I think you're both right. ;-)
We must follow what sources say; if you want to put in a rounded number and make up some error bars, but the source gives an exact number that's a Bad Thing. However, we do also have to be pragmatic; population varies over time, most ways of counting have potential inaccuracies, and we should be open on that point.
So, what do the sources say? An archived link is hardly ideal, so I went looking.
The 2010 census says 24,658,823.
The [UN http://data.un.org/CountryProfile.aspx?crName=Ghana] estimates 24,392,000 (in 2010).
Should we show both to readers? Or if we just said something like "24,658,823 (2010 census)" then readers are still being reminded that the number may be slightly out of date, and that it's a census result (which is a pretty good source but might have certain limitations).