George and Gertrude Blanchard sued Peoples Bank alleging that the Bank improperly foreclosed on a certificate of deposit issued in the name of the Blanchards and their daughter, Barbara Gibson. Gibson pledged the certificate as collateral for business loans she never repaid. The Bank foreclosed on the certificate and the Blanchards sued. We affirm the grant of summary judgment for the Bank, concluding that the Bank had a contracted-for right to foreclose on the pledge of the certificate.
I
In early 1981, George and Gertrude Blanchard sold their home in San Diego, California, and deposited the proceeds of sale in a California bank. Their daughter, Barbara Gibson, convinced them that they would receive a better return on their money if they bought a certificate of deposit from Peoples Bank in Houston, Texas. Following her advice, the Blanchards wired $100,000 to Peoples Bank on April 15, and the Bank issued certificate of deposit number 54767 in that amount. Gibson, who lived in Houston, executed the documents at the Bank. Following her parents’ instructions, she had the Bank make the certificate payable to George, Gertrude, or Gibson herself.
In their depositions and affidavits the Blanchards testified that Gibson recalled telling a Bank employee that her name was to be listed on the certificate as a convenience only; that the money belonged only to her parents and not to her. The Blanch-ards also offered the affidavit of a San Diego attorney, Michael Waterman, in which he described his conversation with a former employee in the Bank’s certificate of deposit department. The employee, Bessie Allen, told Waterman that Gibson told her that the money belonged to her parents, and for this reason the interest checks were to be sent to them in California. Allen made these statements to Waterman after leaving her job with the Bank; she has since died.
The certificate itself made no mention of the source of the funds used to purchase it. In fact, the certificate specified that, “For all purposes ... Peoples Bank ... may deem and treat as the absolute owner hereof any depositor named on the face of this certificate.” The Bank sent monthly inter*266est checks, tax forms, and renewal notices to the Blanchards in San Diego. The interest checks were made payable to all three owners of the certificate.
Five days after the certificate was issued, and unbeknownst to the Blanchards, the Bank issued a business loan to Gibson in the amount of $6,295.30. Gibson and her husband personally guaranteed the loan and Gibson pledged the certificate of deposit as collateral. Gibson delivered the certificate to the Bank’s possession. She continued to borrow from the Bank over the next fifteen months, and by July 23, 1982, she had borrowed over $90,000, all secured by the certificate of deposit.
In late 1982, Gibson made an unauthorized withdrawal from a money market account she held jointly with her parents. Concerned about other possible unauthorized withdrawals, the Blanchards telephoned Peoples Bank on December 2 to request that Gibson’s name be removed from the certificate of deposit and all interest checks. A Bank employee sent to the Blanchards a copy of the certificate with Gibson’s name stricken, though the original certificate, still in the Bank’s vault, remained unaltered. The Bank did, however, issue all subsequent checks only in the names of the Blanchards.
In late January, 1983, the Bank first notified the Blanchards that the certificate had been pledged to secure Gibson’s loans. After efforts to collect payments on the loan from Gibson, the Bank cashed the certificate on March 23 and applied the entire proceeds against the debt.
The Blanchards filed this diversity suit against the Bank, alleging several bases of liability: first, that the Bank breached its contract of deposit with the Blanchards; second, that because the Bank knew or should have known that Gibson held the certificate in trust for her parents, it had no right to set off the Blanchards’ funds to pay Gibson’s debt; and third, that the Bank was negligent in failing to notify the Blanchards when Gibson first pledged the certificate as collateral. The district court granted summary judgment for the Bank, agreeing with the Bank’s contention that it could validly set off the certificate against Gibson’s debt and finding no possible negligence claim. The court made no explicit ruling on the breach-of-contract claim.
II
A
Under Texas law, when a bank’s depositor owes a debt to the bank and defaults on the debt, the bank is entitled to set off the amount owed against the funds on deposit.1 However, the Texas Supreme Court established an exception in National Indemnity Co. v. Spring Branch State Bank,2 ruling that a bank may not exercise its right to set-off if it knows or should know that the funds belong not to the depositor, but to a third party.3 Moreover, even when a bank has no notice or knowledge of a third party’s interests in funds on deposit, the bank may not set off and retain those funds unless it has detrimentally changed its position in reliance on the depositor’s ownership of the funds.4
The Blanchards’ primary argument on appeal is that the National Indemnity rule bars the Bank from exercising setoff because the Bank had notice that Gibson was not the true owner of the certificate. The Bank contends that the National Indemnity rule cannot be applied here because, first, the Uniform Commercial Code renders the rule inapplicable to certificates of *267deposit, and second, the Bank proved beyond dispute that it relied detrimentally on the ownership statement shown on the face of the certificate.
