
990 P.2d 976 (2000)
98 Wash.App. 690
STATE of Washington, Respondent,
v.
Russel J. TRASK and Jane Doe Trask, husband and wife; Bainbridge Marine Services, Inc., a Washington corporation; Mark A. Julian and Jane Doe Julian, husband and wife; Eagle Harbor Boatyard, a Washington corporation, Appellants.
No. 24269-9-II.
Court of Appeals of Washington, Division 2.
January 7, 2000.
*977 David C. Lundsgaard, Larry John Smith, Graham & Dunn PC, Seattle, for Appellants.
Anne Louise Spangler, Atty. Gen. Off. Trans. Div., Olympia, for Respondent.
Kenneth F. Hobbs, Stafford Frey Cooper, Seattle, for other Party.
MORGAN, J.
In the first appeal of this condemnation case,[1] we ruled in part that Russell J. Trask was entitled to interest on an award of "just compensation." We did not address how such interest should be calculated, and that question gives rise to this second appeal.
In January 1994, the State sued to condemn land owned by Trask. The State agreed to pay $2.5 million in exchange for immediate possession and use. The State and Trask also agreed that if a jury later valued the land at more than $2.5 million, the amount by which the jury's award exceeded $2.5 million would bear simple interest at 12 percent per annum, starting October 15, 1994.
In June 1995, a jury valued the land at $4.1 million. On July 12, 1995, the trial court entered judgment for that amount, with credit for the $2.5 million already paid. The *978 court reserved for later ruling the issues of interest, costs and fees.
On July 26, 1995, the State paid $1.6 million into court. On July 28, 1995, Trask withdrew the money.
In September 1995, Trask moved for simple interest on the $1.6 million at 12 percent per annum from October 15, 1994. On November 1, 1995, the trial court denied the motion for reasons set forth in our earlier opinion.
Trask then filed his first appeal. He did not seek to disturb the judgment for $1.6 million, but he did seek to reverse the order denying interest. Ruling essentially in his favor, "we conclude[d] that the State owes interest on $1.6 million from October 15, 1994 (the date on which the parties agreed interest would start) to July 26, 1995 (the date on which the State paid the $1.6 million into the registry of the court)."[2] Neither Trask nor the State sought reconsideration of that ruling.[3]
On June 26, 1998, the State paid $149,917.81 into the registry of the trial court, representing simple interest on $1.6 million at 12 percent per annum from October 15, 1994 to July 26, 1995. Trask later withdrew this amount.
On August 27, 1998, Trask moved the trial court "for an award of post-judgment interest and disbursement of funds."[4] In December 1998, the trial court denied the motion in a formal written order, and in January 1999 Trask filed this second appeal.
In the first appeal, Trask imprecisely presented his interest claim. He argued in his brief:
Trask is entitled to interest on the amount by which final just compensation exceeded the total possession and use payments, from October 15, 1994 to the date on which he received final payment.
...
Trask is therefore entitled to simple interest of 12 percent on $1.6 million from October 15, 1994 to July 28, 1995, when the trial court disbursed the remainder of Trask's condemnation proceeds. This amount is $149,392.52, plus interest on this amount from the time that it was due, i.e., July 28, 1995, to the date on which it is ultimately paid.
This Court should therefore reverse the trial court on this issue, and enter an award of interest accordingly.[[5]]
This claim mixed prejudgment and post-judgment interest by lumping about nine months of the former (interest accruing from October 15, 1994 to July 12, 1995) with 14 days of the latter (interest accruing from July 13, 1995 to July 28, 1995). It also, by part of a single sentence, sought post-judgment interest after July 28, 1995.
When we addressed this claim in our prior opinion, we limited our discussion to (a) whether Trask had lost his right to interest by failing to deliver timely possession of the land; (b) whether the parties could delay the inception of interest by agreement; and (c) how Trask and his lessee should share interest accruing before judgment.[6] We did not consider whether prejudgment interest should be added to the judgment; whether prejudgment interest should draw post-judgment interest; or whether the judgment entered July 12, 1995, should be amended to include prejudgment interest as part of the judgment principal. In short, we failed to distinguish between prejudgment and post-judgment interest, and we overlooked Trask's one-sentence claim for post-judgment interest after July 28, 1995.
