KANNE, Circuit Judge.

Carl Courtright was convicted of production, possession, and receipt of child pornography and sentenced to life plus ten years in prison. Courtright now appeals his conviction, claiming that evidence of a prior sexual assault was erroneously admitted at trial and that certain jury instructions were improper. While we agree that the evidence of Courtright's prior sexual assault was admitted erroneously and that some of the jury instructions may have been incorrect, reversal is unnecessary because these errors were harmless. As such, we affirm Courtright's conviction.

I. BACKGROUND

Courtright fashions himself as something of an amateur photographer. Unfortunately, the subjects of his photographs are underage girls engaged in various sexual activities. Courtright first took up his hobby in 1998, when he met a fifteen-year-old girl, L. Miller, through his roommate. After forging a friendship with Miller, Courtright persuaded Miller to pose for explicit photographs. As part of Courtright's photo shoot, he directed Miller into various poses and took pictures of her exposed breasts and genitalia. At one point during the shoot, Courtright told Miller that he had some medical knowledge and needed to examine her. He then inserted his fingers into her vagina. After this conduct came to light, Courtright pled guilty to aggravated sexual abuse pursuant to 720 ILCS 5/12-16(a)(2). As a result of that conviction, Courtright had to register as a sex offender.

In 2007, the Illinois Attorney General began a probe of social networking sites to determine whether registered sex offenders were active users. This investigation revealed that Courtright had an account on Myspace.com. Officers used the Myspace.com records to learn Courtright's IP address, which they fed into a database of addresses found to have offered child pornography for distribution on the Internet. The IP address Courtright used to check his Myspace.com account matched one used to download child pornography through a file-sharing program called Limewire. Officers used this information to obtain a warrant to search Courtright's residence, where he lived with his parents.

During the search of Courtright's home, officers found several computers and computer equipment. A forensic preview of a laptop found in Courtright's bedroom showed that the hard drive contained child pornography images downloaded through Limewire. In subsequent interviews, Courtright admitted that he was the only user of Limewire in the home and of the laptop found in his bedroom. He went on to state, somewhat ironically, that he downloaded the images after watching an episode of To Catch a Predator.1 He claimed that he was curious about how pornographic images were disseminated and that, after satisfying his curiosity, he immediately deleted the images.

A more detailed analysis of the computers seized from Courtright's home revealed a large inventory of images depicting child pornography, many of which were not deleted. Some of the images were found on a desktop that was password-protected for Courtright's sole access, while others were found on a laptop that Courtright had already conceded was for his lone use. The computers' records also showed that, on multiple occasions, the pornographic images were opened around the same time that Courtright's online bank account or social networking profile was accessed. An analysis of the image files showed that the majority of them were downloaded off of the Internet, while eleven others were transferred to the hard drive directly from a Hewlett-Packard camera. The same girl was depicted in each of the camera photos, but she was not readily identifiable—her face was obscured and bandages were applied to identifying marks.

Officers later identified the mystery girl as S.J., a fourteen-year-old who lived with her father in the garage of a residence owned by Courtright's parents. During a teary interview, S.J. recounted the events that led to the photos being taken. She told officers that Courtright first bought her gifts and let her sleep in a bedroom he often occupied in the adjacent house. After the two became acquainted, Courtright offered to give her lotion rubs and massages, going so far as to rub lotion on her buttocks while telling her to "think of him as a doctor" on one occasion.

S.J. claimed that Courtright eventually asked her to pose for explicit photos. After initially rebuking Courtright's advances, S.J. agreed. At Courtright's direction, S.J. sat in a director's chair and posed in various stages of undress while Courtright took pictures of her. For one photo, Courtright told S.J. to spit on her hand and masturbate. S.J. told officers that Courtright also put his fingers in her vagina during the shoot, telling her that he knew "medical stuff" and needed to "examine" her. Officers later confronted Courtright with this information. While he admitted to owning a Hewlett-Packard camera, he denied ever taking photos of S.J. and had no explanation for how the photos got onto his hard drive.

Based on information from Courtright's computers, officers also learned that Courtright had been ordained as a minister by an online company. He used this status to create an online ministry and then manufactured fake donation checks. Courtright deposited the checks into an account and then used the sums to make a number of large purchases.

On February 18, 2009, Courtright was charged with one count of production of child pornography, two counts of possession of child pornography, one count of receipt of child pornography, and one count of bank fraud. Prior to trial, the government filed a notice indicating that it planned to introduce evidence of Courtright's prior sexual assault of L. Miller and of Courtright's status as a registered sex offender. Courtright conceded that his status as a sex offender was intertwined and admissible, and the district court admitted it on that basis. But Courtright objected to the admission of his prior sexual assault. The district court ultimately agreed with the government and, after determining that the evidence was relevant and not unduly prejudicial, admitted it pursuant to Rule 413.

