§ 20.2031-7 - Valuation of annuities, interests for life or term of years, and remainder or reversionary interests.

§ 20.2031-7 Valuation of annuities, interests for life or term of years, and remainder or reversionary interests.

(a) In general. Except as otherwise provided in paragraph (b) of this section and § 20.7520–3(b) (pertaining to certain limitations on the use of prescribed tables), the fair market value of annuities, life estates, terms of years, remainders, and reversionary interests for estates of decedents is the present value of such interests, determined under paragraph (d) of this section. The regulations in this and in related sections provide tables with standard actuarial factors and examples that illustrate how to use the tables to compute the present value of ordinary annuity, life, and remainder interests in property. These sections also refer to standard and special actuarial factors that may be necessary to compute the present value of similar interests in more unusual fact situations.

(b) Commercial annuities and insurance contracts. The value of annuities issued by companies regularly engaged in their sale, and of insurance policies on the lives of persons other than the decedent, is determined under § 20.2031–8. See § 20.2042–1 with respect to insurance policies on the decedent's life.

(c) Actuarial valuations. The present value of annuities, life estates, terms interests for life or a term of years, remainders, and reversions and remainder or reversionary interests for estates of decedents for which the valuation date of the gross estate is on or after May June 1, 20092023, is determined under paragraph (d) of this section. The present value of annuities, life estates, terms interests for life or a term of years, remainders, and reversions and remainder or reversionary interests for estates of decedents for which the valuation date of the gross estate is before May June 1, 20092023, is determined (subject to paragraph (d)(3) of this section) under the following sections:

Valuation date

Table 1 to Paragraph (c)

Valuation dates		Applicable regulations
After	Before
	—	01–01–52	§ 20.2031–7A(a)
. 12–31–51	01–01–71	20.2031–7A(b)
. 12–31–70	12–01–83	20.2031–7A(c)
. 11–30–83	05–01–89	20.2031–7A(d)
. 04–30–89	05–01–99	20.2031–7A(e)
. 04–30–99	05–01–09	§ 20.2031–7A(f)
04–30–09	06–01–23	20.2031–7A(g)

(d) Actuarial valuations on or after May June 1, 20092023 —

(1) In general. Except as otherwise provided in paragraph (b) of this section and § 20.7520–3(b) (pertaining to certain limitations on the use of prescribed tables), if the valuation date for the gross estate of the decedent is on or after May June 1, 20092023, the fair market value of annuities, life estates, terms interests for life or a term of years, remainders, and remainder or reversionary interests is the present value determined by use of using standard or special section 7520 actuarial factors. These Many of these standard factors are derived by using the actuarial formulas provided in paragraph (d)(2) of this section, the appropriate section 7520 interest rate, and, if applicable, the mortality component for the valuation date of the interest that is being valued. For purposes of the computations described in this section, the age of an individual is the age of that individual at the individual's nearest birthday. For the convenience of taxpayers, paragraph (d)(2) of this section provides for published tables of factors for specific types of interests. These published tables provide factors for rates from 0.2 to 20 percent, inclusive, at intervals of two-tenths of one percent. In general, appropriate factors instead may be computed directly from the actuarial formulas provided in paragraph (d)(2) of this section. In some cases, specific examples in this part and IRS publications illustrate approximation methods (for example, interpolation) for obtaining factors when the required valuation rate falls between two listed rates (such as in the case of a pooled income fund's rate of return or a unitrust's adjusted payout rate). Exact methods of obtaining the applicable actuarial factors are allowed, such as through software using the actual rate of return and the actuarial formulas provided in paragraph (d)(2) of this section, provided that the taxpayer uses at least the same number of decimal places as are provided in the published tables. The approximation method provided in this part, again using at least the same number of decimal places as provided in this part, must be used if more exact methods are not available. See §§ 20.7520–1 through 20.7520–4. The selected method must be applied consistently in valuing all interests in the same property.

(2) Specific interests —

(i) Charitable Pooled income funds and charitable remainder trusts. The fair market value of a remainder interest in a pooled income fund, as defined in § 1.642(c)–5 -5 of this chapter, is its value determined under § 1.642(c)–6-6(e) of this chapter. The fair market value of a remainder interest in a charitable remainder annuity trust, as defined in § 1.664–2(a) of this chapter, is the present value determined under § 1.664–2(c) of this chapter. The fair market value of a remainder interest in a charitable remainder unitrust, as defined in § 1.664–3 of this chapter, is its present value determined under § 1.664–4(e) of this chapter. The fair market value of a life interest or an interest for a term of years in a charitable remainder unitrust is the fair market value of the property as of the date of valuation less the fair market value of the remainder interest on that date determined under § 1.664–4(e)(4) and (5) of this chapter.

(ii) Ordinary remainder and reversionary interests —

(A) Remainder and reversionary interests for a term of years. If the interest to be valued is a remainder or reversionary interest to take effect after a definite number of years

or after the death of one individual

, the present value of the interest is computed by multiplying the value of the property by the appropriate remainder

interest actuarial

factor (that corresponds to the applicable section 7520 interest rate and

remainder interest period) in Table B (for a term certain) or in Table S (for one measuring life), as the case may be. Table B is contained in

the stated term). The factor for an ordinary remainder interest following a term certain may be found using the formula in Figure 1 to this paragraph (d)(2)(ii)(A) and computing the result to at least six decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table B. Table B can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables (or a corresponding URL as may be updated from time to time). Table B is referenced and explained in IRS Publication 1457, Actuarial Valuations Version 4A, which will be available within a reasonable time after June 1, 2023. The remainder factors from Table B also can be found in paragraph (d)(6) of this section

and Table S (for one measuring life when the valuation date is on or after May 1, 2009) is contained

, but only for interest rates from 4.2 to 14 percent, inclusive. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

Figure 1 to Paragraph (d)(2)(ii)(A)—Formula for Determining Term Certain Remainder Factors

(B) Remainder and reversionary interests dependent on the life of one individual. If the interest to be valued is a remainder or reversionary interest to take effect after the death of one individual, the present value of the interest is computed by multiplying the value of the property by the appropriate remainder factor (that corresponds to the applicable section 7520 interest rate and the age of the measuring life of the life interest that precedes the remainder interest). The factor for an ordinary remainder interest following the death of one individual may be found using the formula in Figure 2 to this paragraph (d)(2)(ii)(B) and computing the result to at least five decimal places. The prescribed mortality table is Table 2010CM as set forth in paragraph (d)(7)(ii) of this section

and in Internal Revenue Service Publication 1457. See

, or for periods before June 1, 2023, the appropriate table found in § 20.2031–7A

containing Table S for valuation of interests before May 1, 2009

. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table S. Table S currently is available, at no charge, electronically via the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables (or a corresponding URL as may be updated from time to time). Table S is referenced and explained by IRS Publication 1457, Actuarial Valuations Version 4A, which will be available within a reasonable time after June 1, 2023. For information about obtaining

actuarial

special factors for other

types of remainder interests

situations, see paragraph (d)(4) of this section.

Figure 2 to Paragraph (d)(2)(ii)(B)—Formula for Determining Single Life Remainder Factors

(iii) Ordinary interests for a term - of - years and ordinary interests for life interests. If the interest to be valued is the right of a person to receive the income of certain property, or to the use of certain nonincome-producing property, for a term of years or for the life of one individual, the present value of the interest is computed by multiplying the value of the property by the appropriate actuarial factor for an interest for a term - of - years or for a life interest actuarial factor (that corresponds to the applicable section 7520 interest rate and term-of-years or life interest the durational period). Internal Revenue Service Publication 1457 includes actuarial factors for a remainder interest after a term of years in Table B and after the life of one individual in Table S (for one measuring life when the valuation date is on or after May 1, 2009). However, term-of-years and life interest actuarial factors are not included in Table B in The actuarial factor for an ordinary income interest for a term certain may be found by subtracting from 1.000000 the factor for an ordinary remainder interest following the same term certain that is determined under the formula in paragraph (d)(6) of this section or Table S in paragraph (d)(72)(ii)(A) of this section (or in § 20.2031–7A). If Internal Revenue Service Publication 1457 (or any other reliable source of term-of-years and life interest actuarial factors) is not conveniently available, an actuarial factor for the interest may be derived mathematically. This actuarial factor may be derived by subtracting the correlative remainder factor (that corresponds to the applicable section 7520 interest rate and the term of years or the life) in Table B (for a term of years) in paragraph (d)(6) of this section or in Table S (for the life of one individual) in paragraph (d)(7) of this section, as the case may be, from 1.000000. For information about obtaining actuarial factors for other types of term-of-years and life interests. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Income Interest” column of Table B which can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables (or a corresponding URL as may be updated from time to time). The actuarial factor for an ordinary income interest for the life of one individual may be found by subtracting from 1.00000 the factor for an ordinary remainder interest following the life of the same individual that is determined in paragraph (d)(2)(ii)(B) of this section. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Life Estate” column of Table S. Table S (applicable when the valuation date is on or after June 1, 2023) can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables. Tables B and S are referenced and explained by IRS Publication 1457, Actuarial Valuations Version 4A. See § 20.2031–7A or earlier versions of Publication 1457 for valuation of interests before June 1, 2023. For information about obtaining special factors for other situations, see paragraph (d)(4) of this section.

