Maybe there is no big across the pond difference in this case. I think many N A English speakers would answer exactly as you did.
To reiterate, there is NO cross pond difference with respect to using 'have' in the present simple to denote possession/ownership;
After two years, I finally have a car.
But just because the present simple verb form 'have', can be used in the present simple tense to denote possession/ownership doesn't mean that 'have' can also be used in the simple past or the present perfect to denote possession/ownership.
I hope that Eddkzk and Albertino and other ESLs reading this thread understand this difference.
Now, when we introduce the collocation, <I've got/gotten>, it gets a little more complicated. There are cross pond differences and what I'm going to say here applies only to NaE, NOT to BrE.
Some suggest that <I've got> is a present perfect but I maintain that it is simply an alternative form, but more emphatic form that means the same as <I have>.
<I've gotten> is a present perfect but it has a meaning of "S have/has acquired".
To Eddkzk's original question:
Which tense should I use? I guess the present perfect is better;on the other hand, the time adverb refers to the past, I am not sure. Can you help me please?
After two years, I finally have had a car.
Or,
After two years, I finally had a car.
We now know that 'have' is not possible here in the simple past or the present perfect without a change in meaning; changes that would render/make Eddkzk's original meanings very different, ie. both would be finished/"past tense" meanings denoting that he had a car but doesn't now have a car.
By using the verb 'get', we stay with a meaning denoting that he still has a car, which, I'm quite sure, is Eddkzk's meaning.
NaE uses three different verb collocations for three different purposes:
{I've removed the finally's from all three examples so we can focus on the verb form}
1. After two years, I have
gotten a car.
2. After two years, I
got a car.
3. After two years, I've got a car.
Number 1, with <gotten>, is a true
present perfect that carries the meaning of "acquired".
Number 2, using <got>, is the
past simple that also carries the meaning of "acquired".
Number 3, using the
present perfect FORM plus <got> has a stative meaning denoting ownership/possession.
As I mentioned/As I've mentioned, BrE uses this in a different manner than NaE. I'll leave that description to the Brits.
