After trial, a jury awarded Adrian Bryant nominal compensatory damages and $ 250,000 in punitive damages for his claim of hostile work environment against his former employer, Jeffrey Sand Company. The district court 1 denied Jeffrey Sand's post-trial motions and granted Bryant's motion for attorney's fees. Jeffrey Sand appeals, and we affirm.

I

We recite the facts ascertained at trial, viewed in the light most favorable to the jury's verdict. Morse v. S. Union Co. , 174 F.3d 917 , 920 (8th Cir. 1999). Bryant worked from 2009 to 2013 for Jeffrey Sand as a deckhand on the Cora , a barge that dredges sand from the Arkansas River. During this period, Bryant's co-workers on the Cora were the foreman, Jerry Skaggs; the pumper, Donald Lambert; and another deckhand, Chad Bateman. Bryant was the only black employee on the barge.

The evidence at trial revealed that Skaggs, Bryant's direct supervisor, engaged in a pattern of racially-motivated abuse. Skaggs taunted Bryant with racial slurs, calling him "nigger," "Kunte Kinte," "spear chucker," "monkey," "bitch," "porch monkey," and "boy," among other names. On at least some occasions, he uttered these epithets in the presence of other employees. Skaggs would give Bryant difficult tasks that he would not assign to the Cora 's white employees. Lambert testified that "a number of times," Skaggs would "get up in [Bryant's] face and use his chest *525 to push [Bryant] around trying to get [Bryant] to fight him."

Bryant complained to his plant manager, Ken Bolton, twice and to the then-president of the company, Joe Wickliffe, four times regarding Skaggs's behavior. He testified that he received no response to his complaints. Bolton testified that, in response to a complaint from Bryant on May 4, 2012, he sent another employee, Randy Marshall, to the Cora for a few days in an attempt to corroborate Bryant's allegation that Skaggs was using racial slurs. After Marshall reported back that he had not heard any slurs, Bolton did no further investigation. Bolton did not attempt to interview Bryant or any other employees. Jeffrey Sand has no written anti-harassment or anti-discrimination policy and no human resources personnel.

Bryant testified that the harassment persisted and that he continued to make complaints after May 2012. He testified about a particular incident on August 7, 2012, when Skaggs made him paint rails in the hot sun and would not allow him to come into the air-conditioned part of the barge or to access water. When Bryant attempted to get out of the sun and told Skaggs that he felt ill, Skaggs responded, "[G]o out there and paint those rails like I told your black ass to," and sent him back outside. Bryant felt lightheaded and experienced chest pains, so he went to Lambert for help. Lambert measured Bryant's blood pressure, which was very high, and convinced Skaggs to call an ambulance. It was later determined that Bryant had suffered a heart attack, and he did not return to work for two weeks.

On January 30, 2013, Clay McGeorge, then the sales director (and now the president) of Jeffrey Sand, received an anonymous email stating: "Hi Clay I want to remain anonymous but I would like to inform you about the racist comments I've overheard the foreman on dredge Cora make." McGeorge alerted Wickliffe and Bolton to the email and Bolton interviewed several employees. Lambert corroborated that Skaggs had made racist comments toward Bryant, but Bolton discounted Lambert as merely a disgruntled employee. Several other employees told Bolton that they had heard second-hand about Skaggs using racial slurs. Bateman, the other deckhand, later admitted that he had authored the anonymous email. He testified that he had not heard Skaggs make racist comments personally, but had heard Bryant complaining about it and believed Bryant's accusations. Bolton did not interview Bryant as part of his investigation. The company took no disciplinary action against Skaggs.

Jeffrey Sand fired Bryant shortly after the investigation into the email, purportedly for absenteeism. Bryant brought this suit under 42 U.S.C. § 1981 on July 13, 2016, alleging a racially hostile work environment and retaliatory termination. The district court granted summary judgment in favor of Jeffrey Sand on the retaliation claim but allowed the hostile-work-environment claim to proceed to trial. The jury found in Bryant's favor and awarded him $ 1.00 in compensatory damages and $ 250,000 in punitive damages. The district court denied Jeffrey Sand's post-trial motions for judgment as a matter of law and to amend the award of punitive damages. It also granted Bryant's motion for $ 64,432.50 in attorney's fees and $ 1,028.15 in costs. Jeffrey Sand appeals.