Citing the law of the case doctrine, the State now asserts (1) that we cannot consider anything we failed to consider in the first appeal, and (2) that we cannot correct anything we incompletely or inaccurately considered in the first appeal. We disagree on both counts. The law of the case doctrine *979 does not apply to matters we did not explicitly or implicitly consider,[7] and it is highly discretionary with respect to matters that we did consider.[8] After considering all the circumstances of this case, including the way in which the parties argued the first appeal to this court, we think that "justice would best be served"[9] if we now complete and correct, to the extent necessary, our previous discussion of Trask's claim for interest.
Turning to the merits, we begin with the rules on ordinary judgments. A party is entitled to prejudgment interest as provided by contract.[10] When prejudgment interest is awarded, it is added to the judgment and becomes part of the judgment principal.[11] The judgment principal draws post-judgment interest until paid in full.[12] When a judgment debtor makes a partial payment into the registry of the court, the payment generally is applied first to interest and then to principal, while the remainder of the principal continues to draw post-judgment interest.[13] Interest means simple interest *980 absent agreement or statute to the contrary.[14]
These principles apply with special force when the State takes private property for public use, but does not fully pay for it at that time. "The constitutional mandate for payment of just compensation ... requires that the property owner be put in the same position monetarily as the owner would have occupied had the property not been taken."[15] When the State takes property but does not then fully pay, it leaves the owner with neither the property nor its full value, from when the property is taken to when the property is fully paid for. In that situation, then, "just compensation" necessarily has at least two components: (a) the value of the property on the date it was taken, plus (b) interest on any part of the value of the property from the date the property was taken to the date the property is paid for in full.[16] Apparently for this reason, the statutes require that a trial court include prejudgment interest in its judgment,[17] and that the entire judgment principal draw post-judgment interest until paid.[18]
Sintra II and Sintra III illustrate these principles.[19] In 1987, the landowner's property was taken for public use. In 1994, the trial court included in its original judgment prejudgment interest computed from when the property was taken to when the judgment was entered. In 1997, the Supreme Court affirmed that inclusion but reversed on a different point. In 1998, following remand, the trial court entered a revised judgment that denied postjudgment interest from the time of the original judgment to the time of the revised judgment. Reversing, Division One ruled that the entire original judgment, including its prejudgment interest component, had continuously drawn postjudgment interest after its entry.
In the case now before us, prejudgment interest commenced on October 15, 1994, in accordance with the agreement of the parties.[20] Prejudgment interest accrued until July 12, 1994, the date on which judgment was entered. By July 12, 1994, prejudgment interest came to $142,027 (270 days/365 days, times 12 percent per annum, *981 times $1,600,000). If this amount had been included in the July 12 judgment, as it should have been, the judgment principal would have been $1,742,027, plus costs and fees not pertinent here.
After the entry of judgment on July 12, 1994, the State made two payments. On July 26, 1995, it paid $1.6 million. On June 26, 1998, it paid another $149,917.
By the time of the first payment, July 26, 1995, postjudgment interest had accrued in the amount of $8,018. Accordingly, that first payment should have been allocated $8,018 to postjudgment interest (14 days/365 days, times 12 percent per annum, times $1,742,027) and $1,591,982 to judgment principal, leaving unpaid judgment principal in the amount of $150,045.
By the time of the second payment, June 26, 1998, postjudgment interest had further accrued in the amount of $52,536 (1065 days/365 days, times 12 percent per annum, times the unpaid judgment principal of $150,045). Accordingly, that second payment should have been allocated $52,536 to postjudgment interest and $97,381 to judgment principal, leaving unpaid judgment principal in the amount of $52,664.
After June 26, 1998, the State did not make further payments. Accordingly, it now remains obligated to pay $52,664 (the unpaid judgment principal as of June 26, 1998), plus postjudgment interest of $17.31 per day (1 day/365 days, times 12 percent per annum, times $52,664) from June 26, 1998. On remand, the trial court shall amend its judgment accordingly.
Reversed and remanded.
HOUGHTON, J., and ARMSTRONG, Acting C.J., concur.
