BARRINGTON D. PARKER, Circuit Judge:
After trial in the Northern District of New York (Hurd, /.), a jury convicted Timothy M. McGinn and David L. Smith of various securities, mail, and wire fraud and tax charges. On appeal, McGinn and Smith challenge their convictions, principally contending that the government’s proof of criminal intent was insufficient. A key issue relates to the government’s allegedly improper use of a letter written by Smith a number of years before the events leading to the indictment. The defendants also challenge the legality of the court’s charge on the tax counts and McGinn contends that his sentence was procedurally and substantively unreasonable. Finally, Smith contends that the court’s restitution and forfeiture orders included losses related to conduct for which he was acquitted. The government cross-appeals the district court’s restitution orders.
For the reasons that follow, we affirm the defendants’ convictions and the sentences. As for the government’s cross-appeal, we remand the case for the limited purpose of correcting the written judgments to conform them to the requirements of the MVRA, 18 U.S.C. § 3663A.
BACKGROUND
The charges in this case arise from the operation by McGinn and Smith of McGinn, Smith & Company, Inc. (“MS & C”), an Albany-based investment firm and registered broker-dealer. In October 2012, the government filed a thirty-two count superseding indictment, charging the defendants with conspiracy to commit mail and wire fraud as well as substantive counts of' mail, wire, and securities fraud, and filing false tax returns. See 18 U.S.C. §§ 1341, 1343 and 1349; 15 U.S.C. §§ 78j(b) and 78ff; and 26 U.S.C. § 7206(1).
Viewing the evidence, as we must, in the light most favorable to the government, we find that the evidence adduced at trial established the following. MS & C was a firm founded and run by the defendants. From September 2006 to December 2009, Smith was the Chief Executive Officer and McGinn was Chairman of the Board. MS & C structured and sold to its clients a range of investment vehicles, but the charges arose from three types of offerings sold to MS & C investors. The first consisted of seventeen trusts structured to securitize streams of receivables, the majority of which concerned revenue streams from monthly contracts written by home security and telephone, internet, and cable service providers. The second was a fund managed by an affiliate, McGinn Smith Transaction Funding Corporation (“MSTF”), whose objective was primarily to provide bridge financing for transactions originated and negotiated by MS & C. The third was a series of four funds that invested more broadly in various public and private securities (the “Four Funds”).
With respect to the first type of offering, MS & C sold trust certificates to investors who were promised a specified interest rate payable in monthly installments over [1134]*1134the life of the trust. The terms of each trust offering were set forth in Private Placement Memoranda (“PPMs”), which described the operation of the trusts, including the use of proceeds, the expected rates of return, and the fees payable to MS & C. Each trust had a “minimum offering,” an amount which was required to trigger the operation of the trust. Investor funds were to be held in escrow until the target was reached, at which point escrow was “broken,” and the funds would be released and the trust would invest them. In the first type of investment, MS & C would advance funds to the various service providers. The advances would be secured by the receivables and the trust expected to generate profits from the spread between the amount advanced and the stream of receivables. Alternatively, some trusts advanced funds to entities that had previously purchased monthly service accounts and took as security the underlying contracts.
The government’s proof at trial established that, contrary to the provisions of the PPMs, the defendants withdrew and diverted significant sums of money from certain trusts, largely for personal use. Some of these withdrawals-took place even before the trusts reached their minimum offering and escrow was broken. Furthermore, the proof showed that when certain of the investments made by the trusts did not generate sufficient returns to. cover payments owed to investors, McGinn and Smith diverted funds from one offering to cover shortfalls in another.
At trial, the government devoted significant attention to two loans made by four of the trusts to a company called Firstline Security, Inc. that sold security alarm contracts. The government’s proof established that between October 2007 and June 2008, MS & C raised approximately $3.2 million that investors were told would be invested in two Firstline trusts. During the course of raising these funds, McGinn learned that Firstline was threatened with and then had filed for bankruptcy, but defendants failed to disclose this information to existing and new investors. After Firstline defaulted, McGinn diverted funds from other trusts to cover the shortfall and knowingly concealed these events through false statements to investors.
