Mortgage applications rose during the first week of the year, and refinancing activity has increased two weeks in a row. The Mortgage Bankers Association said its market composite index increased 2.2% on a seasonally adjusted basis for the week ended Jan. 7. Unadjusted, the index climbed 47.5% from the prior week, which included the New Year’s holiday. Refinancing applications fell steadily over the final two months of 2010, but have rebounded the past two weeks and rose 4.9% last week, according to the MBA. The seasonally adjusted purchase index fell 3.7% last week, while the unadjusted purchase index rose nearly 42% from the prior week and was 10.5% lower than a year earlier. After declining consistently as interest rates move away from generational lows, refinancing activity rose slightly last week, accounting for 72.1% of all mortgage applications up from 71% the previous week. When interest rates hovered around 4% in the fall, refinancings were accounting for more than four-fifths of all mortgages. The MBA said the average interest rate for a 30-year fixed mortgage dropped to 4.78% last week from 4.82% the prior week. The average rate for a 15-year fixed mortgage declined to 4.15% from 4.23%. Write to Jason Philyaw.