Mandy Johnson was priced out of Virginia Square Towers, a luxury-apartment building rising across the Potomac River from Washington, where about $3,000 a month would bring perks such as a swimming pool, yoga studio and a game room with virtual golf and zombie dodge ball.

Less than 24 hours after declining to sign the contract in June, she got an e-mail from a leasing manager offering two months’ free rent. That brought the monthly payment down for Johnson and her roommate by about $450 over the term of the lease and put the place within reach.