I broke a Arizona apartment lease in August 2005 by leaving three months early. But I paid over half of what the collection agency billed me for. And I thought we agreed that would be the payoff. But I am still getting letters about two years apart from the agency demanding payment with surging interests. What can I do or not do?

I think you can just about forget this collection agency because the statute of limitations on collecting money owing on a written contract is six years is Arizona. You are probably just squeaking through. After six years they can't colllect.

After the statute runs out the debt is still valid, they just can't get a judge to force payment. Do not acknowledge this debt or offer to pay anything at all, that wiould restasrt the statute and you would likely have a judgement againist you in court.