OPINION OF THE COURT

FISHER, Circuit Judge.

William Lindsay, Jr. appeals his conviction by jury for mailing a threatening communication in violation of 18 U.S.C. § 876 and making false statements in violation of 18 U.S.C. § 1001. He argues the District Court abused its discretion in admitting prior bad acts evidence in violation of Federal Rules of Evidence 404(b) and 403, and that it erred in interpreting the "threat to injure" requirement of 18 U.S.C. § 876. Because we conclude that the District Court properly allowed the evidence and correctly interpreted § 876, we will affirm Lindsay's conviction.

I.

We write exclusively for the parties, who are familiar with the factual context and legal history of this case. Therefore, we will set forth only those facts necessary to our analysis.

A.

Lindsay's appeal arises out of his conviction for mailing an envelope containing a powdery substance that appeared to be anthrax to the Pennsylvania Bureau of Unemployment Compensation (the "Bureau") and subsequently lying to authorities about his involvement in doing so. He has a history of contentious interactions with the Bureau, which is the state agency that handles benefits for unemployed citizens, including the distribution of unemployment compensation benefits, as well as the collection of any Bureau overpayments made to individuals later deemed ineligible for benefits. Lindsay had collected unemployment benefits from the Bureau around early 2004, but in April 2004, the Bureau first notified him that he had received nearly $1,000 more than he was eligible for. The Bureau continued to contact Lindsay by mail on a quarterly basis in an attempt to secure his reimbursement of the overpayment, but he consistently refused to repay this amount. In May 2006, Lindsay submitted a new application for unemployment benefits, which the Bureau initially granted. However, upon further review, the Bureau reversed its decision and denied Lindsay's claim and his subsequent appeal of its decision in November 2006. The Bureau then sent a letter dated March 2, 2007, notifying Lindsay that he still owed $960 from the Bureau's 2004 overpayment of benefits.

Upon receipt of the letter, Lindsay tore it into small pieces, placed it in the return envelope, added a large quantity of gray powder, and mailed it back to the Bureau on March 16, 2007. The Bureau received the letter on March 20, 2007, and when Kim Gottshall, a Bureau employee, opened the envelope, gray powder fell out, covering her and her workstation. Gottshall alerted her supervisor, who contacted the building safety officer, who then summoned the Capitol police, quarantined ten employees, and evacuated thirty-six additional employees from the office. The police were unable to test the powder, so they contacted U.S. Postal Inspector Michael Bond. Inspector Bond determined at the scene that the gray powder was non-hazardous and the letter was a hoax, but took custody of the envelope and its contents. Gottshall later testified at trial that, upon opening the envelope, she thought she had possibly been exposed to something dangerous, but that she did not fear future injury from Lindsay.

During his subsequent investigation, Inspector Bond pieced the torn-up paper together and determined that it was the March 2, 2007 letter the Bureau sent to Lindsay. He also discovered Lindsay's history of adverse dealings with the Bureau. He then interviewed Lindsay, who denied mailing or handling the letter. Lindsay told Inspector Bond that he shreds all letters he receives from the Bureau and throws them in the trash at his boarding house residence. Lindsay intimated that someone else had removed the contents of the shredded letter from the common trash bin, placed it in the return envelope along with the gray powder, and mailed it to the Bureau in an attempt to frame him; Lindsay suggested that perhaps his estranged wife, Dawn Lindsay, might have done so.

Further investigation contradicted Lindsay's statements to Inspector Bond. A June 2007 fingerprint analysis identified Lindsay's right index fingerprint, and no other fingerprints, on the envelope; Dawn was apparently out of the country when the envelope was mailed; and additional evidence indicated Lindsay had a motive to frame his estranged wife because they had a bitter separation period, during which Lindsay left threatening messages on Dawn's voice mail and was found in contempt of court for violation of a protection from abuse ("PFA") order.

Lindsay was arrested and charged in a two-count indictment for mailing a threatening communication in violation of 18 U.S.C. § 876 and making false statements to authorities during the subsequent investigation in violation of 18 U.S.C. § 1001. During Lindsay's pretrial detention, his cellmate reported to investigators, and later testified at trial, that Lindsay told the cellmate that he mailed the letter to the Bureau and then attempted to falsely implicate Dawn due to their hostile separation.

B.

