As in M.B. Claff, Inc. v. Massachusetts Bay Transp. Auth., ante 596 (2004), the present appeal contends that the Superior Court judge erred in utilizing the statutory interest rate set by G. L. c. 79, § 37, to calculate the interest to be awarded as part of an eminent domain damages case. The landowner, Liberty Square Development Trust (Liberty), filed a motion on the day of trial asking the judge to determine the interest rate based on a “prudent investor” standard rather than on the statutory standard. The judge ruled that interest was to be calculated at the statutory rate. After entry of judgment reflecting that rate, Liberty appealed. We transferred the case to this court on our own motion. For the following reasons, we conclude that Liberty did not make a sufficient showing that the statutory rate, as applied to the land taking in question, failed to provide reasonable compensation, and we therefore affirm the judgment.
1. Background. On June 7, 1995, the city of Worcester (city) effected a taking of two parcels of land owned by Liberty, located on Commercial and Central Streets. The city offered a nominal sum as compensation, which Liberty rejected. Liberty filed an action for its damages on May 6, 1998.
On June 19, 2002, immediately prior to the start of trial, Liberty filed a “motion to determine and assess a proper rate of interest.” In that motion, Liberty contended that the interest rate set by G. L. c. 79, § 37, was inadequate to provide it with just compensation. Specifically, whereas the statutory formula would provide a rate of 5.88 per cent per year (that rate being based on the auction price of one-year United States Treasury bills immediately prior to the date of taking), Liberty contended that “[a] prudent investor, investing in a mix of low to moderate risk securities of varying maturity, would have realized an annual return of 6.5% to 7.5% depending upon the mix in the portfolio.” The motion recited the rates earned on various forms of investments during the years 1994 through the first quarter of 1999 (Moody’s AAA rated corporate bonds, thirty-year Treasury bonds, five-year Treasury notes, six-month bankers acceptances, and the prime rate), advising the court that “[ejvidence of the rates quoted shall be provided post-verdict, pre-judgment by affidavit or testimony” and that it was “prepared to offer testimony and/or affidavit as to the prudent investor standard in real estate.” No action was taken on the motion prior to trial.
*607On June 26, 2002, after a one-week trial, the jury returned a verdict in favor of Liberty in the amount of $743,549. The following day, the judge ruled on Liberty’s motion, specifying that interest was to be calculated at the statutory rate, which the judge mistakenly identified as 5.66 per cent per year. Judgment was entered on July 2, 2002, with simple interest from the date of taking calculated at that rate.
On July 17, Liberty filed a motion to amend the judgment, asking to adjust the interest rate from the 5.66 per cent rate referenced in the judge’s ruling to “the correct rate” of 5.88 per cent.2 Liberty’s motion explained that G. L. c. 79, § 37, set the interest rate by reference to the “last auction of 52-week United States Treasury bills settled immediately before the date of taking,” and that the last such auction prior to the June 7, 1995, taking was the auction held on May 25, 1995. The figures reflecting those auction rates were set forth in Federal publications, which specified a rate of 5.88 per cent for the May 25, 1995, auction.3 Liberty’s motion suggested that the clerk had probably obtained the 5.66 per cent rate by consulting an unofficial table of interest rates that contained that error. The motion said nothing about any higher or other rate of interest, and made no reference to Liberty’s prior request to have the judge determine interest based on a “prudent investor” standard.
On July 25, the city also filed a motion to amend the judgment. The city’s motion asked the judge to reduce the interest award on account of Liberty’s dilatory conduct during discovery, which had allegedly caused considerable delay in reaching trial.4
On August 16, prior to any ruling on either party’s motion to amend the judgment, Liberty filed a motion for reconsideration of the judge’s ruling on its earlier motion to determine a proper *608rate of interest, along with an “amended motion to determine and assess a proper rate of interest.” That “amended” motion, like the original motion, asked the judge to apply a rate of interest that would have been earned by a “prudent investor” in lieu of the statutory rate. However, the “amended” motion submitted different figures based on a larger assortment of investment measures than those referenced in the original motion, along with an affidavit from an investment expert and an affidavit from the trustee of Liberty. Whereas the original motion had asked for an interest rate in the range of 6.5 to 7.5 per cent, Liberty’s “amended” motion now sought an interest rate of 11.12 per cent (according to the expert) or 12 per cent (according to the trustee).
