I received $7000 from a government institution a couple of months ago.

Answer

If 12 months after the date of having received the $7000, you still have the Zakaat Nisaab amount or more, then Zakaat has to be paid on that amount, not on the initial $7000.

The Zakaat Nisaab is the value of 612grams or 21.6 ounces of silver. You should ascertain the price of silver in the U.S.A. Assuming that the price for this amount of silver is $500, and 12 months after having received the $7000, you have $2,000, then you have to pay Zakaat on $2000, not on $7000.

If after 12 months the amount remaining is less than $500 (the assumed Nisaab), then there will be no Zakaat payable.