With respect to the second type of offering, the government’s proof showed that in 2008, MS & C, through MSTF, issued investors approximately $6,875 million in notes, ostensibly to invest in transactions originated by MS & C and to invest in other public and private securities including preferred shares of MS & C.
As to the third type of offering, from 2003 to 2005, MS & C raised approximately $90 million from investors for the Four Funds. According to the PPMs, investor money was to be used to acquire a variety of assets including securities, bonds, loans, leases, mortgages, equipment leases, and securitized cash flow instruments. Investors could purchase secured notes, offering between a 5% and 10.25% interest rate.
Although the Four Funds were initially profitable, by late 2007, they were “under water” by about $40 million and MS & C was unable to make the necessary interest payments. Gov’t App’x 206. The government proved that, to cover up this lack of profitability and to continue the interest payments, defendants reduced and suspended payments to investors, and McGinn diverted funds from a MSTF escrow account to preferred Four Funds’ investors. The government also proved that McGinn and Smith failed to disclose these diversions to investors and attempted to conceal them through false accounting entries.
Similarly, as the financial condition of MS & C deteriorated in 2008 and 2009, Smith ordered that accounting entries be [1135]*1135changed to conceal the fact that MS & C was fading. Various expenses such as rent and legal fees were not properly recorded and restricted monies from the Four Funds accounts were used to meet MS & C’s payroll. This and similar fraudulent conduct was concealed from investors and omitted or misstated in required regulatory filings.
The government proved that, while all of this was going on, the defendants improperly diverted some $4.1 million for the personal benefit of themselves and another key insider, that they used this money to fund lavish lifestyles that included luxury homes, vacation properties, thorough-bred race horses, and expensive golf memberships, and that they failed to report these receipts as income on federal tax returns.
As MS & C was unraveling, its financial condition came to the attention of the Financial Industry Regulatory Authority (“FINRA”), which, in June 2009, initiated a “cause based” examination of MS & C. At first, FINRA was concerned about the co-mingling of funds, but FINRA examiners soon realized that significant amounts of the diverted money were ending up in the defendants’ personal bank accounts. The government proved that when questioned about these transactions (including under oath), Smith and McGinn provided the examiners with false explanations and when FINRA requested documentation, the defendants altered and backdated the relevant accounting entries in order to conceal the transactions.
Following a four-week trial, the jury convicted both defendants of conspiracy to commit mail and wire fraud (Count 1); mail and wire fraud (Counts 8, 9, 10, 14 and 17); securities fraud (Counts 21-26); and filing false tax returns (Counts 27-29 for McGinn and Counts 30-32 for Smith). McGinn was also convicted of additional mail and wire fraud counts (Counts 4-7, 11-13,15-16,18-19 and 20).
McGinn was principally sentenced to 180 months’ and Smith to 120 months’ imprisonment on the conspiracy count and the substantive mail, wire, and securities fraud counts to run concurrently with 36 month sentences on the tax counts. The district court ordered McGinn and Smith to pay restitution of $5,992,800 and $5,989,736, respectively, and to forfeit $6,336,440. This appeal followed.
DISCUSSION
I. Sufficiency of the Evidence
We begin with defendants’ contentions regarding the sufficiency of the evidence underlying their convictions. “We review de novo a challenge to the sufficiency of the evidence and affirm if the evidence, when viewed in its totality and in the light most favorable to the government,. would permit any rational jury to find the essential elements of the crime beyond a reasonable doubt.” United States v. Yannotti, 541 F.3d 112, 120 (2d Cir.2008) (quotation marks omitted). “A defendant challenging the sufficiency of the evidence bears a heavy burden, because the reviewing court is required to draw all permissible inferences in favor of the government and resolve all issues of credibility in favor of the jury verdict.” United States v. Kozeny, 667 F.3d 122, 139 (2d Cir.2011).
