N.M. Stat. § 19-7-9
Any state lands offered for sale by the commissioner may be sold at the commissioner's discretion for cash or upon payment of not less than one-tenth of the purchase price in cash and payment of the balance in amortized installments for any period up to thirty years with interest on the principal balance at a rate to be set by the commissioner in the notice of auction pertaining to the particular sale in advance. Additional payments on the principal may be made at any time, but such payments shall not be effective for credit until the date the next installment is due. The purchase contract shall be upon a form prescribed by the commissioner prior to publication of the notice of auction and shall contain the terms and conditions the commissioner may deem to be in the best interest of the state and consistent with law. Should a purchaser die before completing the contract, the due date of the next installment payment shall, upon written application, be deferred by the commissioner for one year. In addition, the commissioner is authorized to convey for any period of time state lands under the commissioner's jurisdiction having value for commercial development or public use purposes, provided that:
NMS § 19-7-9