This is a tort case under the federal admiralty jurisdiction. We are called upon to decide questions of contributory negligence and damage assessment, in particular the question-one of first impression in this circuit-whether, and if so how, to account for inflation in computing lost future wages.

On the day of the accident, Margaret O'Shea was coming off duty as a cook on a towboat plying the Mississippi River. A harbor boat operated by the defendant, Riverway Towing Company, carried Mrs. O'Shea to shore and while getting off the boat she fell and sustained the injury complained of. The district judge found Riverway negligent and Mrs. O'Shea free from contributory negligence, and assessed damages in excess of $150,000. Riverway appeals only from the finding that there was no contributory negligence and from the part of the damage award that was intended to compensate Mrs. O'Shea for her lost future wages.

The accident happened in the following way. When the harbor boat reached shore it tied up to a seawall the top of which was several feet above the boat's deck. There was no ladder. The other passengers, who were seamen, clambered up the seawall without difficulty, but Mrs. O'Shea, a 57-year-old woman who weighs 200 pounds (she is five foot seven), balked. According to Mrs. O'Shea's testimony, which the district court believed, a deckhand instructed her to climb the stairs to a catwalk above the deck and disembark from there. But the catwalk was three feet above the top of the seawall, and again there was no ladder. The deckhand told her that she should jump and that the men who had already disembarked would help her land safely. She did as told, but fell in landing, carrying the assisting seamen down with her, and broke her leg.

Riverway concedes that the instruction to Mrs. O'Shea to jump was negligent, but argues that she was contributorily negligent to jump down the three feet to the seawall, given her age and weight, and therefore that her damages should have been reduced. But if her testimony is believed-and Riverway does not ask us to redetermine any issue of credibility-the finding that she was not contributorily negligent cannot be said to be clearly erroneous. There she was on the boat with no apparent way to get off. The deckhand told her to jump and that the men already on the shore would make sure she landed safely. It was reasonable for her to assume that Riverway knew how to disembark passengers, even overweight middle-aged female passengers, safely in the absence of a ladder (with which the boat curiously was not equipped). The deckhand's apparent expertise made the risks as they reasonably appeared to Mrs. O'Shea small relative to the inconvenience of remaining aboard indefinitely, at some cost in embarrassment as well as time, while the crew rigged some alternative method of exit tailored to her lack of agility.

The more substantial issues in this appeal relate to the computation of lost wages. Mrs. O'Shea's job as a cook paid her $40 a day, and since the custom was to work 30 days consecutively and then have the next 30 days off, this comes to $7200 a year although, as we shall see, she never had earned that much in a single year. She testified that when the accident occurred she had been about to get another cook's job on a Mississippi towboat that would have paid her $60 a day ($10,800 a year). She also testified that she had been intending to work as a boat's cook until she was 70-longer if she was able. An economist who testified on Mrs. O'Shea's behalf used the foregoing testimony as the basis for estimating the wages that she lost because of the accident. He first subtracted federal income tax from yearly wage estimates based on alternative assumptions about her wage rate (that it would be either $40 or $60 a day); assumed that this wage would have grown by between six and eight percent a year; assumed that she would have worked either to age 65 or to age 70; and then discounted the resulting lost-wage estimates to present value, using a discount rate of 8.5 percent a year. These calculations, being based on alternative assumptions concerning starting wage rate, annual wage increases, and length of employment, yielded a range of values rather than a single value. The bottom of the range was $50,000. This is the present value, computed at an 8.5 percent discount rate, of Mrs. O'Shea's lost future wages on the assumption that her starting wage was $40 a day and that it would have grown by six percent a year until she retired at the age of 65. The top of the range was $114,000, which is the present value (again discounted at 8.5 percent) of her lost future wages assuming she would have worked till she was 70 at a wage that would have started at $60 a day and increased by eight percent a year. The judge awarded a figure-$86,033-near the midpoint of this range. He did not explain in his written opinion how he had arrived at this figure, but in a preceding oral opinion he stated that he was "not certain that she would work until age 70 at this type of work," although "she certainly was entitled to" do so and "could have earned something"; and that he had not "felt bound by (the economist's) figure of eight per cent increase in wages" and had "not found the wages based on necessarily a 60 dollar a day job." If this can be taken to mean that he thought Mrs. O'Shea would probably have worked till she was 70, starting at $40 a day but moving up from there at six rather than eight percent a year, the economist's estimate of the present value of her lost future wages would be $75,000.

