
626 F.3d 648 (2010)
Myrella S. FIORENTINO, Plaintiff, Appellee,
v.
RIO MAR ASSOCIATES LP, SE, et al., Defendants, Appellants.
No. 09-2688.
United States Court of Appeals, First Circuit.
Heard October 7, 2010.
Decided December 2, 2010.
*649 Jennifer Suzanne Carroll for appellants.
Eric A. Tulla with whom José Bagué and Rivera, Tulla & Ferrer were on brief for appellee.
Before BOUDIN and HOWARD, Circuit Judges, and BARBADORO,[*] District Judge.
BARBADORO, District Judge.
This case requires us to determine which of several judgments entered by the district court triggers the commencement *650 of interest under the federal postjudgment interest statute, 28 U.S.C. § 1961.

I.
In December of 2000, while vacationing at the Westin Rio Mar Beach Hotel in Puerto Rico, Edward Fiorentino fractured his cervical spine in a swimming accident, rendering him a quadriplegic. A year later, on December 5, 2001, Mr. Fiorentino and his wife Myrella filed suit in the District of Puerto Rico alleging negligence on the part of the hotel and affiliated entities (collectively "Rio Mar") and medical malpractice on the part of the hospital that treated Mr. Fiorentino ("Hospital"). Rio Mar and the Hospital subsequently filed cross-claims against each other.
In June of 2005, the plaintiff[1] settled with the Hospital. Under the settlement agreement, which was not initially disclosed to Rio Mar, the plaintiff received $1.4 million in exchange for releasing the Hospital from further liability. The settlement agreement also provided that
"[i]n the event that the herein appearing settling defendants have or could have any responsibility in this case for the incidents described in the complaint, plaintiffs [sic] assume such responsibility and waive their rights to claim and/or recover from any other defendants or third party, that portion of responsibility attributable to the settling defendants."
See also Rio Mar Assocs., LP, SE v. UHS of P.R., Inc., 522 F.3d 159, 162, 166 (1st Cir.2008) (describing the settlement agreement as akin to a "Pierringer release" or "proportionate share" agreement in which each defendant is responsible for its share of the damages).
The district court turned its attention to what remained of the case shortly after the plaintiff settled her claims against the Hospital. It began by bifurcating the plaintiff's claims against Rio Mar from Rio Mar's cross-claim against the Hospital. As the district court later explained, "[W]hat I've done in this case is ... bifurcation. I have tried plaintiffs' [sic] causes of action against [Rio Mar] first. Once that is over, if there is any reason to go forward with [Rio Mar's] cross-claim against the hospital, then we'll have another jury trial...."
At trial, the court instructed the jury that "[i]f you find that [Rio Mar] ... [is] responsible for Mr. Fiorentino's accident on December 7, 2000, you must also determine that [it is] liable for all damages sustained by him as a consequence of the medical services provided to him to treat the physical injuries [he] suffered...." On August 19, 2005, the jury returned a verdict of $1.844 million against Rio Mar.
A week later, on August 26, the district court granted the plaintiff's motion for judgment against Rio Mar pursuant to Federal Rule of Civil Procedure 54(b), leaving Rio Mar's cross-claim against the Hospital as the only unresolved claim. Although Rio Mar challenged the underlying verdict, it did not object to the Rule 54(b) certification.
Rio Mar obtained a copy of the plaintiff's settlement agreement with the Hospital after the verdict was returned[2] and promptly filed a motion to amend the judgment to reduce the $1.844 million judgment *651 by the $1.4 million the plaintiff had already recovered from the Hospital. While that motion was pending, the Hospital filed a motion to dismiss Rio Mar's cross-claim. On April 3, 2007, the court denied Rio Mar's motion to amend the judgment, granted the Hospital's motion to dismiss Rio Mar's cross-claim, and cleared the way for an appeal by entering a final judgment on all issues.
This court affirmed the jury's verdict on both liability and damages, but concluded that the district court had erred in denying Rio Mar "some process by which it could test how the plaintiff's total damages $1,844,000should be allocated as between it and the Hospital." Rio Mar, 522 F.3d at 164, 168. The decision went on to explain that, although a dollar-for-dollar credit for the $1.4 million settlement was not warranted, Rio Mar was entitled to a setoff for the proportionate share of the plaintiff's damages that were caused by the Hospital's negligence. See id. at 166-67. Consequently, the court vacated the denial of Rio Mar's motion to amend the original judgment, reversed the dismissal of Rio Mar's cross-claim against the Hospital, and remanded the case for a second trial on Rio Mar's cross-claim. Id. at 167-68.
On remand, the jury in the second trial found that Rio Mar was 30 percent at fault and the Hospital was 70 percent at fault. Accordingly, on October 30, 2009, the district court granted Rio Mar's motion to alter the original $1.844 million judgment and reduced the amount Rio Mar owed to $553,200 (30 percent of $1.844 million). At the same time, the district court granted the plaintiff's request for postjudgment interest from the date of the original judgment, and issued an amended judgment ordering relief consistent with its decisions.