A. Mail and Wire Fraud (Counts 4-20)
To prove mail or wire fraud, the government must show (1) a scheme to defraud victims (2) by obtaining their money or property (3) furthered by the use of interstate mail or wires. Fountain v. United States, 357 F.3d 250, 255 (2d Cir. 2004), see also 18 U.S.C. §§ 1341 and 1343. [1136]*1136The government must further establish that the defendant had fraudulent intent or “a conscious knowing intent to defraud,” and that some harm or injury to the property rights of the victim was contemplated. United States v. Guadagna, 183 F.3d 122, 129 (2d Cir.1999) (quotation marks omitted).
Both defendants argue that the government did not establish their intent to defraud and Smith also claims that he was not involved in certain of the charged transactions. McGinn first challenges his mail and wire fraud convictions on Counts 4-6 and 11-13, all of which concern the sales of Firstline certificates, contending that he was not responsible for losses related to Firstline’s bankruptcy because he did not know or believe it would occur. However, the government’s proof showed otherwise. It established that he was immediately informed of the bankruptcy, and that he received regular emails regarding post-bankruptcy sales to investors. Although he testified that he paid very little attention to these emails, this testimony was belied by examples of his responses to these messages. Considering the email evidence and the fact that MS & C had a potent motivation to conceal the bankruptcy because disclosure of the bankruptcy would have made it exceedingly difficult, if not impossible, for MS & C to procure investors, the jury was entitled to reject McGinn’s self-serving testimony and accept the government’s proof that he knowingly concealed material information from prospective investors. After all, as we have held, a defendant’s belief “that ultimately everything would work out so that no one would lose any money” does not excuse fraudulent conduct. See, e.g. United States v. Rossomando, 144 F.3d 197, 199-201 (2d Cir.1998).
Similarly, as to Counts 7, 14-18 and 20, a reasonable jury could have rejected McGinn’s contentions that the transfers out of the trust escrow accounts were not improper because the escrow accounts had been “broken” and so defendants enjoyed-unrestricted access to the funds, and that they were essentially anticipating “profits” that they would realize over time. The jury was also free to accept the government’s proof that, contrary to the defendants’ testimony and to representations in the PPMs, the defendants, without the necessary disclosures, took funds that were required to remain in escrow, diverted them for personal use, shored up other trusts, and funneled money from unrelated entities to make monthly interest payments and that all of this conduct involved material misrepresentations or omissions. This evidence was sufficient for the jury to reasonably infer that defendants intended to defraud investors, or, in other words, that their conduct was willful.1
The evidence introduced at trial regarding the Four Funds was also sufficient to support both defendants’ mail fraud convictions (Counts 8 and 9) and McGinn’s wire fraud conviction (Count 19). McGinn argues that the monies he and Smith diverted were fees legitimately owed to them, which, instead of taking, they applied to other investments in order to forestall losses. The government, however, proved that these diversions were not authorized by the PPMs and were not disclosed to investors, and thus directly called into question their legitimacy. Even more tellingly, the government’s proof established that the defendants caused the ere-[1137]*1137ation of false accounting records intended to disguise the sources of the diverted money and that McGinn applied certain of the transferred funds to his personal use. Smith’s involvement in falsifying the relevant accounting records contradicts his argument that the government did not prove his specific intent with regards to Counts 8 and 9.
As for Count 10, which relates to the mailing sent to investors after Firstline’s bankruptcy, the government’s proof established that the letter falsely identified the source of post-bankruptcy payments and falsely claimed that Firstline’s management had concealed the condition of the company. The defendants contend that the letter, which postdated the bankruptcy by many months, was insufficient to demonstrate intent to defraud. However, as the government correctly pointed out, in a mail fraud scheme, a mailing need not deprive someone of money or property so long as it is in furtherance of the scheme and the letter in question satisfied that requirement. See United States v. Lane, 474 U.S. 438, 451-52, 106 S.Ct. 725, 88 L.Ed.2d 814 (1986) (“[m]ailings occurring after receipt of the goods obtained by fraud are within the statute if they were designed to lull the victims into a false sense of security [or] postpone their ultimate complaint to the authorities”) (quotation marks omitted).