On August 23, the city tendered a check in the amount of $1,059,132.88 to Liberty’s counsel “in full satisfaction” of the judgment. On August 26, Liberty’s counsel replied that, in light of the unresolved issues concerning the interest award, Liberty was not willing to accept the tendered check “in full satisfaction” of the judgment, but would only be willing to accept it as payment on account.
It appears that the judge held a hearing on the outstanding motions on August 28. At that hearing, he denied the city’s motion to amend the judgment (thereby rejecting the city’s contention that Liberty’s pretrial delay warranted a reduction in the interest award) and allowed Liberty’s motion to amend the judgment, correcting the rate from 5.66 per cent to the 5.88 per cent rate provided by G. L. c. 79, § 37. During the course of the hearing, Liberty also asked (for the first time) that the interest be calculated as compound interest, and raised a concern as to whether the city’s tender of its check on August 23 operated to stop the accrual of postjudgment interest as of July 31.5 After each side submitted further memoranda on those remaining two points, the judge ordered that judgment be entered with simple interest, and that postjudgment interest would not accrue past July 31. Ultimately, the total amount of the judgment (including prejudgment interest) was calculated at $1,052,654.21, plus *609costs of $9,564.40 (see note 2, supra), with postjudgment interest through July 31 of $4,951.68. Meanwhile, on September 9, 2002, Liberty had accepted the city’s check “on account.”
2. Discussion. The principal issue on appeal is whether the judge erred in denying Liberty’s request to calculate interest based on a “prudent investor” standard rather than at the rate set by G. L. c. 79, § 37.6 Before reaching the merits of that issue, we must first address the city’s arguments that the issue was not timely or properly raised below.
a. Waiver. As we discussed in M.B. Claff, Inc. v. Massachusetts Bay Transp. Auth., ante 596, 599-601 (2004), there is some merit to requiring a party to plead and then prove at trial a claim that “just compensation” for the taking in question requires application of an interest rate higher than that provided by G. L. c. 79, § 37. Here, Liberty did not raise this issue until literally the morning of trial, normally viewed as a time that is too late to insert a new, substantive claim into the case. Moreover, it did not introduce any evidence on the point at trial, but instead sought leave to produce affidavits or testimony after trial, to the extent that such evidence was deemed necessary to verify the various figures submitted in its motion. However, as we also noted, procedures for determining interest rates in eminent domain cases are not uniform, and property owners have been allowed to challenge the adequacy of statutory interest rates after trial on damages. Id. at 600-601, and cases cited.
Here, it does not appear that the city objected to Liberty’s motion on grounds of untimeliness,* ****7 or that the city objected to the proposal that the judge decide the matter after trial. The *610judge apparently took the motion under advisement, and then ruled on its merits immediately after the verdict was returned. While we have concerns about the late hour at which this issue was inserted into the case, the judge did not abuse his discretion in agreeing to entertain the request, particularly where the city voiced no procedural objection at the time.
The city next argues that, when Liberty did file a motion to amend the judgment pursuant to Mass. R. Civ. R 59 (e), 365 Mass. 827 (1974), it waived its claim to any interest rate higher than the statutory rate because it asked that the judgment be amended to reflect the “correct interest rate” of 5.88 per cent pursuant to the statute. We do not think that that motion operated to waive the issue. Liberty had already requested, by written motion, that the judge set interest at the rate that a “prudent investor” would have earned, rather than at the statutory rate. That motion had effectively been denied with the judge’s determination that the statutory rate should be utilized. When the interest calculation in the subsequent judgment mistakenly utilized a figure even lower than the statutory rate, Liberty could ask that that technical mistake be corrected without thereby waiving its right to claim that the judge’s earlier substantive decision on the issue was erroneous. When a party’s rights on a prior ruling have already been preserved, that party is not required to raise the same issue again in a rule 59 (e) motion. Where, as here, there is another, independent ground for a rule 59 (e) motion, that motion can assert that other ground without waiving prior issues that have already been raised and decided.* ****8
We do agree with the city that Liberty’s later “amended” motion for determination of the interest rate, and Liberty’s *611companion motion for “reconsideration,” were untimely.9 They were not filed until some seven weeks after the original motion had been acted on, and six weeks after judgment had been entered. The judge was not required to entertain Liberty’s belated efforts to improve on its original motion. The “amended” motion did not identify any reason why its new figures, and its expanded factual basis, could not have been presented as part of the original motion. There is no error in the denial of a motion that merely seeks, as this one did, a “second bite at the apple.” Thus, we consider only whether the judge, in denying the original motion as filed, committed error. For the reasons discussed below, we conclude that he did not.
