Dealers can fold the unpaid balance from your old car loan into a new lease by inflating the capitalized cost, and the mechanics deserve a hard look before you agree. Say you owe $3,000 more than your trade is worth. Rolled into a 36-month lease at a 0.002 money factor, that adds about $83 a month of depreciation plus $6 of finance charge, call it $89. Over the term you pay roughly $3,216 to retire debt on a car you no longer drive, and at turn-in you own nothing that could recover any of it. In a purchase, at least the rolled-in balance rides on an asset you eventually own and can sell.
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CFPB's consumer answers on negative equity walk through how these roll-ins work in both leases and loans. If you carry a gap on the old car, the cleanest options are paying it off separately or delaying the new deal until the loan catches up with the car's value.