IN WOOD'S TABLES OR THE PURCHASING OF ESTATES. &c W. SCHOOLING INWOOD'S TABLES OF INTEREST AND MOKTALITY FOR THE PURCHASING OF ESTATES AND VALUATK)N OF PROPERTIES INCLUDING ADVOWSONS LEASEHOLDS ASSURANCE POLICIES LIFE INTERESTS COPYHOLDS MORTGAGES DEFERRED ANNUITIES PERPETUITIES FREEHOLDS RENEWALS OF LEASES GROUND RENTS REVERSIONS IMMEDIATE ANNUITIES SINKING FUNDS ETC. ETC. Bfcttfon, IRevfsefc anD BY WILLIAM SCHOOLING, F.RA.S. WITH LOGARITHMS OF NATURAL NUMBERS AND THOMAN'S LOGARITHMIC INTEREST AND ANNUITY TABLES LONDON CEOSBY LOCKWOOD AND SON 7 STATIONERS' HALL COURT, LUDGATE HILL 1913 NOTE TO THE THIRTIETH EDITION. THE present edition, besides retaining the additions to the preceding issue, has been carefully revised, and in it, thanks to the courtesy of correspondents, a few errors of the press will be found corrected. Should any user of the book discover a mistake in even a single figure, the Publishers will be greatly obliged by having their attention called to it. WILLIAM SCHOOLING. 17 OLD QUEEN STREET, WESTMINSTER, S.W. 26891.3,3 PREFACE TO THE TWENTY-SIXTH EDITION IN response to requests received since the issue of the Twenty-fifth Edition of this work, Tables I. and XVII. of the Twenty-fourth and earlier editions are now given here, in similar form to that in which they there appeared. They have, however, been extended to many more rates of interest, and Table XVII. has been extended to longer terms of years than formerly. The old Table I. will be found in the present edition on pp. xx to xxxi, and the old Table XVII. on pp. xxxii to xxxix. The former of these two Tables, it may be pointed out, appears also for integral years to a larger number of decimal places in the Tables showing the present value of i per annum (pp. 50 to 85, and 92 and 93). The present value of the reversion of a perpetuity appears to a larger number of decimal places on pp. 95 to 98. The values in the Table for purchasing of leases, estates, or annuities (pp. xx to xxxi) do not agree, so far as half- years are concerned, with the Twenty-fourth edition. The method formerly adopted assumed interest to be convertible momently or continuously. This supposition, however, is not usually employed, but in practice the value of a lease or annuity certain, say for 22^ years at 6 per cent, per annum, would be considered to be equivalent to the value of a lease or annuity certain for double the term (or 45 years), at half the rate of interest (or 3 per cent, per annum;. This value would be equal to 12-259, whilst the value given in old editions of ' In wood' is 12-174 on ly> the latter representing the value of an annuity of I for 22\ years, computed at such a rate of interest convertible momently as would be equivalent to an PREFACE TO THE TWENTY-SIXTH EDITION actual or effective rate of 6 per cent, per annum. The value assigned in practice of 12*259 * s based upon a rate of interest at 3 per cent, per half-year, which is equal to an effective annual rate of 6*09, or 6 is. lod. per cent, per annum (see pp. 1 8 and 122). it will be recognised therefore that in conformity with the usual practice the values riov* given for integral years assume interest to be convertible annually ', and the values for the half-years assume it to be convertible half- yearly. In response to a suggestion that the present value of i and of i per annum at 15 per cent, per annum would be found convenient by mining engineers and others, a table giving these values has been computed, and is given on p.xl. The method adopted was as follows. The present value of i per annum due at the end of 100 years was calculated by the aid of Gray's 24 figure logarithms, true to fifteen places of decimals ; multiplying this amount by the rate of interest gives the arithmetical complement of the present value of ^i due at the end of 100 years ; adding these two items together and deducting unity gives the amount of 1 per annum at the end of 99 years, and this process was continued to the end of the Table. In multiplying by the rate of interest it was convenient to employ Tate's Arithmo- meter, by means of which the necessary multiplications and additions were performed with the greatest ease. The results were checked every ten years, and the number of decimal places was reduced from time to time, the result being brought true to nine places when, at the end of the calculations, the first year was reached. In the present edition a few errors, which have been discovered since the publication of the last edition, have been corrected. WILLIAM SCHOOLING. PREFACE TO THE TWENTY-FIFTH EDITION IN the present edition of this work, many extensive additions have been made, and the book has been entirely reset ; the size of the page has been enlarged, to allow of a more convenient arrangement of the Tables ; the whole of it has been carefully revised ; and the Tables have been placed in logical sequence. The volume now contains 336 pages demy 8vo, as compared with 308 pages crown 8vo in the last edition. The principal alterations and additions may be briefly recorded. The Interest Tables, which were formerly scattered throughout the book, are now all brought together. The amount and present value of 1 and of i per annum at the same rate of interest all appear on the same page, instead of each of these items at varying rates of interest being tabu- lated separately. For most purposes this is more convenient, but on pp. 86-93 abbreviated Tables appear in the old form. Throughout the book any Table that occupies two pages is arranged so that the whole of it may be seen at one opening a detail that adds much to the convenience of using the Table. The Rates of Interest for which Tables were previously given were 2, 2j, 3, 34, 4, 4^ 5, 6, 7, 8, 9, 10. These are all retained, and six other rates i, i, i^, ij, 2^, 2j have been added. (vi) PREFACE TO THE TWENTY-FIFTH EDITION Five places of decimals are given instead of four, as was the case for some of the rates in previous editions. The abbreviated Tables in the old form are given at 3^, 3f> 4i> 4f> an d 5 2 P er cent, in addition to the 18 rates mentioned above. The present value of Perpetuities and of the Reversion to a Perpetuity are given in very much greater detail than before, both as regards the rates of interest and the number of decimal places. The Tables dealing with the Renewals of Leases are given at more rates of interest, while the Miscellaneous Tables, such as those on pp. 104, 105, 124, etc., are extended. The Sinking Fund Table is now given for 20 different rates of interest to 6 places of decimals for every year from i to 100, as compared with 10 rates of interest to (mostly) 4 places. The Tables showing the Value of an Annuity yielding interest at one rate, and providing for replacing capital at another rate, now occupy six pages instead of less than two, and are given to 5 places of decimals instead of 2, as well as at many more rates of interest. On pp. 122 and 123 some important Tables appear dealing with Interest payable half-yearly, quarterly, and monthly, together with a Table of constant factors for rinding the values of Annuities payable half-yearly, quarterly, and monthly from the values of yearly annuities. These are quite new to the book. The decimals of i are given for every farthing instead of for every penny, and the decimals of a year are given in more detail. In the Mortality Tables and the combined Mortality and Interest Tables, very many additions of much importance have been made. Apart from more numerous Tables and lower rates of interest, the values of the benefits according to the Healthy Males Table of the Institute of Actuaries and the Govern- (vii) PREFACE TO THE TWENTY-FIFTH EDITION ment Experience Table of 1883 are introduced. These Tables are of the greatest value, and many of the items deduced from them are tabulated in considerable detail. Among the Mortality Tables the English No. 3 also appears; while here, as throughout the book, all kindred tables appear on consecutive pages. Users of the book will find reference to it facilitated, if by a glance at the Table of Contents they grasp the order in which the contents are arranged. It will be seen to be 1. Interest apart from lives. 2. Lives apart from interest. 3. Interest in connection with single lives. 4. Interest in connection with two lives. 5. Interest in connection with three lives. 6. Logarithmic tables. In each of the divisions 3, 4, 5, the same order is main- tained. The additions in the parts of the book dealing with Interest and Mortality combined are too numerous for detailed record. Everything of any value in former editions is retained, while additions have been made that bring the whole thoroughly up to date as regards both the Mortality Tables and the rates of Interest employed. In addition to this, care has been taken to supply such data in the Tables, and such explanations and examples in the Introduction, as to make it a perfectly simple matter to calculate the values of benefits for other ages or at other rates of interest than are contained in the Tables. If any required information is not found in the Tables, a reference to the part of the Introduction dealing with the subject in question will probably show how the information may readily be arrived at. Special attention may perhaps be called to the Premium Conversion Tables on pp. 185 and 186, and to the explana- tion of them given in the Introduction. The Annual Premium Table is given in a novel form, which, it is believedj (viii) PREFACE TO THE TWENTY-FIFTH EDITION offers considerable advantages. Both the Conversion Tables will be found very convenient for many purposes, and readers unfamiliar with such tables would do well to spend a few minutes in grasping their nature, which is quite simple. The Post Office Annuities are given in less detail than before, and the average rates of Insurance Companies for annuities and assurances are added. A Table of Logarithms of Natural Numbers has been introduced in order to facilitate calculation, and especially to enable use to be made of the extremely valuable Logarithmic Tables of Interest by M. F6dor Thoman without reference to any other book. Logarithms are very easy to use, and every one engaged in calculations should avail himself of the enormous advantages they offer. M. Thoman's Tables have been printed from stereotype plates, in which any errors that have been noticed have been corrected, but they have not been re-checked for this edition. The difficulty of ensuring accuracy in so vast a number of figures will be well understood, and it can scarcely be hoped that no errors exist. Very great care has been taken in calcu- lating and checking the Tables, and in reading and re-reading the proofs, but as there are considerably more than a quarter of a million figures in the book, the entire absence of errors is improbable. Any users of the book who come across even a single mistake would confer a benefit by reporting it to the PUBLISHERS for correction in future editions. The great majority of the calculations have been made by Tate's Arithmometer. Even with this powerful aid the preparation of the book, involving the formation of many fresh Tables and the checking of many existing ones, has been an arduous task ; without an efficient calculating machine it would have been scarcely practicable. In former editions the headings of the Tables rather suggested the limitation of their use to one specific purpose, whereas most of the Tables are available for many purposes. fb] PREFACE TO THE TWENTY-FIFTH EDITION The headings of the Tables are now stated in a more general form, and in the Introduction examples are given of some of the various uses to which they may be put. In consequence, some habitual users of ' In wood ' may, perhaps, miss the familiar heading, and at first fail to recognise a well-known Table in its new garb. To obviate any inconvenience of this kind, and to increase the facility with which the book can be consulted, a full and specially arranged Table of Contents (pp. xi-xvi) has been prefixed, by reference to which any information needed may at once be found. An extensive collection of Examples has also been supplied (pp. 42-48), in which the actual working of every Table is illustrated. The book, as it now stands, serves innumerable purposes, but any suggestions (to be addressed to the PUBLISHERS) tending to increase its usefulness and convenience will be greatly appreciated and carefully considered, with a view to their adoption in future issues. In regard to such of the Tables in the book as are based on the Healthy Males Tables of Mortality, I am greatly indebted to the Council of the Institute of Actuaries, who have kindly given permission for the use in this volume of their valuable copyrights. WILLIAM SCHOOLING. CONTENTS Titles Rates of Interest Table Pages Text Pages ' 1 INTRODUCTION AND EXAMPLES ... ... I- 4 8 INTEREST TABLES ... xx-xl, 49 -i24 8-21 | l, If,2,2i, xx-xxiv TABLE FOR THE PURCHASING OF 2 2> 2 f > 3> 3a> xxi-xxv xviii LEASES, ESTATES, &c. 4, 4i 5, 6, xxvi-xxx I "s ( 7, 8, 9, 10 xxvii-xxxi ( i, if, 2, 21, xxxii-xxxiv j PRESENT VALUE OF REVERSION] 25. 2f , 3, 3j, xxxiii-xxxv f xviii OF A PERPETUITY 4, 4^> 5> 6 xxxvi-xxxviii f 13 I 7, 8, 9, 10 xxxvii-xxxix ) PRESENT VALUE OF 1 , 1 xix PRESENT VALUE OF i PER ANNUM > 15 xl t 10,12 AMOUNT OF i f PRESENT VALUE OF i AMOUNT OF i PER ANNUM PRESENT VALUE OF i PER ANNUM ( 2, 2\l 2i, 2f ', 5> 6> 7, 8*' 9> 10 49-57 58-65 66-73 74-81 82-85 8-10 10, II II, 12 12,13 AMOUNT OF i, IO-YR. INTERVALS i to 10 86, 87 8-10 PRESENT VALUE OF i, DO. . i to 10 88,89 IO, II AMOUNT OF i PER ANNUM, DO. . i to 10 90, 91 II, 12 PRESENT VALUE OF i PER ANNUM, DO i to 10 92, 93 12,13 VALUE OF A PERPETUITY to 10 94 13 VALUE OF REVERSION TO A PER- PETUITY ..... i to 6 95-98 13 VALUE OF PERPETUAL FINES FOR RENEWING LEASES 3 to 10 99 14 RENEWAL OF ANY NUMBER OF YEARS IN A IO-YRS.' LEASE 2 tO 17-95 99 I4-I6 (xi) CONTENTS 1 ,' It 4 f * . Rates of Interest Table Pages Text Pages INTEREST TABLES-c 4, 4|, 5 ) 105 16 SINKING FUND .... I to 10 I06-II5 16,17 VALUE OF ANNUITY YIELDING 1 INTEREST ON CAPITAL AT j REPLACING CAPITAL WHEN IN- 3> 3i 4, 5, 6, \ 7, 7%, 8, 9, 10 f 2,2|,3, 32 -, 4 [ Il6-I2lf 18 NOMINAL AND EFFECTIVE RATES OF INTEREST WHEN CONVERTIBLE HALF-YEARLY, QUARTERLY, MONTHLY I tO IO 122 18,19 CONSTANT FACTORS FOR CONVERT- ING VALUES AND AMOUNTS OF YEARLY ANNUITIES INTO THOSE OF ANNUITIES FOR ONE YEAR PAYABLE HALF-YEARLY, QUAR- TERLY, AND MONTHLY I tO 10 123 19,20 VALUE OF ANNUITY FOR 25 YRS. PAYABLE, AND INTEREST CONVER- TIBLE, YEARLY, HALF-YEARLY, QUARTERLY, AND MONTHLY 4 123 20 PRESENT VALUE OF ONE DUE A YEAR HENCE .... I tO IO 123 2C DISCOUNT ON ONE FOR i YEAR . I tO 10 123 20 TIME IN WHICH AN AMOUNT DOUBLES AT SIMPLE AND COM- POUND INTEREST I tO 10 124 21 DECIMALS OF i YEAR 124 21 DECIMALS OF i 125-128 21-23 (xii) CONTENTS Titles Rates of Interest Table Pages Text Pages MORTALITY TABLES- ... 129-136 23-25 EXPECTATION OF LIFE ACCORDING TO THE NORTHAMPTON, CAR- LISLE, EQUITABLE, 17 OFFICES, ENGLISH No. 3, AND HM TABLES 130, 131 23,24 ENGLISH LIFE TABLE, No. 3 ... 132, 133 2 ',24 INSTITUTE OF ACTUARIES HEALTHY MALES (HM) TABLE . 134, 135 23,24 CARLISLE TABLE .... ... 136 23,24 SINGLE LIVES & INTEREST- ... 137-154 25-28 VALUE OF AN ANNUITY : ... 138-145 25-27 NORTHAMPTON TABLE 3, 4, 5, 6 138, 139 25-27 CARLISLE TABLE 3, 4, 5, 6, 7, 8 140, 141 25-27 HEALTHY MALES 2.^,3,35,4,4^5 142, 143 25-27 GOVERNMENT EXP. (1883), MALES 2 I, 3, 3l, 4, 5 144 25-27 Do., FEMALES .... 2 i> 3, 32, 4, 5 145 25-27 SINGLE PAYMENT TO SECURE i AT DFATH : ... 146-149 27,28 CARLISLE TABLE 3, 4, 5, 6, 7, 8 146, 147 27,28 HEALTHY MALES 2^3,32,4,42-, 5 148, 149 27,28 ANNUAL PAYMENT TO SECURE i AT DEATH : HEALTHY MALES TABLE . ... 150, 151 150, 151 28 28 VALUE OF REVERSION TO A PER- PETUITY AT DEATH : 152-154 28 GOVERNMENT (1883) TABLE, MALES 2i- 3, 35, 4, 5 152 -8 Do., FEMALES .... 2, 3, 3!> 4, 5 153 28 NORTHAMPTON TABLE 3, 4, 5, 6 154 28 CARLISLE TABLE 3, 4, 5, 6 154 28 (xiii) CONTENTS Titles Rates of Interest Table Pages Text Pages TWO LIVES & INTEREST- ... iSS-,8, 29-34 JOINT LIFE ANNUITY : ... 156-165 29-31 NORTHAMPTON .... 3 4, 5 I 5 6 29-31 20-^1 GOVERNMENT (1883) . 158-163 s O 29-31 Two MALES .... 2f, 3, 3| 158-160 29-31 Two FEMALES 2|, 3, 3? 158-160 29-31 MALE AND FEMALE *i, 3, 3* 161-163 29-31 HEALTHY MALES 3, 3l> 4 164, 165 29-31 JOINT LIFE ASSURANCE, SINGLE PAYMENTS : ... 166-169 29-31 NORTHAMPTON .... 3 166 29-31 CARLISLE ... 3 167 29-31 HEALTHY MALES 3, 3i 4 1 68, 169 29-31 JOINT LIFE ASSURANCE, ANNUAL PAYMENTS : ... 170 29-31 HEALTHY MALES 3, 3ib 4 170 29-31 LAST SURVIVOR ANNUITY : ... I7I-I73 31,32 NORTHAMPTON .... 3> 4, 5, 6 171 3!,32 CARLISLE 3 172 31,32 HEALTHY MALES 3. 3l, 4 173 31, 32 ASSURANCE AT DEATH OF LAST SURVIVOR, SINGLE PAYMENT : 174-6 31,32 NORTHAMPTON .... 3 174 31,32 CARLISLE ..... 3 175 31,32 HEALTHY MALES 3, 3l 4 176 31,32 (xiv) CONTENTS Titles Rates of Interest Table Pages Text Pages TWO LIVES & INTEREST cont. ASSURANCE AT DEATH OF LAST SURVIVOR, ANNUAL PAYMENT : ... 177 31,32 HEALTHY MALES 3, 31 4 177 31,32 VALUE OF REVERSION TO A PER- PETUITY 3> 3' 2 , 4, 5 178 32 VALUE OF ANNUITY ON y AFTER DEATH OF x 3> 3, 4 179 33 Do. ON y TO BE NOMINATED AT DEATH OF x 3, 31, 4 179 33 ASSURANCE AT DEATH OF x IF y 180, 181 34 BE THEN LIVING, SINGLE PAY- MENT : i NORTHAMPTON .... 3 180 34 CARLISLE 3 180 34 HEALTHY MALES 3, 3i 4 181 34 THREE LIVES & INTEREST ... 182-184 35 JOINT LIFE ANNUITY : ... 182, 183 35 NORTHAMPTON .... 4 182 35 CARLISLE 3 182 35 HEALTHY MALES 3> 3i> 4 183 35 LAST SURVIVOR ANNUITY : NORTHAMPTON .... 34, 184 35 PREMIUM CONVERSION TABLE, SINGLE . . 2|, 3, 3l> 4, 5 185 35-39 Do., ANNUAL .... i to 8 1 86 35-39 POST OFFICE ANNUITIES, etc. ... 187-194 39,40 IMMEDIATE, MALE AND FEMALE ... 189 39 DEFERRED, MONEY RETURN- ABLE ... 190 39 DEFERRED, MONEY NOT DO. 191 39 (XV) CONTENTS Titles Rates of In gble Te POST OFFICE ANNUITIES, &camt. SINGLE PREMIUM TO ASSURE ioo AT DEATH, OR IN 10, 15, OR 20 YEARS .... I 9 2 39,40 Do. DO., 25, 30, 35, AND 40 YRS. 193 39,40 ANNUAL PREMIUMS PAYABLE TILL DEATH OR TILL AGE 50, 55, 60, 65 FOR ASSURANCE OF 100 AT DEATH OR AT AGE 50, 55, 60, 65 194 39,40 GOVERNMENT ANNUITIES (NATIONAL DEBT OFFICE) . ... 195 40 BRITISH LIFE OFFICES- AVERAGE ANNUITY RATES ... I 9 6 40 AVERAGE ANNUAL PREMIUMS FOR WHOLE LIFE AND ENDOW- MENT ASSURANCE, WITH AND WITHOUT PROFITS . 196 40 INCOME TAX TABLES AT 5^., 6^/., Jet., &/., AND gd. IN THE ... 197-204 40,41 LOGARITHMIC TABLES- ... 205-320 205-228 EXPLANATION .... ... ... 205-228 LOGS OF NATURAL NUMBERS ... 229-266 207-215 INTEREST TABLES .... to 12 : 267-320 ?l6-228 AMOUNT OF i | to 12 269-320 216-228 ANNUITY 1 WILL PURCHASE | tO 12 | 269-320 216-228 INTEREST TABLES TABLE FOR THE PURCHASING OF LEASES, ESTATES, OR ANNUITIES FOR TERMS OF YEARS CERTAIN PRESENT VALUE OF THE REVERSION OF A PERPETUITY PRESENT VALUE OF ONE POUND AND OF ONE POUND PER ANNUM For Examples see pages xviii, xix. For Explanations see pages 10, 12, 13. (xvii) a EXAMPLES OF THE USE OF TABLES ON PAGES xx-xl (i) Find the price to be paid for a lease yielding a clear annual rent of ,\$2 for 2$} years in order to make $\per cent, on the purchase price. per annum for 25^ years =^16777 =16777 x 132 = 2214-564 or 132 x 16 = 2112 132 x i= 66 132 x |= 33 132x1611=^2211 There is a difference of ^3*564 or ^3 115. 3^. due to the fact that i6f equals only 16750, whereas the correct figure is 16777. The difference between these two is '027, and this multiplied by 132 gives 3 -5 64, the difference between the two answers. (2) Find the present value of an annuity of && to run for -65 years certain such that the purchaser will obtain interest at 4%. i per annum for 65 years = ^23-047 80 =23-047x80= 1843-760 or 23 x 80=^1840 The explanation of the difference between the two answers is given under example (i). Such transactions as these two imply that if the purchaser drew interest on his capital at the rate assumed and invested the balance of the annuity at compound interest, this balance at the end of the term would amount to the purchase price and so replace the capital invested. Thus, to take the last example : The annual income= / 8o'ooo 4 % on price ,1843-760= 73/75 The annual balance= ^6-250 ^6*250 per annum accumulated for 65 years =6-250 x 294-968 This amount agrees closely with the value found, and would agree exactly if more places of decimals were used in the calculation. (xviii) EXAMPLES (3) Find the present value of a perpetual income of 25 per annum to commence 30 years hence so that the investment may yield 5 per cent. Value of reversion to a perpetuity of i ^4*628 ^25=4-628x25= 115700 xxxvi or 25 X4J= < n8 155-. xxxvi The difference between the answers is explained under { example (i). The nature of reversions is explained on pp. 13, 14. (4) Find the present value of ^1, 000,000 due at the end of 100 years at 15 %. The present value of i in 100 years ^-0000009 xi 1,000,000 \ _ = '0000009 x 1,000,000 ) This example is principally given to show the startling fact that a modest 18.5-. would at 15% compound interest accu- mulate in 100 years to the vast amount of ,1,000,000. (5) Find the present value of ,40 per annum to be received for 20 years certam so that the purchaser would obtain 15 %. \ per annum for 20 years=^6'25933i5 =6-2593315 x 40= 250-3732600 X; Other examples of the working of the tables in this book are given on pp. 42 -48. rt 2 INTEKEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Bates from l.