b. Challenge to the statutory interest rate. Under State and Federal constitutional principles, an owner whose property is taken by eminent domain is entitled to “just” and “reasonable” compensation, under the Fifth Amendment to the United States Constitution (“just compensation”) and art. 10 of the Massachusetts Declaration of Rights (“reasonable compensation”). Where, as here, there is delay between the time of the taking and the time the owner receives compensation, an award of interest to compensate the owner for that delay is itself part of the “just compensation” to which the owner is entitled. See Seaboard Air Line Ry. v. United States, 261 U.S. 299, 306 (1923); Verrochi v. Commonwealth, 394 Mass. 633, 636-637 (1985); Woodworth v. Commonwealth, 353 Mass. 229, 231-233 (1967). Because it is a component of the compensation mandated as a matter of constitutional law, the ultimate determination as to what interest rate will provide adequate *612compensation for delay in payment is a judicial function. Verrochi v. Commonwealth, supra at 638, citing Miller v. United States, 620 F.2d 812, 837 (Ct. Cl. 1980).
However, the Legislature may address the issue of the interest to be paid on damage awards in land taking cases, and any interest rate set by statute enjoys a rebuttable presumption that it is a reasonable rate that would satisfy constitutional requirements. See Tucson Airport Auth. v. Freilich, 136 Ariz. 280, 284 (1983); State v. Jim Lupient Oldsmobile Co., 509 N.W.2d 361, 364 (Minn. 1993); Adventurers Whitestone Corp. v. City of N.Y., 65 N.Y.2d 83, 87-88, appeal dismissed, 474 U.S. 935 (1985). A claimant seeking compensation above the statutory interest rate may overcome that presumption by showing that the statutory rate is so low that it fails to meet the constitutional standard of reasonableness. See Tucson Airport Auth. v. Freilich, supra; Adventurers Whitestone Corp. v. City of N.Y., supra.
A claimant does not meet that burden merely by demonstrating some alternate measurements for an interest rate that might also qualify as “reasonable.” See Tucson Airport Auth. v. Freilich, supra at 283 (finding that twelve per cent was “reasonable rate” did not mean statutory rate of ten per cent was “unreasonable”); Matter of the City of N.Y., 58 N.Y.2d 532, 537-538 (1983), and cases cited (“slight variations” between statutory rate and prevailing rates do not make statutory rate so “unreasonably low” as to be unconstitutional). The concept of a “reasonable” interest rate to compensate for delay in payment connotes a range of figures, not one precise figure. See Tuscon Airport Auth. v. Freilich, supra. Thus, as the first step to proving entitlement to a rate other than the statutory rate, a claimant must demonstrate that the statutory rate is significantly or substantially lower than what would meet the constitutional minimum. See id. at 284 (statutory rate constitutional unless market rates “far in excess”); Redevelopment Agency of Burbank v. Gilmore, 38 Cal. 3d 790, 806 n.19 (1985) (statutory rate provides just compensation if not “substantially below” what prudent investor would have earned); Matter of S. Bronx Neighborhood Dev. Plan, 110 Misc. 2d 571, 572-573 (N.Y. Sup. Ct. 1981), aff’d, 58 N.Y.2d 532 (1983) (statutory rate unconsti*613tutional when all interest rates during relevant period “consistently and substantially greater”). If that showing is made, the statutory rate is no longer applicable, and it is then up to the judge to determine what interest figure to apply. See United States v. 50.50 Acres of Land, 931 F.2d 1349, 1355 (9th Cir. 1991), citing United States v. Blankinship, 543 F.2d 1272, 1274 (9th Cir. 1976). In that second step, selection of an appropriate figure is customarily based on the “prudent investor” standard, a standard that awards the claimant an interest rate comparable to what would have been earned by a “prudent investor” over the same period of time. Id. at 1355-1356. While the same evidence will ordinarily be submitted to prove both the alleged unreasonableness of the statutory rate and what a “prudent investor” would have earned (i.e., evidence of rates of return on reasonably safe investments over the same time period), the inquiry itself remains a two-step process that asks two separate questions: (1) Is the discrepancy between the statutory rate and the rates earned by prudent investors sufficiently large to render the statutory rate unreasonable? (2) If (and only if) so, what rate will represent just and reasonable compensation for the delay in payment? See United States v. 50.50 Acres of Land, supra at 1356 (remanded for further findings when judge imposed rate higher than statutory rate without first determining that statutory rate was unreasonable).
