Sales of single-family homes and condominiums kept climbing in Massachusetts last month as more buyers decided to take advantage of historically low interest rates, ­according to numbers released Thursday.

There were 3,791 single-family homes sold in September, an 8 percent increase compared with the same month last year, according to Warren Group, a Boston company that tracks local real estate. Between January and September, single-family home sales rose nearly 22 percent compared with the same period in 2011.