B. Conspiracy to Commit Mail and Wire Fraud (Count 1)
To prove conspiracy, the government must demonstrate the existence of the conspiracy and the defendant’s knowing participation. See United States v. Story, 891 F.2d 988, 992 (2d Cir.1989). Here, the government adduced sufficient evidence that defendants knowingly and willingly entered into a conspiracy to defraud investors. Particularly probative in this regard was the evidence concerning the defendants’ joint efforts to divert funds, conceal losses through the creation of false accounting records, and the submission of false documents to FINRA. Viewing this evidence in its totality, and in the light most favorable to the government, a rational jury could, have found beyond a reasonable doubt that defendants were knowing participants in a conspiracy to commit mail and wire fraud.
C. Securities Fraud (Counts 21-26)
McGinn and Smith also challenge the sufficiency of the evidence on their securities fraud convictions, arguing principally that there was insufficient evidence demonstrating their intent to defraud. In order to establish a criminal violation of the securities laws, the government must show that defendants acted “willfully.” 15 U.S.C. § 78ff(a). We have defined willfulness in this context as “a realization on the defendant’s part that he was doing a wrongful act under the securities laws, in a situation where the knowingly wrongful act involved a significant risk of effecting the violation that has occurred.” United States v. Cassese, 428 F.3d 92, 98 (2d Cir.2005) (internal quotation marks and citation omitted). As previously mentioned, the securities fraud charges concerned money that defendants took for themselves and for one of their business associates from two of the trusts which MS & C organized. The government’s evidence showed that McGinn and Smith induced investors to part with their money on the understanding that their money would be used by the trust in which they were investing for the limited purposes specified in that trust’s PPM. Instead, defendants transferred significant amounts of investors’ money to their personal accounts and used them for purposes unrelated to the reasons they were invested. These facts supplied a reasonable basis upon which the [1138]*1138jury could conclude that the defendants acted willfully.
D. Filing False Tax Returns (Counts 27-32)
Defendants were each convicted on three counts of filing false tax returns for the years 2006, 2007 and 2008. See 26 U.S.C. § 7206(1). Essentially, the government contended that a series of advances to the defendants were not loans but income. The defendants argued that the advances were, in fact, loans, but that, in any event, the government’s evidence was insufficient to prove that they acted willfully and knowingly. Section 7206(1) requires the government to prove: (1) that the defendant made or caused to be made an income tax return for the relevant year, which he verified was true; (2) that the tax return was false as. to something material; (3) that the defendant willfully signed the return knowing it was false; and (4) that the return stated that it was made under penalty of perjury. United States v. LaSpina, 299 F.3d 165, 179 (2d Cir.2002). While a taxpayer is not ordinarily required to report a loan as income, he must do> so if he does not intend to repay the loan. See United States v. Rosenthal, 470 F.2d 837, 841 (2d Cir.1972).
At trial, the government adduced evidence, apparently accepted by the jury, that Smith did not believe the amounts in question were loans. The government established that Smith initially characterized the loans at issue as “fees” when asked about them by FINRA investigators. McGinn did not disclose the payments as “loans” on a residential mortgage application and neither defendant listed the purported loans as liabilities on their financial statements. Moreover, while McGinn and Smith provided contemporaneous documentation of other loans with promissory notes, neither of them memorialized the terms of the unreported loans at issue. The comptroller for MS & C also testified that the advances were not loans, but fees, and that Smith had directed him to change the entries of certain payments from “fees” to “loans” for “tax reasons.” Gov’t App’x 215-20. Based on this evidence, we have little difficulty concluding that a jury could have reasonably accepted the government’s evidence that defendants knew the payments were income, not-loans, and willfully omitted them from their returns.
II. Jury Instruction on Tax Counts
The defendants contend that the district court’s instruction on the tax counts was generally erroneous and, specifically, that the charge improperly instructed that good faith was not a defense. The district court provided the jury with the following “willfulness” instruction on the tax counts:
The fourth and final element that the government must prove beyond a reasonable doubt is that the defendant under consideration acted willfully. I have already defined the term ‘willfully’ for you. In short, the government must establish that the defendant under consideration acted voluntarily and intentionally with the specific intent to make a false statement on the tax return involved in the count under consideration, despite knowing that it was his legal duty to answer truthfully.