(iv) Annuities.

(A) If the interest to be valued is the right of a person to receive an annuity that is payable at the end of each year for a term of years or for the life of one individual, the present value of the interest is computed by multiplying the aggregate amount payable annually by the appropriate annuity actuarial factor (that corresponds to the applicable section 7520 interest rate and annuity period). Internal Revenue Publication 1457 includes actuarial factors for a remainder interest in Table B (after The appropriate annuity factor for an annuity payable for a term of years ) and in Table S (after an annuity payable for the life of one individual when the valuation date is on or after May 1, 2009). However, annuity actuarial factors are not included in Table B in is computed by subtracting from 1.000000 the factor for an ordinary remainder interest following the same term certain that is determined under the formula in paragraph (d)(6) of this section or Table S in paragraph (d)(7) of this section (or in § 20.2031–7A). If Internal Revenue Service Publication 1457 (or any other reliable source of annuity actuarial factors) is not conveniently available, a required annuity factor for a term of years or for one life may be mathematically derived. This annuity factor may be derived by subtracting the applicable remainder factor (that corresponds to the applicable section 7520 interest rate and annuity period) in Table B (in the case of a term-of-years annuity) 2)(ii)(A) of this section and then dividing the result by the applicable section 7520 interest rate expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Annuity” column of Table B which can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables (or a corresponding URL as may be updated from time to time). The appropriate annuity factor for an annuity payable for the life of one individual is computed by subtracting from 1.00000 the factor for an ordinary remainder interest following the life of the same individual that is determined under the formula in paragraph (d)(6) of this section or in Table S (in the case of a one-life annuity 2)(ii)(B) of this section and then dividing the result by the applicable section 7520 interest rate expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in the “Annuity” column of Table S. Table S (applicable when the valuation date is on or after May June 1, 2009) in 2023) can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables. Tables B and S are referenced and explained in IRS Publication 1457, Actuarial Valuations Version 4A. See § 20.2031–7A or earlier versions of Publication 1457 for valuation of interests before June 1, 2023. For information about obtaining special factors for other situations, see paragraph (d)(74) of this section, as the case may be, from 1. 000000 and then dividing the result by the applicable section 7520 interest rate expressed as a decimal number.

(B) If the annuity is payable at the end of semiannual, quarterly, monthly, or weekly periods, the product obtained by multiplying the annuity factor by the aggregate amount payable annually is then multiplied by the applicable adjustment factor as contained in Table K at the appropriate interest rate component for payments made at the end of the specified periods. The applicable adjustment factor may be found using the formula in Figure 3 to this paragraph (d)(2)(iv)(B) and calculating the result to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table K. Table K, which is referenced and explained by Publication 1457, can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables. The provisions of this paragraph (d)(2)(iv)(B) are illustrated by the example in paragraph (d)(6)2)(iv)(B)(2) of this section for payments made at the end of the specified periods. The provisions of this .

Figure 3 to Paragraph (d)(2)(iv)(B)—Formula for Determining Annuity Adjustment Factor at the End of the Specified Period

(1) Sample factors from actuarial Tables S and K. For purposes of the example in paragraph (d)(2)(iv)(B)

are illustrated by the following example:

(2) of this section, the following factors from Tables S and K will be used:

Table 2 to Paragraph (d)(2)(iv)(B)(1)

Factors From Table S—Based on Table 2010CM

Age	Annuity	Life estate	Remainder
Interest at 3.2 Percent
75	9.4053	0.30097	0.69903
Factors from Table K
Adjustment Factors for Annuities Payable at the End of Each Interval
Interest rate	Semi-annually	Quarterly	Monthly
3.2%	1.0079	1.0119	1.0146

(2) Example. At the time of the decedent's death, the survivor/annuitant, age

72

75, is entitled to receive an annuity of $15,000

a

per year for life payable in equal monthly installments at the end of each

period

month. The section 7520 rate for the month in which the decedent died is

5

3.

6

2 percent. Under Table S

in paragraph (d)(7) of this section

, the

remainder factor at 5.6 percent for an individual aged 72 is .53243. By converting the remainder factor to an

annuity factor

, as described above, the annuity factor at 5.6

at 3.2 percent for an individual aged

72

75 is

8

9.

3495 (1.000000 minus .53243, divided by .056).

4053. Under Table K

in paragraph (d)(6) of this section

, the adjustment factor under the column for payments made at the end of each monthly period at the rate of

5

3.

6

2 percent is 1.

0254

0146. The aggregate annual amount, $15,000, is multiplied by the factor

8

9.

3495

4053 and the product then is multiplied by 1.

0254

0146. The present value of the annuity at the date of the decedent's death is, therefore,

$128

$143,

423

139.

66

26 ($15,000 ×

8

9.

3495

4053 × 1.

0254

0146).

(C) If an annuity is payable at the beginning of annual, semiannual, quarterly, monthly, or weekly periods for a term of years, the value of the annuity is computed by multiplying the aggregate amount payable annually by the annuity factor described in paragraph (d)(2)(iv)(A) of this section, ; and the product so obtained then is then multiplied by the applicable adjustment factor in Table J in paragraph (d)(6) of this section at the appropriate interest rate component for payments made at the beginning of specified periods. The applicable adjustment factor may be found using the formula in Figure 4 to this paragraph (d)(2)(iv)(C) and calculating the result to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table J. Table J, which is referenced and explained by Publication 1457, can be found on the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables. If an annuity is payable at the beginning of annual, semiannual, quarterly, monthly, or weekly periods for one or more lives, the value of the annuity is the sum of the first payment plus the present value of a similar annuity, the first payment of which is not to be made until the end of the payment period, determined as provided in this paragraph (d)(2)(iv)(B) of this section.

Figure 4 to Paragraph (d)(2)(iv)(C)—Formula for Determining Annuity Adjustment Factor at the Beginning of the Specified Period

(v) Annuity and unitrust interests for a term of years or until the prior death of an individual. See § 25.2512–5(d)(2)(v) of this chapter for examples explaining how to compute the present value of an annuity or unitrust interest that is payable until the earlier of the lapse of a specific number term of years or the death of an individual.

(3) Transitional rule.

(i)

If a decedent dies

on or

after

May 1

April 30,

2009

2019, and

if

on

May

or before June 1,

2009, the decedent was mentally incompetent so that the disposition of the decedent's property could not be changed, and the decedent dies without having regained competency to dispose of the decedent's property or dies within 90 days of the date on which the decedent first regains competency, the

2023, the fair market value of annuities,

life estates, terms for years, remainders, and reversions included in the gross estate of the decedent is their present value determined either under this section or under the corresponding section applicable at the time the decedent became mentally incompetent, at the option of the decedent's executor. For examples, see § 20.2031–7A(d). (ii) If a decedent dies on or after May 1, 2009, and before July 1, 2009, the fair market value of annuities, life estates, remainders, and reversions

interests for life or a term of years, and remainder or reversionary interests based on one or more measuring lives included in the gross estate of the decedent is their present value determined under this section by

use of

using the section 7520 interest rate for the month in which the valuation date occurs (see §§ 20.7520–1(b) and 20.7520–2(a)(2)) and

the appropriate actuarial tables under either

factors derived from the selected mortality table, either Table 2010CM in paragraph (d)(7)(ii) of this section or Table 2000CM in § 20.2031–7A(

f

g)(4), at the option of the donor or the decedent's executor

. (iii) For purposes of paragraphs (d)(3)(i) and (d)(3)(ii) of this section, where the decedent's executor is given the option to use the appropriate actuarial tables under either

, as the case may be. If any previously filed estate tax return is supplemented to use the actuarial factors based on Table 2010CM, the supplemental return must state at the top “AMENDED PURSUANT TO TD 9974.” For the convenience of taxpayers, actuarial factors based on Table 2010CM appear in the current version of Table S, and actuarial factors based on Table 2000CM appear in the previous version of Table S. Both versions of Table S will be available as provided in paragraph (d)(

7

4) of this section

or § 20.2031–7A(f)(4), the

. The decedent's executor must consistently use the same

actuarial table

mortality basis with respect to each

individual transaction

interest (income, remainder, partial, etc.) in the same property, and with respect to all transfers occurring on the same valuation date. For example, gift and income tax charitable deductions with respect to the same transfer must be determined based on factors with the same

tables

mortality basis, and all assets includible in the gross estate and/or estate tax deductions claimed must be valued based on factors with the same

tables

mortality basis.