NOTES
[1]  See State v. Trask, 91 Wash.App. 253, 957 P.2d 781 (1998), review denied, 137 Wash.2d 1020, 980 P.2d 1282 (1999).
[2]  Trask, 91 Wash.App. at 268-69, 957 P.2d 781.
[3]  Trask's lessee, Julian, did seek reconsideration, but he and the State settled before his motion was decided. Julian is not involved in this second appeal.
[4]  Clerk's Papers at 1 (emphasis added).
[5]  Brief of Appellant at 45-46.
[6]  Trask, 91 Wash.App. at 265-69, 957 P.2d 781.
[7]  Lutheran Day Care v. Snohomish County, 119 Wash.2d 91, 113, 829 P.2d 746 (1992) (law of the case doctrine "express[es] the principle that an appellate court will generally not make a redetermination of the rules of law which it has announced in a prior determination in the same case or which were necessarily implicit in such prior determination"), cert. denied, 506 U.S. 1079, 113 S.Ct. 1044, 122 L.Ed.2d 353 (1993).
[8]  RAP 2.5(c)(2) provides:

(c) Law of the Case Doctrine Restricted. The following provisions apply if the same case is again before the appellate court following a remand:
...
(2) Prior Appellate Court Decision. The appellate court may at the instance of a party review the propriety of an earlier decision of the appellate court in the same case and, where justice would best be served, decide the case on the basis of the appellate court's opinion of the law at the time of the later review.
Accord, Lutheran, 119 Wash.2d at 113, 829 P.2d 746 (law of case doctrine "has been limited by case law and rules of court"); Folsom v. County of Spokane, 111 Wash.2d 256, 264, 759 P.2d 1196 (1988) ("the law of the case doctrine is discretionary, not mandatory").
[9]  RAP 2.5(c).
[10]  Pacific Erectors, Inc. v. Gall Landau Young Constr. Co., Inc., 62 Wash.App. 158, 171-72, 813 P.2d 1243 (1991), review denied, 118 Wash.2d 1015, 827 P.2d 1011 (1992); Seattle-First Nat'l. Bank v. Washington Ins. Guar. Assoc., 94 Wash. App. 744, 759-60, 972 P.2d 1282 (1999).
[11]  Xebek, Inc. v. Nickum & Spaulding Assoc., Inc., 43 Wash.App. 740, 743, 718 P.2d 851 (1986); See Walter Implement, Inc. v. Focht, 107 Wash.2d 553, 562, 730 P.2d 1340 (1987) (reversing judgment comprised of liquidated damages and prejudgment interest for recomputation of damages only); Dautel v. Heritage Home Ctr., Inc., 89 Wash.App. 148, 155, 948 P.2d 397 (1997) (remanding for entry of modified judgment granting prejudgment interest), review denied, 135 Wash.2d 1003, 959 P.2d 126 (1998); Ernst Home Ctr., Inc. v. Sato, 80 Wash.App. 473, 491, 910 P.2d 486 (1996) (remanding for entry of modified judgment granting prejudgment interest); Smoke v. City of Seattle, 79 Wash.App. 412, 421-22, 902 P.2d 678 (1995) (stating that "a judgment is composed of distinct parts," including prejudgment interest), rev'd on other grounds, 132 Wash.2d 214, 937 P.2d 186 (1997); Aquarian Foundation v. KTVW, Inc., 11 Wash.App. 476, 480, 523 P.2d 969 (1974) (remanding for entry of judgment including prejudgment interest).
[12]  RCW 4.56.110; Caruso v. Local Union No. 690, 50 Wash.App. 688, 690, 749 P.2d 1304 (1988); Xebek, 43 Wash.App. at 743, 718 P.2d 851.
