How is the Zakat calculated on money saved for past years that reached the minimum threshold, but its Zakat was not paid due to ignorance, along with not knowing the exact amount of money saved at the end of each year?

Zakat becomes obligatory on wealth under two conditions: reaching the nisab (the equivalent of 85 grams of gold or 595 grams of silver), and the passing of a complete lunar year (hawl). If these two conditions were met for your wealth in past years, then Zakat became obligatory on it and is not nullified by the passage of time. You can refer to your bank statements and the prices of gold and silver to determine when the nisab was reached and the hawl passed. You should pay Zakat for every year in which you did not pay it, and for the entire amount if a hawl passed over it, not just on the increase. Newly acquired wealth during the year that is not a result of the initial wealth has its own independent hawl, or it can be zakated along with the initial wealth.