SACK, Circuit Judge:

This appeal and cross-appeal concern the pension benefits owed to plaintiff Carlo Novella, a retired carpenter, and members of a class he purports to represent. During Novella’s three-decade career, he performed jobs for which his employers were obligated, under collective bargaining agreements, to pay into the defendant pension fund on his behalf. But there were multi-year periods — principally from 1982 to 1986 — during which Novella did not perform any work requiring his employer to make such a contribution. In 1995, when Novella was nearing his sixty-second birthday, he became disabled as a result of injuries sustained while he was on the job. He applied for, and received, a pension (“Disability Pension”); however, he was disappointed to learn that his benefits were not calculated using the pension rate in effect in 1995, but rather using two different rates for Novella’s two periods of service. The rate applicable in 1995 was applied to benefits for work performed between 1987 and 1995, and the lower rate in effect in 1981 was applied to benefits for work performed between 1962 and 1981. The use of the 1981 rate for the earlier period resulted in a lower aggregate monthly pension payment.

After unsuccessfully seeking administrative redress from the pension fund, Novella filed suit in the United States District Court for the Southern District of New York on his own behalf and on behalf of a class of pensioners whose benefits also were allegedly miscalculated. He asserted that the fund was guilty of seven violations of the Employee Retirement Income Security Act (“ERISA”) and sought declaratory and injunctive relief. On cross-motions for summary judgment, the district court agreed with Novella that the defendants— the pension fund and its trustees — had erred in calculating his Disability Pension at two different rates. The court did not reach Novella’s other claims.

*132 Novella then moved to certify a class action on behalf of either of two classes: one including recipients of various types of pensions whose benefits were calculated using multiple per-credit rates, and the other limited to disability pensioners whose benefits were affected by the same practice. The district court concluded that in light of Novella’s success on his individual claims, only the narrower class of disability pensioners was eligible for certification. The court determined that the statute of limitations for the absent class members’ claims did not accrue until each class member affirmatively challenged the defendants’ two-rate benefit calculation, and was rebuffed. The court found twenty-four putative class members whose claims were timely and determined that this number met the numerosity requirement of Rule 23(a)(1) of the Federal Rules of Civil Procedure. Finding the other requirements of Rule 23(a) and (b) to have been met, the court certified this narrower class of disability pensioners.

The parties then cross-moved for summary judgment on the class claims, which motions the district court referred to a magistrate judge. The magistrate judge recommended granting the plaintiff class’s motion on the merits and denying the defendants’, the latter of which the magistrate judge characterized as an untimely motion for reconsideration of the decision certifying the class. The district court reviewed the magistrate judge’s recommendation, adopted it, and entered judgment in favor of the class. The court also awarded prejudgment interest at the fund’s assumed annual rate of return to both Novella and the members of the plaintiff class. Both parties appealed.

We agree with the district court that the defendants’ use of two rates in calculating disability pensions finds no support in the language of the fund’s controlling documents — the Summary Plan Description and the Rules of the Pension Plan. We therefore affirm the district court’s judgment in Novella’s favor on his individual claims. We also affirm its award of prejudgment interest to Novella, and its setting of the rate and date of accrual for the award. However, we conclude that the district court erred in identifying the time at which a claim for miscalculation of benefits accrues. In light of our view that such a claim accrues when the pensioner knew or should have known that his benefits were miscalculated, we vacate the certification of the class, the judgment in favor of the class, and the award of prejudgment interest to the class members, and remand the case for further proceedings before the district court. These proceedings may include a case-by-case inquiry into when each putative class member knew or had sufficient information so that he should have known that the defendants were using two different rates to calculate his pension.

BACKGROUND

Factual History

The relevant facts are not in dispute.

The plaintiff, Carlo Novella, is a 78-year-old former carpenter. From 1962 through 1995, he worked in Westchester County, New York, and in New York City, and participated in both the defendant Westchester County, New York Carpenters’ Pension Fund (the “Westchester Fund” or the “Fund”) 1 — which is adminis *133 tered by the defendant eight-member Board of Trustees of the Fund — and the New York City District Council of Carpenters Pension Plan. It is Novella’s pension under the Westchester Fund — which is an employer-funded employee pension benefit plan within the meaning of ERISA, see 29 U.S.C. § 1002(2)(A) — that is at issue in this appeal. Novella’s pension benefits under the Fund are determined by the Pension Fund Rules (the “Plan”) and Summary Plan Description (the “SPD”) 2 , which have been in effect and unchanged since January 1, 1986. The Plan creates six classes of benefits, four of which are pension-type allowances: “Regular Pension” benefits, governed by sections 3.02-3.03 of the Plan; “Early Retirement Pension” benefits, governed by sections 3.04-3.05 of the Plan; “Deferred Pension” benefits, dictated by sections 3.06-3.07 of the Plan; and “Disability Pension” benefits, as set forth in sections 3.08-3.11 of the Plan. 3 See J.A. 151-54. 4 Each participant is entitled to only one type of benefit, “except that a Disability Pensioner who recovers [from his disabling injury] may be entitled to a different type of pension.” Id. at 155.

Fund participants earn pension credits based on the number of hours they serve in jobs that are covered by the Plan. A job constitutes “Covered Employment” if the employer is “obligated by its [collective bargaining] agreement to contribute to the Fund” on behalf of the relevant Plan participant. Id. at 146. Novella has had two periods of covered employment: from 1962 through 1981, 5 during which time he earned 13.20 pension credits, and from 1987 to 1995, during which time he earned an additional 6.30 pension credits. 6 In the years between 1982 and 1986, Novella performed work in New York City, which was covered by the New York City Fund — not a party to this action — but he did not perform any work covered by the defendant Westchester Fund.

On March 22, 1995, Novella, then sixty-one years old, suffered a disabling accident *134 while at work, for which he immediately began to receive workers’ compensation. He also applied to the Fund for pension benefits. To calculate the amount of Novella’s monthly pension, the defendants used two different rates: They applied a rate of $17 per credit to the 13.20 pension credits Novella earned between 1962 and 1981, and a second rate of $40 per credit for the credits he earned between 1987 and 1995.

Immediately after receiving notice in fall 1995 that his pension would be calculated using two different rates, Novella asked the Fund trustees for an explanation of his benefits. The defendants explained to him that the two-rate calculation was appropriate because of the break in his covered service from 1982 through 1986, during which time he performed no work covered under the Westchester Plan.

The defendants denied Novella’s repeated appeals from the two-benefit rate calculation, referring Novella to section 3.07 of the Westchester Plan, which applies to Deferred Pensions. 7 By letter dated August 28, 1997, the defendants explained that under that section of the Plan,

a Deferred Pension is calculated based on the rate in effect on the last day you worked in Covered Employment prior to the accumulation of three One-Year Breaks in Service.... Since each of the years you were not working in covered employment was a Break in Service,[ 8 ] the credits you had accumulated up to 1981 when you left covered employment under the Plan (13.20) were calculated at the 1981 rate ($17.00).

Section 3.07 also provides that if any additional credits were earned after the Break in Service, the benefit amount for the additional credits shall be calculated on the rate that was in effect at the time of termination. The credits you earned after the Break in Service (6.30) were calculated at the rate in effect when you terminated ($40.00).

J.A. 194. Although Novella was awarded a Disability Pension, not a Deferred Pension, the letter did not cite the sections of the Plan governing Disability Pensions: sections 3.08 to 3.11. The letter also failed to cite section 3.16 of the Plan, entitled “Application to Benefit Increases,” on which the defendants would later rely in this litigation. Id. at 156. Section 3.16 provides that a Fund participant is entitled to a Pension in an amount to be “determined under the terms of the Plan and [at] the benefit level, as in effect at the time the Participant last separates from Covered Employment.” Id. Under section 3.16, “[a Plan participant shall be deemed to have last separated from Covered Employment on the last day of Work which is followed by three consecutive calendar years of less than 1,000 hours of Covered Employment in each year.” Id.