Lindsay pleaded not guilty to the crimes and proceeded to trial. His counsel filed a motion in limine seeking to exclude motive evidence from the trial, including PFA orders, indirect criminal contempt charges, and other examples of Lindsay's problems with anger or aggression. The District Court deferred its decision on the motion and, at trial, decided to exclude evidence of the PFA orders, the contempt charges, and a recording of a threatening voice mail Lindsay left for Dawn, on the basis that this evidence was more prejudicial than probative. However, the District Court allowed the Government to elicit testimony regarding, and argue during opening and closing about, Lindsay's history of disputes with the Bureau and his contentious separation from and child custody disputes with Dawn, to the extent that this evidence went to Lindsay's motive to commit the crimes charged. Lindsay's counsel objected numerous times during the course of the trial and the District Court considered each objection. At the close of trial, the District Court carefully instructed the jury on the limited use it could make of the motive evidence.

The jury convicted Lindsay of both charges. Lindsay filed a motion for a new trial based on the admission of the motive evidence, and a motion for a judgment of acquittal, arguing that mailing an envelope with powder does not satisfy the "threat to injure" requirement of 18 U.S.C. § 876. The District Court denied both motions, and later sentenced Lindsay to twenty-seven months of imprisonment and two years of supervised release. Lindsay filed this timely appeal.

II.

The District Court had jurisdiction pursuant to 18 U.S.C. § 3231, and we exercise jurisdiction over this appeal pursuant to 28 U.S.C. § 1291.

"We review the District Court's decision to exclude or admit evidence for an abuse of discretion, but we have plenary review of the District Court's interpretation of the Federal Rules of Evidence." United States v. Gilmore, 553 F.3d 266, 271 (3d Cir. 2009) (citing United States v. Mornan, 413 F.3d 372, 377 (3d Cir. 2005)). We may reverse the District Court's rulings with respect to Rule 404(b) "only when they are 'clearly contrary to reason and not justified by the evidence.'" United States v. Kellogg, 510 F.3d 188, 197 (3d Cir. 2007) (quoting United States v. Balter, 91 F.3d 427, 437 (3d Cir. 1996)). Likewise, to reverse "a District Court's balancing of probative and unfairly prejudicial qualities of evidence under Rule 403, the District Court's 'analysis and resulting conclusion must be arbitrary or irrational.'" Id. (internal quotation marks omitted) (quoting United States v. Universal Rehab. Servs. (PA), Inc., 205 F.3d 657, 665 (3d Cir. 2000)).

With respect to Lindsay's challenge to the District Court's interpretation of the "threat to injure" requirement of 18 U.S.C. § 876, we "exercise plenary review of the legal issue of statutory construction." United States v. Dees, 467 F.3d 847, 851 (3d Cir. 2006) (citing Lieberman v. Cambridge Partners, L.L.C., 432 F.3d 482, 486 (3d Cir. 2005)); see also United States v. Zavrel, 384 F.3d 130, 132 (3d Cir. 2004).

III. A.

Lindsay argues the District Court abused its discretion in allowing the Government to present evidence at trial of his prior bad acts, including examples of his anger toward Dawn and the Bureau. Rule 404(b) provides that:

"Evidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show action in conformity therewith. It may, however, be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident. . . ."

Fed.R.Evid. 404(b). The Supreme Court has stated that evidence advanced as an exception to Rule 404(b), such as that of a defendant's prior bad acts, is admissible only when: (1) the evidence is offered for a proper purpose; (2) it is relevant under Rules 402 and 104(b); (3) the trial court determines under Rule 403 that "the probative value of the similar acts evidence" is not "substantially outweighed by its potential for unfair prejudice"; and (4) the trial court, under Rule 105, "shall, upon request, instruct the jury that the similar acts evidence is to be considered only for the proper purpose for which it was admitted." Huddleston v. United States, 485 U.S. 681, 691-92, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988); see also United States v. Cross, 308 F.3d 308, 320-21 (3d Cir. 2002). In the instant appeal, Lindsay challenges the presence of factors one and three. Although not contested, we note that, in accord with factors two and four, the prior bad acts evidence at issue was relevant and the District Court properly instructed the jury regarding its limited purpose.

While we have acknowledged that Rule 404(b) is "construed as a rule of inclusion rather than exclusion," United States v. Scarfo, 850 F.2d 1015, 1019 (3d Cir. 1988) (internal quotation marks omitted), we have also cautioned that the government's reasons for introducing prior bad acts evidence may be a combination of showing a "consequential fact as well as . . . impugn[ing] the defendant's character." United States v. Jemal, 26 F.3d 1267, 1272 (3d Cir. 1994) (quoting United States v. Sampson, 980 F.2d 883, 886 (3d Cir. 1992)). Therefore, "when evidence of prior bad acts is offered, the proponent must clearly articulate how that evidence fits into a chain of logical inferences, no link of which can be the inference that the defendant has the propensity to commit the crime charged." United States v. Himelwright, 42 F.3d 777, 782 (3d Cir. 1994) (citing Jemal, 26 F.3d at 1272).

