HILL, Senior Circuit Judge:
Charles S. Cancelliere appeals his conviction and sentence on each of three counts of bank fraud in violation of 18 U.S.C. § 1344, two counts of false statements to insured depository institutions in violation of 18 U.S.C. § 1014, and two counts of money laundering in violation of 18 U.S.C. § 1956(a)(1)(A)®. Cancelliere was convicted on all counts after a jury trial and sentenced to fifty-seven months imprisonment as to each count, with all counts running concurrently, followed by thirty-six months of supervised release. For the following reasons, we affirm his convictions and sentences on Counts 1-5, and reverse his convictions and sentences on Counts 6 and 7.
I. BACKGROUND
During the relevant time period, Cancelli-ere was a bank officer at several banks in Florida. Between December of 1984 and December of 1988, Cancelliere secured numerous unsecured loans from three different banks. Counts 1, 2 and 3 of the Indictment allege that Cancelliere committed bank fraud in violation of 18 U.S.C. § 1344 by misrepresenting to three different banks his assets and liabilities. Counts 4 and 5 allege that Cancelliere made false statements to a financial institution in violation of 18 U.S.C. § 1014 by representing to a bank that he owned stock in the Daily News Publishing Company (Count 4) and by representing to a different bank that he was the beneficiary of a trust account in Pittsburgh, Pennsylvania (Count 5). Counts 6 and 7 allege that Can-eelliere committed money laundering in violation of 18 U.S.C. § 1956 by writing two checks from his personal checking account knowing that the cheeks represented the proceeds of illegal activity.
Over objection, the government was allowed to introduce into evidence three letters written to Cancelliere by his deceased father. The first letter discusses the father’s purchase of his son’s stock in the Daily News Publishing Company. The second letter states that Cancelliere’s mother’s estate no longer existed. Caneelliere’s father also wrote that he would no longer help his son financially and suggested that Cancelliere sell his jewelry to ease his financial situation. In the last letter, Cancelliere’s father offered financial advice on how to deal with his creditors, but criticized Cancelliere for his self-indulgence and profligacy.
Also over objection, the government introduced evidence of other allegedly fraudulent transactions which are not charged or mentioned in the Indictment. Under Fed. R.Evid.Rule 404(b), the district court permitted the government to introduce evidence that Cancelliere (1) obtained a fraudulent loan from an individual named David Diaz; [1119]*1119(2) made false statements to two banks other than those named in the Indictment; and (3) bounced checks from his personal checking account.
At trial, the government sought to prove the money laundering counts by establishing (1) that Cancelliere deposited the proceeds of the fraudulently-obtained loans into his personal checking account; and (2) that some of the checks he wrote against this account were to pay interest on the fraudulently-obtained loans.
After the close of the evidence, the government moved to strike the word “willfully” from Counts 6 and 7 of the Indictment which charged Cancelliere with “knowingly and willfully” committing the offense of money laundering. Over objection, the district court permitted this redaction.
II. ISSUES
A. Was the evidence on Counts 6 and 7 (money laundering) sufficient to prove that the financial transaction in each count “involved” proceeds of a specified unlawful activity as required by 18 U.S.C. § 1956?
B. Did the district court err in striking the word “willfully” from Counts 6 and 7 of the Indictment after the close of evidence?
C. Did the district court abuse its discretion in admitting letters written by Cancelli-ere’s deceased father in violation of the hearsay rule.
D. Did the district court abuse its discretion in admitting evidence of several other fraudulent transactions as extrinsic evidence under Rule 404(b)?
III. DISCUSSION
A. Money Laundering
In order to establish the crime of money laundering, the government must prove that Cancelliere “eonduct[ed] ... a financial transaction which in fact involve[d] the proceeds of specified unlawful activity....” 18 U.S.C. § 1956. The government introduced evidence that Cancelliere wrote two checks on his personal bank account into which he had deposited the proceeds of the fraudulently-obtained loans. The district court instructed the jury that “the Government need not prove that all of the money involved in the transaction was the proceeds of bank fraud. It is sufficient if the Government proves that at least part of the money represents such proceeds.”
Cancelliere does not contest on appeal that there was evidence that he deposited fraudulent loan proceeds into his checking account or that he wrote two cheeks from this account to pay interest on his loans. He contends, however, that the government failed to prove that the money paid by these cheeks came from previously deposited fraudulent loan proceeds, either in whole or in part.
