Title 26
SECTION 20.2031-7
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 of years, remainders, and reversions for estates of decedents for which the valuation date of the gross estate is on or after May 1, 2009, is determined under paragraph (d) of this section. The present value of annuities, life estates, terms of years, remainders, and reversions for estates of decedents for which the valuation date of the gross estate is before May 1, 2009, is determined under the following sections:
| Valuation date | 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). |
(d) Actuarial valuations on or after May 1, 2009 - (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 1, 2009, the fair market value of annuities, life estates, terms of years, remainders, and reversionary interests is the present value determined by use of standard or special section 7520 actuarial factors. These factors are derived by using 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. See §§ 20.7520-1 through 20.7520-4.
(2) Specific interests - (i) Charitable remainder trusts. The fair market value of a remainder interest in a pooled income fund, as defined in § 1.642(c)-5 of this chapter, is its value determined under § 1.642(c)-6(e). The fair market value of a remainder interest in a charitable remainder annuity trust, as defined in § 1.664-2(a), is the present value determined under § 1.664-2(c). The fair market value of a remainder interest in a charitable remainder unitrust, as defined in § 1.664-3, is its present value determined under § 1.664-4(e). The fair market value of a life interest or 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).
(ii) Ordinary remainder and reversionary interests. If the interest to be valued is 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 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 in paragraph (d)(7) of this section and in Internal Revenue Service Publication 1457. See § 20.2031-7A containing Table S for valuation of interests before May 1, 2009. For information about obtaining actuarial factors for other types of remainder interests, see paragraph (d)(4) of this section.
(iii) Ordinary term-of-years and life interests. If the interest to be valued is the right of a person to receive the income of certain property, or to use 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 term-of-years or life interest actuarial factor (that corresponds to the applicable section 7520 interest rate and term-of-years or life interest 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 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 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, 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 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 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) in paragraph (d)(6) of this section or in Table S (in the case of a one-life annuity when the valuation date is on or after May 1, 2009) in paragraph (d)(7) 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 in paragraph (d)(6) of this section for payments made at the end of the specified periods. The provisions of this paragraph (d)(2)(iv)(B) are illustrated by the following example:
Example.At the time of the decedent's death, the survivor/annuitant, age 72, is entitled to receive an annuity of $15,000 a year for life payable in equal monthly installments at the end of each period. The section 7520 rate for the month in which the decedent died is 5.6 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 percent for an individual aged 72 is 8.3495 (1.000000 minus .53243, divided by .056). 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 5.6 percent is 1.0254. The aggregate annual amount, $15,000, is multiplied by the factor 8.3495 and the product is multiplied by 1.0254. The present value of the annuity at the date of the decedent's death is, therefore, $128,423.66 ($15,000 × 8.3495 × 1.0254).(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 is then multiplied by the 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. 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).
(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 of years or the death of an individual.
(3) Transitional rule. (i) If a decedent dies on or after May 1, 2009, and if on May 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 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 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 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 paragraph (d)(7) of this section or § 20.2031-7A(f)(4), at the option of 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 paragraph (d)(7) of this section or § 20.2031-7A(f)(4), the decedent's executor must use the same actuarial table with respect to each individual transaction and with respect to all transfers occurring on the valuation date. For example, gift and income tax charitable deductions with respect to the same transfer must be determined based on the same tables, and all assets includible in the gross estate and/or estate tax deductions claimed must be valued based on the same tables.
(4) Publications and actuarial computations by the Internal Revenue Service. Many standard actuarial factors not included in paragraph (d)(6) or (d)(7) of this section are included in Internal Revenue Service Publication 1457, “Actuarial Valuations Version 3A” (2009). Publication 1457 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. 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 ruling. 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. 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 years and 5 months old. In the month in which the decedent died, the section 7520 rate was 6.2 percent. Under Table S in paragraph (d)(7) of this section, the remainder factor at 6.2 percent for determining the present value of the remainder interest due at the death of a person aged 47, the number of years nearest A's actual age at the decedent's death, is .18672. The present value of the remainder interest at the date of the decedent's death is, therefore, $9,336.00 ($50,000 × .18672). 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 6.2 percent. Under Table S in paragraph (d)(7) of this section, the remainder factor at 6.2 percent for determining the present value of the remainder interest due at the death of a person aged 31, the number of years closest to A's age at the decedent's death, is .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. The present value of A's interest at the time of the parent's death is, therefore, $45,651.50 ($50,000 × .91303). 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 4.8 percent. Under Table S in paragraph (d)(7) of this section, the factor at 4.8 percent for determining the present value of the remainder interest at 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). The adjustment factor from Table K in paragraph (d)(6) of this section at an interest rate of 4.8 percent for semiannual annuity payments made at the end of the period is 1.0119. The present value of the annuity at the date of A's death is, therefore, $158,585.98 ($10,000 × 15.6721 × 1.0119). 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 9.8 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 9.8 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 a term of 5 years is 3.8102 (1.000000 minus .626597, divided by .098). The adjustment factor from Table K in paragraph (d)(6) of this section at an interest rate of 9.8 percent for quarterly annuity payments made at the end of the period is 1.0360. The present value of the annuity is, therefore, $39,473.67 ($10,000 × 3.8102 × 1.0360).(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 where the valuation date is on or after May 1, 2009. Except as provided in § 20.7520-2(b) (pertaining to certain limitations on the use of prescribed tables), for determination of the present value of an 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 paragraph (d)(7) and Table J and Table K contained in paragraph (d)(6) of this section, must be used in the application of the provisions of this section when the section 7520 interest rate component is between 0.2 and 14 percent.
(e) Effective/applicability dates. This section applies after April 30, 1999, and before May 1, 2009.
[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]