ALVIN B. RUBIN, Circuit Judge:
The conviction in this criminal prosecution for willful evasion of income taxes1 was based entirely on the government’s evidence that it had reconstructed the medical doctor-taxpayer’s income during the years [1167]*1167in question by means of the bank deposits or cash expenditures method. Because the prosecution established the amount of cash on hand at the start of the period with reasonable certainty and performed the duties incumbent on it in attempting to separate taxable income from other sources in the doctor’s gross bank deposits and cash expenditures, the question of guilt or innocence was correctly submitted to the jury by the trial court. Therefore, the judgment of conviction is affirmed.2
I.
The defendant, a general practitioner of medicine, whose office was in LaRose, Louisiana, was charged with willful evasion of income taxes for the years 1969, 1970, 1971 and 1972. Dr. Boulet was on a calendar year basis. To prove its charges, the government relied upon one of the two traditional indirect methods of proof, analysis of the taxpayer’s bank deposits and cash expenditures. Under this method, all deposits to the taxpayer’s bank and similar accounts in a single year are added together to determine the gross deposits. An effort is made to identify amounts deposited that are non-taxable, such as gifts, transfers of money between accounts, repayment of loans and cash that the taxpayer had in his possession prior to that year that was deposited in a bank during that year. This process is called “purification.” It results in a figure called net taxable bank deposits.
The government agent then adds the amount of expenditures made in cash, for example, in this case, cash the doctor received from fees, did not deposit, but gave to his wife to buy groceries. The total of this amount and net taxable bank deposits is deemed to equal gross income. This is in turn reduced by the applicable deductions and exemptions. The figure arrived at is considered to be “corrected taxable income.” It is then compared with the taxable income reported by the taxpayer on his return.3
In. asking the jury to rely on this analysis, as a basis for deciding that the taxpayer willfully underestimated his true income, the government necessarily relies on circumstantial evidence. United States v. Marshall, 5 Cir. 1977, 557 F.2d 527, 530, note 3; United States v. Slutsky, 2 Cir. 1973, 487 F.2d 832, 839, cert. denied, 1974, 416 U.S. 937, 94 S.Ct. 1937, 40 L.Ed.2d 287; United States v. Penosi, 5 Cir. 1971, 452 F.2d 217, 219-220, cert. denied, 1972, 405 U.S. 1065, 92 S.Ct. 1495, 31 L.Ed.2d 795; United States v. Doyle, 7 Cir. 1956, 234 F.2d 788, 793, cert. denied, 1956, 352 U.S. 893, 77 S.Ct. 132, 1 L.Ed.2d 87.
It is part of the government’s burden of proof to establish beyond a reasonable doubt that the expenditures and deposits come from taxable income for the very year in question. Because our income tax system is on an annual basis, failure to report income must be charged for a specific year. The statute of limitations applica[1168]*1168ble to prosecutions penalizes only failure to report income for specific years. Moreover, the indictment charges an offense for a specific year, and the proof must conform to the indictment.
There is always the possibility that the taxpayer deposited cash that he received from a non-taxable source or from income taxed in a prior year but kept on hand as cash or even from unreported income from a prior year kept on hand in cash. Such events are common human occurrences, and this possibility may of itself create reasonable doubt. Therefore, the government must establish in some fashion the amount of cash the taxpayer had on hand at the start of the period. This is part of the government’s duty to negate the possibility that bank deposits or cash expenditures in the year under investigation originated from non-taxable sources. United States v. Penosi, supra, 452 F.2d at 219-220. See United States v. Bianco, 2 Cir. 1976, 534 F.2d 501, 507, cert. denied, 1976, 429 U.S. 822, 97 S.Ct. 73, 50 L.Ed.2d 84, suggesting that, in a cash expenditure case, proof of a likely taxable source does not suffice to relieve the prosecution of its duty to negate probable sources of non-taxable income. Compare United States v. Massei, 1958, 355 U.S. 595, 78 S.Ct. 495, 2 L.Ed.2d 517 (net-worth method).