\ to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' -J 1 o / Purchase 1 2 /O Years' 1 3 o/ Purchase IT /O Years' Q o / Purchase ^ /o Years' Q 1 q/ Purchase ^14. /O Years i 496 i 496 i 495 i "494 i i i 985 I 983 i 980 i 97 8 I I ii 1-478 ji I'474 ji 1-470 ii 1-467 ii ji 2 1-956 2 1-949 2 1-942 2 1-934 2 2 2| 2 I 2-436 2| 2-427 2| 2-418 2 2 2 5 3 2-912 3 2-898 3 2-884 3 2-870 2 f 3 31 3397 35 3-38I 3i 3-364 3-348 3i 4 3-854 3l 3-83I 3| 3-808 3t 3785 3f 4 2 4336 4-309 4-283 4i 4-257 $ 4-783 4f 4-748 4! 4-713 4f 4-679 4} 5 2 ? 5-260 Si 5* 5-222 5-649 ll 5-184 5-601 5l 5-I46 5-554 si 6 2 6f 6-171 6 ! 6-119 6 6-067 6 6-016 6 3 51 7 6*598 6-535 6% 6-472 63 6-410 6i 7 7-069 7 S 7-000 7 6-933 7^ 6-866 6f S* 7-486 7i 7-405 71 7-325 7? 7-247 7i 8 2 8| 7-953 8 7-866 71 7-781 7t 7-697 7f 8 9 8-361 8i 8-260 8-162 4 8-066 8 9 91 8-823 8| 8-717 8f 8-613 82 8-510 83 91 10 9-222 9i 9-101 9 8-983 9 8-866 8f 10 io| 9-681 91 9-554 9l 9-428 9| 9-306 9? io| ii 10-071 10 9-927 10" 9-787 9-649 9! ii "1 10-527 IO ^ 10-376 ; ioi 10-228 io| 10-083 10 XI 2 12 10-908 ii 10740 ! lOf iQ-575 | 10} 10-415 lOij 12 ia| n-359 ii* 11-184 ! Il 11-012 j II 10-843 lof I2| 13 11-732 "i 11-538 lU II-348 iij 11-164 j Ili I3 i If 12-180 12-543 I2 1 11-977 12 12322 I2 II-780 12-106 "I 12 II-587 II-896 12" I4 i I4l 12-988 13' 12758 I2| 12-533 12^ I2-3I4 I2 4 *5 I3-343 i3i I3-093 13 12-849 12} I2-6I2 I2 2 is 2 13784 ; 3 f 13-524 13! 13-271 134 I3-025 13 16" 14-131 I3-85 1 ; : 3l I3-578 13^ I3-3I3 13! i6 2 16^ 14-569 14^ 14-278 14^ I3-995 H" I3-720 I3| 165 I7 i 14-908 15 14-595 Hi I4-292 1 I4y I3-998 14 I7 i I5-34I isi 15-018 15 14-704 I4f I4-400 J 4| i8 2 15-673 15! 15327 I5 14-992 15 14-668 14! i8 2 igi 16-103 16 15-746 i i5f 15-400 15* I5-064 IS 1 8^ I9 1 16-426 l6i 16-046 16 15-678 isf IS^S I9 i 16-853 i6f 16-461 i6 16-082 16 I5-7I5 15} 20 17-169 17^ 16-753 j l6 f 16-351 i6 15-964 16 20" 20| 17-592 J 7a 17-163 17^ 16-750 i6| I6-350 l6 i 20| 21 17-900 18 17-448 i i7i 17-011 17 I6-590 1 6^ 21 21 i 22 18-319 18-621 III 17-854 i;2 18-130 i8 17-658 i7? i7f I6-972 I7-203 I7 i 22 22| 19-037 19 18-533 ! i8i 18-047 18 I7-580 I 7i 22| 23 I 9'33 I igi. 18-801 184 18-292 ' i8y I7-803 17! 23 24" I9-743 20-030 20 19-200 19-461 HI 18-677 i8f 18-914 19 18-174 i i8 18-389 i8i 231 24 241 20-439 20| I9-855 i9t I9-294 19? 18-755 18} 24^ 25 20-720 20f 20-109 20 19-523 I9i 18-962 19 25" EXAMPLES. A lease or annuity for 14 years to make 2 per cent, and to get back the principal is worth 12-106, or 12 years' purchase of the dear annual rent. At 3 per cent, it is worth 11-296, or 11 years' purchase. (xx) INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Rates from If to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' 1 o / Purchase A 2 /O Years' O3 O/ Purchase & 4 /O Years' Q Q/ Purchase O /O Years' Q 1 O/ Purchase U~2 / Years * "494 2 '493 i 493 i 491 ^ A i 976 I 973 i 971 i 966 I I i^ 1 -463 1 2 1-460 J 2 I-456 i| I '449 l 2" I -927 2 1-920 2 1-913 2 I -900 2 2 2-3 2 -409 2| 2-400 2 f 2-39I 2\ 2-374 2 2 2 3 2-856 2| 2-842 2| 2-829 2 f 2-802 2f 3 3i 3-331 3k 3-3I5 3? 3-299 3i 3-267 3 i 4 3-762 3f 3-739 3f 3717 3f 3-673 3l 4 44 4-231 44 4-206 4i 4-180 4i 4-130 4? 41 5 4-646 4f 4-613 42 4-580 4-5I5 42 5 52 5-109 ! 5 5-072 5 5-036 5 t 4-964 5 6 5*508 5| 5-462 5*- 5-4I7 5329 5k 5 6| 5-965 6 5-9I5 6 t 5-866 sl 5-769 5f 51 7 6-349 6-800 6| 6-289 6-736 6| 6-230 6-672 6{ 6f 6-115 6-546 6 ?; 8^ 7-170 7k 7-094 7 7-020 7 6-874 6| 8 8 2 9 t 7-615 7-971 7k 8 7-534 7-878 7-454 7-786 7f 7-298 7-608 7k Ik 9 8-410 8 8-311 a 8-213 8-023 8 10 8-752 8f 8-640 8f 8-530 8 8-317 8i 10 io| 9-185 9k 9-066 9 8-950 9 8-724 8f IQi ii 9-5I4 9^ 9-382 9ft 9' 2 53 9* 9-002 9 ii~ iii 9-94I I0~ 9-802 9t 9-665 9f 9-401 95 ui 12 10-258 10] 10-104 10 9*954 10 9-663 9f 12" I2| 10-679 lOf 10-518 IOJ 10-360 10} 10-054 10 I2| I3 i 10-983 ii 10-807 lOf 10-635 lOf 10-303 I0 i 11-398 I li 11-214 "1 1 1 -034 II 10-686 i of I3~ I 4~ 11-691 Il| n-49 1 IlA 1 1 -296 Ili 10-921 ii X 4 4i 12-100 12 11-891 12 11-688 "! 11-296 iii i^i i5 12-381 12^ 12-157 I2 i 11-938 12 11-517 n| 15 ?| 12785 I2| 12-551 I2 2 12-323 I2 4 11-885 12 X 5i I3-055 13 12-805 I2 12-561 I2;V 12-094 12 16 17 I3-452 I3-7I2 I 3 i I3 13-192 13-435 13! 12-939 13-166 13 12-454 I2f I2-65I I2| i6 I4-I04 14 13-817 13! I3-538 I3| I3-004 13 17^ i8~ I4353 I4i 14-049 14 13754 I3| 13-190 13^ 18 i8| 14-739 14! 14-424 14^ 14-119 H 13-535 135 183 I9 i 14-979 15 14-646 Hf 14-324 14^ 13710 13! 19 15-359 I 5? 15-015 I5 x 14-682 I 44 14-047 14 20 2 I5-589 iSt 15-227 14-877 15 14-212 14^ 20 20| 15-964 16 I5-59I I Sa 15-229 I 5k 14-543 14^ 20 21 16-185 16^ 15793 J 5f I5-4I5 J 5o 14-698 14^ 21 24 16-554 16-150 1 6 15-761 15! 15-021 15 2I 2 22 16-765 16-344 '64 I5-937 16 15-167 15! 22 - 22| I7-I29 16-695 i6f 16-276 l6i 15-483 152 22^ 23 i 17-332 i7i 16-879 17 16-444 l6i 15-620 15^ 23 17-690 I7f 17-225 *7k 16-777 i6f 15-929 16 23^ 24 I7-885 18 17-401 iji 16-936 I7 i 16-058 16 2 4 24 1- 18-238 18^- 17-740 i7f 17-262 16-361 i6| 24^ 25" 18-424 i8 17-908 18 I7-4I3 r 7.} 16-482 i6| 25 For Explanations and Examples see pp. xviii., xix. pp. xxii. to xxxi. Tables continued on INTEEEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Bates from 1| to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' . _i Q/ 'urchase A 2 /o Years' . 3. o/ urchase 1 4 To Years' Q o/ urchase ^ % Years' O 1. o/ Purchase 4- /o ears It* 2I'I25 21-399 21 2.\\ 20-499 20-746 2G> 20| 19-894 ; 20-121 20 20 19-324 I9-523 31 2? 26* 21-800 1 2lf 21-132 21} 20-492 i 20* 19-880 20 26 27 22-068 22 21-372 2l| 20-707 20f 2O-O72 20 27 27^ 22-466 22* 21-754 2I| 21-074 : 21 20-423 20 271 28 22-727 22| 21-987 22 2I-28I 21* 20-608 20* 28 28* 23-I2I 23 22-365 : 22i 21-644 ! 2I| 20-955 21 28^ 29 23-376 235 22-592 22^ 21-844 2I| 21-132 21* 29 29l 23-767 231 22-966 23 22-202 22^ 21-474 21* 291 30 24-016 24 23-186 ; 23ir 22-396 22i 21-645 2i| 30 3<* 24-404 24^ 23-556 23i 22-750 22f 21-983 22 30^ 3i 24-646 24f 23-770 j 23! 22-938 2 3 22-147 22^ 31 3*1 25-031 25 24-I36 24i 23-287 23i 22-480 22| 3i* 32 25-267 25i 24-344 24i 23-468 23^ 22-638 22f 32 32^ 25-648 2St 24-707 24f 23-813 23f 22-966 23 32! 33 25-879 26 24-908 25 23-989 24 23-118 23 33 331 26-257 26^ 25-267 25i 24-329 24i 23-441 23i 33^ 34 26-482 26j 25^62 25i 24-499 24i 23-587 23i 34 341 26-856 26| 25-8I7 25t 24-835 24? 23-905 24 34^ 35 27-076 27 26-007 26 24-999 25 24-046 24 35 351 36 27-446 27-661 27i 27f 26-359 26-543 26J 26 25-33 1 25-489 25i 251 24-360 24-495 24* 24^ 3? 36k 28-028 28 26-890 27 25-8I7 25f 24-804 24| 361 37 28-237 28* 27-069 27 25-969 26 24*934 25 37 37* 28-60I 28} 27-4I3 27i 26-294 26| 25-239 254 1 374 38 28-805 28f 27-586 271 26-441 26* 25-363 25^ 38 38! 29-166 29* 27^26 28 26-761 26| 25-664 25! 38* 39 29365 29i 28-O95 28 26-903 27 25-783 251 39 39^ 29-722 29f 28-431 28* 27-2I9 27i 26-079 26 39 40 29-916 30 28-59 4 28* 27355 27i 26-194 26^ 40 40| 30-270 1 30* 28^27 29 27-667 27t 26-486 26| 4<> 41 30-459 i 30* 29-085 29 27-799 27! 26-595 26^ 4i 4i* 30-8IO 3of 29-4I4 29* 28-I07 28 26-883 27 4ii 42 30-994 3i 29-568 291 28-235 28J 26-988 27 42 42| 3I-342 ! 31* 29-893 30 28-5-39 28^ 27-272 27^ 42^ 43 3I-52I 3i* 3O-O42 3 28-662 28f 27-372 27^ 43 43* 31-866 3*1 30-364 30* 28-962 29 27-652 27! 431 44 32-041 32 30-508 30] 29-080 29 27-748 27| 44 44i 32-382 32 30-826 3of 29-376 29* 28-023 28 44^ 45 32-552 32* 30-966 31 29-490 29* 28-115 28 45 3? 32-89I 33-056 32f 33 3I-28I 3I-4I6 3it 31* 29-783 29-892 29| 30 28-386 28^ 28-474 28j 45i 46 4** 33-392 33 3I-728 3i| 30-l8l 31* 28-742 28f 46^ 47 33-553 331 3I-859 3 1 ! 30-287 30^ 28-826 28f 47 47? 33-885 34 32-I67 32t 30-57I 3o| 29-089 29 47^1 48 34-043 34 32^94 32^ 30-673 3o| 29-170 29^ 48 48^ 34-371 34i 32-598 32| 30-954 31 29-429 29^ 48! 49 34-525 34 32-72I 32f 3I-052 31 29-506 29^ 49 491 34-850 34f 33^22 33 3I-330 31* 29-761 29! 49* 50 35'OOQ 35 33'!4i 33f 3 r> 424 3ii 29-834 29! So EXAMPLES. A lease or annuity for 49^ years to make 2\ per cent, and to get back the principal is worth 29-761 or 29! years' purchase of the clear annual rent. At 3^ per cent, it is worth 23-443 or 23^ years' purchase. INTEREST TABLES TABLE for the PURCHASING of Leases, Estates , or Annuities, for terms of years certain at Bates from 1^- to 10 per cent. Interest which the Purchaser may thereby make of his money Year? Years' O 1 o/ 'urchase * 2 /O Years' O 3. o / Pvrchase 14/0 Years' o Q/ 'urchase O /o Years' Q 1 o/ urchase O 2 /O r ears 2 5l 18772 i8f 18-242 18} I7-734 I7 a 16-777 I6f 25^ 26 18-951 19 18-402 18*- 17-877 i8 4 16-890 17 26 2&T 19-293 19} 18-730 i8| 18-192 18} I7-I79 17} 26| 27" 19-464 19! 18-883 19 18-327 18* 17-285 17* 27 271 19-801 19! 19-206 19) 18-636 i8f I7-568 X 7s 27^ 28 19-965 20 19-351 i9i 18-764 i8f 17-667 i7| 28 28.V 20-297 20} 19-668 19! 19-067 19 I7-943 18 28^ 29 20-454 20,^ 19-806 19! 19-188 18-036 18 29 29i 20-780 20f 20-118 20 19-485 IQi I8-305 18} 291 30 20-930 21 20-249 20} 19-600 19! 18-392 i8| 30 301? 2I-252 21} 20-555 20?- 19-892 2O 18-656 i8f 3a 3 1 21-395 2l 2O-68I 2O| 2O-OOO 2O 18736 i8f 31 31* 2I-7I2 2lf 20-981 21 20-286 20| 18-994 j 19 32 2I-849 2I 4 21-100 21 20-389 19-069 19 32 2 22-I60 22} 21-396 2li 20-669 20| I9-320 19* 32^ 33 22-292 22 j 2I-509 2I| 20-766 20f 19-390 19* 33 331 22-598 22^ 21799 2I| 21-040 21 19-636 i9| 33* 34 22-724 22f 21-906 22 21-132 21] I970I i9f 34 341 23-025 23 22-I9I 22} 21-401 2I 5 19-941 20 34^ 35 23-I45 23} 22-293 22} 21-487 21 k 20-001 20 35 35^ 23-442 23| 22-573 22-1 21-751 2l| 20-235 20} 35a 36" 22-670 22f 21-832 2lf 20-290 20} 36 3*1 23-848 2 3 | 22-945 23 22-091 22 20-5I9 20| 36* 37 23'957 24 23-036 23 22-167 22} 20-57I 37 37* 24-244 24} 23-306 23} 22-421 22^. 20-794 20| 37* 38 24-349 24] 23-393 23^ 22-492 22 o- 20-841 20| 38 38* 24-631 24! 23-658 2 3 | 22-741 22f 21-059 21 383 39 24-730 24! 23-740 23! 22-808 22f 21-103 21 39 39^ 25-008 25 24-000 24 23-052 23 21-315 2I i 39* 40 25-103 25 24-078 ; 24 23-115 23 21-355 21} 40 25-376 25! 24-334 ; 24} 23'353 23^ 21-563 2I * 40a 4I x 25-466 25!- 24-407 ! 24^ 23-412 23^ 21-599 2*2 41 25-735 25! 24-658 I 24! 23-646 23! 21-802 2l| 4 x a ! 42 2 25-821 25! 24-727 ! 24} 23-70I 23l 21-835 2lf 42^ 26-085 26 24-973 25 23-930 24 22-033 22 43 26-166 26} 25-038 ; 25 23-982 24 22 -063 22 43 431 26-426 265 25-280 ; 25} 24-206 24} 22-255 22} 43* 44 26-504 265 25-341 25} 24*254 244 1 22*283 22} 44jk 44^ 26-760 26| 24-474 24^ 22-47I 22iy 45 26-833 26f 25-636 , 25! 24-5*9 241 22-495 22^ 45 2 451 27-084 27 25-869 ; 2 5 f 24734 24f 22-679 22| 45* ; 46 27-154 27} 25-924 26 24-775 24f 22-7OI 22f 46 46^ 27-401 27^ 26-152 ; 26} 24-986 25 22-880 23 46* 47 27-467 27^ 26-203 j 26} 25-025 25 22-899 23 47 47* 27711 27! 26-427 1 26| 25-231 i 25} 23-074 23 48 27773 27f 26-475 ' 26i 25-267 25} 23-09I 23 1 4 8 2 48* 28-012 28 26-695 i 26f 2 5 f 23-261 48* 49 28-071 28 26-740 26f 25-502 23'277 23} 49 49 2 ^ 28-306 28} 26-955 27 25-700 25! 23-443 : 23^ 49* 50 28-362 28} 26-997 i 27 25-730 25! 23-456 23^, So For Explanations and Examples see pp. xviii., xix. pp. xx., xxi. and on pp xxiv. to xxxi. Tables continued on (xxiii) INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Rates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money. Years Years' 1 1 o / 'urchase J. 2 /O Years' 1 3 Q/ Purchase J. 4. /o Years' O o/ Purchase ^ /o Years' Q 1 o/ Purchase ^14 /O Fears 51 35-468 35* 33*554 33! 31788 3't 30-I56 3? 51 52 35-929 3 6* 33-960 34 32-145 3 2 ? 30-470 32 52 53 34-358 34? 32-495 30-778 3t 53 54 36-83? 36f 34-750 34? 32-838 32! 31-079 31 54 55 37-27I 37? 35-135 35? 33-175 33i 31-373 55 56 37706 37f 35W 351 33-505 33* 3 1 -660 3i| 56 57 38-I34 28| 35-886 36 33-828 33! 31-942 32 57 58 38-556 38^ 36-252 36^ 34-145 32-217 32| 58 59 38-971 39~ 36-611 i 365 34-456 34-j 32-486 59 60 39-380 39 36-964 37 34-761 34f 32-749 3 2 f 60 6z 39-784 39t 37-311 37? 35-060 35 33-006 33 61 62 40-181 405- 37-652 371 35-353 35i 33-258 33| 62 63 40-572 4 oi 37 -987 38 35-640 35! 33-504 63 64 40-958 41 38-3I7 38^ 35-92I 36 1 33-745 33f 64 65 4I-338 41? 38-641 38! 36-197 34 65 66 41-712 4 if 38-959 39 36-468 36* 34-211 34i 66 67 42-081 42 39-272 39? 36733 36f 34-436 34* 67 68 42-444 | 42! 39-579 391 36*994 37 34f 68 69 42-802 42! 39-881 40 37-249 37^ 34-871 34! 69 70 43-155 43? 40-178 40? 37-499 371 35 70 71 43-502 43* 40-470 4* 37744 37! 35-288 i 351" 71 72 43-845 43t 40-756 40| 37-984 38 35-490 35^ 72 73 44-182 44| 41 -038 4 1 38-220 3 P 35-687 : 35! 73 74 44-5I4 44* 4I-3I5 41? 38-45I 35'879 36 74 75 44-842 44! 41-587 4 1 * 38-677 38| 36-068 i 36 75 76 45" l6 4 45| 41-855 4if 38-899 39 36-252 76 77 45-482 42-118 42 39-117 36| 78 45-795 45! 42-376 42* 39-330 39? 36-609 36| 78 79 46-103 42-630 42f 39-539 36781 79 80 46-407 4 6* 42-880 43 39-745 39l 36-950 37 80 81 46-707 46f 43-125 43 1 39-946 40 37TI5 37 81 82 47-002 47 43-366 43? 40-I43 40^ 37-276 37^ 82 83 47-292 47i 43-603 431 40-336 40^ 37-434 371 83 84 47-579 47* 43*836 43! 40-526 405 37-588 37* 84 85 47-861 471 44*065 44 40-711 4of- 37739 o 37! 85 86 48-I39 48i- 44-290 44? 40-893 41 37-886 38 86 87 48-412 48* 44-511 44! 41-072 41 38-031 38 87 88 48-682 48f 44-728 ! 44! 4I-247 41- 38-172 88 89 48-948 49 44-942 45 41-419 41* 38-310 38| 89 90 49-210 49k 45" I 5 2 45? 41-587 38-445 38* 90 91 49-468 49* 45-358 45^ 4I-752 i4if 38-577 381 91 92 49-722 49! 45-56I 45* 41-914 i 42 38-706 38! 92 93 5 i 45-76o ! 45f 42-072 i 42 38-832 38f 93 94 50-219 45-956 | 46 42-228 j 42* 39 94 95 50-462 52 46-148 46!- 42-380 39-077 39 95 96 50-702 5l 46-337 ! 46 42-529 ' 42 t 39-I95 39i 96 97 50-938 51 46-523 465 42-676 39-310 391 97 98 51-170 5ii 46-706 46! 42-820 42! 391 98 99 5J-399 5 1 * 46-885 47 42-960 ! 43 39-534 39* 99 IOO 51-625 51! 47-061 47 43-098 |43 39-642 39! IOO EXAMPLES. A lease or annuity for 75 years to make i| per cent, and to get back the principal is worth 44-842 or 44! years' purchase of the clear annual rent. At 2 per cent, it is worth 38-677 or 38! years' purchase. (xxiv) INTEEEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Bates from If to 10 per cent. Interest which the Purchaser may thereby make of his money. Years Years' 1 o / Purchase <3~2 /O Years' Q.3. o/ Purchase f-i 4. /Q Years' Q n/ Purchase O % Years' Oj, o/ Purchase O p, /o years 51 28-646 28} 27-248 27^ 25-951 26 23-629 23f 51 52 28-923 29 27-492 27* 26-166 26\ 23*796 23^ 52 53 29-193 29^ 27-729 27} 26-375 26^ 23-957 24 53 54 29-457 29* 27-960 | 28 26-578 26^ 24-II3 24 54 55 29714 29f 28-185 28^ 26-774 26f 24-264 24^ 55 56 29-965 3 28-404 28* 26-965 27 24-410 24^ 56 57 3O-2IO 34 28-617 28^ 27-151 27] 24-550 24^ 58 30-448 3l 28-825 28| 27-331 24-686 24f 58 59 30-68I 3t 29-026 29 27-506 i 27| 24-818 24f 59 60 30-909 31 29-223 29! 27-676 27} 24-945 25 60 61 3I-I30 3'f 29-414 29* 27-840 27f 25-067 25 61 62 3i| 29-600 29* 28-000 ! 28 25-186 25^ 62 63 3 l 'S5* 3 r 2 29-781 29! 28-156 28 25-300 ! 25^ 63 64 31-764 31! 29-957 : 30 28-306 28 25-411 25^ 64 65 3 T -965 32 30-128 30^ 28-453 28| 25-518 25^ 65 66 32-161 323. 30-295 30^ 28-595 28^ 25-621 25^ 66 67 32-352 3 2 i 30-458 32 28-733 28| 25-721 25! 67 68 32-538 325 30-616 30s- 28-867 28} 25-817 25} 68 69 32-720 32f 30-770 30} 28-997 29 25-910 26 69 70 32-898 33 30-919 i 31 29-123 29 26-000 26 70 71 33-071 33 31-065 ! 31 29-246 29* 26-087 26 71 72 33-240 33T 31-207 34 29-365 ; 29^ 26-171 264; 72 73 33| 31-345 ; 31* 29-481 | 29^ 26-253 26^ 73 74 33-566 31-479 : 3 1 * 29-593 29* 26-331 26^ 74 75 33723 33} 31-610 , 34 29-702 ! 29} 26-407 265 75 76 33-876 34 31737 31! 29-808 ; 29! 26-480 26^ 76 34-025 31-861 31} 29-910 ! 30 26-551 26^ 78 34-I7I 34i 31-982 32 30-010 1 30 26-619 26^ 78 g 34-3I3 34-452 34* 345 32-099 32-213 3 2 32* 30-107 j 30 30-201 i 30^ 26-685 26f 26-749 ! 26f g 81 34-587 34* 32-324 32^ 30-292 3o 26-810 26} 81 82 34719 34} 32-432 325 30-381 32 26-870 26} 82 83 34-848 34} 32-537 325 30-467 3o 26-928 27 83 84 34-974 35 32-640 32} 30-550 30* 26-983 27 84 85 35-096 35 32-739 32} 30-631 304 27-037 27 85 86 35-216 35i 32-836 32} 30-710 304 27-089 27 86 87 35-333 35i 32-931 33 30-786 30} 27-139 27* 87 88 35^ 33-023 ! 33 30-860 27-187 27* 88 89 35-557 352 33-H2 1 33 30-932 31 27-234 27? 89 90 35-666 35* 33-J99 33* 31-002 3 1 27-279 2 7 i 90 9 1 35771 35} 33-284 33i 31-070 31 27-323 27T 91 92 35-875 35f 33i 31-136 3 ! i 27-365 92 93 35-975 36 33-447 33^ 31-200 3i| 27-406 27* 93 94 36-073 36 33^ 31-262 34 27-445 27* 94 95 36-169 361 33-6oi 331 31-323 34 27-484 95 96 36-263 36* 33-675 331 3i-38i 34 27-520 27! 06 97 36-354 36* 33-746 331 3I-438 34 27-556 27 97 98 36-443 36^ 33-817 33} 31-493 34 27-590 27* 98 99 36-529 36| 33-885 34 3 1 '547 34 27-623 27-2- 99 100 36-614 36| 33-95I 34 31-599 34 27-655 27} 100 For Explanations and Examples see pp. xviii., xix. pp. xx. to xx.iii., and on pp. xxvi. to xxxi. (XXV) Tables continued on INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Rates from 1| to 10 per cent. Interest which the Purchaser may thereby make of his money Years Yta^' A (} / Purchase TC /O Years' X 1 o / Purchase TC2 / Years' C n/ Purchase O /O Years' f* Q / Purchasa O /O * 490 tJ 489 ! 488 % 485 ! I 962 I 957 I 952 943 i I* 1-442 4 1*435 IQ 1-428 J ! 1-414 i! 2 1-886 2 r-873 if I-8 59 i? 1-833 if 2! 2-357 ^ 2-340 2 2-323 2* 2-290 2\ 3 2775 2f 2-749 2 f 2723 2| 2-673 21 3! 3-236 3i 3-205 3i 3-175 3i 3-II5 3 4 3'630 3? 3-588 , 3! 3-546 3! 3-465 3! 41 4-081 4 4-033 4 3-985 4 3 '893 4 5 4'45 2 4! 4-390 4! 4-329 4i 4-212 4J 51 4-893 5 4-825 4| 4757 4f 4-626 4f 5-242 5t 5-158 Si 5-076 5 4-9I7 5 6! 5-674 5~ 5-582 5! 5-492 5| 5-3I7 Si 7 6-002 6 5-893 6 5786 51 5-582 5! 7! 6-425 6! 6-306 6i 6-191 6 5-969 6 8 6733 6f 6-596 6! 6-463 6| 6-210 6i 8! 7-146 ?{ 6-999 7 6-856 4 6-583 6! 9 7*435 7! 7-269 7j 7-108 7 6-802 6| 9! 7'839 71 7-661 71 7-489 7! 7-162 7* 10 8-in 8 7-913 8 7-722 71 7-360 ! 7i io| 8-506 8! 8-295 ! 8} 8-092 8 7-708 j 7f ii 8-760 8 8-529 8i 8-306 8 7-887 8 "! 9-146 9k 8-901 9 8-666 8f 8-222 9 12 9-385 9! 9-119 9 8-863 8f 8-384 8! 12! 9-762 91 9-48i | 91 9-212 9 8-707 8| 13 9-986 10 9*683 9? 9-394 9! 8-853 8f 13! iQ-353 io 10-036 10 9-732 9t 9-164 9i J 4 10-563 10! 10-223 IQJ 9-899 10 9-295 9i 14! 10-922 II 10-566 10! 10-227 loj 9'594 9! ^5 11-118 II 10-740 io| 10-380 10! 9712 91 i5! 1 1 -469 n! 1 1 -074 II 10-698 10^ 10-000 10 16 11-652 ! 11-234 ni 10-838 io;| 10-106 10 16! 1 1 '99* 12 "559 IJ ! 11-146 ii 10-383 io| 17 12-166 I2i 11707 i if 11-274 i ii 10-477 IQi i7! 12-499 12! I2'023 12 n-573 n 10-744 ! lof 18 12-659 I2| I2-I60 I2 11-690 i if 10-828 io- 18! 12-985 13 12-467 I2| 11-979 12 11-084 ! ir 19 I3-I34 13* 12-593 i2i I2-085 12 11-158 11^ 19! I3-45I 13! 12-891 13 I2-365 I2{ 11-404 Il 20 I3-590 13! 13-008 13 12-462 I2| 11-470 ni 20! 13-900 14 13-298 I3i 12733 i2f 11-706 I if 21 14-029 14 13-405 [ 13! 12-821 I2'f 11-764 Il 21! H'33 1 14* 13-686 i3f I3-083 13 11-991 12 22 I4-45I H! 13-784 13? 13-163 i3i I2-042 : 12 22| I4-745 Hf 14-058 14 I3-4I7 13! 12-259 12\ 23 14-857 J 4| 14-148 I4i I3-489 13! 12-303 I2| 23! I5-I43 I5r 14-413 H! 13734 i3f I2-5I2 I2| 24 15-247 15* 14-495 1 4! 13799 i3l 12-550 I2| 24! 15-526 15! 14-753 14! 14-036 14 I2-75I I2f 25 15-622 15! 14-828 14^ 14-094 14 12783 I2f EXAMPLES. A lease or annuity for 13 years to make 4^ per cent, and to get back the principal is worth 9-683 or 9* years' purchase of the clear annual rent. At 5 per cent, it is worth 9-394 or 9| years' purchase. (xxvi) INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Bates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' 17 Q/ Purchase 1 /O Years' Q Q/ Purchase O /O Years' Q q/ Purchase t7 /O Years' 1 f\ o / Purchase 1U % Years 4 483 4 -48l i | 478 ; 4 476 i 4 i 935 1 i 926 I 917 1 I 909 i i i4 1-401 , i| 1-388 14 1-374 1^ 1-362 i ii 2 i -808 if 1783 If 1759 If 1-736 if 2 2 4 2-258 2* 2-226 2-195 2 i 2-165 2i 2 4 3 2-624 2^ 2-577 2 4 2-53I 2* 2-487 2 4 3 34 3-057 3 3-001 l 2-946 3 3 4 3-387 34 3*312 3i 3-240 j 3i 2 -i 9 o 4 2 44 3-804 31 3-718 3-634 ! 