>>7Even if the interest rate is only 3%, that's still non-zero. Your plan to put the car purchase money in an index fund now has its floor raised from 0% to 3% in terms of actual return. This makes absolutely no sense to do.
Only poor people are dumb enough to get a loan for a car.
Wealthy people get mortgages for assets which can appreciate or generate revenue, like real estate or construction equipment. For these asset classes, the revenue over the course of the mortgage outweighs the interest payments and justifies the indebted acquisition now versus later when they could hypothetically be bought with cash. Also getting a mortgage provides the benefit of the extra cash being used as leverage for purchasing other assets. None of these benefits are to be seen with cars, because cars DEPRECIATE in value rapidly--it is not just possible but inevitable for many borrowers to carry a lein on a car with a greater principal than the car's value, something that literally never happens with real estate.