Cancelliere argues that it is not enough for the government simply to show that fraudulent loan proceeds went into his checking account at some indefinite point, and that subsequently two checks were written from this account to pay interest on the loans if the account at issue has other sources of deposit. He contends that because the checking account contained many legitimate deposits, including his salary deposits, the government failed to prove that the money paid by these checks came from previously deposited fraudulent loan proceeds, either in whole or in part. According to Cancelliere, salary or other legitimate deposits paid these two checks.
To convict under § 1956(a)(l)(A)(i), the government bears the burden of proving beyond a reasonable doubt that the party engaged in the transaction knew that the funds used represented, in whole or in part, proceeds of a specified unlawful activity.1 Can-celliere argues that unless the government proved that the checks written to pay the interest on his loans were actually paid at least in part with fraudulently-obtained [1120]*1120funds, the government did not carry its burden.
The issue is whether the government should be required to trace the origin of all funds deposited into a bank account to determine exactly which funds were used for what transaction. Although Caneelliere characterizes this issue as one of the sufficiency of the evidence, we believe that initially it is one of statutory construction. The statute requires that a transaction “involve” the proceeds of an activity which the participant knows is unlawful. The question is what Congress intended by the word “involve.”
Although this question has not yet been answered in this circuit, we find persuasive the reasoning of the Seventh Circuit in United States v. Jackson, 935 F.2d 832 (7th Cir.1991). In Jackson, the defendant deposited proceeds from his drug-dealing activities into the checking account of the 15th Street Baptist Church, where he was the preacher. The defendant then wrote checks from this account to pay for beepers which were used for drug dealing. After his conviction for money laundering, the defendant argued that no rational juror could decide that the checks alleged in the indictment involved money derived from drug proceeds.
The Seventh Circuit affirmed the conviction, reasoning that:
We do not read Congress’ use of the word “involve” as imposing the requirement that the government trace the origin of all funds deposited into a bank account to determine exactly which funds were used for what transaction. Moreover, we cannot believe that Congress intended that participants in unlawful activities could prevent their own convictions under the money laundering statute simply by commingling funds derived from both “specified unlawful activities” and other activities. Indeed, the commingling in this case is itself suggestive of a design to hide the source of ill-gotten gains.... (citation omitted)
id at 840. We agree and hold that Section 1956(a)(1)(A)© allows for convictions where the funds involved in the transaction are derived from a commingled account of which only a part comes from “specified unlawful activities.”
The evidence in this case was that Cancel-liere fraudulently obtained over $80,000 in loans from banks and systematically deposited the loan proceeds into his personal checking account. Thereafter, Caneelliere wrote two checks on this account to pay the interest on these loans. A rational juror could find that the government sustained its burden of proving beyond a reasonable doubt that Caneelliere’s payment of the checks alleged in Counts 6 and 7 “involved” the proceeds of his fraudulently-obtained loans and we find no error regarding this issue.
B. The Redaction of “Willfully”
Caneelliere asserts that reversal is required on the convictions for Counts 6 and 7 because the district court impermissibly amended the Indictment by redacting the willfulness allegation from those counts and by so instructing the jury. The government counters that the willfulness allegation was surplusage which the district court may redact without error.
Counts 6 and 7 of the Indictment charged Caneelliere with “knowingly and willfully” committing the offense of money laundering.2 Caneelliere testified at trial. His defense from the stand, and throughout trial, was that his personal finances were indeed in disastrous condition, but that the statements he made to procure loans were made with a good faith belief in their truth, without fraudulent scienter, but without meticulous accuracy.
After the close of the evidence, the government moved to strike the word “willfully” from Counts 6 and 7. Over objection, the district court permitted the redaction. The jury instructions did not contain “willfulness” as an element of money laundering, but did mention willfulness in defining the term “intentionally.”
[1121]*1121We have held that “a fundamental principle stemming from the [fifth] amendment is that a defendant can only be convicted for a crime charged in the indictment.” United States v. Keller, 916 F.2d 628, 633 (11th Cir.1990), cert. denied, 499 U.S. 978, 111 S.Ct. 1628, 113 L.Ed.2d 724 (1991). Per se reversible error occurs “when the essential elements of the offense are altered to broaden the possible bases for conviction beyond what is contained in the indictment.” Id. at 634. An amendment to an indictment occurs when the charging terms of the indictment are altered. United States v. Weissman, 899 F.2d 1111, 1114 (11th Cir.1990). A jury instruction that constructively amends a grand jury indictment constitutes per se reversible error because such an instruction violates a defendant’s constitutional right to be tried on only those charges presented in a grand jury indictment and creates the possibility that the defendant may have been convicted on grounds not alleged in the indictment. Stirone v. United States, 361 U.S. 212, 217-18, 80 S.Ct. 270, 273-74, 4 L.Ed.2d 252 (1960); Weissman, 899 F.2d at 1114.
