OPINION OF THE COURT BY
JUSTICE NOBLEThis case -raises three legal questions. First, does a reviewing court owe any deference to the Kentucky Board of Tax Appeals as to questions of law? Second, may inheritance taxes paid as a “cost of administration” under a will’s tax-exoneration provision be deducted from the value of distributive shares under KRS 140.090 and thereby reduce the overall tax liability? And, third, is the payment of tax by an estate on behalf of a beneficiary under a tax-exoneration clause itself a taxable “bequest of tax”?
As to the first question, because the Board of Tax Appeals does not administer the statutes at issue in this ease, and because the statutes are not ambiguous, no deference is owed. Because this case raises only questions of law, de novo review is appropriate.
As to the second and third questions, inheritance taxes-paid by the estate on behalf of a beneficiary of the estate are not “costs of administration” but are rather separate bequests which are subject to inheritance taxes. Those taxes paid by the estate do not reduce the total tax liability.
When a will has a tax-exoneration clause requiring inheritance taxes owed by the beneficiaries of the will to be paid from the residuary estate; and calls such payment of taxes a “cost of administration” (which is the case here), those taxes paid on behalf of the beneficiaries by the estate are nonetheless a bequest. The legislature has set forth in KRS 140.090 a list of what may be deducted from the gross value of an estate, and inheritance taxes paid by the estate on behalf of the beneficiaries are not on that list, nor do they fit under the deduction for “costs.” As such, there can be no deduction from the estate’s gross value when the estate pays those taxes for the beneficiaries.
Regardless of the language in the will saying these taxes are to be paid as a “cost of administration,’’ such, costs are defined by law and not the will of the testator. It is a simple maxim that only the legislature may say what property may be deducted, because the purpose of inheritance taxes— or any tax — is to provide revenue for the government. If a beneficiary receives property, or the benefit of the property, he simply owes taxes on that property to the government.
These legal principles seem simple, but the complex nature and variety of bequests in Mrs. McVey’s will and the disposition of other property outside the will cloud their application, as will be set forth below. This case requires the application of higher-order math or dogged calculations. Careful attention must also be paid to the order in which bequests under the will (and otherwise) are to be made. In light of this, it is apparent that neither the Estate’s original inheritance-tax return nor the Department of Revenue’s audit revisions were correct, as will be set forth below.
The Court of Appeals reached the correct legal.conclusions in this case, for the most part, in affirming the Department’s assessment of tax. Like the Department, it properly limited the Estate’s attempted deductions and concluded that tax is -owed on a bequest of tax. But, again like the Department-of Revenue, the court did not properly apply the law to the facts of this case. Specifically, the court, and the Department, ignored that the will requires payment of inheritance taxes for all taxable parts' of the estate before calculation *236of a residue to be distributed to residuary beneficiaries, which ■ substantially affects how the tax in this case should be calculate ed. But» the Department’s attempted correction of the inheritance-tax return resulted in an under-calculation of the tax, meaning that at least the full' amount of the tax asséssed is properly owed. However, the Department has not appealéd or claimed the Estate; owed more tax' than was assessed. The judgment of the Court of Appeals is therefore affirmed. ' ■' '
The above conclusions are substantiated by the background and analysis that follows. , .
I. Background
Mildred L. McVey died on January 23, 2007. 'At the time of-her death, she had a substantial estate valtíed at $1,973,939.
The bulk of her property consisted of a transfer-on-death (or TOD) securities account with Smith Barney Investments with a total value of $1,73&,417. Such accounts pass outside of probate, with ownership passing directly to the named beneficiaries on the death of the owner. KRS 292.6507. The transfer “is effective by reason of the contract regarding the registration be,tween the owner and the registering entity and KRS 292.6501 to 292.6512 and is not testamentary.” KRS 292.6509. However, the property in this, account remains subject to inheritance taxes as if part of the estate, unless the beneficiary is exempt by statute. This account appears to have been transferred to Mrs. McVey’s stepdaughter, Jimmy Lois Tureene, and nephew, Stanley K. Laughlin, Jr., with each taking 50%.
The remainder of her property, valued at $240,522, was subject to á will, which was probated in Pike District Court as the Estate of Mildred McVey.1 Mrs. McVey’s nephew, Laughlin, was appointed administrator of the estate. The properly deductible costs of administering the will totaled $25,687.03,2 leaving $214,834.97 in property to be distributed. Mrs. McVey'made various specific bequests of money and property, real and personal, to individuals and churches. These bequests had a total value of $71,922^ leaving a total of $142,912.97 as the residuary estate.3
Of the residuary estate, half 'was slated to be left to three individuals in varying percentages.4 Mrs. McVey’s step-daughter, Jimmy Lois Tureene, ’ was given 64.71%; ' her nephew, Stanley Laughlin, was given 29.41%; and' ’Billy Rice, who apparently was not kin to Mrs. McVey, was given 5.88%. The other half of the *237residuary estate was not addressed in the will and thus was set to pass through intestacy to her heirs at law. Her , only heir at law was Laughlin.
The residuary estate, however, was not free and clear to pass to these beneficiaries and heir. Mrs. McVey intended her estate to pass “tax'free” to the beneficiaries, with their inheritance taxes paid instead out of the residuary estate. Thus, she included the following “tax-free clause” or “tax-exoneration clause” (or in reality a bequest of tax) in her will:
Any death or inheritance taxes payable at my death on my estate whether on property passing under this will or otherwise shall be paid out of my residuary estate as a cost of administration and shall not be charged in any way to any beneficiary or recipient of my estate.
The Estate prepared a Kentucky inheritance and estate tax return. The return reflects the transfers on death to Tureene and Laughlin, which were taxable events to the extent not exempted by nature of their relationship to Mrs. McVey. (Under the statute, Tureene’s transfer was exempt because she was a step-child; Laughlin’s was not, because he was a nephew,) The return also reflects the specific bequests in the will, though the specific cash amounts listed are less than their face value in the will, apparently because, the Estate believed, based on its view that the tax-exoneration clause should be given effect before the specific bequests, that there would be insufficient cash after payment of costs and taxes to cover the full bequests.
The return does not show a residuary estate to pass after payment of taxes because,, according to the Estate’s calculations, the entire residue will be consumed by costs and taxes. (This is stated in the future tense, because the estate has not yet been finally settled.) In addition to the allowed costs noted above, the Estate included the costs of taxes as a debt of the decedent, which reduced the property available in calculating the distributive-shares of beneficiaries.
The return includes a tax-computation page with a multi-column table showing all the gifts from the estate and the tax owed on them. One column describes the beneficiaries and the gifts they received. The second shows the beneficiaries’ relationship to the decedent. Another column, labeled “Distributive Share,” shows the value of each gift. The final column shows the amount- of tax ■ owed, if any, on each gift. Several of the beneficiaries were exempt from tax, such as the step-daughter Tureene, see KRS 140.080(l)(c)(4), and the churches, see KRS 140.060, which is reflected in the tax column.
