This is very much a “how long is a piece of string” type of question as, unlike humans, there is no definite period of time between being born as fry and becoming a fully grown adult for tropical fish.
Tropical fish all grow at different rates and it is often extremely different dependant on the fish itself. If we take the fast growers for example, the obvious ones which stick out in my mind are the Silver Arowana which will grow to around 12 inches in the first year, this is roughly the same growth rate of 1 inch per month as the Red Tail Catfish has. Other fast growers include the Oscar cichlid fish and other American Cichlids.
Although the fast growers all appear to be what you might call monster fish and so it appears to be relevant, this is far from the case. If we take the ever popular clown loach for example, their reported maximum adult size is around 12 inches, although I have only seen a few at this size, it is rare to see them much bigger than 4-7 inches. The rough growth rate of these fish is much less than the ones we mentioned above and is closer to 1 inch per year rather than 1 inch per month!
If we look at another type of fish and take the African cichlids as an example, a Tropheus species will often take ages to get much bigger than 2 inches and then have a growth spurt to around 4 inches and the growth rate will then slow down a bit more as it gets closer to 6 inches. To get to the 4-6 inches stage can take 2-3 years though in total, which when compared to many of the cichlids, especially haps from lake Malawi is a long time. The haps in lake Malawi will have a similar type of growth spurt but be at the larger size within a year.
So although we haven’t technically given an exact answer to this question, I hope you can appreciate the amount of variation in growth rates between different types of tropical fish. As a note to end on, personally I have a Synodontis Granulosus which I bought at around 5 inches and 2 years later it is around 6 inches, adult size is meant to be around 10-12 inches so we are a little way off still……!