II.
Rio Mar challenges the district court's determination that postjudgment interest began to accrue on August 26, 2005, when the court first entered judgment. Rio Mar's primary argument is that the original judgment should not have started the interest clock because the extent of its liability was not determined until the Hospital's proportionate share of the liability was ascertained and deducted from the original verdict. Alternatively, Rio Mar argues that postjudgment interest should not have run from the date of the original judgment because the judgment did not comply with Rule 54(b). We address each argument in turn under the de novo standard of review. Radford Trust v. First Unum Life Ins. Co. of Am., 491 F.3d 21, 24 (1st Cir.2007) (explaining that the determination as to when postjudgment interest begins to run presents a legal issue that is reviewed de novo).

A.
The postjudgment interest statute applies to "any money judgment in a civil case recovered in a district court." 28 U.S.C. § 1961(a). Interest begins to run "from the date of the entry of the judgment." Id. The statute does not explain what should happen when the original judgment is altered, but both Supreme Court and First Circuit precedents provide guidance.
In Kaiser Aluminum & Chemical Corp. v. Bonjorno, 494 U.S. 827, 110 S.Ct. 1570, 108 L.Ed.2d 842 (1990), the Supreme Court considered whether postjudgment interest should run from a judgment that was later vacated. In that case, after a jury verdict and judgment in the plaintiff's favor, the district court ordered a new trial on damages only because the evidence did not support the jury's damages award. Id. at 830, 110 S.Ct. 1570. The retrial resulted *652 in a new damages determination that was upheld on appeal. Id. Noting that "[t]he purpose of postjudgment interest is to compensate the successful plaintiff for being deprived of compensation for the loss from the time between the ascertainment of the damages and the payment by the defendant," id. at 828, 110 S.Ct. 1570, the Supreme Court held that postjudgment interest did not begin to run with the entry of the initial judgment because "damages have not been `ascertained' in any meaningful way" by a verdict that is not supported by sufficient evidence, id. at 836, 110 S.Ct. 1570 (internal quotations omitted).
In Cordero v. De Jesus-Mendez, 922 F.2d 11 (1st Cir.1990), we were faced with a case in which a new trial was required on damages because the court's instructions to the jury may have led it to award duplicative damages. Id. at 15-16. In holding that postjudgment interest should run from the date of the original judgment, we distinguished Kaiser because sufficient evidence had been introduced during the first trial in Cordero to support the original damages award. Id. at 18.
More recently, in Radford Trust, 491 F.3d at 24, the district court awarded partial summary judgment to the plaintiff on liability in an ERISA case and determined that the plaintiff was entitled to collect twenty-four months of benefits. Id. at 23. Judgment was entered on the partial summary judgment order, but the amount that was due to the plaintiff could not be determined until later in the case after the benefits due had been calculated and a substantial legal issue concerning the applicability of a claimed offset for Social Security benefits had been resolved. Id. We held that the original judgment was not a "money judgment" and therefore did not start the postjudgment interest clock because the judgment "left open the possibility that the parties would dispute the amount of damages." Id. at 24.
The parties draw different conclusions from these precedents. The plaintiff argues that this case is controlled by Cordero because the jury's verdict on liability was not disturbed, judgment was entered for a sum certain, and sufficient evidence was produced during the first trial to support the damages that were ultimately awarded. Rio Mar argues that Radford Trust is determinative because, as in that case, the original judgment did not finally establish the specific amount that the defendant owed to the plaintiff.
We conclude that the plaintiff has the better argument. The original judgment in the present case followed a trial in which Rio Mar was found liable and the plaintiff's total recoverable damages were assessed. The jury's liability determination was upheld on appeal and no credible argument was advanced that the damages determination was insupportable. Although the original judgment was later modified, all of the damages that were ultimately awarded were embodied in the original judgment. See Tinsley v. Sea-Land Corp., 979 F.2d 1382, 1383 (9th Cir. 1992) (finding that first judgment meaningfully ascertained damages where finding of ship's unseaworthiness and total damages figure were affirmed despite remand to determine plaintiff's comparative negligence and to reduce the award accordingly). The case is thus indistinguishable from Cordero and quite different from Radford Trust, where we held that the original judgment did not qualify as a "money judgment" under the statute.
The result we reach is also consistent with the purpose that underlies the postjudgment interest statute. Rio Mar has retained the use of the money that was ultimately awarded to the plaintiff by the 2009 judgment, even though both Rio *653 Mar's liability to the plaintiff and the total amount of plaintiff's damages were determined as of the date of the original judgment in August 2005. Where, as in this case, the damages that are ultimately awarded are embodied in an original money judgment that is later reduced but that is otherwise unassailable, there is no good reason why the defendant should not be required to compensate plaintiff for her loss of the use of the money embodied in the original judgment from the time that the original judgment issued.