31 3-554 34 5 4-100 4 3-993 4 3-890 4 3-79I , 3f 5 2 f 4-767 4 I 41 4-380 4-| 4-623 44 4-264 4i 4-486 4 4-153 4i 4-355 4i 63 5i 4-993 5 4-841 4* 6\ 7 5-389 54 5-206 5^ 5-033 s 4-868 4f 7 74 5-759 5f S'559 54 5-370 54 5-I90 5i 74 8 5-971 6 5-747 5? 5-535 si S'335 5i 8 82 6-326 6\ 6-083 6 5-854 si 84 9 6-5J5 6 I 6-247 6| 5*995 6 5-759 5f Q 9k 6-855 6| 6-567 6 6-297 6^ 6-043 6 9a 10 7-024 7 6-710 6 6-418 61 6-145- 6^ IO IO| 7*349 7i 7-015 7 6-702 I 6! 6-411 6^ io II 7-499 74 7-139 7i 6-805 1 6| 6'495 6^ II Ili 7-810 7f 7-428 7 | 7-074 7 6-744 6J Hi 12 7-943 8 7-161 ft 6-814 6| 12 12* 8-241 8i 7-811 7f 7-4I4 ft 7-047 7 4 13 8-358 8i 7-904 8 7-487 n 7-103 7 13 13! 8-643 8 8-165 84 7-726 71 7322 ; 7i 134 14 8745 8| 8-244 8 7-786 71 7-367 7i 14 144 9-018 ! 9 8-492 84 8-01 1 8 7-571 74 144 15 9-108 9 8-559 84 8-061 8 7-606 74 15 15! 9-368 9i 8-794 8 ? 8-272 8^ 7-796 71 r 54 16 9*447 9| 8-851 84 8-313 8 : 7-824 7f 1 6 16^ 9*695 9-074 9 8-511 1 8-001 8 1 6^ I7 i 9-763 9j 9-122 9 8-544 8j 8-022 8 17 10-000 10 9-332 9i 8-731 8; 8-187 8i 174 i8 2 10*059 10 9-372 9i 8-756 i 8-201 fi 18 185 10-285 io 9-571 94 8-931 9 8-356 8i 18^ X 9 10-336 io{- 9-604 9a 8-950 9 8-365 8i 19" I0 1 - 10-551 ioi 9-792 9 I 9 8-509 8| 194 20 IQ'594 ; IO| 9-818 9-129 9i 8-514 20 20^ 10-800 lof 9-997 10 9-283 9? f 8-647 8 f 204 21 10-836 ioi 10-017 10 9-292 9< : 8-649 8| 21 1 211 II-03I ii 10-185 i io 9*437 9 8-773 81 214 22 22\ 11-061 11-248 ii 10-201 10^ 10-360 io 9-578 94 91 8-772 8-887 8| 9 22 23 11-272 nj IO-37I 10} 9-580 9* 8-883 9 2i 11-450 Ho IO-52I I0| 9-707 9f 8-991 9 234 24 2 24! 1 1 -469 11-638 "I Ilf IO-529 IO-67I 9-707 9-826 9 9 j 8-985 9-084 9 9 24 244 25 11-654 nj 10-675 \o\ 9-823 9 i 9-077 9 25 For Explanations and Examples see pp. xviii., xix. pp. xx. to xxv. and on pp. xxviii. to xxxi. (xxvii) Tables continued on INTEKEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Rates from 1! to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' A o / Purchase M /O Years' J_ 1 O/ Purchase T: 2 / Years' C o / Purchase O /O Years' O Q/ Purchase D /O Years 25! I5-894 16 I5-078 i5 x 14-323 I 4 1 12-976 13 2 5! 26 I5-983 16 I5-I47 I4-375 I 14* I3-003 13 26 26! 16-248 i6| 15389 15! I4-597 14* 13-187 13* 26! 16-330 167 I5-45I I 5! 14-643 I 4 f I3-2II J3i 27 27! 16-587 16! 15-686 15! 14-857 I4f I3-387 13! 27! 28 16-663 i6f 15743 15! 14-898 15 13-406 135 28 28! 16-914 17 I5-97I 16 15-105 15 13-575 13! 28! 29 16-984 16-022 16 15-141 15^ I3-59I 29 29^ 17-228 17* 16-243 16^ 15-341 15^ 13753 13! 29! 30 17-292 17* 16-289 I6| !5"372 15* 13-765 J 3t 30 3 2 I7-530 172 16-503 16! 15-565 15! 13-920 14 30! 31 17-588 172 16-544 16! I5-593 15! 13*929 14 31 1 3i! 17-820 17! 16-752 i6f 15-779 i5f 14-078 14 32 i 17-874 16-789 i6f 15-803 i 51 14-084 14 32 2 18-099 18 16-990 17 15-982 16 14-226 14* 32! 33 18-148 18* 17-023 17 16-003 16 I4-230 J 4i 33 33! 18-367 18* I7-2I8 16-176 14-367 14^ 33! 34 18-411 1 8! 17-247 171 16-193 I4-368 H* 34 34! 18-624 18! 17-436 I7 L 16-360 *"4 14-499 14! 34! 35 18-665 i8| 17-461 17! 16-374 i6 14-498 14! 35 35! 18-872 i8f 17-644 17! 16-536 16! 14-623 14* 35! 36 18-908 17-666 i7f I6-547 1 6! 14-621 14! 36 36! I9-IIO 19 I7-843 17! 16-702 i6f 14-740 I4f 36! 37 19*143 19* 17-862 173 16-711 i6f I4-737 14^ 37 37! I9339 19* 18-034 i8 4 16-861 i6f 14-851 u! 37! 38 19368 19* 18-050 18 16-868 i6f 14-846 I4t 38 38! I9-558 19! 18-216 i8j 17-013 17 14-955 15 38! 39 I9-584 19! 18-230 i8| 17-017 17 14-949 15 39 39! 19-770 19! 18-391 1 8! 17-157 171- I5-053 15 39! 40 I9-793 18-402 1 8! I7-I59 17* 15-046 15 40 40! 19-973 20 18-557 ! 18! 17-294 17^ 15-146 IS* 4! 41 1 19-993 20 18-566 18! 17-294 J 7i I5-I38 20-168 20* 18-717 i i8f 17-424 17! I5-233 I 54 44 42 2 20-186 18-724 i8f 17-423 !7! 15-225 5? 42 42! 20-356 20* 18-869 i8f I7-548 i Ik I5-3I6 15* 42! 43 20-371 20^ 18-874 i i8f 17-546 17! 15-306 15* 43 43! 20-536 20! 19-015 19 17-666 I5-393 43! 44 20-549 20! 19-018 19 17-663 i7i I5-383 J 5! 44 44! 20-709 20f I9-I55 ! 19* 17-779 172 15-466 15! 44! 45 20-720 20f 19-156 19^ 17-774 17! I5-456 J 5! 45 45! 20-876 20-885 21 21 19-288 19^ 19-288 igi 17-886 17-880 18 18 I5-535 I5-524 ; 5 f f 46! 21-036 21 19-416 19! 17-988 18 15-600 15! 46! 47 21-043 21 I9-4I5 19! 17-981 i 18 I5-589 ^5i 47 47! 21-190 21* I9-538 19! 18-085 ! 18 15-661 J 5l 47! 48 21-195 * I9-536 19! 18-077 , 18 15-650 15! 48 48! 21-338 2I * I9-655 19! 18-177 1 i8i I5-7I9 I 5f 48! 49 21-341 2I 4 19-651 19! 18-169 18* 15708 15! 49 49! 21-480 2I ! 19-767 i9f 18-265 i8 15773 15! 49! 5 21-482 2I| 19-762 i9f 18-256 18* 15-762 J 5f 50 EXAMPLES. A lease or annuity for 40 years to make 4 per cent, and to get back the principal is worth 19-793 or J 9l years' purchase of the clear annual rent. At 6 per cent, it is worth 15-046 or 15 years' purchase. (xxviii) INTEKEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Bates from 1 to 10 per cent. Interest which the Purchaser may thereby make of his money Years Years' 17 o/ Purchase I /O Years' Q Q/ Purchase O /O Years' Q o / Purchase V SO Years' 1 A o/ Purchase 1U /O Yeais 25* 11-814 Ilf 10-809 I Of 9-934 IO 9-169 9^ 255 26 11-826 ! i if 10-810 iof 9-929 IO 9-161 9i 26 26k 11-979 12 10-936 II 10-033 10 9-247 9k 26| 27 II- 9 87 12 io-935 II 10-027 10 9-237 ; 9? 27 27i I2-I32 12* 1 1 -054 II 10-124 IO 93I7 9 275 28 12-137 I2i 11-051 II 10-116 10 9-307 9? 28 a6i 12-275 I2i 11-163 Hi 10-207 ioi 9-38o 9s 28| 29 I2-278 I2 11-158 "i 10*198 I4 9-370 , 9l 29 291 I2-409 12^ 1 1 -264 "I 10-283 I4 9-438 9s 291 30 12-409 12^ 11-258 ! 10-274 Io i 9-427 95 30 30| 12-534 12^ n-357 "i 10-353 I0 4 9-490 9^ 30| 3i 12-532 I2i ii-35o n io-343 IOj 9-479 i 95 3i 3i I2-650 I2f 1 1 -444 IT 2 10-417 I2 9-538 : gi 34 32 12-647 I2f u-435 IlJ 10-406 io| 9-526 9i 3 2 32* 12-759 i2f 11-523 II* 10-475 IO I 9-58i 9 i 32| 33 12754 I2f n*5M "i 10-464 io| 9-569 95 33 331 12-860 I2| "597 IJ * IO-529 10^ 9-620 95 331 34 I2-854 I2| 11-587 Ilf IO-5I8 I0| 9-609 95 34 341 12-955 13 1 1 -665 "I 10-578 io| 9-655 9f 341 35 12-948 13 ii-655 Hi 10-567 ioi 9-644 9f 35 f 13-044 13 13-035 13 11-728 11-717 H\ Ilf 10-623 IQi 10-612 10^ 9-687 9-677 9f 9f 3? 36| 13-126 13 1 1 -786 JI f 10-664 io| 9-716 9i 36 37 13-117 13 n-775 Uf 10-653 lof 9-706 9i 37 37* 13-203 13? 1 1 -840 Ilf 10-702 iof 9-742 9i 375 38 13-193 13* 11-829 Uf 10-691 loj 9-733 9i 38 3% 13-275 13* 11-890 12 10-736 ; I0i 9-766 9l 38 39 13-265 13* 11-879 12 10-726 io; 9757 9; 39 391 13-342 I3f 11-936 12 10-768 io; 9-788 9f 39* 40 13-332 13? 11-925 12 10-757 ! 10; 9-779 9f 40 40! 13-405 13* 11-979 12 10-797 io| 9-808 9f 4(4 4 1 13-394 132 11-967 12 10-787 ioi 9*799 i 9f 4 1 44 13-464 135 12-018 12 10-823 loj 9-826 9f 44 42 13-452 13* 12-007 12 10-813 lof 9-817 9f 42 42! 13-518 13* 12-054 12 10-848 io; 9*842 i 9f 42^ 43 I3-507 i3i 12-043 12 10-838 ioi 9-834 1 9^ 43 43* 13-569 i 13* 12-088 12 10-870 10; 9-857 9^ 43^ 44 I3-558 135 12-077 12 10-861 io; 9-849 i gi- 44 441 13-617 13* 12-119 12 10-890 ii 9-870 gl 441 45 13-606 i3fc 12-108 12 10-881 II 9-863 9|- 45 * 13-662 13! 13-650 13] 12-148 12-137 iaj i 10-909 10-900 II ii 9-882 9-875 10 IO f 465 13703 i3i 12-174 Mf 10-926 II 9-893 10 46| 47 13-692 ! I3i 12-164 l4 10-918 II 9-887 10 47 47* I3-742 I3i 12-199 1 I2i 10-941 II 9-903 IO 47^ 48 I3-730 13! 12-189 i I2r 10-934 II 9-897 10 48 4 8| 13778 I3i 12-222 12; 10-956 II 9-912 IO 48| 49 13-767 13 12-212 12 10-948 II 9-906 10 49 491 13-812 13; 12-243 i 12; 10-969 II 9-920 10 49* J>o 13-801 I3f 12-233 12; 10-962 II 9-9I5 10 50 For Explanations and Examples see pp. xviii., xix. Tables continued on pp. xx. to xxvii. and on pp. xxx., xxxi. (xxix) INTEKEST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Kates from 1^ to 10 per cent. Interest which the Purchaser may thereby make of his money. Years Years' A n/ Purchase **. % Pur e c a h r ase4i% Years' C o/ Purchase U /O Years' * o/ Purchase D /O Years 51 2I-6I7 21}, 19-868 i I9| 18-339 18} ^813 IS* 51 52 21-748 2I| 19-969 20 18-418 i8| 15-861 S 2 53 21-873 2lf 20-066 20 I8-493 i8| 15-907 i6 4 53 54 21-993 22 20-159 20} 18-565 1 8^ I5-950 16 54 55 22-109 22 20-248 20} 18-633 iSJ I5-99I 16 55 56 22-220 22^ 20-333 20 18-699 16-029 [ 16 56 57 22*327 22} 20-414 2O| 18-761 18* 16-065 j 16 58 22-430 22^ 20-492 2C>J I8-820 1 8* 16-099 16 58 22-528 22^ 20-567 20^ 20-638 20| 18-876 18-929 19 16-131 16-161 16} 16} g 61 22-715 22f 20-706 20f 18-980 19 16-190 it)} 61 62 22-8O3 22| 20-772 20| 19-029 19 16-217 16} 62 63 22-887 23 20-834 20f 19-075 19 16-242 16} 63 64 j 22-969 23 20-894 21 I9-II9 I9 i 16-266 16} 64 65 | 23-047 23 20-95I 21 16-289 16} 65 66 23-I22 23 21-006 21 I9-20I I9 } 16-310 16} 66 67 23-I94 23i 21-058 21 19-239 19} 16-331 l6 ! 67 68 23-264 23.1 2I'IO8 21 19-275 ig} 16-350 68 69 23-330 ! 23} 21*156 2'l} 19-310 19} 16-368 I6 i 69 70 23-395 23* 2I-2O2 21 j I9-343 19} 16-385 i6| 70 71 23-456 2 3i 21-246 2I ? J 9'374 ig} 16-401 1 6iy 7 1 72 23-516 i 23! 21-288 2I T 19-404 igi 16-412 16} 72 73 23-573 j 235 2I-328 21} 19-432 I9 f 16-430 1 6^ 73 74 23-628 23! 21-367 21} J 9'459 16-443 :6| 74 75 23-680 i 23! 21-404 21^ 19-485 I9| 16-456 i6| 75 76 23-731 23f 21-439 21* 19-509 I9| 16-468 | l6Ir 76 77 23-780 23f 21-473 21 J J 9"533 igi 16-479 ' i6k 78 23-827 231 21-505 2l| J 9'555 I 9 | 16-490 i6\ 78 79 23-872 23? 2I-536 21* 19-576 16-500 1 6^ 79 80 23-915 24 2I-565 2U- 19-596 19* 16-509 i6^ 80 81 23-957 24 21-594 2I 19-616 19* 16-518 16^ 81 i 82 23-997 24 21-621 ; 2lk 19-634 I9l 16-526 ! i6l 82 83 24-036 i 24 2I-647 2lf 19-651 19! 16-534 165 83 84 24-073 J 24 2I-67I 2lf 19-668 19* 16-542 i6| 84 85 24-109 ; 24 2I-695 2I| 19-684 I9f 16-549 16\ 85 86 24-143 24} 2I-7I8 2lf 19-699 19* 16-556 1 6k 86 87 24-176 24} 2I-740 . 2lf 19-713 16-562 i6k 87 88 24-207 21-760 ; 2i| 19-727 19! 16-568 i6 88 89 24-238 24} 21-780 2I| 19-740 I9f 16-573 16^ 89 90 24-267 24} 21-799 \ 2if 19-752 16-579 I6| 90 91 24-295 24} 2I-8I7 2lf 19-764 J 9? 16-584 i6^ 91 92 93 24-323 24-349 24} 21-835 2lf 2I-852 ! 2lf 19775 19-786 I9f I9 1 16-588 16-593 l6iy 162 92 93 94 24-374 24} 21-868 2if 19-796 16-597 l6i 94 95 24-398 24^ 21-883 22 19-806 19! 16-601 165- 95 96 24-421 24^ 21-897 22 19-815 19* 16-605 16^ 96 97 24-443 24^ 2I-9II 22 19-824 19! 16-608 i 16^ 97 i 98 24-465 24* 21-925 22 19-832 19* 16-611 i6| 98 99 24-485 21-938 22 1 9 -840 16-615 i J 6" 99 100 24-50 24! 21-950 22 19-848 19! 16-618 ) 16} 100 EXAMPLES. A lease or annuity for 70 years to make 4 per cent, and to get back the principal is worth 23-395 or 23.^ years' purchase of the clear annual rent. At 6 per cent, it is worth 16-385 or i6| years' purchase. INTEREST TABLES TABLE for the PURCHASING of Leases, Estates, or Annuities, for terms of years certain at Kates from 1 to 10 per cent. Interest which the Purchaser may thereby make of his money. Years Years' n o/ Purchase 1 /O Years' Q o / Purchase O /O Years' Q O/ Purchase t7 /O Years' \ f\ O/ Purchase 1U /" Years 51 13-832 I3f 12-253 12} 10-974 ii 9-923 10 51 5 2 13-862 *3 f 12-272 12} 10-985 | ii 9-930 IO 52 53 13-890 14 12-288 12} 10-996 ii 9'936 10 53 54 13-916 14 12-304 I2 i 1 1 -005 1 1 9-942 10 54 55 13-940 14 I2-3I9 12} 11-014 ll 9-947 IO 55 56 I3-963 14 12-332 12} 1 1 -022 1 1 9-952 10 56 I3-984 14-003 H 14 12-344 12-356 12} 12} 1 1 -029 1 1 1 1 -036 1 1 9-960 10 IO i 59 14-022 12-367 12} 1 1 -042 1 1 9-964 IO 59 66 14-039 14 12-377 1 1 -048 1 1 9-967 IO 60 61 I4-055 14 12-386 I2 2 11-053 II 9-970 IO 61 62 14-070 14 12-394 I2 2 II-058 II 9'973 IO 62 63 14-084 14 12-402 I2 2 1 1 -062 1 1 9'975 10 63 64 14-098 H 12-409 I2 i 1 1 -066 1 1 9-978 10 64 65 14-110 14 12-416 I2 2 1 1 -070 1 1 9-980 10 65 66 14-121 14 12-422 I2 2 11-073 II 9-981 10 66 67 14-132 H} 12-428 I2 2 II-O77 II 9'983 10 67 68 14-142 Ml 12-433 12^ 1 1 -079 1 1 9^5 10 68 69 14-152 M 12-438 1 4 1 1 -082 1 1 9-986 10 69 70 14-160 H} 12-443 1 1 -084 1 1 9-987 10 70 7 1 14-169 *4} 12-447 12^ 1 1 -087 1 1 9-988 10 71 72 14-176 14} 12-451 12^ 1 1 -089 1 1 9-990 10 72 73 14-183 Ml 12-455 I2 | II-09I II 9-990 10 73 74 14-190 *4} 12-458 12^ 1 1 -092 1 1 9-991 10 74 75 14-196 14} 12-461 I2 J 1 1 -094 1 1 9-992 10 75 76 14-202 Ml 12-464 i at 1 1 -095 1 1 9-993 10 76 14-208 14-213 ; 4 i 12-467 12-469 | 1 1 -097 1 1 1 1 -098 1 1 9-994 9-994 10 10 79 14-218 M* 12-471 12! 1 1 -099 1 1 9-995 10 79 86 14-222 M] 12-474 12 J II-IOO II 9-995 10 80 81 14-226 H} 12-475 I2i II-IOI II 9-996 10 81 82 14-230 H} 12-477 1 21 11-102 II 9-996 10 82 83 H} 12-479 I2i 11-102 II IO 83 84 I4-237 M| 12-481 j4 11-103 ll 9-997 IO 84 85 14-240 '4} 12-482 11-104 II 9-997 10 85 86 I4-243 , '4} 12-483 2 11-104 II 9-997 10 86 87 14-246 '4} 12-485 11-105 II 9-997 IO 87 88 14-249 14} 12-486 12^ II-IO5 II 9-998 10 88 89 14-251 : 141 12-487 I2 I 11-106 n 9-998 10 89 90 I4-253 '4} 12-488 I2 5 11-106 ii 9-998 IO 90 9 1 I4-255 i 14} 12-489 j I2i 11-107 ii 9-998 10 91 92 I4-257 i '4} 12-489 12! 11-107 ii 9-998 IO 92 93 14-259 *4} 12-490 12} 11-107 ii 9-999 IO 93 94 14-261 MJ 12-491 I2 2- 11-108 ii 9-999 10 94 95 14-263 ; J 4} 12-492 I2 I 11-108 ii 9-999 10 95 96 14-264 14} 12-492 "* ii-ios n 9-999 IO 96 97 98 14-266 14-267 I4i 14} 12-493 12-493 11-109 ii 11-109 ii 9-999 9-999 10 10 % 99 14-268 I4J 12-494 12^ 11-109 ii 9-999 IO 99 100 14-269 | 141 12-494 I2 5 11-109 ii 9-999 10 100 For Explanations and Examples see pp. xviii., xix. pp. xx. to xxix. (xxxi) Tables continued on INTEREST TABLES The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Pur'SSse 1^ % Years' 1 3 o/ Purchase l^/O Years' Purchase 2% Years' Q 1 o/ Purchase 14. /O After Years I 65-681 65f 56-160 56i 49-020 49 43-466 434 I 2 64711 64f 55-194 55i 48-058 48 42-510 42* 2 3 63754 63* 54-245 54i 47-n6 47 4I-575 41? 3 4 62-8I2 62| 53-3 J 2 53i 46-192 46i 40-660 40f 4 5 61-884 62 52-395 52i 45-287 45i 39-765 391 5 6 60-969 61 51-494 5 J 2 44-399 44* 38-890 39 6 7 60-068 60 50-608 52 43-528 43^ 38-034 38 7 8 59-lSl 59i 49-738 49| 42-675 42f 37-197 37i 8 9 58-306 5S 48-882 49 41-838 4if 36-379 36* 9 10 57-444 571 48-042 48 4I-OI7 41 35-578 351 10 ii 56-596 56 47-215 47i 40-213 4oi 34795 341 ii 12 55759 55! 46-403 46^ 39-425 39i 34-030 34 12 13 54-935 55 45-605 45i 38-652 38f 33-281 33^ 13 14 54'i23 54 44-821 44f 37^94 38 32 '549 32| 14 J 5 53-323 53i 44-050 44 37-I5I 37i 31-832 3if 15 16 52-535 52* 43-292 43i 36-422 36| 31*132 3i? 16 17 51759 Sif 42-548 42i 35-708 35f 30-447 30* i7 18 50-994 5i 41-816 4if 35-008 35 29-777 29f 18 19 50-241 5oi 41-097 41 34-322 34i 29-122 29 19 20 49-498 49* 40-390 4>* 33-649 33f 28-481 28i- 20 21 48-767 48| 39-695 391 32-989 33 27-854 271 21 22 48-046 48 39-013 39 32342 3 2 i 27-241 27i 22 23 47336 47i 38-342 38i 31-708 3 1 ! 26-642 26f 23 24 46-636 46! 37-682 37f 31-086 3 1 26-055 26 24 25 45*947 46 37-034 37 30-477 30| 25-482 251 25 26 45-268 45i 36-397 36* 29-879 3 24-921 25 26 27 44-599 44* 35-771 351 29-293 291 24-373 24} 2 7 28 43-940 44 35-156 35i 28719 28f 23-837 23f 28 29 43-291 43i 34-551 34^ 28-156 28i 23-312 23? 29 30 42-651 42| 33-957 34 27-604 27^ 22-799 22f 30 31 42-021 4 2 33-373 33* 27-062 27 22-297 22^ 3 1 32 41-400 44 32-799 32| 26-532 26J 21-807 2lf 32 33 40-788 40* 32-235 32k 26-011 26 21-327 2ll 33 34 40-185 4i 31-680 3if 25-50I 25i 20-858 20| 34 35 39-59I 391 3i"!36 31* 25-001 25 20-399 20* 35 36 39-006 39 30-600 30^ 24-511 24* 19-950 20 36 38-430 38^ 30-074 30 24-031 24 19-511 19* 38 37-862 37 29-557 2 9 | 23-559 23i 19-081 19 38 39 37-302 37|- 29-048 i 29 23-097 23 18-662 i8f 39 40 36-75I 36! 28-549 | 28| 22-645 22| 18-251 4 40 4i 36-208 ; 3 6 $ 28-058 28 22-201 22| 17-849 i7f 4i 42 35-673 35f 27-575 I 271 2I-765 2I| I7-457 17* 42 43 35-145 35i 27-101 27 2I-338 2lf 17-072 i7 43 44 34-626 34! 26-635 26| 2O-92O 21 16-697 i6f 44 45 34-114 34 26-177 26^ 2O-5IO 20| 16-329 i6 45 46 33-6io 33i 25-726 251 20-108 20 15-970 16 46 47 33-II3 33 25-284 25i I97I3 I9f 15-619 15* 47 48 32-624 3*i 24-849 24! 19-327 I9i I5-275 IS* 48 49 32-142 32i 24-422 24^ 18-948 19 I4-939 15 49 50 31-667 3if 24-002 24 I8-576 18* 14-610 M* 50 EXAMPLES. The perpetuity of an annuity of 1 is worth in present money : At H per cent., 54- at 2 per cent., 37 -894 or 38 years r purchase. (xxxii) per annum after 14 years 123 or 54 years' purchase ; INTEREST TABLES The Present Value of the REVERSION OF A PERPETUITY after Term not exceeding 100 Years any given After Years Years' O 1 o / Purchase A 2 /O Years' O 3 o / Purchase A \ /o Years' O o/ Purchase > /o Years' Ql o / Purchase O^ % Aft(-i Yeai> I 39-024 39 35-390 35^ 32-362 : 32^ 27 -605 27-J- I 2 38-073 38 34-443 34| 31-420 34 26-672 26f 2 3 37-144 37} 33-52I 30-505 30-1 25770 25f 3 4 36-238 361 32-624 32 -i 29-616 29, V 24-898 25 A 5 35-354 35? 31-751 3 1 ! 28-754 28} 24-056 24 5 6 34-492 j 34^ 30-901 31 27-916 28 23-243 23! 6 j 33-65I 33f 30-074 30 27-103 27 22-457 22} 7 g 32-830 ; 32! 29-269 29} 26-314 26} 21-697 2lf 8 9 32-029 32 28-486 28^ 25-547 2 5.V 20-964 21 9 10 31-248 31} 27724 27! 24-803 24! 20-255 2O{ 10 ii 30-486 30! 26-982 27 24-081 24 19-570 19.} ii 12 29742 29! 26-259 26| 23*379 2 3 2 18-908 19" 12 13 29-017 29 22-697 22f 18-269 iS] 13 28-309 28^ 24-873 24! 22-037 22 17-651 i7f 14 15 27-619 27-1- 24-207 24} 21-395 2l I7-054 17 15 i5 26-945 27 23-559 23* 20-772 20f 16-477 i6-J- 16 17 18 26-288 26} 25-647 25! 22-929 22-315 1 20-I67 19-580 20.J 19! 15-920 I5382 16" I5 t 2 19 25-021 25 21-718 I9-OIO 19 14-862 Hf 19 20 24-411 24! 21-136 2l| I8-456 I 8-y- I4-359 14} 20 21 23-815 23! 20-571 20| I7-9I8 18 I3-873 i3f 21 22 23-235 23.1 20-020 2O I7-396 17-0 I3-404 I 3a 22 23 22-668 22| 19-484 19^ 16-890 17 12-951 13 23 24 22-II5 22 18-963 19 16-398 i6| I2-5I3 I2 | 24 25 21-576 2I-| 18-455 I5-920 16 12-090 12" 25 26 21-049 21 I7-96I i8 2 I5-456 15* II-68I Ilf 26 27 20-536 2O 17-481 '7* I5-006 15 1 1 -286 11} 27 28 2O-O35 2O I7-OI3 17 I4-569 '4f 10-904 II 28 2 9 19-546 I9| 16-557 i6|- I4-I45 14} IO-536 ioiV 29 30 19-070 19" I6-II4 16 13733 '3f 10-179 10} 30 31 18-605 ! i8| I5-683 15! I3-333 !3 9-835 9f 31 32 18-151 i 18} 15-263 I 5 12-945 i3 9-503 9 7 >" 32 33 17-708 i7f I4-855 X 4f 12-568 I2 2 9-l8l 9k 33 34 17-276 17} 14-457 14^ 12-201 4* 8-871 8 f 34 35 16-855 i6| 14-070 14 1 1 -846 nf 8-571 8i 35 36 16-444 i6| 13-694 i3f II-50I Ili 8281 8} 36 16-043 l6 ~ 13-327 "3* 11-166 11} 8-001 8 37 38 15-651 isf I2-97I 13 10-841 iof 7730 7f 38 39 15-270 15} I2-623 I2| 10-525 | ioi 7-469 7^ 39 40 14-897 15 12-286 12} 10-219 10} 7-216 71 40 41 14-534 14-1- 1 1 "957 12 9-921 10 6-972 7 41 42 I4-I79 Ml II-637 Ilf 9-632 9f 6-737 6f 42 43 I3-834 13! II-325 "J 9-351 9i 6-509 6| 43 44 I3-496 , 13^ 1 1 -022 II 9-079 9 6-289 6} 44 45 I3" l6 7 13? IO-727 iof 8-815 8f 6-076 6 45 46 12-846 i2f IO-440 8-558 5-87I 51 46 47 12-533 I2 2" 10-161 IO 4 8-309 8} 5-672 5f 47 48 12-227 i 12^ 9-889 10 8-067 8 5-480 Si 48 49 II-929 12 9-624 gi 7-832 7f 5' 2 95 54 49 50 II-638 Ilf 9-366 9\ 7-604 5-116 5 50 For Explanations and Examples, see pp. xviii. and xix. on pp. xxxiv.-xxxix. Tables continued (xxxiii) INTEEEST TABLES The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Years' 1 1 o/ Purchase A 2 /O Years' 1 3 o/ Purchase 4 70 Years' O n / Purchase & % Years' 1 o/ Purchase ^4/0 After Years 51 31-199 3I i 23-589 23! I8-2I2 ; 8 t 14-289 14* 51 52 30-738 3l 23-183 23! I7-855 I3-974 14 52 53 30-284 3i 22-784 I7-505 1 7^ 13-667 13! 53 54 29-836 29| 22-393 22 2 I7'l62 X 7i 13-366 134 54 55 29-395 29! 22-007 22 16-825 i6| 13-072 13 55 56 28-961 29 21 '629 2lf I6-495 i6| 12784 I2| 56 11 28-533 28-111 28| 28 21-257 20-891 21 16-172 I5-855 1^ I2-503 12-228 I2| 59 27-696 2 7f 20-532 2O 2 I5-544 n-959 12 59 60 27-286 2 7i 20-179 20^ I5-239 !5* 11-695 H| 60 61 26-883 27 19-832 I9'T 14-940 15,^ 1 1 -438 II| 61 62 26-486 26| I9-49I I9o I4-647 11-186 Iji 62 63 26-094 26" I9-I56 19 I4-360 Z 44 10-940 II 63 64 25-709 25| 18-826 1 i8f I4-079 H 3 10-700 io| 64 65 25-329 18-502 i8| 13-803 10-464 65 66 2 4-955 25 18-184 18}- I3-532 J 3o 10-234 io| 66 67 24-586 245 17-871 17- I3-267 I-jl 10-009 IO 67 68 24-222 24* 17-564 17! 13-006 13 9-788 9f 68 69 23-864 23! 17-262 i7i I2-75I I2| 9-573 9| 69 70 23-5I2 16-965 17 12-501 9-362 70 71 23-164 2 3i 16-673 i6| 12-256 I2 i 9-156 9i 71 72 22-822 22| 16-386 i6| 12-016 12 8-955 9 72 73 22-485 22k 16-105 16 11-780 ; iif 8f 73 74 22-152 22* 15-828 I5f ii-549 1 4 8-565 8| 74 75 21-825 21} I5-555 J 5l 11-323 Ir ? ?'377 8 i 75 76 21-503 2li 15-288 'Si 11*101 ii 8-192 8? 76 21-185 2l\ 15-025 15 10-883 ii 8-012 8 77 78 20-872 20.f 14-766 I4f 10-670 lof 7-836 7! 