Mr. Justice Saldaña
delivered the opinion of the Court.
The problem presented in this appeal is, briefly, the following: What was the amount or extent of taxpayer’s travel and business expenses for the years 1945, 1947, and 1948? The Secretary of the Treasury fixed administratively that deduction, under § 16(a) of the applicable law (13 L.P.R.A. § 695), at the sums of $15,312.62 in 1945, $16,627.38 in 1947, and $16,318.09 in 1948. The taxpayer claimed in the Superior Court the sum of $32,000 for each of those years. At the trial the defendant offered no evidence whatsoever; he relied exclusively on the presumption of correctness. On the basis of the oral evidence presented by plaintiff on the nature and amount of those expenses, the trial court sustained the complaint. Feeling aggrieved, the Secretary of the Treasury alleges on appeal (1) that the presumption of correctness of the administrative determination of deficiency was not overcome, nor was it shown that the method used by him in computing those expenses was 'incorrect, and (2) that the evidence is insufficient to support ■ the findings of fact made by the lower court as to the travel [353]*353and business expenses. We believe that appellant’s contentions are unfounded and untenable.
At the trial held in the Superior Court the parties stipulated that the controversy hinged solely on the amount of the travel and business expenses. In other words, the defendant admitted (1) that the expenses were incurred in the taxpayer’s business or trade, (2) that they were ordinary and necessary expenses and were paid in each of the taxable years in controversy, and (3) that the traveling expenses were incurred while the taxpayer was away from home in the pursuit of business. Cf. 4 Mertens, Law of Federal Income Taxation (rev. ed.), 25.07 et seq., 25.88 et seq., 25.91 et seq.
Plaintiff’s oral evidence consisted of the testimony of accountant Jaime A. Montoya, Luis A. Valiente, exchange broker and investment banker, and his own.1 Carrión testified that, in his capacity as executive vice president of the Banco Popular, he received annually from that institution the sums of $12,000 for business expenses in Puerto Rico, and $20,000 for travel and business expenses in the United States; that he had considerable expenses on those accounts every year, but did not keep a detailed record of them such as vouchers, invoices, receipts, or other records; [354]*354that in Puerto Rico at least once a week he gave entertainments, dinners, and other gifts to clients of the Bank and to distinguished and influential persons in business, industries, and finance; that very often it was necessary for him to entertain distinguished visitors from the United States with whom the Bank was interested in establishing relations, or who were already clients or friends of the Bank; that on numerous occasions he entertained those visitors as guests in his own house and extended all kinds of courtesies to them; that, by reason of his office as chief executive of the Banco Popular and of the important role which that Bank played in the local economy, it was necessary for him to maintain in Puerto Rico at first one automobile and later three, which were used exclusively for business and indispensable social activities; that in addition to the weekly entertainments to which he invited groups of ten or more persons, it was necessary for him to extend invitations for lunch and cocktails almost daily to numerous clients and acquaintances of the Bank; that he also gave big receptions in his house (which was especially designed for that type of activities) : for example, in 1945 one single party cost him $1,200 and in 1948, on the occasion of the inauguration of the Governor, for business purposes, he invited more than 400 persons to a party in his home which cost him $4,600; that his total business expenses in Puerto Rico (apart from personal expenses) in each of the years in controversy exceeded by far the sum of $12,000.
[355]*355Regarding his traveling expenses (including meals and lodging) and business expenses in the United States, Carrión testified briefly that in 1945 he made nine trips and remained outside of Puerto Rico 195 days; that in 1947 he made five trips and his stay in New York lasted 226 days; that in 1948 he made four trips and his stay in that city lasted 187 days; that (on the basis of a cost of $330 for round trip, meals, tips, etc.), he spent in connection with those trips a total of $3,000 in 1945, $1,650 in 1947, and $1,330 in 1948; that (on the basis of the -fixed monthly rent for an apartment consisting of living room, bedroom, and bathroom which he occupied in the Biltmore Hotel and later in the Croydon Hotel), he spent in lodging alone $3,720 in 1945 and 1947, and $4,590 in 1948; that during his stays in New York he used to spend $500 every three or four days in activities connected with his business, drawing checks on his account in the Continental Bank & Trust Co.; that it was continually necessary for him to invite his clients and acquaintances, in groups ranging from 6 to 25 persons, to the best hotels, restaurants, theaters, and clubs of New York, and also, at times, he had to give special entertainments (some of which he described specifically and in which he never spent less than $6,000 a year) in order to establish in that way connections with big. business executives (bank, finance, and industry) in the United States, with members of the National Congress, and with officials of important government agencies; that it was also necessary for him to deliver gifts, such as works of art, flowers, etc., to the wives of the latter; that his wife accompanied him on practically all his trips and stays in New York in order to help him in numerous matters and social contacts which he mentioned; that in order to establish close relations with the persons referred to, his wife’s presence in New York was absolutely necessary not only in planning adequate entertainments and activities, but also in making friends with the wives and families of [356]*356other bankers, businessmen, industrialists, etc.; that in the years in controversy the Banco Popular transacted operations in the United States which represented substantial profits, but that in 1950 the business pace changed and his presence in New York was not as necessary as before; that he kept a permanent office in that city until 1950 in one of the Chemical Bank buildings; that he estimated the travel and business expenses incurred in New York in 1950 at approximately 50 per cent of the expenses incurred during the years in controversy; that his total expenses in New York in 1945, 1947, and 1948 were never less than $45,000 a year, but that in his opinion the expenses strictly related with the business of the Bank amounted annually to at least $20,000.