We therefore look at Liberty’s motion, as originally filed, to assess whether Liberty made that initial, threshold showing of unreasonableness.10 Liberty’s motion asserted that a prudent investor would have earned 6.5 per cent per year to 7.5 per cent per year during the relevant time period. In other words, on Liberty’s own calculation, a rate as low as 6.5 per cent would satisfy constitutional requirements. The rate set by G. L. c. 79, § 37, would set a rate of 5.88 per cent for this particular taking, or only 0.62 percentage points below what Liberty concedes would be constitutionally adequate. Liberty cites no precedent suggesting that a discrepancy that small suffices to demonstrate *614that the statutory rate is substantially or significantly below constitutional requirements. Cf. United States v. 319.46 Acres of Land, 508 F. Supp. 288, 290 (W.D. Okla. 1981) (average rate of “composite” securities 2.5 percentage points above statutory rate); Redevelopment Agency of Burbank v. Gilmore, supra at 195 Sc n.4 (all rate measures at least three percentage points higher than statutory rate); Matter of the City of N.Y., supra at 538 (six per cent rate unconstitutional when average rates on “stable investments” and public securities ranged between 8.3 per cent and 12.5 per cent).
Moreover, while Liberty’s motion did not set forth how it weighed the investment figures presented to reach its ostensible pmdent investor range of 6.5 per cent to 7.5 per cent, it is apparent from the face of the motion that Liberty’s calculation included higher rates from a time period that was totally irrelevant. Specifically, in each of the investment categories listed, Liberty included rates prevailing in 1994, and in every one of those categories, the rates in 1994 were higher than in any of the subsequent years.11 However, the taking in this case did not occur until June, 1995 — prevailing rates in 1994 have no bearing on what Liberty might have earned had it been paid and then prudently invested the proceeds in June, 1995. Presumably, if those higher 1994 figures are removed from the calculation (as they must be due to their irrelevance), the over-all range itself would be at least somewhat lower.12 Thus, on a purely numerical basis, the judge would have been warranted in *615concluding that Liberty had failed to establish that the 5.88 per cent rate set by G. L. c. 79, § 37, was so far below a reasonable rate as to be unconstitutional.
The judge’s assessment of the reasonableness of the statutory rate could also consider the method by which that rate was set. Much of the jurisprudence concerning the inadequacy of statutory rates concerns statutes that set a single, flat rate to be applied to every taking, without regard to any rate being set by the marketplace. See, e.g., United States v. Blankinship, supra at 1276; Miller v. United States, 620 F.2d 812, 837-840 (Ct. Cl. 1980); Redevelopment Agency of Burbank v. Gilmore, supra at 795; Matter of the City of N.Y., supra at 538. By their nature, such fixed rates have a degree of arbitrariness, reflecting a Legislature’s attempt to set its own price for the taking of property without regard to the market.
