Ambiguity between methods of calculating quartiles. Which method is more correct?

I am having confusion between two methods of calculating the first quartiles.

Let me explain by an example:

$A=[1,2,3,4,5]$

The method that I know:

To find the first quartile in the list above I first find the median = $3$ that is the 3rd element.

Now I split the list in the following fashion:

$(1,2)$

$3$

$(4,5)$

Now we take the list $(1,2)$ and we find the media between them that is $(1+2)/2=1.5$

So according to my calculation the first quartile ${Q}_{1}=1.5$

The nearest rank method

$n=\lceil \frac{P}{100}\times N\rceil $

So for the above list the $0.25$ percentile or the first quartile ${Q}_{1}$ will be

$\lceil \frac{25}{100}\times 5\rceil =2$

which is 2nd position.

So which is correct $1.5$ or $2$ ? Or does chosing any of them is fine ?

If I am correct in my original calculation why am I getting a difference between the 2 methods.