But the remaining beneficiaries — a trio of great-nieces, a recipient of a specific cash bequest (North Middletown Cemetery), and Laughlin — were not exempt. Their total inheritance-tax liability was calculated as $134,369.48. This number included the taxes to be paid on behalf of the great-nieces and the cemetery. It also-included a calculation of two instances of “bequest of tax”: the tax on the tax to be paid on behalf of the great-nieces, and a second, level of tax on the first bequest of tax.5 The bulk of the total tax, $132,387.80 *238of it, reflected the tax on the portion of the TOD account and other property that passed to Laughlin. The return does not show a bequest of tax for Laughlin.
The Department of Revenue conducted an audit of the return, finding several claimed errors.
First, the Department corrected an error in how the tax was calculated on the great-nieces’ gifts, and added a calculation for bequest of tax for the cemetery. At the hearing before the Kentucky Board of Tax Appeals, and before this Court, the Department claimed that its adjustments here were only to correct a simple math error, but that is only half correct as examination of the corrected return shows more than a simple math error.
As to the great-nieces, the Department did find a math error. Specifically, the number in the entry for the first bequest of tax did not match the number showing the calculated tax on the great-nieces’ shares, though it correctly showed what the tax and bequest of tax should have been. The return also unnecessarily included an entry showing a bequest of tax on the bequest of tax paid for the great-nieces’ shares. The Department corrected this by removing the separate entries for the bequests of tax, and adding the properly calculated bequest of tax to the nieces’ distributive shares. The Department also changed the calculation of tax on then.’ shares to reflect the full tax (the basic tax plus the additional bequest of tax).
At that same time, the Department altered the amounts listed for the will’s specific cash gifts (to two churches, a cemetery, and an individual) to reflect their full face values as laid out in the will. It then calculated the tax on the non-exempt cash gift to the cemetery, and included a bequest of tax, whereas the Estate had included no such calculation, and assigned this amount to the cemetery’s distributive share. This number, when added to the amount of tax on the great-nieces’ shares as calculated by the Department, exceeds the value of the bequests of tax calculated on the original return for the nieces by a little over $10.
Second, the Department disallowed the deduction of the inheritance-tax liability from the value of the distributive shares, seemingly increasing the overall property available for those shares. Although various deductions against the distributive shares are allowed by KRS 140.090, including debts of the decedent, the Department reasoned that the inheritance tax could not be deducted because it was not a debt of the decedent, having not existed at the time of her death.
The Department also presumed that the disallowed tax deduction meant there was, in fact, some residuary estate, which it attributed to the distributive shares of the residuary beneficiaries. The Department took the value it had calculated for the estate after costs and debts (a total of $1,948,251.91), and subtracted the TOD transfers and specific bequests, and the bequests of tax it had calculated for the specific bequests to the great-nieces and the cemetery, to arrive at what it believed was the residuary estate (a total of $140,921.04). It then proceeded to assign6 *239this money to the distributive shares of Tureene (an additional $45,595) and Laughlin (an additional $91,182.96), and created a new entry for Billy Rice (who is mentioned only in the residuary clause) showing a gift of $4,143.08. -With this property added to the various shares, the Department concluded that an additional $14,818.10 in tax was owed, most of which was related to the increase in Laughlin’s share, plus interest.7
The Estate protested this additional inheritance-tax assessment. On July 2, 2010, the Department issued its Final Ruling No. 2010-41 affirming the assessment of additional tax. The Estate appealed the Department’s ruling to the Kentucky Board of Tax Appeals, as allowed under KRS 131.110(5). The Board is an administrative agency created under KRS Chapter 131, and is vested with exclusive jurisdiction to hear and determine appeals from final rulings, orders, and determinations of any agency of state or county government affecting revenue and taxation, KRS 131.340.
The Board reversed the assessment. At the hearing, the Board stated simply that the Estate was entitled to-judgment as a matter of law and asked the Estate to prepare an order. The Board’s written order concluded that the inheritance taxes were properly deducted as a “cost of administration” under KRS 140.090 because McVey’s will “so directed.” The Board also disallowed the Department’s attempt to impose a tax on the bequests of tax. In reaching this conclusion, the Board complained that “[i]f the Revenue Cabinet follows its logic to its end there would be a tax on the tax and then on ad infinitum,” an odd finding given that the Department has consistently done just that over the years.
The Department sought judicial review of the Board’s decision in Franklin Circuit Court; The circuit court reversed, correctly'conclüding that the Estate could not deduct the taxes as a cost of administering the estate or debt of the decedent under KRS 140.090, notwithstanding the language in the will. The court also concluded that the will’s direction that inheritance taxes be paid out of the residuary estate created additional gifts or “bequests of tax,” which are also subject to the inheritance tax. The court reviewed the Board’s decision de novo.
The Court of Appeals affirmed, and this Court accepted discretionary review to address questions related to how much deference, if any, is owed by a reviewing court to the Board’s interpretation of statutes, whether inheritance taxes may be deducted from the value of distributive shares of an estate, and whether inheritance tax paid from the estate on behalf of a beneficiary — a bequest of tax — is itself a taxable event.
II. Analysis
A. The proper standard of review is de novo, and the Board of Tax Appeals is owéd no deference as to legal questions.
Before turning to the substantive issues in this case, we must first address the standard of review to be applied. The Estate admits that because no facts are in dispute and this case involves only ques-tións of law, the matter is. reviewed de novo.
Nevertheless, the Estate claims that the Board’s interpretation of the stat*240utes -in question is entitled to deference under Chevron, U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). This Court has frequently, applied so-called Chevron deference to the decisions of state administrative agencies. See, e.g., Louisville/Jefferson County Metro Government v. TDC Group, LLC, 283 S.W.3d 657, 661 (Ky.2009). But such deference is only afforded “if the statute .is silent or ambiguous with respect to the specific issue.” Chevron, 467 U.S. at 843, 104 S.Ct. 2778. As explained below, the statutes in .question are neither.
More importantly, deference is given only to an administrative agency’s interpretation of a. “statute which it administers.” Id, at.842, 104 S.Ct. 2778; see also Board of Trustees of Judicial Form Retirement System v. Attorney General of Commonwealth, 132 S.W.3d 770, 786-87 (Ky.2003) (deference afforded only to “administrative agency’s construction of a statute that. it is charged with implementing”). The statutes in question, those addressing inheritance tax, are not administered by the Kentucky Board of Tax Appeals. The Board is “an administrative review agency.” KRS 131.310 (emphasis added). Its limited purpose is to determine appeals of. tax rulings, and its decisions in turn are subject to judicial review under KRS Chapter 13B. A reviewing court can reverse such a decision if the Board’s decision is in violation of a statute. KRS 13B.150(2)(a). The Board, then, has a limited function as a reviewing tribunal, not as a full administrative agency charged with implementing a portion of the Kentucky Revised Statutes.
