Being charged after lease had ended

By Cars

Hi, I am renting an apartment, and my lease is up on Aug. 3, 2013. I was given a letter yesterday (7-5-2013) about lease renewal amounts and at the bottom it stated that if I was not planning on renewing then I needed to provide written notification 60 days before my lease ends. Well I took the letter in today and they said I would be charged market rates from Aug 3- Sept 4. I was wondering if there is any way that I can avoid paying this because I will have 2 rents to pay for August now, and one is significantly higher than my lease amount is. Throughout my lease I have also had a lot of complaints about bugs (mainly roaches) and asked on several occasions for them to fix my front door because there was a big space where bugs could easily enter. They sent someone to spray for bugs every time I asked, but it never worked, and they never tried to solve this issue in any way. Does any one have any advice on how I should handle this situation? Its about $1200 for an apartment that I will no longer be living in, which puts my August rent up to $2000 and I really cannot afford it. 

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Holy Cow, we couldn't find any other related post. Sorry. :(