(4) Publications and actuarial computations by the Internal Revenue Service. Many standard actuarial factors not included in The factor for determining the present value of a remainder interest that is dependent on the termination of the life of one individual may be computed by using the formula in paragraph (d)(2)(ii)(B) of this section to derive a remainder factor from the appropriate mortality table expressed to at least five decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table S. The remainder factor for determining the present value of a remainder interest following a term certain may be computed by using the formula in paragraph (d)(62) or ((ii)(A) of this section expressed to at least six decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table B. Adjustment factors for term certain annuities payable at the beginning of each interval may be computed by using the formula in paragraph (d)(7) of this section are included in Internal Revenue Service Publication 1457, “Actuarial Valuations Version 3A” (2009). Publication 1457 2)(iv)(C) of this section expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table J. Adjustment factors for annuities payable at the end of each interval may be computed by using the formula in paragraph (d)(2)(iv)(B) of this section expressed to at least four decimal places. For the convenience of taxpayers, actuarial factors have been computed by the IRS and appear in Table K. These tables currently are available, at no charge, electronically via the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables (or a corresponding URL as may be updated from time to time). IRS Publication 1457, Actuarial Valuations Version 4A (2023), references and explains the factors contained in the actuarial tables and also includes examples that illustrate how to compute many special factors for more unusual situations. This publication is available, at no charge, electronically via the Internal Revenue Service Internet site at http://www.irs.gov. will be available within a reasonable time after June 1, 2023. Tables B, J, and K also can be found in paragraph (d)(6) of this section, but only for interest rates from 4.2 to 14 percent, inclusive. If a special factor is required in the case of an actual decedent, the Internal Revenue Service may furnish the factor to the executor upon a request for a rulingspecial factor may be calculated by the executor using the actuarial formulas in paragraph (d)(2) of this section or the executor may request a ruling to obtain the factor from the Internal Revenue Service. The request for a ruling must be accompanied by a recitation of the facts including a statement of the date of birth for each measuring life, the date of the decedent's death, any other applicable dates, and a copy of the will, trust, or other relevant documents. A request for a ruling must comply with the instructions for requesting a ruling published periodically in the Internal Revenue Bulletin (see §§ 601.201 and 601.601(d)(2)(ii)(b) of this chapter) and must include payment of the required user fee.

(5) Examples. The provisions of this section are illustrated by the following examples:

Example 1.

examples in this paragraph (d)(5). For purposes of these examples, the following factors from Tables S, B, and K will be used:

Table 3 to Paragraph (d)(5)

Age	Annuity	Life estate	Remainder
Factors From Table S—Based on Table 2010CM
Interest at 3.2 Percent
31	23.8334	0.76267	0.23733
46	20.0146	0.64047	0.35953
Interest at 4.6 Percent
65	11.7691	0.54138	0.45862
Factors from Table B
Annuity, Income, and Remainder Interests for a Term Certain
Interest at 2.6 Percent
Years	Annuity	Income interest	Remainder
5	4.6325	0.120445	0.879555
Factors From Table K
Adjustment Factors for Annuities Payable at the End of Each Interval
Interest Rate	Semi-annually	Quarterly	Monthly
2.6%	1.0065	1.0097	1.0119
3.2%	1.0079	1.0119	1.0146

(i) Example 1: Remainder payable at an individual's death

,

. The decedent, or the decedent's estate, was entitled to receive certain property worth $50,000 upon the death of A, to whom the income was bequeathed for life. At the time of the decedent's death, A was

47

65 years and 5 months old. In the month in which the decedent died, the section 7520 rate was 4.6

.2

percent. Under Table S

in paragraph (d)(7) of this section

, the remainder factor at 4.6

.2

percent for determining the present value of the remainder interest due at the death of a person aged

47

65,

the number of years nearest

A's

actual

age at A's nearest birthday to the date of the decedent's death, is 0.

18672

45862. The present value of the remainder interest at the date of the decedent's death is, therefore,

$9

$22,

336.00

931 ($50,000

×

times 0.

18672

45862).

(ii) Example 2

.

: Income payable for an individual's life

,

. A's parent bequeathed an income interest in property to A for life, with the remainder interest passing to B at A's death. At the time of the parent's death, the value of the property was $50,000 and A was 30 years and 10 months old. The section 7520 rate at the time of the parent's death was

6

3.2 percent. Under Table S

in paragraph (d)(7) of this section

, the

remainder

factor at

6

3.2 percent for determining the present value of the

remainder interest due at the death of

life estate given to a person aged 31,

the number of years closest to

A's age at A's nearest birthday to the date of the decedent's death, is 0.

08697. Converting this remainder factor to an income factor, as described in paragraph (d)(2)(iii) of this section, the factor for determining the present value of an income interest for the life of a person aged 31 is .91303.

76267. The present value of A's income interest at the time of the parent's death is, therefore,

$45

$38,

651

133.50 ($50,000.00 × 0.

91303

76267).

(iii) Example 3

.

: Annuity payable for an individual's life

,

. A purchased an annuity for the benefit of both A and B. Under the terms of the annuity contract, at A's death, a survivor annuity of $10,000 per year, payable in equal semiannual installments made at the end of each interval is payable to B for life. At A's death, B was 45 years and 7 months old. Also, at A's death, the section 7520 rate was

4

3.

8

2 percent. Under Table S

in paragraph (d)(7) of this section

, the factor at

4

3.

8

2 percent for determining the present value of

the remainder interest at

an annuity interest payable until the death of a person age 46 (

the number of years nearest

B's

actual age) is .24774. By converting the factor to an annuity factor, as described in paragraph (d)(2)(iv)(A) of this section, the factor for the present value of an annuity payable until the death of a person age 46 is 15.6721 (1.000000 minus .24774, divided by .048).

age at B's nearest birthday to the date of A's death) is 20.0146. The adjustment factor from Table K

in paragraph (d)(6) of this section

at an interest rate of

4

3.

8

2 percent for semiannual annuity payments made at the end of the period is 1.

0119

0079. The present value of the annuity at the date of A's death is, therefore,

$158

$201,

585

727.

98

15 ($10,000 ×

15

20.

6721

0146 × 1.

0119

0079).

(iv) Example 4

.

: Annuity payable for a term of years

,

. The decedent, or the decedent's estate, was entitled to receive an annuity of $10,000 per year payable in equal quarterly installments at the end of each quarter throughout a term certain. At the time of the decedent's death, the section 7520 rate was

9

2.

8

6 percent. A quarterly payment had been made immediately prior to the decedent's death and payments were to continue for 5 more years. Under Table B

in paragraph (d)(6) of this section

for the interest rate of

9

2.

8

6 percent, the factor for the present value of

a remainder interest due after a term of 5 years is .626597. Converting the factor to an annuity factor, as described in paragraph (d)(2)(iv)(A) of this section, the factor for the present value of an annuity for

an annuity with a term of 5 years is

3

4.

8102 (1.000000 minus .626597, divided by .098).

6325. The adjustment factor from Table K

in paragraph (d)(6) of this section

at an interest rate of

9

2.

8

6 percent for quarterly annuity payments made at the end of the

period

quarter is 1.

0360

0097. The present value of the annuity is, therefore,

$39

$46,

473

774.

67

35 ($10,000 ×

3

4.

8102

6325 × 1.

0360

0097).

(6) Actuarial Table B, Table J, and Table K where the valuation date is after April 30, 1989. Except as provided in § 20.7520–3(b) (pertaining to certain limitations on prescribed tables), for determination of the present value of an interest that is dependent on a term of years, the tables in this paragraph (d)(6) must be used in the application of the provisions of this section when the section 7520 interest rate component is between 4.2 and 14 percent.

