How is the zakat calculated and paid for a sum of money designated for speculation in pure stocks, especially since this amount has changed over previous years, given that the questioner was not previously aware of the obligation of zakat upon it?

You must pay Zakat (definition) on your wealth for past years if it reached the nisab (definition) and a full year has passed. The nisab is equivalent to 85 grams of gold or 595 grams of silver. You can determine the number of shares and their value by reviewing your account statement. You should pay 2.5% of the principal and profits. If you are unable to determine the exact amount, then exert your best effort and strive to ascertain what you believe to be most likely correct, so as to clear your liability. This applies if the shares are for trading. However, if they are fixed assets intended for benefiting from their income, then Zakat is only due on the profits.