Housing starts shot up 15% in September from the previous month to the highest rate since April 2010, reaching a seasonally adjusted annual rate of 658,000 units, according to Commerce Department data. Starts are up 10.2% above September 2010’s rate of 597,000 units, the Census Bureau and the Department of Housing and Urban Development said Wednesday. The September figure is up from 572,000 starts in August. Apartment starts saw the biggest swing. Permits for apartments with five or more units rocketed up by 53.4% over August and by 57.6% over the year-ago period, according to the data. The Commerce Department data shows 227,000 apartments with five or more units were started in September, up from 144,000 in the year-ago period. Single-family starts were up 1.7% over August and down 4.9% over September 2010. September building permits fell 5% to a seasonally adjusted annual rate of 594,000 from 625,000 in August, but rose 5.7% from 562,000 a year earlier. Single-family housing starts in September reached a rate of 425,000 units, up 1.7% from August when the rate hit 418,000 units. Home completions last month grew 2.1% from the year-ago rate of 634,000 units. “The September starts report shows new housing activity to be stronger than expected,” according to analysts with Econoday. “The big question is whether the demand exists to absorb added supply.” Write to Kerri Panchuk.