78 79 20-563 2Oiy I4-5I3 i4 10-461 io| 7-663 7f 79 80 20-259 20^ 14-263 r4 IO-255 IO 4 7-495 71 80 85 18-806 i8f 13-078 : 13 9-289 gi 6-706 6| 85 90 I7-457 17^ 11-991 12 8-413 8| 6-000 6 90 95 16-204 i6l 10-995 II 7-620 7f 5-368 5i 95 100 I5-042 15 10-081 ' 10 I 6-902 7 4-803 4t 100 EXAMPLES. The perpetuity of an annuity of i per annum after 65 years is worth in present money: at if per cent. 18-502, or 18^ years' purchase; at 2\ per cent. 10-464, or io| years' purchase. (xxxiv) INTEREST TABLES The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Years' O 1 o/ Purchase * 2 /O Years' O 3. o/ Purchase 14. /o Years' On/ Purchase O % Years' O 1 o / Purchase O 3 /f> After Years 51 1 1 '354 ni 9-116 9 7-382 7* 4-943 5 51 52 1 1 -077 ii 8-872 8f 7-167 7t 4-776 4f 52 53 10-807 iof 8-634 81 6-958 7 4-614 44 53 54 10-543 10! 8-403 8f 6756 6f 4-458 4| 54 55 10-286 I0 4 8-178 8i 6-559 6} 4-307 4* 55 56 10-035 10 7-959 8 6-368 6i 4-162 4? 56 9-790 9! 7-746 7f 6-182 61 4-021 4 57 58 9-552 9| 7-539 72 6-002 6 3-885 4 58 59 60 9-091 9 7-337 7-141 H 5-828 5-658 5f 5! 3-754 3f 3f g 61 8-870 8| 6-950 7^ 5-493 5s 3-504 3o 61 62 8-653 8f 6764 5-333 51 3-386 3-| 62 63 8-442 8| 6*583 6;V 5-178 51" 3-271 3i 63 64 8-236 8x 6-407 6^ 5-027 5 3-160 -i 64 65 8-035 8 6-235 6] 4-880 5 3-054 3" 65 66 7-839 7! 6-068 6 4-738 4| 2-950 3 66 67 7-648 7| 5-906 6 4-600 2-851 67 68 7-462 5f 4-466 4^" 2-754 2 4 68 69 7-280 74 5-594 5s 4-336 4r 2-661 2 : i 69 70 7-IO2 7 5-444 5i 4-210 4^ 2-571 2.V 70 71 6-929 7 5-299 5' 4-087 4 2-484 2 i 7 1 72 6-760 6! 5-157 5! 3-968 4 2-400 2^ 72 73 6-595 6| 5-019 5 3-853 3! 2-319 2 i 73 74 6-434 6^ 4-884 5 3-740 3! 2-241 2j 74 75 6-277 6* 4-754 4! 3-632 3f 2-165 75 76 6-124 6 4-626 4f 3-526 3i 2-092 2 76 5-975 6 5-829 , 5f 5-687 s! 4-503 4-382 3 3-423 3-233 3-227 3 i 2 -O2 1 1-952 1-886 2 2 80 5-548 j s 4" I 5 I 4i 3-133 3i 1-823 * 4 80 85 4-904 5 3-624 34 2-702 2? 1*535 4 85 90 4-334 4* 3-164 3| 2-331 2 i 1-292 jl 90 95 100 3-831 I 3t 3-386 3 i 2-763 2-413 2'OII 2 1734 if i -088 916 I I 95 IOO For Explanations and Examples, see pp. xviii. and xix. Tables continued on pp. xxxii., xxxiii. and xxxvi.-xxxix. (XXXT) INTEREST TABLES The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Years' A o/ Purchase TC 70 Years' A I o/ Purchase TC"2 /O Years' C o / Purchase U /O Years' / Q/ Purchase D /O After Years I 24-038 24 21'265 2Ij 19-048 19 15723 i is! I 2 23-114 23 20-350 20^ 18-141 i8f I4-833 Hi 2 3 22-225 22^ I9-473 19! 17-277 ; i7i I3-994 14 3 4 21-370 i 21^ 18-635 i8| 16-454 ! i6| 13-202 J 3l 4 5 2O'548 2O| 17-832 i7f 15-671 15! 12-454 I2 2 5 6 I9-758 19? 17-064 i 17 14-924 15 H'749 Hf 6 7 18-998 19 16-330 16! 14-214 ; 14^ 1 1 -084 j II 7 8 18-267 i8i 15-626 15! I3-537 i3l io-457 IO 2 8 9 17-565 : I7i 14-953 15 12-892 13 9-865 9l 9 IO 16-889 ; 17 14-310 i4i 12-278 I2i 9-307 91 IO ii 16*240 16^ 13-693 l 13! 1 1 -694 iif 8-780 8f ii 12 15-615 151 13-104 13 11-137 ni 8-283 12 13 15-014 15 12-539 I2 -| IO-6o6 IQi 7-814 7f 13 14 I4-437 142 11-999 12" lO'IOI 10 7-372 : 71 14 15 13-882 14 11-483 Il| 9-620 92 6-954 7 15 16 I3-348 i3i 10-988 II 9-162 9l 6-561 6-i 16 17 12-834 12\ 10-515 I2 8-726 8f 6-189 61 17 18 12-341 12\ 10-062 IO 8-310 81 5-839 51 18 19 1 1 -866 Hi 9-629 9t 7-915 8 5-509 51 19 20 11-410 IJ 2 9-214 91 7-538 7i 5-197 51 20 21 10-971 II 8-818 i 8f 7-179 7i 4-903 5 21 22 10-549 io|- 8-438 8| 6-837 6f 4-625 4f 22 23 10-143 Ii 8-074 8 6-511 6^ 4-363 4 23 24 9-753 9l 7727 71 6-201 61 4-116 4 24 25 9-378 9k 7-394 5-906 6 3-883 3t 25 26 9-017 9 7-076 7 5-625 5f 3;66 3 3f 26 27 8-670 8f 6-771 6f 5-357 5i 3i 27 28 8-337 8? 6-479 6 2 - 5-102 5 3-261 3l 28 29 8-016 8 6-200 61 4-859 4t 3-076 3 29 30 7-708 7f 5-933 6 4-628 4| 2-902 3 30 31 7-412 7^ 5-678 5f 4-407 42 2-738 2 2 I 31 32 7-126 71 5-433 Si 4-I97 4i 2-583 32 33 6-852 6| 5-I99 51 3-997 4 2-436 2 i 33 34 6-589 6| 4-975 5 3-807 3t 2-299 2 i 34 35 6-335 61 4-761 4l 3-626 3 f 2-168 2 i 35 36 6-092 6 4-556 4^ 3-453 33 2-046 2 36 37 5-857 si 4-360 41 3-289 31 930 2 37 38 5-632 5f 4-172 4l 3-132 3l 821 jl 38 39 5-416 5s 3-993 4 2-983 i 3 718 39 40 5-207 51 3-821 3f 2-841 2f 620 1 2 40 4 1 5-007 5 3-656 3f 2-706 ; 2f 529 l k 41 42 4-814 4f 3-499 j 3i 2-577 i 2| 442 l| 42 43 4-629 4f 3-348 3! 2-454 2^ 360 il 43 44 4-45i 4i 3-204 3l 2-337 2\ 283 !i 44 45 4-280 4i 3-066 3 2-226 2| 211 ii 45 46 4-115 : 4 2-934 3 2-I2O 2 142 il 46 47 3-957 j 4 2-808 2 4 2-OI9 2 078 i 47 48 3-805 i 3f 2-687 2f I-923 2 017 i 48 49 31 2-571 I-83I If '959 i 49 1 50 3'5 l8 2-460 2 5 1744 905 1 50 EXAMPLES. The perpetuity of an annuity of i per annum after 37 years is worth in present money : at 4 per cent., 5-857, or 5f years' purchase ; at 5 per cent., '3-289, or 3^ years' purchase. (xxxvi) INTEREST TABLES The Present Value of the EEVEESION OF A PEEPETUITY after any given Term not exceeding 100 Years After Years Years' 17 Q/ Purchase I /O Years' Q Q/ Purchase O /O Years' ( Purchase v )% Years' 1 f\ o / Purchase 1U /O After Years I I3-35 1 J 3l H-574 ni 10-194 Il 9-091 9 I 2 12-477 I2 | 10-717 IOj 9l 8-264 81 2 3 9-923 10 8-580 82 7-5I3 7s 3 4 IO-898 II 4 9-188 9l 7-872 71 6-830 6f 4 5 IO-I85 I0 1 8-507 85 7-222 71 6-210 61 5 6 9-519 9| 7;877 71 6-626 6f 5-645 5f 6 7 8-896 9 7l 6-078 6 5-132 51 7 8 8-314 81 6-753 6| 5-577 51 4-665 4f 8 9 7-770 7f 6-253 61 5-116 5 4-241 4| 9 10 7-262 71 5-790 51 4-694 4f 10 ii 6-787 6f 5-361 51 4-306 4l 3-505 3o- ii 12 6-343 6 1 4-964 5 3-95 1 4 3-186 3l ' 12 13 5-928 6 4-596 42 3-625 35 2-897 3^ 13 5-540 5 4-256 41 3l 2-633 15 5-I78 51 3-940 4 3-051 3 2-394 2^ 15 16 4-839 4f 3-649 3f 2-799 2| 2-176 2l 16 17 18 4-522 4^ 4-226 4l 3-128 3 31 2-568 2-356 3 I-978 i 2 1-799 if 3 J 9 3-950 4 2-896 3 q 2-161 2 4 1-635 ; if 19 20 3-691 3f 2-682 983 2 1-486 i^ 20 21 3-450 3a 2-483 2k 819 f 1-351 i| 21 22 3-224 3l 2-299 21 669 | 1-229 J l 22 23 3-013 3 2-129 21 53i i 1-117 i 23 24 2-8l6 2| 971 405 i 24 25 2-632 i 2* 825 1 i 289 1 920 i 25 26 2-460 2| 690 If 182 I 839 f 26 ; 27 2-299 | 2 565 I.', 1-085 763 27 28 2-148 2| '449 i.V 1-005 693 f 28 29 2-008 2 342 I j 913 '630 29 30 1-876 2 242 il 838 & '573 1 30 3 1 754 if 150 il 769 I 521 i 3 1 32 639 if 065 I 705 j 474 i 32 33 532 ; ii 986 I 647 ; ' i 33 34 43i ii 913 I '594 ; 391 ^ 34 35 338 , il 845 f '545 || 356 i 35 36 1-250 II 783 3 4 500 I 323 I 36 1-168 il 725 f 458 '- 294 37 38 I -092 I 671 f 421 ; , 267 i 4 38 39 I -021 I 621 386 ] 243 39 40 954 i 575 i 354 ] ! 221 i 40 4i 891 i 533 i 325 -- 2OI i 4 1 42 833 f '493 i 298 i 183 I 42 43 778 f 457 i 273 ! i 4 166 43 44 728 | 423 i 251 151 ^ 44 45 680 f 392 i 230 i 137 i 45 46 '63^1 f 363 A 211 i 125 i 46 47 594 I 336 J 194 i 113 i 47 48 '555 i i 311 ^ 178 ^- 103 _L 48 49 50 519 i 485 i 288 267 1 'ISO J 094 085 49 50 For Explanations and Examples, see pp. xviii. and xix. Tables continued on pp. xxxii.-xxxv. and xxxviii., xxxix. (xxxvii) INTEREST TABLES The Present Value of the REVERSION OF A PERPETUITY after any given Term not exceeding 100 Years After Years Years' A Q/ Purchase Tt /o Years' A Q Purchase Tt2 / 'o Years' C Q/ Purchase O /o Years' /J n/ Purchase O % After Years 51 3-383 3* 2-354 2\ I-66I I If 854 i - 51 52 3-253 si 2-253 582 l| 806 . : r 52 53 3-128 3? 2-156 2- 507 1 2 7 60 3 4 53 54 3-007 3 4 2-063 2 435 717 . . 54 55 2-892 3 1-974 2 367 4 677 . i ! 55 56 2781 2f 889 2 302 639 1 < I 56 2-674 2f 808 If 240 ji 603 i i S^ 2-571 2^ 730 I 181 i 568 \ 58 2-472 2-377 4 2| 655 584 :i 125 071 536 \ 506 \ i g 61 2-285 2k 5 I6 " 1-020 477 i ; 61 62 2-197 2\ 451 ^ 971 450 ; 62 63 2-II3 2 388 l\ 925 424 ; 63 64 2-03I 2 328 i 88 1 400 i - 64 65 1-953 2 271 J 839 f 378 ; r 65 66 878 2 217 ~4 799 3 356 66 68 806 If 736 If 164 114 3 761 725 | 336 7 317 I 3 69 670 If 1-066 690 f 299 69 70 605 I| I-O2O 657 f 282 i 70 7 1 '544 i| 976 626 f 266 71 72 484 li '934 596 i 255 ' 72 73 427 I-| 894 568 i 237 - 73 74 372 ^4" 855 1 541 i 223 \ 74 75 320 4 819 j 515 | 211 j 75 76 269 ii 783 j 491 1 199 5 76 220 173 Jf 750 717 * 467 "445 I 188 177 ! r> 7s 79 80 128 085 ? 686 657 I 424 404 1 167 158 i 1 1 6 79 80 85 8 9 I j 527 i 316 i 118 i 85 90 733 f 423 1 248 i 088 j r 90 95 602 | 339 j 194 1 5 066 a 1 5 95 100 495 * 272 i 4 152 1 049 3 T 100 EXAMPLES. The perpetuity of an annuity of i per annum after 65 years is worth in present money: at 4 percent., 1-953, or 1 2 years' purchase; at 4^ per cent., f 1-271, or if years' purchase. (xxxviii) INTEKEST TABLES The Present Value of the EEVEESION OF A PEEPETUITY after any given Term not exceeding 100 Years After Years Years' n Q/ Purchase 1 /o Years' Q o/ Purchase O /o Years' Q Q/ Purchase v /o Years' in r/ Purchase 1U % After Years 51 453 i 247 JL 137 ; * 078 1 i 51 52 423 \ 229 126 071 ' ^ 52 S3 396 ^ 212 1 116 064 ^ 53 54 370 i I 9 6 * 106 j i '59 tV 54 55 346 k 182 I 5 97 TO '53 ig 55 56 323 302 t 168 156 j 089 i ^ 082 , i 49 ^ '44 ^ 56 58 282 i 4 144 *75 ^ 040 ^ 58 S9 264 J, 4 134 [ 069 I ^ '37 aV 59 60 246 1 4 124 8 063 ! i 33 r'o 5 61 230 1 4 114 1 058 ! 030 i 61 62 215 I 106 s *53 j ^ 027 ^ 62 63 64 201 188 1 098 091 I 49 i 5o *45 ^ ' 02 5 41) 022 63 64 65 176 i . c> 084 041 020 g 1 ,, 65 66 164 77 078 13 038 i 019 gL 66 67 68 154 143 i 072 067 2 <0 35 & 32 ^ * OI 5 ^V S 69 134 | 062 Te 029 ^ 014 ^j 69 70 125 8 057 A 027 J f 013 Vr 70 72 117 109 T> 053 049 i O24 Jg 022 ^ ;oi2 ^ 100 72 73 TO2 To 045 i 021 ^L 73 74 096 J_ 10 042 i ' OI 9 4 009 -J- - 74 75 089 s 039 & ' OI 7 ^ 008 ^ 75 76 084 i 036 JL 016 ^ 007 ^T- 76 078 073 1 033 031 i 015 I3 ?V OO6 yiy 006 ^ a 79 068 TB~ 029 gL -012 ife OO5 77^ 79 80 064 s 026 31 " 9T 005 ^L 80 85 045 $ 018 5^ OO7 yig 003 3^3 85 90 032 3V 012 i 5 200 O 02 5^5 00 95 023 ^ 008 _i_ 3 353 ' l To^o 95 100 016 i 006 A 002 500 100 For Explanations and Examples, see pp. xviii. and xix. Tables continued on pp. xxxii.-xxxvii. INTEKEST TABLES Years PRESENT VALUE OF Years PRESENT VALUE OF One Pound 1 per Annum One Pound 1 per Annum I 8695652 8695652 51 0008024 6-6613171 2 7561437 1-6257089 52 0006978 6-6620149 3 6575162 2-2832251 53 0006068 6-6626216 4 57I753 2 2-8549784 54 0005276 6-6631492 5 4971767 3-35 2 i55i 55 , 0004588 6-6636080 6 4323276 3-7844827 56 0003990 6-6640070 7 3759370 4-1604197 57 0003469 6-6643539 8 3269018 4-4873215 58 0003017 6-6646556 9 2842624 47715839 59 0002623 6-6649179 10 2471847 5-0187686 60 0002281 6-6651460 ii 2149432 5-2337ii8 61 0001983 6-6653443 12 1869072 5-4206190 62 0001725 6-6655168 *3 1625280 5-583I470 63 0001500 6-6656668 14 1413287 5-7244756 64 0001304 6-6657972 '5 1228945 5-8473701 65 0001134 6-6659106 16 1068648 5-9542349 66 0000986 6-6660092 17 0929259 6-0471608 67 0000858 6-6660950 18 0808051 6-1279659 68 0000746 6-6661696 19 0702653 6-1982312 69 0000648 6-6662344 20 0611003 6-25933I5 70 0000564 6-6662908 21 0531307 6-3124622 71 0000490 6-6663398 22 0462006 6-3586627 72 0000426 6-6663824 23 0401744 6-3988372 73 0000371 6-6664195 24 0349343 6-4337714 74 0000322 6-6664518 25 0303776 6-4641491 75 0000280 6-6664798 26 0264153 6-4905644 76 0000244 6-6665042 27 0229699 6-5!35343 77 OOOO2I2 6-6665254 28 0199738 6-5335081 78 OOOOI84 6-6665438 29 0173685 6-5508766 79 0000l6o 6-6665598 30 0151031 6'5659796 80 0000139 6-6665738 | 31 0131331 6-5791127 81 COOOI2I 6-6665859 32 0114201 6-5905328 82 0000105 6-6665964 33 0099305 6-6004633 83 0000092 6-6666056 34 0086352 6-6090985 84 OOOOOSo 6-6666135 35 0075089 6-6166074 85 OOOOO69 6-6666205 36 0065295 6-6231369 86 OOOOO6O 6-6666265 37 0056778 6-6288147 87 OOOOO52 6-6666317 38 0049372 6-6337519 88 OOOOO46 6-6666363 39 0042932 6-6380451 89 OOOOO4O 6-6666403 40 0037332 6-6417784 90 0000034 6-6666437 4 1 0032463 6-6450247 9 1 OOOO030 6-6666467 42 0028229 6-6478475 92 OOOOO26 6-6666493 43 0024547 6-6503022 93 0000023 6-6666516 44 0021345 6-6524367 94 OOOOO2O 6-6666535 45 0018561 6-6542928 95 0000017 6-6666552 46 0016140 6-6559068 96 0000015 6-6666567 47 0014035 6-6573102 97 OOOOOI3 6-6666580 48 0012204 6-6585306 98 ooooon 6-6666592 49 0010612 6-65959I9 99 oooooio 6-6666601 50 0009228 6-6605147 100 0000009 6-6666610 For explanation see pp. xviii, 10, 12 (xl) INTRODUCTION ON THE NATURE AND USE OF DECIMALS IN order to render the following tables intelligible to persons only moderately acquainted with common arithmetic it may be well to /;ive a brief explanation of decimals, since most of the tables here given involve their use. Our entire system of numbering (if for the moment we leave fractions out of consideration) is, in fact, the decimal system, which means literally a system of tens, for if any number consist of a single figure say, 6 we call that number six that is, six units or six ones but if another figure a 4, for instance stand before it, making the number 46, we do not call this 4 four ones, but four tens, and thus regard the number as forty-six. In like manner if another figure 3, tor instance be prefixed making the number 346, we regard this 3 not as three ones, nor as three tens, but as three hundreds. In this way we give to every figure in a number ten times the value the same figure would have if it were moved one place more to the right ; so that the value of a figure depends upon its position. When we arc dealing with whole numbers the figure occupying the first place on the right denotes so many ones, the next figure so many tens, the next so many hundreds, and so on. This tenfold increase of value which every advance towards the left gives to a figure is properly called the decimal system of notation. Now what are more particularly called decimals are numbers that are less than unity, and they are dealt with on exactly the same principle as numbers that are more than unity, a decimal dot being placed to indicate what numbers are more than unity and what numbers are less than unity. Whether we are dealing with numbers greater or less than unity the value of a figure is ten times as much as the value of the same figure placed next to it on the right-hand side and one tenth as much as the value of the same figure placed (i) a INTRODUCTION next to it on the left-hand side. It is, therefore, just as simple to deal with decimals as it is to deal with whole numbers. If we see a number, such as 346, without any decimal dot we understand, as explained above, that the 6 stands for six ones, but if between the four and the six we place a decimal dot, 34*6, we then know that the four no longer stands for four tens, but for four ones, and the 6 no longer stands for six ones, but for six tenths of one. So if we write 3*46 the 3 no longer stands for three hundreds, but for three ones, the 4 for four tenths of one, and the 6 for six hundredths of one. The decimal dot, therefore, is simply employed to tell us where the ones come, for the figure immediately to the left of the decimal dot always stands for so many ones. If these uniform grada- tions by tens and tenths are kept in mind no difficulty will arise in dealing with the decimals. Decimals and Fractions From this it will be seen that any decimal may be converted into its equivalent fraction at once : we have only to write the decimal, removing the dot, for numerator, and to write for denominator i followed by as many cyphers as there are figures, or places, in the decimal. Thus : 0-6= 6 ; -06= 6 ... ; -006= JL; -42=-^; -423=^3 IO IOO 1000 IOO IOOO and so on. Every fraction too of which the denominator i is followed by cyphers may just as readily be written as a decimal, thus 3 =.3 ; _L = . o; ; _9_=.oo 9 ; 2463 =2 4 -6 3 , &c. 10 IOO IOOO IOO We have only to write down the numerator and to point off from the right as many decimal places as there are cyphers in the denominator, supplying this necessary number of places by cyphers immediately after the decimal point, should the number of figures in the nume- rator be too few. Fractions, whatever be their denominators, may also be converted into decimals, as will be seen presently. Addition of Decimals From what has been already said it will be seen that the important thing in the addition of decimals is to take care that the decimal dots all come under one another, just as in the addition of whole (2) USE OF DECIMALS numbers the units have to come under the units, the tens under the tens, and so on. If this point is attended to the matter is perfectly simple, and is conducted exactly like simple addition. A few examples are given below : 1. Add together 2-345, -64, 237, -02. 2. 7-4325 16-207, 'O2i, '4628. 3. -005, 61-4, -368, 7-2. (0 (2) (3) 2-345 7'43 2 '005 64 16-207 61-4 237 '021 -368 02 '4628 7-2 26705 24-1228 68-973 Subtraction of Decimals In subtracting decimals, as in adding them, the important thing is to see that the decimal dots come under one another, and if this is done the subtraction of decimals is carried out in exactly the same way as simple subtraction. A few examples of subtraction are also given : 1. Subtract 3*725 from 5-103. 2. 27-846 from 31-3. 3. -026 from 12-4. (0 (2) (3) 5' 10 3 3i'3 12-4 3-725 27-846 -026 3'454 12-374 In the third example of addition two cyphers appear immediately to the right of the decimal dot. These o's serve to indicate the position^ and therefore the value, of the figure to the right of them ; thus '005 indicates that there are no tenths nor hundredths, and that the five stands for five thousandths ; and similarly in the third example of subtraction -026 indicates that there are no tenths, but that the 2 stands for two hundredths and the 6 for six thousandths. Multiplication of Decimals It will have already been seen that we multiply a number involving decimals by 10 by simply removing the decimal point one place to (3) a 2 INTRODUCTION the right ; we multiply by 100 by removing the point two places to the right, and so on. Thus : 6xio=6; '6x100=60; *oo6xioo='6. 42 x 10=4*2 ; '42 x 100=42 ; 4*2 x 100=420. In order to multiply a number containing decimals by any whole number that is, by any number without decimals we proceed exactly as we should do if there were no decimals at all ; only when the product is obtained we must point off, as decimals, as many places as there are places pointed off in the number 24*623 multiplied. Thus, if we have to multiply 24-623 by 47, 47 we proceed as in the margin, and so in all similar 172361 cases. As the number multiplied has three decimal 98492 places, we mark off three places of decimals in the pro- 1157*281 duct. If we have to multiply together two numbers which both contain decimals we proceed as in simple multiplication, and place the decimal dot in the answer in such a position that the number of decimals is the same in the answer as in the two numbers when their decimal places are added together. Thus : 1*2X1*1 = 1*32; *I2 X *I2 = *OI44 j *222 X 3*1 =*6882 ; '033 X *22 = *00726. Division of Decimals In dividing a number containing decimals by a whole number we place the decimal dot in the quotient as soon as we bring down a decimal of the dividend. Thus to divide 27*344 by 4 we proceed as follows : - 6-836* After dividing 27 by 4 we come to the decimal -3, and so the decimal dot had to be placed between the 6 and 8 of the quotient. If we have to divide by a number that will not go into the decimal part of the dividend we must be careful to record the fact by putting a cypher in the quotient. Thus '372H-4 gives 4)'372 093 and 0372 ^4 giveo 4)337? 