Is zakat obligatory on a sum of money that has been accumulated over many years for emergency purposes, knowing that its owner does not know when it reached the nisab?

Zakat becomes obligatory on wealth once it reaches the nisab (minimum threshold) and a hawl (full lunar year) has passed, even for many past years. It is not waived due to ignorance of its obligation, forgetfulness, or the passage of a long time.

If you do not know when the wealth reached the nisab, you must estimate your monthly savings and the prices of gold and silver for each year to determine when it reached the nisab and then calculate the Zakat for each hawl thereafter. The amount of Zakat is one-quarter of one-tenth (2.5%). The nisab for gold is 85 grams, and for silver is 595 grams.

You can seek assistance from scholars in your country for this estimation.