More recently, however, statutes setting interest rates for eminent domain cases have shifted (as has G. L. c. 79, § 37) to specification of a formula or methodology that is itself tied to some market rate. See, e.g., 40 U.S.C. § 258e-l (2000) (recodified at 40 U.S.C. § 3116); Minn. Stat. § 117.195 (1997); Minn. Stat. § 549.09 (2000). Such fluctuating statutory rates respond to the marketplace and are thus driven by forces that are outside the control of the Legislature (or the taking authority). While an owner remains free to challenge such a rate (see United States v. 50.50 Acres of Land, supra at 1355-1356), courts have been inclined to show greater deference to statutory rates that rise and fall in accordance with market forces on the theory that it is “reasonable” to use a market-driven measure as a fair means of determining just compensation. See United States v. Certain Land Situated in Detroit, 286 F. Supp. 2d 865, 871 (E.D. Mich. 2003); Tulare Lake Basin Water Storage Dist. v. United States, 59 Fed. Cl. 246, 266 (2003). See also Redevelopment Agency of Burbank v. Gilmore, supra at 807 n.21 (court would show deference to legislative adoption of “prevailing-rate formula” as *616long as “general requirements of ‘just compensation’ ” satisfied).13
For these purposes, a legislative selection of an extremely safe form of investment as the yardstick for the interest rate in eminent domain cases is a reasonable choice of measure — judgments in eminent domain cases, after all, are virtually certain of being paid, and the rate of return on a conservative investment with a comparable degree of safety fairly compensates the owner for the delay in payment. See State v. Jim Lupient Oldsmobile Co., 509 N.W.2d 361, 364 (Minn. 1993) (comparing statutory rate to rate on investments that “guarantees safety of principal”). See also United States v. Blankinship, supra at 1276; United States v. Certain Land Situated in Detroit, supra; Matter of S. Bronx Neighborhood Dev. Plan, 110 Misc. 2d 571, 573 (N.Y. Sup. Ct. 1981) (medium term public securities provide basis for calculating proper rate). But see Miller v. United States, supra at 839; United States v. 429.59 Acres of Land, 612 F.2d 459, 464-465 (9th Cir. 1980); Redevelopment Agency of Burbank v. Gilmore, supra at 804-805. Put differently, the constitutional standard of “just compensation” does not require that someone who is guaranteed a return of principal (which is effectively the position of a landowner awaiting payment for a governmental taking) nevertheless be allowed to recoup a rate of return that could only be achieved by placing that principal at greater risk.
Since 1993, G. L. c. 79, § 37, has employed a fluctuating market rate to determine the interest payable on eminent domain damages awards. See St. 1993, c. 110, § 137. The statute employs an interest rate based on the auction price of one-year Treasury bills, a very conservative investment vehicle that appropriately reflects the essentially nonexistent risk that the landowner faces with respect to ultimate payment of the principal owed. See Pettro v. United States, 47 Fed. Cl. 136, 155 (2000) (one-year Treasury bills represent reasonable rate for eminent domain cases because they “account for inflation while avoiding a reward for risks which the plaintiff did not undertake”). Liberty has not identified anything unreasonable *617about utilizing that particular market-driven measure. All it has done is to point to other market-driven measures and demonstrate that they yield rates slightly higher.14 The fact that various conservative investments do not yield precisely identical rates does not make it “unreasonable” for the Legislature to have chosen the particular conservative investment of the one-year Treasury bill as the measuring rate.
We recognize that the rate set by § 37 could, despite the fact that it is set by a market measure, result in a rate that would be unreasonable in a particular case. Specifically, § 37 sets the rate as of the date of taking (by reference to the last auction prior to the taking), and that rate then remains fixed.15 Obviously, if rates rose significantly between the date of taking and the date of payment, the rate prevailing at the very beginning of the period would be an artificially low measure of the over-all rate during that entire period. See Miller v. United States, 620 F.2d 812, 838 (Ct. Cl. 1980). However, that did not happen in this case. To the contrary, just as other market rates fell in the years subsequent to this particular taking, the rate for one-year Treasury bills also fell. In fact, the May 25, 1995, auction that set the rate for this case at 5.88 per cent was one of the highest for that particular security over the years in question. See 28 U.S.C. § 1961. Cf. Roberts v. Worcester Redevelopment Auth., 53 Mass. App. Ct. 454, 457 n.4 (2001) (during four years following taking, rates for one-year Treasury bills averaged almost two percentage points higher than rate as of date of taking). Thus, as applied to this case, the market-driven interest measure specified in § 37 did not have the effect of setting an unreasonable interest rate.
We thus conclude that there was no error in denying Liberty’s request for an alternative computation of interest, as Liberty did not meet its burden of demonstrating that the statutory rate of 5.88 per cent was so unreasonably low as to deprive it of just *618compensation for the delay in payment of its damages. Where Liberty failed to make that threshold showing, the judge was not required to assess what other market rates might also have been reasonable.16
However, we note with some urgency that other developments now render G. L. c. 79, § 37, obsolete, as the interest rate defined in that section is premised on the issuance of a form of United States Treasury security that no longer exists. The statute sets the interest rate at the “annual rate equal to the coupon issue yield equivalent, as determined by the United States Secretary of the Treasury, of the average accepted auction price for the last auction of 52-week United States Treasury bills settled immediately before the date of taking.” G. L. c. 79, § 37. However, the fifty-two week United States Treasury bill was discontinued in 2001, with the final auction of that security occurring on February 27, 2001.17 A literal reading of § 37 would thus provide that the rate of interest for a taking occurring today would be based on a rate defined by a sale of Treasury securities that occurred over three years ago — that February 27, 2001, auction would technically qualify (and will indefinitely continue to qualify) as the “last auction of 52-week *619United States Treasury bills settled immediately before the date of taking.” See G. L. c. 79, § 37.
