Mortgage applications bounced back last week with increased demand for both purchases and refinancings. The Mortgage Bankers Association market composite index rose 3.2% for the week ended Oct. 22 spurred by a 3.9% gain in purchase applications and a 3% climb in refinancings. The index fell 10.5% the prior week. The unadjusted index rose 3.1% last week, as the unadjusted purchase index increased 3.5% and is now 30.3% lower than the year earlier. In four-week moving averages, the seasonally adjusted market index is up 1.4%, the purchase index is down 0.7% and the refinance index is up 1.9%. Refinancings accounted for 82.3% of all mortgage applications last week, down slightly from 82.4% the week earlier. Lower demand for adjustable-rate mortgages lowered that loan’s share to 5.3% of applications last week from 5.8% the week prior. The MBA said interest rates for 30-year, fixed and 15-year, fixed mortgages slid back closer to record lows last week after rising the week earlier. The average rate for the 30-year fell to 4.25% from 4.34% and the 15-year decreased to 3.67% from 3.74%. Write to Jason Philyaw. ?