There is no doubt that the accident disabled Mrs. O'Shea from working as a cook on a boat. The break in her leg was very serious: it reduced the stability of the leg and caused her to fall frequently. It is impossible to see how she could have continued working as a cook, a job performed mostly while standing up, and especially on a boat, with its unsteady motion. But Riverway argues that Mrs. O'Shea (who has not worked at all since the accident, which occurred two years before the trial) could have gotten some sort of job and that the wages in that job should be deducted from the admittedly higher wages that she could have earned as a cook on a boat.

The question is not whether Mrs. O'Shea is totally disabled in the sense, relevant to social security disability cases but not tort cases, that there is no job in the American economy for which she is medically fit. Compare Cummins v. Schweiker, 670 F.2d 81 (7th Cir. 1982), with New Orleans (Gulfwide) Stevedores v. Turner, 661 F.2d 1031, 1037-38 (5th Cir. 1981). It is whether she can by reasonable diligence find gainful employment, given the physical condition in which the accident left her. See, e.g., Baker v. Baltimore & Ohio R. R., 502 F.2d 638, 644 (6th Cir. 1974). Here is a middle-aged woman, very overweight, badly scarred on one arm and one leg, unsteady on her feet, in constant and serious pain from the accident, with no education beyond high school and no work skills other than cooking, a job that happens to require standing for long periods which she is incapable of doing. It seems unlikely that someone in this condition could find gainful work at the minimum wage. True, the probability is not zero; and a better procedure, therefore, might have been to subtract from Mrs. O'Shea's lost future wages as a boat's cook the wages in some other job, discounted (i.e., multiplied) by the probability-very low-that she would in fact be able to get another job. But the district judge cannot be criticized for having failed to use a procedure not suggested by either party. The question put to him was the dichotomous one, would she or would she not get another job if she made reasonable efforts to do so? This required him to decide whether there was a more than 50 percent probability that she would. We cannot say that the negative answer he gave to that question was clearly erroneous.

Riverway argues next that it was wrong for the judge to award damages on the basis of a wage not validated, as it were, by at least a year's employment at that wage. Mrs. O'Shea had never worked full time, had never in fact earned more than $3600 in a full year, and in the year preceding the accident had earned only $900. But previous wages do not put a cap on an award of lost future wages. If a man who had never worked in his life graduated from law school, began working at a law firm at an annual salary of $35,000, and was killed the second day on the job, his lack of a past wage history would be irrelevant to computing his lost future wages. The present case is similar if less dramatic. Mrs. O'Shea did not work at all until 1974, when her husband died. She then lived on her inheritance and worked at a variety of part-time jobs till January 1979, when she started working as a cook on the towboat. According to her testimony, which the trial judge believed, she was then working full time. It is immaterial that this was her first full-time job and that the accident occurred before she had held it for a full year. Her job history was typical of women who return to the labor force after their children are grown or, as in Mrs. O'Shea's case, after their husband dies, and these women are, like any tort victims, entitled to damages based on what they would have earned in the future rather than on what they may or may not have earned in the past.