It was the Legislature’s obvious intent in § 37 that the interest rate for eminent domain takings be set by reference to a specific market rate that prevailed immediately prior to the date of taking. Now, however, the statute has the effect of setting a permanently fixed rate that does not, even as of the date of taking, reflect market reality by any measure. It has been suggested that the problem of allegedly confiscatory interest rates can be better dealt with by a legislative solution (i.e., the adoption of a market-driven method for calculating interest that would, at least in most cases, satisfy the constitutional requirement of just and reasonable compensation) than by judicial determination on a case-by-case basis, an approach that leads to uncertainty and inconsistency. See Pettro v. United States, 47 Fed. Cl. 136, 154 (2000) (favoring “uniform interest rates in order to avoid discrimination among litigants”); Tucson Airport Auth. v. Freilich, 136 Ariz. 280, 283 (1983). However, if the statute does not utilize a reasonable method for determining an interest rate, constitutional requirements will necessitate judicial determination, and the resulting uncertainty and inconsistency will be unavoidable. Although G. L. c. 79, § 37, operated to set a rate that met constitutional requirements for this particular taking back in 1995, the statute is now outdated, no longer serves the purpose the Legislature originally intended, and may fail to satisfy constitutional requirements in future. We thus commend this issue to the Legislature’s immediate attention.
Judgment affirmed.
The motion also asked that the judgment be amended to reflect the addition of costs in the amount of $9,564.40.
See 28 U.S.C. § 1961 (2000).
In the course of pretrial discovery motions, the city had raised objections to the delay and had asked that, as a result of that delay, no interest be awarded as part of any judgment ultimately rendered in favor of Liberty. The judge who heard those discovery motions declined to grant that particular form of relief at the time, noting that the request should be referred to the trial judge.
The statute provides that postjudgment interest ceases to accrue as of “the last day of the month prior to the month in which such judgment is satisfied.” G. L. c. 79, § 37.
In its appeal, Liberty also attempts to raise a series of new theories and claims, all of which have been waived. Liberty’s claim that the city violated its civil rights, that G. L. c. 79, § 37, violates equal protection guarantees, and that it is entitled to attorney’s fees were not raised below, and therefore cannot be raised on appeal.
The city’s brief on appeal, submitted prior to the Appeals Court’s decision in M.B. Claff, Inc. v. Massachusetts Bay Transp. Auth., 59 Mass. App. Ct. 669 (2003), suggested the precise opposite, namely, that Liberty’s motion regarding interest was premature because the issue could only be raised by way of a motion to amend the judgment under Mass. R. Civ. P. 59 (e), 365 Mass. 827 (1974). See Shawmut Community Bank, N.A. v. Zagami, 419 Mass. 220, 223 (1994); J.W. Smith & H.B. Zobel, Rules Practice § 59.15, at 454 (1977 & Supp. 2004). In M.B. Claff, Inc. v. Massachusetts Bay Transp. Auth., ante 596, 603 *610n.7 (2004), we noted that a rule 59 (e) motion has been suggested as an appropriate method by which to challenge the statutory rate of interest, see United States v. 329.73 Acres of Land, 695 F.2d 922, 925 (5th Cir. 1983), but there is no basis for suggesting that a rule 59 (e) motion would be the only appropriate method.
The mere fact that Liberty’s motion used the term “correct interest rate” when referring to the statutory rate of 5.88 per cent does not change this analysis. In context, the motion was simply (and accurately) noting that the 5.66 per cent rate used by the clerk was based on an error in an unofficial source, with 5.88 per cent being the “correct” rate under the statute.
