The average interest rate for a 30-year, fixed-rate mortgage increased 24 basis points, hitting 4.85% in January, according to the Federal Housing Finance Agency. The agency bases its average rates on purchase mortgages of $417,000 or less that closed during the Jan. 25-31 period. On Thursday, Freddie Mac also reported that the average interest rate for a 30-year, fixed-rate mortgage fell from 5% to 4.95% for the week ending Feb. 24, according to Freddie’s Primary Mortgage Market Survey. The average contract mortgage rate for the purchase of previously occupied homes — used as an index in some adjustable-rate mortgages — hovered at 4.71% last month, up 0.13% from December, according to the FHFA. The latest report is a reflection of loan rates closed during the Jan. 25-31 period. Because interest rates are generally determined by activity in the market 30 to 45 days before a loan is closed, the new rates depict market conditions in mid- to late-December, the FHFA said. When studying all loans — fixed-and adjustable-rate — the average contract rate hit 4.70% last month, up 18 basis points from 4.52% in December. The average term for loans originated in January fell to 27.3 years, and the average loan-to-price ratio hit 73.4%, down 2.2% from December. The overall average loan amount also fell between December and January from $209,500 to $202,400. Freddie’s Primary Mortgage Market Survey for the past week showed a drop in long-term rates overall.  Not only did the 30-year fixed-rate mortgage fall to 4.95%, the 15-year fixed-rate mortgage dropped from 4.27% to 4.22% in the most recent week, and the 5-year Treasury-indexed hybrid adjustable-rate mortgage fell from 3.87% to 3.8%. The 1-year Treasury-indexed ARM rose slightly from 3.39% last week to 3.40% in the latest market study. Write to Kerri Panchuk.