On the other hand, mere surplus-age may be deleted from an indictment without error. United States v. Miller, 471 U.S. 130, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985). Willfulness is not a statutory element of money laundering, and “[a] part of an indictment unnecessary to and independent from the allegations of the offense proved may normally be treated as a useless averment that may be ignored.” Id. at 136, 105 S.Ct. at 1815. It is not an unconstitutional amendment to “drop from an indictment those allegations that are unnecessary to an offense that is clearly contained within it....” Id. at 144, 105 S.Ct. at 1819.
We believe the redaction in this case more closely resembles the impermissible broadening of the indictment condemned by Keller than the simple elimination of unnecessary averments approved by Miller. In this case, the government moved the district court to delete the requirement that they prove willfulness after Cancelliere prepared and put on a defense based upon good faith. Although the inclusion of the term “willful” was a mistake by the government,3 the charge was read to the jury at the beginning of the trial, the jury listened to Cancelliere attempt to prove he had not acted willfully, and then the court instructed them that they could convict without mentioning any requirement that they find he acted willfully.
This impermissible broadening of the bases upon which the jury could convict is similar to that in United States v. Leichtnam, 948 F.2d 370 (7th Cir.1991). In Leichtnam, the indictment charged that Leichtnam “knowingly used and carried a firearm, to wit a Mossberg rifle.” At trial, the government showed the jury three guns, including the Mossberg rifle. The judge then instructed the jury that it could convict if Leichtnam had used “a firearm.” On appeal, the Seventh Circuit reversed Leichtnam’s conviction, holding that “the introduction of the handguns, together with the jury instructions, inpermissibly amended the indictment by broadening the possible bases for conviction to include knowingly using or carrying any firearm. That was clear error, and Leicht-nam’s firearm conviction on count two must be reversed.” Id. at 380-81.
In Leichtnam, changing the term “Moss-berg rifle” to “a firearm” impermissibly broadened the bases for conviction, even though proving the use of a particular firearm is not required under the firearm statute. Similarly, in this ease, changing the requirement from proof of “knowingly and willfully” to “knowingly” impermissibly broadened the bases for Cancelliere’s conviction, even though willfulness is not required under the money laundering statute. We agree with the Seventh Circuit that:
New [bases for conviction] may not be added without resubmitting the indictment [1122]*1122to the grand jury, whether they are added literally, by a formal amendment to the indictment ... or by instructions to the trial jury which would allow a conviction on grounds not charged by the grand jury.
Leichtnam, 948 F.2d at 379 (internal citations omitted).
We do not agree with the government that the district court’s use of the word willful in defining the term “intentional” renders the error harmless. Cancelliere prepared his defense to a charge of “knowing and willful” money laundering. Indeed his whole defense to this charge rested on his lack of willfulness. The government alleged it even though it need not have, and it must be charged with proving it. The government may not decide after the close of evidence that it would prefer not to have the jury hear that term again. The redaction was error, and it was not harmless. Conviction on these two counts must be reversed.
C. Admission of the Letters
The letters from Cancelliere’s father were hearsay if they were admitted to prove the truth of the matter asserted in them, i.e., that Cancelliere’s trust fund was depleted and that his father would not help him financially. Cancelliere argues that they were so offered, because if the statements in the letters are not true they would be irrelevant to the government’s case, and therefore, inadmissible.
The government counters that the letters were not offered to prove the truth of the matters asserted therein, but rather to establish Caneelliere’s state of mind, knowledge, beliefs or intent as a consequence of reading them. Cancelliere’s knowledge and intent were in issue both with regard to the allegations of the Indictment and his good-faith defense. The letters, the government concludes, were relevant, non-hearsay evidence.