We need not address these arguments because we find that the Bank had a valid security interest in the certificate that was not limited by the National Indemnity rule. In a National Indemnity situation the third party owner of the funds subject to setoff has made no agreement with the Bank governing the parties’ relative interests in the funds. Here, by contrast, the parties established their interests in the certificate through two contracts: the certificate of deposit, an agreement between the Bank, the Blanchards, and Gibson; and the pledge agreement, a contract between the Bank and Gibson premised on the certificate. Hence, in cashing the certificate of deposit, the Bank need not have exercised any right to set-off. Rather, the Bank could assert its contractual rights under the certificate and pledge contracts.5 This case turns then on whether the Bank had an enforceable claim against the certificate on the basis of Gibson’s ownership and pledge. The problem would be no different if Gibson had simply cashed the certificate on April 20 instead of pledging it as collateral for a loan.
Even assuming that the parol-evidence rule would not bar extrinsic evidence to vary the unambiguous terms of the certificate,6 the Blanchards have presented no competent evidence of a different agreement with the Bank. The Blanchards’ own testimony as to their daughters’ recollections is inadmissible hearsay. So, too, are Waterman’s affidavit statements about the recollections of Bessie Allen.7 We are left with a written contract between the Bank and the Blanchards that gave the Bank the right to take the pledge of the CD for the loan.
B
The Blanchards’ complaint posed as an alternative theory of liability that the Bank was negligent in failing to inform the Blanchards that Gibson had pledged the certificate for personal loans. The Blanchards build their case on the principle that a party to a contract has a duty to exercise reasonable care in performing its obligations under the contract.8 In the Blanchards’ view, reasonable care under these circumstances required the Bank at least to notify them when Gibson first pledged the certificate.
It is not disputed that the terms of the contract, as contained in the certificate itself, mention no notice requirement; indeed, the opposite was implied in the provision permitting the Bank to treat each named owner as an absolute owner. To conclude that the contract relationship itself carried a duty of notification would be to add a new term to the contract.9 Such a *268result would also be inconsistent with the Banking Code provision permitting the Bank to treat co-owners of a deposit account as absolute owners where their interests are described disjunctively.10 Thus, we are persuaded that the district court did not err in rejecting the Blanchards’ claim of negligence.
AFFIRMED.
. See, e.g., First Nat'l Bank v. Winkler, 139 Tex. 131, 161 S.W.2d 1053, 1056 (1942).
. 162 Tex. 521, 348 S.W.2d 528, 529 (1961).
. The National Indemnity rule has been applied in a wide variety of situations, most of which involved savings or checking account deposits. See, e.g., Energetics, Inc. v. Allied Bank, 784 F.2d 1300 (5th Cir.1986) (bank offset prior debt of drilling company against company's account that included drilling expenses prepaid by drilling company’s client); South Central Livestock Dealers, Inc. v. Security State Bank, 614 F.2d 1056 (5th Cir.1980) (bank offset prior debt of feedlot company against account that included proceeds of cattle sales made by the feedlot on behalf of cattle owners).
. Citibank v. Interfirst Bank, 784 F.2d 619, 621 (5th Cir.1986).
. Even if the certificate had not expressly given Gibson a right to pledge the certificate as an absolute owner, the fact that it was payable to George Blanchard or Gertrude Blanchard or Barbara Gibson would probably suffice to give Gibson such a right. Cf. Tex.Rev.Civ.Stat.Ann. art. 342-706 (Vernon 1973) ("A bank may pay a present or future deposit, payable to or on the order of ... any one of two or more persons ... to any one of such joint depositors_”). See also Leinert v. Sabine National Bank, 541 S.W.2d 872, 874 (Tex. Civ. App. — Beaumont 1976, writ ref'd, n.r.e.) ("[A] checking account in the names of A or B enables either party to exercise total control over it; either A or B can draw a check on said account to the same extent as if it were A’s or B’s separate account.”).
. See Betty Lee Shoes, Inc. v. Karl’s Shoe Stores, Ltd., 293 F.2d 429, 436 (5th Cir.1961).
. Allen’s statements would not be excluded from the hearsay rule as an admission by the agent of a party opponent, see Fed. R. Evid. 801(d)(2)(D), because the rule applies only to statements made "during the existence of the [agency] relationship." See also Jack B. Weinstein & Margaret A. Berger, Weinstein’s Evidence 801-222 n. 16 (Supp.1987) (citing cases).
. See Montgomery Ward & Co. v. Scharrenbeck, 146 Tex. 153, 204 S.W.2d 508, 510 (1947).
. See Jim Walter Homes, Inc. v. Reed, 711 S.W. 2d 617, 618 (Tex.1986) (finding no independent tort arising from breach of good-workmanship warrant in construction of a house); Group Hospital Services, Inc. v. Daniel, 704 S.W.2d 870, 877 (Tex.App.—Corpus Christi 1985, no writ) (finding "no independent [tort] duty owed ... outside of that which existed in the contract between the two parties").
. See supra note 5.