Question about credit?

I have an outstanding & delinquent balance of $4600 to my former school- long story short, they never put it into a federal loan even though I'd done all the paperwork, then demanded I pay them the balance in full when I graduated 2 & a half yrs ago. I haven't been able to give them the thousands of dollars I owe outright & have since done nothing. It has been a mark on my credit for over 2 years. Now my school is offering to settle for half the amount, but I only have 2 weeks to pay it in full. They said once I pay it, they will report to the credit agencies that it is paid, but it will still be a negative report on my credit. I've heard that once you pay something off, it will stay on your credit report for 7 years from the day you paid it off. Which would basically mean if I don't, it should be off my credit in 4 & a half years. Is this true? What's the best approach to something like this?