POSNER, Circuit Judge.

This class action suit under ERISA was filed by a retired employee of the LTV Steel Company. The principal defendants are two pension plans sponsored by LTV and the plaintiff's union (a detail we can ignore), one a defined benefit plan and the other a defined contribution plan. The district court granted summary judgment for the defendants and also denied class certification.

A defined benefit plan entitles the plan participant to a specified pension benefit, usually based primarily on his years of service and his wages, payable to him periodically for the rest of his life (or often his and his wife's life). The benefits under LTV's defined benefit plan are paid out of a trust that LTV established. A defined contribution (often called a "profit sharing") plan is different. See generally Hughes Aircraft Co. v. Jacobson, 525 U.S. 432, 439-41, 119 S.Ct. 755, 142 L.Ed.2d 881 (1999); 1 Jeffrey D. Mamorsky, Employee Benefits Law: ERISA and Beyond §§ 1.01-.02, 2.01 (2000). It specifies the contributions that the employer is required to make to the plan participant's defined contribution account, but the value of the plan to the participant depends on the investment performance of the account. Under LTV's defined contribution plan, the employee may liquidate the account when he retires, or later if he wishes. When he decides to liquidate it, the account is valued on the basis of the current market value of the investments in it. Depending on the size of the account, the participant cannot take it all in cash, but must use some of the account to purchase an annuity from one of several insurance companies designated by the plan. An annuity is purchased for cash and yields a fixed annual return for the life of the annuitant (or, often, annuitant plus spouse). It thus provides the same type of benefit as a defined benefit plan, the only difference being that annuities are sold by insurance companies.

LTV's two plans are integrated in what is commonly referred to as a "floor offset" (or, less commonly, a "feeder") arrangement. See Lunn v. Montgomery Ward Co., 166 F.3d 880 (7th Cir. 1999); Pritchard v. Rainfair, Inc., 945 F.2d 185, 187-90 (7th Cir. 1991); Holliday v. Xerox Corp., 732 F.2d 548 (6th Cir. 1984); Regina T. Jefferson, "Rethinking the Risk of Defined Contribution Plans," 4 Fla. Tax Rev. 607, 669-70 (2000). (Other forms of integration, for example with workers' compensation benefits, are permitted, see, e.g., Alessi v. Raybestos-Manhattan, Inc., 451 U.S. 504, 514-17, 101 S.Ct. 1895, 68 L.Ed.2d 402 (1981); Lunn v. Montgomery Ward Co., supra, 166 F.3d at 884, but are not involved in this case.) Under that arrangement, the amount of the defined benefit is determined in part by the value of the retiree's defined contribution account. Concretely, LTV's defined benefit plan specifies a gross and a net pension entitlement (we are simplifying a bit, but without affecting the legal analysis), and the retiree's defined contribution account is used to help fund the gross entitlement, the dollar value of which is the floor in the floor arrangement. The plans' administrator computes the annuity value of the defined contribution account, that is, the size of the annuity that could be purchased for the employee with the entire balance in his account. That is a hypothetical calculation; no annuity need be purchased at this juncture. Suppose the gross pension entitlement, the "floor," specified in the defined benefit plan is $200 a month and the hypothetical annuity that could be purchased with the entire balance in the defined contribution account would yield $50 a month. Then the defined benefit to which the retiree would be entitled would be $150 a month, that being the amount necessary to bridge the gap between the annuity value of the defined contribution account and the gross pension entitlement, the latter being, to repeat, the minimum amount to which he is entitled, the floor, in other words, specified in the defined benefit plan. If the retiree decides to defer the liquidation of his defined contribution account, then the annuitized value of that account, which must be determined in order to fix the defined benefit to which he is entitled, is determined on the basis of the value of the account and the price of annuities on the date of his retirement.

Why this complicated method of determining the retirement benefit? Why not in our example just specify a defined value of $200 and not bother with a defined contribution plan? Were there only a defined benefit plan, and the defined benefit (for an employee of given salary and years of service) was $200 a month, the employee's only entitlement would be to that periodic payment. It is here that the character of the gross pension entitlement as a floor becomes significant. With the two integrated plans, the retired worker gets $150 plus the money in his defined contribution account. If he uses all that money to buy an annuity, and does so when he retires, he will have two annuity-type benefits that add up to $200 a month. But if he prefers, he can elect to take just the $150 defined benefit and allow his defined contribution account to grow, and when he decides to liquidate that account he can take some of it in cash rather than having it all converted to an annuity. So the substitution of the two different types of plan for one plan, while not increasing the expected value of the participant's retirement benefits, gives him more flexibility in the form and timing of the benefits; and if he is lucky he will end up with a gross retirement benefit that exceeds his gross pension entitlement, the $200 in our example, while if he is unlucky his fall is broken by the floor.

