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If I were you and really looking to save monthly payment, I would sell the car, pay off whatever you owe and get into cheap lease like G37 for 24 month for $370 a month, then come back to BMW with better lease deal.
What you are proposing here doesn't really save you much money. You are talking about $3600 in saving in course of 3 years (if you do 36month on E82) but you are already incurred loss of $400 by paying $4000 to pay off your current car.
AND, at the end of your 36month lease, you are out with $0 in your pocket if you lease, where as you could possibily bank some money by selling your current car after 3 years.
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