Procedural History

On March 19, 2002, having contested the two-rate calculation through the Fund’s *135 administrative review process and having failed to obtain relief, Novella filed suit in the United States District Court for the Southern District of New York against the defendant Fund and its Board of Trustees, asserting violations of ERISA, and seeking declaratory and injunctive relief. 9 He filed an amended complaint on October 27, 2003. His suit was brought on behalf of himself and a class of “[a]ll [others similarly [sjituated.” J.A. 24.

The amended complaint asserted seven claims falling into two categories: Claims One and Two challenged the defendants’ failure to accord Novella credit for the workers’ compensation hours he received; Claims Three through Seven contested the defendants’ calculation of Novella’s (and the class members’) pensions using two different rates because of a break in service. As relevant to this appeal, Claim Six asserted that the defendants’ practice of applying section 3.07 of the Plan, which governs Deferred Pensions, to recipients of Disability Pensions violated the Plan’s terms, and Claim Seven alleged that because the Plan “does not contain any provision describing the application of two benefit rates when a participant suffers a three-year interruption in service,” the defendants had violated ERISA in calculating Novella’s pension using two rates. Id. at 31-32.

In early 2004, before moving for class certification, Novella moved for summary judgment on his individual claims. The defendants cross-moved for the same. The district court (Michael B. Mukasey, then-Chief Judge) granted Novella’s motion in part. The court dismissed as unexhausted 10 Novella’s claims (styled as Claims One and Two) regarding the “defendants’ refusal to credit him with hours of service, and therefore pension credits, during the time he received workers’ compensation benefits.” 11 Novella v. Westchester County, N.Y. Carpenters’ Pension Fund (Novella I), No. 02-cv-2192, 2004 WL 1752820, at *6, 2004 U.S. Dist. LEXIS 15152, at *16 (S.D.N.Y. Aug. 4, 2004); see id. at *6-*7, 2004 U.S. Dist. LEXIS 15152, at *16-*22.

With regard to Novella’s challenge to the two-rate pension calculation (Claim Six), the court concluded that the defendants had acted arbitrarily and capriciously 12 by using two different rates to *136 calculate Novella’s pension because “their decision was based on an interpretation of the Westchester Plan that is inconsistent with the plain words of that Plan.” Id. at *3, 2004 U.S. Dist. LEXIS 15152, at *8. Citing sections 3.03 and 3.10 of the Plan, the court reasoned that the “Plan plainly provides that a participant who collects a Disability Pension should be entitled to the amount of a Regular Pension, which is calculated at one benefit rate.” Id., 2004 WL 1752820, at *3, 2004 U.S. Dist. LEXIS 15152, at *9. The court rejected the defendants’ argument that they were entitled to rely on the provisions governing Deferred Pensions — section 3.07 — because, at the time of his disability, Novella was not eligible for a Regular Pension as a result of his break in service. See id. at *4, 2004 U.S. Dist. LEXIS 15152, at *10-*13. The court concluded instead that “[njothing in [the section of the plan] ... describing] the eligibility requirements for a Disability Pension ... states that a [P]lan participant must satisfy the eligibility requirements for a Regular Pension ... in order to collect a Disability Pension.” Id., 2004 WL 1752820, at *4, 2004 U.S. Dist. LEXIS 15152, at *12. The court explained that section 3.10’s “use of the word ‘eligible’ in the phrase ‘the Regular Pension amount for which the Employee would have been eligible,’ ... referred] to a ‘Regular Pension amount, ’ rather than simply to a ‘Regular Pension.’ ” Id. (emphasis in Novella I) (quoting the Plan).

The court also addressed the defendants’ theory, raised for the first time after commencement of this lawsuit, that section 3.16 of the Plan supported their decision to use two different rates because it “authorizes [P]lan administrators to apply multiple benefit levels when calculating the pension of a [P]lan participant who has had a break in service.” Id. at *5, 2004 U.S. Dist. LEXIS 15152, at *14, *15. The court concluded that the defendants’ reliance on section 3.16 was misplaced because that section “does not reasonably allow [for the] interpretation” urged by the defendants. Id. In sum, the court rejected each of the defendants’ arguments, concluding that the defendants were not entitled under the terms of the Plan to use two different rates to calculate Novella’s Disability Pension.

Having granted Novella’s motion on the basis of his challenge to the two-rate calculation, the district court “dismissed as moot” Novella’s other claims regarding the amount of his Disability Pension (Claims Three, Four, Five, and Seven), which were argued “in the alternative,” and were “premised on the assumption that the terms of the ... Plan support [the] defendants’ decision.” Id. at *2, 2004 U.S. Dist. LEXIS 15152, at *6. Although the district court granted summary judgment to Novella on the merits of Claim Six, it did not award final relief at that time.

Following the district court’s decision in Novella’s favor on his individual claims, Novella moved for class certification under Rules 23(b)(1) and (2) of the Federal Rules of Civil Procedure, seeking certification of a class to include recipients of various types of pensions calculated using two rates, or, in the alternative, a narrower class of disability pensioners injured by the same practice. 13 The district court first determined that the only class for which *137 Novella potentially could serve as class representative was the “more limited class of Disability Pensioners” affected by the defendants’ practice of applying section 3.07 of the Plan — which pertains to Deferred Pensions and permits the use of multiple per-credit rates — to Disability Pensions. Novella v. Westchester County, N.Y. Carpenters’ Pension Fund (Novella II), No. 02-cv-2192, 2004 WL 3035405, at *4-*5, 2004 U.S. Dist. LEXIS 26149, at *14 (S.D.N.Y. Dec. 29, 2004). Turning to the requirements of Rule 23(a), the district court concluded that the commonality, typicality, and adequacy-of-representation prongs were met, but that an evidentiary hearing was necessary to determine whether the numerosity prong was satisfied. Id. at *6-*7, 2004 U.S. Dist. LEXIS 26149, at *16-*22. And, although the court had not yet decided whether Novella could satisfy Rule 23(a), it concluded that, should the class be numerous enough to satisfy Rule 23(a), “the class action [could] be maintained under Rule 23(b)(1)” because “[r]eformation of [the] defendants’ practice in calculating these Disability Pensions will result in pensions amounts being due to [all] these class members”— that is, “Plan-wide relief.” Id. at *8, 2004 U.S. Dist. LEXIS 26149, at *23, *24.

On August 2, 2006, after conducting the evidentiary hearing, the district court certified the class of Disability Pension recipients. See Novella v. Westchester County, N.Y. Carpenters’ Pension Fund (Novella III), 443 F.Supp.2d 540, 542-43 (S.D.N.Y. 2006). The court concluded that the proposed class of twenty-four “disability pensioners whose pensions were calculated using more than one rate due to a break in service” met the numerosity requirement of Rule 23(a)(1). 14 Id. at 544. The court’s determination turned on its view of the event necessary to start the running of the six-year statute of limitations for an ERISA claim. The defendants had argued that the statute of limitations applicable to each class member’s claim accrued as soon as the putative class member’s pension was calculated, and that only eight of the pensioners had begun receiving pensions within six years before Novella filed his complaint. Id. Novella asserted to the contrary that the court should adopt a continuing-violation approach to the statute of limitations, under which each month’s pension check would begin a new six-year limitations period. Id. at 545. The district court chose a third alternative, concluding that

[t]he relevant date for fixing the accrual of [the putative class members’] claim[s] is when a plaintiff was put on notice that the defendants believed the method used to calculate his disability pension was correct. Thus, the claim does not begin to run until a prospective class member inquires about the calculation of his benefits and the Plan rejects his claim that the benefits were miscalculated.

Id. (emphasis added).

Applying this rule, the court found Novella’s claim timely. Id. With regard to the *138 other putative class members, the court determined that, “[b]ecause the defendants ha[d] presented no evidence that they confirmed the correctness of the dual-rate benefits ealculation[s] more than six years before the filing of this lawsuit, th[e] court [could not] find [that] the statute of limitations ha[d] run on the claims of any of the 24 proposed class members.” Id. at 546. The court therefore concluded that the class consisted of twenty-four disability pensioners with timely claims and therefore was sufficiently large to satisfy Rule 28, and certified it. See id. at 546-48.