If we are correct so far, Mrs. O'Shea was entitled to have her lost wages determined on the assumption that she would have earned at least $7200 in the first year after the accident and that the accident caused her to lose that entire amount by disabling her from any gainful employment. And since Riverway neither challenges the district judge's (apparent) finding that Mrs. O'Shea would have worked till she was 70 nor contends that the lost wages for each year until then should be discounted by the probability that she would in fact have been alive and working as a boat's cook throughout the damage period, we may also assume that her wages would have been at least $7200 a year for the 12 years between the date of the accident and her seventieth birthday. But Riverway does argue that we cannot assume she might have earned $10,800 a year rather than $7200, despite her testimony that at the time of the accident she was about to take another job as a boat's cook where she would have been paid at the rate of $60 rather than $40 a day. The point is not terribly important since the trial judge gave little weight to this testimony, but we shall discuss it briefly. Mrs. O'Shea was asked on direct examination what "pay you would have worked" for in the new job. Riverway's counsel objected on the ground of hearsay, the judge overruled his objection, and she answered $60 a day. The objection was not well taken. Riverway argues that only her prospective employer knew what her wage was, and hence when she said it was $60 she was testifying to what he had told her. But an employee's wage is as much in the personal knowledge of the employee as of the employer. If Mrs. O'Shea's prospective employer had testified that he would have paid her $60, Riverway's counsel could have made the converse hearsay objection that the employer was really testifying to what Mrs. O'Shea had told him she was willing to work for. Riverway's counsel could on cross-examination have probed the basis for Mrs. O'Shea's belief that she was going to get $60 a day in a new job, but he did not do so and cannot complain now that the judge may have given her testimony some (though little) weight.

We come at last to the most important issue in the case, which is the proper treatment of inflation in calculating lost future wages. Mrs. O'Shea's economist based the six to eight percent range which he used to estimate future increases in the wages of a boat's cook on the general pattern of wage increases in service occupations over the past 25 years. During the second half of this period the rate of inflation has been substantial and has accounted for much of the increase in nominal wages in this period; and to use that increase to project future wage increases is therefore to assume that inflation will continue, and continue to push up wages. Riverway argues that it is improper as a matter of law to take inflation into account in projecting lost future wages. Yet Riverway itself wants to take inflation into account-one-sidedly, to reduce the amount of the damages computed. For Riverway does not object to the economist's choice of an 8.5 percent discount rate for reducing Mrs. O'Shea's lost future wages to present value, although the rate includes an allowance-a very large allowance-for inflation.

To explain, the object of discounting lost future wages to present value is to give the plaintiff an amount of money which, invested safely, will grow to a sum equal to those wages. So if we thought that but for the accident Mrs. O'Shea would have earned $7200 in 1990, and we were computing in 1980 (when this case was tried) her damages based on those lost earnings, we would need to determine the sum of money that, invested safely for a period of 10 years, would grow to $7200. Suppose that in 1980 the rate of interest on ultra-safe (i.e., federal government) bonds or notes maturing in 10 years was 12 percent. Then we would consult a table of present values to see what sum of money invested at 12 percent for 10 years would at the end of that time have grown to $7200. The answer is $2318. But a moment's reflection will show that to give Mrs. O'Shea $2318 to compensate her for lost wages in 1990 would grossly undercompensate her. People demand 12 percent to lend money risklessly for 10 years because they expect their principal to have much less purchasing power when they get it back at the end of the time. In other words, when long-term interest rates are high, they are high in order to compensate lenders for the fact that they will be repaid in cheaper dollars. In periods when no inflation is anticipated, the risk-free interest rate is between one and three percent. See references in Doca v. Marina Mercante Nicaraguense, S.A., 634 F.2d 30, 39 n.2 (2d Cir. 1980). Additional percentage points above that level reflect inflation anticipated over the life of the loan. But if there is inflation it will affect wages as well as prices. Therefore to give Mrs. O'Shea $2318 today because that is the present value of $7200 10 years hence, computed at a discount rate-12 percent-that consists mainly of an allowance for anticipated inflation, is in fact to give her less than she would have been earning then if she was earning $7200 on the date of the accident, even if the only wage increases she would have received would have been those necessary to keep pace with inflation.