0093 (4) USE OF DECIMALS The values o f the 9 and the 3 depend on their position, and they must be put in their right place by prefixing cyphers to the left of them if necessary. Placing cyphers to the right of a decimal dot alters the value of the number. Placing cyphers to the right of a decimal number with no other number after the cyphers makes no difference in its value. With whole numbers it is just the opposite of this. Thus: '73= 73 ; -073= 73 ; -0073= 73 ; 73= 7 - 3 or 73 J 100 1000 1 0000 1000 100 These facts have to be borne in mind in the division of decimals. We may add as many cyphers as we please to the right of a decimal number, and so carry our division as far as we choose. Thus 4-3 7 may just as well be called 4-30000-1-7. It makes no difference in the value, but there is no need to actually write the cyphers in working out the sum. We may put 7)4-3000000 7)4- 6142857 -6142857' and the result is the same. The benefit of proceeding in this way is that we may get an answer that is more nearly correct than if we left off at the last figure of the dividend. Thus the result of 4-3-=- 7 is approximately , more nearly , still more nearly ^ , and so 10 100 1000 on. If both the divisor and the dividend contain decimals there must be as many decimal places in the divisor and quotient together as there are in the dividend. This is obvious from what has been said in regard to multiplication. It was there shown that 222 x 3- 1 = -6882, and so if we have to divide -6882 by -222 we have 222)-6882(3'I 666 222 m 222 There are three decimal places in the divisor '222, and four in the dividend -6882, so there must be one in the quotient 3-1 to add to the three in the divisor to make up the four in the dividend. In applying this rule it must be borne in mind that the number of decimal places in the dividend means the number actually used in division, and the number of cyphers added to it ranks as decimal places. Thus 8'973H--24 = 37'3 or 37-38 or 37-387 or 37-3875, as we may see. (5). INTRODUCTION 72 177 168 93 72 210 I 9 2 1 80 168 1 20 120 There are one, or two, or three, or four places of decimals in the answer, depending upon the extent to which we carry the division. Obviously the answer cannot sometimes be 37-3 ( i.e. 37 5. ), some- V io/ times 373 (i.e. 3 Z3 j } and so on : it must always be 37 and a little \ iooy more. Hence the number of decimal places used in the dividend have to be noted, and the number in the quotient added to those in the divisor must make up the number used in the dividend. Some examples of division are appended. (i) 44-406-7-12 (2) 44-406 ---i 2 (3) -44406 -4-1 -2 1 2 )44'4Q6 '12)44 '46o i 2 ) -444060 ._3'-7gl 370*05 '37005 (4) 89-648-347-3 ^9'648oooo 6946 20188 17365 28230 27784 4460 3473 9870 6946 29240 14560 13892 668 (6) USE OF DECIMALS For most of the purposes for which the tables in this book are likely to be used four or five places of decimals is amply sufficient, and it is unnecessary to carry the calculations any further. Fractions and Decimals We have already shown how readily decimals may be converted into fractions, and we must now show how fractions may be converted into decimals. We saw that a decimal may be thought of as a fraction with the decimal as numerator, and for denominator i followed by as many cyphers as there are decimal places in the decimal. Thus 'i =- 1 ; '23 = , and so on. Now it is obvious 10 100 we do not alter the value of any fraction if we multiply both the numerator and denominator by the same quantity. Thus 1 = 2 = 4 = = l , and so on. All these fractions are of the same 2 4 8 16 32 value. If, therefore, we multiply the denominator by a quantity that makes it equal to 10 or 100, or any other multiple of 10, and then multiply the numerator by the same quantity as we multiplied the denominator by, we at once get a fraction that can be converted into a decimal at sight. Thus i __ 5 _ . 2~~ 10 2 _ 4 5 ro ' It is often, however, a clumsy way of working to divide TO or some power of 10 by the denominator, and then multiply the numerator by the result. To do so may involve a long multiplica- tion sum. We therefore multiply the numerator by i followed by any number of cyphers we want and divide by the denominator. In other words, we divide the numerator by the denominator. Thus in converting 2 into a decimal it makes no difference in the result 5 whether we have 2 ~^ = 2 x 2 = ='4, or whether we have 5x10-7-5 5x2 10 But it makes a great deal of difference in the working whether in converting, say, '-- into a decimal we first divide i by 3736 and (7) INTRODUCTION multiply the result by 1868, or whether we divide 1868 by 3736 and get -5 as our answer at once. A few examples of converting fractions into decimals are appended. I--s;i 5;|-7s;|^*Si'i-^j|-* 2 4 4 o 33 These are useful fractions of which to know the corresponding decimals. A recurring decimal is marked with a dot above it, and means that it is repeated continuously. Where a group of several figures recurs it is marked with a dot over the first and last of the group. Thus 1 -= '33333 and as many more threes as we care to write. It is shortly expressed as '3. If we wish to convert into a decimal, we have 711 142857, which means that at this stage there is i over, and the numbers 142857 would be repeated indefinitely if the division were con- tinued for an indefinitely long time. Other examples are : 4| = 4'375; 7- 9 6 = 7-5625; IZ = -809523; ^='0375335+. INTEREST TABLES On pp. xx-xl and 50-124 Interest Tables of various kinds are given. Their construction and use is here explained, in order to facilitate their employment, and to make it possible for those unfamiliar with the subject to perform calculations at other rates and for other periods than those given in the table. Unless otherwise stated the tables throughout the book are calculated at compound interest, not at simple interest. Compound interest, of course, means that the interest as it becomes due is added to the original debt, and the interest for subsequent periods is calculated on the original debt increased by all the previous accumulations of interest. The Amount of i On pp. 50-85 are tables which show for various rates of interest (i) The sum which i will amount to in any number of years from i to 100. (8) THE AMOUNT OF 1 (2) The present value of i due at the end of any number of years from i to 100. (3) The sum to which i per annum will amount in any number of years from i to 100. (4) The present value of i per annum to be received for any number of years. We will consider these in the order stated, taking our illus- trations principally from the 4 % table on pp. 70 and 71. It will be convenient to give the explanations by quite simple algebra first, and then to give the arithmetical explanations or numerical examples. If by / we represent the rate of interest, it is clear that one pound, or one dollar, or any other unit, will amount in one year to i +/; and if we represent the amount by s, we have s = i +/*. If the rate of interest is 4%, or 4 on one hundred, it is '04 on a unit and !+/= 1-04. At the beginning of the second year, if the interest has not been paid, the loan or investment, s, is i + /*, = i "04, and the interest on this is / (i +/), = 1*04 x "04 = '0416. To find the amount at the end of the second year we must add the second year's interest to the amount at the beginning of the second year. Thus we have (i + 1) + i(i + /) = (i + z) x (i + /') = (i 4- *) 2 > or I>0 4 + (*4 x r 4) = i '04 + "0416 = 1*0816 = 1*04 x 1*04 = i*o4 2 . We begin the third year with s = (i -f-/)(i-fz'), and the interest for the third year is this amount multiplied by t = i(i + *)(i+/), and, adding this to the amount at the beginning of the third year, we have(i -M')(i + t)(i + i) = (i + O 3 , = i'o8i6 + ('04 x 1*0816) = 1*0816 -f '043264= 1*124864 = i*o4 3 . Thus the amount of one in any number of years, , is the amount of one in one year raised to the n th power. This is expressed as ( i+/')", and, if ? = 'O4, then (i +/)" = 1-04*. If = 5 this is ixx^A This may be seen below. Amount at Beginning Year of Year Process Amount at End of Year I I XI '04= I '04 = I '04 2 1*04 x 1*04 = i*O4 2 = i'o8i6 3 1*0816 X 1*04= 1*04*= 1*124864 4 1*124864 x 1*04= i *04 4 = 1*16985856 . 5 1*16985856 x 1*04= rc>4 5 = 1*2166529024 This tells us the amount of i, and, if we want to know what any other sum comes to, we must multiply the sum by the amount of i. What is the amount of ^,17 in five years' at 4%? (9) INTRODUCTION The amount of The amount of is therefore We might get this result more exact by using more places of decimals. Thus, 1-2166529024 x 17 = 20-6830993408, which is 0000493408 more than we previously had. The difference is less than 5 - of -XT i, which is ^ of a shilling, or almost r of a 100000 1000 20 farthing. This shows that five places of decimals, as given in the tables, give results quite near enough for most purposes. It is explained later on (pp. 206-228) how easily a table of this kind can be constructed by means of logarithms the practical use of which is extremely simple, and if other rates of interest than those tabulated are needed they should be obtained by logarithms. It should be noted that the table gives the amount of one pound at the end of the year, i.e. just after the year's interest has been added. The amount at the beginning of any year is the same as the amount at the end of the preceding year. Before explaining some of the uses of these tables it will be best to explain the contents of the other columns on these pages. We at present assume that the interest is reckoned annually, but later on we shall consider the case of interest convertible half-yearly and at other intervals. The Present Value of i If, as we have seen, i amounts to ^1*04 in one year the present value of this i'o^ is obviously i. In other words, i invested now at 4% will amount to ^1-04 in one year. But if the present value of , 1-04=1 the present value of i := * , and using v to represent the present value of i one year 1*04 hence we have v = ., and v" = j~ . , where, as before, n i + * (i -M)" represents the term. If /= '04 and n = 5 we have Whatever the term may be .+,-=! V V (l + *)=! (10) THE AMOUNT OF i PER ANNUM Thus to take 10 years at 4 % 1 .= I __ = -67556 = i+z 1-48024 i + /= i -48024= * = 1 67556 v v(i+ /)= 1-48024 x -67556= '99999 By calculating the values of * and v to more places of decimals we may obtain as close an approximation as we please to i by multiplying #by (i -f i). To find the present value of any other sum than i we multiply the sum by the present value of i for the number of years required. Thus, the present value of ^83 due at the end of 10 years at 4 % is 67556x83=^56-07148. It will be noticed that the table of present values, like the table of amounts, refers to the end of the year. See also pp. xviii, 218. The Amount of i per Annum The third table on each page gives the amount of i per annum immediately after each annual payment is made. Thus the first line is in all cases i-ooooo. This table may be found from the amount of i by a series of additions. Thus at 4 %, if to the initial payment of i we add 1*04000, the amount of ^i in one year, we obtain 2-04000, which is the amount of i per annum immediately after the second annual payment has been made. If to this amount we add 1-081 60, the amount of i at the end of the second year, we obtain ^3*12160, the amount of ) \ per annum immediately after the third annual payment has been made. We can, however, obtain the result in another way. The amount of i in five years at 4 % is 1-21665, f which amount i was the original payment and -2 1665 the accumulated interest. Now i yields 04 every year at interest at 4 %, therefore the amount of -04 per annum for 5 years is "21665. But if *4 P er annum amounts to 21665 i n 5 years "01 per annum will amount to one fourth of this sum, which is -054163, and i amounts to 100 times this sum, which is 5-41632, which we see to be the amount of i per annum in 5 years. Hence it follows that we can obtain the amount of i per annum by subtracting unity from the amount of i and dividing the result by the rate of interest. Hence we get the following expression : - where s n is the amount of i per annum in n years, /' is the rate of interest, and (i + i) n is the amount of i in n years. (n) INTRODUCTION To find the amount of any other sum for any number of years we take from the table the amount of i per annum at the rate of interest and for the number of years required, and multiply this amount by the sum with which we have to deal. Thus the amount f lS P er annum for 30 years at 4 % = ^56*08494 (p. 70) x 75 = ;42o6'37o5. For further details see p. 224. The Present Value of .1 per Annum By similar reasoning we see that the present value of i per annum may be obtained from the present value of i that is to say, by a series of additions the present value of i per annum can be obtained from the present value of i. It may also be obtained by a second method similar to the second method of finding the amount of i per annum from the amount of i. Thus the present value of i at the end of 10 years is '67556, and the difference between this amount and unity is '32444, which is the present value of '04 per annum for 10 years. The value of -01 per annum is one fourth of this amount, which is "08111. The present value of i per annum is 100 times this amount, viz. 8"in, which is seen (p. 70) to be the present value of i per annum for 10 years at 4 %. It will be noticed that the present value of i per annum for 10 years is stated to be 8 - i 1090, not 8"i 1 1. This slight discrepancy is due to the fact that the present value of i is only given to five places of decimals. If we calculate the present value of i due at the end of 10 years at 4 % to six places of decimals instead of five we find that it comes to '675564. Subtracting this amount from unity we obtain -324436, which divided by 4 and multiplied by 100 gives us 8-11090 as the present value of i per annum for 10 years, which is in accordance with the table. This relation between the present value of i and i per annum may be expressed by the formula where a^ is the present value of i per annum for n years, v n is the present value of i due at the end of // years, and / is the rate of interest. A knowledge of the methods by which the tables are constructed greatly facilitates their use. Hence in all cases we first describe the construction of the tables and then give some account of the purposes to which they may be applied. See also pp. xviii, 222. The table giving the present value of i per annum is applicable to many different purposes. Thus if we want to know the present value of an annuity, or pension for a definite number of years- the (12) PRESENT VALUE OF A PERPETUITY value, that is to say, of what is called an 'annuity certain,' or the value of a lease, or of any other property yielding a fixed and certain yearly income, we can readily obtain it from this table. Thus a lease, or annuity, yielding i per annum, with 25 years to run, if purchased for ^15*62208, would yield the purchaser 4% on his money and replace the capital by the end of 25 years. If the annuity were ^10 a year its value would be ten times as much ; if 20 a year, twenty times as much, and so on. We sometimes want to know what rate of interest will be yielded by purchasing an annuity for a given amount at a certain price, which may not be exactly any rate of interest that is here tabulated. In order to ascertain this we must see what an annuity of i per annum would cost at the same price, and then turning to tables at various rates we shall be able to see approximately what rate the investment would yield. Thus, if we buy an annuity of 30 a year, for 20 years, for ^450 we see that an annuity of i per annum at the same price would cost .15. A reference to the tables on pp. 64 and 66 shows that this is less than we should pay to yield 2^ % on the investment, and more than we should pay to yield interest at 3% ; but the return would be more nearly 3 % than 2 J% being, in fact, a trifle over 2^%. It is sometimes convenient to be able to see the results at different rates of interest in this way ; consequently on pp. 86-93 abbreviated tables showing the amount and present value of i and of ^i per annum are printed. These are only extracts from the tables on pp. 50-85 arranged in a different form with a few other rates of interest added. The Present Value of a Perpetuity On p. 94 is given the present value of a perpetuity of i per annum for every % up to 10 %. These results are obtained by dividing 100 by the rate of interest. From this table the value of freehold property, advowsons, &c., can be obtained, it of course being necessary to ascertain the net annual value of the property on which to base the price to be paid for it. Thus a freehold yielding ;8o per annum, after deduction of all expenses connected with it, would yield 4 %, if purchased for ^2,000, for 25 x 80 = 2,000. If the same property were purchased for ^1,800, which is at the rate of ^22 i os. (for 1,800-^80= -2 2-5) for each i per annum, the yield upon the capital invested would be between 4$ and 4^%. Present Value of Reversions On pp. xxxii-xxxix and 95-98 is given the present value of a Rever- sion to a Perpetuity of^i. On p. 94 we have the present value of a (13) INTRODUCTION perpetuity to be entered upon immediately, and on pp. xx-xxxi and 50-85 we have the present value of an annuity for any number of years from i to TOO. By subtracting the present value of an annuity for a certain number of years from the present value of a perpetuity we obtain the present value of a perpetuity deferred for that certain number of years. Thus we see that the present value of a perpetuity of 1 per annum at 4% is "25 (p. 94). The present value of an annuity of i per annum for 20 years at 4% is ^13*59033 (p. 70). Deducting this amount from ^25, we have ^11*40967 as the present value of the Reversion after 20 years of a Perpetuity of i t which is the amount given on p. 98. The present value of a per- petuity of any other amount than i is obtained by multiplying the value of a perpetuity of i by the amount of the perpetuity the value of which it is desired to obtain. Commutation of Fines for Renewing Estates Estates held in perpetuity are sometimes subject to a renewal fine to be paid by the holder at regular specified intervals. These periodical fines may be compounded for by a single payment down. The first table on p. 99 shows what this payment ought to be, so that the holder of the estate may redeem all these continually recurring fines and at the same time be allowed such interest upon the money thus paid in advance as may be agreed upon. Thus if the renewal fine is payable every 7 years for ever then the redemp- tion money to bear 5 % interest is found by the table to be 2-4564. This means that 2 '45 64 must be paid to redeem a fine of i pay- able every 7 years. To redeem a fine that is equivalent to one year's rent a sum equal to 2-4564 times the annual rent must be paid. It is obvious that the redemption money must be that sum the interest upon which, if allowed to accumulate at compound interest at the rate agreed upon for the period between the fines, will just suffice to pay the fine. A reference to p. 74 shows that the amount of i for seven years is ^"1-40710. Deducting from this amount the original i invested, we see that the interest on i invested for 7 years is ^-40710. If now we multiply -40710 by 2-4564, the amount required to redeem a fine of i payable every / years, reckoning interest at 5 %, we have -40710 x 2-4564=1. Thus it will be seen that in every 7 years the interest on the redemption money amounts to exactly enough to pay the fine. Renewal of any Number of Years Expired in a Lease The second table on p. 99 and the tables on pp. 100-103 show the number of years' purchase for the renewal of any number of years (H) RENEWAL OF LEASES expired in leases of various length. A reference to p. 70 shows that the present value ofi per annum for 10 years is ^8-11090, and on p. 99 we see that the amount to be paid for the renewal of a 10 years' lease is this same sum of ^8* 11090, which may be read as either ^8-11090 for every i of income annually derived from the lease, or as 8-11090 years' purchase of the annual income from the lease. But if we own a lease that has, say, 5 years to run and we want to convert it into a lease that has 10 years to run, it is obvious that we must pay something for the extension of the lease. Reckoning interest at 4 % we have just seen that the value of a lease for 10 years is 8-11090 times its annual value, and another reference to p. 70 shows that the value of the 5 years' lease we at present possess is ^4-45182 for every i of annual income ; in other words, the value of the 5 years' lease we hold is 4-45182 times the annual value of the lease. Deducting this value of the 5 years' lease we own from the total value of the 10 years' lease we wish to obtain, we have 3-65908 as the number of years' purchase to be paid for extending our 5 -year lease into a lo-year lease. We could obtain the same result from the table on p. 70 showing the present value of i instead of the present value of i per annum. We are obviously entitled to the benefit of the lease for the next 5 years, and the additional benefit we have to pay for by having the lease extended to 10 years is equivalent to the present value of i due at the end of 6 years = 79031 l 7 =75992 * >, 3 =-73069 i 9 =70259 1 I0 Total . . . 