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

Years	Interest rate
	4.2%	4.4%	4.6%	4.8%	5.0%	5.2%	5.4%	5.6%	5.8%	6.0%
1	.959693	.957854	.956023	.954198	.952381	.950570	.948767	.946970	.945180	.943396
2	.921010	.917485	.913980	.910495	.907029	.903584	.900158	.896752	.893364	.889996
3	.883887	.878817	.873786	.868793	.863838	.858920	.854040	.849197	.844390	.839619
4	.848260	.841779	.835359	.829001	.822702	.816464	.810285	.804163	.798100	.792094
5	.814069	.806302	.798623	.791031	.783526	.776106	.768771	.761518	.754348	.747258
6	.781257	.772320	.763501	.754801	.746215	.737744	.729384	.721135	.712994	.704961
7	.749766	.739770	.729925	.720230	.710681	.701277	.692015	.682893	.673908	.665057
8	.719545	.708592	.697825	.687242	.676839	.666613	.656561	.646679	.636964	.627412
9	.690543	.678728	.667137	.655765	.644609	.633663	.622923	.612385	.602045	.591898
10	.662709	.650122	.637798	.625730	.613913	.602341	.591009	.579910	.569041	.558395
11	.635997	.622722	.609750	.597071	.584679	.572568	.560729	.549157	.537846	.526788
12	.610362	.596477	.582935	.569724	.556837	.544266	.532001	.520035	.508361	.496969
13	.585760	.571339	.557299	.543630	.530321	.517363	.504745	.492458	.480492	.468839
14	.562150	.547259	.532790	.518731	.505068	.491790	.478885	.466343	.454151	.442301
15	.539491	.524195	.509360	.494972	.481017	.467481	.454350	.441612	.429255	.417265
16	.517746	.502102	.486960	.472302	.458112	.444374	.431072	.418194	.405723	.393646
17	.496877	.480941	.465545	.450670	.436297	.422408	.408987	.396017	.383481	.371364
18	.476849	.460671	.445071	.430028	.415521	.401529	.388033	.375016	.362458	.350344
19	.457629	.441256	.425498	.410332	.395734	.381681	.368153	.355129	.342588	.330513
20	.439183	.422659	.406786	.391538	.376889	.362815	.349291	.336296	.323807	.311805
21	.421481	.404846	.388897	.373605	.358942	.344881	.331396	.318462	.306056	.294155
22	.404492	.387783	.371794	.356494	.341850	.327834	.314417	.301574	.289278	.277505
23	.388188	.371440	.355444	.340166	.325571	.311629	.298309	.285581	.273420	.261797
24	.372542	.355785	.339813	.324586	.310068	.296225	.283025	.270437	.258431	.246979
25	.357526	.340791	.324869	.309719	.295303	.281583	.268525	.256096	.244263	.232999
26	.343115	.326428	.310582	.295533	.281241	.267664	.254768	.242515	.230873	.219810
27	.329285	.312670	.296923	.281998	.267848	.254434	.241715	.229654	.218216	.207368
28	.316012	.299493	.283866	.269082	.255094	.241857	.229331	.217475	.206253	.195630
29	.303275	.286870	.271382	.256757	.242946	.229902	.217582	.205943	.194947	.184557
30	.291051	.274780	.259447	.244997	.231377	.218538	.206434	.195021	.184260	.174110
31	.279319	.263199	.248038	.233776	.220359	.207736	.195858	.184679	.174158	.164255
32	.268061	.252106	.237130	.223069	.209866	.197468	.185823	.174886	.164611	.154957
33	.257256	.241481	.226702	.212852	.199873	.187707	.176303	.165612	.155587	.146186
34	.246887	.231304	.216732	.203103	.190355	.178429	.167270	.156829	.147058	.137912
35	.236935	.221556	.207201	.193801	.181290	.169609	.158701	.148512	.138996	.130105
36	.227385	.212218	.198089	.184924	.172657	.161225	.150570	.140637	.131376	.122741
37	.218220	.203274	.189377	.176454	.164436	.153256	.142856	.133179	.124174	.115793
38	.209424	.194707	.181049	.168373	.156605	.145681	.135537	.126116	.117367	.109239
39	.200983	.186501	.173087	.160661	.149148	.138480	.128593	.119428	.110933	.103056
40	.192882	.178641	.165475	.153302	.142046	.131635	.122004	.113095	.104851	.097222
41	.185107	.171112	.158198	.146281	.135282	.125128	.115754	.107098	.099103	.091719
42	.177646	.163900	.151241	.139581	.128840	.118943	.109823	.101418	.093670	.086527
43	.170486	.156992	.144590	.133188	.122704	.113064	.104197	.096040	.088535	.081630
44	.163614	.150376	.138231	.127088	.116861	.107475	.098858	.090947	.083682	.077009
45	.157019	.144038	.132152	.121267	.111297	.102163	.093793	.086124	.079094	.072650
46	.150690	.137968	.126340	.115713	.105997	.097113	.088988	.081557	.074758	.068538
47	.144616	.132153	.120784	.110413	.100949	.092312	.084429	.077232	.070660	.064658
48	.138787	.126583	.115473	.105356	.096142	.087749	.080103	.073136	.066786	.060998
49	.133193	.121248	.110395	.100530	.091564	.083412	.075999	.069258	.063125	.057546
50	.127824	.116138	.105540	.095926	.087204	.079289	.072106	.065585	.059665	.054288
51	.122672	.111243	.100898	.091532	.083051	.075370	.068411	.062107	.056394	.051215
52	.117728	.106555	.096461	.087340	.079096	.071644	.064907	.058813	.053302	.048316
53	.112982	.102064	.092219	.083340	.075330	.068103	.061581	.055695	.050380	.045582
54	.108428	.097763	.088164	.079523	.071743	.064737	.058426	.052741	.047618	.043001
55	.104058	.093642	.084286	.075880	.068326	.061537	.055433	.049944	.045008	.040567
56	.099864	.089696	.080580	.072405	.065073	.058495	.052593	.047296	.042541	.038271
57	.095839	.085916	.077036	.069089	.061974	.055604	.049898	.044787	.040208	.036105
58	.091976	.082295	.073648	.065924	.059023	.052855	.047342	.042412	.038004	.034061
59	.088268	.078826	.070409	.062905	.056212	.050243	.044916	.040163	.035921	.032133
60	.084710	.075504	.067313	.060024	.053536	.047759	.042615	.038033	.033952	.030314