We, therefore, review the record “bearing constantly in mind the difficulties that arise when circumstantial evidence as to guilt is the chief weapon of a method that is itself only an approximation.” Holland v. United States, 1954, 348 U.S. 121, 129, 75 S.Ct. 127, 132, 99 L.Ed. 150. The government must prove a full and adequate investigation in a bank-deposits case just as it must in a net-worth case. Holland v. United States, supra. “Such investigation must establish a guarantee of essential accuracy in the circumstantial proof at trial as an element of the government’s burden of proving guilt beyond a reasonable doubt. . . . ” United States v. Slutsky, supra, 487 F.2d at 840.
II.
It is contended that, in investigating Dr. Boulet, the government failed in two particulars: (a) it did not establish with reasonable certainty the amount of cash that he had in his personal possession, as currency, at the start of each year; these funds were substantial and, when later deposited in a bank account, were erroneously considered income; (b) among his deposits were other items that were not income, such as checks he cashed for patients; failure to delete and exclude these distorted his apparent income. The case does not present the typical problem of an unknown source of income: Dr. Boulet collected his fees in cash. The source of unreported income is contended to be fees paid Dr. Boulet in cash and not reported as income that were detected because they eventually found their way into his bank account.
Because the government did not, and, perhaps, could not, analyze each deposit separately to prove that it was from a taxable source, it is the government’s dual burden to establish with reasonable certainty the cash on hand at the beginning of each of the years in question and to negate all other sources of non-taxable income during each of those years. United States v. Marshall, supra. The latter requirement may be satisfied by proof of an adequate investigation that did not disclose non-taxable sources. United States v. Penosi, supra, 452 F.2d at 219; See also United States v. Mackey, 7 Cir. 1965, 345 F.2d 499, 506, cert. denied, 1965, 382 U.S. 824, 86 S.Ct. 54, 15 L.Ed.2d 69.
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ALVIN B. RUBIN, Circuit Judge:
The conviction in this criminal prosecution for willful evasion of income taxes1 was based entirely on the government’s evidence that it had reconstructed the medical doctor-taxpayer’s income during the years [1167]*1167in question by means of the bank deposits or cash expenditures method. Because the prosecution established the amount of cash on hand at the start of the period with reasonable certainty and performed the duties incumbent on it in attempting to separate taxable income from other sources in the doctor’s gross bank deposits and cash expenditures, the question of guilt or innocence was correctly submitted to the jury by the trial court. Therefore, the judgment of conviction is affirmed.2
I.
The defendant, a general practitioner of medicine, whose office was in LaRose, Louisiana, was charged with willful evasion of income taxes for the years 1969, 1970, 1971 and 1972. Dr. Boulet was on a calendar year basis. To prove its charges, the government relied upon one of the two traditional indirect methods of proof, analysis of the taxpayer’s bank deposits and cash expenditures. Under this method, all deposits to the taxpayer’s bank and similar accounts in a single year are added together to determine the gross deposits. An effort is made to identify amounts deposited that are non-taxable, such as gifts, transfers of money between accounts, repayment of loans and cash that the taxpayer had in his possession prior to that year that was deposited in a bank during that year. This process is called “purification.” It results in a figure called net taxable bank deposits.
The government agent then adds the amount of expenditures made in cash, for example, in this case, cash the doctor received from fees, did not deposit, but gave to his wife to buy groceries. The total of this amount and net taxable bank deposits is deemed to equal gross income. This is in turn reduced by the applicable deductions and exemptions. The figure arrived at is considered to be “corrected taxable income.” It is then compared with the taxable income reported by the taxpayer on his return.3
In. asking the jury to rely on this analysis, as a basis for deciding that the taxpayer willfully underestimated his true income, the government necessarily relies on circumstantial evidence. United States v. Marshall, 5 Cir. 1977, 557 F.2d 527, 530, note 3; United States v. Slutsky, 2 Cir. 1973, 487 F.2d 832, 839, cert. denied, 1974, 416 U.S. 937, 94 S.Ct. 1937, 40 L.Ed.2d 287; United States v. Penosi, 5 Cir. 1971, 452 F.2d 217, 219-220, cert. denied, 1972, 405 U.S. 1065, 92 S.Ct. 1495, 31 L.Ed.2d 795; United States v. Doyle, 7 Cir. 1956, 234 F.2d 788, 793, cert. denied, 1956, 352 U.S. 893, 77 S.Ct. 132, 1 L.Ed.2d 87.