■Instead, the statutes in question are administered by the Department of Revenue. See, e.g., KRS 140.160(1) (“The Department of Revenue shall have full supervision of the collection of all taxes due under the provisions of this chapter, including the power to institute suit in this and other states.”); KRS 140.165 (“The department may make such audits, appraisals, and examinations of records according to KRS 131.130 to properly supervise the collection of all taxes due under the provisions of this chapter.”). Thus, as noted by the Department, if any deference is to be given, it is to the Department’s formal- interpretation of a statute that it administers. But the Department has not actually claimed that it is entitled to deference, or at least has not identified a formal interpretation of the statutes in question to which deference could be afforded.'
Regardless, it is clear that “the role of judicial review of a decision by the Kentucky Board of Tax Appeals is that of determining the propriety of ‘questions of law.’ ”. Epsilon Trading Co., Inc. v. Revenue Cabinet, 775 S.W.2d 937, 940 (Ky.App. 1989). Our review, therefore, is de novo, and no deference is given to the Board’s interpretation of tax statutes.
B. No deduction is allowed for inheritance taxes paid.
The Department’s main concern is whether the inheritance taxes to be paid out of the estate may be deducted from the gross estate as costs, thereby reducing the value of the distributive shares.' The primary effect would be on the amount of the residuary estate that would be subject to tax. As we stated above, the inheritance taxes paid cannot be deducted. '<
Deductions from the value of the gross estate are controlled by KRS 140.090. The statute is explicit that only the'listed deductions are allowed and that “no others shall be allowed.” KRS 140.090. The allowable deductions include “debts of the decedent,” KRS 140.090(l)(a); “taxes accrued and unpaid,” 140.090(l)(b); and “costs of administration,” KRS *241140.090(l)(h). Inheritance taxes are none of these, as' this Court’s predecessor has already held. Lynch v. Kentucky Tax Commission, 333 S.W.2d 257, 261 (Ky. 1960).
Debts of the decedent are “debts which have accrued and are unpaid at the instant.of death, not a debt which accrues by reason of death.” Id. But the inheritance tax accrues only by reason of death. Thus, “it is not a debt of the decedent.” Id. For the same reason, the inheritance tax is not a tax accrued and unpaid (as opposed, for example, to income tax that accrued, during the decedent’s life). Id.
Finally, inheritance taxes are not the type of cost of administration contemplated by the deduction statute. Id. As this Court’s predecessor has already stated, “tax paid does not constitute a cost of administration.” Id. Though Lynch spoke specifically of inheritance taxes paid in other states, the reasoning is the same for inheritance taxes paid in Kentucky. Taxes are taxes, not costs.
' Despite longstanding law to the contrary, the Board nonetheless concluded that the taxes could be deducted as a cost of administration because Mrs. McVey’s will “so directed.” The Estate cites Northcutt’s Executrix v. Fanners National Bank, 292 Ky. 628, 166 S.W.2d 971, 974 (1942), to support this position, claiming that it directs the order in which various aspects of the estate are to be used to pay costs and debts; But that case addresses only whether a lapsed gift should be used to pay debts of the decedent and costs of administration before other property when the will is silent. The will in this case was not silent as to the source of payments of the inheritance tax, and thus Northcutt’s Executrix has no applicability here.
The Estate also cites Brodie v. DeVatz, 556 S.W.2d 444, 444 (Ky.1977), which it claims requires the collection of inheritance tax to be forgiven where the will states that taxes are to be paid out of the gross estate. This Court does not disagree with that description of Brodie’s holding. But that case said nothing about allowing a deduction for taxes paid under a tax-exoneration clause. Instead, it simply declares that a will may direct that property in the estate be used to pay the taxes on the transfers of estate property, including property passing outside probate.
The Estate’^ argument hinges on the notion that the direction in the will that the taxes be paid as a “cost of administration” dictates that they be treated as such under the statute and, thus, can be deducted. But that notion is clearly incorrect. Although the general rule is that a testator’s intent controls construction of a will, that rule only has effect if the testal tor’s intent “is not contrary to some positive rule of law.” Citizens’ Trust Co. v. Fidelity Trust Co., 136 Ky., 540, 124 S.W. 824, 825 (1910) (quoting Finlay v. King’s Lessee, 28 U.S. 346, 377, 3 Pet. 346, 7 L.Ed. 701 (1830) (Marshall, C.J.)j. The direction of the will does not control whether the taxes fall under an expressly limited statutory deduction. Rather, the deduction statute itself controls. Indeed, if the Board’s and Estate’s reasoning were sound, anything could be labeled a cost of administration in the will and thus be deducted from the value of distributive shares., Taken to its logical conclusion, this could even include the value of bequests themselves, which would effectively liberate .them of any inheritance tax burden. Such a reading is plainly absurd. Instead, costs of administration are limited to those expenses traditionally allowed, such as attorney’s and accountant’s fees. Inheritance taxes are exactly that: taxes, not costs.
*242C. A bequest of tax is itself taxable.
The remaining question is whether a bequest of tax under a tax-exoneration clause, like that in Mrs. McVey’s will, is itself a taxable transfer of estate property. The Board of Tax Appeals concluded that it is not. But under the inheritance-tax scheme, it is clear that it is.
An inheritance tax is levied on any transfer of real or personal property by reason of a person’s death. KRS 140.010. Thus, the tax extends to property transferred “by will or by the laws regulating intestate succession, or by deed, grant, bargain, sale or gift made in contemplation of death or made or intended to take effect in possession or enjoyment at or after the death of the grantor or donor.” Id. The tax also extends to sums paid on “an obligation of a contractual nature ... in favor of any person payable at or after death of the decedent.” KRS 140.030(1). Thus, the inheritance tax extends to all of the property in Mrs. McVey’s estate, including both property passing through probate (the bequests made in the will and any property passing under intestacy), and non-testamentary property passing outside probate (the TOD account),
The inheritance tax is not a tax on property “but one on the privilege or right of succession.” Booth’s Ex’r v. Commonwealth, 130 Ky. 88, 113 S.W. 61, 64 (1908).8 It is an excise tax. See Martin v. Storrs, 277 Ky. 199, 126 S.W.2d 445, 447 (1939) (“It is well settled that an inheritance tax is an excise tax upon the privilege of receiving property from a decedent by reason of his death.”). Importantly, inheritance tax is “imposed when any such person or corporation becomes beneficially entitled in possession or expectancy to any property or the income thereof by any such transfer.” KRS 140.010 (emphasis added).
Ordinarily, inheritance taxes are paid out of the shares received by the beneficiaries (or out of their own funds if their gifts consist of specific property), “unless the will of the decedent directs to the contrary.” Gratz v. Hamilton, 309 S.W.2d 181, 182 (Ky.1958). But a “testator may, if he elects so to do, shift the burden of taxation from the person or fund which is ordinarily liable under the law to some other person or fund of his choice.” Id. That is what Mrs. McVey did in this case by directing that the inheritance' taxes be paid out of the residue of her estate so that the beneficiaries would take their gifts at full face value.