After the class was certified, both parties again moved for summary judgment, this time to resolve the class-action claims. The district court (Barbara S. Jones, Judge 15 ) referred the motions to a magistrate judge for a report and recommendation. On September 10, 2007, Magistrate Judge James C. Francis IV issued a Report & Recommendation (the “R & R”) recommending that the district court grant the plaintiffs motion and deny the defendants’. See Novella v. Westchester County, N.Y. Carpenters’ Pension Fund (Novella IV), No. 02-cv-2192, 2007 WL 2582171, at *1, 2007 U.S. Dist. LEXIS 66235, at *2 (S.D.N.Y. Sept. 10, 2007).

The R & R first addressed the defendants’ motion, in which the defendants “renewed] their argument that fifteen of the pensioners^ claims] are time-barred.” Id. at *2, 2007 U.S. Dist. LEXIS 66235, at *5. As a preliminary matter, the magistrate judge construed the motion for summary judgment as “an untimely application for reconsideration” of the district court’s ruling in Novella III determining the accrual of the statute of limitations and certifying the class. Id. The magistrate judge further concluded that “[e]ven if the defendants’ motion were timely, there is no basis for reconsideration,” id., 2007 WL 2582171, at *2, 2007 U.S. Dist. LEXIS 66235, at *7, because “[t]he law of the case doctrine requires a court to adhere to its own decision at an earlier stage of the litigation” absent “cogent or compelling reasons not to,” id., 2007 WL 2582171, at *2, 2007 U.S. Dist. LEXIS 66235, at *8 (internal quotation marks omitted), and the defendants had not shown that they would suffer any “injustice” if the court adhered to then-Chief Judge Mukasey’s prior'decisions, id. at *3, 2007 U.S. Dist. LEXIS 66235, at *10. The magistrate judge rejected the defendants’ argument that Novella III would “ ‘wreak havoc [on] Taft-Hartley Funds, such as [the] defendant [Fund], which rely on actuarial soundness for their very continued existence.’ ” Id. (quoting Defs.’ Mem. of Law in Support of Summ. J. 9). Finally, the magistrate judge refused to credit the defendants’ contention that the class members’ claims were not tolled by the filing of Novella’s suit because, based on the holding of Novella III, “ ‘their individual claims never accrued in the first instance.’ ” Id. at *4, 2007 U.S. Dist. LEXIS 66235, at *11 (quoting Defs.’ Mem. of Law in Support of Summ. J. 11). In the magistrate judge’s view, the absent class members’ claims accrued “once Mr. Novella filed his complaint challenging the Fund’s practice of applying two benefit rates.” Id., 2007 WL 2582171, at *4, 2007 U.S. Dist. LEXIS 66235, at *12.

The magistrate judge then turned to Novella’s motion for summary judgment on behalf of the class, agreeing with Novella that the defendants’ argument denying liability for the class members’ claims was “based exclusively on the theory of accrual *139 that Judge Mukasey previously rejected.” Id. at *5, 2007 U.S. Dist. LEXIS 66235, at *15. The magistrate judge therefore recommended granting summary judgment to the class “on the issue of liability ... with respect to the entire plaintiff class.” Id. With regard to Novella’s request for prejudgment interest for himself and for the class members, the magistrate judge decided that such an award was “appropriate.” Id. at *6, 2007 U.S. Dist. LEXIS 66235, at *18. Analogizing Novella’s and the class’s claims to those based upon latent injuries, he set the interest accrual date, for Novella, as “the date that the Fund denied his claim,” id. at *7, 2007 U.S. Dist. LEXIS 66235, at *20, and, for the absent class members, as “the date of the filing of the complaint,” id. Lastly, the magistrate judge recommended setting the interest rate at “the Fund’s assumed return of seven and one-half percent,” which the magistrate judge found to be more equitable than either New York’s statutory rate of 9 percent or the federal post-judgment rate. Id. at *8, 2007 U.S. Dist. LEXIS 66235, at *21-*22.

Over both parties’ objections and on de novo review, see Fed.R.Civ.P. 72(b)(3), the district court (Barbara S. Jones, Judge) adopted the R & R in its entirety. See Novella v. Westchester County, N.Y. Carpenters’ Pension Fund (Novella V), No. 02-cv-2192, 2008 WL 1743342, at *1, 2008 U.S. Dist. LEXIS 108341, at *2-*3 (S.D.N.Y. Jan. 14, 2008).

The parties each appeal. 16 The defendants appeal from the summary judgment in favor of Novella individually, from the certification of the class, from the summary judgment in favor of the class, and from the awards of prejudgment interest to Novella and the class members. Novella challenges the district court’s refusal to certify a broader class and its decision to award prejudgment interest to the class members only from the date that the complaint was filed.

DISCUSSION

I. Interpretation of the Plan

A. Standard of Review

“We review de novo a district court’s ruling on cross-motions for summary judgment, in each case construing the evidence in the light most favorable to the non-moving party.” Fund for Animals v. Kempthorne, 538 F.3d 124, 131 (2d Cir.2008) (internal quotation marks omitted). “Summary judgment is appropriate where there exists no genuine issue of material fact and, based on the undisputed facts, the moving party is entitled to judgment as a matter of law.” O & G Indus., Inc. v. Nat’l R.R. Passenger Corp., 537 F.3d 153, 159 (2d Cir.2008) (brackets and internal quotation marks omitted), cert. de *140 nied, — U.S. —, 129 S.Ct. 2043, 173 L.Ed.2d 1084 (2009); see also Fed.R.Civ.P. 56(a) (“The court shall grant summary judgment if the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law.”).

“ERISA does not itself prescribe the standard of review [by district courts] for challenges to benefit eligibility determinations.” Celardo v. GNY Auto. Dealers Health & Welfare Trust, 318 F.3d 142, 145 (2d Cir.2003). The Supreme Court has instructed that “plans investing the administrator with broad discretionary authority to determine eligibility are reviewed under the arbitrary and capricious standard.” Id. (citing Firestone Tire & Rubber Co. v. Bruch, 489 U.S. 101, 115, 109 S.Ct. 948, 103 L.Ed.2d 80 (1989)). Otherwise, courts review plan administrators’ determinations de novo. See Mario v. P & C Food Mkts., Inc., 313 F.3d 758, 763 (2d Cir.2002) (citing Firestone Tire, 489 U.S. at 115, 109 S.Ct. 948).

When the arbitrary-and-capricious standard applies, “[a] court may overturn a plan administrator’s decision ... only if the decision was without reason, unsupported by substantial evidence^] or erroneous as a matter of law.” Celardo, 318 F.3d at 146 (internal quotation marks omitted). “Where both the trustees of [an ERISA plan] and a rejected applicant offer rational, though conflicting, interpretations of plan provisions, the trustees’ interpretation must be allowed to control.” Miles v. N.Y. State Teamsters Conference Pension & Ret. Fund Emp. Pension Benefit Plan, 698 F.2d 593, 601 (2d Cir.), cert. denied, 464 U.S. 829, 104 S.Ct. 105, 78 L.Ed.2d 108 (1983).

Here, the district court did not decide which of the two standards of review should apply, because it concluded that the defendants’ interpretation of the Plan could not be sustained under either standard. However, in their briefing to this Court, the parties appear to agree that the arbitrary-and-caprieious standard applies in this case. See Defs.-Appellants’ Br. 17 [hereinafter Appellants’ Br.]; Pl.-Appellee’s Br. 49, 56 [hereinafter Appellee’s Br.]. We therefore address the defendants’ interpretation of the Plan only under that deferential standard, although, like the district court, we think that the outcome under the other, less deferential option — de novo review — would be no different.

B. The Merits

The question before us is whether the defendants acted arbitrarily and capriciously in interpreting the Plan to permit them to calculate Disability Pensions using two different per-credit rates if the pensioner had a break in service. The district court held that doing so was arbitrary and capricious because “[n]othing in the provisions of the [Plan provides] that a Disability Pension may be calculated using two different benefit rates when a participant has had a break in service.” Novella I, 2004 WL 1752820, at *3, 2004 U.S. Dist. LEXIS 15152, at *8-*9. We agree.

