Atlanta-based apartment developer Post Properties reported strong quarterly gains on Monday, the latest sign of recovery of the multifamily business.

Higher occupancy rates and a boost in monthly rental rates helped Post Properties report a third-quarter gain of more than $21 million, almost tripling the net income of $7.9 million it reported the same quarter last year.

“We overbuilt housing for years and now we’re dramatically under-building housing. And that’s benefiting rental homes,” said Dave Stockert, the company’s chief executive. “We’re not producing a lot of new housing, and what’s out there is being rented.”

The company’s average monthly rental rate per unit jumped 6.4 percent compared with the third quarter of 2011. Post’s occupancy rates also ticked up slightly from last year, to 96.6 percent, but were well above the metro area’s average. About 91 percent of apartments across metro Atlanta were rented in September, according to ALN Apartment Data of Texas, an analysis firm.

An increased demand for apartments in Atlanta and other markets has helped feed the company’s growth as it continues to expand beyond the metro area.

Post has about 45,000 square feet of retail space and 2,000 new units in development. The developer is adding to the total, announcing a plan on Monday for a $40 million apartment project in Tampa that is expected to be complete by 2014.