The government points to United States v. Harris, 942 F.2d 1125 (7th Cir.1991) as support for their theory that letters offered to prove a defendant’s state of mind are not inadmissible hearsay. In Harris, several letters from a man to his mistress, in which he wrote that the things he was giving her were gifts, were excluded as hearsay from her tax fraud trial. In reversing their exclusion, the Seventh Circuit wrote that the letters were not hearsay because they were offered to prove the mistress’s lack of wilfulness in not reporting the gifts as income, not for the truth of the matters asserted. Id. at 1130. In reversing, the court noted:
But the letters were not hearsay for the purpose of showing what [the mistress] believed, became her belief does not depend on the actual truth of the matters asserted in the letters. Even if [the de-clarant] were lying, the letters could have caused [the mistress] to believe in good faith that the things he gave her were intended as gifts. This good faith belief, in turn, would preclude any finding of willfulness on her part.
Id. at 1131 (emphasis added).
In this case, however, unless the statements in the letters are true, Cancelliere is guilty of no crime. There is no law against knowingly making true statements to a financial institution (if the statements in the letters were false and Cancelliere in fact had a trust fund as he represented to the banks). Unlike Harris, the truth of the statements in the letters is relevant to the element to be proved by its admission — that Cancelliere knowingly made false statements.
Hearsay issues like this one where evidence is admissible for one purpose but not for another present difficult problems. As the Seventh Circuit noted in Harris, jurors are not robots, and can rarely consider evidence strictly for the sole purpose admitted to the exclusion of the other, often more obvious, purpose. Id. at 1130. In Harris, the letters were admitted because they were of crucial importance to the defense of good faith even though the court noted that the jury would be hard pressed not to consider them on the impermissible issue of what the declarant actually intended.
For Cancelliere, the letters were of crucial importance as well. Cancelliere is correct that his father — through the letters — turned out to be one of the most damaging witnesses against him at trial. Therefore, the evidence, if it was hearsay, was highly prejudicial.
[1123]*1123Furthermore, this issue is not readily resolved. The government is correct that proof of Cancelliere’s state of mind was an element of its case, and that the letters are probative of that state. Cancelliere is also correct, however, that unless the statements in the letters were true, i.e., that the trust fund was exhausted and the father would no longer assist him financially, the letters were irrelevant. If in fact Cancelliere did have a trust fund he could not have been guilty of the underlying crime of making false statements. So the truth of the statements contained in the letters is not unrelated to their relevance in proving Cancelliere’s state of mind, as in Harris.
Nevertheless, we are persuaded that the letters were not inadmissible hearsay. The government was required to prove two things. It had to prove (1) that Cancelliere made false statements to the banks (e.g., that he was beneficiary of a trust fund; that he could count on financial help from his father, eie.); and (2) that Cancelliere knew that the statements were, in fact, false.
The statements, under the circumstances here, bore at least a patina of truth. Cancelliere had, at one time, an interest in a trust fund; he had received substantial funds from a well-to-do father. He mounted a persuasive defense that he believed he still had access to these resources. There was ample proof that the trust fund was long-since depleted and the family assets were no longer available to him.4 The letters went to show that he knew these facts at the time he misrepresented them because he had been advised, specifically, that these sources of funds were gone.
The letters could not be considered as evidence that the funds were non-existent or unavailable. However, if the jury was persuaded by other evidence of the truth of the matters asserted in the letters, it was proper for the jurors to conclude, from the letters, that Cancelliere knew when he made the statements to the banks, that the statements were false.
The judge dissected the situation with the scalpel of instruction to the jury to consider the letters for the proper purpose and not to consider them for any other — improper— purpose. As we noted above, there is a danger that jurors will consider such letters for the improper purpose — their truth. Nevertheless, we expect jurors to follow instructions.
Furthermore, if there be such danger, it is assumed by the defendant who puts the government to its proof of his knowledge and then protests that its ready-at-hand proof of that knowledge might harm him.
We conclude, therefore, that the letters were not hearsay when admitted to prove Cancelliere’s state of mind.
D. The Admission of the Extrinsic Evidence
The district court permitted extrinsic evidence in the following categories: (1) the testimony of Dennis Diaz regarding an uncharged loan; (2) evidence involving uncharged false statements; and (3) evidence that Cancelliere bounced checks from his personal checking account.
Diaz testified that Cancelliere obtained fraudulent loans from an institution not charged in this case. The government maintains, however, that this testimony is not extrinsic because it is inextricably intertwined with evidence of the charged crimes.