But when a will directs payment of the inheritance taxes in this way, the beneficiary also receives the benefit of the tax paid by the estate, even though it does not pass through his or her hands. Because the beneficiary receives the benefit of the tax paid on his or her behalf, the tax paid is itself a taxable transfer of property and is part of the overall bequest. It is referred to as a bequest of tax for a reason. And the full value of a bequest is taxable, unless the beneficiary is exempt from tax. Inheritance tax must be paid “upon the value of the whole estate transmitted,” Booth’s Ex’r, 113 S.W. at 65 (quoting Eyre v. Jacob, 55 Va. 422, 428, 14 Gratt. 422 (1858)), except for those portions passing to an exempt beneficiary. The whole estate transmitted includes amounts paid as bequests of tax.
This appears to have long been the position of the Department of Revenue.9 The *243Department cites an issue of Kentucky Tax Alert, a newsletter for tax professionals, from 1987 noting that bequested tax is itself subject to additional tax. See Dep’t of Revenue, Computation of Inheritance Tax on Transfers Not to Be Reduced by the Inheritance Tax, Kentucky Tax Alert, Nov. 1987,'at 2-3. And the instructions included with the tax forms for 2007, the year Mrs. McVey died, directed that “[i]f the will directs that the estate- pay the inheritance tax' from the residue and the beneficiary does not share in the residue, the bequest of the tax is added to and made a part of the distributive'share of the beneficiary receiving the specific bequest or devise.” Dep’t of Revenue, General Information, Kentucky Inheritance and Estate Tax Forms and Instructions 5 (Oct. 2008).
More interestingly, the Kentucky Board of Tax Appeals itself appears to have concurred, at least until the Board’s decision in this case. Indeed, before this case, the Board had repeatedly held that “the tax-free aspect, of a bequest is itself taxable.” Estate of Samuels v. Dep’t of Revenue, K80-R-35, KBTA Order No. K-6766, 1981 WL 14732, at *1 (Ky. Bd. of Tax App. Oct. 20, 1981); see also Ky; Trust Co. v. Dep’t of Revenue, K65-R-40, KBTA Order No. K-258 (Ky. Bd. of Tax App.1966) (“The practical effect of a testamentary provision freeing a bequest, etc. from the burden of an inheritance tax which would otherwise fall upon such bequest is to make an additional bequest which is subject to tax. The total gift is described as the amount of the tax-free gift plus such an amount that when the tax on the whole is computed and deducted from the whole, the tax-free gift is the remainder.”).
And it appears that the Estate itself understood that bequests of tax were taxable, since it calculated the bequest of tax on at least three gifts (those to the great nieces). Of course, its calculation was slightly erroneous, and it did not include such a calculation for all the bequests of tax, as explained above.
Though only a few states have addressed this issue in published cases, this is the clear majority rule among those to have addressed it.10 In fact, the Board *244itself acknowledged > this in 1981, stating clearly.that- “[t]his is .tKe majority rulé in this country.” Estate of Samuels, K80-R-35, KBTA Order No. K6766, 1981 WL 14732, at *l;.Of course, that a majority of jurisdictions follow this rule is not binding on this Court, but it is persuasive.
In the end, howevér, it is the language of the inheritance-tax statutes that requires "this rule. The inheritance tax is intended to apply to the óash value of the estate, minus allowed deductions. See ERS 140,010 (levying tax on “the fair cash value as of the date of the death of the grantor or donor of the property in excess of'the exemptions granted and at the rates prescribed in this chapter”). And, again, inheritance tax must be paid “upon" the value of the whole estate transmitted.” Booth’s Ex’r, 113 S.W. at 65 (quoting Eyre v. Jacob, 55 Va, 422, 428, 14 Gratt. 422 (1858)). But to hold that the property used to pay a bequest of tax is not to be taxed would be to allow part of .the full cash value of the estate to avoid taxation. In some cases, that could be a considerable portion of the estate. Indeed, in this case, the total tax to be paid by the estate on behalf of various beneficiaries is at least $130,000, the bulk.of which is to -be taxed at a high rate (16%).11
It has been argued that the Department has no authority to increase the amount of bequests made by a testator to account for this tax on bequests of tax. But this misses the point. It is not’ the Department that increases the bequest. Rather, .it is the testator who. “increased”' the bequest by leaving a gift and requiring, .usually in another clause of-the will, that the taxes be paid out of the -estate or part of the estate. The better way to think of it is that the testator has .made a bequest in two parts; the specifically gifted property and, via the tax-exoneration clause, an additional amount calculated based on the applicable tax rates. The amount of the overall bequest is knowable from the moment the will is drafted (unless, of course, the tax rates change or the value of the property in question changes). The testator’s possible failure to calculate or approximate this amount and to know the specific number or approxirhation’does not change the fact that the testator has given an additional gift to the beneficiary. This indeterminacy is commonly accepted in wills; ■ indeed, the very idea of a residuary estate reflects indeterminacy at the time a will is executed. And given that we know tax rates12 *245and property values do change, to require more specificity in wills in calculating the overall amount of a, bequest involving a bequest of tax would be untenable.
The simple fact is that the tax is paid from the estate on the beneficiary’s behalf. It is no different than if the decedent had increased the specific bequest to cover the tax, thus leaving the game net amount to the beneficiary. Tax-free clauses are used to liberate a specific bequest of tax instead, in many instances, because they have advantages other than tax avoidance. For example, they can be used to lessen the administrative burden in probate, since the administrator is charged with collecting the inheritance taxes even though the beneficiaries are ultimately liable for them, KRS 140.220. Such clauses may also be used to allow for passage of specific pieces of property to beneficiaries who may not have sufficient -funds to pay the tax .out of their own pockets. -
The basic rule, then, is that a tax must be paid on a' bequest of tax paid out of an estate on behalf of a beneficiary: But a sub-question of whether a bequest of tax is itself taxable is whether this is a one-time tax calculated on only the initial bequest of tax or an infinite series of tax calculations.
It has been claimed that the Department only taxes the bequest' of tax one time. See L. Rush Hunt & Lara Rae Hunt, Baldwin’s Kentucky Wills and Trusts § 5.13, at 93 (rev. ed. 2004) (claiming the Department “only applies the extra ‘hit’ one time”). For example, if the tax rate were 10%, and a beneficiary was left $100,000 in a will with a tax-exoneration clause, the tax paid on the beneficiary’s behalf would be $10,000. If the Department only charges tax on the bequest of tax one time, this $10,000 bequest of tax would lead to an additional tax of $1,000, for a total bequest of $111,000. The final $1,000 tax on a tax, though paid by the estate for the beneficiary, would not itself be subject to tax under this practice.
Despite the Department’s alleged practice, the Board Objected to the notion of any tax 'on the Requested tax because it believed this would lead to an improper infinite calculation of tax, noting as it did that “[i]f the Revenue Cabinet follows its logic to its end there would be a tax on the tax and then on-ad infinitum.” -The‘concern, also raised by the Estate, is that the tax would not stop after one such calculation but would extend infinitely.