3-65907 This gives us ^3*65907 as the present value of i per annum for the 6th to the loth years, or 3*65907 years' purchase of the annual value of the lease, and is the same result as we obtained before, except that the last figure is a 7 instead of an 8, which is due to the number of decimal places to which the calculations were carried not being sufficient to produce absolutely identical results. The tables referring to the Renewals of any number of years in leases for 20, 21, and 40 years are calculated in the same way, and the renewal of leases for different times, or at other rates of interest than those given on pp. 99-103, may be readily calculated from the present value of i per annum given on pp. 50-85 by subtracting the present value of i per annum for the number of years the lease we own has to run from the present value of i per annum for INTRODUCTION the number of years for which the fresh lease will be granted. It will be noticed that the last column in the table dealing with the 10 years' lease is headed 17*95 % ; m tne 20 years' lease 12-304 % ; in the 21 years' lease 11-564 % ; and in the 40 years' lease 8%. These rates of interest are respectively equivalent to a fine of i year's rent every 4, 7, 7, and 14 years. The extraordinary rates of interest here referred to result from customs that must presumably have originated from ignorance of the real rates of interest involved. Yield per cent, and Years' Purchase The percentage per annum which each number of years' purchase of a perpetuity yields to a purchaser is obtained by dividing 100 by the number of years' purchase. The results are given on p. 104. Interest, Amount, and Discount On p. 105 are shown the interest, amount, and discount of i in a year, and in 9, 6, and 3 months. The interest is calculated annually, and consequently in 9 months it is J of the interest earned in a year ; in 6 months ^, and in 3 months ] of the annual interest. The * amount ' of i is simply the addition of the interest to the original 1. Were the interest to be calculated at other intervals than that of i year the figures here given would be different, as we shall see (p. 18) when we come to refer to the question in detail. Discount is the value at the beginning of a period of the interest to be received at the endin other words, discount is the interest paid in advance. Thus the present value of i due at the end of a year, reckoning interest at 4 %, is ^"'96154 (p. 70). The value of i now due is, of course, ^i, and the discount is the difference between these two amounts, which is ^'03846.; that is to say, if we owe an amount of i which is due to be paid one year hence, and, to suit the convenience of a creditor, we pay it twelve months in advance, we ought to be allowed a discount of ^'03846 ; that is to say, we should pay ^-96154 now instead of paying i a year hence. This is obviously fair, since if we invested the ^'96 154 at 4 % for a year it would at the end of that time amount to the t we should have to pay. Sinking Fund On pp. 106-115 is given the annual amount to be set aside and invested in order to replace the capital at the end of the selected period. This table is obtained by dividing unity by the amount of one pound per annum, as given on pp. 50-85. Thus, comparing the amount of i per annum at 4 %, as given on p. 70, divided into unity with the Sinking Fund in the 4 % column on p. 112, we have tor . (16) SINKING FUND Year i, i 10, i 20, i I '00000 = I'OOOOOO , I2"oo6n = "083291 ; 2977808 = -033582 ; 30,1 56-08494= -017830. This may be stated the other way about, and we may say that ^08329 i per annum accumulated for ten years at 4 % amounts to i, or -083291 x 12-00611 = i. In this table no provision is made for paying interest on the capital. If this has to be done the amounts given in the sinking fund table must be increased each year by the interest on 1. Thus to repay i in ten years, and to pay interest annually at 4 %, needs an annual payment of -083291 -f "04 = -123291. Of this amount -04 pays the interest each year, and "083291 accumulated at 4 % replaces the original i invested. If we take -123291 and accumulate it at 4 %, we find that in ten years it amounts to -123291 x 12-00611 = 1-48024, which, from p. 70, we find is the amount to which ^i amounts in ten years at 4 % if the interest on it is allowed to accumulate instead of being drawn annually. In using this table care must be taken to notice whether the purpose for which it is required calls for interest on the original investment to be paid annually or not. See pp. 225 and 219. If the purchaser of a leasehold property wishes to set aside out of the net rent received sufficient to replace the purchase price by the time the lease expires, the table must be used as it stands, the difference between the net rent and the sinking fund constituting the interest on the purchase price of the lease. If, on the other hand, a loan has to be repaid, say, in TO years, with interest at 4 %, either the interest on the loan must be paid annually, in addition to the sinking fund as given in the table, or 04 must be added to the sinking fund for every i borrowed, and allowed to accumulate with it. If the interest is at i % there must be an addition of *oi to the annual sinking fund for every \ borrowed; if at 2 % an addition of "02 ; if at 5 %, of "05 ; if at 10 %, of -i ; and so on. INTRODUCTION Value of Annuity to Yield Interest on Capital at One Rate, and Replace Capital at a Lower Rate On pp. n6-i2ifare given the annual payments required to pay interest at comparatively high rates, and to replace the capital by a sinking fund accumulating at a lower rate. From p. no we learn that -087231 per annum at 3% for 10 years will amount to i. But if we have to pay 5 % per annum upon the i we must add '05 to the sinking fund payment of "087231. These two amounts come to 1 37 23 1, and would suffice, if paid annually for 10 years, to pay 5 % per annum on the original loan of i, and to replace the"i by accumulation at 3 %. The present value of this annuity of '137231 on these terms as to interest is therefore obviously 1. But if the value of an annuity of .'137231 is 1, the value of an annuity of i is - - =7-287, which, on reference to p. 120, we see to be the value of an annuity of i yielding interest on capital a ^ 5 %> and replacing capital when invested at 3 %. These terms are very onerous to the borrower, since he has to pay interest at a high rate on the whole capital for the whole term, although by the accumulation of the sinking fund the capital may be rightly considered as partly repaid. These tables may be readily extended to other periods and rates of interest by taking the reciprocal of the amount obtained by adding to the sinking fund payment the annual interest on the loan. The reciprocal of a number is obtained by dividing unity by the number. The value of an annuity of any other amount than i per annum is obtained by multiplying the figures in the table by. the amount of the annuity. See also p. 226. Nominal and Effective Rates of Interest On p. 122 is given a table comparing nominal and effective rates of interest. This subject is a somewhat intricate one, but the main principles underlying it may be grasped without much diffi- culty. Hitherto we have been considering that the rate of interest was calculated annually. We now have to deal with the case of interest calculated half-yearly, quarterly, and monthly. Suppose the nominal rate to be 4 % per annum ; it will obviously be 2% for 6 months, and at the end of the first half-year an original investment of t will amount to 1*02. For the second half-year interest at the rate of 2% for every 6 months is now earned upon "1*02 instead of upon onlyi. This brings the amount of the original investment at the end of the second half-year to 1-0404 instead of (18) NOMINAL AND EFFECTIVE RATES OF INTEREST to only ;Vo4, which is the amount it would have been if the inte- rest had been calculated annually instead of half-yearly. A reference to p. 58 will show that this is the amount that i amounts to in 2 years at 2 %. Hence we see that if we want to calculate interest at more frequent intervals than i year we can divide the nominal rate of interest by the number of periods (at which interest is to be calcu- lated) that are contained in a year, and take the interest for this number of years at the resulting rate of interest. In other words, we see that instead of talking about years we can talk about periods, and if we want to talk about interest that is nominally 4 % per annum, but really 2 % for 6 months, or if convertible quarterly i % for 3 months, we may turn to a 2 % table and look at the result after 2 periods and a i % table to find the result after 4 periods. Thus on p. 50 we see that i accumulated for 4 periods at i % amounts to ; 1*0406, the interest being ^-0406, which is the effective annual rate when interest is convertible quarterly, shown on p. 122 as corresponding to a nominal annual rate of 4%. The same thing holds if interest is convertible monthly. The amount of ^i accumulated for 1 2 periods, whatever their length, at ^ % per period, would amount to ^"1-061678, and -061678 is shown on p. 122 to be the effective annual rate when interest is convertible monthly, if the nominal rate is 6 % per annum. The lower part of the table is the converse of the upper. If the real or effective rate is 4 % per annum the nominal annual rate, when interest is convertible half-yearly, is ^"'039608, or 019804 per half-year. Thus i for 6 months at -019804% per 6 months amounts to ^1-019804. During a second period of 6 months this amount at the same rate of interest earns '020 196, which added to the ^1*019804 makes up ;i'04, which is equi- valent to the amount of i at an effective annual rate of 4 %. The higher the rate of interest and the more frequently the interest is convertible the greater is the difference between the effective and the nominal rates. See Preface to 26th Edition. Annuities Payable Half-yearly, Quarterly, and Monthly If we are entitled to receive an annuity of i per annum, payable yearly, but, instead of receiving it annually, receive it every 6 months, we obviously receive the amount of the half-yearly payment sooner than we are entitled to; and if that half-yearly payment were invested for 6 months, the 2 half-yearly payments, together with this 6 months' interest on one of them, would amount to more than the annual payment to which we are entitled supposing the half- yearly payments were exactly half the yearly payment. That is to say, if the annuity to which we are entitled annually is divided into 2, or (19) b 2 INTRODUCTION 4, or 12 equal parts, and paid half-yearly, quarterly, or monthly, its capital value is greater than if the annuity were paid annually. As a concrete instance of this we have, on p. 123, the value of an annuity of i per annum for 25 years at 4%. If the annuity is payable annually and the interest convertible annually, the present value or the annuity is ^15-62208, which is the figure given for its value on p. 70, as also on p. 123. To find the value of an annuity of los. every 6 months for 25 years at 4% we multiply ^15*62208 by 1^0099, tne factor given in the upper table on p. 123. This gives us 1577677 as the value of an annuity of los. every 6 months for twenty-five years, reckoning interest at 4 % per annum. Similarly an annuity of i per annum payable quarterly that is, 5.?. every three months is worth 15 '6 2 208 x i '01488, or 1$ '85449. The value of an annuity payable monthly is calculated on similar principles, the constant factor by which to multiply the value of the annuity payable yearly being 1*0182. If the interest is convertible half-yearly, and the annuity payable half-yearly, we can obtain the value of the annuity from the tables on pp. 50-85, by considering that we have an annuity of one-half per period for 50 periods at 2 % instead of an annuity of i for 25 periods at 4%. A reference to p. 58 shows us that the present value of i per annum for 50 periods is ^31*42361, the half of which is ;i5'7ii8o, which is the value given in the middle table on p. 123 for an annuity payable half-yearly when the interest is con- vertible half-yearly. Similarly an annuity of $s. every three months at 4 % per annum convertible quarterly, which is i % every three months, is J of ^"63-02888, which on p. 51 is seen to be the amount of i per annum for 100 periods at i %. Now ; 63'02888-7-4= ^15-75722, which on p. 123 is seen to be the value of an annuity for 25 years at 4 % payable quarterly, with interest convertible quarterly. This subject is dealt with and the appropriate formulae given in the ' Theory of Compound Interest and Annuities ' by Fdor Thoman.* Present Value and Discount The bottom table on p. 123 gives to 9 places of decimals the present value of i due one year hence, which has already been given to fewer places of decimals on pp. 50-85, and explained on p. 10. The discount has been given for most rates of interest, but fewer places of decimals, on p. 105, and explained on p. 16. No further explanation is therefore necessary here, but for some pur- * London : Crosby Lockwood and Son. (20) DECIMALS Ol< ONE YEAR poses it is convenient to have these items calculated with greater approach to accuracy, as is here done. Time in which an Amount Doubles at Interest On p. 124 is stated the number of years in which an amount is doubled at simple and compound interest. At simple interest all we have to do is to divide 100 by the rate of interest ; thus, ^100 at 4% yields ^4 per annum, and dividing 100 by 4 we obtain 25 years as the time it will take for the interest to amount to the same as the principal, or, in other words, double the principal. At compound interest we obtain the number of years in which the interest will amount to the capital approximately by dividing '69 by the rate of interest, and still more nearly by dividing '693 by the rate of interest and adding -35 to the result. Thus 93 + '35 = *5 Decimals of One Year On p. 124 are given the decimals of i year, representing various numbers of weeks, months, and days. From what has been said on p. 7 it will readily be apparent how these figures are arrived at. There being 52 weeks in a year, 13 weeks, for example, is obviously -^ of a year. To convert the fraction * into a decimal we divide 52 52 13 by 52 and find that it goes '25 times. We assume the year to contain exactly 52 weeks, exactly 12 months, and exactly 365 days, the con- sequence being that though the figures given are right for practical purposes they are not entirely accurate. There are more than 52 weeks and more than 365 days in a year, while no calendar month is exactly r of a year. If we meet with the decimal of a year different from any given in the table, and desire to know how many weeks, or months, or days it corresponds to, we must multiply by 12 to get the answer in months, multiply by 52 to get the answer in weeks, and multiply by 365 to get the answer in days. Decimals of i On pp. 125-128 is given the decimal corresponding to every farthing in the i. The first and last columns on each page give (21) INTRODUCTION the pence and farthings up to nf<, while at the top of each of the other columns the shillings are stated to which the figures in the columns refer. Thus if we wish to know the decimal corresponding to 4-f. $d. we look in the column marked 45". on the line marked 3^., and find that the required decimal is "21250. Again, if we want the decimal corresponding to 13^. i\d. we look on p. 127, column i$s., line 7j an <* on the life aged 60 ^"10-491, the value of the two together being ^30-047. To pay these annuities would involve paying 2 per annum so long as both persons were alive, and \ per annum to the survivor of the two. But the annuities we are now considering, those given on p. 172, only require i per annum to be paid during the joint continuance of the two lives, and (30 INTRODUCTION ^i per annum to the survivor of the two. The difference between these two arrangements is, therefore, i per annum during their joint lives, and from the joint life annuity tables on p. 157 we know the value of this to be y 529. Hence we get the rule that to find the value of an annuity on the survivor of two lives we must take the value of an annuity on each of the single lives, and deduct from the sum of these two the value of an annuity on the two joint lives. Thus according to the Carlisle Table at 3 % the value of an annuity On a life age 50 is (p. 140) . . . 14*303 On a life age 70 is (p. 141) .... 7*123 On the two single lives is .... 21*426 On the joint lives is (p. 157). . . . 6-338 During the continuance of either of the two 1 .... > i ^'oob lives is (p. 172) ] In this way survivorship annuities for other ages and by other tables than those given on pp. 171-173 may readily be arrived at. The single payment to secure ;i at the death of the last of two lives is given on pp. 174-176. These amounts, like so many others, may be at once obtained by means of premium conversion tables. The same remark applies to the annual payments to secure the same benefit, which are given on p. 177, it being noted that the annual payments have to be continued during the continuance of either of the two lives. Reversions to Perpetuities On p. 178 tne values of the Reversion to a Perpetuity on the death of the first and on the death of the last of two lives are given. It has already been explained (p. 28) how the value of a reversion to a perpetuity on the death of a single life may be obtained. Where two lives are concerned the process is exactly the same. Thus at 4 % the value of a perpetuity to be entered upon imme- diately is (p. 94) ^"25 ; the value of an annuity during the joint continuance of two lives, each aged 60, according to the Healthy Males Table at 4 %, is ^6779. Deducting this amount from the previous one we have (25*000 6779 ) ; 18-221, which is the amount given in the upper table on p. 178. Similarly the value of an annuity during the continuance of either of two lives, each age 60, is, according to the Healthy Males Table at 4 % (p. 173), ^"12-139. Deducting this from the value of a perpetuity to be entered upon immediately, we have (25-000 12-139 = ) 12-861, which is the amount given in the lower table on p. 178. (32) REVERSIONARY ANNUITIES Reversionary Annuities In the upper table on p. 179 we have the value of an annuity during the life of y after the death of x. Thus, suppose a father to be age 45 and his son to be age 20, this table tells us the present value of the annuity to be entered upon by the son on the father's death and to continue during the time that the son survives the father. The value of the annuity on the son's life only is, by the Carlisle Table at 3 % (p. 140), ^21-694. The joint life annuity is (p. 157) ^14-207; the difference between the two 15^7-487, which is the amount given on p. 179 as the value of an annuity during the life of y aged 20 after the death of x aged 45. Owing to the facility with which this calculation can be made it is not worth while to give in the tables more than a few examples of the results. In the lower table on p. 179 we have the value of an annuity during the life of y t who is to be nominated at the death of x. In the preceding case y is supposed to be alive now, and there is, of course, the possibility that he may die before x t with the result that he would never come into the annuity at all. In the present case, however, we have the certainty that y will be alive at the death of x. Thus, suppose we wish to ascertain the value of a next presentation to a living, we may take the age of the person to be presented at 25, and suppose the present incumbent to be 45 ; then the problem is to find the value of an annuity on the life of a man aged 25 who is to be nominated at the death of a man aged 45. According to the Carlisle Table at 3 %, the present value of i to be received at the death of a man aged 45 is (p. 146) ,'50885, and the value of an annuity on a life aged 25 is (p. 140) ^20-665. This, however, is the value of an annuity the first payment of which has to be made one year after purchase, but it is here supposed that the annuity is to be entered upon immediately, so that the first annuity payment of i must be added to the value of the annuity on the life aged 25, making it 21-665. The present value of this sum, payable at the death of a life aged 45, is therefore 21*665 x -50885 = 11-024, which is the amount given on p. 179 as the value by the Carlisle Table at 3 % of an annuity during the life of y, aged 25, who is to be nominated at the death of x, aged 45, y, of course, being supposed to enter on the annuity immediately after the death of x. In using a next presenta- tion to illustrate the point it is not implied that next presentations can now be sold. It may, however, at times still be useful to calcu- late their value, while in connection with appointments, leases on lives, and certain other kinds of property it may be convenient to know how to calculate the values of annuities on successive lives. (33) c INTRODUCTION Contingent Assurances On pp. 1 80 and 181 we have the single payments to secure i at the death of x provided he dies before y. This is a somewhat more complicated matter to calculate than any that we have dealt with pre- viously. To obtain it we must take the single premium for joint life assurance on the two lives, and add to it the value of an annuity on two joint lives, one a year younger than x t the other of the age of y, divided by the probability of a life one year younger than x living one year. Then take the value of an annuity on two joint lives, one the age of x, the other one year younger than y, divided by the chance of a life one year younger than y living one year, subtract this result from the former result, and divide by 2. This process may be more clearly apprehended by the following formula and example : vrhcre A^ = the single premium for an assurance on the life of x provided y be then alive. AJJ, = the single premium for an assurance payable at the first death of x or y. a x . y = the value of a joint life annuity on .v and y. p x = the probability of a life age x dying within a year. As an example let # = 30 and ^ = 50, and let us employ the Healthy Males Table with interest at 3 %. Then : 168) -6077 A-x A 9 By addition = 13*2161 -984780 By subtraction = o'2C6o Divided by 2 0*1430= Ai tf which is the amount given on p. 181. In the above example the values p x _^ or / 29 and /> a _ t or p 49 are found on p. 134, and of A xy on p. 168. The values of a x ^. y and a xi V -a = #29-50 and a ZJ .