CASSEL, Judge.

INTRODUCTION

In a prior appeal between these same parties, we affirmed the district court's order which rendered judgment with interest accruing at the rate of 12 percent per annum from the day after a demand letter was sent. This appeal concerns the applicable interest rate following entry of the judgment. The district court determined that interest at 12 percent continued to run. Because we conclude that after entry of judgment, the judgment rate applied rather than the 12-percent prejudgment interest rate, we reverse, and remand for further proceedings in conformity with this opinion.

BACKGROUND

These parties were previously before us in Valley Cty. Sch. Dist. 88-0005 v. Ericson State Bank, No. A-08-913, 2009 WL 1639739 (Neb.App. June 9, 2009) (selected for posting to court Web site) (Valley Cty. I). That case involved the refusal of Ericson State Bank (Bank) to deliver funds held in two escrow accounts to Ord Public Schools (OPS). The funds were put into escrow by two Class I school districts which were dissolved and merged with OPS. The Bank contended that because the legislative bill which mandated the dissolution and merger of Class I school districts had been repealed, the escrow funds belonged to the two Class I school districts that put the money into escrow. On December 12, 2007, OPS filed a complaint against the Bank, seeking to recover the $30,000 in escrow funds. On August 1, 2008, the district court granted summary judgment in favor of OPS and rendered judgment "in the amount of $30,000.00 with interest accruing since July 20, 2006[,] at the rate of 12 percent per annum." On appeal, the Bank assigned error to, among other things, the granting of prejudgment interest and the setting of the rate at 12 percent. We affirmed via a memorandum opinion, concluding, "We also find that OPS is entitled to prejudgment interest at a rate of 12 percent per annum beginning July 20, 2006." Valley Cty. I at *6. Our mandate was filed with the clerk of the district court on September 14, 2009, and spread on the record of the district court on September 24.

The transcript in the present case shows that on October 20, 2009, OPS moved for an order stating the amount owing on the judgment. On October 27, the district court entered an order which stated that OPS "is entitled to 12% interest on the judgment principal of $30,000.00 from July 20, 2006[,] to September 24, 2009, the date the mandate from the Court of Appeals was spread." The district court ordered that the Bank owed OPS "an additional $11,771.81 as of October 23, 2009, with interest accruing at the rate of $3.86 per day from and after October 23, 2009." The Bank timely filed a motion to alter or amend, contending that the order was contrary to law, that it included an order for compound interest, and that after August 1, 2008, the interest rate on the judgment should be at the judgment rate of 4.188 percent. The district court overruled the motion without a hearing, stating that it "has considered the issues in the motion to alter or amend twice and the Court of Appeals has returned a mandate affirming the decision. No further hearings are necessary or required."

The Bank timely appeals.

ASSIGNMENT OF ERROR

The Bank's sole assignment of error is that the district court erred in determining that prejudgment interest of 12 percent, as provided in Neb.Rev.Stat. § 45-104 (Reissue 2004), should continue to accrue postjudgment, when Neb.Rev.Stat. § 45-103.01 (Reissue 2004) specifically states that interest as provided in Neb.Rev.Stat. § 45-103 (Reissue 2004) shall accrue on all decrees and judgments for the payment of money from the date of entry of judgment until satisfaction of judgment.

STANDARD OF REVIEW

The determination of the applicability of a statute is a question of law, and when considering a question of law, the appellate court makes a determination independent of the trial court. Eikmeier v. City of Omaha, 280 Neb. 173, 783 N.W.2d 795 (2010).

ANALYSIS

There is no dispute that the Bank must pay the 12-percent prejudgment interest from July 20, 2006, to the date of entry of summary judgment on August 1, 2008. This appeal presents the narrow issue of the appropriate interest rate after August 1.

Generally, prejudgment interest accrues on the unpaid balance of liquidated claims arising from an instrument in writing from the date the cause of action arose until the entry of judgment, pursuant to Neb.Rev.Stat. §§ 45-103.02(2) (Reissue 2004) and 45-104. Eikmeier v. City of Omaha, supra. In Valley Cty. I at *5, we determined that the case involved a liquidated claim and that OPS was "entitled to prejudgment interest from the date the cause of action arose until the entry of judgment," and we cited to § 45-103.02(2). We further cited § 45-104 and stated that because no interest rate had otherwise been agreed upon, the statutory default rate of 12 percent per annum applied. Because we have already determined these issues, we need not again decide them. Under the law-of-the-case doctrine, an appellate court's holdings on questions presented to it in reviewing the trial court's proceedings become the law of the case; those holdings conclusively settle, for that litigation, all matters ruled upon, either expressly or by necessary implication. Money v. Tyrrell Flowers, 275 Neb. 602, 748 N.W.2d 49 (2008). The law-of-the-case doctrine reflects the principle that an issue that has been litigated and decided in one stage of a case should not be relitigated in a later stage. Pennfield Oil Co. v. Winstrom, 276 Neb. 123, 752 N.W.2d 588 (2008). The doctrine promotes judicial efficiency and protects parties' settled expectations by preventing parties from relitigating settled issues within a single action. Id.