Disability Pensions are governed by section 3.10 of the Plan, which provides in relevant part that “[t]he Disability Pension amount shall be equal to the Regular Pension amount for which the Employee would have been eligible if he had been age 65 when he became disabled if the Participant had 10 or more units of credit at the time of his disability.” J.A. 153. Section 3.03 sets forth the means of calculating the Regular Pension amount. It authorizes calculation of that amount by reference to the number of credits a pensioner earned during “the period during which the Employer is obligated ... to contribute to the Fund” on behalf of the pensioner. See id. at 147, 151. The defendants offer four *141 arguments in support of their contentions that this Plan language permits a two-rate benefit calculation for recipients of Disability Pensions, and that the district court erred in concluding to the contrary.

First, the defendants assert that the Trustees awarded Novella the full benefit amount to which he was entitled because, although Novella was only sixty-one years old at the time of his disability, they treated him as if he were sixty-five years old when he became disabled as required by section 3.10, the Plan section governing Disability Pensions. They did not apply the age-based reduction that would otherwise have been permissible under section 3.05, which is entitled “Early Retirement Pension — Amount.” 17 Id. at 152. The defendants contend that they therefore complied with section 3.10’s requirements.

Although it is correct that, had Novella received an Early Retirement Pension, the pension amount would have been reduced to reflect his age, the argument is irrelevant. Throughout this lengthy dispute, Novella has never contended that his pension was reduced because of his age at retirement, nor has any party argued that he should have been awarded an Early Retirement Pension instead of a Disability Pension. Novella’s grievance, and these judicial proceedings, have focused entirely on whether the defendants’ use of two different rates to calculate Novella’s Disability Pension was improper.

Second, under section 3.02 of the Plan, to qualify for a Regular Pension, a pensioner’s employment — and consequently, employer contributions on his behalf— must have been “more or less continuous to his retirement date.” Id. at 151. The Plan’s provisions explain that, in this context, “more or less continuous” means that there must be “no period of three or more consecutive years without [his performing] at least” a small, specified, amount of covered work. Id. The defendants argue that because Novella’s employment was not “more or less continuous to his retirement date,” id., 18 Novella “was not ... eligible for the single accrual rate Regular Pension.” Appellants’ Br. 22.

The defendants may be correct that Novella is ineligible for a Regular Pension, but any such eligibility is not material to this dispute in light of the fact that he was awarded a Disability Pension. We agree with the district court that nothing in the Plan provisions governing Disability Pensions requires that a disability pensioner actually be eligible for another type of pension as a prerequisite to receipt of his Disability Pension. See Novella I, 2004 WL 1752820, at *3, 2004 U.S. Dist. LEXIS 15152, at *8-*9. Section 3.10’s reference to “the Regular Pension amount for which [Novella] would have been eligible if he had been age 65 when he became disabled,” J.A. 153 (emphases added), establishes not an eligibility requirement for a Disability Pension but a reference point for determining the proper amount of such a pension.

Moreover, were we to endorse a reading of the Plan requiring a Disability Pension recipient also to be eligible for a Regular Pension, we would render the Plan’s inclusion of a Disability Pension meaningless, inasmuch as any person who qualified for a Disability Pension would also be eligible *142 for a Regular Pension. It would appear likely that the Plan’s drafters established both Disability Pensions and Regular Pensions — and assigned different eligibility requirements to each — because they contemplated that Plan participants might become disabled before they become eligible for a Regular Pension, and did not want to bar such participants from receiving pension benefits.

Third, the defendants contend that because Novella did not meet the eligibility requirements for a Regular Pension due to his failure to perform covered work from 1982 to 1986, his pension benefit amount was “calculated pursuant to the only other methodology [i.e., section 3.07, which governs Deferred Pensions] for calculating a pension where there was a break in service.” Appellants’ Br. 22. Section 3.07 states that when a pensioner has a break in service that lasts at least three years, his pension shall be calculated using two rates: compensation for all credits earned before the break in service is “based on the benefit level that was in effect on the last day [the pensioner w]orked prior to” the break, while “the benefit amount for [any] additional units of credit” earned after a three-year break in service is “based on the benefit level in effect when the additional units were earned.” J.A. 152. The defendants argue that because Novella’s break in covered employment spanned more than three years, they are permitted to “us[e] two separate benefit accrual rates.” Appellant’s Br. 21.

The defendants’ argument is fatally flawed. The quoted section, Section 3.07, explicitly applies to Deferred Pensions; however, Novella was awarded a Disability Pension, not a Deferred Pension. Nothing in the Plan permits the defendants to apply a section controlling one specific type of pension to a pension of a different kind. In other words, the fact that the Disability Pension provisions do not include language permitting a two-rate calculation does not entitle the defendants to search for authorization to do so elsewhere in the Plan. Indeed — following both the presumption of consistent usage and meaningful variation, and the textual canon of expressio unius est exclusio alterius, see Cordiano v. Metacon Gun Club, Inc., 575 F.3d 199, 221 (2d Cir.2009)—the presence of that provision applicable to one type of pension makes clear that the omission of that provision in the part of the Plan governing another type of plan was deliberate. To permit the defendants to pick and choose language from disparate sections of the Plan would subvert the intention of the Plan’s drafters and the reasonable expectations of Plan participants.

Finally, the defendants argue that section 3.16, which is entitled “Application to Benefit Increases,” J.A. 156, justifies a two-rate method for calculating Disability Pensions. That section provides: “The pension to which a Participant is entitled shall be determined under the terms of the Plan and the benefit level as in effect at the time the Participant last separates from Covered Employment.” Id. The Plan defines a “last separation] from Covered Employment” as the “last day of [covered] Work which is followed by three consecutive calendar years of less than 1,000 hours of Covered Employment in each year.” Id. The defendants argue that a person can “last separate” from employment more than once, and that Novella did so in 1981 and again in 1995, thus permitting the defendants to calculate a pension using multiple benefit levels.

It is apparent from the record, however, that the defendants did not use Section 3.16 to calculate Novella’s pension in the first instance. As the district court noted, the defendants identified this section as justification for their calculation of Novel *143 la’s pension “for the first time in litigation.” Novella I, 2004 WL 1752820, at *5, 2004 U.S. Dist. LEXIS 15152, at *13. They did not cite this section of the Plan in their letters to Novella explaining the calculation of his benefits. See J.A. 183-94 (letters between Novella and the Fund). Nor did they indicate to Novella at any point during his administrative appeals that their two-rate calculation relied in any way on section 3.16. To permit them to assert this newly coined rationale in litigation despite their failure to rely upon it during the internal Fund proceedings that preceded this lawsuit would subvert some of the chief purposes of ERISA exhaustion: to “ ‘uphold Congresses] desire that ERISA trustees be responsible for their actions, not the federal courts,’ ” and to “ ‘provide a sufficiently clear record of administrative action’ ” should litigation ensue. Paese v. Hartford Life & Accident Ins. Co., 449 F.3d 435, 445 (2d Cir.2006) (quoting Kennedy v. Empire Blue Cross & Blue Shield, 989 F.2d 588, 594 (2d Cir.1993)). It would also clearly be inequitable. See id. at 447-48 (equitably estopping the defendant from arguing that the plaintiff had failed to exhaust an issue because a letter from the defendant had misled the plaintiff into thinking that he had no other administrative remedies to pursue). 19

Because we agree with the district court’s determination that the defendants’ two-rate calculation of Novella’s disability pension was arbitrary and capricious, we affirm its entry of summary judgment in favor of Novella individually. However, for the reasons discussed below, we nonetheless decline to affirm the summary judgment in favor of the plaintiff class.

II. Statute of Limitations and Class Certification

A. Standards of Review

We review the question of the application of the relevant statute of limitations — as we do all questions of law — de novo. United States v. Domino Sugar Corp., 349 F.3d 84, 86 (2d Cir.2003). However, “[a] district court’s certification of a class under Rule 23 is reviewed for abuse of discretion, provided that ... the court applied the proper legal standard[ ].” Brown v. Kelly, 609 F.3d 467, 475 (2d Cir.2010). This standard “applies both to the district court’s ultimate decision on class certification and to its rulings as to the individual Rule 23 requirements.” Id.

