
462 A.2d 428 (1983)
DISTRICT OF COLUMBIA, Appellant,
v.
AETNA INSURANCE COMPANY, Appellee.
No. 82-541.
District of Columbia Court of Appeals.
Argued January 25, 1983.
Decided May 26, 1983.
Lutz Alexander Prager, Asst. Corp. Counsel, Washington, D.C., with whom Judith *429 W. Rogers, Corp. Counsel, and Charles L. Reischel, Deputy Corp. Counsel, Washington, D.C., were on the brief, for appellant.
Edward Graham Gallagher, Washington, D.C., for appellee.
Before FERREN, PRYOR and TERRY, Associate Judges.
PRYOR, Associate Judge:
This is an appeal from a grant of summary judgment in favor of Aetna Insurance Company (Aetna), the surety under a construction contract involving the District of Columbia. There being no factual issues alleged, our review is limited to whether, as a matter of law, a performance bond surety for one of two public works projects involving the same contractor, upon default of the contractor on one job and full performance by the surety, is subrogated to the rights and remedies against the contractor that the District would have had if it had completed the project itself. The trial court ruled that the surety could property assert its right of subrogation. Finding no error, we affirm.

I
CSH Contractors, Inc. (CSH) posted performance and payment bonds to cover a contract that it entered into with the District's Department of General Services to build a firehouse.[1] Aetna, the appellee, served as surety on these bonds. The performance bond obligated Aetna to complete the contract or pay a liquidated sum if CSH defaulted on performance. Similarly the payment bond required the surety to pay suppliers, subcontractors, and employees if the contractor failed to pay them. Under a separate contract with the District's Department of Environmental Services, CSH agreed to build a water pumping station. As with the firehouse contract, performance and payment bonds were executed. However, Aetna was not the surety in the latter agreements. CSH successfully performed its obligation under the water pumping station contract, but in April of 1978, defaulted on the firehouse project. Aetna, pursuant to its role as surety, completed the project on April 30, 1979. The District released the firehouse contract retainages[2] of $122,844.70 to Aetna; however, Aetna's cost of performance was in excess of this amount. Aetna expended $380,672.70 under its performance bond obligations; in addition, it paid $149,535.15 to subcontractors and suppliers who had furnished labor and materials to CSH for use on the firehouse project but whom CSH had not paid. During the course of its performance on the firehouse project, Aetna mailed notices to the District government asserting its right to the water pumping station retainages. In August and October of 1978, respectively, Aetna wrote to the contracting officers of the Department of General Services and Department of Environmental Services demanding that the water pumping station retainages be released to it and not the contractor. The record reveals that, except for the contractor, there was no *430 other claimant to the money. Disregarding Aetna's notices and asserting no claim of its own, the District, over a year after Aetna's completion of the firehouse project, disbursed payment to the president of CSH.
Aetna filed suit against the District asserting, by reason of the losses sustained in the firehouse contract, that it was subrogated to the rights of the District government against CSH, including the right to setoff the loss on the firehouse contract against the retainage on the water pumping station contract. Summary judgment was entered for Aetna on this question and the District of Columbia appeals.

II
Subrogation is the entitlement of one who has been compelled to satisfy an obligation (either the payment of money or contract performance) which was the responsibility of another, to a cession of all the remedies which the creditor might have against the other. H. SHELDON, LAW OF SUBROGATION 10 (1882); see Pearlman v. Reliance Insurance Co., 371 U.S. 132, 136-37, 83 S.Ct. 232, 234-35, 9 L.Ed.2d 190 (1962); Mungall, The Buffetting of the Subrogation Rights of the Construction Contract Bond Surety by United States v. Munsey Trust Co., 46 Insurance Counsel Journal 607 (1979) (hereafter cited as Mungall).[3] In the present context "[t]he elements necessary for a successful application of the subrogation principle are:
1. An obligation of the contractor to the owner;
2. The failure of the contractor to perform that obligation;
3. Rights in the owner arising from the contractor's failure to perform;
4. The performance by the surety pursuant to the suretyship of the obligation which the contractor has failed to perform.
When these elements exist the surety is substituted for the owner with respect to the rights which the owner has against the contractor as a result of the latter's failure to perform." Mungall, supra, at 607; see also Pearlman v. Reliance Insurance Co., supra, 371 U.S. at 136-37, 83 S.Ct. at 234-35, citing Hampton v. Phipps, 108 U.S. 260, 263, 2 S.Ct. 622, 623, 27 L.Ed. 719 (1883).