There are (at least) two ways to deal with inflation in computing the present value of lost future wages. One is to take it out of both the wages and the discount rate-to say to Mrs. O'Shea, "we are going to calculate your probable wage in 1990 on the assumption, unrealistic as it is, that there will be zero inflation between now and then; and, to be consistent, we are going to discount the amount thus calculated by the interest rate that would be charged under the same assumption of zero inflation." Thus, if we thought Mrs. O'Shea's real (i.e., inflation-free) wage rate would not rise in the future, we would fix her lost earnings in 1990 as $7200 and, to be consistent, we would discount that to present (1980) value using an estimate of the real interest rate. At two percent, this procedure would yield a present value of $5906. Of course, she would not invest this money at a mere two percent. She would invest it at the much higher prevailing interest rate. But that would not give her a windfall; it would just enable her to replace her lost 1990 earnings with an amount equal to what she would in fact have earned in that year if inflation continues, as most people expect it to do. (If people did not expect continued inflation, long-term interest rates would be much lower; those rates impound investors' inflationary expectations.)

An alternative approach, which yields the same result, is to use a (higher) discount rate based on the current risk-free 10-year interest rate, but apply that rate to an estimate of lost future wages that includes expected inflation. Contrary to Riverway's argument, this projection would not require gazing into a crystal ball. The expected rate of inflation can, as just suggested, be read off from the current long-term interest rate. If that rate is 12 percent, and if as suggested earlier the real or inflationfree interest rate is only one to three percent, this implies that the market is anticipating 9-11 percent inflation over the next 10 years, for a long-term interest rate is simply the sum of the real interest rate and the anticipated rate of inflation during the term.

Either approach to dealing with inflation is acceptable (they are, in fact, equivalent) and we by no means rule out others; but it is illogical and indefensible to build inflation into the discount rate yet ignore it in calculating the lost future wages that are to be discounted. That results in systematic undercompensation, just as building inflation into the estimate of future lost earnings and then discounting using the real rate of interest would systematically overcompensate. The former error is committed, we respectfully suggest, by those circuits, notably the Fifth, that refuse to allow inflation to be used in projecting lost future earnings but then use a discount rate that has built into it a large allowance for inflation. See, e.g., Culver v. Slater Boat Co., 644 F.2d 460, 464 (5th Cir. 1981) (using a 9.125 percent discount rate). We align ourselves instead with those circuits (a majority, see Doca v. Marina Mercante Nicaraguense, S.A., supra, 634 F.2d at 35-36), notably the Second, that require that inflation be treated consistently in choosing a discount rate and in estimating the future lost wages to be discounted to present value using that rate. See id. at 36-39. We note that in Byrd v. Reederei, 638 F.2d 1300, 1307-08 (5th Cir. 1981), a panel of the Fifth Circuit indicated misgivings over that circuit's position and that rehearing en banc has been granted. 650 F.2d 1324 (1981).

Applying our analysis to the present case, we cannot pronounce the approach taken by the plaintiff's economist unreasonable. He chose a discount rate-8.5 percent-well above the real rate of interest, and therefore containing an allowance for inflation. Consistency required him to inflate Mrs. O'Shea's starting wage as a boat's cook in calculating her lost future wages, and he did so at a rate of six to eight percent a year. If this rate had been intended as a forecast of purely inflationary wage changes, his approach would be open to question, especially at the upper end of his range. For if the estimated rate of inflation were eight percent, the use of a discount rate of 8.5 percent would imply that the real rate of interest was only .5 percent, which is lower than most economists believe it to be for any substantial period of time. But wages do not rise just because of inflation. Mrs. O'Shea could expect her real wages as a boat's cook to rise as she became more experienced and as average real wage rates throughout the economy rose, as they usually do over a decade or more. It would not be outlandish to assume that even if there were no inflation, Mrs. O'Shea's wages would have risen by three percent a year. If we subtract that from the economist's six to eight percent range, the inflation allowance built into his estimated future wage increases is only three to five percent; and when we subtract these figures from 8.5 percent we see that his implicit estimate of the real rate of interest was very high (3.5-5.5 percent). This means he was conservative, because the higher the discount rate used the lower the damages calculated.

