided that lower mortgage rates are what they want, and so they will drive them lower," said Jason Brady, a bond manager at Santa Fe, New Mexico-based Thornburg Investment Management, which invests $35 billion.

Mortgage rates have declined nearly 1.5 percentage points since October, creating a savings of about $184 per month on a $200,000 loan, Frank Nothaft, chief economist at McLean, Virginia-based Freddie Mac, said in a statement.

The Fed's move is seen as one of the most promising federal efforts to stabilize the housing market, which is in its worst downturn since the 1930s and exacerbating a recession. Still, analysts say it is not a cure-all, since tighter lending standards will prevent many borrowers from refinancing high-cost loans.