Car Loan Rates

If an auto loan rate is 3.9%, it makes sense to put any money down, except to lower the monthly payments?
Ok, here's more. I keep cars forever, so I'll have it long after the loan is up. I'll get Gap Ins. And what about inflation? If I keep the money in the bank, instead of a Down PMT how inflation factor into the equation with such a low int rate?
You should always put money down on a car loan. Then you can avoid being "on head "if you decide to trade a car before the end of the loan