II

Jeffrey Sand argues it was entitled to judgment as a matter of law because there was insufficient evidence to charge punitive damages to the jury and because Bryant's claim is time-barred. We review the district court's denial of Jeffrey Sand's *526 motion de novo, viewing the facts in the light most favorable to Bryant and drawing all reasonable inferences in his favor. Weitz Co. v. MacKenzie House, LLC , 665 F.3d 970 , 974 (8th Cir. 2012). Judgment as a matter of law is proper if "a party has been fully heard on an issue and there is no legally sufficient evidentiary basis for a reasonable jury to find for that party on that issue." Id. (quoting Fed. R. Civ. P. 50(a)(1) ).

Under either Title VII or § 1981, an award of punitive damages requires the plaintiff to show that his employer engaged in a discriminatory practice with "malice" or "reckless indifference" to his federally protected rights. 42 U.S.C. § 1981a(b)(1) ; Kim v. Nash Finch Co. , 123 F.3d 1046 , 1063 (8th Cir. 1997). This standard may be satisfied when an employer exhibits reckless indifference toward discriminatory actions taken by those serving in a managerial capacity, MacGregor v. Mallinckrodt, Inc. , 373 F.3d 923 , 931 (8th Cir. 2004), or when a supervisor's "sufficiently abusive" behavior manifests malice, Ogden v. Wax Works, Inc. , 214 F.3d 999 , 1009-10 (8th Cir. 2000) (quoting Kimbrough v. Loma Linda Dev., Inc. , 183 F.3d 782 , 785 (8th Cir. 1999) ).

The award of punitive damages is supported by the record. Bryant repeatedly complained to supervisors that his manager, Skaggs, was using racial slurs. Those supervisors never interviewed Bryant in response to his complaints, even though Skaggs's comments evidenced a "clear intent" to discriminate against Bryant based on race. MacGregor , 373 F.3d at 932 . Even when another employee corroborated Bryant's allegations, the company did not take any action to discipline Skaggs or prevent further harassment. Jeffrey Sand also lacked any formal or informal policy prohibiting workplace discrimination. The jury could have reasonably concluded from these facts that Jeffrey Sand exhibited reckless indifference to Bryant's rights. See Williams v. ConAgra Poultry Co. , 378 F.3d 790 , 796 (8th Cir. 2004) ("[W]hen the victim of harassment repeatedly complains to various supervisors of harassment and the harassment is not stopped, a submissible case on punitive damages has been made.").

We also conclude that Bryant's § 1981 claim was timely under the applicable four-year statute of limitations. See Jones v. R.R. Donnelley & Sons Co. , 541 U.S. 369 , 383-85, 124 S.Ct. 1836 , 158 L.Ed.2d 645 (2004) (explaining that federal statute of limitations in 28 U.S.C. § 1658 applies to such claims). "[U]nder federal law one act of the hostile work environment must occur ... within the § 1981 statute of limitations period. If that requirement is met, a party may then recover for all illegal acts that made up the hostile work environment." Madison v. IBP, Inc. , 330 F.3d 1051 , 1061 (8th Cir. 2003). The continuing violation rule applies to punitive, as well as compensatory, damages. See id. at 1060-61 . 2 Thus, in order for Bryant's claim to be timely, at least one act of the hostile work environment must have occurred after July 13, 2012-four years before Bryant filed his complaint.

*527 Several witnesses testified that Skaggs's abuse continued into the limitations period and that Jeffrey Sand was on notice of that abuse. Bryant suffered a heart attack in August 2012 after Skaggs forced him to work in the hot sun without access to water, even after Bryant told Skaggs that he felt ill. The jury readily could have inferred-from Skaggs's own words-that this abuse was motivated by racial animus. Jeffrey Sand was on notice of Skaggs's abuse from Bryant's earlier complaints but was alerted again to the issue in January 2013 when another employee sent an anonymous email asserting that he overheard the abuse. The jury reasonably could have concluded that the company's response to this complaint was inadequate and evidenced a reckless disregard for Bryant's protected rights continuing well into the limitations period. We accordingly find no error in the district court's denial of Jeffrey Sand's motion for judgment as a matter of law.

