Unfortunately, just because the dealer has informed you they secured better terms for your loan does not, in general, give you a chance to renegotiate. It is likely that if you do not sign the paperwork for the new loan that the dealer will just submit and finalize your purchase with the previously signed loan documents (and terms).
That is not to say you do not have an independent basis to renegotiate and/or cancel the original purchase contract and loan documents. The facts as you state them seem a little odd, but are also vague.
In any event, in order to provide you with further useful information and more concrete advice it would necessary to discuss the situation in more detail and gather additional facts. After such discussion it would be possible to formulate a plan to assist you or for you to proceed on your own. You should definitely discuss this with and likely retain an attorney to assist you.
Now, while I realize many people prefer to handle matters themselves, for this one (you have a purchase contract and likely significant legal obligations and liabilities riding on this one), you should contact a qualified, local attorney with experience in handling this type of case (I have experience with these type of cases) for a consultation so that the attorney can gather all the necesasry facts and provide you with useful information to handle the matter yourself, or to assist you with the situation.
Also, remember, this is a public forum and anything posted here is not privileged or confidential, so do not post more specific information here. Contact a local attorney for a confidential and privileged consultation.
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What do they mean by a "better loan"? Lower interest rate? Smaller payments?
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We do consumer protection work, and I will tell you that there is a lot of this going on among car dealers. It's usually slightly different: You buy the car, get to loving it, and then receive a notice or call from the dealer saying you have to come back in to reconsider the financing arrangments. You get there and they tell you that the original loan did not go through and they had to get another one (higher rate, of course). You're attached to the car and go along with them, though grumbling. This conduct by the dealer is illegal, unless at the original purchase you signed a separate sheet (not language stuck into the purchase agreement) acknowledging that the financing may have to be reworked. I doubt seriously that you got such a paper to sign. I've only run across one dealer so far who does it right.
If the old contract is not being lived up to by the dealer, or is being cancelled and they want you to sign a new one, then there is no contract so you can walk away or renegotiate if you want. That's the law in just about every state. This sounds like the usual car dealer yo you scam. It may be hard to believe, but car dealers will often sign a contract and deliver a car to the customer but have no idea if the loan is really approved or not. They do it because they know that if they can put you in their car, and take you out of your’s, then that keeps you from buying somewhere else. They may get “preliminary” loan approval and set up the financing later. If the lender balks, then they call you back and say you need a cosigner or they need you to get your own loan or you have to come back to the lot and sign a new contract or say you don't qualify, or they need more money down, etc. How they do it can make it illegal. Look at your sales paperwork for a document that is often called a Spot Delivery Agreement. A Spot Delivery Agreement is a paper that says what how long the dealer has to set up the loan and what happens if they don't get it done on time. It usually says they have a few days or a few weeks to get loan approval and that if they can't set up a loan then you have to give them back the car and maybe pay for the mileage you drove on it. Whether or not you get your trade in or down payment back should also be covered. If there is no spot delivery document, then the odds are the dealer is stuck having to take your payments. This whole process is called "dehorsing" by the car dealers themselves (you can read a Car Dealer's Slang Dictionary at the link below) and doing it can be a violation of most state Udap (Unfair & Deceptive Acts and Practices) laws (there’s a link below for that too), if you were buying the vehicle for personal use. If your amount being financed is less than $50,000 (look at your finance contract) then it's very likely to also be a violation of the federal Truth In Lending Act too (that’s a federal financing disclosure law that protects consumers). Some states also have a law that specifically applies to car dealers doing this sort of thing. If you don't have any spot delivery document in your deal and there is nothing on the finance contract that says it is contingent on financing approval and it says on it that the dealer (by its name) is the "creditor" (usually on the front page at the top), then your deal may be a final contract and if the dealer can't get a lender to finance the sale for you then legally the dealer is probably stuck having to take your loan payments or accepting your cancellation of the deal, but of course they won't tell you that. In fact, they will likely say you have to bring the car back and the deal is being cancelled if you don’t go along with their new deal. That could be a lie. You need to talk to a local Consumer Law attorney who deals with this kind of case (it's called "autofraud" or car sales fraud). To learn more about Fraud, check the link below for Avvo’s Legal Guide “What is Fraud?” You can go to this web site page for a Free Online 50 State National List of Consumer Law Lawyers (http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml) and find one near you (lawyers don’t pay to get listed here and most of them are members of the only national association for Consumer Law lawyers, NACA.net). You can also look for one here on Avvo under the Find a Lawyer tab. Or you can call your local attorney's Bar Association and ask for a referral to a Consumer Law attorney near you. But act quickly because for every legal right you have, there is only a limited amount of time to actually file a lawsuit in court or your rights expire (it's called the statute of limitations), so don't waste your time getting to a Consumer Law attorney and finding out what your rights are. If this answer was helpful, please give a “Vote Up” review below. Thanks for asking and Good Luck
This answer is for general purposes only and does not establish an attorney-client relationship. The law in your state may differ and your best answer will always come from a local attorney that you meet with privately. If you need a Consumer Law attorney, click the link above to find a Consumer Law attorney near you.