Smith App’x 495. The court had previously defined the term willfully as when a person acts “purposely and with an intent to do something unlawful.” Gov’t App’x 736. Smith argues, citing United States v. Pirro, 212 F.3d 86, 90-91 (2d Cir.2000), that this instruction was not sufficiently specific as to defendants’ willfulness. We do not believe that Pirro is apposite, but, more to the point, Smith has no basis for complaint because he requested virtually identical language in his proposed jury [1139]*1139instruction. Moreover, the legal sufficiency of the instruction delivered on this point by the district court is well settled. See United States v. Pomponio, 429 U.S. 10, 11, 97 S.Ct. 22, 50 L.Ed.2d 12 (1976) (finding that similar instruction given by the trial court was appropriate).
Before issuing the general instruction on the tax counts, the court, without objection from the defendants, told the jury that “the defense of good faith is not applicable to the filing of false tax returns charges.” See Gov’t App’x 738. The government concedes that this statement was incorrect. The Supreme Court has held that, in criminal tax cases, the prosecutor must prove “actual knowledge of the pertinent legal duty,” which “requires negating a defendant’s claim of ignorance of the law or a claim that because of a misunderstanding of the law, he had a good faith belief that he was not violating any of the provisions of the tax laws.” Cheek v. United States, 498 U.S. 192, 202-03, 111 S.Ct. 604, 112 L.Ed.2d 617 (1991).
But just before this mistaken instruction, the court instructed the jury that to act willfully “means to act purposely and with an intent to do something unlawful.” Gov’t App’x 736. The government argues that any fair understanding of this definition is that the jury could not convict the defendants if it found that they had acted in good faith. We have stated that while “the existence vel non of culpable intent or lack of good faith is a crucially important issue” for tax fraud, United States v. Regan, 937 F.2d 823, 827 (2d Cir.1991), a standard jury instruction on the willfulness element of tax evasion generally encompasses a good faith defense, United States v. Evangelista, 122 F.3d 112, 118 n. 5 (2d Cir.1997).
Defendants nonetheless argue that this mistaken reference to the inapplicability of the good faith defense tainted the entire instruction and requires vacatur of their convictions on the tax charges. “A jury instruction is erroneous if it misleads the jury as to the correct legal standard or does not adequately inform the jury on the law.” United States v. Dinome, 86 F.3d 277, 282 (2d Cir.1996) (quotations marks omitted). If, as here, a defendant does not object to a charge we review for plain error. See United States v. Kopstein, 759 F.3d 168, 180 n. 6 (2d Cir.2014); see also Fed.R.Crim.P. 30(d), 52(b). Plain error requires an appellant to show that the error is clear or obvious, that it affected his substantial rights, which ordinarily means it affected the outcome of the district court proceedings, and “seriously affect[ed] the fairness, integrity or public reputation of the judicial proceedings.” United States v. Vilar, 729 F.3d 62, 70 (2d Cir.2013) (quotation marks omitted).
We agree with the government that, when examined in the context of the instructions as a whole, the court’s erroneous statement does not rise to the level of plain error. “In determining whether the district court properly instructed the jury, we must not judge any instruction in isolation but must instead view the charge as a whole.... [W]e will not make our determination on the basis of excerpts taken out of context.” United States v. Josephberg, 562 F.3d 478, 500 (2d Cir.2009) (quotation marks and citations omitted). The district court properly instructed the jury on the government’s burden of proof, that the jury had to find that the defendants knew that the payments they received were not legitimate loans because they lacked a bona fide intent to repay the money in question, and that the defendants knew that the declarations on their tax returns were not truthful because they did not include these payments. The jury instruction thus conveyed that the defendants’ good faith belief that the payments were [1140]*1140legitimate loans would preclude conviction. Under plain error review, the district court’s mistaken reference, when taken in context, did not eviscerate the rest of the ■instruction. This is especially so in light of the overwhelming evidence that the defendants knew their returns were false when they filed them. Accordingly, we affirm the defendants’ convictions for filing false tax returns.
