If a person possesses the Nisaab of Zakaah at the beginning of the lunar year (612.36 g of silver or its equivalent in cash or stock or only 87.48g of gold) and at the ending of the lunar year he still possesses the Nisaab, then Zakaah will be Fardh on him as long as he did not use up all the money during the year. However, if he used up or lost the entire amount anytime during the year then his Zakaah year will terminate and his new Zakaatable year will begin from the time he possesses the Nisaab again and will end after 12 lunar months only.
In your case $1000 made you the Maalik (owner) of Nisaab, therefore if at the end of the lunar Zakaatable year you still possess the Nisaab then Zakaat will be Fardh on you as long as you do not use up the entire $1000 during the year. If you use up the entire $1000 then your Zakaatable year will be terminated and you will only start counting your Zakaatable year when you take possession of Nisaab again.
As for a person who becomes Maalik of Nisaab every month, but at the end of the month he has nothing left then the conditions for paying Zakaah are not found which then means that at the beginning of every month (if he possesses Nisaab again) he will be starting a new Zakaatable year. However, if he has something left over at the end of each month throughout his Zakaatable year and at the end of the Zakaatable year he still possess Zakaah Nisaab then he will have to pay Zakaah. (Raddul Muhtaar, Vol. 2, Page 30 & 36, Ahsanul Fataawaa, Vol. 4, Page 265)
As for the ruling of Qurbani, it will only become Waajib on a person if he possesses 612.36g of silver or any amount of wealth which amounts to the Nisaab of silver and it is over and above his Haajat-e-Asliyyah, be it gold, silver, merchandise, extra house, etc. One should note that it is unnecessary to own the Nisaab of Qurbani for the entire year before Qurbani become Waajib. (Raddul Muhtaar, Vol. 5, Page 219 & 221, Ahsanul Fataawaa, Vol. 7, Page 502-503)
This is ruling is the same for both cases mentioned in your question.
And Allah Ta’ala knows best
Ilyaas bin Hashim Limbada
Attested to as correct by:
Mufti Muhammad Ashraf
13 May 2004
22 Rabee’ul Awwal 1425