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

Years	Interest rate
	6.2%	6.4%	6.6%	6.8%	7.0%	7.2%	7.4%	7.6%	7.8%	8.0%
1	.941620	.939850	.938086	.936330	.934579	.932836	.931099	.929368	.927644	.925926
2	.886647	.883317	.880006	.876713	.873439	.870183	.866945	.863725	.860523	.857339
3	.834885	.830185	.825521	.820892	.816298	.811738	.807211	.802718	.798259	.793832
4	.786144	.780249	.774410	.768626	.762895	.757218	.751593	.746021	.740500	.735030
5	.740248	.733317	.726464	.719687	.712986	.706360	.699808	.693328	.686920	.680583
6	.697032	.689208	.681486	.673864	.666342	.658918	.651590	.644357	.637217	.630170
7	.656339	.647752	.639292	.630959	.622750	.614662	.606694	.598845	.591111	.583490
8	.618022	.608789	.599711	.590786	.582009	.573379	.564892	.556547	.548340	.540269
9	.581942	.572170	.562581	.553170	.543934	.534868	.525971	.517237	.508664	.500249
10	.547968	.537754	.527750	.517950	.508349	.498944	.489731	.480704	.471859	.463193
11	.515977	.505408	.495075	.484972	.475093	.465433	.455987	.446750	.437717	.428883
12	.485854	.475007	.464423	.454093	.444012	.434173	.424569	.415196	.406046	.397114
13	.457490	.446436	.435669	.425181	.414964	.405012	.395316	.385870	.376666	.367698
14	.430781	.419582	.408695	.398109	.387817	.377810	.368078	.358615	.349412	.340461
15	.405632	.394344	.383391	.372762	.362446	.352434	.342717	.333285	.324130	.315242
16	.381951	.370624	.359654	.349028	.338735	.328763	.319103	.309745	.300677	.291890
17	.359653	.348331	.337386	.326805	.316574	.306682	.297117	.287867	.278921	.270269
18	.338656	.327379	.316498	.305997	.295864	.286084	.276645	.267534	.258739	.250249
19	.318885	.307687	.296902	.286514	.276508	.266870	.257584	.248638	.240018	.231712
20	.300268	.289179	.278520	.268272	.258419	.248946	.239836	.231076	.222651	.214548
21	.282739	.271785	.261276	.251191	.241513	.232225	.223311	.214755	.206541	.198656
22	.266232	.255437	.245099	.235197	.225713	.216628	.207925	.199586	.191596	.183941
23	.250689	.240073	.229924	.220222	.210947	.202078	.193598	.185489	.177733	.170315
24	.236054	.225632	.215689	.206201	.197147	.188506	.180259	.172387	.164873	.157699
25	.222273	.212060	.202334	.193072	.184249	.175845	.167839	.160211	.152943	.146018
26	.209297	.199305	.189807	.180779	.172195	.164035	.156275	.148895	.141877	.135202
27	.197078	.187317	.178056	.169269	.160930	.153017	.145507	.138379	.131611	.125187
28	.185572	.176049	.167031	.158491	.150402	.142740	.135482	.128605	.122088	.115914
29	.174739	.165460	.156690	.148400	.140563	.133153	.126147	.119521	.113255	.107328
30	.164537	.155507	.146989	.138951	.131367	.124210	.117455	.111079	.105060	.099377
31	.154932	.146154	.137888	.130104	.122773	.115868	.109362	.103233	.097458	.092016
32	.145887	.137362	.129351	.121820	.114741	.108085	.101827	.095942	.090406	.085200
33	.137370	.129100	.121342	.114064	.107235	.100826	.094811	.089165	.083865	.078889
34	.129350	.121335	.113830	.106802	.100219	.094054	.088278	.082867	.077797	.073045
35	.121798	.114036	.106782	.100001	.093663	.087737	.082196	.077014	.072168	.067635
36	.114688	.107177	.100171	.093634	.087535	.081844	.076532	.071574	.066946	.062625
37	.107992	.100730	.093969	.087673	.081809	.076347	.071259	.066519	.062102	.057986
38	.101688	.094671	.088151	.082090	.076457	.071219	.066349	.061821	.057609	.053690
39	.095751	.088977	.082693	.076864	.071455	.066436	.061778	.057454	.053440	.049713
40	.090161	.083625	.077573	.071970	.066780	.061974	.057521	.053396	.049573	.046031
41	.084897	.078595	.072770	.067387	.062412	.057811	.053558	.049625	.045987	.042621
42	.079941	.073867	.068265	.063097	.058329	.053929	.049868	.046120	.042659	.039464
43	.075274	.069424	.064038	.059079	.054513	.050307	.046432	.042862	.039572	.036541
44	.070880	.065248	.060074	.055318	.050946	.046928	.043233	.039835	.036709	.033834
45	.066742	.061323	.056354	.051796	.047613	.043776	.040254	.037021	.034053	.031328
46	.062845	.057635	.052865	.048498	.044499	.040836	.037480	.034406	.031589	.029007
47	.059176	.054168	.049592	.045410	.041587	.038093	.034898	.031976	.029303	.026859
48	.055722	.050910	.046522	.042519	.038867	.035535	.032493	.029717	.027183	.024869
49	.052469	.047848	.043641	.039812	.036324	.033148	.030255	.027618	.025216	.023027
50	.049405	.044970	.040939	.037277	.033948	.030922	.028170	.025668	.023392	.021321
51	.046521	.042265	.038405	.034903	.031727	.028845	.026229	.023855	.021699	.019742
52	.043805	.039722	.036027	.032681	.029651	.026907	.024422	.022170	.020129	.018280
53	.041248	.037333	.033796	.030600	.027711	.025100	.022739	.020604	.018673	.016925
54	.038840	.035087	.031704	.028652	.025899	.023414	.021172	.019149	.017322	.015672
55	.036572	.032977	.029741	.026828	.024204	.021842	.019714	.017796	.016068	.014511
56	.034437	.030993	.027900	.025119	.022621	.020375	.018355	.016539	.014906	.013436
57	.032427	.029129	.026172	.023520	.021141	.019006	.017091	.015371	.013827	.012441
58	.030534	.027377	.024552	.022023	.019758	.017730	.015913	.014285	.012827	.011519
59	.028751	.025730	.023032	.020620	.018465	.016539	.014817	.013276	.011899	.010666
60	.027073	.024183	.021606	.019307	.017257	.015428	.013796	.012339	.011038	.009876

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

Years	Interest rate
	8.2%	8.4%	8.6%	8.8%	9.0%	9.2%	9.4%	9.6%	9.8%	10.0%
1	.924214	.922509	.920810	.919118	.917431	.915751	.914077	.912409	.910747	.909091
2	.854172	.851023	.847892	.844777	.841680	.838600	.835536	.832490	.829460	.826446
3	.789438	.785077	.780747	.776450	.772183	.767948	.763744	.759571	.755428	.751315
4	.729610	.724241	.718920	.713649	.708425	.703250	.698121	.693039	.688003	.683013
5	.674316	.668119	.661989	.655927	.649931	.644001	.638136	.632335	.626597	.620921
6	.623213	.616346	.609566	.602874	.596267	.589745	.583305	.576948	.570671	.564474
7	.575982	.568585	.561295	.554112	.547034	.540059	.533186	.526412	.519737	.513158
8	.532331	.524524	.516846	.509294	.501866	.494560	.487373	.480303	.473349	.466507
9	.491988	.483879	.475917	.468101	.460428	.452894	.445496	.438233	.431101	.424098
10	.454703	.446383	.438230	.430240	.422411	.414738	.407218	.399848	.392624	.385543
11	.420243	.411792	.403526	.395441	.387533	.379797	.372228	.364824	.357581	.350494
12	.388394	.379882	.371571	.363457	.355535	.347799	.340245	.332869	.325666	.318631
13	.358960	.350445	.342147	.334060	.326179	.318497	.311010	.303713	.296599	.289664
14	.331756	.323288	.315052	.307040	.299246	.291664	.284287	.277110	.270127	.263331
15	.306613	.298236	.290103	.282206	.274538	.267092	.259860	.252838	.246017	.239392
16	.283376	.275126	.267130	.259381	.251870	.244589	.237532	.230691	.224059	.217629
17	.261901	.253806	.245976	.238401	.231073	.223983	.217123	.210485	.204061	.197845
18	.242052	.234139	.226497	.219119	.211994	.205113	.198467	.192048	.185848	.179859
19	.223708	.215995	.208561	.201396	.194490	.187832	.181414	.175226	.169260	.163508
20	.206754	.199257	.192045	.185107	.178431	.172007	.165826	.159878	.154153	.148644
21	.191085	.183817	.176837	.170135	.163698	.157516	.151578	.145874	.140395	.135131
22	.176604	.169573	.162834	.156374	.150182	.144245	.138554	.133097	.127864	.122846
23	.163220	.156432	.149939	.143726	.137781	.132093	.126649	.121439	.116452	.111678
24	.150850	.144310	.138065	.132101	.126405	.120964	.115767	.110802	.106058	.101526
25	.139418	.133128	.127132	.121416	.115968	.110773	.105820	.101097	.096592	.092296
26	.128852	.122811	.117064	.111596	.106393	.101441	.096727	.092241	.087971	.083905
27	.119087	.113295	.107794	.102570	.097608	.092894	.088416	.084162	.080119	.076278
28	.110062	.104515	.099258	.094274	.089548	.085068	.080819	.076790	.072968	.069343
29	.101721	.096416	.091398	.086649	.082155	.077901	.073875	.070064	.066456	.063039
30	.094012	.088945	.084160	.079640	.075371	.071338	.067527	.063927	.060524	.057309
31	.086887	.082053	.077495	.073199	.069148	.065328	.061725	.058327	.055122	.052099
32	.080302	.075694	.071358	.067278	.063438	.059824	.056422	.053218	.050202	.047362
33	.074216	.069829	.065708	.061837	.058200	.054784	.051574	.048557	.045722	.043057
34	.068592	.064418	.060504	.056835	.053395	.050168	.047142	.044304	.041641	.039143
35	.063394	.059426	.055713	.052238	.048986	.045942	.043092	.040423	.037924	.035584
36	.058589	.054821	.051301	.048013	.044941	.042071	.039389	.036882	.034539	.032349
37	.054149	.050573	.047239	.044130	.041231	.038527	.036005	.033652	.031457	.029408
38	.050045	.046654	.043498	.040560	.037826	.035281	.032911	.030704	.028649	.026735
39	.046253	.043039	.040053	.037280	.034703	.032309	.030083	.028015	.026092	.024304
40	.042747	.039703	.036881	.034264	.031838	.029587	.027498	.025561	.023763	.022095
41	.039508	.036627	.033961	.031493	.029209	.027094	.025136	.023322	.021642	.020086
42	.036514	.033789	.031271	.028946	.026797	.024811	.022976	.021279	.019711	.018260
43	.033746	.031170	.028795	.026605	.024584	.022721	.021002	.019415	.017951	.016600
44	.031189	.028755	.026515	.024453	.022555	.020807	.019197	.017715	.016349	.015091
45	.028825	.026527	.024415	.022475	.020692	.019054	.017548	.016163	.014890	.013719
46	.026641	.024471	.022482	.020657	.018984	.017449	.016040	.014747	.013561	.012472
47	.024622	.022575	.020701	.018986	.017416	.015978	.014662	.013456	.012351	.011338
48	.022756	.020825	.019062	.017451	.015978	.014632	.013402	.012277	.011248	.010307
49	.021031	.019212	.017552	.016039	.014659	.013400	.012250	.011202	.010244	.009370
50	.019437	.017723	.016163	.014742	.013449	.012271	.011198	.010221	.009330	.008519
51	.017964	.016350	.014883	.013550	.012338	.011237	.010236	.009325	.008497	.007744
52	.016603	.015083	.013704	.012454	.011319	.010290	.009356	.008508	.007739	.007040
53	.015345	.013914	.012619	.011446	.010385	.009423	.008552	.007763	.007048	.006400
54	.014182	.012836	.011620	.010521	.009527	.008629	.007817	.007083	.006419	.005818
55	.013107	.011841	.010699	.009670	.008741	.007902	.007146	.006463	.005846	.005289
56	.012114	.010923	.009852	.008888	.008019	.007237	.006532	.005897	.005324	.004809
57	.011196	.010077	.009072	.008169	.007357	.006627	.005971	.005380	.004849	.004371
58	.010347	.009296	.008354	.007508	.006749	.006069	.005458	.004909	.004416	.003974
59	.009563	.008576	.007692	.006901	.006192	.005557	.004989	.004479	.004022	.003613
60	.008838	.007911	.007083	.006343	.005681	.005089	.004560	.004087	.003663	.003284