III. Admitting Portions of Smith’s 1999 Letter
Before trial and during its case in chief, the government sought to introduce a document that Smith composed, in 1999, years before the events underlying the indictment, as evidence of conspiracy and of the defendants’ knowledge and intent. While the document was addressed to McGinn, the government did not present evidence demonstrating that it was ever sent. The document contained statements such as “if our trusts go into default, everything else will come apart;” “I, unlike you, feel that we are vulnerable to criminal prosecution;” “I believe that we are at risk for the continual raising of investment dollars, that are now clearly unlikely to be repaid in full;” and characterized what was going on at MS & C as a “Ponzi scheme.” Gov’t App’x 1625-51.
Initially, the district court held that the document was inadmissible because it related to conduct that occurred years before the frauds alleged in the indictment, and did not concern the same entities as those involved in the charged crimes. The court, however, warned that the letter could be admitted if the defendants opened the door by pursuing a good faith defense, blaming what happened on the financial crisis, or claiming ignorance of the implications of their conduct.
After McGinn testified, the district court held that the government could ask McGinn (who had not written the letter) about certain specific portions of the document relating to the “default” of the trusts and required disclosures to investors, but could not introduce the draft letter itself or ask him about events occurring in 1999. Similarly, the district court found that Smith’s testimony had opened the door to portions of the document and limited the government’s use to the same portions that were used with McGinn, as well as several additional sections. McGinn and Smith contend that the district court abused its discretion by permitting the government to cross-examine them using portions of a draft letter that Smith wrote in 1999, and that the government’s use of the document resulted in a constructive amendment of the indictment or a prejudicial variance.
A. Cross-Examination Using Smith’s 1999 Letter
We review a district court’s ev-identiary rulings under a deferential abuse of discretion standard, and we will disturb an evidentiary ruling only where the decision to admit or exclude evidence was “manifestly erroneous.” United States v. Samet, 466 F.3d 251, 254 (2d Cir.2006). Moreover, even if a ruling was “manifestly erroneous,” we will still affirm if the error was harmless. United States v. Miller, 626 F.3d 682, 688 (2d Cir.2010). The error was harmless if it is not likely that it contributed to the verdict. United States v. Gomez, 617 F.3d 88, 95 (2d Cir.2010). “The following factors must be weighed in determining whether the wrongful admission of evidence constituted harmless error: (1) the overall strength of the prosecutor’s case; (2) the prosecutor’s conduct with respect to the improperly admitted evidence; (3) the importance of the wrongly admitted testimony; and (4) whether such evidence was cumulative of other [1141]*1141properly admitted evidence.” Id. (quotation marks omitted).
Upon review of the record, we conclude that allowing portions of this letter to be read during cross-examination of the defendants, without context and without any limiting instruction, was “manifestly erroneous.” Although the letter was never admitted into evidence, the district court nonetheless permitted the government to simply read to the jury the most prejudicial and inflammatory portions of the letter under the guise of asking questions. {See, e.g., Gov’t App’x 652 (“Did Mr. Smith, your business partner, write: ... ?”).) The fact that the 1999 letter was permitted to be used in this manner in the cross-examination of McGinn, who testified that he had never received the letter, was especially prejudicial and improper.
However, to vacate a conviction on this basis, allowing the prosecution to use the 1999 letter in the manner that it did, cannot have been harmless—we must be able to “conclude with fair assurance” that the improper use of evidence “did not substantially influence the jury.” United States v. Groysman, 766 F.3d 147, 155 (2d Cir.2014). Considering the overall strength of the government’s case and the fact that the letter was cumulative of other properly admitted evidence, we find that the district court’s treatment of the 1999 letter was harmless error. As previously noted, the government adduced substantial evidence that McGinn and Smith, among other things, directed that money be diverted from various accounts and entities for improper purposes, ordered MS & C’s accounting staff to make false entries intended to conceal unauthorized transactions, misappropriated millions of dollars for themselves and offered false explanations and directed the creation of false documents in response to the FINRA investigation. When considered in the context of a record containing substantial evidence of the defendants’ guilt, we cannot conclude that the improper use of the document had a substantial impact on the result of the trial.