Were the Department’s clear practice to calculate the tax only one time, .we could stop there, as they would, and readily dispose. of the Board’s and the Estate’s concerns. But in this case, the Department calculated the tax on the.bequested tax for the' specific bequests beyond the one step.13 And' the documents submitted by the Department showing how the calculation is tó be done show more than one level of tax on tax. See Dep’t of Revenue, Computation of Inheritance Tax on Transfers Not to Be Reduced by the Inheritance, Kentucky Tax Alert, Nov. 1987, at 2-3 (showing brute-force method of calculating tax ad infinitum).
*246Thus, to fully address the bequest nature of the estate paying inheritance taxes for the beneficiaries, we are tasked with determining whether only one level of tax on tax is called for. We conclude that it is not. As noted above, the inheritance tax is assessed on the fair cash value of the whole estate at the time of death, reduced only by those deductions expressly allowed by statute. KRS 140.010. In other words, the full cash value of the estate must be accounted for to avoid part of the estate passing tax-free, and allowing only one level of tax on bequest of tax fails to do this. Instead, the tax must be calculated ad infinitum.
This also avoids discrepancies in tax treatment of otherwise identical gifts under different types of wills (i.e., those with tax-exoneration clauses versus those without). Returning to the example above, with only a single level of tax, the $100,000 given under a tax-free clause and taxed at a rate of 10% would result in a total payment from of the estate of $111,000, with $11,000 in tax being paid and the beneficiary receiving $100,000. But a gift of $111,000 under a will without such a tax-free clause, and with the same tax rate, would result in $ 11,100 in taxes being paid, and the beneficiary receiving only $99,900. The difference is small here, but as the size of gifts and the overall estate increases, so does the discrepancy. On the other hand, if the tax on tax is calculated ad infinitum on the same tax-free bequest, the overall amount paid out of the estate is $111,111.11, with $11,111.11 of that being tax; a plain bequest of $111,111.11 at the same rate results in the same tax amount, and the same net amount for the beneficiary.14
Calculating the tax ad infinitum does not mean the tax is limitless. Instead, the tax owed on each “tax on the tax” paid on a beneficiary’s behalf grows smaller with each new level, approaching zero. This was demonstrated by the example in the Department’s brief showing a decreasing amount of tax at each step until the amount essentially became too small for any recoverable tax to be charged. Though the tax is calculated ad infinitum, the resulting tax is always a finite sum.
As noted above, the Board was concerned that this infinite computation of tax is absurd. And this concern has been raised elsewhere. See, e.g., Old Colony Trust Co. v. Commissioner of Internal Revenue, 279 U.S. 716, 730-31, 49 S.Ct. 499, 73 L.Ed. 918 (1929) (noting argument that infinite compounding of income tax paid by company for employee, the “tax paid on a tax,” “results in an absurdity”). But that concern is misplaced, driven perhaps by a misapprehension of the complexity or scope of the calculation involved, when, in fact, the solution is quite simple; or by a misunderstanding that the “infi*247nite” calculation leads to an ever-increasing amount of tax.
The ad infinitum calculation simply describes what happens mathematically when such a tax is calculated, but it does not result in ever-increasing amounts of tax. The type of calculation required and used by the Department of Revenue is often used in accounting where, for example, a company wishes to pay the income tax for an employee. E.g., Westinghouse Savannah River Co. v. United States, 168 F.3d 1316 (Fed.Cir.1998) (“Income tax gross-up is a method of paying an employee an additional amount of money to offset the taxes incurred due to relocation expenses”). It is commonly called “grossing up,” since the gross amount paid will have to be increased to arrive at the intended net amount.
The same concept applies to a tax-free bequest where the testator seeks to pay the tax for the beneficiary out of the residuary estate, and the “bequest of tax” is itself a taxable event. ■ The grossed-up number can be calculated using what is known as an infinite geometric series, the sum of which can be calculated using a simple algebraic formula15:
[[Image here]]
if and only if %COr%CO < l,16 where a is the amount of the tax-free bequest, and r is the tax rate expressed as a decimal (e.g., 20% is .20). Thus, a $1,000 tax-free bequest, with a 20% tax rate, would result in a “grossed up” overall bequest of $1,250 ($1000 ⅛- (1 — .20) = $1000 -5- .80 = After payment of 20% of that amount in tax, the beneficiary would be left with $1,000.
The process becomes slightly more complicated when there is not a flat tax but instead a graduated or progressive tax, as is the case in Kentucky. In that instance, the same formula can be used solely to determine the tax owed, which can be added to the face value of the bequest to arrive at a grossed-up number. See, e.g., 18 Cal.Code Regs. § 13601.4 (applying the formula to determine amount of tax owed in graduated system). In that scenario, the amount of overall tax to be added to intended tax-free amount of bequest is calculated by applying the tax rates to the intended bequest to arrive at a base tax, which is the number used for a in the formula above, with r. being the marginal tax rate.
To see how simply this works in action, consider the example offered by the Revenue Cabinet of a $10,000 bequest to a “Class C” beneficiary.17 The first $500 of *248that amount is exempted. KRS 14Q.080(l)(e), The remaining $9,500 is taxed at 6%, See .KRS 140.070(3) (levying tax of 6% on the first $10,000). The basic tax, then, is $570. That amount, paid by the estate for the beneficiary, brings the total bequest over $10,000. Any amount over $10,000 and up to $20,000 is taxed at 8%. Id. Thus, the '$570 bequest of tax is taxed .at a rate of 8%, as is any additional tax on tax, up to a total of $20,000.
The' Revenue Cabinet suggests that the overall answer can be computed through brute force — that is, by showing each step until the amount of tax at the next step would be rounded down to zero — as follows:
[[Image here]]
This results in a very close approximation of the tax, though rounding can result in very minor errors.
' But run through the algebraic equation above, the calculation is even simpler. As explained above, the base amount of tax owed on the bequest is $570, and that “bequest” falls into the 8% tax bracket. Thus, a is equal to $570, and r is equal to 0.08. Determining how much, the estate would need to .pay to cover the total bequest of tax requires only the following calculation (shown here step by step but requiring only two simple calculations with a calculator):
[[Image here]]
*249This amount of tax is added'to the intended tax-free bequest to arrive at the overall distributive share.
It has also been argued-that the algebraic formula required to carry out the tax calculation above is “not lightly to be imputed to legislators.” In re Loeb’s Estate, 400 Pa. 368, 162 A.2d 207, 213 (1960) (quoting Edwards v. Slocum, 264 U.S. 61, 63, 44 S.Ct. 293, 68 L.Ed. 664 (1924) (Holmes, J.)). But the simple fact is that this formula is the only way to account for the tax commanded by the General Assembly, which must be calculated on the fair cash value of all estate property not exempted. A single-level calculation — one “hit” of the tax on bequests of tax — allows tax to be assessed against less than the full cash value of the estate (less allowed deductions). In essence, taxes paid on bequests of tax — themselves bequests of tax being paid on • behalf of a beneficiary — would pass tax free. Though not expressly written into the statute, the algebraic equation is no less necessary than addition, subtraction, multiplication, and division are in calculating tax; and those operations, like the algebraic formula, are not expressly listed in the statutes. The equation, like any other mathematical tool, is implicitly part of the statutory scheme for calculating the tax required by the statute.