The trial began on March 2, 2009, and lasted five days. On the first day of testimony, the district court gave an erroneous elements instruction to the jury, to which the government objected. On the following day, the district court recognized the problem and corrected the elements instruction, despite Courtright's argument that the initial instruction was correct.

During the remainder of the trial, the government called fourteen witnesses. The witnesses included forensic experts and investigating officers who had participated in the investigation, who testified to the contents of the hard drives and Courtright's statements to law enforcement, respectively. S.J. also testified as to all of the details she had previously told officers, with one exception—she did not state that Courtright had inserted his fingers into her vagina during the photo shoot. S.J.'s father testified that Courtright had asked him about taking photographs of S.J. Courtright's cellmate testified that Courtright had admitted to taking pictures of a young girl. Finally, L. Miller testified about the details of Courtright's prior sexual assault, with the district court giving a limiting instruction before and after her testimony. Courtright presented no witnesses.

Following closing arguments, the jury found Courtright guilty of all counts. The district court sentenced him to life plus 120 months' imprisonment for the production count, 240 months' imprisonment for the possession counts, 480 months' imprisonment for the receipt count, and 360 months' imprisonment for the fraud count. Courtright timely appealed his conviction.

II. ANALYSIS

On appeal, Courtright argues that the district court made a number of errors warranting a new trial. He claims that evidence of his prior sexual assault was erroneously admitted, that a number of the jury instructions were improper, and that the cumulative effect of these errors deprived him of a fair trial. We will address each argument in turn.

A. Prior Bad Act

Courtright's first claim is that the district court erred when it admitted evidence of his prior sexual assault. We review a district court's interpretation of the rules of evidence de novo and its decision to admit evidence for an abuse of discretion, United States v. Rogers, 587 F.3d 816, 819 (7th Cir.2009), mindful that evidentiary errors do not require reversal if they were harmless, United States v. Taylor, 604 F.3d 1011, 1016 (7th Cir.2010).

The district court admitted the prior sexual assault pursuant to Federal Rule of Evidence 413. Rule 413 provides, in relevant part:

Fed.R.Evid. 413(a). In admitting the evidence, the district court interpreted the word "accused" broadly, holding that Rule 413 is triggered when a defendant has been verbally accused of sexual assault during the course of an investigation into a separate offense. Courtright takes issue with this interpretation of Rule 413, arguing that Rule 413 applies only when a party has been charged with an "offense of sexual assault" in the indictment.

We do not agree with the district court's reading of Rule 413. The district court's interpretation was based on the fact that Rule 413 uses the word "accused" instead of "charged" to indicate when it is triggered. The government defends the district court's reading by noting that, because the rule drafters use the word "charged" elsewhere, the use of the word "accused" in this instance should be given broader effect. We believe the government makes too much of this distinction— at the time Rule 413 was drafted (and today), the word "accused" was often used in a technical sense to describe someone who was charged with a crime. See Black's Law Dictionary 22-23 (6th ed. 1990) (defining "accuse" as "to bring a formal charge against a person"); Webster's Third New International Dictionary 14 (1986) (defining "accuse" as, among other things, "to charge with an offense judicially or by public process"). There is nothing in the text or committee notes of Rule 413 to indicate that the word "accused" was used in a broader fashion.

We find additional support for this reading of Rule 413 in nearby Rule 412. Rule 412 permits the admission of a victim's sexual behavior by the accused in certain limited circumstances. The committee notes to Rule 412 specify that, for this Rule, "accused" is meant in a broader, "non-technical sense," and that there is "no requirement that there be a criminal charge pending against the person or even that the misconduct would constitute a criminal offense" before evidence of a victim's sexual behavior can be admitted. Fed.R.Evid. 412 advisory committee's note. Rule 413 provides no similar clarification for the use of the word "accused," nor do the rest of the rules.

We therefore conclude that Rule 413 uses the term "accused" in the more narrow, technical sense generally invoked throughout the federal rules.2 See 23 Charles Alan Wright & Michael W. Graham, Federal Practice and Procedure § 5413, at 549-50 (Supp. 2010) ("Since [Rule 413] does not employ the language of Revised Rule 412, it seems reasonable to suppose that the words are used in the technical sense; that is, the evidence of other sexual crimes is only admissible against a criminal defendant and only if the crime charged is sexual assault.").

