Is the value of lost gold to be paid at the time of its purchase or at the time its loss is discovered, knowing that the person who lost his memory might be the reason for its loss?

The gold you found is a trust (amanah) that must be kept in a safe place. Your negligence in safeguarding it by placing it in a paper close to people's hands makes you liable to guarantee it. The principle of guarantee is that it should be guaranteed with an equivalent amount on the day it was lost. If it is not possible to provide an equivalent, then it should be guaranteed by its value at the time of loss.