We also agree with the city that Liberty’s request for compound interest was untimely. That request was not made in Liberty’s original motion, in its rule 59 (e) motion, or in its “amended” motion, and was raised for the first time at a hearing more than two months after trial. We therefore do not address the question whether the constitutional requirement of just and reasonable compensation mandates the compounding of interest in eminent domain cases. Compare United States v. 429.59 Acres of Land, 612 F.2d 459, 465 (9th Cir. 1980) (upholding award of compound interest), and United States v. 319.46 Acres of Land, 508 F. Supp. 288, 290-291 (W.D. Okla. 1981) (awarding compound interest), with Washington Metro. Transit Auth. v. One Parcel of Land, 706 F.2d 1312, 1322 n.22 (4th Cir.), cert. denied, 464 U.S. 893 (1983) (declining to award compound interest), and United States v. 97.19 Acres, 511 F. Supp. 565, 569-570 (D. Md. 1981) (same).
While Liberty’s motion ostensibly asked leave to submit evidence on the issue after trial, the motion as filed referenced the sources and figures it intended to present and verify (if need be). We thus take those figures as given and assume their accuracy.
For example, Liberty’s motion referenced that Moody’s AAA bonds had averaged a return of 7.96 per cent in 1994, but had fallen to 6.53 per cent in 1998. Thirty-year Treasury bonds, also referenced in Liberty’s motion, were at 7.37 per cent in 1994, but had fallen to 5.69 per cent (a rate slightly below the statutory rate) in 1998. Five-year Treasury notes (which covered a time period “closest in duration to the delay in payment in this case”) averaged 6.69 per cent in 1994, but had fallen to 5.15 per cent (a figure well below the statutory rate) by 1998. For reasons that are unclear, Liberty’s motion, although filed in June, 2002, also failed to include any reference to prevailing rates for any time period later than 1998 or the first quarter of 1999. In its later amended motion, some of those figures were updated, and those updates confirmed that rates had continued at lower levels than the 1994 fates utilized in Liberty’s original calculation.
It also appears that Liberty’s calculation paid no heed to the rates for fifty-two week Treasury bills, the measuring rate for the statute itself and a security that ought to be considered. See United States v. 50.50 Acres of Land, *615931 F.2d 1349, 1356 (9th Cir. 1991). Those rates were lower than some of the other investments identified in Liberty’s motion, and they fell even lower in the years subsequent to the taking. See 28 U.S.C. § 1961 (2000). Inclusion of those lower rates in the over-all assessment presumably would have reduced the proposed “reasonable” range of rates even further.
Indeed, Liberty has cited no example of a market-driven statutory rate being found inadequate to provide just compensation.
In its “amended” motion, Liberty pointed to some rates of return that were considerably higher, but the investments referenced went far beyond the low-risk investments that are properly used for these purposes.
By comparison, when payment for a Federal taking is delayed by more than one year, the Federal statute now computes the interest rate separately for each year according to that year’s market formula. 40 U.S.C. § 3116. The Federal statute also compounds the interest. Id.
Our affirmance of the judge’s order on the issue of prejudgment interest also resolves Liberty’s claim for one more month of postjudgment interest. The check tendered by the city in August, 2002, was in an amount sufficient to satisfy the judgment and all accrued postjudgment interest — in fact, due to a slight arithmetic error, it was slightly more than the amount owed — and the city therefore cannot be held liable for any additional postjudgment interest. We understand that Liberty initially balked at the provision that that check was “in full satisfaction” of the judgment, but when that check has turned out to be sufficient to satisfy the entire judgment, we see no basis on which the city could be required to pay an additional month’s worth of interest.
The interest rate on Federal takings, and on money judgments in civil cases in Federal court, was also tied to the auction price of fifty-two week United States Treasury bills. See Pub. L. 99-656 § 1(2), 100 Stat. 3668 (1986); Pub. L. 97-164, § 302(a)(1), 96 Stat. 25 (1982). In anticipation of the United States Treasury Department’s decision to cease issuing fifty-two week Treasury bills, Congress amended various statutory provisions that had calculated interest based on that security, substituting instead “the weekly average 1-year constant maturity Treasury yield, as published by the Board of Governors of the Federal Reserve System.” See Pub. L. 106-554, § 1(a)(7) (Title III, § 307), 114 Stat. 2763, 2763A-635 (2000), amending 40 U.S.C. 258e-l (2000), 18 U.S.C. § 3612(f)(2)(B) (2000), 28 U.S.C. §§ 1961(a), 2516(b) (2000), and I.R.C. § 995(f)(4) (2000).