^ are not given in this book. U) ANNUITIES ON THREE LIVES Annuities on Three Lives On pp. 182 and 183 the values of annuities for the joint con- tinuance of three lives are given. Full tables for annuities on three lives would be very extensive, and it is therefore generally necessary to obtain them from the values of annuities on two joint lives by some such method as the following : Take the present value of the annuity on the joint lives of the two oldest, and find at what age the present value of an annuity on a single life will be equal thereto; the value of an annuity on the joint lives of the youngest of the three lives and the life of the age just found will be approximately the value of the annuity on the three lives. In general we shall be nearer the truth if we subtract 05 from the value just found. The two-life tables given in this book are not sufficiently full to enable the calculation of three-life annuities to be made in very many cases. On p. 184 is given the value of an annuity during the longest of three lives. The values are obtained by adding together the values of the annuities on each single life, and subtracting from the sum the value of the annuity on each pair of joint lives, then adding the value of the annuity on the three joint lives. In this table, as in the previous one, complete tables of annuities on two joint lives are necessary to enable these values to be calculated. Premium Conversion Tables Pages 185 and 186 contain short Premium Conversion Tables, by means of which the single and annual premiums to secure ^i at death may be found by inspection. On p. 142 we see that according to the Institute of Actuaries Table at 3 % the value of an annuity on a life aged 40 is ^17-176, and on p. 148 we find the single payment to secure i at death is ^"-4706. This latter value may readily be found from the Single Premium Conversion Table on p. 185. Re- ferring to the 3 ( % column, we find that the single premium corre- sponding to an annuity value of i 7 is ; '47573. The difference in the single premium corresponding to the decimal part of the annuity- value is found from the lower table on p. 185, and must be subtracted from the premium corresponding to the annuity value of ^17. The difference corresponding to i = '00291 07 = '0204 006 = '017 'OOO2 = 'I J_76j = -005 1 3 (35) c 2 INTRODUCTION We thus have the single premium corresponding to an annuity of ^17 = '47573 Subtract difference = '005 1 3 Single premium for annuity of i 7 i 762 = "47060 which is the amount given on p. 148. The differences, as can be seen from the above example, vary with the position of the figures in them in relation to the decimal point. Thus at 3 % : The difference for 'i is -00291 for 'oi it is "000291 for *ooi it is '0000291 and so on. The explanation of this connection is very simple. The annuity value designated a gives the present value of i per annum on the supposition that the first payment of the annuity has to be made one year hence, and that the last payment is to be made on the anniversary of the first which immediately precedes the death of the annuitant. If, however, one further annual payment is to be made after the death of the annuitant, and we know the value of an annuity on these conditions, the difference between the value of an annuity with the last payment before the death of the annuitant and that of an annuity providing for one payment after death will give the value of i to be received at death. The value of an annuity providing for this one extra payment is obtained by taking the present value of i + a due one year hence, which may be ex- pressed by the formula v (i + a\ where #is the value of \ due one year hence. Clearly, after the first payment has been made on such an annuity as this, there still remains the same number of payments to make as under an ordinary annuity. Therefore, if we know the present value of the first payment of \ which has to be made one year hence, and the present value of an ordinary annuity one year hence, we have the value of an annuity providing for one pay- ment after the death of the annuitant. Using the same example as before, we have : a = 17-1762 (see p. 142) i + a = 18-1762 v = -97087 (see p. 123} v (i + a) = 18-1762 x "97087 = 17-6468 Deducts 17-1762 v (i + a) a = '4706 (36) PREMIUM CONVERSION TABLES This amount ^"-4706 is the single premium to secure i at death given on p. 148. This table may be used to find the single premium for assurance on single lives, joint lives, the last survivor or survivors of any number of lives, and on successive lives ; but not for contingent assurances. The single premium for the assurance of \ at death may very easily be found from the annuity value by a quite simple calculation even when no Conversion Table is available. We have just seen that v (i +a) a = A, or the single premium. Now v, which is the present value of i due i year hence, is equal to i d, where d is the discount on i for i year. Hence we find that v (T +a)a =(i d ) (i -f a) a, which is the same as i d ( i + a). The value of ^is given on p. 123 for various rates of interest. Therefore the single premium is at once found by adding i to the value of the annuity, multiplying it by the rate of discount 0 55 02 > i +a 18-176 d= '05502 -02913 = -02589, which is the annual pay- i -\- a ment during life to secure 1 at death given on p. 150. If we make use of the Annual Premium Conversion Table on p. 1 86, we can only approximate to this result. The Conversion Table is only a short one and deals with the annuity value to the first decimal place. Looking on line ' 17 17-9,' column -i, we find that the annual premium corresponding to an annuity value of 17-1 is -0261, which is a larger amount than the true value. If we look on the same line in column -2 we find the annual premium corre- sponding to an annuity value of 17*2 is '0258, which is less than the true value. The annuity value being 17-176 is approximately | of the way between these two amounts, so that if we take J of their difference, which is -0003 x equals -0002, and subtract it from 0261, we have "0259, which corresponds very nearly with the annual premium given on p. 150. In the Annual Premium Conversion Table we have no differences to deal with of the same kind as we have in the Single Premium Conversion Table. What we are concerned with in the Annual Premium Conversion Table is the variation in the rate of discount. If we want to know the annual premium to assure i at death on a life aged 40, according to the HM Table, with interest at 4 % instead of at 3 %, as previously, we must take the 4 % annuity value from p. 142, where it is given as 15*135, find from p. 186 the annual premium corresponding to this annuity value, which is '0329, and subtract from it -0093 (difference p. 186), so obtaining -0236 as the annual premium at 4 %, which corresponds fairly well with the amount given on p. 150. If a closer approximation to the truth is required it can be obtained, as mentioned above, by adding i to the annuity value, dividing unity by this amount, and subtracting the rate of discount given on p. 123. Thus, to repeat the last example, we have the annuity value 15*1347, which with i added amounts to 16-1347. Dividing unity by this amount, we have '06198, and subtracting the rate of discount -03846 we obtain '02352, which is the exact amount given on p. 150. Repeating the calculation in connection with the symbols we have P= - 1 d~ , - 1 --03846 = -06 1 98- -03846=: -02352. 16-1347 (38) POST OFFICE ANNUITIES AND ASSURANCES Annual premiums, like single premiums, may be obtained from annuity values in this way in connection with single lives, joint lives, the last survivor or survivors of any number of lives, and successive lives. The premiums for contingent assurances cannot be obtained in this way. Post Office Annuities and Assurances Hitherto we have been considering the values of annuities and other benefits on what may be called a theoretical basis. That is to say, we have been supposing deaths to occur in exact accordance with certain mortality tables, and interest to be earned at various specified rates. We have now to consider the terms on which annuities and other benefits can be obtained from various Government Depart- ments. Page 189 gives the cost of immediate life annuities of i per annum when purchased through the Post Office. A distinction is made between the cost of annuities on male and female lives, and the annuities are payable by half-yearly instalments on January 5 and July 5, or April 5 and October 10, according to the date of purchase, the first half-yearly instalment becoming due on the second quarterly day of payment next following the day of purchase. The table gives the cost of an annuity of i t and an annuity of a larger amount costs a larger sum in exact proportion. For instance, an annuity of ^10 a year would cost ten times the amount given in the table. The cost of deferred life annuities under which the purchase money will be returned on application or on the death of the nominee if an instalment of the annuity shall not have become due, is given on p. 190. The annuities are payable half-yearly, the first payment of the annuity being made six months after the number of years they are deferred has expired. Thus the first payment under an annuity deferred 10 years will become due and payable on the second quarterly day of payment next following the expiration of ten years. The Table of Annual Payments shows the amount of each annual payment that has to be made for a number of years exceeding by one the number of years the annuity is deferred. Thus if the annuity is deferred ten years, 1 1 payments have to be made ; if it is deferred twenty years, 2 1 payments have to be made, and so on. On p. 191 a corresponding table is given, showing the cost of deferred life annuities under which the purchase price is not return- able in the event of the life on which the annuity is granted ceasing before the first payment of the annuity becomes due. (39) INTRODUCTION Pages i92-i94give the premiums for life assurance effected through the Post Office. It will be noticed that the sum assured is sometimes payable at death and sometimes payable in various numbers of years after being effected or at death if previous. The annual premiums for life assurances given on p. 194 differ, in regard to assurances pay- able at a certain age, from the ordinary practice of life assurance companies. The great majority of life assurance offices, when they assure an amount payable at a specified age or at death if previous, only require as a maximum number of payments the difference between the age at entry and the age at maturity. Thus an endow- ment assurance effected by a man aged thirty, payable at age sixty or at death if previous, only calls for (60 30 =)3o annual payments in the eventof the assured surviving till the age of sixty, while Post Office assurance in such a case as this would require 31 annual premiums to be paid. Government annuities are also granted by the National Debt Office, and are made chargeable upon the Consolidated Fund of the United Kingdom. Further particulars in connection with these annuities are given at the bottom of the table on p. 195. Annuities and Assurances Granted by Life Offices It is probable that any person wanting to purchase an annuity or to assure to the best advantage would go to a well-established life assurance company rather than to a Government department. He would obtain much better value for money by so doing, and the security offered by the best life offices is so ample and altogether beyond question that no advantage attaches to Government guarantee as compared with the guarantee of first-class life assurance companies. The rates given on p. 196 for annuities and assurances granted by British life offices are only the average rates. Many companies of the highest standing guarantee these benefits on terms much more favourable than the average. Details for each company may be obtained from various publica- tions, such as Whitaker's Almanack. They are also given, much more fully, in Bourne's * Insurance Directory ' and Bourne's ' Assur- ance Manual.' INCOME TAX The Income Tax Tables on pp. 198-204 require little explana- tion. The amounts are arrived at by multiplying the income by the pence in the tax per pound, and dividing the result by 12 and 20 to obtain the answer in pounds. Thus the income tax on ,130 (40) LOGARITHMIC TABLES J. d. S. a. at j. = 5 at 7* = I3 I2 X - 7 = 75 10 = 3 15 10 ; at W. = I3 2 8 = 86 8 = 4 6 8; 3t9 ,/. = '3>L? = 97 6 = 4I7 6. If it is desired to find the income tax on other amounts than those quoted, may easily be done by addition. Thus the tax at *]d. on ;],493 is s. d. on 1,490 (p. 202) 43 9 2 on ___ 3 (p. 198) i 9 on 1,493 43_io_JJ If the tax is desired at a rate not given in the tables, it can be obtained by addition or subtraction. Thus the tax on .680 at nd. is s. L on 680 at 6d. (P- 200) 17 on 680 at .5* (P. 200) 14 _3_ _4 on 680 at nd. 3i 3 4 LOGARITHMIC TABLES On pp. 230-320 there are various logarithmic tables by means of which many calculations required to be made by users of this book can be performed with the greatest ease. These tables are fully explained on pp. 207-228, and with the explanation there given the logarithmic tables may readily be employed by people previously unacquainted with logarithms. It cannot be too strongly urged upon everybody who has calculations to make that logarithms offer a very short and at the same time quite simple means of performing calculations that without their aid frequently involve long and tedious processes. EXAMPLES On pp. 42-48 a collection of examples is given showing some of the many purposes to which the tables in this book may be applied. These, in conjunction with the explanations already given, will, it is hoped, make the use of the tables perfectly clear, and at the same time show how many results not specifically tabulated may be arrived at. EXAMPLES Amount of a Sum in Any Number of Years (i) Find the amount of ^437 at the end of '35 years at 2\%. i in 35 years= 2*17879 437 in 35 years=2-i7879X437=,952-i3i23 or 437=log 2-640481 i in 35 years=log 0-338216 437 in 35 years=log 2-978697=^952-13 (2) Required, the amount of 62$ in 127 years at 4^ %. i in 100 years= 81-58852 i in 27 = 3-28201 i in 127 years= 81-58852x3-28201= 267-77434 625 127 =267-77434x625 =167358-96250 or 625=log 2-795880 i in 127 years=log 0-01911629 x i27=log 2-427769 625 in 127 years=log 5-223649=^167359 (3) Find the amount of 475 in 30 years at 2^=27 %. 475 =1 g 2-676694 T in 30 years=log 0-0115 7044 X3o=log '347H3 475 in 3 years=l or i in 30 years at 2-75 %= 2 -25660 t V 2-5 %=2*o 9 757 Difference=o" 1 5903-7-5 = 0*03181 i in^oyrs.at 2-7 = 2-25660 0-03181 = 2-22479 475 i" 30 years =2-22479x475 =1056"]% approximately (42) EXAMPLES (4) Find the rate of interest at which ^530 must be invested in order to amount to ^3,000 in So years. If 530 amounts to 3,000 This is between 2 % and 2^ %, but nearer 2\ %. or 3,ooo=log3'477i2i 53o=log 2724276 i in 80 years=log 0752845 i i year =log 0752845-1-80=^ 0-009411 = 1-0219 The rate of interest therefore is 2*19 %. Present Value of a Sum to be Received in the Future (5) // is required to know the present value of ^913 to be received at the end of 37 years, reckoning interest at 4 %. Present value of i in 37 years = "2343 913=^23430 x 9i3=gl3.19j59 or 9i3=log 2-960471 i in 37 years=log o--log 0-630234=^ 1-369766 913 in 37 years=log 2-330237 ^213-92 (6) Find the present value 0/^350 due in 30 years at 4^ %. 35o=log 2-544068 P.V. of i in 30 yrs.=logo- log 0-5 26650 =log 7-473350 Present value of 350 in 30 years=log 2-017418=^104-1 or Present value of i at 4 %='3o832 i 4^ %= -26700 Difference =-041 32 4 =-0103 3 Present value of i at 4^= -30832 -01033= -29799 350=^29799 x 35=^ I0 4'3 approximately (7) At the end of 20 years an institution will enter into possession of a property which, it is agreed, will then be worth (43) EXAMPLES 5,000. Meantime it receives no income, but must spend 100 upon the property at the end of 5 years, 100 in 10 years, and 100 in 15 years. Find the present value of the property, reckoning interest at 3 %. Present value of 5,000 in 20 years='55368 x 5000=2768-4 100 5 =86-261 100 10 =74-409 100 15 =64-186 expenditure 224-856 = 224-9 property according to conditions = Seep. 66 66 66 66 (8) Find the present value of 1,000 due at the end of 120 years at 2\ %. P.V. of 1,000 due in 100 years = 84*65 84-65 20 =84-65 X "61027=^5^659 or 1000== log 3-0 P.V. of i in i2oyrs.=log o' log i'286864_ (year 12 log r" x 10) =log 2-713136 Present value of 1,000 in 120 years=log 1-713136=^51-66 63 62 279 247 Amount of i per Annum (9) Find the amount of 93 per annum in 27 years at 3^ %. Amount of i per annum in 27 years = 4375906 68 93 = 4375906 x 93 = 4069-59258 or 93 = log 1-968483 Amount of i in 27 years = log 0*4033894 i p. a. " = log 1-2376785 262 287 1224 (287 93 p. a. in 27 years = log 3-609551 = 4069-59 | 243 (10) Find the amount of '735 per annum in 34 years' at 2 %. 735 p. a. in 34 years at 2 % log 4-6175421 = 41451-68 or per annum at 3 % = 57-73018 per annum at 2J% = 55-10023 Difference = 2-62995 (44) 225 66 64 EXAMPLES i p.a. at 2| + i diff.=55'ioo23+ 1-31497=56-41520 735 at 4% =56-4i5 2 X735 =4H65 roughly The error here is considerable. Taking half the difference between 2| and 3 % to obtain 2 J % is only a means of roughly approximating to the correct amount. Present Value of Annuity (n) Find the present value of 47*25 per annum for 30 years <** 5 %- P. V. of i per annum = 15*37245 I 74 47' 2 5 per annum= 15*37245 X47'25=726*^48 i or Log 1*186743 + log 1*674402 -log 2*86ii45=726*35 (12) Find the value of a lease yielding i$T P& annum for 27 years to make 3 % and to get back the principal by the end of the term. p.a. for 27 years= x i8'32703 or 18-32703 yrs. purchase = 18-32703x137=^2510-8 or i 3 7=log 2-136721 i p.a. for 27 years==log 1*263092 =log (13) Find the present value of \ per annum for 75 years at 37 % Present value=log 1-4023555=^25-2555 (14) If leasehold property yielding a net annual income of ;ioo a year for 30 years is bought for ,2,000, find the yield per cent. If ^100 per annum costs ^2,000, i per annum costs ,20. This is seen to be between 2^ and 3 % or i p.a. costs ^2o=log 1-30103 log o log i*3oio3=log 2*69897 2j %=log o log 2'7oo69 = log 1-29931 = 19-92 This is very close to 20, and therefore the required rate is a trifle less than 2^ %. (45) EXAMPLES Present Value of a Perpetuity ue of a perpetuity of ^"60 a interest at 3| %. 