In the uncontroverted circumstances of this case, we observe that CSH had a contractual obligation to construct a firehouse for the District of Columbia. Although it had previously completed the construction of a water pumping station pursuant to an independent agreement, it nonetheless failed to complete the firehouse. As a consequence, Aetna, performing as surety, finished the project. Our inquiry is therefore focused upon Aetna's claim for monies which would otherwise be owed by the District to CSH for work which was done on the pumping station and was unrelated to the default.
It seems clear that a government entity which has encountered the default of a construction contract, has the same right "which belongs to every creditor, to apply the unappropriated monies of his debtor in extinguishment of the debts due him." Gratiot v. United States, 40 U.S. (15 Pet.) 336, 370, 10 L.Ed. 759 (1841), quoted in United States v. Munsey Trust Co., 332 U.S. 234, 239, 67 S.Ct. 1599, 1601, 91 L.Ed. 2022 (1947); Pearlman v. Reliance Insurance Co., supra, 371 U.S. at 140, 83 S.Ct. at 236; Ammerman v. Miller, 159 U.S.App.D.C. 385, 488 F.2d 1285 (1973); Orem v. Wrightson, 51 Md. 34, 34 Am.Rep. 286 (1878). This right to setoff unrelated losses has been generally recognized without reservation. See, e.g., Pearlman v. Reliance Insurance Co., supra; Centron Corp. v. United States, 585 F.2d 982 (Ct.Cl.1978); Project Map, Inc. v. United States, 486 F.2d 1375 (Ct.Cl.1973); Aetna Insurance Co. v. United States, 456 F.2d 773 (Ct.Cl.1973); Johnson Motor *431 Transport v. United States, 149 F.Supp. 175 (Ct.Cl.1957).
In confronting this question, the District does not challenge the traditional concepts of subrogation nor the remedy of setoff. Rather, it urges that in the present circumstances, the surety cannot avail itself of such relief. In taking this position, the District intimates that the right to subrogation is governed by a contractual requirement of privity between the surety and the obligee (in this case Aetna and the District Government, respectively), and absent privity, subrogation should be restricted to agreements to which the surety was a party. It is suggested that if this court should rule otherwise, such expanded claims by sureties will be encouraged, causing a multitude of legal and administrative problems for contracting governmental agencies.
It is true in the simplest form of construction agreement  a three party arrangement involving a governmental agency, a contractor and a surety for a single project  that a contractual basis for the surety's rights can be identified, because the surety is generally a party to the initial agreement. The more fundamental analysis of the right of subrogation, however, is equitable in nature and allows the surety to be viewed as the owner because he has met the responsibilities of a defaulting contractor to the owner. Fairness would dictate that the surety be accorded the owner's rights and remedies with respect to the contractor. In circumstances, like the present, where the same contractor is engaged in more than one project, it becomes clearer that it is the reach or scope of the remedy rather than the equitable right itself which is at issue. Finding no persuasive reasons to the contrary, we adopt the view that, "[t]he right of subrogation is not founded on contract. It is a creature of equity; is enforced solely for the purpose of accomplishing the ends of substantial justice; and is independent of any contractual relations between the parties." Memphis L.R.R. Co. v. Dow, 120 U.S. 287, 301-02, 7 S.Ct. 482, 488-89, 30 L.Ed. 595 (1887); see City Stores Company v. Lerner Shops of District of Columbia, Inc., 133 U.S.App.D.C. 311, 410 F.2d 1010 (1969); G. HARRIS, A TREATISE ON THE LAW OF SUBROGATION 123-24 (1889); H. SHELDON, supra at 2, 10, 107-08.
The District's reliance on the decision in Glens Falls Indemnity Co. v. American Awning and Tent Co., 55 R.I. 284, 180 A. 367 (R.I.1935), is misplaced. That case involved a dispute between a surety and creditors of a construction company in circumstances where the State of Rhode Island entered three separate contracts for construction of roads. The agreements involved the same construction company and the same surety. While one of the roads was completed by the company, it was necessary for the surety to complete construction of the remaining two. At the close of all construction, both the surety and unpaid creditors sought the balance of monies held by the state on all three of the jobs.
The surety sought recovery of the money on the basis of an indemnity agreement with the contractor and alternatively invoked the right of subrogation. Having construed the indemnity agreement against the surety company, the court found that the bond in question covered performance only and was not an undertaking to pay for labor and materials. The court thus reasoned that since the surety was not obligated to pay all laborers and suppliers, and in fact did not do so, it was not entitled to subrogation on that basis.[4]
It was critical in Glens Falls that, unlike the instant case, the surety was not bound to pay all suppliers and other creditors. Thus, there were competing equities to be weighed. In doing so, the Rhode Island court concluded that the retainage fund could be withheld from the contractor and used to pay the laborers and suppliers. Id. *432 180 A. at 372. Significantly, we have no such competing claims in the present case.