OPS argues that the Bank should have raised the issue now before us in Valley Cty. I. OPS contends that because the summary judgment stated that interest accrued since July 20, 2006, at 12 percent per annum, it implied that § 45-104 was being applied. OPS reasons that because the Bank did not challenge that part of the order in the original appeal, the issue is waived under the law-of-the-case doctrine. Under the mandate branch of the law-of-the-case doctrine, a decision made at a previous stage of litigation, which could have been challenged in the ensuing appeal but was not, becomes the law of the case; the parties are deemed to have waived the right to challenge that decision. Pennfield Oil Co. v. Winstrom, supra. An issue is not considered waived if a party did not have both an opportunity and an incentive to raise it in a previous appeal. Id. In Valley Cty. I at *5, we specifically stated that § 45-104 applied "[b]ecause there was no `otherwise agreed' upon rate for prejudgment interest" and that OPS was entitled to the 12-percent prejudgment interest until the entry of judgment. Neither the district court's judgment nor our opinion stated that the 12-percent interest rate would continue to be applied after entry of judgment; thus, the Bank did not have a reason to raise the issue of the appropriate postjudgment interest rate at that time. Had the district court's initial judgment expressly stated a postjudgment interest rate, OPS' argument would have had merit. But because the judgment was silent on the matter of postjudgment interest, we reject OPS' argument that the matter should have been raised in the prior appeal.

The Bank argues that § 45-103.01 controls the amount of interest accruing on a money judgment after the entry of judgment until satisfaction of the judgment. We agree. Under § 45-103.01, "[i]nterest as provided in section 45-103 shall accrue on decrees and judgments for the payment of money from the date of entry of judgment until satisfaction of judgment." Section 45-103 provides in pertinent part:

OPS, on the other hand, argues that § 45-103 does not apply due to the language of § 45-103(1), because interest at 12 percent is specified in § 45-104 and thus is "specifically provided by law." We disagree. Section 45-104 provides the interest rate for prejudgment interest upon the happening of events outlined in the statute. BSB Constr. v. Pinnacle Bank, 278 Neb. 1027, 776 N.W.2d 188 (2009). We conclude that the 12-percent prejudgment interest rate does not continue to run after the entry of judgment.

Alternatively, OPS argues that the Bank unlawfully held funds belonging to OPS, thereby subjecting it to the interest provisions of § 45-104 rather than § 45-103. In Valley Cty. I at *6, we stated, with reference to a paragraph of the escrow agreement which purported to protect the Bank from any liability unless the Bank showed gross negligence or willful misconduct, "We believe that the Bank's continued failure to turn the escrow funds over to OPS, as rightful owner, without any lawful basis to do so constitutes willful misconduct." Section 45-104 allows interest at 12 percent per annum "on money received to the use of another and retained without the owner's consent, express or implied, from the receipt thereof, and on money loaned or due and withheld by unreasonable delay of payment."

In our view, the authority cited by OPS does not support its argument. In Cheloha v. Cheloha, 255 Neb. 32, 582 N.W.2d 291 (1998), the district court found that the agent converted $33,495.05 in either principal or interest from certificates of deposit to his own use, and it awarded the principal that amount plus postjudgment interest and costs. On appeal, the Nebraska Supreme Court stated that under § 45-104, the agent was chargeable with interest at the legal rate from the time the money was wrongfully withheld from the principal, and that the principal "was entitled to prejudgment interest as a matter of law on [$33,495.05] from the time [the agent] received the certificates of deposit." 255 Neb. at 44, 582 N.W.2d at 301. The Supreme Court clearly referred to the interest under § 45-104 as prejudgment interest. Thus, even if OPS is entitled to interest under § 45-104 due to any wrongful actions of the Bank, the 12-percent rate under § 45-104 is still applied as prejudgment interest and does not continue to run following entry of judgment.