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

Years	Interest rate
	10.2%	10.4%	10.6%	10.8%	11.0%	11.2%	11.4%	11.6%	11.8%	12.0%
1	.907441	.905797	.904159	.902527	.900901	.899281	.897666	.896057	.894454	.892857
2	.823449	.820468	.817504	.814555	.811622	.808706	.805804	.802919	.800049	.797194
3	.747232	.743178	.739153	.735158	.731191	.727253	.723343	.719461	.715607	.711780
4	.678069	.673168	.668312	.663500	.658731	.654005	.649321	.644679	.640078	.635518
5	.615307	.609754	.604261	.598827	.593451	.588134	.582873	.577669	.572520	.567427
6	.558355	.552313	.546348	.540457	.534641	.528897	.523225	.517625	.512093	.506631
7	.506674	.500284	.493985	.487777	.481658	.475627	.469682	.463821	.458044	.452349
8	.459777	.453156	.446641	.440232	.433926	.427722	.421617	.415610	.409700	.403883
9	.417221	.410467	.403835	.397322	.390925	.384642	.378472	.372411	.366458	.360610
10	.378603	.371800	.365131	.358593	.352184	.345901	.339741	.333701	.327780	.321973
11	.343560	.336775	.330137	.323640	.317283	.311062	.304974	.299016	.293184	.287476
12	.311760	.305050	.298496	.292094	.285841	.279732	.273765	.267935	.262240	.256675
13	.282904	.276313	.269888	.263623	.257514	.251558	.245749	.240085	.234561	.229174
14	.256719	.250284	.244022	.237927	.231995	.226221	.220601	.215130	.209804	.204620
15	.232957	.226706	.220634	.214735	.209004	.203436	.198026	.192769	.187661	.182696
16	.211395	.205350	.199489	.193804	.188292	.182946	.177761	.172732	.167854	.163122
17	.191828	.186005	.180369	.174914	.169633	.164520	.159570	.154778	.150138	.145644
18	.174073	.168483	.163083	.157864	.152822	.147950	.143241	.138690	.134291	.130040
19	.157961	.152612	.147453	.142477	.137678	.133048	.128582	.124274	.120117	.116107
20	.143340	.138235	.133321	.128589	.124034	.119648	.115424	.111357	.107439	.103667
21	.130073	.125213	.120543	.116055	.111742	.107597	.103612	.099782	.096100	.092560
22	.118033	.113418	.108990	.104743	.100669	.096760	.093009	.089410	.085957	.082643
23	.107108	.102733	.098544	.094533	.090693	.087014	.083491	.080117	.076884	.073788
24	.097195	.093056	.089100	.085319	.081705	.078250	.074947	.071789	.068770	.065882
25	.088198	.084289	.080560	.077003	.073608	.070369	.067278	.064327	.061511	.058823
26	.080035	.076349	.072839	.069497	.066314	.063281	.060393	.057641	.055019	.052521
27	.072627	.069157	.065858	.062723	.059742	.056908	.054213	.051650	.049212	.046894
28	.065905	.062642	.059547	.056609	.053822	.051176	.048665	.046281	.044018	.041869
29	.059804	.056741	.053840	.051091	.048488	.046022	.043685	.041470	.039372	.037383
30	.054269	.051396	.048680	.046111	.043683	.041386	.039214	.037160	.035216	.033378
31	.049246	.046554	.044014	.041617	.039354	.037218	.035201	.033297	.031500	.029802
32	.044688	.042169	.039796	.037560	.035454	.033469	.031599	.029836	.028175	.026609
33	.040552	.038196	.035982	.033899	.031940	.030098	.028365	.026735	.025201	.023758
34	.036798	.034598	.032533	.030595	.028775	.027067	.025463	.023956	.022541	.021212
35	.033392	.031339	.029415	.027613	.025924	.024341	.022857	.021466	.020162	.018940
36	.030301	.028387	.026596	.024921	.023355	.021889	.020518	.019235	.018034	.016910
37	.027497	.025712	.024047	.022492	.021040	.019684	.018418	.017236	.016131	.015098
38	.024952	.023290	.021742	.020300	.018955	.017702	.016533	.015444	.014428	.013481
39	.022642	.021096	.019658	.018321	.017077	.015919	.014841	.013839	.012905	.012036
40	.020546	.019109	.017774	.016535	.015384	.014316	.013323	.012400	.011543	.010747
41	.018645	.017309	.016071	.014923	.013860	.012874	.011959	.011111	.010325	.009595
42	.016919	.015678	.014531	.013469	.012486	.011577	.010735	.009956	.009235	.008567
43	.015353	.014201	.013138	.012156	.011249	.010411	.009637	.008922	.008260	.007649
44	.013932	.012864	.011879	.010971	.010134	.009362	.008651	.007994	.007389	.006830
45	.012642	.011652	.010740	.009902	.009130	.008419	.007765	.007163	.006609	.006098
46	.011472	.010554	.009711	.008937	.008225	.007571	.006971	.006419	.005911	.005445
47	.010410	.009560	.008780	.008065	.007410	.006809	.006257	.005752	.005287	.004861
48	.009447	.008659	.007939	.007279	.006676	.006123	.005617	.005154	.004729	.004340
49	.008572	.007844	.007178	.006570	.006014	.005506	.005042	.004618	.004230	.003875
50	.007779	.007105	.006490	.005929	.005418	.004952	.004526	.004138	.003784	.003460
51	.007059	.006435	.005868	.005351	.004881	.004453	.004063	.003708	.003384	.003089
52	.006406	.005829	.005306	.004830	.004397	.004005	.003647	.003322	.003027	.002758
53	.005813	.005280	.004797	.004359	.003962	.003601	.003274	.002977	.002708	.002463
54	.005275	.004783	.004337	.003934	.003569	.003238	.002939	.002668	.002422	.002199
55	.004786	.004332	.003922	.003551	.003215	.002912	.002638	.002390	.002166	.001963
56	.004343	.003924	.003546	.003205	.002897	.002619	.002368	.002142	.001938	.001753
57	.003941	.003554	.003206	.002892	.002610	.002355	.002126	.001919	.001733	.001565
58	.003577	.003220	.002899	.002610	.002351	.002118	.001908	.001720	.001550	.001398
59	.003246	.002916	.002621	.002356	.002118	.001905	.001713	.001541	.001387	.001248
60	.002945	.002642	.002370	.002126	.001908	.001713	.001538	.001381	.001240	.001114