B. The Merits

1. Accrual of the Statute of Limitations. The Federal Rules of Civil Procedure permit maintenance of a class action only if the “class is so numerous that joinder of all members is impracticable.” Fed.R.Civ.P. 23(a)(1). This “numerosity” requirement “does not mandate that joinder of all parties be impossible — only that the difficulty or inconvenience of joining all members of the class make use of the class action appropriate.” Cent. States Se. & Sw. Areas Health & Welfare Fund v. Merck-Medco Managed Care, L.L.C., 504 F.3d 229, 244-45 (2d Cir.2007). “Determination of practicability depends on all the *144 circumstances surrounding a case, not on mere numbers.” Robidoux v. Celani, 987 F.2d 931, 936 (2d Cir.1993). Nonetheless, several district courts in our Circuit have suggested that courts are likely to conclude that the “numerosity” requirement is satisfied “when the class comprises 40 or more members” and unlikely to be satisfied “when the class comprises 21 or fewer.” Ansari v. N.Y. Univ., 179 F.R.D. 112, 114 (S.D.N.Y.1998).

In this case, the question of whether the certified class was sufficiently large to satisfy Rule 23 hinges on whether the statute of limitations for each class member’s claim began to run upon receipt of his first pension payment, as the defendants contend, or upon a class member’s first inquiry to the Fund regarding the amount of his benefits and the Fund’s rejection of his request that his pension be calculated using one rate, as the district court concluded and as Novella urges on appeal.

The parties agree that a six-year statute of limitations governs ERISA claims and that “[t]he relevant date for fixing the accrual of a miscalculation claim is when a plaintiff was put on notice that the defendants believed the method used to calculate his disability pension was correct.” Appellants’ Br. 26 (brackets omitted) (quoting Novella III, 443 F.Supp.2d at 545); see also id. at 27 (“The Fund agrees with the ... sentence quoted above. It makes perfect sense for a claim to accrue when the participant is put on notice that the Fund ‘believed the method used to calculate his disability pension was correct.’ ”); Appellees’ Br. 57 (asserting that federal courts generally apply a “discovery rule” for the “purposes of triggering the statute of limitations on an ERISA benefit claim”). The parties dispute, however, the time at which a pensioner can be considered to have been put on such notice. The issue is undecided in this Circuit. 20

The defendants urge us to reject the district court’s determination that the statute of limitations on a class member’s claim does “not begin to run until a prospective class member inquires about the calculation of his benefits and the Plan rejects his claim that the benefits were miscalculated,” Novella III, 443 F.Supp.2d at 545, and the court’s consequent finding that the existence of twenty-four class members whose claims were therefore timely meant that the class was numerous enough to meet the requirement of Rule 23(a)(1) of the Federal Rules of Civil Procedure. They argue that we should instead adopt a strict first-payment approach under which the statute of limitations for a miscalculation claim would begin to run when the pensioner receives his first check.

In support, the defendants point to Miller v. Fortis Benefits Insurance Co., 475 F.3d 516 (3d Cir.2007), in which the Third Circuit concluded that the statute of limitations on a claim that benefits have been *145 miscalculated starts to run when the calculation or repudiation is both “clear and made known to the beneficiary.” Id. at 521-22. The Miller court observed that this “ordinarily” will be “when [the beneficiary] first receives his miscalculated benefit award” because “[a]t that point, the beneficiary should be aware that he has been underpaid and that his right to a greater award has been repudiated.” Id. The court explicitly “rejected]” the rule proposed by the plaintiff in that case, which would have required a “formal denial of benefits to trigger the statute of limitations.” Id. at 521. The court did, however, require that a Fund’s “repudiation of the benefits [be] dear and [be] made known to the beneficiary” in order for the limitations period to begin running. Id. at 520-21 (emphasis in original). The court explained that it “considered] the clear repudiation concept to be useful ..., as it represents a refinement of the federal discovery rule in the context of ERISA claims for benefits.” Id. at 521. The defendants rely on Miller to support their contention that the Third Circuit has adopted a strict first-payment test for the accrual of the statute of limitations in ERISA miscalculation claims, and argue that we should follow suit.

Some other courts, however, including the district court in this case, have required that an ERISA fund provide a formal denial of a plaintiff’s application for the adjustment of benefits to trigger the running of the statute of limitations. In Miele v. Pension Plan of New York State Teamsters Conference Pension & Retirement Fund, 72 F.Supp.2d 88 (E.D.N.Y.1999), for example, the court considered the argument that “a miscalculation claim accrues on the date that a plaintiff is clearly and unequivocally informed of the amount of his benefit.” Id. at 99. The court noted the “logic and appeal” of such a “bright-line rule,” which would be “easily enforced and would correspond directly to the ... rule that a clear and unequivocal denial of benefits commences the statute of limitations period.” Id. (emphasis added). But, mindful of the fact that “a miscalculation generally involves an award of benefits rather than a denial of benefits and thus is less likely to put a plaintiff on notice of a possible claim,” id., the Miele court applied the rule adopted by the district court here: that “a miscalculation claim does not accrue until a plaintiff ‘inquires about the amount of benefits and is told that those benefits were correctly computed.’ ” Id. (brackets and ellipses omitted) (quoting Kiefer v. Ceridian Corp., 976 F.Supp. 829, 843 (D.Minn.1997)).

Still other courts have applied a continuing-violation theory to the accrual of a claim in similar circumstances. See Meagher v. Int’l Ass’n of Machinists & Aerospace Workers Pension Plan, 856 F.2d 1418 (9th Cir.1988). Under this theory, each payment based upon an alleged miscalculation “constitutes a fresh breach by the [defendants] of their duty to administer the pension plan in accordance ... with ERISA,” gives rise to “[a] separate cause of action,” and starts the running of a new “limitations period ... for each cause of action.” Id. at 1423. Many courts have, however, expressly rejected this method. See, e.g., Miller, 475 F.3d at 522 (collecting Third Circuit cases declining to apply a continuing-violation approach to claim accrual); Edes v. Verizon Commc’ns, Inc., 417 F.3d 133, 139-40 (1st Cir.2005) (rejecting a continuing-violation theory where the wrongful conduct was the defendant’s single misclassification of plaintiffs as off-payroll employees); Pisciotta v. Teledyne Indus., 91 F.3d 1326, 1332 (9th Cir.1996) (“Although the [plaintiffs] now contend that each and every time that they were entitled to a reimbursement payment it constituted a new and separate *146 breach of ERISA ..., the applicable four-year statute of limitations begins to run ‘when a plaintiff knows or has reason to know of the injury that is the basis of the action.’ ”); Phillips v. Alaska Hotel & Rest. Emps. Pension Fund, 944 F.2d 509, 520-21 (9th Cir.1991) (declining to apply a continuing-violation approach), cert. denied, 504 U.S. 911, 112 S.Ct. 1942, 118 L.Ed.2d 548 (1992).

We do not adopt the continuing-violation theory. We think that method is appropriate in ERISA cases, as elsewhere, only “where separate violations of the same type, or character, are repeated over time.” L.I. Head Start Child Dev. Servs., Inc. v. Econ. Opportunity Comm’n of Nassau County, Inc., 558 F.Supp.2d 378, 400 (E.D.N.Y.2008). Usually, “[t]hese cases are marked by repeated decision-making, of the same character, by the fiduciaries.” Id. But it is not as clear a fit in cases where, as here, “the plaintiff[’s] claims are based on a single decision that results in lasting negative effects.” Id. at 401; see also Schultz v. Texaco, Inc., 127 F.Supp.2d 443, 447 (S.D.N.Y.2001) (“[T]he mere fact that the effects of a single, wrongful act continue to be felt over a period of time does not render that single, wrongful act a single ‘continuing violation.’ ”); Miele, 72 F.Supp.2d at 102 n. 14 (rejecting application of the continuing-violation theory of accrual because a pension fund has no obligation “to continually reassess claim denials or benefit underpayments on a monthly basis”).