D. The Department incorrectly applied this law to portions of the estate in light of the directions of the will.
So the Department is correct in both respects as to the law in Kentucky. The inheritance tax cannot be deducted from the. estate to reduce distributive shares of the beneficiaries. And bequests of tax are themselves taxable. Thus, the Department acted correctly in denying the inheritance-tax deduction from the gross estate and in- calculating a bequest of tax on each specific, bequest to the greats nieces and the cemetery. •
But thát' dbes not mean the Department’s overall treatment of the return was correct. The problem was with the Department’s decision to adjust the return to’ reflect a gift' of the residuary estate to Tureené, Laughlin, and Rice. The Department assumed that because the tax to be paid could not be deducted from the distributive shares, it must have instead constituted a residue to be distributed to these three beneficiaries. But this ignores how the will directs the residue to be disposed of.
The Department’s adjustment here assumed the amount' that the Estate had claimed as a deduction from the gross estate for taxes, $134,369.48, along with other disallowed adjustments, for total of $140,921.04, would constitute the residue of the estate and would be distributed to the residuary beneficiaries,' Tureen, Laughlin, and Rice, even though'no such gifts are shown on the original return. Instead,' the Department- imputed residuary gifts to these beneficiaries. These added gifts increased the base inheritance tax by a total of $14,807.86. The Department’s adjustments purported to' show the distribution of the residue of the estate and the tax on those gifts.
But given how the estate is to be distributed under the will, thére will be no residue left to give. Instead, the vast majority of the value of the estate is being used to pay the taxes on Laughlin’s receipt of half of the TOD account that passed to him outside probate. The Department correct*250ly noted that the “residuary estate,” after deduction of the bequest of tax for the specific bequests, totaled $140,921.04.19 But the residue does not automatically pass to the residuary beneficiaries at, that point because the will calls for other taxes to be paid first. Specifically, the tax-exoneration clause directs payment of the taxes on Laughlin’s pre-residuary take.
Laughlin’s distributive share of the estate includes several specific testamentary bequests and a substantial amount of .property taken outside probate through a TOD account. The bequest of tax on this property is at least $132,397.80 (the amount calculated by the estate). Of course, this amount, paid on Laughlin’s behalf and thereby benefiting him, is itself taxable. That was the first level of tax — the base tax. And the tax on that (at a rate of 16%) is $21,182.05, bringing the total tax owed on his share to $153,569.85.20 That alone exhausts the remaining residue. Thus, there is notfiing to pass to Tureen, Laugh-lin, or Rice under the residuary clause.
The Department appears to have handled the estate in this fashion because, according to its brief, “[n]o additional value is added to a beneficiary’s distributive share if the beneficiary also shares in the residue of the estate.” See also Dep’t of Revenue, Computation of Inheritance Tax on Transfers Not to Be Reduced by the Inheritance Tax, Kentucky Tax Alert, Nov. 1987, at 2 (noting the Department “does not compute the bequest of tax for inheritance tax purposes when the beneficiary’s share includes any part of the residue”). Beqause Laughlin shared in the residuary estate, the Department declined to treat the tax paid on his specific testamentary bequests and the TOD account as bequests of tax. The Department instead assumed that the residue property it had calculated would pass to the residuary beneficiaries, and then taxes would come out. It thus assigned to Laughlin the part of the residue of the estate that it had calculated without taking into account that he was first to receive a bequest of tax on his specific bequests and TOD account. But they ignored the fact that Laughlin was not the only beneficiary of the residuary clause.
The Department’s approach makes sense when the beneficiary in question is only a residuary beneficiary, or where the beneficiary is the only residuary beneficiary. Where the beneficiary is only a residuary beneficiary, the tax-free clause in this case would have no effect, because taxes are paid before calculating the ultimate residue. Thus, there would be no bequest of tax. And where the beneficiary is the only residuary beneficiary, even though he or she also has specific bequests, the tax calculation is the same whether a bequest *251of tax is made or not because the taxes will be calculated on that beneficiary’s overall distributive share and the timing of the tax calculation has no effect on the size of the distributive share. Indeed, this was the reasoning behind the assertion in the Department’s brief that “the tax may simply be calculated on the aggregate distribution.”
But here, Laughlin received specific bequests and non-probated gifts and shared in the residuary estate. And to further complicate matters, he shared in only part of the residue of the estate. The Department’s approach ignores that the will calls for the taxes on all parts of Mrs; McVey’s estate to be paid from the residuary estate, which takes place before the residuary beneficiaries receive their share. The will is explicit that “inheritance taxes ... shall not be charged in any way to any beneficiary or recipient of [Mrs. McVey’s] estate,” and that this provision was to apply to “property passing under this will or otherwise,” (emphasis added). The clause was not limited to gifts made under the will, or to property passing through probate. Instead, it expressly applied to Mrs. McVey’s estate, which consists of all property she owned at the time of her death, and it expressly applied to property passing outside the will. Such a tax-exoneration provision applies to probated property, obviously, but it also extends to non-probate property, such as the TOD account. See Brodie v, DeVatz, 556 S.W.2d 444, 445 (Ky.1977) (reading tax-exoneration clause with no limits to extend to non-probate transfers).
Because Laughlin received specific testamentary bequests and the TOD account, under -the terms of the will, the taxes on these gifts should have been paid from the residuary estate. Even though Laughlin also shares in the residue, the bequest of tax takes precedence over distribution of any residue, even if it consumes the residue and deprives the residuary beneficiaries of any gift under the residuary clause. The- operation of the tax-free clause cannot be ignored. And only after that clause is given effect would anything left — the residue of the residue — be distributed per the dictates of the will to Tureene, Laughlin, and Rice. Hughes v. Threlkeld, 276 Ky. 657, 124 S.W.2d 1042, 1043 (1939).
The order- in which the taxes are paid matters, of course, because it affects the size of Laughlin’s distributive share. In fact, because his non-probate gift was so large, a bequest of tax on that gift will end up being much larger than what he would receive if the residue were paid out. In essence, the Department’s claim that the tax can be calculated on his aggregate distribution is mistaken because the size of Laughlin’s aggregate gift depends on whether the bequest of tax is paid on his non-probate gift or he instead is given a share of the residue. As even the Department acknowledges, the effect of a tax-exoneration clause is not to diminish the overall estate but, at most, to diminish the distributive shares of residuary beneficiaries.
By calculating the tax as it did, the Department, would either require that the estate be distributed in .contradiction of the will or it would treat these residuary beneficiaries as potentially receiving property that they, in fact, will never receive because the residue, instead, will have been used to pay taxes .for Laughlin and others. The three bequests at issue— those to Tureene, Laughlin, and Rice — can never occur because the bequests of tax (primarily that to Laughlin) will consume the entire residuary estate.
