This is correct. Average annual returns are not as simple as taking an arithmetic average of returns over the time period. This is because your first year's 2.5

This is correct. Average annual returns are not as simple as taking an arithmetic average of returns over the time period. This is because your first year's 2.56% return is not the same amount as your next year's - because the second year's return is 2.56% of the original capital PLUS the 2.56% you earned the year before... And so on and so forth. Hence your correct derivation of the "compound annual growth rate".