We also decline, however, to accept either of the approaches urged by the parties. The defendants’ bright-line approach is too harsh in that it places the burden on the pensioner — a party less likely to have a clear understanding of the terms of the pension plan and their application to his case — to confirm the correctness of his pension award immediately upon the first payment of benefits, regardless of the complexity of the calculations, or of the adequacy of the defendants’ explanation of the basis for the calculation. Indeed, this case illustrates the hazards of the defendants’ approach. The SPD — the document provided to all Plan participants, including Novella and the plaintiff class, to explain the rules of the pension plan — is silent on the underlying issue of multiple benefit calculation rates for Disability Pensions. And, unlike the simple percentage calculation at issue in Miller, see Miller, 475 F.3d at 522; cf. Young v. Verizon’s Bell Atl. Cash Balance Plan, 615 F.3d 808, 816 (7th Cir.2010) (finding a claim timely because the lump-sum payment the plaintiff received more than six years before was “not so inconsistent with her current claim for additional benefits as to serve as a clear repudiation”), cert. denied, — U.S. —, 131 S.Ct. 2924, 179 L.Ed.2d 1245 (2011), the determination of a Disability Pension award under the defendants’ Plan may have required more than a simple multiplication of two static numbers. 21

The district court’s and Novella’s bright-line approach — in which a limitations period does not begin to run “until a prospective class member inquires about the calculation of his benefits and the Plan rejects his claim,” Novella III, 443 F.Supp.2d at 545—also poses problems. Under that method, a pensioner could collect benefit checks for twenty or thirty years without any obligation to inquire as *147 to the correctness of the calculations underlying the benefit payments and could still thereafter assert a timely claim for miscalculation. Indeed, as the defendants point out, at least one class member is long dead. See Appellants’ Br. 29-30. Allowing that class member’s survivors to pursue his claim, the defendants say, despite the fact that he collected his benefits for years before passing away, would undermine the purpose of a statute of limitations. See, e.g., Order of R.R. Telegraphers v. Ry. Express Agency, Inc., 321 U.S. 342, 348-49, 64 S.Ct. 582, 88 L.Ed. 788 (1944) (“Statutes of limitation ... in their conclusive effects are designed to promote justice by preventing surprises through the revival of claims that have been allowed to slumber until evidence has been lost, memories have faded, and witnesses have disappeared.”); Carey v. Int’l Bhd. of Elec. Workers Local 363 Pension Plan, 201 F.3d 44, 47 (2d Cir.1999) (“Statutes of limitation serve several important policies, including rapid resolution of disputes, repose for those against whom a claim could be brought, and avoidance of litigation involving lost evidence or distorted testimony of witnesses.”). To the extent that the defendants could show that the deceased class member or his survivors had information available to them by which they reasonably could have discovered the alleged miscalculation, the district court might well agree with the defendants that permitting his survivors to assert a claim more than six years after receiving such information would be inequitable.

Having rejected each party’s views, we choose a third approach: We conclude that notice of a miscalculation can be imputed to a pensioner — and the statute of limitations will start to run — when there is enough information available to the pensioner to assure that he knows or reasonably should know of the miscalculation. We think this method best balances a pension plan’s legitimate interest in predictability and finality with a pensioner’s equally legitimate interest in having a fair opportunity to challenge a miscalculation of benefits once it becomes known — or should have become known — to him. Stated another way, this case-by-case reasonableness inquiry mitigates some of the harshness of the defendants’ proffered approach, while better respecting the defendants’ interests in finality and repose than the district court’s and Novella’s chosen method. 22

We think this method is consistent with the Third Circuit’s reasoning in Miller, which we read to endorse not a strict first-payment theory — such as that urged by the defendants — but rather a similar reasonableness approach. Indeed, in Miller, the Third Circuit appeared to contemplate that its “clear repudiation” rule would vary in its application to the facts of any individual case. See Miller, 475 F.3d at 521 (rejecting the plaintiffs “proposed application of the clear repudiation rule,” which would have required an explicit demand and refusal, and concluding that a court should ask “when a beneficiary knows or should know he has a cause of action” (emphasis added)); see also Fletcher v. Comcast Comprehensive Health and Wel *148 fare Plan, No. 209-cv-1272, 2011 WL 743459, at *5, *3, 2011 U.S. Dist. LEXIS 18199, at, *13, *14-*15 (W.D.Pa. Feb. 24, 2011) (noting that “Miller ... does not stand for the proposition that every erroneously calculated benefit award automatically serves as a ‘clear repudiation,’ ” and holding that “[a] reasonable finder of fact could conclude that ... [communications between the Plan and the plaintiff beneficiary] did not suffice to alert plaintiff that his benefits were being repudiated”).

Turning to the present case: In light of the standard we adopt, on the factual record before us, we are unable to determine whether, and if so when, each class member had information by which he knew or should have known of the miscalculation. We note that, based on the foregoing discussion, simply receiving a lower pension payment is not enough to put a pensioner on notice of a miscalculation. Conversely, actual notice to a pensioner that a double rate method was used would put him on notice. Similarly, informing a pensioner of the correct rate-times-units calculation, so that any difference between the putative calculation and the actual amount of the check would be obvious, is also probably enough. However, we cannot yet tell how many of the class members’ claims are timely. We therefore cannot, at this stage of the proceedings, confirm the district court’s conclusion that the class is sufficiently large to satisfy Rule 23(a)(l)’s numerosity requirement.

We therefore vacate the class certification and remand to the district court for further factfinding regarding when each plaintiff class member knew or should have known that the Fund had miscalculated his Disability Pension payments, and for consideration of whether there are enough class members with timely claims to merit certification. We therefore also vacate the summary judgment in favor of the class.

Finally on this score, we note that the method we adopt may in some cases require a resource-intensive, claimant-by-claimant inquiry to determine when a pensioner knew or reasonably should have known that his benefits were miscalculated. And this fact-dependent inquiry into each pensioner’s accrual date may in turn lessen the value, and indeed the availability, of class actions in this kind of litigation. However, that sort of problem is not unique to this context. See, e.g., Avila v. Willits Envt’l Remediation Trust, 633 F.3d 828, 841-42 (9th Cir.) (concluding that material issues of fact precluded summary judgment regarding whether certain class members in toxic-tort class action knew or should have known of their injuries), cert. denied, — U.S. —, 132 S.Ct. 120, 181 L.Ed.2d 44, 2011 WL 4530474 (Oct. 3, 2011); In re Brooklyn Navy Yard Asbestos Litig., 971 F.2d 831, 836 n. 1 (2d Cir.1992) (differentiating between joint trials which are “not questioned by plaintiffs or defendants” in mass tort cases from the issue of “the propriety of class actions” in such cases).

Moreover, the fact-intensive nature of our reasonableness approach could make it difficult for a potential class representative to meet the typicality requirement of Fed.R.Civ.P. 23(a)(3). But the case law on the effect of an individualized statute-of-limitations-accrual evaluation on a proposed class’s ability to meet the typicality requirement, if any, is sparse, see Chiang v. Veneman, 385 F.3d 256, 269 (3d Cir.2004); Ruppert v. Alliant Energy Cash Balance Pension Plan, 255 F.R.D. 628, 633-34 (W.D.Wis.2009), and we decline to address whether that requirement is satisfied on the record before us. We note, however, the well-established rule that a plaintiff must satisfy all of the require *149 ments of Rule 23, by a preponderance of the evidence, to obtain class certification, see Teamsters Local 445 Freight Div. Pension Fund v. Bombardier, Inc., 546 F.3d 196, 202 (2d Cir.2008); In re Initial Pub. Offerings Sec. Litig., 471 F.3d 24, 41 (2d Cir.2006), including the numerosity and typicality requirements of Rule 23(a), see Marisol A. v. Giuliani, 126 F.3d 372, 375-76 (2d Cir.1997) (citing Comer v. Cisneros, 37 F.3d 775, 796 (2d Cir.1994)).

2. Novella’s Cross-Appeal. We find no merit in Novella’s contention, asserted in his cross-appeal, that the certified class was too narrow inasmuch as the district court should not have limited it to persons receiving Disability Pensions.