The bequest of -tax is like any other bequest: it can only be given once. And once it is given, it necessarily reduces any other distributive shares that might come *252from the residuary. Although Laughlin takes, under, either approach, as he. is entitled to payment of.his tax and a share of the residue if any remains, the order of the transactions matters. If his tax is; paid first, he receives a bequest’ of tax. of $132,397.80 (the amount calculated by the Estate). And as described above, - this amount is' also taxable and will be paid, in part, out of the estate. If the Department’s approach is followed, he takes, only $91,182.96 from the residue.
’' The order of the transactions also matters for the other residuary beneficiaries. Take, for example, Tureene’s' purported share of the residue, 64.71% of one half of the residuary estate. The Department calculated her share as totaling $45,595. But Tureene will never receive this money if the dictates of the will are actually followed because that monéy will be used to pay Laughlin’s taxes instead. Of course, Tureen’s share is tax exempt, so she is not harmed by the Department’s action here (other than the audited return suggesting that she is entitled to money that will not be paid to her). The better example here is the share of the residue that the Department imputed to Billy Rice, totaling $4,143.08, the tax on which was calculated as $218.58. • Because the bequest of tax is to be paid out of the’ residuary estate,’ and the bequest of tax to Laughlin will consume the entire residuary estate, this bequest will never happen. Nevertheless, the Department claims that tax is due on Rice’s share. And since the total tax due even by the Department’s own calculations ($149,187.58),- would exhaust the residuary estate, the excess unpaid tax will be owed by the 'beneficiaries in proportionate shares. That would- mean that Billy Rice would owe the unpaid portion of' the $218.58 calculated by the Department despite never receiving a dime from the estate! .
That, however, does not mean that,the Estate correctly, calculated the tax due. There were,.in fact, errors on both -sides. A proper calculation of the tax must reflect how the estate is actually to be distributed and the order of the transactions. First, the statutory costs must be deducted from the gross estate. Then, specific bequests must be accounted for at their full value. This determines the value of the residue, before bequests of tax are paid.
The-next step would be to calculate the tax owed on gifts covered by the tax-exoneration clause, taking into consideration any gifts that are statutorily exempt from taxation. Because the estate was to pay this tax, -as explained above, there was an additional tax, on any bequest of tax, calculated ad. infinitum. Here, this:process clearly results .-in a total tax liability greater than -that -claimed by the Department, because the Department did not include the taxes to be paid on behalf of one of the beneficiaries, Laughlin. A cursory calculation shows that-this greater tax exceeds the residue of the estate, and would only allow for the payment of- the bequests of tax on - a partial, pro rata basis. The entire- residue would be consumed, and thus there would be no residuary estate to distribute.
As noted above, Laughlin’s share if he receives a bequest of tax is much larger than if the residue is distributed without first paying his taxes, as proposed 'by -the Department. Laughlin’s share is taxable, at a substantial rate. The Department’s approach would also assign a significant portion of the residue to ■ a tax-exempt person, Tureene, who would not take any of the residue if Laughlin’s. tax- ■ is first paid. Thus, by assigning parts of the residue to the .residuary beneficiaries, who could not receive from a residue that had been - exhausted, the Department actually under-calculated the taxes owed, specifical*253ly on the bequests of tax for Laughlin. The Department thus shorted the .government of its proper taxes. We do not detail this calculation any more than we already have.
Nevertheless, the Department was certainly entitled at least to the lesser amount of taxes it assessed. More importantly, we cannot award any additional taxes that might be owed, because the Department has not asked for them.
III. Conclusion
This Court concludes that inheritance taxes may not be deducted from the value of the distributive shares of an estate, under KRS 140.090, and that when a will includes a provision directing that inheritance taxes be paid out of the estate or a portion of the estate on behalf of the estate’s beneficiaries, this “bequest of tax” is itself taxable. At the same time, the Department of Revenue’s adjustments to the tax return of the distributive shares of the residuary beneficiaries ignored how the will directed the estate to be’ distributed, and were thus done incorrectly. This, however, resulted in ah under-calculation of the tax owed. Thus, the amount of additional tax assessed by the Department, while not representing all of .the tax owed and not calculated by the correct method, was nevertheless properly assessed because it was owed. The end result of the Court of Appeals’ opinion was to uphold the Department’s assessment of additional tax, therefore its judgment upholding the assessment is affirmed.
Minton, C.J.; Abramson, Cunningham, Keller, Noble and Venters, JJ., sitting. All concur. Wright, J., not sitting.. In this opinion, "Estate” is used as an abbreviation of Estate of Mildred McVey, the party charged with administering the estate. The lower-case "estate,” on the other hand, refers' to the property, Mrs, McVey owned- at .the, time of her death to be administered by the Estate.
. This amount includes attorney and accountant fees, and various debts of the decedent owed at death. It also includes the statutory maximum funeral costs of $5,000, though the funeral expenses exceeded that limit. This amount does not include other costs claimed by the Estate and disallowed by the Department of Revenue, such as the funeral expenses exceeding the statutory limit, Most , importantly,, it does not include the value of inheritance taxes, even though those were to be paid by the Estate to the extent possible and the Estate attempted to claim them as a deduction, as discussed below. ’
. This number is actually inflated because additional non-deductible expenses, such as funeral expenses in excess of the statutory exemption, were necessarily paid from it.
, The will actually named four individuals, ■ but one of them died-before Mrs. McVey, and that lapsed bequest was divided among the remaining three. The percentages laid.out here are the adjusted ones, not the ones originally laid out in the will.
. This concept is addressed in more detail below, but it suffices at this point to note that when a will directs that a beneficiary’s inheritance tax be paid out of the residuary estate, the payment of that tax is a benefit to the beneficiary and is thus a taxable transaction.
The tax due on the tax paid is paid by the estate, again creating a taxable transaction. This continues ad infinitum with smaller and smaller transactions until the taxable amount effectively reaches zero or the estate is exhausted, leaving the beneficiary liable for the finál tax on tax. This ad infinitum calculation *238can be approximated through brute force, by calculating the tax on the tax paid, and then the tax on that number, and so on, until the tax owed reaches a small enough number to be rounded down to zero. This rarely goes beyond a few steps, though the number of steps increases as the tax-free bequest increases. The calculation is more properly accomplished though application of a simple algebraic equation, again explained below.
. The Department did not actually change the amount of money received by any beneficiary. Instead, this adjustment was only for the purpose of calculating the tax owed.
. The Department also objected to an adjustment to the overall value of the estate for the funeral costs above the statutorily deductible amount, and some income taxes and refunds, totaling $7,861.15. This disallowed adjustment is no longer part of the appeal.'
. Indeed, given that inheritance tax rates are not uniform, this distinction is why the tax is constitutional. Booth’s Ex’r, 113 S.W. at 64.