It is part of the government’s burden of proof to establish beyond a reasonable doubt that the expenditures and deposits come from taxable income for the very year in question. Because our income tax system is on an annual basis, failure to report income must be charged for a specific year. The statute of limitations applica[1168]*1168ble to prosecutions penalizes only failure to report income for specific years. Moreover, the indictment charges an offense for a specific year, and the proof must conform to the indictment.
There is always the possibility that the taxpayer deposited cash that he received from a non-taxable source or from income taxed in a prior year but kept on hand as cash or even from unreported income from a prior year kept on hand in cash. Such events are common human occurrences, and this possibility may of itself create reasonable doubt. Therefore, the government must establish in some fashion the amount of cash the taxpayer had on hand at the start of the period. This is part of the government’s duty to negate the possibility that bank deposits or cash expenditures in the year under investigation originated from non-taxable sources. United States v. Penosi, supra, 452 F.2d at 219-220. See United States v. Bianco, 2 Cir. 1976, 534 F.2d 501, 507, cert. denied, 1976, 429 U.S. 822, 97 S.Ct. 73, 50 L.Ed.2d 84, suggesting that, in a cash expenditure case, proof of a likely taxable source does not suffice to relieve the prosecution of its duty to negate probable sources of non-taxable income. Compare United States v. Massei, 1958, 355 U.S. 595, 78 S.Ct. 495, 2 L.Ed.2d 517 (net-worth method).
We, therefore, review the record “bearing constantly in mind the difficulties that arise when circumstantial evidence as to guilt is the chief weapon of a method that is itself only an approximation.” Holland v. United States, 1954, 348 U.S. 121, 129, 75 S.Ct. 127, 132, 99 L.Ed. 150. The government must prove a full and adequate investigation in a bank-deposits case just as it must in a net-worth case. Holland v. United States, supra. “Such investigation must establish a guarantee of essential accuracy in the circumstantial proof at trial as an element of the government’s burden of proving guilt beyond a reasonable doubt. . . . ” United States v. Slutsky, supra, 487 F.2d at 840.
II.
It is contended that, in investigating Dr. Boulet, the government failed in two particulars: (a) it did not establish with reasonable certainty the amount of cash that he had in his personal possession, as currency, at the start of each year; these funds were substantial and, when later deposited in a bank account, were erroneously considered income; (b) among his deposits were other items that were not income, such as checks he cashed for patients; failure to delete and exclude these distorted his apparent income. The case does not present the typical problem of an unknown source of income: Dr. Boulet collected his fees in cash. The source of unreported income is contended to be fees paid Dr. Boulet in cash and not reported as income that were detected because they eventually found their way into his bank account.
Because the government did not, and, perhaps, could not, analyze each deposit separately to prove that it was from a taxable source, it is the government’s dual burden to establish with reasonable certainty the cash on hand at the beginning of each of the years in question and to negate all other sources of non-taxable income during each of those years. United States v. Marshall, supra. The latter requirement may be satisfied by proof of an adequate investigation that did not disclose non-taxable sources. United States v. Penosi, supra, 452 F.2d at 219; See also United States v. Mackey, 7 Cir. 1965, 345 F.2d 499, 506, cert. denied, 1965, 382 U.S. 824, 86 S.Ct. 54, 15 L.Ed.2d 69.
With respect to both non-taxable sources and cash on hand, the government must prove its case beyond reasonable doubt. However, “once the Government has established its case [in this fashion], the defendant remains quiet at his peril.” United States v. Holland, supra, 348 U.S. at 138-139,75 S.Ct. at 137.