We, therefore, hold that where, as here, the only claimants to monies held by a government agency are the surety and a defaulting contractor, the surety who has performed under a public works performance bond agreement, upon full satisfaction of its surety obligation, is subrogated to all of the rights and remedies which the government might have had against the principal had the government been forced to complete the project itself. Among these remedies is the common law right of setoff.

III
Lastly, we consider the concern which the District has expressed regarding the consequences which may ensue from this decision. We note at the outset the limiting circumstances of this case as between the competing claims of Aetna, the surety, and CSH, the contractor, and the District as a stakeholder. Even when viewing Aetna's right to the fund as an inchoate right, see American Surety Co. v. Westinghouse Electric Mfg. Co., 296 U.S. 133, 135, 56 S.Ct. 9, 10, 80 L.Ed. 105 (1935); see also Street v. Pacific Indemnity Co., 79 F.2d 68, 69 (9th Cir.1935), cert. denied, 297 U.S. 718, 56 S.Ct. 595, 80 L.Ed. 1003 (1936), such right relates back to the time the bond was executed, Industrial Bank of Washington v. United States, 138 U.S.App.D.C. 19, 22, 424 F.2d 932, 934 (1970) (per curiam). The letters from Aetna should, at a minimum, have placed the District on notice that there was a bona fide competing claim to the fund.[5]Firemen's Fund Insurance Co. v. United States, 190 Ct.Cl. 804, 421 F.2d 706 (1970) (notification by telegram and letter before government's final payment to contractor was sufficient to put government on notice of surety's superior equitable right to the fund, and government was liable to surety for improper payment). The act of releasing the monies to the contractor does not save the District from liability to the party who rightfully should have been paid. See Newark Insurance Co. v. United States, 169 F.Supp. 955, 957 (Ct.Cl.1959). Interpleader was created precisely for situations such as this  to protect against double or multiple vexation with respect to a single liability. C. WRIGHT, FEDERAL COURTS § 74, at 363 (3d ed. 1976).
If it is made to appear that the [government]... after due notice of the facts giving rise to an equitable right in the plaintiff surety company, and of the plaintiff's assertion of such a right, paid out, without a valid reason for so doing, the money in question to someone other than the plaintiff, the plaintiff will be entitled to a judgment.
Newark Insurance Co., supra, 169 F.Supp. at 957.
In the present situation, the District had notice of both the facts giving rise to an equitable right in Aetna,[6] and Aetna's claim under these rights as manifested in the letters of August and October 1978. We have found no limitations upon the right of subrogation which would justify the District's actions in this instance.
In reaching our decision, we do not suggest that the District of Columbia must or should engage in an interpleader action in each of its many construction projects. Rather, we simply hold that in the absence of other competing parties where a surety gives a reasonable written notice of a claim adverse to that of a defaulting contractor for whom it has performed its bond, prudent use of the interpleader process may assist the District in resolving the dispute rather than burden it.
Affirmed.
NOTES
[1]  D.C.Code § 1-1104(a) (1981) provides:

Bonds required from public contractors, amount; waiver.
Before any contract, exceeding $10,000 in amount, for the construction, alteration, or repair of any public building or public work of the District of Columbia is awarded to any person, such person shall furnish to the District of Columbia the following bonds, which shall become binding upon the award of the contract to such person, who is hereinafter designated as "contractor": (1) A performance bond with a surety or sureties satisfactory to the Mayor of the District of Columbia, and in such amount as he shall deem adequate, for the protection of the District of Columbia; (2) a payment bond with a surety or sureties satisfactory to the Mayor for the protection of all persons supplying labor and material in the prosecution of the work provided for in said contract for the use of each such person.
* * * * * * *
[2]  Under D.C.Code § 1-1109 (1981) all contracts made by the District for construction work require that, until completion and acceptance of the work, the District shall retain 10 per centum of the total contract price as a guaranty that the terms of the contract shall be strictly and faithfully performed.
[3]  See also Home Owners' Loan Corp. v. Sears, Roebuck & Co., 123 Conn. 232, 193 A. 769 (1937).
[4]  The surety was, however, deemed entitled to a portion of the retainage fund on the basis of losses incurred when completing its performance bond obligations.
[5]  No issues of sovereignty were raised or addressed.
[6]  The record reveals that it was the District who called Aetna to perform on its bond obligations upon the default of the contractor.
