Is it permissible to pay the zakat on jewelry that has been in one's possession for a full year based on its original purchase price plus an estimated surplus, in the event that one is unable to access it and determine its current value?

Firstly: Zakat (definition) on jewelry depends on the stability of its ownership. If the ownership is unstable (e.g., usurped or lost), then there is no Zakat until it becomes stable. However, if the ownership is stable and you are able to retrieve it, then Zakat becomes due once a full year has passed. If the jewelry is in someone else's possession without your permission, you may delay paying its Zakat until you retrieve it. If the jewelry is under your full ownership and you have the financial means, then Zakat is due immediately.

Secondly: Zakat on jewelry is paid based on its value on the day Zakat becomes due, not on the day of purchase, and at the price of used gold. Zakat is estimated at 2.5% (one-quarter of a tenth) of the gold's weight, then converted into a monetary value according to the price of used gold on that day.

Thirdly: The basis of Islamic rulings is certainty, but if that is not possible, then one acts upon what is most likely. Therefore, estimate the value of the gold based on what you most likely believe, and pay its Zakat. If it later becomes clear that the Zakat was deficient, you must pay the remaining amount.