Having established that it conducted a thorough investigation, “the government is not required to negate all possible non-income sources of the deposits, particularly [1169]*1169where the source of the income is uniquely within the knowledge of the taxpayer. At the same time, however, the government may not ‘disregard explanations of the defendant reasonably susceptible of being cheeked.’ ” United States v. Slutsky, supra, 487 F.2d at 841, quoting from United States v. Holland, supra, 348 U.S. at 138, 75 S.Ct. at 137. Hence, the government also has a duty to investigate leads furnished by the taxpayer with respect to cash on hand that are susceptible of being checked. United States v. Slutsky, supra, 487 F.2d at 843-844. But proof of the amount of cash on hand, if any exists, depends upon an analysis of accumulated assets and liabilities and not merely upon satisfactory pursuance of those leads, if any, offered by the defendant. See United States v. Marshall, supra, 557 F.2d at 529; United States v. Slutsky, supra, 487 F.2d at 842-843. We consider separately whether the government has satisfied its burden with respect to cash on hand and separation of funds that came from non-taxable sources.
A. Opening Cash on Hand
As in a net-worth case, Holland v. United States, supra, 348 U.S. at 132-135, 75 S.Ct. at 134-135, it is essential for the government to establish an accurate cash on hand figure for the beginning of each taxable year. See United States v. Marshall, supra, 557 F.2d at 530. If the taxpayer’s deposits or expenditures during any taxable year came from a safety deposit box or a secret cache, “they are not ‘income’ when taken from their storage place and deposited in a checking account” or when spent. United States v. Frank, 3 Cir. 1957, 245 F.2d 284, 287, cert. denied, 1957, 355 U.S. 819, 78 S.Ct. 25, 2 L.Ed.2d 35.
Here, the government initially had no cash on hand figure for the start of 1969. Dr. Boulet had informed the agents, and they confirmed with the bank, that he periodically converted currency of small denominations into $100 bills, which he did not immediately deposit. Dr. Boulet himself said he had kept currency in a safe in his mother’s home, across the street from his office, until he accumulated $3000 to $4000. He would then convert the money into $100 bills, and keep them in a safety deposit box in the bank, a block from his office. He had no record of the amount of cash he had on hand on January 1, 1969. The government attempted to establish how much cash Dr. Boulet had on January 1, 1969, by taking as a starting point the year the taxpayer began medical practice, 1962. The taxpayer had made the statement that he had “at most $5000 in cash then.” The agents then proceeded to analyze the sources of Dr. Boulet’s funds and the uses to which he applied them during the 1962-1968 period, in an effort to establish the amount of cash he had on hand at the end of the calendar year 1968. See United States v. Marshall, supra. Its analysis reflected an anomalous negative cash on hand figure on December 31,1968; if the taxpayer had the assets he owned, and no greater liabilities than he owed, he must have had over $14,000 in cash on hand not reflected either in bank accounts or other places that the investigation had revealed. Moreover, the investigation showed that, on January 2, 1969, Dr. Boulet purchased a bank cashier’s check for $15,000 with cash from a source that could not be identified. The investigator therefore concluded that Dr. Boulet had $15,000 in cash on hand (in a bank safety deposit box or some other secret place) on January 1, 1969.
Dr. Boulet does not dispute the logic of the government’s analysis, but its accuracy; he attempted to impeach this on the basis that the government failed to discover the source of the $15,000 and by its apparently inexplicable conclusion that there was “negative” cash on hand. He argues that the investigation simply was not pursued far enough. He had in fact a much larger amount in cash at the time, not reflected in bank accounts or other places that maintain records. It was this cash that was deposited in 1969-1972, and thus the source of the deposits in the taxable years was not income for those years, but, as he argues with apparent candor, unreported income from the period 1962-1968; prosecution for these years is, of course, barred by the statute of limitations. [1170]*1170During the investigation, the taxpayer told the IRS agents he had $30,000 to $50,-000 in cash on hand on December 31, 1968. Because the IRS study credited him with having $15,000 on hand, this amounted to a claim that he had $15,000 to $35,000 more than the amount credited to him.
The government showed, however, that, from 1966 to 1968, Dr. Boulet consistently deposited cash into a special bank account from which he eventually withdrew funds to build a house. Dr. Boulet had told the agents that he made frequent purchases of savings bonds, certificates of deposit and cashier’s checks, and they verified this. In later years he also accumulated savings in a homestead association account that would bear interest, and he purchased interest-bearing bank certificates of deposit from time to time. In 1969 he built a home, and paid for it without executing a mortgage. Although he had said the home cost him about $80,000, he disbursed about $150,000 mostly from the special bank account, but also including $40,000 that he withdrew from interest-bearing accounts.