In his testimony, Carrión mentioned specially the different persons and entities with which he was bound to maintain continuous and close relations in the United States, and explained in detail why such relations and his personal negotiations were of inestimable value to the Banco Popular during the years involved in this litigation. He stated, among other things, that the Bank used to purchase and sell bonds in the United States in an amount of $200,000 annually; that it negotiated mortgages secured by the Federal Housing Authority; that it made arrangements with the Continental & Trust Company of New York to make or propose operations with the portfolio of the Banco Popular, so that the latter could easily convert
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Mr. Justice Saldaña
delivered the opinion of the Court.
The problem presented in this appeal is, briefly, the following: What was the amount or extent of taxpayer’s travel and business expenses for the years 1945, 1947, and 1948? The Secretary of the Treasury fixed administratively that deduction, under § 16(a) of the applicable law (13 L.P.R.A. § 695), at the sums of $15,312.62 in 1945, $16,627.38 in 1947, and $16,318.09 in 1948. The taxpayer claimed in the Superior Court the sum of $32,000 for each of those years. At the trial the defendant offered no evidence whatsoever; he relied exclusively on the presumption of correctness. On the basis of the oral evidence presented by plaintiff on the nature and amount of those expenses, the trial court sustained the complaint. Feeling aggrieved, the Secretary of the Treasury alleges on appeal (1) that the presumption of correctness of the administrative determination of deficiency was not overcome, nor was it shown that the method used by him in computing those expenses was 'incorrect, and (2) that the evidence is insufficient to support ■ the findings of fact made by the lower court as to the travel [353]*353and business expenses. We believe that appellant’s contentions are unfounded and untenable.
At the trial held in the Superior Court the parties stipulated that the controversy hinged solely on the amount of the travel and business expenses. In other words, the defendant admitted (1) that the expenses were incurred in the taxpayer’s business or trade, (2) that they were ordinary and necessary expenses and were paid in each of the taxable years in controversy, and (3) that the traveling expenses were incurred while the taxpayer was away from home in the pursuit of business. Cf. 4 Mertens, Law of Federal Income Taxation (rev. ed.), 25.07 et seq., 25.88 et seq., 25.91 et seq.
Plaintiff’s oral evidence consisted of the testimony of accountant Jaime A. Montoya, Luis A. Valiente, exchange broker and investment banker, and his own.1 Carrión testified that, in his capacity as executive vice president of the Banco Popular, he received annually from that institution the sums of $12,000 for business expenses in Puerto Rico, and $20,000 for travel and business expenses in the United States; that he had considerable expenses on those accounts every year, but did not keep a detailed record of them such as vouchers, invoices, receipts, or other records; [354]*354that in Puerto Rico at least once a week he gave entertainments, dinners, and other gifts to clients of the Bank and to distinguished and influential persons in business, industries, and finance; that very often it was necessary for him to entertain distinguished visitors from the United States with whom the Bank was interested in establishing relations, or who were already clients or friends of the Bank; that on numerous occasions he entertained those visitors as guests in his own house and extended all kinds of courtesies to them; that, by reason of his office as chief executive of the Banco Popular and of the important role which that Bank played in the local economy, it was necessary for him to maintain in Puerto Rico at first one automobile and later three, which were used exclusively for business and indispensable social activities; that in addition to the weekly entertainments to which he invited groups of ten or more persons, it was necessary for him to extend invitations for lunch and cocktails almost daily to numerous clients and acquaintances of the Bank; that he also gave big receptions in his house (which was especially designed for that type of activities) : for example, in 1945 one single party cost him $1,200 and in 1948, on the occasion of the inauguration of the Governor, for business purposes, he invited more than 400 persons to a party in his home which cost him $4,600; that his total business expenses in Puerto Rico (apart from personal expenses) in each of the years in controversy exceeded by far the sum of $12,000.
