I purchased a new vehicle in 2015, but had a remaining balance on the trade. How do i figure the correct purchase price of the new car bought in 2015?

[RobertG]

That depends. 

The purchase price of the new vehicle in 2015 is the total price of the new vehicle

The amount of the loan that the dealer paid off in 2015 is considered part of what the dealer paid for the car traded-in.  The amount of the loan paid off by the dealer plus any reduction of the price of the new car equals the total amount the dealer paid for the trade-in.

When you bought the car you paid cash plus a trade-in. the total of those two things is the purchase price of the car; if the trade-in vehicle was never used for business

If the trade-in vehicle was used for business prior to trading it in, and you deferred the gain on that transaction into the new vehicle, then your basis in the new vehicle is reduced by any deferred gain.