Finally, OPS argues that at the very least, it was entitled to the 12-percent interest rate until September 24, 2009, the date it asserts the mandate was spread after Valley Cty. I. It argues that "it is reasonable to view the district court's [m]andate [o]rder of September 24 ... as the date of `judgment' per § 4[5]-103." Brief for appellee at 9.

We believe that OPS' argument is contrary to analogous precedent. In Ramaekers, McPherron & Skiles v. Ramaekers, 4 Neb.App. 733, 549 N.W.2d 662 (1996), this court explained that when a judgment is modified upon appeal, interest runs on the full amount of the judgment as modified from the date the original judgment was rendered by the trial court. In Gallner v. Gallner, 257 Neb. 158, 595 N.W.2d 904 (1999), the Nebraska Supreme Court adopted the Ramaekers rationale. Thus, when a judgment is modified on appeal, whether increased or decreased, the interest accrues on the judgment from the date the original judgment was due. See Gallner v. Gallner, supra. If the original date of judgment is controlling where the amount of the judgment is modified, it would make no sense to adopt a different date in cases where the judgment is not changed. We therefore find no merit to this argument and determine that the controlling date is the original date of the district court's judgment, i.e., August 1, 2008.

Before turning to our own calculations regarding the amount of the judgment, we recall general principles regarding interest and judgments. Prejudgment interest is part of the judgment. See, Knox v. Cook, 233 Neb. 387, 446 N.W.2d 1 (1989); D.K. Meyer Corp. v. Bevco, Inc., 206 Neb. 318, 292 N.W.2d 773 (1980). Although compound interest generally is not allowable on a judgment, it is established that a judgment bears interest on the whole amount from its date even though the amount is in part made up of interest. Ramaekers, McPherron & Skiles v. Ramaekers, supra. As a general rule, interest on a judgment or debt is computed up to the time of the first payment, and that payment is first applied to interest and the balance to principal. Camp v. Camp, 14 Neb.App. 473, 709 N.W.2d 696 (2006). Costs are considered part of the judgment. Smeal Fire Apparatus Co. v. Kreikemeier, 271 Neb. 616, 715 N.W.2d 134 (2006). With these principles in mind, we calculate the amount owing to the extent that the record permits.

Although the Bank has provided us with the district court's records regarding payments on the judgment, we do not have the court's records regarding taxable costs before us, and thus, we do not have all of the necessary information to calculate the amount owed on the judgment as of the date of the payment record. However, we do have sufficient records to determine the amount of the judgment, exclusive of costs, as of August 1, 2008. We also have sufficient information to guide the district court in calculating the amount, if any, remaining on the judgment. As determined above, prejudgment interest accrued on the principal amount of $30,000, from July 20, 2006, to August 1, 2008. There are 743 days between July 20, 2006, up to and including August 1, 2008, so the total prejudgment interest amount is $7,328.22 ($30,000 × 12 percent × 743 days ÷ 365 days per year). Thus, on August 1, 2008, the court's summary judgment should have included judgment for $30,000, plus prejudgment interest of $7,328.22, for a judgment of $37,328.22, plus any taxable costs (which were taxed to the Bank in an unspecified amount in the court's original summary judgment). The total judgment in turn bears postjudgment interest of 4.188 percent until satisfied.

The total judgment will accrue interest after August 1, 2008, at the applicable judgment rate of 4.188 percent per annum. However, because we do not have the record of taxable costs, we cannot calculate the precise judgment. Nonetheless, we recognize that the district court's records show that the Bank has made three partial payments since entry of judgment. On October 14, 2009-439 days after entry of judgment — the Bank made two payments totaling $29,921: one in the amount of $14,921 and the other in the amount of $15,000. The other payment of $7,328.22 was made on November 18, 35 days later. As stated above, the partial payments must first be applied to the accrued postjudgment interest and then to the unpaid judgment, including the original principal, prejudgment interest, and costs. The district court would make an initial calculation as of October 14 and then make a further calculation as of November 18. The court would then make a further calculation recognizing accrual of interest on the judgment and any further payments made by the Bank after November 18 and prior to the spreading of this court's mandate.

CONCLUSION

We conclude that OPS is entitled to 12-percent prejudgment interest from July 20, 2006, to the date of entry of summary judgment on August 1, 2008. Thereafter, interest on the entire judgment—including the original principal, prejudgment interest, and taxable costs—accrued at the judgment rate of 4.188 percent. Because the district court's order calculated the amount due as including interest at the 12-percent prejudgment interest rate after the date of judgment, we reverse, and remand for further proceedings in conformity with this opinion.

REVERSED AND REMANDED FOR FURTHER PROCEEDINGS.