[13]  The general principle is that absent an agreement, direction or statute to the contrary, a payment on an installment agreement is applied first to interest and then to principal. Clausing v. Virginia Lee Homes, Inc., 62 Wash.2d 771, 776, 384 P.2d 644 (1963); Western Loan & Bldg. Co. v. Larsen, 110 Wash. 213, 215, 188 P. 390 (1920). A specific application of this principle is a judgment debtor's partial satisfaction of a judgment is applied first to interest and then to principal. Security Ins. Co. of Hartford v. Houser, 191 Colo. 189, 552 P.2d 308, 311 (1976); Claudio v. School City of Gary, 448 N.E.2d 1212, 1215 (Ind.App. 1983); Christensen v. Snap-On Tools Corp., 554 N.W.2d 254, 261-62 (Iowa 1996); Gail v. Western Convenience Stores, 434 N.W.2d 862, 864 (Iowa 1989); Landess v. State, 335 P.2d 1077, 1079 (Okla.1958); Morley v. Morley, 102 N.C.App. 713, 403 S.E.2d 574, 575 (1991). As stated in 45 Am.Jur.2d, Interest and Usury § 75 at 85 (1999):

In applying partial payments to an interest-bearing debt which is due, the rule known as the "United States rule," is that in the absence of an agreement or statute to the contrary, the payment will be first applied to the interest due.
If the payment exceeds the interest due, the surplus goes toward discharging the principal, and the subsequent interest is computed on the balance of the principal. If the payment falls short of the amount of the interest due, the balance of the interest is not generally added to the principal so as to produce interest.
[14]  Sintra, Inc. v. City of Seattle (Sintra II), 131 Wash.2d 640, 660, 935 P.2d 555 (1997); Caruso, 50 Wash.App. at 690, 749 P.2d 1304; Xebek, 43 Wash.App. at 743, 718 P.2d 851.
[15]  Sintra, Inc. v. City of Seattle (Sintra III), 96 Wash.App. 757, 761, 980 P.2d 796 (1999), citing Sintra II, 131 Wash.2d at 655, 935 P.2d 555.
[16]  Sintra II, 131 Wash.2d at 656, 935 P.2d 555 (in a "quick-take action under RCW 8.04.090, property is taken before just compensation is paid. In these cases, ... interest is necessary to compensate the property owner for the loss of the use of the monetary value of the taking or damage from the time of the taking until just compensation is paid.") (citing Smithrock Quarry, Inc. v. State, 60 Wash.2d 387, 391, 374 P.2d 168 (1962)); In re Anacortes, 81 Wash.2d 166, 168-69, 500 P.2d 546 (1972); Consolidated Diking Imp. Dist. No. 3 v. Davis, 36 Wash.App. 125, 128, 672 P.2d 414 (1983); State v. Hallauer, 28 Wash.App. 453, 456-58, 624 P.2d 736 (1981); accord, Sintra III, 96 Wash.App. at 759-60, 980 P.2d 796 (trial court included prejudgment interest in judgment "as an additional element of just compensation;" Supreme Court "affirmed the award of interest as part of the required just compensation").
[17]  RCW 8.04.092 (in quick-take condemnation case, jury values property as of "the date of entry of the order granting to the state immediate possession and use of the property"; after jury returns its verdict, "court shall order the excess [i.e. any portion of the verdict that the State did not pay earlier] paid to respondents with interest thereon from the time of the entry of the order of immediate possession"); see also Sintra II, 131 Wash.2d at 656, 935 P.2d 555 (quick-take provisions of RCW 8.04.090 and RCW 8.04.092 "mak[e] the State liable for interest on the difference between what it pays into the court registry and the amount to which the owner is entitled").
[18]  RCW 8.28.040; Hallauer, 28 Wash.App. at 458, 624 P.2d 736; see also State v. Lacey, 84 Wash.2d 33, 37-38, 524 P.2d 1351 (1974); Sintra III, 96 Wash.App. at 762, 980 P.2d 796; RCW 4.56.110. Neither party relies, nor could it rely, on the proviso in RCW 8.28.040. The proviso may toll prejudgment interest when an appeal is taken before judgment, see, e.g., RAP 2.2(a)(4), but both appeals in this case were taken after judgment.
[19]  Sintra is analogous to this case even though it involved an inverse condemnation rather than a statutory "quick-take." That is so because in each case the taking was effected without full payment. See Sintra II, 131 Wash.2d at 656, 935 P.2d 555.
[20]  See Trask, 91 Wash.App. at 268, 957 P.2d 781.
