You should not pay off your student loan before filing for bankruptcy. The bankruptcy trustee would potentially get this payment back and re-distribute it to all of your creditors.
As to what is in savings, this amount may or may not be exempt depending on your circumstances and other assets.
You should seek a free consultation. I am in your area.
First, rather than trying to do this in the abstract through a web-based service, you should contact a reputable local bankruptcy attorney to see if s/he will give you a free consultation. It is not improper to engage in "bankruptcy planning," meaning taking strategic steps in an attempt to place assets out of the reach of Trustees. Local bankruptcy lawyers also will know the amounts and types of exemptions you can use to retain your assets (e.g., whether you can take the Federal exemptions, or Florida exemptions, and which would be to your advantage).
You also need to know that for the 90-day period prior to your filing for bankruptcy relief, the law presumes that you were effectively bankrupt, meaning, you couldn't pay creditors. If you "favor" one of them (e.g., your student loan), the Trustee may be able to ask the student loan company to pay the money back so the Trustee can split it up amongst all your creditors. And student loans are almost never dischargeable in Bankruptcy. This is why it is important to discuss these matters with a local bankruptcy attorney; each case is very fact-specific, and the local practitioner will be able to determine whether the "some money in savings" you refer to can be protected.
Generally speaking, the Trustees look back six months in your bank statements. I always ask my Clients for a year's worth of the statements, however, because the Trustee can ask for that (and a lot of other) information, and you would be obligated to provide it. Again, I can't stress enough that you need to speak with a local bankruptcy attorney to explore what your best options are or might be.
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There is a different question here. You have to disclose payments made to creditors totaling more than $600 over the 90 days prior to filing and payments made to family members and business partners over the last year. Trustees can look back even further if they suspect fraud. I agree with the prior post. Before you do something that you cannot undo (but a trustee can) consult a bankruptcy attorney near you.
A little bit of information goes a long way to avoiding fraudulent transfers and will keep you out of trouble.
And, to answer your question, the Florida Fraudulent Conveyance Act [Chapter 726 Florida Statutes] has a 4-year statute of limitations.
You really should sit with a lawyer to discuss all factors.