If conservative in one sense, the economist was most liberal in another. He made no allowance for the fact that Mrs. O'Shea, whose health history quite apart from the accident is not outstanding, might very well not have survived-let alone survived and been working as a boat's cook or in an equivalent job-until the age of 70. The damage award is a sum certain, but the lost future wages to which that award is equated by means of the discount rate are mere probabilities. If the probability of her being employed as a boat's cook full time in 1990 was only 75 percent, for example, then her estimated wages in that year should have been multiplied by .75 to determine the value of the expectation that she lost as a result of the accident; and so with each of the other future years. Cf. Conte v. Flota Mercante del Estado, 277 F.2d 664, 670 (2d Cir. 1960). The economist did not do this, and by failing to do this he overstated the loss due to the accident.

But Riverway does not make an issue of this aspect of the economist's analysis. Nor of another: the economist selected the 8.5 percent figure for the discount rate because that was the current interest rate on Triple A 10-year state and municipal bonds, but it would not make sense in Mrs. O'Shea's federal income tax bracket to invest in tax-free bonds. If he wanted to use nominal rather than real interest rates and wage increases (as we said was proper), the economist should have used a higher discount rate and a higher expected rate of inflation. But as these adjustments would have been largely or entirely offsetting, the failure to make them was not a critical error.

Although we are not entirely satisfied with the economic analysis on which the judge, in the absence of any other evidence of the present value of Mrs. O'Shea's lost future wages, must have relied heavily, we recognize that the exactness which economic analysis rigorously pursued appears to offer is, at least in the litigation setting, somewhat delusive. Therefore, we will not reverse an award of damages for lost wages because of questionable assumptions unless it yields an unreasonable result-especially when, as in the present case, the defendant does not offer any economic evidence himself and does not object to the questionable steps in the plaintiff's economic analysis. We cannot say the result here was unreasonable. If the economist's method of estimating damages was too generous to Mrs. O'Shea in one important respect it was, as we have seen, niggardly in another. Another error against Mrs. O'Shea should be noted: the economist should not have deducted her entire income tax liability in estimating her future lost wages. Cf. Norfolk & W. Ry. v. Liepelt, 444 U.S. 490, 495, 100 S. Ct. 755, 758, 62 L. Ed. 2d 689 (1980). While it is true that the damage award is not taxable, the interest she earns on it will be (a point the economist may have ignored because of his erroneous assumption that she would invest the award in tax-exempt bonds), so that his method involved an element of double taxation.

If we assume that Mrs. O'Shea could have expected a three percent annual increase in her real wages from a base of $7200, that the real risk-free rate of interest (and therefore the appropriate discount rate if we are considering only real wage increases) is two percent, and that she would have worked till she was 70, the present value of her lost future wages would be $91,310. This figure ignores the fact that she did not have a 100 percent probability of actually working till age 70 as a boat's cook, and fails to make the appropriate (though probably, in her bracket, very small) net income tax adjustment; but it also ignores the possibility, small but not totally negligible, that the proper base is really $10,800 rather than $7200.

So we cannot say that the figure arrived at by the judge, $86,033, was unreasonably high. But we are distressed that he made no attempt to explain how he had arrived at that figure, since it was not one contained in the economist's testimony though it must in some way have been derived from that testimony. Unlike many other damage items in a personal injury case, notably pain and suffering, the calculation of damages for lost earnings can and should be an analytical rather than an intuitive undertaking. Therefore, compliance with Rule 52(a) of the Federal Rules of Civil Procedure requires that in a bench trial the district judge set out the steps by which he arrived at his award for lost future earnings, in order to assist the appellate court in reviewing the award. Cf. Rucker v. Higher Educ. Aids Bd., 669 F.2d 1179, 1183-84 (7th Cir. 1982). The district judge failed to do that here. We do not consider this reversible error, because our own analysis convinces us that the award of damages for lost future wages was reasonable. But for the future we ask the district judges in this circuit to indicate the steps by which they arrive at damage awards for lost future earnings.

JUDGMENT AFFIRMED.