Table B—Term Certain Remainder Factors Applicable After April 30, 1989

Years	Interest rate
	12.2%	12.4%	12.6%	12.8%	13.0%	13.2%	13.4%	13.6%	13.8%	14.0%
1	.891266	.889680	.888099	.886525	.884956	.883392	.881834	.880282	.878735	.877193
2	.794354	.791530	.788721	.785926	.783147	.780382	.777632	.774896	.772175	.769468
3	.707981	.704208	.700462	.696743	.693050	.689383	.685742	.682127	.678536	.674972
4	.630999	.626520	.622080	.617680	.613319	.608996	.604711	.600464	.596254	.592080
5	.562388	.557402	.552469	.547589	.542760	.537982	.533255	.528577	.523949	.519369
6	.501237	.495909	.490648	.485451	.480319	.475249	.470242	.465297	.460412	.455587
7	.446735	.441200	.435744	.430364	.425061	.419831	.414676	.409592	.404580	.399637
8	.398160	.392527	.386984	.381529	.376160	.370876	.365675	.360557	.355518	.350559
9	.354866	.349223	.343680	.338235	.332885	.327629	.322465	.317391	.312406	.307508
10	.316280	.310697	.305222	.299853	.294588	.289425	.284361	.279394	.274522	.269744
11	.281889	.276421	.271068	.265827	.260698	.255676	.250759	.245945	.241232	.236617
12	.251238	.245926	.240735	.235663	.230706	.225862	.221128	.216501	.211979	.207559
13	.223920	.218795	.213797	.208921	.204165	.199525	.194998	.190582	.186273	.182069
14	.199572	.194658	.189873	.185213	.180677	.176258	.171956	.167766	.163685	.159710
15	.177872	.173183	.168626	.164196	.159891	.155705	.151637	.147681	.143835	.140096
16	.158531	.154077	.149757	.145564	.141496	.137549	.133718	.130001	.126393	.122892
17	.141293	.137080	.132999	.129046	.125218	.121510	.117917	.114438	.111066	.107800
18	.125930	.121957	.118116	.114403	.110812	.107341	.103984	.100737	.097598	.094561
19	.112237	.108503	.104899	.101421	.098064	.094824	.091696	.088677	.085762	.082948
20	.100033	.096533	.093161	.089912	.086782	.083767	.080861	.078061	.075362	.072762
21	.089156	.085883	.082736	.079709	.076798	.073999	.071306	.068716	.066224	.063826
22	.079462	.076408	.073478	.070664	.067963	.065370	.062880	.060489	.058193	.055988
23	.070821	.067979	.065255	.062646	.060144	.057747	.055450	.053247	.051136	.049112
24	.063121	.060480	.057953	.055537	.053225	.051014	.048898	.046873	.044935	.043081
25	.056257	.053807	.051468	.049235	.047102	.045065	.043119	.041261	.039486	.037790
26	.050140	.047871	.045709	.043648	.041683	.039810	.038024	.036321	.034698	.033149
27	.044688	.042590	.040594	.038695	.036888	.035168	.033531	.031973	.030490	.029078
28	.039829	.037892	.036052	.034304	.032644	.031067	.029569	.028145	.026793	.025507
29	.035498	.033711	.032017	.030411	.028889	.027444	.026075	.024776	.023544	.022375
30	.031638	.029992	.028435	.026960	.025565	.024244	.022994	.021810	.020689	.019627
31	.028198	.026684	.025253	.023901	.022624	.021417	.020277	.019199	.018180	.017217
32	.025132	.023740	.022427	.021189	.020021	.018920	.017881	.016900	.015975	.015102
33	.022399	.021121	.019917	.018785	.017718	.016714	.015768	.014877	.014038	.013248
34	.019964	.018791	.017689	.016653	.015680	.014765	.013905	.013096	.012336	.011621
35	.017793	.016718	.015709	.014763	.013876	.013043	.012261	.011528	.010840	.010194
36	.015858	.014873	.013951	.013088	.012279	.011522	.010813	.010148	.009525	.008942
37	.014134	.013233	.012390	.011603	.010867	.010178	.009535	.008933	.008370	.007844
38	.012597	.011773	.011004	.010286	.009617	.008992	.008408	.007864	.007355	.006880
39	.011227	.010474	.009772	.009119	.008510	.007943	.007415	.006922	.006463	.006035
40	.010007	.009319	.008679	.008084	.007531	.007017	.006538	.006093	.005679	.005294
41	.008919	.008291	.007708	.007167	.006665	.006199	.005766	.005364	.004991	.004644
42	.007949	.007376	.006845	.006354	.005898	.005476	.005085	.004722	.004386	.004074
43	.007084	.006562	.006079	.005633	.005219	.004837	.004484	.004157	.003854	.003573
44	.006314	.005838	.005399	.004993	.004619	.004273	.003954	.003659	.003386	.003135
45	.005628	.005194	.004795	.004427	.004088	.003775	.003487	.003221	.002976	.002750
46	.005016	.004621	.004258	.003924	.003617	.003335	.003075	.002835	.002615	.002412
47	.004470	.004111	.003782	.003479	.003201	.002946	.002711	.002496	.002298	.002116
48	.003984	.003658	.003359	.003084	.002833	.002602	.002391	.002197	.002019	.001856
49	.003551	.003254	.002983	.002734	.002507	.002299	.002108	.001934	.001774	.001628
50	.003165	.002895	.002649	.002424	.002219	.002031	.001859	.001702	.001559	.001428
51	.002821	.002576	.002353	.002149	.001963	.001794	.001640	.001499	.001370	.001253
52	.002514	.002292	.002089	.001905	.001737	.001585	.001446	.001319	.001204	.001099
53	.002241	.002039	.001856	.001689	.001538	.001400	.001275	.001161	.001058	.000964
54	.001997	.001814	.001648	.001497	.001361	.001237	.001124	.001022	.000930	.000846
55	.001780	.001614	.001463	.001327	.001204	.001093	.000991	.000900	.000817	.000742
56	.001586	.001436	.001300	.001177	.001066	.000965	.000874	.000792	.000718	.000651
57	.001414	.001277	.001154	.001043	.000943	.000853	.000771	.000697	.000631	.000571
58	.001260	.001136	.001025	.000925	.000835	.000753	.000680	.000614	.000554	.000501
59	.001123	.001011	.000910	.000820	.000739	.000665	.000600	.000540	.000487	.000439
60	.001001	.000900	.000809	.000727	.000654	.000588	.000529	.000476	.000428	.000385

Table J—Adjustment Factors for Term Certain Annuities Payable at the Beginning of Each Interval Applicable After April 30, 1989

[Frequency of payments]

Interest rate	Annually	Semi annually	Quarterly	Monthly	Weekly
4.2	1.0420	1.0314	1.0261	1.0226	1.0213
4.4	1.0440	1.0329	1.0274	1.0237	1.0223
4.6	1.0460	1.0344	1.0286	1.0247	1.0233
4.8	1.0480	1.0359	1.0298	1.0258	1.0243
5.0	1.0500	1.0373	1.0311	1.0269	1.0253
5.2	1.0520	1.0388	1.0323	1.0279	1.0263
5.4	1.0540	1.0403	1.0335	1.0290	1.0273
5.6	1.0560	1.0418	1.0348	1.0301	1.0283
5.8	1.0580	1.0433	1.0360	1.0311	1.0293
6.0	1.0600	1.0448	1.0372	1.0322	1.0303
6.2	1.0620	1.0463	1.0385	1.0333	1.0313
6.4	1.0640	1.0478	1.0397	1.0343	1.0323
6.6	1.0660	1.0492	1.0409	1.0354	1.0333
6.8	1.0680	1.0507	1.0422	1.0365	1.0343
7.0	1.0700	1.0522	1.0434	1.0375	1.0353
7.2	1.0720	1.0537	1.0446	1.0386	1.0363
7.4	1.0740	1.0552	1.0458	1.0396	1.0373
7.6	1.0760	1.0567	1.0471	1.0407	1.0383
7.8	1.0780	1.0581	1.0483	1.0418	1.0393
8.0	1.0800	1.0596	1.0495	1.0428	1.0403
8.2	1.0820	1.0611	1.0507	1.0439	1.0413
8.4	1.0840	1.0626	1.0520	1.0449	1.0422
8.6	1.0860	1.0641	1.0532	1.0460	1.0432
8.8	1.0880	1.0655	1.0544	1.0471	1.0442
9.0	1.0900	1.0670	1.0556	1.0481	1.0452
9.2	1.0920	1.0685	1.0569	1.0492	1.0462
9.4	1.0940	1.0700	1.0581	1.0502	1.0472
9.6	1.0960	1.0715	1.0593	1.0513	1.0482
9.8	1.0980	1.0729	1.0605	1.0523	1.0492
10.0	1.1000	1.0744	1.0618	1.0534	1.0502
10.2	1.1020	1.0759	1.0630	1.0544	1.0512
10.4	1.1040	1.0774	1.0642	1.0555	1.0521
10.6	1.1060	1.0788	1.0654	1.0565	1.0531
10.8	1.1080	1.0803	1.0666	1.0576	1.0541
11.0	1.1100	1.0818	1.0679	1.0586	1.0551
11.2	1.1120	1.0833	1.0691	1.0597	1.0561
11.4	1.1140	1.0847	1.0703	1.0607	1.0571
11.6	1.1160	1.0862	1.0715	1.0618	1.0581
11.8	1.1180	1.0877	1.0727	1.0628	1.0590
12.0	1.1200	1.0892	1.0739	1.0639	1.0600
12.2	1.1220	1.0906	1.0752	1.0649	1.0610
12.4	1.1240	1.0921	1.0764	1.0660	1.0620
12.6	1.1260	1.0936	1.0776	1.0670	1.0630
12.8	1.1280	1.0950	1.0788	1.0681	1.0639
13.0	1.1300	1.0965	1.0800	1.0691	1.0649
13.2	1.1320	1.0980	1.0812	1.0701	1.0659
13.4	1.1340	1.0994	1.0824	1.0712	1.0669
13.6	1.1360	1.1009	1.0836	1.0722	1.0679
13.8	1.1380	1.1024	1.0849	1.0733	1.0688
14.0	1.1400	1.1039	1.0861	1.0743	1.0698