B. Whether Reading Portions of the Letter Constituted a Constructive Amendment or Variance
Because defendants raise their constructive amendment claim for the first time on appeal, we review it for plain error. United States v. Bastian, 770 F.3d 212, 219 (2d Cir.2014). “To prevail on a constructive amendment claim, a defendant must demonstrate that the terms of the indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment.” United States v. D’Amelio, 683 F.3d 412, 416 (2d Cir.2012) (emphasis in original, quotation marks omitted). A variance occurs when the charging terms of the indictment are not changed, but the evidence at trial proves facts materially different from those alleged. However, the “proof at trial need not, indeed cannot, be a precise replica of the charges contained in an indictment [and] this court has consistently permitted significant flexibility in proof, provided that the defendant was given notice of the ‘core of criminality’ to be proven at trial.” United States v. Heimann, 705 F.2d 662, 666 (2d Cir.1983).
Defendants’ argument that the use of excerpts from Smith’s 1999 letter constituted a constructive amendment or prejudicial variance is unavailing. The government’s arguments, the indictment, and the evidence- introduced at trial all related to charged conduct that occurred from 2006 to 2010. The jurors were fur[1142]*1142ther instructed that, to find the defendants guilty of conspiracy, they had to find that, for some time between September 29, 2006 and April 20, 2010, the defendants had entered into an unlawful agreement to commit mail or wire fraud. McGinn and Smith also had ■ sufficient notice of the “core of criminality to be proven at trial,” as they had been warned from the beginning that portions of the letter could be admitted and the evidence adduced at trial did not establish facts different from those alleged in the indictment. Heimann, 705 F.2d at 666. Accordingly, we conclude that there was no constructive amendment or fatal variance.
IV. McGinn’s Sentence
We review sentences under a “deferential abuse-of-discretion standard” for procedural and substantive reasonableness. United States v. Cavera, 550 F.3d 180, 189 (2d Cir.2008). We review a district court’s interpretation of the Sentencing Guidelines de novo and its findings of fact for clear error. United States v. Mejia, 461 F.3d 158, 162 (2d Cir.2006). To impose a procedurally reasonable sentence, a district court must (1) determine the applicable Guidelines range, (2) consider the Guidelines and other section 3553(a) factors and (3) determine whether to impose a Guidelines or a non-Guidelines sentence. United States v. Villafuerte, 502 F.3d 204, 206-07 (2d Cir.2007). A sentence is substantively unreasonable only if it “cannot be located within the range of permissible decisions,” Cavera, 550 F.3d at 189, and would “damage the administration of justice” because it was shockingly high or low or not legally supportable, United States v. Rigas, 583 F.3d 108, 123 (2d Cir.2009).
McGinn argues that his sentence was procedurally unreasonable because the district court made erroneous factual findings as to loss calculation; the specific offense characteristics of the Guidelines impose cumulative punishments and disproportionately emphasize loss amount; and the district court failed to adequately consider the section 3553(a) factors. Our examination of the record, however, indicates that the district court had reviewed the Pre-Sentence Investigation Report (“PSR”), considered all of the sentencing submissions, and correctly applied the Guidelines. The court adopted the PSR’s calculations of loss amounts, and, consistent with those calculations, did not hold McGinn accountable for total investor losses. Moreover, the district court appropriately took into account the fact that, for years, McGinn had run MS & C with little apparent regard for the legality of his conduct and that he continued to lack contrition. Thus, we see no basis for concluding that the district court failed to adequately consider the section 3553(a) factors or otherwise fashioned a sentence that was procedurally unreasonable.
Finally, McGinn argues that his sentence was substantively unreasonable. We see no merit to this contention. Notably, he received a sentence of 180 months, a sentence that was significantly lower than his Guidelines range of 210 to 262 months. In any event, we cannot say that the sentence the district court imposed was unreasonable in view of the large number of investors who were defrauded, the large amounts of money that they lost, and the lengthy time period during which his sophisticated criminal activity was ongoing.