[355]*355Regarding his traveling expenses (including meals and lodging) and business expenses in the United States, Carrión testified briefly that in 1945 he made nine trips and remained outside of Puerto Rico 195 days; that in 1947 he made five trips and his stay in New York lasted 226 days; that in 1948 he made four trips and his stay in that city lasted 187 days; that (on the basis of a cost of $330 for round trip, meals, tips, etc.), he spent in connection with those trips a total of $3,000 in 1945, $1,650 in 1947, and $1,330 in 1948; that (on the basis of the -fixed monthly rent for an apartment consisting of living room, bedroom, and bathroom which he occupied in the Biltmore Hotel and later in the Croydon Hotel), he spent in lodging alone $3,720 in 1945 and 1947, and $4,590 in 1948; that during his stays in New York he used to spend $500 every three or four days in activities connected with his business, drawing checks on his account in the Continental Bank & Trust Co.; that it was continually necessary for him to invite his clients and acquaintances, in groups ranging from 6 to 25 persons, to the best hotels, restaurants, theaters, and clubs of New York, and also, at times, he had to give special entertainments (some of which he described specifically and in which he never spent less than $6,000 a year) in order to establish in that way connections with big. business executives (bank, finance, and industry) in the United States, with members of the National Congress, and with officials of important government agencies; that it was also necessary for him to deliver gifts, such as works of art, flowers, etc., to the wives of the latter; that his wife accompanied him on practically all his trips and stays in New York in order to help him in numerous matters and social contacts which he mentioned; that in order to establish close relations with the persons referred to, his wife’s presence in New York was absolutely necessary not only in planning adequate entertainments and activities, but also in making friends with the wives and families of [356]*356other bankers, businessmen, industrialists, etc.; that in the years in controversy the Banco Popular transacted operations in the United States which represented substantial profits, but that in 1950 the business pace changed and his presence in New York was not as necessary as before; that he kept a permanent office in that city until 1950 in one of the Chemical Bank buildings; that he estimated the travel and business expenses incurred in New York in 1950 at approximately 50 per cent of the expenses incurred during the years in controversy; that his total expenses in New York in 1945, 1947, and 1948 were never less than $45,000 a year, but that in his opinion the expenses strictly related with the business of the Bank amounted annually to at least $20,000.
In his testimony, Carrión mentioned specially the different persons and entities with which he was bound to maintain continuous and close relations in the United States, and explained in detail why such relations and his personal negotiations were of inestimable value to the Banco Popular during the years involved in this litigation. He stated, among other things, that the Bank used to purchase and sell bonds in the United States in an amount of $200,000 annually; that it negotiated mortgages secured by the Federal Housing Authority; that it made arrangements with the Continental & Trust Company of New York to make or propose operations with the portfolio of the Banco Popular, so that the latter could easily convert its assets into cash, liquidating obligations in its favor whenever it was necessary; that the borrowing capacity of the Banco Popular was limited, and only with the cooperation of continental banks were they able to transact operations in amounts involving several millions of dollars, among which was a $7,000,000 loan to the Land Authority of Puerto Rico; that those and other operations of the Banco Popular made necessary his personal activities in New York; that the average of the assets of the Banco Popular was approximately $60,000,000 [357]*357in 1945 and went up to $70,000,000 in 1948; that the volume of business from 1945 to 1948 amounted to hundreds of millions of dollars, consisting of investments, loans, and other hanking operations.
