WASHINGTON — Interest rates on short-term Treasury bills were mixed in Tuesday’s auction, with rates on three-month bills falling while rates on six-month bills rose to the highest level in nine years.

The Treasury Department auctioned $48 billion in three-month bills at a discount rate of 1.435 percent, down from 1.445 percent last week. Another $42 billion in six-month bills was auctioned at a discount rate of 1.575 percent, up from 1.530 percent last week.

The three-month rate was the lowest since these bills averaged 1.355 percent two weeks ago on Dec. 18. The six-month rate was the highest since these bills averaged 1.800 percent on Oct. 20, 2008.

The discount rates reflect that the bills sell for less than face value. For a $10,000 bill, the three-month price was $9,963.73 while a six-month bill sold for $9,920.38. That would equal an annualized rate of 1.460 percent for the three-month bills and 1.610 percent for the six-month bills.

The weekly Treasury auction of three-month and six-month bills normally takes place on Monday but was held on Tuesday this week because of the New Year’s holiday.

Separately, the Federal Reserve said Tuesday that the average yield for one-year Treasury bills, a popular index for making changes in adjustable rate mortgages, stood at 1.76 percent at the end of last week on Friday, little changed from 1.75 percent at the beginning of last week.