Table K—Adjustment Factors For Annuities Payable At The End Of Each Interval Applicable After April 30, 1989

[Frequency of Payments]

Interest Rate	Annually	Semi annually	Quarterly	Monthly	Weekly
4.2	1.0000	1.0104	1.0156	1.0191	1.0205
4.4	1.0000	1.0109	1.0164	1.0200	1.0214
4.6	1.0000	1.0114	1.0171	1.0209	1.0224
4.8	1.0000	1.0119	1.0178	1.0218	1.0234
5.0	1.0000	1.0123	1.0186	1.0227	1.0243
5.2	1.0000	1.0128	1.0193	1.0236	1.0253
5.4	1.0000	1.0133	1.0200	1.0245	1.0262
5.6	1.0000	1.0138	1.0208	1.0254	1.0272
5.8	1.0000	1.0143	1.0215	1.0263	1.0282
6.0	1.0000	1.0148	1.0222	1.0272	1.0291
6.2	1.0000	1.0153	1.0230	1.0281	1.0301
6.4	1.0000	1.0158	1.0237	1.0290	1.0311
6.6	1.0000	1.0162	1.0244	1.0299	1.0320
6.8	1.0000	1.0167	1.0252	1.0308	1.0330
7.0	1.0000	1.0172	1.0259	1.0317	1.0339
7.2	1.0000	1.0177	1.0266	1.0326	1.0349
7.4	1.0000	1.0182	1.0273	1.0335	1.0358
7.6	1.0000	1.0187	1.0281	1.0344	1.0368
7.8	1.0000	1.0191	1.0288	1.0353	1.0378
8.0	1.0000	1.0196	1.0295	1.0362	1.0387
8.2	1.0000	1.0201	1.0302	1.0370	1.0397
8.4	1.0000	1.0206	1.0310	1.0379	1.0406
8.6	1.0000	1.0211	1.0317	1.0388	1.0416
8.8	1.0000	1.0215	1.0324	1.0397	1.0425
9.0	1.0000	1.0220	1.0331	1.0406	1.0435
9.2	1.0000	1.0225	1.0339	1.0415	1.0444
9.4	1.0000	1.0230	1.0346	1.0424	1.0454
9.6	1.0000	1.0235	1.0353	1.0433	1.0463
9.8	1.0000	1.0239	1.0360	1.0442	1.0473
10.0	1.0000	1.0244	1.0368	1.0450	1.0482
10.2	1.0000	1.0249	1.0375	1.0459	1.0492
10.4	1.0000	1.0254	1.0382	1.0468	1.0501
10.6	1.0000	1.0258	1.0389	1.0477	1.0511
10.8	1.0000	1.0263	1.0396	1.0486	1.0520
11.0	1.0000	1.0268	1.0404	1.0495	1.0530
11.2	1.0000	1.0273	1.0411	1.0503	1.0539
11.4	1.0000	1.0277	1.0418	1.0512	1.0549
11.6	1.0000	1.0282	1.0425	1.0521	1.0558
11.8	1.0000	1.0287	1.0432	1.0530	1.0568
12.0	1.0000	1.0292	1.0439	1.0539	1.0577
12.2	1.0000	1.0296	1.0447	1.0548	1.0587
12.4	1.0000	1.0301	1.0454	1.0556	1.0596
12.6	1.0000	1.0306	1.0461	1.0565	1.0605
12.8	1.0000	1.0310	1.0468	1.0574	1.0615
13.0	1.0000	1.0315	1.0475	1.0583	1.0624
13.2	1.0000	1.0320	1.0482	1.0591	1.0634
13.4	1.0000	1.0324	1.0489	1.0600	1.0643
13.6	1.0000	1.0329	1.0496	1.0609	1.0652
13.8	1.0000	1.0334	1.0504	1.0618	1.0662
14.0	1.0000	1.0339	1.0511	1.0626	1.0671

(7) Actuarial Table S and Table 2000CM 2010CM where the valuation date is on or after May June 1, 20092023 —

(i) Determination of required factors. Except as provided in § 20.

7520–2

7520–3(b) (pertaining to certain limitations on the use of prescribed tables), for determination of the present value of

an

a remainder interest that is dependent on the termination of a life interest,

Table 2000CM and Table S (single life remainder factors applicable

where the valuation date is on or after

May 1, 2009) contained in this

June 1, 2023, actuarial remainder factors computed to at least five decimal places directly by using the formula in paragraph (d)(

7) and Table J and Table K contained in paragraph (d)(6

2)(ii)(B) of this section,

must be

Table 2010CM, and the section 7520 rate are used in the application of the provisions of this section. For the convenience of taxpayers, the actuarial factors, when the section 7520 interest rate component is

between

from 0.2 to 20 percent, inclusive, have been computed by the IRS and

14 percent.

(e) Effective/applicability dates. This section applies after April 30, 1999, and before May 1, 2009

can be found in Table S. Table S currently is available, at no charge, electronically via the IRS website at https://www.irs.gov/retirement-plans/actuarial-tables. Table S is also referenced and explained by IRS Publication 1457, Actuarial Valuations Version 4A, which will be available within a reasonable time after June 1, 2023.

(ii)

Table 4 to Paragraph (d)(7)(ii)

Age x	lx	Age x	lx	Age x	lx
0	100,000.00	37	97,193.66	74	71,177.55
1	99,382.28	38	97,058.84	75	69,174.83
2	99,341.16	39	96,915.25	76	67,044.59
3	99,313.80	40	96,761.20	77	64,773.93
4	99,292.72	41	96,595.51	78	62,366.05
5	99,276.45	42	96,416.30	79	59,795.50
6	99,261.55	43	96,220.61	80	57,080.84
7	99,248.33	44	96,005.41	81	54,213.71
8	99,236.50	45	95,768.60	82	51,205.27
9	99,226.09	46	95,509.98	83	48,059.88
10	99,217.03	47	95,229.06	84	44,808.51
11	99,208.80	48	94,923.45	85	41,399.79
12	99,199.98	49	94,589.88	86	37,895.25
13	99,188.21	50	94,225.50	87	34,313.98
14	99,170.64	51	93,828.33	88	30,700.82
15	99,145.34	52	93,398.01	89	27,106.68
16	99,111.91	53	92,934.52	90	23,586.75
17	99,070.69	54	92,438.08	91	20,198.02
18	99,021.50	55	91,907.95	92	16,996.17
19	98,964.16	56	91,342.02	93	14,032.08
20	98,898.61	57	90,737.24	94	11,348.23
21	98,824.20	58	90,090.97	95	8,975.661
22	98,741.32	59	89,401.06	96	6,931.559
23	98,652.16	60	88,665.95	97	5,218.261
24	98,559.87	61	87,883.66	98	3,823.642
25	98,466.80	62	87,051.88	99	2,722.994
26	98,373.71	63	86,167.86	100	1,882.108
27	98,280.09	64	85,226.77	101	1,261.083
28	98,185.51	65	84,221.59	102	818.2641
29	98,089.05	66	83,142.34	103	513.7236
30	97,989.90	67	81,978.28	104	311.8784
31	97,887.47	68	80,728.83	105	183.0200
32	97,781.58	69	79,387.95	106	103.8046
33	97,672.13	70	77,957.53	107	56.91106
34	97,559.20	71	76,429.84	108	30.17214
35	97,442.53	72	74,797.63	109	15.47804
36	97,321.14	73	73,049.33	110	0.000000

(e) Applicability date. This section applies on and after June 1, 2023.

[T.D. 8540, 59 FR 30152, June 10, 1994, as amended by T.D. 8819, 64 FR 23212, Apr. 30, 1999; T.D. 8886, 65 FR 36929, June 12, 2000; T.D. 9448, 74 FR 21484, May 7, 2009; T.D. 9540, 76 FR 49612, Aug. 10, 2011; T.D. 9974, 88 FR 37439, June 7, 2023]