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If trade in is $15,600, then selling to a private party would go for more, maybe what you owe. Is there a reason you want to go negative equity? That's $3,400 you either have to come up with in cash, or you have to borrow in new loan and pay with interest.
I suggest selling current car privately, then buying new car without the trade in. Trade in is at discount price, because obviously they will sell it for more than they give in trade in.
However, if you just don't want to bother selling, for whatever reason, then you must either get financing that will cover new car plus old car negative equity or pay the negative out of pocket.
Kepp in mind a couple of things:
1) You are trading from a Honda to a Honda - this will allow you to negotiate with the dealership and they can work out numbers and pricing to make it so it will "look on paper" as if you are not paying anything on the old trade-in. In real terms, you probably are, but they can inflate the trade-in value or play with rebates to get away with paying bare minimum. I leased 2 audi's before I bought my first and I always turned them in with over 20k+ overmileage and they always worked with me due to the fact that I bought a new audi.
2) Honda's hold their value pretty well, so the dealership probably wont have a tough time selling it, or at least in comparison to other models - so that should work in your favor.
3) Again, Honda's are VERY popular among the private sellers market, especially for certain groups of people who dont like buying from dealerships and prefer to pay in cash. Which again, will work in your favor.
Good Luck - If you have any other questions, let me know.
LOL. You can play with the paper and numbers and get as creative as you want. But in the end you have to pay it. Up front over the term with interest.
If they can rebate and provide incentives to cover the negative equity, you could take that money toward a lower principle amount on the car if you didn't have the negative equity to deal with.
Regardless, that is literally throwing over $3000 plus interest away....no different than flushing it down the toilet, blowing it in Vegas on a long shot roullete roll.
Trade in is trade in. It is below value (what a buyer will pay) in every instance. Whatever deal you can make with a trade in, you can make without the trade in and keep the difference.
But good luck with your auto endeavors.