The plaintiff's complaint focuses on the possible discrepancy between the annuitized value of a retiree's defined contribution account on the date of his retirement and that value when he decides to liquidate the account, which as we have noted he can defer doing. The price of an annuity is inverse to interest rates. The higher those rates, the cheaper an annuity yielding a given benefit will be, because the insurance company can earn a higher income from investing the purchase price of the annuity the higher interest rates are. For a given price of an annuity, therefore, the higher the interest rate the higher the annuity's yield to the annuitant, and therefore for a given sum available to buy an annuity the monthly benefits generated by the purchase of the annuity will be greater the higher the interest rate when it's purchased. The plaintiff retired on the last day of 1995 but did not liquidate his defined contribution account until July of the following year. Apparently, interest rates fell during this interval, because the annuitized value of his account declined, and as a result the expected value of his retirement benefit (the sum of the defined benefit determined back in December and the benefit the plaintiff could have gotten by using the full assets in his defined contribution account in July to buy an annuity) fell. The floor turned out to be a ceiling.

It is difficult, however, to understand what injustice resulted. By waiting to liquidate his defined contribution account, the plaintiff was speculating on interest rates. If he wanted certainty, he should have liquidated the account when he retired. Against this he argues that the pension plan takes two or three months to liquidate a defined contribution plan. That seems long, but it is not a violation of the plan, and anyway the plaintiff has no standing to complain, since he waited seven months after retiring to request that his account be liquidated.

Injustice or not, since he received the full benefits to which the plan documents entitled him, he has no basis for complaining of a violation of the terms of the plan or a forfeiture of vested benefits. 29 U.S.C. §§ 1053(a), 1132(a)(1)(B); Alessi v. Raybestos-Manhattan, Inc., supra, 451 U.S. at 512, 101 S.Ct. 1895. No amendment to the plans curtailed his benefits, so he cannot appeal to the anti-cutback provision of ERISA either. 29 U.S.C. § 1054(g). His argument that because the price of annuities changes with interest rates the plan is amended every time the administrator recalculates entitlements on the basis of those changes is frivolous. Dooley v. American Airlines, Inc., 797 F.2d 1447, 1452 (7th Cir. 1986); Krumme v. Westpoint Stevens, Inc., 143 F.3d 71, 85-86 (2d Cir. 1998). He is left with the argument that the defined benefit plan is not qualified for favorable tax treatment under the Internal Revenue Code because the benefits it provides are not "definitely determinable." 26 U.S.C. § 401. He has no right to make this argument, see, e.g., Reklau v. Merchants National Corp., 808 F.2d 628, 631 (7th Cir. 1986); Stamper v. Total Petroleum, Inc. Retirement Plan, 188 F.3d 1233, 1238 (10th Cir. 1999); Abraham v. Exxon Corp., 85 F.3d 1126, 1131 (5th Cir. 1996); Crawford v. Roane, 53 F.3d 750, 756 (6th Cir. 1995), the effect of which if it succeeded would not be to benefit him but to hurt the company, the trust, and maybe other participants and beneficiaries by killing the plans' tax exemption. See 26 U.S.C. §§ 402(a), (b), 404(a)(5); Ludden v. Commissioner, 620 F.2d 700 (9th Cir. 1980); 1 Mamorsky, supra, § 3A.01[1][a]. A more plausible suit would be one complaining that by failing to maintain tax-exempt status a retirement plan had hurt the participants!

Anyway the plaintiff's argument has no merit. The Internal Revenue Code does not require that the defined benefit be fixed, but only that it be determinable according to criteria specified in advance that do not permit the plan to play favorites. 26 U.S.C. § 401(a)(25); 26 C.F.R. § 1.401-1(b)(1)(i). Since it is the participant's choice when to liquidate the defined contribution plan, the deferral option is not a form of favoritism.

We take it that the appeal from the denial of class certification was intended to be conditional on the plaintiff's prevailing on the merits, since otherwise class certification could only hurt the class. See Aiello v. Providian Financial Corp., 239 F.3d 876, 881 (7th Cir. 2001); Amati v. City of Woodstock, 176 F.3d 952, 957 (7th Cir. 1999). The defendants could have pressed for certification on their own, to maximize the value of their prevailing, but they have not done so, and it is too late for them to try.

AFFIRMED.