So we are left with the district court's admission of evidence pursuant to an erroneous interpretation of Rule 413. "[A]n error of law is, by definition, an abuse of discretion." Almonacid v. United States, 476 F.3d 518, 521 (7th Cir.2007). But this error would be harmless, and no new trial would be necessary, if the evidence was admissible under another rule. United States v. Albiola, 624 F.3d 431, 437 (7th Cir.2010). The government argues that the error was harmless because the evidence was also admissible pursuant to Rule 404(b). Evidence is admissible under Rule 404(b) if:

United States v. Stotler, 591 F.3d 935, 941 (7th Cir.2010).

The government claims that the first prong is satisfied because the prior bad act evidence was admissible to prove Courtright's intent, motive, or identity. We agree that the evidence was at least probative of Courtright's motive. L. Miller's testimony shows that, in the past, Courtright engaged in sexually explicit contact with an underage girl. This prior instance of sexual misconduct tends to establish a motive for the crime against S.J.: Courtright may have induced S.J. to take the pictures so that he could again achieve sexual gratification with a minor. See United States v. Sebolt, 460 F.3d 910, 917 (7th Cir.2006) (finding that prior bad acts toward a young victim may show that a defendant has a sexual interest in that age group and therefore provide evidence of a motive to commit future sexually motivated crimes against children); United States v. Cunningham, 103 F.3d 553, 556 (7th Cir.1996) ("Most people do not have a taste for sexually molesting children. As between two suspected molesters, then, only one of whom has a history of such molestation, the history establishes a motive that enables the two suspects to be distinguished.").

The government also claims that the second and third prongs are satisfied, and we agree. Admittedly, there was one distinction between the two crimes—in the first, Courtright actually sexual assaulted the victim during the course of the photo shoot, while in the second he only encouraged her to touch herself in an explicit manner while taking the photographs. But the two crimes are still similar in important respects. In both crimes, the perpetrator took time to develop a relationship with the victims, bought gifts for them, and engaged in sexually explicit acts with them under the auspices of providing medical advice. In addition, although there was a nine-year gap between the assault of L. Miller and the photo shoot with S.J., Courtright was incarcerated— and thus incapacitated—for a large part of that time. Finally, Courtright was found guilty by a jury of the prior bad act.

The government finally argues that the last prong is satisfied because the district court found the evidence probative, analyzed it under Rule 403, and determined that any prejudice could be cured via a limiting instruction. But, as Courtright correctly points out, the trial court conducted a Rule 403 prejudice analysis on the premise that the evidence was being admitted under Rule 413. Rule 413 expressly allows the government to use prior bad acts to show that a defendant acted in conformity therewith—in other words, for propensity purposes. Accordingly, a Rule 413 prejudice analysis is limited and focuses on other sources of prejudice. Rogers, 587 F.3d at 823.

Unlike a prejudice analysis for Rule 413, a Rule 404(b) prejudice determination also evaluates whether the evidence will be improperly used by the jury as proof of propensity. Id. The risk of a jury using the evidence for this purpose is particularly high where, as here, the prior bad act may establish an addiction to something— like pyromania, drug use, or sexual gratification through the assault of minors—and thus a motive to commit that crime again. Cunningham, 103 F.3d at 556. Especially in sex crimes, motive and propensity often dovetail, and a court must be careful "about admitting under the rubric of motive evidence that the jury is likely to use instead as a basis for inferring the defendant's propensity." Id. at 557. The government does not address this propensity problem in its brief, and "we are not in the business of formulating arguments for the parties." United States v. McClellan, 165 F.3d 535, 550 (7th Cir.1999). Accordingly, the government's Rule 404(b) argument is incomplete and waived.

But even assuming the prior bad act evidence was not admissible, reversal is unnecessary if the error had no effect on the outcome of the trial. United States v. Conner, 583 F.3d 1011, 1025 (7th Cir.2009). We are convinced that is the case here. Courtright's status as a sex offender was already before the jury, and thus the likelihood that the prior bad act testimony from L. Miller had any effect on the jury is negligible. More importantly, the evidence of Courtright's guilt was overwhelming. See United States v. Dennis, 497 F.3d 765, 769-70 (7th Cir.2007) (finding harmless error when there was abundant evidence of the defendant's guilt). The images of S.J., along with numerous other images of child pornography and data on the bank fraud scheme, were found on two computers at Courtright's home. Courtright admitted that one of the computers was his, and only Courtright had access to the second. Courtright also stated to law enforcement that he had downloaded a number of the child pornography images found on his hard drives. Furthermore, S.J. testified that Courtright took the pictures of her, her father testified that Courtright asked about taking pictures of S.J., and Courtright's cellmate testified that Courtright confessed to taking pictures of a young girl. Finally, Courtright called no witnesses and offered no evidence of his innocence, lending further support to a finding of harmless error. See United States v. Taylor, 522 F.3d 731, 735 (7th Cir.2008).