B.
Rio Mar also argues that postjudgment interest should not accrue from the original Rule 54(b) judgment even if the judgment meaningfully ascertained the plaintiff's damages because the judgment did not include the express findings required by Rule 54(b) and, in any event, it should not have been issued while Rio Mar's cross-claim remained pending.[3] We hold that Rio Mar has forfeited its right to raise these arguments by failing to present a timely challenge to the Rule 54(b) judgment in the district court.
Rule 54(b) permits "the court [to] direct entry of a final judgment as to one or more, but fewer than all, claims or parties only if the court expressly determines that there is no just reason for delay." Fed. R.Civ.P. 54(b). A Rule 54(b) judgment can have both jurisdictional and non-jurisdictional consequences. Compare Kersey v. Dennison Mfg. Co., 3 F.3d 482, 485-86 (1st Cir.1993) (holding that circuit court lacks appellate jurisdiction when district court abuses its discretion in issuing Rule 54(b) certification), with Fratus v. Republic W. Ins. Co., 147 F.3d 25, 29-30 (1st Cir.1998) (recognizing that entitlement to postjudgment interest may be triggered by a proper Rule 54(b) certification). When a proper Rule 54(b) judgment is a prerequisite to appellate jurisdiction, the court must undertake its own inquiry on the subject and the right to raise the issue on appeal cannot be lost through inattention. See Spiegel v. Trs. of Tufts Coll., 843 F.2d 38, 43 (1st Cir.1988) (noting that appellate court has duty to assess the sufficiency of a Rule 54(b) judgment sua sponte when it is the basis for a claim of appellate jurisdiction). In contrast, when a Rule 54(b) judgment has been relied on only for the non-jurisdictional purpose of determining when postjudgment interest should begin to run, a challenge to the judgment is subject to the general rule that appellate arguments may be lost by failing to present them in the district court. See Dávila v. Corporación de P.R. Para La Difusión Pública, 498 F.3d 9, 14-15 (1st Cir.2007) (describing forfeiture rule).
In the present case, the district court's Rule 54(b) judgment had no effect on this court's appellate jurisdiction. The first appeal was not taken until after the district court had dismissed the cross-claim, denied the motion to amend the judgment, and entered a final judgment with respect to all claims in 2007. The current appeal was taken from the final judgment entered in 2009 following the trial on Rio Mar's cross-claim. Thus, Rio Mar's challenge to the Rule 54(b) judgment is non-jurisdictional and, therefore, subject to forfeiture if it was not properly preserved for appeal.
*654 Forfeited claims are subject to review only for plain error. Tasker v. DHL Ret. Sav. Plan, 621 F.3d 34, 40 (1st Cir.2010). Accordingly, such claims cannot succeed unless "the appellant demonstrates that (1) an error occurred (2) which was clear or obvious and which not only (3) affected the [appellant's] substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of the judicial proceedings." Dávila, 498 F.3d at 14-15 (internal citations and quotation marks omitted).
Regardless of whether the district court erred in issuing the Rule 54(b) judgment, any such error was not so grave as to seriously threaten the fairness, integrity, or reputation of the proceedings. The only effect of the allegedly deficient judgment was to trigger the accrual of postjudgment interest on August 26, 2005. Far from causing unfairness or undermining the integrity of this litigation, the resulting interest award merely requires Rio Mar to pay a reasonable interest rate for the time that it controlled the funds at issue. We need go no further. Because even an erroneous Rule 54(b) judgment would not undermine the fairness, integrity, or reputation of these proceedings, Rio Mar's challenge to the judgment cannot prevail under plain error review.

III.
For the foregoing reasons, we affirm the district court's award of postjudgment interest running from the original judgment on August 26, 2005.
NOTES
[*]  Of the District of New Hampshire, sitting by designation.
[1]  Mr. Fiorentino died of unrelated causes prior to trial and Mrs. Fiorentino moved forward with the suit as both his personal representative and on her own behalf. Thus, we refer to Mrs. Fiorentino when we use the term "plaintiff."
[2]  Rio Mar filed a motion to compel disclosure of the settlement agreement prior to the trial but the district court did not rule on the motion until after the jury verdict.
[3]  Although Rio Mar contends otherwise, its argument, at most, would prevent interest from starting to run until April 3, 2007, when the court entered a final judgment disposing of both the cross-claim and the motion to amend the original judgment. At that point, a final judgment had been entered with respect to all claims and any deficiency in the Rule 54(b) judgment would not prevent postjudgment interest from beginning to accrue from that date.
