Sales tax and auto trade-ins

Long story short, an auto salesperson told me yesterday that if I buy a car for $20,000 and get $15,000 for a trade-in as part of the purchase, I would
only have to pay sales tax on the $5,000 difference between the two figures. I am in New Jersey and the sales tax is 7%.
I already bought a car (with no trade-in), so I am not trying to decide what to do. But I started thinking about what he said and it made me wonder if the sales tax savings on a trade-in is something that buyers should consider.
For example, here are 2 different scenarios:
1) I buy a car for $20,000 and get $15,000 for a trade-in. So, my sales tax on the transaction would be 7% of $5,000 or $350.
2) I buy a car for $20,000 but sell my car privately for $16,000 (instead of taking $15,000 for it as a trade-in). My sales tax on the transaction would be 7% of the $20,000 purchase price or $1,400.
According to scenario 2, even though I got $1,000 more for my car by selling it privately rather than trading it in, the whole transaction would actually cost me $50 more than scenario 1 due to the higher sales tax I would have to pay.
In other words, in order for me to benefit by selling my car privately versus trading it in, the private sale price would have to be at least 7% higher the trade-in allowance.
Is that correct?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a site by and for consumers of financial services and advice. We are not affiliated with any of the banks, financial services or software manufacturers discussed here. All logos and trade names are the property of their respective owners.

Tax and financial advice you come across on this site is freely given by your peers and professionals on their own time and out of the kindness of their hearts. We can guarantee neither accuracy of such advice nor its applicability for your situation. Simply put, you are fully responsible for the results of using information from this site in real life situations.