III

Jeffrey Sand also argues that the jury's award of $ 250,000 in punitive damages violates due process because it is excessive and disproportionate to the nominal compensatory damages award. We review the constitutionality of the punitive damages award de novo. Cooper Indus., Inc. v. Leatherman Tool Grp., Inc. , 532 U.S. 424 , 436, 121 S.Ct. 1678 , 149 L.Ed.2d 674 (2001).

"Juries have considerable flexibility in determining the level of punitive damages." Ondrisek v. Hoffman , 698 F.3d 1020 , 1028 (8th Cir. 2012). An award of punitive damages nonetheless violates due process when it is so "grossly excessive" or "arbitrary" that the defendant failed to receive fair notice of the severity of the penalty that might be imposed. State Farm Mut. Auto. Ins. Co. v. Campbell , 538 U.S. 408 , 416-17, 123 S.Ct. 1513 , 155 L.Ed.2d 585 (2003) ; see BMW of N. Am., Inc. v. Gore , 517 U.S. 559 , 574, 116 S.Ct. 1589 , 134 L.Ed.2d 809 (1996). The Supreme Court has identified three factors that guide our inquiry: "(1) the degree of reprehensibility of the defendant's misconduct; (2) the disparity between the actual or potential harm suffered by the plaintiff and the punitive damages award; and (3) the difference between the punitive damages awarded by the jury and the civil penalties authorized or imposed in comparable cases." State Farm , 538 U.S. at 418 , 123 S.Ct. 1513 .

The degree of a party's reprehensibility is the "most important" factor in our analysis. Id. at 419 , 123 S.Ct. 1513 (quoting Gore , 517 U.S. at 575 , 116 S.Ct. 1589 ); Bowles v. Osmose Utilities Servs., Inc. , 443 F.3d 671 , 675 (8th Cir. 2006). We must consider whether:

the harm caused was physical as opposed to economic; the tortious conduct evinced an indifference to or a reckless disregard of the health or safety of others; the target of the conduct had financial vulnerability; the conduct involved repeated actions or was an isolated incident; and the harm was the result of intentional malice, trickery, or deceit, or mere accident.

State Farm , 538 U.S. at 419 , 123 S.Ct. 1513 . Citing these factors, the district court opined that Jeffrey Sand's conduct was "clearly ... reprehensible." Skaggs's abuse was repeated, not isolated, and involved both verbal racist insults and physical altercations. His actions were not accidental but intentionally malicious. Jeffrey Sand failed to meaningfully investigate repeated complaints from Bryant and other employees. The district court also concluded that Bryant was financially vulnerable because he had a criminal record and so could not easily find another job.

*528 We agree that these facts, viewed in Bryant's favor, show that Jeffrey Sand's actions were "so reprehensible as to warrant the imposition of further sanctions to achieve punishment or deterrence." Id. The company argues that its response to Bryant's complaints was more fulsome than in other cases where we have upheld sizeable punitive damage awards. See, e.g. , Henderson v. Simmons Foods, Inc. , 217 F.3d 612 , 619 (8th Cir. 2000) (affirming award of $ 100,000 in punitive damages where employer only half-heartedly responded to plaintiff's numerous complaints of sexual harassment); Blackmon v. Pinkerton Sec. & Investigative Servs. , 182 F.3d 629 , 636-37 (8th Cir. 1999) (reinstating jury's $ 100,000 punitive damages award where employee was sexually harassed by her supervisors, company failed to investigate her complaints or take remedial action, and company engaged in retaliation). We disagree. Jeffrey Sand's indifference to Bryant's complaints was no less egregious than the meager efforts of the employers in Henderson and Blackmon . In particular, Skaggs's verbal and physical abuse went unchecked even after another employee corroborated Bryant's allegations, and even after Skaggs placed Bryant at risk of serious injury. These circumstances are at least as repugnant as those in Williams , where the plaintiff received $ 600,000 in punitive damages after his supervisor regularly swore at him, used racist language, and treated him differently than white employees. See 378 F.3d at 798-99 .

