
530 N.W.2d 912 (1995)
247 Neb. 894
Ross A. PANTANO, Appellee,
v.
John J. McGOWAN, Appellant.
No. S-93-760.
Supreme Court of Nebraska.
May 5, 1995.
*913 Mark E. Novotny and Robert J. Murray, of Kennedy, Holland, DeLacy & Svoboda, Omaha, for appellant.
Allen E. Daubman, of Koley, Jessen, Daubman & Rupiper, P.C., Omaha, for appellee.
WHITE, C.J., CAPORALE, FAHRNBRUCH, LANPHIER, WRIGHT and CONNOLLY, JJ., and BUCKLEY, District Judge.
FAHRNBRUCH, J.
Ross A. Pantano wanted to buy Business Interiors and Design, Inc. (Company), a family-owned corporation, by purchasing all of its outstanding capital stock for $1,060,000.
Pursuant to a written agreement with the Company and its shareholders, Pantano purchased 345 shares of the Company's stock for $40,000. In the agreement, the shareholders granted Pantano an option to purchase the Company's remaining outstanding capital stock. John J. McGowan, the Company's majority shareholder, agreed that if Pantano did not exercise his option, that he, McGowan, would personally purchase Pantano's 345 shares of stock for $40,000.
After Pantano failed to obtain financing, he did not exercise his option to purchase the remaining outstanding stock. Pursuant to the written agreement, Pantano demanded in writing that McGowan purchase from him the 345 shares Pantano had purchased from the Company's shareholders. Pantano's demand was sent by certified mail to, and received by, McGowan. McGowan refused to purchase Pantano's stock.
Pantano successfully sued McGowan for breach of the written contract in which McGowan agreed to purchase Pantano's stock. McGowan filed two counterclaims against Pantano, but those were dismissed by the trial court.
McGowan appealed the judgment entered by the district court for Douglas County to the Nebraska Court of Appeals, but on appeal he did not assign any errors. In order to regulate the caseloads of the appellate courts of this state, we removed this case to the Supreme Court.
Because McGowan failed to assign any error, we limit our review to plain error. Noting plain error, we vacate the district court's award of prejudgment interest.

ADDITIONAL FACTS
The written agreement between Pantano and the Company and its shareholders was entered into on October 23, 1991.
Paragraph 11 of the agreement provides: "All notices, offers, acceptances, exercise of options, waivers and other acts under this Agreement shall be in writing and shall be deemed to have been duly given when delivered in person or sent by certified mail addressed to the Company...." (Emphasis supplied.)
Paragraph 12(a) of the agreement provides: "This instrument and the agreements referred to herein contain the entire agreement among the parties ... and no modification shall be binding upon a party unless set forth in writing and duly executed by each party affected." (Emphasis supplied.)
*914 Also on October 23, McGowan, as president of the Company, executed an employment contract under which the Company hired Pantano for 1 year, retroactive from July 1991 to July 1992, at a salary of $6,250 per month for the first 6 months and thereafter at $4,166.66 per month plus commissions.
Paragraph 16 of the employment agreement provides: "This Agreement and the Agreement referred to in the recitals hereto constitutes the full and complete understanding and agreement of the parties ... and cannot be amended, changed, or modified without the consent, in writing, of the parties hereto." (Emphasis supplied.)
On March 10, 1993, Pantano filed his petition seeking $40,000 plus interest because of McGowan's refusal to personally purchase the 345 shares of stock Pantano had bought from the Company's shareholders.
In his answer, McGowan alleged that between July and September 1992, Pantano and McGowan had orally modified the stock purchase agreement so that McGowan would continue to pay Pantano the original salary of $6,250 per month "until such time [Pantano] exercised his option."
As previously stated, McGowan also filed two counterclaims. The first counterclaim alleged that the oral agreement to employ Pantano at $6,250 per month until such time as Pantano exercised his option modified the stock purchase agreement and the employment contract. McGowan alleged that the oral modification caused Pantano to receive enhanced wages. McGowan sought $27,083.42 in damages plus interest and attorney fees due to McGowan's reliance on the purported oral modification of the two agreements.
In the second counterclaim, McGowan alleged that since June 1991, "extraordinary events" reduced the Company's net worth approximately 66 percent. McGowan sought damages in his second counterclaim in the amount of between $244,100.14 and $739,697.40 plus interest and attorney fees because of Pantano's alleged breach of the alleged oral modification to the stock purchase agreement.
Pantano filed a demurrer to McGowan's answer and counterclaims, and the district court sustained the demurrer based upon the statute of frauds contained in Neb.U.C.C. § 8-319 (Reissue 1992). The court dismissed the counterclaims after McGowan elected to stand on them.
Pantano then filed a motion for summary judgment which was sustained by the district court. The court entered judgment for Pantano in the amount of $40,000 plus prejudgment interest from March 2, 1993, the date McGowan received Pantano's demand letter for the $40,000.

