Obviously the exact answer depends on a lot of specific numbers that I'm not laying out, but broadly speaking, is this a sensible thing that people sometimes do or is it likely a bad idea?
I still feel better paying off a car in 3 years rather than 5, so I usually suggest making a few extra payments to make that happen.
You will get a better deal with more incentives with dealer purchased cars if you finance. They may give you more for a trade and negotiate more on the final price. Perhaps even give you a few extra options for free.
But if it's really a necessity, just buy it rather than trying to optimize for that 1% extra income.
Is the return from investments more than you would pay in interest on a car loan?
If yes, then take out a loan for the maximum amount possible and invest the remaining, available funds that would have gone toward the car and you will come out ahead. Otherwise, just forget the loan and pay cash.
But it was all for naught; the car ended up being a lemon and VW of America bought it back from me soon thereafter.
The best financial decision is to not have a car, it only generates expenses and usually are high cost to maintain, as you need insurance, maintenance and so on. As public transport isn't available everywhere, let's go on with the list...
The second best decisionis to buy a used car and pay with cash, not getting a loan.
The third of buying a cheap used car and getting a loan.
The 4th is buying a new car without a loan.
And the worse being buying a car you can't really afford, brand new with a loan.
The value of the purchase value of the car is pointless. What matters is how long you intend to stay with it, because when you do. You can factor in insurance + maintenance + depreciation and divide it to understand how much you will spend per month(This is how companies do accounting, you should as well do for yourself!). A lot of cars you lose at least $1K per month. You want to reduce this value as much as you can. Get a car that gives you just enough comfort, has a good reputation of not breaking down and doesn't consume a lot of fuel.
Just imagine instead if you had that $1k per month for yourself, invested it and perhaps was lending it to a clueless person to buy their own car. This is wealth :-)
As you can see, buying a new car is a bad idea. Sometimes it is even better to get a loan to buy a used car. A lot of used cars are sold very cheapily after 2 years and most of its value is lost. A used car has actually a better resale value than a new car, supposing when you bought it it was used.
So even if you end up buying some crooked car with real issues despite being only 2 years old(uncommon), you can always resell and buy another 2 years old used car.
If you really like cars and driving... and want to drive expensive cars, it is likely cheaper to rent them, drive it for a while and return it. You even get to experience different cars.
Brand new cars is for emotional buys, people who don't really grasp economics or are just too rich to care about it. Are you any of those options?
[Advice I should have given myself many years ago.]