Lindsay argues the Government used evidence of his prior bad acts not to show motive, but rather to demonstrate his propensity to commit the crimes charged, and thereby offered it for an improper purpose. During the course of the trial, the Government elicited evidence that indicated Lindsay had difficulty controlling his anger, particularly toward Dawn. The Government asserts that it offered evidence of Lindsay's anger toward the Bureau and Dawn in order to show his motive for sending the anthrax hoax letter to the Bureau and his subsequent attempt to falsely implicate Dawn for the crime. We agree with the Government that evidence of Lindsay's anger toward Dawn and the Bureau goes directly to his motive to commit the two crimes charged. To the extent that Lindsay argues it was unnecessary for the Government to present evidence demonstrating that he had a motive to suggest someone else's culpability in mailing the letter, we disagree. Lindsay specifically implicated Dawn, and the Government therefore had reason to show Lindsay's incentive for suggesting her involvement in the crime. Thus, we conclude that the District Court's decision to allow evidence of Lindsay's prior bad acts was not clearly contrary to reason or unjustified, and that the evidence was instead admitted for the proper purpose of demonstrating Lindsay's motive to send the anthrax hoax letter to the Bureau and to implicate his estranged wife for the crime.

Lindsay argues, in the alternative, that the District Court abused its discretion in admitting the prior bad acts evidence because the danger of unfair prejudice substantially outweighed the probative value under Rule 403. We have stated that when a district court "engages in a Rule 403 balancing and articulates on the record a rational explanation for its determination, we will rarely disturb its ruling." Id. at 785 (citing Sampson, 980 F.2d at 889). While we recognize that evidence of Lindsay's anger could have had some prejudicial effect on the jury, we cannot conclude that the evidence admitted was so unfair that its potential for prejudice substantially outweighed its probative value. The motive evidence was highly probative because Lindsay's history of adverse interactions with the Bureau provided evidence of his potential motive to send the anthrax hoax letter, and Lindsay's contentious separation from Dawn indicated why he may have attempted to blame her for sending the letter. Further, the District Court limited evidence of Lindsay's anger to exclude past episodes that would have been unduly prejudicial, such as the recording of a threatening voice mail he left for Dawn and his violation of a PFA order. It is not difficult for us to conclude, here, that the District Court's balancing of the evidence in question was not arbitrary or irrational. Therefore, we conclude that all four factors required for the admission of the motive evidence at issue under Rule 404(b) were satisfied and, accordingly, the District Court did not abuse its discretion in admitting this evidence at Lindsay's trial.

B.

Lindsay also argues that the act of mailing an anthrax hoax letter to the Bureau does not, as a matter of law, satisfy 18 U.S.C. § 876 because it does not constitute a "threat to injure." The statute provides:

"Whoever knowingly so deposits or causes to be delivered [by the U.S. Postal Service], any communication with or without a name or designating mark subscribed thereto, addressed to any other person and containing . . . any threat to injure the person of the addressee or of another, shall be fined under this title or imprisoned not more than five years, or both."

18 U.S.C. § 876(c). In United States v. Zavrel, we held that "mailing a white powdery substance intended to cause fear and distress plainly constitutes a communication under § 876." 384 F.3d 130, 134 (3d Cir. 2004). Regarding the statute's "threat to injure" requirement, we stated that "[a] reasonable person opening an envelope containing a white powdery substance, during the height of the anthrax crisis in this country, would doubtless fear immediate and future injury," as the recipients of Rosemary Zavrel's anthrax hoax letters did. Accordingly, we held that the threat of imminent harm alone was sufficient to satisfy this part of the statute, and affirmed Zavrel's conviction. Id. at 136-37.

While Lindsay does not dispute the "communication" element of § 876(c), he argues that his letter did not constitute a "threat to injure" because the Bureau employees affected did not fear future harm from him, and he relies primarily on the dissent in Zavrel for support. However, the Zavrel majority held that fear of imminent harm is sufficient to satisfy § 876's "threat to injure" requirement, but nevertheless concluded as well that an anthrax hoax letter, which "communicates to the intended victim the sender's hostility," could also "create an apprehension of . . . future harm." Id. at 136-37; see also United States v. Evans, 478 F.3d 1332, 1339 (11th Cir. 2007) (holding that § 876(c) "simply does not suggest a temporal limitation to only future actions"); United States v. Davila, 461 F.3d 298, 304 (2d Cir. 2006) (same). We also disagree with Lindsay that Zavrel is factually distinguishable from the instant case merely because Lindsay's letter was determined to be a hoax relatively quickly. Therefore, we conclude that mailing an anthrax hoax letter satisfies the "threat to injure" requirement of § 876 and that Lindsay's actions fell within the proscribed conduct of the statute.

IV.

For the foregoing reasons, we will affirm Lindsay's conviction.