B. Jury Instructions

Courtright's second claim on appeal is that a number of the jury instructions were erroneous. Courtright did not object to these instructions at trial, so we review for plain error. United States v. Noel, 581 F.3d 490, 499 (7th Cir.2009). To establish plain error, Courtright must show that there was an actual error, that the error was plain, that the error "affect[ed] the defendant's substantial rights," and that the error "seriously affect[ed] the fairness, integrity, or public reputation of judicial proceedings." United States v. Canady, 578 F.3d 665, 670 (7th Cir.2009). Plain error review of jury instructions is "particularly light handed," and we will reverse only if the error was of such a "great magnitude that it probably changed the outcome of the trial." United States v. Moore, 115 F.3d 1348, 1362 (7th Cir.1997).

Courtright first takes issue with the initial elements instruction, which was given as a preliminary instruction at the beginning of the trial. That instruction informed the jury that the government had to prove an additional element for the production and possession counts—namely that the "defendant had been previously convicted of a sex offense in which a minor was the victim" for the production count and that the "defendant had a prior conviction. . . relating to aggravated sexual abuse, sexual abuse, or abusive sexual conduct involving a minor . . . or the production, possession, receipt, mailing, sale, [or] distribution . . . of child pornography" for the possession count. The government realized the additional elements were erroneous and objected. Courtright countered that the instruction was appropriate, but the district court corrected the instruction the following day.

We need not determine whether the initial elements instruction was erroneous because Courtright has waived this claim. A defendant waives an objection to a jury instruction when he affirmatively approves the instruction at issue. United States v. DiSantis, 565 F.3d 354, 361 (7th Cir.2009). By opposing the government's initial objection to the elements instruction and indicating that the instruction was correct, we conclude that Courtright approved the initial instruction and thus foreclosed any appellate review.

Courtright next claims that the corrected jury instruction was erroneous. The argument goes: because the initial instruction provided that the government had to show that Courtright engaged in child molestation in the past, the jury believed that Courtright had actually engaged in child molestation. Without a clear explanation of the differences between the initial instruction and the corrected instruction, Courtright claims that this erroneous belief persisted throughout the trial. We find this argument unpersuasive for a number of reasons. First, as discussed above, Courtright sanctioned the very instruction that produced this purported belief. Second, and more importantly, an error is not plain unless it was extraordinary—so "obvious, crucial, and egregious that we may and should correct it even though no objection was made below." Backwater, Inc. v. Penn-American Ins. Co., 448 F.3d 962, 965 (7th Cir.2006). We do not believe that the district court's omission of specific advice regarding the differences between the initial preliminary instruction and the corrected preliminary instruction clears this hurdle.

Courtright finally claims that the limiting instructions given before and after L. Miller's testimony were erroneous, not just because her testimony should not have been considered by the jury at all, but also because the language of the instructions improperly suggested that Courtright was presently charged with a crime of sexual assault and that he was a child molester. We need not determine whether these instructions were erroneous for the simple reason that any error flowing from them had no effect on the outcome of the trial. See United States v. Peters, 435 F.3d 746, 754 (7th Cir.2006). As we have already noted, the evidence of Courtright's guilt was overwhelming, and he has not established that the jury's consideration of his prior offense had an appreciable impact on the verdict. Accordingly, we find that Courtright has failed to establish that the instructions were plainly erroneous.

C. Cumulative Error

Courtright's final claim on appeal is that, even if each of the individual errors was harmless, taken together the errors were so prejudicial as to deprive him of due process. For Courtright to demonstrate cumulative error, he must show that there were at least two errors committed during the course of the trial and those errors "so infected the jury's deliberation that they denied [him] a fundamentally fair trial." United States v. Avila, 557 F.3d 809, 821-22 (7th Cir.2009).

At the end of the day, the only errors Courtright has established are the admission of his prior sexual assault of L. Miller under Rule 413 and possibly the jury instructions related to that admission. Even if we assume that these interrelated errors suffice to qualify as two independent errors, reversal is appropriate only if "the errors, considered together, could not have been harmless." Alvarez v. Boyd, 225 F.3d 820, 825 (7th Cir.2000). Again, there was abundant evidence of Courtright's guilt, so L. Miller's testimony and the related jury instructions could not have had any appreciable impact on the jury's verdict. Courtright's claim of cumulative error thus fails. See Avila, 557 F.3d at 822.

III. CONCLUSION

For the foregoing reasons, we AFFIRM Courtright's conviction.