. The Department at one time had an officially promulgated policy addressing this: "Revenue Policy 92P140 (6/1/83), relating to taxa-bility of bequest of inheritance tax (KRS *243140.010 and case law).” 103 KAR 2:030, § 1(20). But the policy was “formally rescinded” because the Department believed it "merely restate[d] or summarize[d] the requirements or provisions of the inheritance and estate tax statutes of KRS Chapter 140." Id. § 1. That policy, therefore, is not relied on in this opinion.
. Apparently only a dozen jurisdictions (eleven states and the Virgin Islands) have addressed it. So far, only West Virginia and Pennsylvania have held that a bequest of tax is not taxable under statutes similar to Kentucky’s. See Glessner’s Estate v. Carman, 146 W.Va. 282, 118 S,E,2d 873, 877 (1961); In re Loeb's Estate, 400 Pa. 368, 162 A.2d 207, 210 (1960). Massachusetts has employed a similar rule, albeit under a statute expressly barring a tax on a tax. See Wellington v. Comm’r of Corps., and Taxation, 359 Mass. 448, 269 N.E.2d-264, 265 (1971).
But the other eight states and the Virgin Islands have all held that a bequest of tax is taxable. See Morrison's Estate v. Idaho State Tax Commission, 98 Idaho 766, 572 P.2d 869, 875 (1977) ("A payment discharging a distrib-utee’s debt is in substance a gift to the distrib-utee because the distributee has received the benefit of the payment. Indeed, the distribu-tee not only has this beneficial interest in the payment; the distributee also' has a legally enforceable interest in the payment because the distributee may sue to compel the estate to pay the tax if the estate declines to do so.”); Succession of Anderson, 152 So.2d 874, 876 (La.Ct.App.1963) (“the payment of taxes by the estate is an additional bequest, subject to taxation”); In re McKinnon’s Estate, 212 Or. 213, 319 P.2d 579, 58.1 (1957); Bouse v. Hutzler, 180 Md. 682, 26 A.2d 767, 769 (1942); In re Henry’s Estate, 189 Wash. 510, 66 P.2d 350, 353 (1937); In re Bowlin’s Estate, 189 Minn. 196, 248 N.W. 741, 742 (1933); In re Levalley’s Estate, 191 Wis. 356, 210 N.W. 941, 941-42 (1926); Read v. Sayles, 48 R.I. 370, 136 A. 440, 442 (1927); In re Irwin's Estate, *244196 Cal. 366, 237 P, 1074, 1077 (1925); In re Vose’s Estate, 256 F.Supp. 558, 561.(D.V.I. 1966) ("It is quite clear, therefore, that when a will provides that the, estate is to pay the inheritance tax, the ‘inheritance’ to be taxed is the, sum of what the heir physically gets plus the amount directed to be paid by the estate for the inheritance tax.”); see also Old Colony Trust Co. v. Commissioner of Internal Revenue, 279 U.S. 716, 729, 49 S.Ct. 499, 73 L.Ed. 918 (1929) (applying same rule to employer’s payment of income tax on behalf of employee, noting; "The discharge by a third person of an obligation to him is equivalent to receipt by the person taxed.”).
. The vast majority of the taxable property consisted of. the TOD account passing., to Laughlin, As Mrs. McVey’s nephew, he is a Class B .beneficiary. ICRS 140.070(2). (Inheritance tax rates differ based on. the beneficiary’s. relationship with the decedent, with the tax rate increasing as the relationship grows more distant.) Any amount of gift to such a beneficiary over $200,000 is taxed at a rate of 16%. Id. Because the bulk of the taxes are to be paid on Laughlin’s behalf, and his share of the estate far exceeds $200,000, all of the tax paid on his behalf would itself be taxed at 16%.
. Tax rates change in theory. As it stands, Kentucky’s inheritance-tax rates, have barely changed since 1936. In fact, the. only inheritance-tax rates that have changed since then • are .those for Class A beneficiaries, which used to have smaller brackets at the lower rates and reached up to 16%. for the highest rates, see KRS 140.070 (1942), Ky. St. *245§ 428 la-19 (1936), where they are now capped at 10% for property over $500,000.
. For-example, as to the bequest of $5,000 to a cemetery, the Department calculated the full tax, inclusive of tax on bequest of tax, at $287.23. But the tax on $5,000 of such a beneficiary would be $270, and the tax on. that amount is $16.20, for a total of $286.20. The only way to arrive at the. number pro- . posed by the Department is to continue calculating tax beyond the first step. In fact, the number it proposed is the one derived from calculating the tax op tax on tax ad infinitum.
. The Court of Appeals appears to have concluded that there is only one level of tax on tax, having stated that the Estate's argument that the tax on a tax would go on ad infinitum would result in double taxation. Presumably, the complaint is only about impermissible double taxation by the state of Kentucky, as "[djouble taxation is permitted,” Lynch v. Kentucky Tax Comm'n, 333 S.W.2d 257, 261 (Ky.1960), at least where the taxes are charged by separate states.
Regardless, this example showing the same amount of tax paid on a bequest of tax and a regular bequest of the total amount of the intended net bequest plus the tax to be paid demonstrates why calculating the tax ad infi-nitum does not result in double taxation by Kentucky. Each dollar paid on the beneficiary’s behalf, whether as the gift passing to the beneficiary or the tax paid for the beneficiary, is taxed only one time. The added tax is only calculated on the marginal bequest of tax at each level, not the overall amount. The tax does not compound as interest would.
. The infinite geometric series is often presented in its full form as follows:
[[Image here]]
if and only if %COr%CO < 1. The equation on the right is the means for arriving at the sum of all values in the series.
. The latter portion of the equation, "if and only if %COr%CO < 1,” means only that the tax rate cannot exceed 100%.
. Inheritance tax rates depend on the kinship relationship between the beneficiary and *248the decedent, with rates increasing as the relationship becomes more attenuated. Kentucky divides beneficiaries into three classes. KRS 140.070. Class C beneficiaries .include distant relatives, such as great-niecés, and “strangers” who are not related to the decedent at all.
. This number differs by about $10 from the amount stated to be the residue in the Background section above. That is because in describing the facts of this case, we were tracking the transactions as calculated on the tax return. This number reflects the corrected calculations for the bequests of tax for the great-nieces and the cemetery.
, The tax is not calculated ad infinitum in this instance because the tax owed on Laugh-lin’s share alone exceeds the amount of the residuary estate by $12,639.80. And since other beneficiaries' taxes are also being paid out of the estate, the amount of tax to be paid by the estate must be calculated pro rata for each. Because the amount of tax exceeding the residue cannot be paid out of the estate on Laughlin’s or the other beneficiaries' behalf, the bequest of tax terminates. That said, some portion of the tax on the bequest of tax, the amount that exhausts the residue, is itself part of the bequest of tax and is taxable at the appropriate rate (in Laughlin’s case, 16%). We will not try to calculate the exact amount, because the amount of tax paid on behalf of the beneficiaries must be calculated based on their proportionate shares, with any remaining liability passing to them personally.