N.M. Stat. § 7-8A-11
If property other than money is delivered to the administrator under the Uniform Unclaimed Property Act (1995), the owner is entitled to receive from the administrator any income or gain realized or accruing on the property at or before liquidation or conversion of the property into money. If the property was an interest-bearing demand, savings, or time deposit, including a deposit that is automatically renewable, the administrator shall pay interest at a rate of five percent a year or any lesser rate the property earned while in the possession of the holder. Interest begins to accrue when the property is delivered to the administrator and ceases on the earlier of the expiration of ten years after delivery or the date on which payment is made to the owner. Interest on interest-bearing property is not payable for any period before the effective date of the Uniform Unclaimed Property Act (1995), unless authorized by law superseded by that act.
NMS § 7-8A-11