The mere fact that there were no detailed lists of hills or vouchers, invoices, receipts, or other records, does not automatically destroy the right to claim a deduction for travel and business expenses which were ordinary and necessary. Of course, neither the Secretary of the Treasury nor the Superior Court may permit reductions for personal expenses. And as it is often difficult to distinguish or separate one kind of expenses from another, the failure to keep detailed accounts supported by proper vouchers always places the taxpayer in a very dangerous position. However, if any other admissible and trustworthy evidence shows that such travel and business expenses were actually incurred, and, even if it is not exact and complete, it also shows the amount thereof, a deduction should be allowed on the basis of a computation of what ordinarily and in good economic sense, in view of the circumstances surrounding the case and the taxpayer’s business, constitutes a reasonable amount for such expenses. Cohan v. Commissioner, 39 F. 2d 540 (C. A. 2, 1930); Wodehouse v. Comm’r, 178 F. 2d 987 (C. A. 4, 1949).2 Of course, in making this approximate computation the trial court has ample discretion which may rarely be disturbed on appeal. Cf. Malgor & Co. v. Tax Court, 64 P.R.R. 549, 552 (1945); Amoroso v. Commissioner, 193 F. 2d 583, 586 (C. A. 1, 1952), cert. denied, 343 U. S. 926 (1952); Marx v. Commissioner, 179 F. 2d 938, 942-43 (C. A. 1, 1950), cert. denied, 339 U. S. 964 (1950). Without exceeding the limits of justice, de[358]*358pending on the circumstances of each concrete case, the trial court “should make as close an approximation as it can, bearing heavily if it chooses upon the taxpayer whose inexactitude is of his own making. . . However, in any case “it is not fatal that the result will inevitably be speculative; many important decisions must be such.” Cohan v. Commissioner, supra, pp. 544-45.
In this case, however, the lower court held correctly, in our opinion, that the method employed by the Secretary of the Treasury in making an estimate of the taxpayer’s travel and business expenses in 1945, 1947, and 1948 was erroneous. - In the first place, there is no justification to allocate half of those expenses to personal expenses of Carrion’s wife, since (1) the explanation given by him as to why his wife accompanied him in all his trips and stays in New York is not unreasonable, and his unimpeached testimony in this connection deserved credit by the trial court; and particularly (2) in his findings of fact, which are supported by the evidence, the trial judge stated that “the total expenses [of the taxpayer] in New York, including the nondeductible expenses which were personal and not properly business expenses, were not less than $45,000 per year, and in Puerto Rico, some $30,000 per year”; that “all the amounts paid by plaintiff’s wife to cover the expenses for entertainment and gifts to businessmen and their wives were charged to the funds allocated by the Bank and placed at plaintiff’s disposal for such purposes”; and that such amounts “were justifiably considered by the Bank and by plaintiff himself as expenses of the latter’s business and not as personal expenses of his wife.” Therefore, the amount claimed for travel and business expenses ($20,000 in New York and $12,000 in Puerto Rico) did not include the personal expenses of Carrion’s wife, despite the fact that she accompanied him in all his trips and stays in New York and took active part in many fetes and entertainments given by the taxpayer in [359]*359Puerto Rico.3 In the second place, the daily average of business expenses in Puerto Rico could not be obtained by using as divisor the 365 days of the year, since in all the years in controversy the taxpayer and his wife were away for several months. Lastly, there being specific evidence on the amount of the travel and business expenses in the years 1945, 1947, and 1948, the Treasurer should not have taken as an exclusive basis the expenses incurred in 1950. Thus, for example, Carrion’s stay outside of Puerto Rico in that year was only 147 days, while in 1945, 1947, and 1948 it was 195, 226, and 187 days, respectively. Moreover, as held by the trial court on the basis of the reasonable accounts contained in Carrion’s unrefuted testimony, the expenses incurred in 1950 were much lower than those incurred in the other years.
As already stated, the Secretary of the Treasury did not offer evidence of any kind at the trial.4 Yet, the taxpayer presented oral evidence which was believed by the trial judge and which, as a whole, is sufficient to support the latter’s findings regarding the amount of the travel and business expenses in the years involved in this litigation. We [360]*360are therefore dealing with a case in which, without question, the presumption of correctness of the tax determination made by the Treasurer was refuted by the evidence. It is well to point out that such presumption of correctness involves a danger which may lead the Secretary of the Treasury to assume a passive attitude: why struggle to achieve something which will be brought about just the same? We must now dispel, without reservation, this dangerous mistake.
