If the beginning of Muharram is the first day of your khums fiscal year then khums is payable at the end of Dhil-Hijjah, even if you started saving in Dhil-Qa’dah and did not save anything before that. The khums fiscal year begins when one gains any money in his life, even when he was a child. If you know that day then this is when you pay khums on any profit that remains unspent, even if you received the money days before this date. If you do not know that day exactly, then you should refer to the religious authority, i.e. the marja that you follow or his agents, to determine a day to be the start of your khums fiscal year.