The evidence involving uncharged false statements came in through a witness named Passer, who testified that Cancelliere filed Chapter Seven bankruptcy after accumulating substantial unsecured debts from many banks, including two uncharged banks. Can-celliere contends that Passer’s testimony went beyond the purpose of Rule 404(b) because through this testimony the government established that Cancelliere’s debt to the three charged banks was discharged in bank[1124]*1124ruptcy. The two uncharged banks filed adversary complaints alleging fraud in the non-dischargeability bankruptcy proceeding. The district court admitted into evidence the entire bankruptcy court files. The government contends that this evidence is proper Rule 404(b) evidence going to show knowledge, intent, or absence of mistake or accident because Cancelliere made certain admissions in the bankruptcy ease concerning his representations to the charged banks.
Finally, the government introduced evidence that Cancelliere bounced checks from his personal checking account. Cancelliere contends that this evidence did not involve any scheme to defraud. Rather, it served only to establish bad character. The government responds that this evidence is linked in time and circumstances with the charged crimes and provides a context for the charged crimes for the jury.
Cancelliere asserts that all the extrinsic evidence allowed by the district court was highly prejudicial, unnecessary to the government’s case, and served only to establish propensity, rather than some permissible purpose under Rule 404(b) such as absence of mistake or accident.
Rule 404(b) provides that “[e]videnee 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....” The rule permits the introduction of evidence of a prior or uncharged act if the government can demonstrate: (1) a proper purpose for introducing the evidence; (2) that the prior act occurred and that the defendant was the actor; and (3) that the probative value of introducing the evidence outweighs any prejudicial effect the evidence might have. United States v. Perez-Garcia, 904 F.2d 1534, 1544 (11th Cir.1990).
Evidence of criminal activity other than the offense charged, however, is not extrinsic evidence if it is inextricably intertwined with the evidence of the charged offense. United States v. Collins, 779 F.2d 1520, 1531-1532 (11th Cir.1986). Furthermore, Rule 404(b) does not apply where the evidence concerns the “context, motive, and set-up of the crime” and is “linked in time and circumstances with the charged crime, or forms an integral and natural part of an account of the crime, or is necessary to complete the story of the crime for the jury.” United States v. Williford, 764 F.2d 1493, 1499 (11th Cir.1985).
(1) The testimony of Diaz regarding bank fraud was not extrinsic. Although not charged, these loans were alleged in the bank fraud counts as part of the manner and means by which Cancelliere carried out his scheme to defraud. Cancelliere understated his liabilities to the uncharged institution in order to obtain loans from the charged banks. In view of these allegations, the evidence was not extrinsic and Rule 404(b) is inapplicable.
(2) The evidence in the bankruptcy files established that Cancelliere testified at a creditors’ meeting that he did not own any shares of the Daily News stock on the date that he had told one of the banks that he did in order to secure a charged loan. The files also demonstrated that he signed a financial statement claiming ownership of a trust fund valued at $195,000. Finally, the bankruptcy files revealed that Cancelliere agreed to exempt from bankruptcy a portion of two loans he obtained from uncharged institutions because he had obtained them through fraudulent representations. This evidence, although extrinsic, was properly admitted under Rule 404(b) as going to knowledge, intent or plan. At the relevant time, Cancelliere was making the same misrepresentations to uncharged banks as he was making to the charged banks. The prejudice of having the jury hear of two more victims was minimal in light of the evidence of his repeated fraudulent representations over the course of the four years alleged in the Indictment. The probative value of this evidence outweighed its prejudicial effect. The district court give an appropriate limiting instruction which was agreed upon by the parties at the time of admission and in final instructions. There was no abuse of discretion in the admission of this evidence.
[1125]*1125(3) Cancelliere contends that the evidence concerning his issuance of insufficient funds checks was improperly admitted to establish bad character in violation of Rule 404(b). The government’s position is that the evidence was linked in time and circumstances with the charged crimes and formed an integral and natural part of the account of the crimes, and was admissible to complete the story of the crimes for the jury. See Williford, 764 F.2d at 1499.
The testimony concerning the bad checks came in through the president of the bank where Cancelliere was employed. After Cancelliere wrote the bad checks, the president met with him on several different occasions to counsel him regarding his financial situation. During one of these sessions, Cancelliere admitted that he had understated his debt to one of the charged banks. The admission came in, therefore, through the context of the bad check discussions between Cancelliere and his bank president. Such evidence is not extrinsic under Williford, and Rule 404(b) is inapplicable.
IV. CONCLUSION
The convictions on Counts 6 and 7 were based upon an unconstitutional redaction of the Indictment and are REVERSED. Having found no error in the admission of the letters or the extrinsic evidence, the convictions and sentences on Counts 1-5 are AFFIRMED.