V. Smith’s Restitution and Forfeiture Orders
Smith contends that the district court incorrectly computed the amounts he owed as restitution and forfeiture. Because he did not object below on this [1143]*1143ground, we review for plain error. See United States v. Thorn, 446 F.3d 378, 387 (2d Cir.2006) (restitution); United States v. Uddin, 551 F.3d 176, 181 (2d Cir.2009) (forfeiture). When determining whether to award restitution, the court should consider the amount of the loss sustained by the victim as a result of the offense, the financial resources of the defendant and the financial needs of the defendant’s dependents, and such other factors as the court deems appropriate. 18 U.S.C. § 3663(a)(B)(i)(I)-(II). “Any dispute as to the proper amount or type of restitution shall be resolved by the court by the preponderance of the evidence” with the burden of determining loss on the government. 18 U.S.C. § 3664(e). When the government seeks to impose criminal forfeiture, it must also establish the requisite nexus between the offense and the assets to be forfeited by a preponderance of the evidence. United States v. Capoccia, 503 F.3d 103, 110 (2d Cir.2007).
Smith argues that his restitution and forfeiture orders improperly include $600,000 attributable to sales of Firstline following its bankruptcy and he was acquitted of certain counts relating to these sales. The fact that he was acquitted on these counts, he contends, must mean that the jury had determined that he was unaware of the bankruptcy until after the sales occurred.
But these contentions overlook the fact that he was also convicted of the conspiracy charged in Count 1, which encompassed fraud related to the post-bankruptcy First-line sales and of mail fraud in Count 10, which pertained to the September 10, 2009, Firstline post-bankruptcy memorandum. The jury’s determination that he was acquitted on certain of the substantive mail fraud charges related, to the post-bankruptcy mailings is not inconsistent with a conclusion that he entered into a conspiracy involving these sales and does not absolve him of liability for the conspiracy and the losses it caused. Specifically, the government introduced evidence in support of Counts 1 and 10 that Smith learned about the Firstline bankruptcy before the 2009 mailing, and knowingly concealed material information about First-line. Accordingly, it was not error, plain or otherwise, to include the $600,000 in the two orders. We have considered defendants’ remaining arguments and find them to be without merit.
VI. Government’s Cross-Appeal
The MVRA provides that the court shall order restitution to each victim in the full amount of each victim’s losses and, when calculating restitution, the fact that the victim is entitled to recéive compensation from another source may not be considered. The Act further provides that any amount paid pursuant to a restitution order is reduced by any amount later recovered for the same loss by the victim in any federal or state civil proceeding. See 18 U.S.C. § 3664(f)(l)(A)-(B),(j)(2).
At sentencing, the district court ordered McGinn and Smith jointly and severally liable for $5,748,722 in restitution to their 841 victims. The court further stated that any restitution “collected thus far by the receiver ... may be deducted from the total restitution amount and may be distributed to the victims by the receiver ... as such assets are available for distribution.” Gov’t App’x 1868-69, 1883 (emphasis added). After filing its notice of cross-appeal, the government moved the district court to clarify its restitution orders, arguing that they could be understood to provide that the restitution could be offset by the amount of money collected by the court-appointed Receiver in the separate SEC action, rather than the amount that the Receiver actually distributes to these [1144]*1144victims. This reading would violate the MVRA, which only permits offset for money “recovered” as opposed to “collected” but not necessarily distributed. 18 U.S.C. § 3664(j)(2).
On January 23, 2015, the district court denied the government’s motion, holding that the original restitution orders were clear and there was no need for clarification. The district court stated that, under the circumstances at the time of sentene-ings, the restitution orders should be understood as ordering that “[a]ny sums distributed to the victims by the Receiver shall be deducted from the total restitution.” See 12 CR. 28(DNH) (Dckt. Entry 268). The government, noting that the judgments remain unrevised, argues that the January 23, 2015 order failed to make clear that funds should be credited against restitution only when they are distributed to victims and not when they are merely collected by the Receiver. We agree. Accordingly, we remand to the district court for the limited purpose of correcting the judgments to clarify that only the Receiver’s actual distribution of funds to the victims may offset the defendants’ restitution obligations.
CONCLUSION
The judgments of the district court are AFFIRMED. The case is REMANDED to the district court for the limited purpose of correcting the written judgments to conform them to the requirements of the MVRA.