This evidence cumulatively tended to show that Dr. Boulet accumulated $100 bills, and that he also periodically invested the accumulation. It tended further to show he was not likely to have maintained a non-interest bearing cash hoard sufficient to account for the unreported income that he was alleged to have concealed (all represented by bank deposits in excess of reported income): a total in excess of $124,000, consisting of $31,600 in 1969, almost $53,000 in 1970, over $32,000 in 1971; and over $8,700 in 1972. As the trial court found in denying a motion for a judgment of acquittal, “his cash on hand was in a constant state of flux because he methodically put his money to work earning interest;” it was therefore at least a permissible conclusion that, whatever non-interest bearing cash he may have secretly kept, he would have spent this before depleting an income-producing account to build his home in 1969, the first year under investigation.
The prosecution was not required to prove the opening cash figure with mathematical exactitude. The government’s proof was reasonably certain; it led to the conclusion that, when Dr. Boulet bought a certificate of deposit for $15,000 on January 2, 1969, he invested all of his cash on hand. The government investigated all “leads” furnished by the taxpayer. United States v. Slutsky, supra, 487 F.2d at 843; United States v. Ramsdell, 10 Cir. 1971, 450 F.2d 130, 133; United States v. Stein, 7 Cir. 1971, 437 F.2d 775, 778, cert. denied, 1971, 403 U.S. 905, 91 S.Ct. 2205, 29 L.Ed.2d 680; see also, United States v. Marshall, supra.
There is a distinction between proof of cash on hand sufficient to be submitted to the jury and proof enough to convict. As a matter of law the court must be satisfied in a circumstantial evidence type case that the opening cash balance is established with reasonable certainty. If this is done, then the further question remains whether guilt has been proved beyond reasonable doubt. The jury was correctly instructed on its duty. It was not obliged to credit the proof. The evidence was, however, sufficient to go to the jury free from the taint of inadequate investigation; it satisfied the standard of reasonable certainty that safeguards the accuracy of the circumstantial proof. United States v. Newman, 5 Cir. 1972, 468 F.2d 791, 795; cert. denied, 1973, 411 U.S. 905, 93 S.Ct. 1527, 36 L.Ed.2d 194.
B. Purification of Bank Deposits
Dr. Boulet’s receptionist received payments from patients and prepared a list of checks received each day. At the end of the day he and his receptionist would total the cash and checks and enter them on a deposit slip. About noon every day he went to the bank in person and made a deposit. This deposit was the basis used by him to report income.
Sometimes patients presented a check to the receptionist in payment of a bill that was less than the amount of the check; she cashed the check if the cash on hand was sufficient. During the investigation, Dr. Boulet informed the agent that his recep[1171]*1171tionist kept only about $30 in cash on hand for this purpose. If the receptionist did not have enough cash from the $30 “till money” and from cash fees already collected that day, she referred the patient to the bank, which was only a block away. The patient would go there, cash the check, then return and pay the bill in cash. The agent, therefore, treated all deposits of checks not otherwise identified as reflecting medical fees.
At the trial, however, the receptionist testified that patients frequently presented social security or welfare checks for amounts substantially in excess of their bills, and she would give these cheeks to Dr. Boulet who would cash them. This contention had never before been made known to the agents. Dr. Boulet now argues that the bank deposits reflect a substantial infusion of cash from his hoard, and are not entirely earned income; hence the government failed adequately to “purify” his bank deposits. He points by contrast to the effort made in United States v. Slutsky, supra, where the government analyzed each check deposited with a face amount in excess of $1000. In Slutsky, however, bank deposits in each of the years under examination exceeded $5,000,000 and the taxpayer had informed the agents that the deposits included non-income items; the IRS made an income analysis of items under $1000, but actually examined in detail only the deposited checks in excess of $1000 each. It treated all currency deposited in some or all of the six bank accounts as income.