ANALYSIS
Initially, we note that the proper manner in which to challenge the appropriateness of a counterclaim is by a motion to strike rather than by a demurrer. Barks v. Cosgriff Co., 247 Neb. 660, 529 N.W.2d 749 (1995). We will treat Pantano's action as a demurrer because both parties and the district court treated it as such. See id.
As previously stated, McGowan's brief does not contain any assignment of error. To be considered by an appellate court, an error must be assigned and discussed in the brief of the one claiming that prejudicial error has occurred. Gravel v. Schmidt, 247 Neb. 404, 527 N.W.2d 199 (1995). See, also, Neb.Ct.R. of Prac. 9D(1)d (rev. 1992). Thus, errors which are argued but not assigned will not be considered by an appellate court. Manske v. Manske, 246 Neb. 314, 518 N.W.2d 144 (1994).
Where an appellant fails to assign any specific error, the decision appealed from will be affirmed unless the court elects to note plain error. In re Interest of A.W., 224 Neb. 764, 401 N.W.2d 477 (1987). Plain error is error plainly evident from the record and of such a nature that to leave it uncorrected would result in damage to the integrity, reputation, or fairness of the judicial process. First Nat. Bank in Morrill v. Union Ins. Co., 246 Neb. 636, 522 N.W.2d 168 (1994). Plain error may be noted by an appellate court on its own motion. See Long v. Hacker, 246 Neb. 547, 520 N.W.2d 195 (1994).
*915 Upon sustaining Pantano's summary judgment motion, the district court entered judgment for Pantano in the amount of $40,000 plus prejudgment interest. We elect to note plain error in regard to the trial court's award of prejudgment interest.
At the time the trial court entered its judgment, a litigant in all causes of action needed to comply with Neb.Rev.Stat. § 45-103.02 (Reissue 1993), in order to receive prejudgment interest. Section 45-103.02 provides, in relevant part:
[J]udgment interest shall also accrue on decrees and judgments for the payment of money from the date of the plaintiff's first offer of settlement which is exceeded by the judgment until the rendition of judgment if all of the following conditions are met:
(1) The offer is made in writing upon the defendant by certified mail, return receipt requested, to allow judgment to be taken in accordance with the terms and conditions stated in the offer;
(2) The offer is made not less than ten days prior to the commencement of the trial;
(3) A copy of the offer and proof of delivery to the defendant in the form of a receipt signed by the party or his or her attorney is filed with the clerk of the court in which the action is pending; and
(4) The offer is not accepted prior to trial or within thirty days of the date of the offer, whichever occurs first.
There is nothing in the record to reflect that Pantano complied with the provisions of § 45-103.02. Thus, at the time the district court entered its judgment, Pantano was not entitled to any prejudgment interest. It was plain error for the district court to award prejudgment interest to a litigant who failed to comply with § 45-103.02. See Peterson v. Kellner, 245 Neb. 515, 513 N.W.2d 517 (1994).
The trial court's order sustaining Pantano's demurrer to McGowan's amended counterclaims, which counterclaims incorporate the employment agreement and the stock purchase agreement containing the stock option, was correct because each document plainly states that neither could be modified except in writing. Each counterclaim alleged an oral modification of written agreements. Therefore, neither of the counterclaims stated a cause of action. We also note that the stock agreement expressly provides that Pantano's option to purchase additional stock could be exercised only in writing. There is no allegation in the pleadings that Pantano ever exercised in writing his option to purchase the remaining outstanding stock of the Company.
Pantano's demurrer was also sustainable even if there was a purported oral exercise of his agreement by the words "until such time [as] I exercise the option." Those words are illusory and do not constitute an enforceable promise. See Chadd v. Midwest Franchise Corp., 226 Neb. 502, 412 N.W.2d 453 (1987) (holding that an agreement that depends upon the wish, will, or pleasure of one of the parties is unenforceable). For the reasons stated herein, the trial court properly sustained Pantano's demurrer, and we need not address the district court's ruling on the statute of frauds. See Schlake v. Jacobsen, 246 Neb. 921, 524 N.W.2d 316 (1994).
The district court order sustaining Pantano's summary judgment motion was also proper as a matter of law. McGowan's affidavit in response to the summary judgment motion does not demonstrate a genuine issue of material fact. According to McGowan's affidavit, Pantano spent the spring and summer of 1992 trying to "[obtain] the necessary financing." In January 1993, Pantano notified McGowan that "he was having serious difficulty in obtaining financing." In his affidavit, McGowan stated that in the alleged "oral modification" he promised to provide Pantano continued employment "until such time as [Pantano] could finalize the necessary financing." On February 4, Pantano informed McGowan that he "was unable to obtain financing and was unable to consummate the sale and purchase of the Company."
Giving McGowan the benefit of all reasonable inferences, the record fails to reflect that Pantano orally offered an enforceable promise upon which McGowan could rely.
*916 Without question, the district court was correct in holding that McGowan was contractually obligated to purchase the 345 shares of the Company's capital stock from Pantano.

CONCLUSION
We vacate the district court's award of prejudgment interest to Pantano, but in all other respects affirm the judgment of the district court.
Affirmed as modified.