Novella’s amended complaint asserted claims relating both to the two-rate calculation for disability pensioners and to the Plan’s “accrued benefit” provisions. See J.A. 30-31. The district court granted summary judgment to Novella on his individual Disability Pension claims and did not reach the other “accrued benefit” claims, but rather dismissed them as moot in light of the fact that the other claims would entitle Novella to no further relief. When Novella subsequently moved for class certification with regard to both the Disability Pension claim and the other claims, the district court certified only the former class because it concluded that Novella lost standing to pursue the “accrued benefit” claims when he had already “succeeded on an alternative theory of recovery.” Novella II, 2004 WL 3035405, at *4, 2004 U.S. Dist. LEXIS 26149, at *13.

Novella asserts in his cross-appeal that the district court “confused the mootness of an issue with the mootness of a case,” Appellee’s Br. 16 (emphasis in original), and therefore erred in dismissing Novella’s non-Disability Pension claims as “moot.” We agree that the claims were not “moot” in the technical sense; “it is cases rather than reasons that become moot” within the meaning of Article III. 23 Air Line Pilots Ass’n Int’l v. UAL Corp., 897 F.2d 1394, 1397 (7th Cir.1990). But where, as here, a litigant asserts multiple arguments in support of the relief he seeks, and the court grants him complete relief based upon one contention, courts also sometimes use “the word ‘moot’ ... to refer to an issue that need not be decided in light of the resolution [by the court] in the same opinion of another issue.” Id. It is in this sense that we understand the district court to have said that some of Novella’s claims were “moot.”

In any event, we agree with the district court’s decision not to certify the broader class. It was Novella’s choice to proceed individually first and only later move for class certification. In his briefing on his individual motion for summary judgment, Novella offered his various arguments in support of his motion in the alternative. See Novella I, 2004 WL 1752820, at *2, 2004 U.S. Dist. LEXIS 1266, at *6. The district court granted Novella complete relief on one claim and, in the exercise of its discretion, did not decide the merits of the others. It is the latter, unresolved claims that relate to the broader class for which Novella later sought certification. But by *150 the time Novella moved for class certification, his individual claims no longer matched the claims of the broader purported class, and he therefore was no longer an appropriate representative of that broader class. 24 Stated otherwise, Novella’s interest as a litigant would be to pursue the claim based on the Disability Pensions, while some class members’ interest would be to pursue the claims based on the Plan’s “accrued benefit” provisions instead. Novella therefore would not satisfy the typicality or adequacy-of-representation prongs of Rule 23(a).

III. Prejudgment Interest

A. Standard of Review

“The decision whether to grant prejudgment interest and the rate used if such interest is granted are matters confided to the district court’s broad discretion, and will not be overturned on appeal absent an abuse of discretion.” Endico Potatoes, Inc. v. CIT Group/Factoring, Inc., 67 F.3d 1063, 1071-72 (2d Cir.1995) (internal quotation marks omitted); see also Slupinski v. First Unum Life Ins. Co., 554 F.3d 38, 53-55 (2d Cir.2009); Commercial Union Assurance Co. v. Milken, 17 F.3d 608, 613-15 (2d Cir.), cert. denied, 513 U.S. 873, 115 S.Ct. 198, 130 L.Ed.2d 130 (1994).

B. The Merits

The district court awarded prejudgment interest to both Novella— beginning on the date the Fund denied his claim — and to the individual class members — beginning on the date Novella first asserted the class claims. We find no abuse of discretion in the district court’s award of prejudgment interest to Novella individually or in its selection of the appropriate rate. 25 We nonetheless vacate the award of prejudgment interest to the class in light of our determination that we must decertify the class and vacate the judgment in its favor.

The defendants argue that the district court’s award of prejudgment interest to Novella amounts to a “windfall” because such an award would compensate him without regard to his break in service, even though his employers did not pay contributions to the Fund during that time. But this argument essentially restates the defendants’ arguments on the merits of the two-rate calculation, which we have rejected. To the extent that the payment of prejudgment interest creates a financial burden on the Fund, that is a result of the Fund’s misinterpretation of its own Plan. It does not render the district court’s conclusion that prejudgment interest is necessary to fully compensate Novella an abuse of discretion.

We similarly conclude that the district court’s determination that the proper interest rate is 7.5 percent — the Fund’s assumed rate of return — was within its discretion. In light of the other options before the court, this rate seems to us to be entirely consistent with the principle that plaintiffs should be “made whole” and that defendants should “not profit by their failure to comply with their ERISA obligations.” Algie v. RCA Global *151 Commc’ns, Inc., 891 F.Supp. 875, 899 (S.D.N.Y.1994), aff'd, 60 F.3d 956 (2d Cir.1995); see also Slupinski, 554 F.3d at 54 (quoting Algie, 891 F.Supp. at 899).

We find no merit in Novella’s argument that the district court should have awarded prejudgment interest from the date of the first miscalculated check. In his R & R, the magistrate judge acknowledged three possible dates for the accrual of prejudgment interest: “the date of each underpayment, the date that a plaintiff asserted a claim, or the date that the Fund denied the claim.” Novella IV, 2007 WL 2582171, at *6, 2007 U.S. Dist. LEXIS 66235, at *18. The R & R recommended — and the district court concluded — that it would, in this case, be “anomalous to calculate interest from the date of injury, since it was within the power of the plaintiffs-to assert a claim of underpayment at any time and thus trigger review by the Fund.” Id., 2007 WL 2582171, at *7, 2007 U.S. Dist. LEXIS 66235, at *19. We have been given no reason to conclude that the district court abused its discretion in this regard.

CONCLUSION

For the foregoing reasons, we affirm the district court’s judgment in favor of Novella on his individual ERISA claims and its award to Novella of prejudgment interest. We vacate the district court’s certification of the class of Disability Pension recipients, its grant of judgment on the merits in favor of the class, and its award of prejudgment interest to the class members. We remand the case to the district court for further proceedings.

Each party shall bear its own costs.

. In approximately 1998, the Westchester Fund "merged with and into the Suburban New York Regional Council Pension Fund, which is now known as the Empire State Carpenters Pension Fund.” J.A. 57. The Westchester Fund no longer exists as a distinct entity.

.The SPD is the simplified explanation of the Plan that must be provided to participants under ERISA. According to the Department of Labor, "[t]he summary plan description ... tells participants what the plan provides and how it operates. It provides information on when an employee can begin to participate in the plan, how service and benefits are calculated, when benefits becomes vested, when and in what form benefits are paid, and how to file a claim for benefits.” U.S. Dep't of Labor, ERISA — Plan Information, http:// www.dol.gov/dol/topic/health-plans/ planinformation.htm (latest visit Sept. 5, 2011); see also Wilkins v. Mason Tenders Dist. Council Pension Fund, 445 F.3d 572, 580-81 (2d Cir.2006) ("Among other things, an SPD must set out the ‘circumstances which may result in disqualification, ineligibility, or denial or loss of benefits.’ 29 U.S.C. § 1022(b).”). The defendants printed the SPD and Plan together in one booklet, which they then provided to Plan participants. Although there are some differences between the SPD and the Plan, they are not material to our resolution of this appeal.

. The other two allowances provided for in the Plan are lump-sum benefits: the “Death Benefit” and the "Termination Benefit.” See J.A. 154-55.

. For reasons described infra note 16, all citations to the parties’ submissions on appeal, including briefs, refer to documents filed in connection with an earlier appeal in this case, docketed as numbers 08-0788-cv(L) and 08-0807-cv(XAP).

. According to the plaintiff's Local Rule 56.1 statement, he did not perform any work covered by the Plan between 1965 and 1975 because there were no jobs available to him. See J.A. 220. This break in service is not at issue in this appeal.

. The Plan sets out various schedules for the accumulation of pension credits, which depend on the year in which the credits were earned. See J.A. 130-34.

. That section reads:

Section 3.07 Deferred Pension — Amount

The Deferred Pension shall be calculated in the same manner as the Regular or Early Retirement Pension but shall be based on the benefit level that was in effect on the last day he Worked prior to accumulation of three One-Year Breaks in Service. If additional units of credit were earned after the period in which he accumulated three consecutive One-Year Breaks in Service, the benefit amount for such additional units of credit shall be based on the benefit level in effect when the additional units were earned.