Neither Dr. Boulet nor his receptionist gave this kind of information to the agents during the investigation. Moreover, even if the microfilm of every bank deposit had been located and reproduced, and every check made payable to a patient and endorsed by him had been reviewed, there was no way to separate non-income items. If a check had been found in the amount of $150.00, made payable to a patient and endorsed by him, and it was established that his doctor’s bill was $8.00, and that he received $142.00 in change, there would be no way to determine whether the receptionist obtained the change from fees already collected that day (together with the till money kept from earlier fees) or obtained some of it from Dr. Boulet. Even if she obtained some funds from Dr. Boulet, because he said he kept some fees on hand in cash, there would be no way to determine whether the cash he then gave was from current and as yet unreported income or from the alleged hoard built up in earlier years.
There were only two possible sources for any change: cash on hand from prior years or fees received from other patients during the current year and not yet deposited. Because cash on hand was established with reasonable certainty, the money paid the patients in exchange for checks could have consisted of undeposited earnings from other patients. Hence, it was a reasonable inference that the deposits consisted of earned income.
As our brethren of the Second Circuit said, in United States v. Slutsky, supra, 487 F.2d at 841, “The adequacy of a bank deposits investigation necessarily turns on its own circumstances.” The critical question is whether the investigation was sufficient to support the inference that the unexplained excess in deposits was in fact attributable to currently taxable income. The government is not required to negate every possible non-income source of each deposit, particularly where the source of the funds is uniquely within the knowledge of the taxpayer and it checks those explanations given by him that are reasonably susceptible of investigation.
Remembering that the suggestion that non-income funds were used to cash checks that were later deposited was made for the first time at the trial, we conclude that the government satisfied its obligation to explore leads thoroughly, and to make an adequate investigation of all the facts reasonably ascertainable. It may not present a case to the jury with less. It may not fling a handful of circumstantial evidence in front of a jury. It must do whatever is reasonable under the circumstances. But it is not required to conjecture about and either prove or negate every conceivable defense once it has met its own burden, ex[1172]*1172plored every reasonable avenue and investigated every lead furnished by the taxpayer and his employees.
C. The Net-Worth Schedules
At the trial Dr. Boulet tested the IRS Special Agent’s testimony and the government’s case by introducing an analysis of his net worth as of the end of 1968. This was based on another method used by the government in reviewing his income for the years 1962-1968: analyzing the source and application of his funds during that period. Comparison of Dr. Boulet’s net worth in 1962 with the net worth this indicated at the end of 1968 might lead to the conclusion that Dr. Boulet had $145,000 in unreported net income during the period 1962-1968. However, the 1968 schedule thus prepared did not show $145,000 on hand at the end of that period in a cash hoard. It showed in cash only the $15,000 attributed to the taxpayer by the government. The analysis merely established the possibility of $145,-000 in income that was not accounted for in the government’s schedules; but, at the end of 1968, this sum was accounted for by increases in items other than cash on hand.
Although this evidence impeaches the thoroughness of the government’s investigation of income during the years 1962-1968 (years not included in the indictment), it is not inconsistent with the cash on hand figure attributed to appellant as of January 1,1969. It does not establish a discrepancy between source figures and application figures, but merely that each might be too low by the same amount. Were this an appeal from a conviction for the years 1962-1968, this evidence might yield a reasonable doubt as to the adequacy of the investigation of income in those years; but here, the proof is relevant only to establishing a reasonably certain cash on hand figure at the end of that period. The defendant’s schedules, although appropriate grist for the jury, are not so probative with respect to the existence of a cash hoard for the indictment years as to require acquittal as a matter of law.
Even if Dr. Boulet had' $145,000 in unreported income from 1962 through 1968, the net worth analysis for this period does not, therefore, undermine the government’s case or demonstrate that the cash on hand as of December 31, 1968 was more than $15,000. The exhibit was offered to the jury in an effort to show the government’s failure to prove its case beyond reasonable doubt; it failed to convince them.
For these reasons we conclude that the case was properly submitted to the jury, the taxpayer’s motions for a directed verdict were properly denied, and the conviction is therefore AFFIRMED.