The next guidepost for our consideration is proportionality. While punitive damage awards are ordinarily within a single-digit multiple of the compensatory damage award, this ratio's usefulness diminishes when the jury awards only nominal damages. The Supreme Court has "consistently rejected the notion that the constitutional line is marked by a simple mathematical formula" comparing compensatory and punitive damages. Gore , 517 U.S. at 582 , 116 S.Ct. 1589 . "Punitive damages may withstand constitutional scrutiny when only nominal or a small amount of compensatory damages have been assigned, even though the ratio between the two will necessarily be large." JCB, Inc. v. Union Planters Bank, NA , 539 F.3d 862 , 876 (8th Cir. 2008).

As in prior cases addressing nominal damages, we decline to place undue weight on the mathematical ratio between compensatory and punitive damages. See, e.g. , Haynes v. Stephenson , 588 F.3d 1152 , 1158 (8th Cir. 2009). The "general goal" of the proportionality factor is to ensure that punitive damages are "proportional to the actual injury suffered." Arizona v. ASARCO LLC , 773 F.3d 1050 , 1056 (9th Cir. 2014) (en banc). The higher award of punitive damages is justified in this case because "a particularly egregious act has resulted in only a small amount of economic damages" and "the monetary value of noneconomic harm might have been difficult to determine." Gore , 517 U.S. at 582 , 116 S.Ct. 1589 . The jury may not have been able to easily quantify the monetary value of Bryant's injuries. But that does not mean the indignities he suffered were insubstantial, or that a punitive damages award of $ 250,000 is unreasonable. See id. at 583 , 116 S.Ct. 1589 ("[A] general concern of reasonableness properly enters into the constitutional calculus." (cleaned up) (quoting TXO Prod. Corp. v. All. Res. Corp. , 509 U.S. 443 , 458, 113 S.Ct. 2711 , 125 L.Ed.2d 366 (1993) )).

The final factor for consideration is how the award compares to penalties authorized for similar misconduct. Jeffrey Sand emphasizes that, had Bryant brought his hostile-work-environment claim under Title VII, any award of punitive damages would be statutorily capped at $ 50,000 *529 because the company has fewer than 101 employees. 42 U.S.C. § 1981a(b)(3)(A). But Bryant brought his claim under § 1981, so Jeffrey Sand was on fair notice that the jury's award could exceed the Title VII cap. See Williams , 378 F.3d at 798-99 (declining to find any "constitutionally required ratio between § 1981 damages awards and the Title VII cap"). Considering the egregiousness of Jeffrey Sand's conduct, the company should have been aware that the trial could result in a substantial monetary award if the jury concluded that one was "necessary to deter future misconduct." Gore , 517 U.S. at 584 , 116 S.Ct. 1589 . We conclude that the jury's punitive damages award was constitutionally sound.

IV

Finally, Jeffrey Sand argues that the district court erred in awarding Bryant attorney's fees. A prevailing party in a § 1981 action may be awarded a reasonable attorney's fee. 42 U.S.C. § 1988 (b). "Attorney's fees are within the broad discretion of the district court and will not be reversed absent an abuse of discretion." Hanig v. Lee , 415 F.3d 822 , 825 (8th Cir. 2005). To calculate attorney's fees, courts typically begin by using the lodestar method, which multiplies the number of hours reasonably expended by reasonable hourly rates. Brewington v. Keener , 902 F.3d 796 , 805 (8th Cir. 2018). "When determining reasonable hourly rates, district courts may rely on their own experience and knowledge of prevailing market rates." Hanig , 415 F.3d at 825 .

Jeffrey Sand does not dispute that Bryant was the prevailing party at trial and that the hours expended by Bryant's counsel were reasonable. Instead, it argues only that the district court erroneously accepted the lodestar rate of $ 350 per hour based solely on Bryant's counsel's representation that he had been awarded fees at this rate in similar recent cases. Jeffrey Sand argues that the district court should have demanded a sworn affidavit attesting that this was his counsel's "normal" hourly rate.

The law imposes no such requirement. Bryant's counsel averred that his requested rate was "reasonable and commensurate" with his qualifications and extensive experience. He supported that statement by providing a list of recent fee awards he had obtained, including one from only a few months prior in which the same district court had concluded his $ 350 rate was reasonable. Jeffrey Sand has produced no evidence undermining the reasonableness of the rate. The district court's decision to accept the rate as reasonable, in light of its own experience and knowledge, was not an abuse of discretion.

Accordingly, we affirm the judgment of the district court.