This question made me wonder how, according to the OP of that question, a car that cost about $16,000 can be worth only $4,000–$6,000 after a mere three years.
Does a new car usually depreciate that much?
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It depends completely on the car. Some cars retain their value much better, and others drop in value like a rock (no pun intended). The mileage and condition on a car also has a huge impact on value.
According to this site, cars on average lose 46% of their value in three years, so seeing one that drops 62% in roughly 3 years does not seem impossible.
That value could also have been trade-in value, which is significantly lower than what you could get with a private party sale (or what you'd pay to get that same car from a dealer)
One example: a new Ford Taurus (lowest model) has a Kelly Blue Book value of $28,000. A 2014 Taurus (lowest model) with average mileage and in fair condition has a private party value of about $12,000, for a 57% drop in value.
Note: I picked Taurus because it's a car that should not have exceptional resale value (unlike BMW, trucks, SUVs), not to make any kind of judgement of the quality or resellability of the car)
It's possible the $16,000 was for more than the car. Perhaps extras were added on at purchase time; or perhaps they were folded into the retail price of the car. Here's an example.
2014: I'm ready to buy. My 3-year-old trade-in originally cost $15,000, and I financed it for 6 years and still owe $6500. It has lots of miles and excess wear, so fair blue-book is $4500. I'm "upside down" by $2000, meaning I'd have to pay $2000 cash just to walk away from the car. I'll never have that, because I'm not a saver.
So how can we get you in a new car today? Dealer says "If you pay the full $15,000 retail price plus $1000 of worthless dealer add-ons like wax undercoat (instead of the common discounted $14,000 price), I'll eat your $2000 loss on the trade." All gets folded into my new car financing. It's magic! (actually it's called rollover.)
2017: I'm getting itchy to trade up, and doggone it, I'm upside down on this car. Why does this keep happening to me?
In this case, it's rollover and other add-ons, combined with too-long car loans (6 year), combined with excessive mileage and wear on the vehicle.
It isn't common to lose that much value in 3 years, but it is possible.
If you don't take care of small dents, scratches, etc., you can quickly reduce the value far beyond what you might expect looking at graphs.
Another big factor is the trim level of the car that you purchase. If you spend $30,000 for the highest trim level of a car, instead of $22,000 for the lowest trim level, the higher trim car could lose 50% of it's value while the lower trim car loses only 35%.
There's no way to know why the OP of your linked question had such a large loss, but again, that's not the usual experience. It is definitely a good idea to consider used though.