What makes a number binomial? Finale

From the binomial expansion of $(1 + 0.2)^{1000} = \sum_{k = 0}^{1000}A_{k},$

when $A_{k} = \binom{1000}{k}(0.2)^{k},$

find the value of $k$ where the maximum value of $A_{k}$ is reached.

Credit goes to an AIME problem.