I'm a little puzzled by the question. The percentage is speculative, so why should it be used in the caluclation of the variance or standard error? What were the results of the survey? That proportion may be more valid. In the absence of additional data, I'm inclined to use 0.5, giving 0.0456, quite a bit larger than your value.
1) Let's decide this, first.
2) Make sure this is the ENTIRE problem statement.