According to the well-established rule, by virtue of such presumption the Secretary of the Treasury is not bound to present any evidence to establish the correctness of his tax determinations, as long as no creditable and reasonable evidence to support the taxpayer’s contentions is offered and received.5 However, if there is such evidence in the record, the presumption is dissipated and the Secretary of the Treasury is then required to present evidence in support of his contentions. If he does, the trial court should determine the facts involved in the litigation as in any other civil case: on the basis of the preponderance of the evidence. The only additional effect of such presumption in reality is presented only as exceptional: after the evidence is heard [361]*361and the case has been submitted, if the trial judge finds that the evidence of both parties on a particular issue is perfectly balanced, he should then pass judgment in favor of the Secretary of the Treasury because the burden is also on the taxpayer to persuade the trier. In other words, the taxpayer bears in fact two risks: the risk of nonproduetion of evidence and the risk of nonpersuasion. We must speak in terms of “risks,” since in the course of the trial either party may present evidence which is sufficient to comply with both aspects of the weight or burden of the evidence.6
Appellant here contends that his determination was not “arbitrary or whimsical and that it should have therefore been upheld by the respondent court.” The preponderance of the evidence does not refer, naturally, to the number of witnesses or quantity of documents. It denotes the convincing or persuasive force of the evidence in the trier’s mind. We can not postulate here a strict objectivity which would be illusory: it is necessary to recognize, on the contrary, the imponderable subjective factors involved in the process that runs through the trier’s mind. Perhaps the only acceptable formula is the following: the party having [362]*362the burden of persuasion must induce the judge to believe that the existence of the facts it asserts is more probable than their nonexistence. But the “presumption of correctness” does not constitute evidence, and it would be absurd to hold that it is the function of the judge to weigh it together with the rest of the evidence to make a proper finding of the facts. See A. & A. Tool & Supply Co. v. Commissioner, 182 F. 2d 300 (C. A. 6, 1950); Maguire, Evidence: Common Sense and Common Law (1947), pp. 175-99; and Morgan, Some Observations Concerning Presumptions, 44 Harv. L. Rev. 906 (1931). Cf. Soto v. Secretary of the Treasury, 78 P.R.R. 169 (1955). The taxpayer is only bound to prove, first, that the Treasurer’s determination or assessment is erroneous, and second, which is the basis that can be used in computing the correct tax. It is not necessary to prove that “to uphold the Treasurer’s determination would be equivalent to sanctioning a manifest injustice,” or that the tax determined or assessed is “confiscatory and oppressive,” or that the Treasurer’s action is “arbitrary, unjust, or whimsical.” Nor is there anything requiring a special quantum of evidence, or a particular force or quality therein. In other words, the evidence does not have to be extraordinarily “persuasive and authentic,” or “clear, strong, and convincing,” beyond the degree and measure of persuasion required in all other civil cases. Morgan, Some Problems of Proof Under the Anglo-American System of Litigation (1956), pp. 77-86; 9 Wigmore, Evidence, § 2498. Cf. Figueroa v. Díaz, 75 P.R.R. 154, 173, 181 (1953). Therefore, the only problem for the lower court is to determine, by a preponderance of the creditable and admissible evidence, in a manner which is not clearly erroneous, the correct amount of the tax due the Treasury.7
[363]*363Hence, if there is creditable evidence in the record which reasonably supports the taxpayer’s contentions, in the opinion of the trial court, the Secretary of the Treasury can not remain idle and rely on the presumption of correctness. If he does, the judgment necessarily has to be adverse to him. Soto v. Secretary of the Treasury, 78 P.R.R. 169 (1955), and Cía Marítima, etc. v. Descartes, Treas., 78 P.R.R. 560, 565-6 (1955). It will be readily seen also that it is futile to invoke the presumption of correctness in this appeal as ground for reversal of the judgment of the Superior Court, since in this case also there is no contradictory evidence in the record.8
Moreover, we must emphasize that the trial court found, as a question of fact, that the amount of the travel and business expenses of the taxpayer in each of those years was at least $32,000. We can not set aside such findings, based on the oral testimony which the trial court had under [364]*364consideration, unless they are clearly erroneous.9 Otherwise stated, upon further consideration we are faced with this flexible rule which must always be applied strictly: inasmuch as the adequacy between the evidence and the findings of fact is not and can never be exact or mathematical, and, according to the circumstances of each case, it will be more or less adjusted, more or less rigorous, the only thing we can demand of the trial court is to stay within certain limits beyond which we could not properly speak of adequacy, even if it were lax, but of discordance or manifest error. Cf. Comm’r of Education v. District Court, 74 P.R.R. 306, 319 (1953); Morales v. Vélez, 75 P.R.R. 901 (1954); 5 Moore, Federal Practice, 2d ed., §§ 52.03 and 52.04. As it appears even from the summary of the evidence made above, the findings of fact made by the lower court are not clearly erroneous.
[365]*365The judgment will be affirmed.
Mr. Justice Negrón Fernández and Mr. Justice Sifre took no part on the consideration or in the decision of this case.