J.A. 152.

. Any calendar year "after 1974 in which [the participant] fails to complete 100 hours of Covered Employment” constitutes a one-year Break in Service. J.A. 163.

. Subject matter jurisdiction was premised upon the questions of federal law that underlie this dispute. See 28 U.S.C. § 1331(a).

. Although "ERISA does not contain an explicit exhaustion[-]of[-]remedies requirement ... this Circuit has inferred [one].” Burke v. PriceWaterHouseCoopers LLP Long Term Disability Plan, 572 F.3d 76, 79 n. 3 (2d Cir.2009); see also id. at 79 (noting that "an ERISA action may not be brought in federal court until administrative remedies are exhausted”).

. After exhausting these claims, Novella again filed suit asserting Claims One and Two against the same defendants in the United States District Court for the Southern District of New York. On March 26, 2009, the district court (Barbara S. Jones, Judge) granted the defendants’ motion for summary judgment and denied Novella’s cross-motion. See Novella v. Empire State Carpenters Pension Fund, No. 05-cv-2079, 2009 WL 812271, at *1, 2009 U.S. Dist. LEXIS 25245, at *1-*2 (S.D.N.Y. Mar. 26, 2009); see also id. at *1 n. 1, 2009 U.S. Dist. LEXIS 25245, at *2 n. 1 (explaining the history of Novella's litigation against the Fund and its successor, the Empire State Carpenters Pension Fund). Novella appealed from the district court’s judgment. On November 18, 2009, another panel of this Court affirmed the judgment in favor of the defendants. See Novella v. Empire State Carpenters Pension Fund, 353 Fed.Appx. 596 (2d Cir.2009) (summary order).

.The court noted that there was some question regarding whether the arbitrary-and-capricious or de novo standard of review was appropriate to the circumstances of this case, but concluded that the defendants’ interpretation of the Plan failed under either standard. *136 See Novella I, 2004 WL 1752820, at *3, 2004 U.S. Dist. LEXIS 15152, at *8.

. The defendants argued that the motion was untimely because it was not made until after the court had resolved the summary judgment motions in Novella’s favor. See Novella v. Westchester County, N.Y. Carpenters’ Pension Fund, No. 02-cv-2192, 2004 WL 3035405, at *2, 2004 U.S. Dist. LEXIS 15152, at *5 (S.D.N.Y. Dec. 29, 2004). The court rejected this argument, noting that "Rule 23 *137 [of the Federal Rules of Civil Procedure] does not prohibit the filing of a class certification motion ... after a decision on the merits of the named individual plaintiff's claims." Id., 2004 WL 3035405, at *2, 2004 U.S. Dist. LEXIS 15152, at *7.

. The court explained that, while a class of twenty-four does not in all cases satisfy the numerosity requirement, Novella III, 443 F.Supp.2d at 546, a balancing of the relevant factors in this case justified certification of the relatively small class, id. at 546-48 (discussing the five factors for numerosity set forth in Ansari v. N.Y. Univ., 179 F.R.D. 112, 114-15 (S.D.N.Y.1998): "(1) ... judicial economy ...; (2) the geographic dispersion of members of the proposed class; (3) the financial resources of those members; (4) the ability of the members to file individual suits; and (5) requests for prospective relief that may have an effect on future class members.”).

. The case was reassigned to Judge Jones in October 2006, after Chief Judge Mukasey retired.

. After hearing argument in these cross-appeals on March 11, 2009, this panel determined that the district court’s judgments on appeal were not final and that we therefore lacked jurisdiction over the appeals. We therefore dismissed the appeals and instructed the parties that ”[i]n the event a final judgment is entered,” they could file a new, timely notice of appeal to return the cross-appeals to this panel for disposition. See Novella v. Westchester County, 335 Fed.Appx. 73, 74 (2d Cir.2009) (summary order). We also denied the defendants’ subsequent motion for panel rehearing. See id. at 74-76 (appending the Court’s order denying rehearing).

In September 2009, the parties each filed a notice of appeal, and their cross-appeals were returned to this panel. See Docket, Novella v. Westchester County, Nos. 09-4061(L), 09-3826(XAP) (2d Cir.). Pursuant to a scheduling order issued by this panel, the parties filed supplemental briefing, which briefing was later withdrawn on the parties' motion. As a result, we now address only the issues presented when the parties first filed their cross-appeals in 2008.

. Section 3.05 provides: "The monthly amount of the Early Retirement Pension is the amount of the Regular Pension reduced by one-half of one percent for each month by which the Participant is under age 65 on the Effective Date of his Pension.” J.A. 152.

. Novella does not dispute that he performed no covered work between 1982 and 1986, and therefore that his employment was not "more or less continuous” as defined in the Plan.

. Novella also argues, and the district court concluded, that even if the defendants had cited to section 3.16 to justify their calculation, the defendants' interpretation of that section fails because the phrase "last separated from Covered Employment” must be read to contemplate only one such "last separat[ion].” See Novella I, 2004 WL 1752820, at *5, 2004 U.S. Dist. LEXIS 15152, at *14-*16. While Judge Walker agrees with the district court on this score, Judge Koeltl and Judge Sack are not persuaded that the plain language of section 3.16 forecloses multiple dates of "last separation] from Covered Employment.” But because we think the defendants’ reliance on this section fails on other grounds, we need not reach this particular rationale of the district court.

. In Larsen v. NMU Pension Trust of the NMU Pension & Welfare Plan, 902 F.2d 1069 (2d Cir.1990), we concluded that on the facts of that case — which involved a claim by a pensioner's widow seeking to receive her late husband’s pension as a "husband and wife pension” payable after his death, id. at 1070-71 — the defendant fund had not "clear[ly] repudiated]” her claim until it responded to an inquiry made on the widow's behalf and stated that "[a]ll monies have been paid that are payable and there are no further monies due [the plaintiff],” id. at 1074. We did not, however, decide that an ERISA claim cannot under any circumstances accrue before an affirmative demand is made and an explicit rejection is offered. Moreover, Larsen is factually distinguishable. That case concerned not an underpayment claim like the one at issue in the present appeal, but a denial of benefits. We therefore do not think that Larsen provides binding Circuit precedent on the statute-of-limitations issue before us.

. We do not intend to suggest that the underlying basis for the class members’ claims was undiscoverable at the time of the first payment. Rather, it is for the district court to determine in the first instance at what point the defendants provided sufficient information to each class member such that that pensioner should have been able to recognize the miscalculation.

. And it may be that in many cases, our reasonableness approach will yield the same result as the first-payment theory favored by the defendants, in that the miscalculation will be apparent from the face of a payment check, or will readily be discoverable from information furnished to pensioners by the pension plan at the time the first check is issued, thereby starting the running of the statute of limitations as of that date. Nevertheless, whether that is the case is for each district court to determine in the first instance.

. Mootness in the Article III sense occurs when there "no longer is an actual controversy between adverse litigants,” and the plaintiff therefore lacks standing to continue to pursue his claims in federal court. Erwin Chemerinsky, Federal Jurisdiction 130 (5th ed. 2007); see also In re Zarnel, 619 F.3d 156, 162 (2d Cir.2010); County of Suffolk, N.Y. v. Sebelius, 605 F.3d 135, 140 (2d Cir.2010); ABN Amro Verzekeringen BV v. Geologistics Americas, Inc., 485 F.3d 85, 94 (2d Cir.2007); Richard H. Fallon, Jr. et al., Hart and Wechsler’s The Federal Courts and the Federal System 205 (5th ed. 2003) (summarizing the "foundations” of the mootness doctrine).

. Notwithstanding Novella's success on his individual claim, Novella had standing to represent the class of Disability Pension recipients inasmuch as the district court had not yet reduced Novella’s victory to a final judgment.

. Although ERISA does not explicitly provide for prejudgment interest, courts can make such awards as part of their “wide discretion in fashioning equitable relief to protect the rights of pension fund beneficiaries.” Katsaros v. Cody, 744 F.2d 270, 281 (2d Cir.), cert. denied, 469 U.S. 1072, 105 S.Ct. 565, 83 L.Ed.2d 506 (1984).