29-62963 x 60= 17777778 (15) Find the value of a perpetuity of ^"60 a year, reckoning interest at . (16) Find the value of a property yielding 2$ per annum for the next 15 years and ^no in perpetuity thereafter, reckoning interest at 3 %. Take the value of a perpetuity of ^no per annum and deduct the value of (no 25 -) ^85 per annum for 15 years. Perpetuity=33 x 1 10= 3666*666 P.V. of ^85 p. a. for 15 years= 1 1-93794x85 = 1014-725 Value required 2 6 5 1 -941 or P.V. of 2$ p. a. for 15 years = ii'93794X 25= 298*448 P.V. of perpetuity 110 deferred 15 years = 21-39539x110= 2353-493 Value required =^2651-94 1 (17) Find the value of the reversion /? a perpetuity of ^496 per annum after 22 years at 2 %. Value of perpetuity of i at 2 %= 38*09524 P.V. of i p. a. for 22 years at 2 J %= 16*76541 2 1 %= 16*34350 Difference = -42191 P.V. at 2g % (=16-34350 -H -21095)= i6'55445 Approximate P.V. of perpetuity of i p. a. at 2 1 % deferred 22 years = 21*54079 Approximate P.V. of perpetuity of ^496 p. a. at 2 J % deferred 22 years = 2 1 "54079 x 496=^10684 or Value of perpetuity at P.V. of i p. a. for 22 years at 20 % =log 1*2188635 = 16-5525 P.V. of perp. deferred 22 years=2i*54 2 7 - lo g I '3333 4g6=log 2*695482 P.V. of perp. of ^"496 deferred 22 years at 2 | % =log 4*028782 = (46) EXAMPLES Sinking Fund I / (18) Find the sum to be set aside annually to amount to 750 in 30 years reckoning interest at 4 %. The sum to amount to \ /oi7 8 3 or 750 = log 2-875061 Annuity i will buy = log 2-762154 75 =log 1-637215= 43'373 Deduct 4 % on 750 = -04 x 750 = 30-000 Annual sum to amount to 750 in 30 years = 13-373 Annuity a Given Sum will Purchase (19) Find the annuity for 35 years that may be bought for , I >573> reckoning interest at 3^ %. Annuity i will buy = log 2*698956 1573 = log i '895685 = 78-6, or 20*00066 will buy an annuity of i p. a. 1573 will buy an annuity of ,, = 7^6474 2O'ooo66 Annuities and Assurances on Lives (20) Find the value of an annuity of 250 on the life of a male aged 45, according to the Government Experience Table at 3%- ' Value of i p. a. = ^15-152 ^250 = 15-152 x 250 = ^3788 (21) Find the value of 1,500 to be received at the death of a male aged 50, according to the Healthy Males Table at 3l%- 52023 x 1500 = ^780-345 (22) Find the annual payment to secure ,1,500 at the death of a male aged 50, according to the Healthy Males Table at si%- 03667 x 1 500 = 55 -005 (23) Find the value of the reversion to a perpetuity of ^100 per annum at the death of a male aged 60, according to the Government Experience Table at 3 %, and according to the Healthy Males Table at 3 %. (47) EXAMPLES Seep. By Government Experience 22*732 x 100 = 2273*2 , 152 By Healthy Males Value of a perpetuity of 100 = 3333*3 100 p. a. for life = 1023*6 deferred perpetuity = 2309*7 (24) Find value of annuity of 135 so long as two female lives, aged 25 and 45, both continue to live. Government Table 3%. * 14-650 x 135 =i97775 (25) Find value of annuity of 250 so long as either of two male /ives, aged 30 and 50, continue to live. Healthy Males Table &%. 19-7251 x 25o (26) Find the single payment to secure 1,250 (a) at the death of the first and(ti) at the death of the last of two male lives ^ aged 45 and 60. Healthy Males Table 4 %. (a) At death of first "64328 x 1250 = 804-1 (b) last -3814 x 1250 =47675 Single and Annual Premiums by Conversion Tables (27) Find the single payment to secure 1,000 at death of a person aged 43. Northampton Table 3 %. Annuity on life aged 43 = 14-162 Single payment for annuity of 14 =. -563 1 1 'i =00291 -06 =001748 -002 = 000058 ,, 14*162 = Single payment to secure 1,000 = or 1000 [i '029126 (14*162 + i)] = 558-3916 (28) Find the annual payment to secure 1,000 at the death of a person aged 43. Carlisle Table 4 %. Annuity on life aged 43 = 14*505 Annual premium for annuity of 14-5 = '0354 '0093 = -0261 1,000 at death = 26-1. ' -5^+1 ~' 3846 ) = 64 ' 5 -3 8 -46 =26-04 (48) INTEREST TABLES AMOUNT AND PRESENT VALUE OF ONE POUND AND OF ONE POUND PER ANNUM VALUES OF PERPETUITIES AND REVERSIONS NOMINAL AND EFFECTIVE RATES OF INTEREST AND OTHER TABLES For explanation see pp. 8-23 49 1% INTEREST TABLES Years ONE POUND ONE POUND PEE ANNUM Yna.ru Amount Present Value Amount JL ears Present Value I I -01 000 ' -99010 i-ooooo 0-99010 I 2 I -O2OIO -98030 2-OIOOO I -97040 2 3 I "03030 97059 3-03 010 2-94099 3 4 I '04060 -96098 4-06040 3-90197 4 5 I-05IOI 95147 5-10101 4-85343 5 6 I-06I52 -94205 6-15202 579548 6 I 1-07214 I -08286 93272 7-2I354 92348 8-28567 6-72819 7 7-65168 8 9 1-09369 91434 9'36853 8-56602 9 10 1-10462 90529 10-46221 9-47130 10 ii 1-11567 89632 1 1 -56683 10-36763 ii 12 1-12683 '88745 12-68250 11-25508 12 13 I-I380 9 87866 13-80933 12-13374 13 14 I-I4947 86996 I4-94742 13-00370 14 15 I-I6097 '86135 16-09690 13-86505 15 16 1-17258 '85282 17-25786 1471787 16 17 1-18430 18 1-19615 84438 18-43044 83602 19-61475 15-56225 17 16-39827 18 19 i -2081 1 '82774 20-81089 17-22601 19 20 I-220I9 '81954 22-01900 18-04555 20 21 1-23239 81143 23-23919 18-85698 21 22 1-24472 80340 24-47159 19-66038 22 23 1-25716 '79544 25-71630 20-45582 23 24 I -26973 78757 26-97346 21-24339 24 25 I -28243 77977 28-24320 22-02316 25 26 1-29526 77205 29-52563 22-79520 26 27 I-3082I '76440 30-82089 23-55961 27 28 I-32I29 '75684 32-12910 24-31644 28 29 1-33450 "74934 33-45039 25-06579 29 30 I-34785 '74192 34-78489 25-80771 30 31 I-36I33 '7345 8 36"I3274 26-54229 31 32 1 '37494 7273 37-49407 27-26959 32 33 i -38869 "72010 38-86901 27-98969 33 34 i -40258 71297 40-25770 28-70267 34 35 1-41660 '7059 1 41 -66028 29-40858 35 36 1-43077 '69892 43-07688 30-10750 36 i -44508 "69200 44-50765 3o-7995i ! 37 38 1-45953 "68515 45-95272 31-48466 38 39 1-47412 '67837 47-41225 32-16303 39 40 1-48886 67165 48-88637 32-83469 40 4 1 I-50375 66500 50-37524 33-49969 4i 42 1-51879 65842 51-87899 34-15811 42 43 I-53398 65190 53'39778 34-81001 43 44 J '54932 64545 54-93I76 35-45545 44 45 1-56481 63906 56-48107 36-09451 45 46 i -58046 63273 58'04588 36-72724 46 47 1-59626 62646 59-62634 37-35370 47 48 1-61223 62026 61-22261 37-97396 48 49 1-62835 61412 62-83483 38-58808 49 50 i -64463 60804 64-46318 39-19612 50 For explanation see pp. 8-13 INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM V OD Amount Present Value Amount Present Value 51 i -66 1 08 6O2O2 66-10781 39-79814 51 52 i -67769 59606 67-76889 40-394I9 5 2 53 i -69447 59016 69-44658 40-98435 53 54 1-71141 58431 71-14105 41-56866 54 55 1-72852 57853 72-85246 42-14719 55 56 I7458i 57280 74-58098 42-71999 56 1-76327 1-78090 56713 56151 76-32679 43-28712 57 78-09006 43-84863 58 1 1-79871 1-81670 '55595 55045 79-87096 44-40459 59 81-66967 44-95504 ! 60 61 i -83486 545o 83-48637 45-50004 61 62 1-85321 53960 85-32123 46-03964 62 63 1-87174 53426 87-17444 46-57390 63 64 i -89046 52897 89-04619 47-10287 64 65 1-90937 52373 90-93665 47-62661 65 66 i -92846 51855 92-84601 48-14516 66 67 i -94774 5i34i 94-77447 48-65857 67 68 i -96722 50833 96-72222 49-16690 68 69 i -98689 50330 98-68944 49-67020 69 70 2 -00676 49831 100-67634 50-16851 70 7i 2-02683 49338 102-68310 50-66190 71 72 2-O47IO 48850 104-70993 51 -15039 72 73 2-06757 48366 106-75703 51-63405 73 74 2-08825 47887 108-82460 52-11292 74 75 2-10913 47413 110-91285 52-58705 75 76 2-13022 46944 113-02197 53-05649 ?6 77 2-15152 78 2-17304 46479 46019 115-15219 53-52127 77 117-30372 53-98146 7 8 79 2-19477 80 2-21672 45563 45112 119-47675 121-67152 54-43709 79 54-88821 80 81 2-23888 44665 123-88824 55-33486 81 82 2-26I27 44223 126-12712 55-77709 82 83 2-28388 43785 128-38839 56-21494 83 84 2-30672 43352 130-67227 56-64845 84 85 2-32979 42922 132-97900 57-07768 85 86 2-35309 42497 135-30879 57-50265 86 87 2-37662 42077 137-66187 57-92342 87 88 2-40038 41660 140-03849 58-34002 88 89 2-42439 41248 142-43888 58-75249 89 90 2-44863 40839 144-86327 59-16088 90 91 2-47312 40435 147-31190 59-56523 9i 92 2-49785 40034 149-78502 59-96557 92 93 2-52283 39638 152-28287 60-36195 93 94 2-54806 39246 154-80570 6075441 94 95 2-57354 38857 I5735375 61-14298 95 96 2-59927 38472 159-92729 61-52770 96 97 2-62527 38091 162-52656 61-90862 97 98 2-65152 377H 165-15183 62-28576 98 99 2-67803 37341 167-80335 62-65917 99 xoo 2-70481 36971 170-48138 63-02888 100 See also Tables on pp. xx-xxxi (50 B 2 11% INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I 1-01250 98765 I -00000 0-98765 I 2 1-02516 97546 2-01250 1-96312 2 3 -03797 96342 3-03766 2-92653 3 4 -05095 95152 4'O7563 3-87806 4 5 06408 93978 5-12657 4-81783 5 6 07738 92817 6-19065 5-74601 6 7 8 09085 10449 91672 90540 7-26804 8-35889 6-66273 7-56812 I 9 11829 89422 8-46234 9 10 13227 88318 10-58167 934553 10 ii 14642 87228 11-71394 10-21780 ii 12 16075 86151 12-86036 11-07931 12 13 17526 85087 14-02112 11-93018 13 14 18995 84037 15-19638 1277055 14 15 20483 82999 16-38633 13-60055 15 16 21989 81975 17-59116 14-42029 16 17 -235H 80963 18-81105 15-22992 17 18 -25058 79963 20-04619 I 16-02955 ! 1 8 19 -26621 78976 21-29677 16-81931 19 20 -28204 78001 22-56298 I7-59932 20 21 -29806 77038 23-84502 18-36969 21 22 31429 76087 25-14308 19-13056 22 23 -33072 75*47 26-45737 19-88204 23 24 '34735 74220 27-78808 20-62423 2 4 25 -36419 73303 29-13544 2I-35727 25 26 38125 72398 30-49963 22-08125 26 27 39851 71505 31-88087 22-79630 27 28 41599 70622 33-27938 23-50252 28 29 43369 69750 34-69538 24-20002 29 30 -45161 68889 36-12907 24-88891 30 31 -46976 68038 37-58068 25-56929 31 32 -48813 67198 39-05044 26-24127 32 33 : -50673 -66369 40-53857 26-90496 33 34 -52557 65549 42-04530 27-56046 34 35 j -54464 64740 43*57087 28-20786 35 36 56394 63941 45-11551 28-84727 36 37 58349 63152 46-67945 29-47878 37 38 60329 62372 48-26294 30-I0250 38 39 '62333 61602 49-88623 3071852 39 40 64362 60841 51-48956 31-32693 40 41 66416 60090 53'i33i8 3 1 -92784 41 42 68497 59348 5479734 32-52132 42 43 70603 58616 56-48231 33-10748 43 44 72735 57892 58-18834 33-68640 44 45 74895 57177 59-91569 34-25817 45 46 7708I 56471 61-66464 34-82288 46 79294 81535 55774 55086 63-43545 35'38o62 65-22839 35-93H8 41 49 '83805 54406 67-04374 36'47554 49 50 86102 53734 68-88179 37-01288 50 For explanation see pp. 8-13 (52) INTEREST TABLES 110/ I 10 Years ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value 51 I -88429 53071 70-74281 37-54358 51 52 I -90784 52415 72-62710 38-06773 52 5* 1-93169 51768 74-53494 38-58542 53 54 1-95583 5H29 76-46662 39-09671 54 55 1-98028 '50498 78-42246 39-60169 55 56 2-00503 -49874 80-40274 40-10043 56 57 2-03010 ^9259 82-40777 40-59302 58 2-05547 -48651 84-43787 41-07952 58 59 2*08117 48050 86-49334 41-56002 59 60 2-I07I8 '47457 88-57451 42-03459 60 61 2-I3352 46871 90-68169 42-50330 61 62 2-16019 46292 92-81521 42-96622 62 63 2-18719 45721 94-97540 43-42343 63 64 2-21453 45156 97-16259 43^7499 64 65 2-24221 '44599 99-377I3 44-32098 65 66 2-27024 44048 101-61934 44-76146 66 67 2-29862 43504 103-88958 45-19651 67 68 232735 42967 106-18820 45-62618 68 69 42437 io8-5i555 46-05055 69 70 2-38590 4I9I3 110-87200 46-46968 70 71 2-41572 41395 113-25790 46-88363 71 72 2-44592 40884 115-67362 47-29247 72 73 2-47649 40380 118-11954 47-69627 73 74 2-50745 39881 120-59604 48-09508 74 75 39389 123-10349 48-48897 75 76 2-57053 38903 125-64228 48-87800 76 77 2-60266 38422 128-21281 49-26222 77 78 2-63519 37948 130-81547 49-64170 78 g 2-66813 270149 '37479 37017 133-45066 136-11880 50-01649 50-38666 80 81 273525 36560 138-82028 50-75225 81 82 2-76944 36108 I4I-55554 5 I " II 334 82 83 2 -80406 35663 144-32498 51-46996 83 84 2-839II 35222 147-12904 51-82219 84 85 2-87460 34787 149-96815 52-17006 85 86 2-9I053 34358 152-84276 52-51364 86 87 2-94692 '33934 15575329 52-85298 87 88 2^375 33515 158-70021 53-18813 88 89 3-O2IO5 33101 161-68396 89 90 3-05881 32692 164-70501 53-84606 90 91 3-09705 32289 167-76382 54-16895 91 92 3'i3576 31890 170-86087 54*48785 92 93 3-I7496 31496 173-99663 54-80282 93 94 3-21464 31108 I77-I7I59 55-11389 94 95 3-25483 30724 180-38623 55-42II3 95 96 3-29551 30344 183-64106 55-72457 96 97 3-3367I 29970 186-93658 56-02427 98 3-37842 29600 190-27328 56-32026 98 99 3*42065 '29234 193-65170 56-61261 99 100 3-46340 -28873 197-07234 56-90134 100 See also Tables on pp. xx-xxxi (53) 11% INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I 1-01500 98522 I'OOOOO 0-98522 I 2 I -03023 97066 2-01500 1-95588 2 3 I -04568 95632 3-04523 2-91220 3 4 1-06136 94218 4-09090 3-85438 4 5 I -07728 92826 5-15227 478265 6 1-09344 91454 6-22955 5-69719 6 7 10984 90103 7-32299 6-59821 7 8 12649 88771 8-43284 7-48593 8 9 14339 87459 9-55933 8-36052 9 10 16054 86167 10-70272 9-22219 10 II 17795 84893 1 1 -86326 IO-07II2 II 12 19562 83639 13-04121 10-90751 12 13 21355 82403 14-23683 11-73153 13 I 4 23176 81185 15-45038 12-54338 14 15 25023 79985 16-68214 13-34323 15 16 26899 78803 17-93237 14-13126 16 11 28802 30734 77639 76491 19-20136 14-90765 20-48938 15-67256 18 J 9 32695 75361 21-79672 16-42617 19 20 34686 74247 23-12367 17-16864 20 21 36706 73150 24-47052 17-90014 21 22 38756 72069 25*83758 18-62083 22 23 40838 71004 27-22515 19-33086 23 24 42950 69954 28-63352 20-03041 24 25 45095 68921 30-06302 20-71961 25 26 47271 67902 3i-5i397 21-39863 26 27 49480 66899 32-98668 22-06762 27 28 51722 "65910 34-48148 22-72672 28 29 53998 64936 35-99870 23-37608 I 29 30 56308 63976 37-53868 24-01584 30 31 58653 63031 39-10176 24-64615 31 32 61032 62099 40-68829 25-26714 32 33 63448 61182 42-29862 25-87896 33 34 65900 60277 43-93309 26-48173 34 35 68388 59387 45-59209 27-07560 35 36 70914 58509 47-27597 27-66068 36 73478 57644 48-98511 28-23713 37 38 76080 56792 50-71989 28-80505 38 39 78721 '55953 52-48068 29-36458 39 40 81402 55126 54-26789 29-91585 40 4i 84123 54312 56-08191 30-45896 4i 42 86885 53509 57-92314 30-99405 42 43 89688 52718 59-79I99 31-52123 43 44 I-92533 51939 61-68887 32-04062 44 45 1-95421 51171 63-61420 32-55234 45 46 I-98353 50415 65-56841 33-05649 46 47 2-01328 49670 67-55 J 94 33-553I9 47 48 2-04348 48936 69-56522 34-04255 48 49 2-07413 48213 71-60870 34-52468 49 50 2-10524 47500 73-68283 34-99969 50 For explanation see pp. 8-13 (54) INTEREST TABLES ,_ ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value 5i 2-13682 46798 75-78807 35-46767 51 52 2-16887 46107 77-92489 35-92874 S 2 53 2-20141 45426 80-09376 36-38300 53 54 2-23443 '44754 82-29517 36-83054 54 55 2-26794 44093 84-52962 37-27147 55 56 2-30196 43441 86-79754 37-70588 56 57 2*33649 42799 89-09951 38T3387 58 2-37I54 42167 91-43600 38-55554 58 2-40711 41544 93-80754 38-97097 59 6o 2-44322 40930 96-21465 39-38027 60 61 2-47987 40325 98-65787 39-78352 61 62 2-5I707 39729 101-13774 40-18080 62 63 39H2 103-65481 40-57222 63 64 2-593H 38563 106-20963 40-95785 64 65 2-63204 -37993 108-80277 4I-33779 65 66 2-67152 37432 111-43481 4I7I2II 66 67 2-71160 36879 114-10634 42-08089 67 68 2-75227 -36334 116-81793 42-44423 68 69 2-79355 '35797 119-57020 42-80220 69 70 2-83546 -35268 122-36375 43 "i 5487 70 7i 2-87799 -34746 125-19921 43-50234 71 72 2-92116 -34233 128-07720 43-84467 72 73 2-96498 -33727 130-99836 44-18194 73 74 3'00945 -33229 I33-96333 44-51422 74 75 3-05459 -32738 136-97278 44-84160 75 76 3-10041 -32254 140-02737 45-16414 76 3-14692 -31777 143-12778 45-48191 78 3-19412 -31308 146-27470 45*79499 78 g 3-24203 -30845 3-29066 -30389 149-46882 152-71085 46-10343 46-40732 79 80 81 3-34002 -29940 156-00152 46-70672 81 82 3-39012 -29497 I5934I54 47-00170 82 83 3-44097 -29062 162-73166 47-29231 83 84 3-49259 -28632 166-17264 47-57863 84 85 3-54498 -28209 169-66523 47-86072 85 86 3-59815 -27792 173-21020 48-13864 86 87 3-65213 -27381 176-80836 48-41246 87 88 3-70691 -26977 180-46048 48-68222 88 89 3-76251 26578 184-16739 48-94800 89 90 3-81895 26185 187-92990 49-20985 90 91 3-87623 25798 19174885 49-46784 9 1 92 3-93438 25417 195-62508 49-72201 92 93 3-99339 25041 199-55946 49-97242 93 94 24671 203-55285 50-21913 94 95 4-11409 24307 207-60614 50-46220 95 96 4-17580 -23947 211-72023 50-70168 96 97 4-23844 -23594 215-89604 5o-9376i 98 4-30202 -23245 220-13448 51-17006 98 99 4-36655 -22901 224-43650 5I-39907 99 100 4-43205 -22563 228-80304 51-62470 100 See also Tables on pp. xx zxii (55) ISO/ 4 /< INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I 1-01750 98280 I -00000 0-98280 I 2 I-0353I 96590 2-01750 I -94870 2 3 I -05342 94929 3-05281 2-89798 3 4 1-07186 93296 4-10623 3^3094 4 5 I -09062 91691 5-17809 474786 5 6 10970 90114 6-26871 5-64900 6 7 12912 -88564 737841 6-53464 7 8 14888 -87041 8-50753 7-40505 8 9 16899 85544 9-65641 8-26049 9 10 18944 84073 10-82540 9-IOI22 10 ii 21026 82627 12-01484 9-92749 ii 12 23H4 81206 13-22510 iQ-73955 12 13 25299 79809 14-45654 11-53764 13 14 1 -27492 78436 1 5 70953 12-32201 14 15 1 '29723 77087 16-98445 13-09288 15 16 -31993 75762 18-28168 13-85050 16 17 | '34303 74459 18 | -36653 -73178 19-60161 14-59508 20-94463 15-32686 11 19 '39045 7i9i9 22-31117 16-04606 19 20 I -41478 -70682 23-70161 16-75288 20 21 '43954 '69467 25-11639 I7-44755 21 22 46473 -68272 26-55593 18-13027 22 23 -49036 -67098 28-02065 18-80125 23 24 '5 l6 44 '65944 29-51102 19-46069 24 25 54298 '64810 31-02746 20-10878 25 26 56998 -63695 32-57044 20-74573 26 27 59746 '62599 34-14042 21-37173 27 28 62541 -61523 35-73788 21-98695 28 29 65386 '60465 37-36329 22-59160 29 30 68280 59425 39-01715 23-18585 30 31 71225 58403 40-69995 23-76988 31 32 74221 57398 42-41220 24-34386 32 33 77270 56411 44-15441 24-90797 33 34 80372 -55441 45-92712 25-46238 34 35 83529 -54487 47-73084 26-00725 35 36 86741 -53550 49-56613 26-54275 36 37 -90009 -52629 51-43354 27-06904 38 '93334 '51724 53-33362 27-58628 38 39 '96717 -50834 55-26696 28-09463 39 40 2-00160 -49960 57-23413 28-59423 40 41 2-03663 -49101 59-23573 29-08524 4i 42 2-07227 -48256 61-27236 29-56780 42 43 2-10853 -47426 63-34462 30-04207 43 44 2-14543 -46611 65-453I5 30-50817 44 45 ! 2-18298 -45809 67-59858 30-96626 45 46 2-22118 -45021 69-78156 31-41647 46 47 2-26005 -44247 72-00274 31'85894 47 48 2-29960 -43486 74-26278 32-29380 48 49 2-33984 -42738 76-56238 32-72118 49 50 2-38079 -42003 78-90222 33-14121 50 For explanation see pp. 8-13 (56) INTEREST TABLES I! /. Years ONE POUND ONE POUND PEE ANNUM Years Amount j Present Value Amount Present Value 51 2-42245 -41280 81-28301 33-5540I 51 52 2-46485 '40570 83*70547 33-95972 52 53 2-50798 -39873 86-17031 34-35845 53 54 2-55187 -39187 88-67829 34-75032 54 55 2-59653 -38513 91-23016 35*13545 1 55 56 2-64197 -37851 93-82669 35*5i395 56 57 2-68820 -37200 96-46866 35*88595 57 58 2-73524 '36560 99-15686 36-25155 58 2-78311 -35931 2-83182 -35313 101-89210 104-67522 36-61086 59 36-96399 60 61 2-88137 -34706 107-50703 37-31104 6x 62 2-93180 -34109 110-38841 37*65213 62 63 2-98310 -33522 II3-32020 37-98735 63 64 3' 353i -32946 116-30331 38-31681 64 65 3-08843 -32379 119-33861 38-64060 65 66 3-14247 -31822 122-42704 38-95882 66 67 3-19747 -31275 I25-5695I 39-27157 67 68 3*25342 -30737 128-76698 39-57893 68 69 3'S 1 036 -30208 132-02040 39-88102 69 70 3-36829 -29689 I35*33076 40-I7790 70 71 3*42723 -29178 138-69905 40-46968 71 72 3*48721 -28676 73 3*54824 -28183 142-12628 40-75645 145-61349 41-03828 72 73 74 3-61033 -27698 149-16173 41-31526 74 75 3-67351 -27222 152-77206 4I-58748 75 76 3-73780 -26754 I56-44557 4I-85502 76 3-80321 -26294 160-18336 42-11795 78 3-86977 -25841 163-98657 42-37636 78 8? 3-93749 -25397 4-00639 -24960 167-85634 42-63033 171-79382 42-87994 B 81 4-07650 -24531 I75-80022 43-12524 81 82 4-14784 -24109 179-87672 43*36633 82 83 4-22043 -23694 184-02456 43-60328 83 84 4-29429 -23287 188-24499 43*836l4 84 85 4-36944 -22886 192-53928 44-06501 85 86 4-44590 -22493 196-90872 44*28993 86 87 4*52371 -22106 201-35462 44-5I099 87 88 4-60287 -21726 205-87833 44-72824 88 89 4-68342 -21352 210-48120 44-94176 89 90 4*76538 -20985 215-16462 45-15161 90 91 4-84877 -20624 219-93000 45*35785 9 1 92 4'93363 -20269 224-77877 45*56054 92 93 5* OI 997 -19920 229-71240 45*75974 93 94 5-10782 -19578 234*73237 45*95552 94 95 5^9720 -19241 239-84018 46-I4793 95 96 5-28815 -18910 245-03739 46-33704 96 97 5-38070 -18585 08 5-47486 -18265 250-32554 46-52288 97 255-70624 46-70554 98 99 5-57067 -17951 261-18110 46-88505 09 100 5-66816 -17642 266-75177 47-06147 100 See also Tables on pp. xx-xxxi (57) 2A INTEREST TABLES Years ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value I 1-02000 98039 I'OOOOO 98039 I 2, 1-04040 -96117 2*02000 1-94156 2 3 I -06 1 21 -94232 3-06040 2-88388 3 4 I -08243 -9 2 385 4-12161 3-80773 4 5 1-10408 '9O573 5 -20404 471346 5 6 I26l6 '88797 6-30812 5-60143 6 7 -14869 '87056 7-43428 6-47199 7 8 -17166 '85349 8-58297 7-32548 8 9 -19509 -83676 975463 8-16224 9 10 -21899 "82035 10-94972 8-98258 10 ii -24337 -80426 12-16872 978685 ii 12 -26824 78849 I 3 -29361 i -77303 13-41209 14-68033 J o-57534 12 1 1 -34837 13 14 -31948 75788 1 5 '97394 12-10625 14 15 -34587 74301 17-29342 12-84926 15 16 -37279 -72845 18-63928 i3'5777i 16 17 -40024 -71416 18 '42825 -70016 20-01207 21-41231 14-29187 17 14-99203 18 19 '45681 '68643 22-84056 15-67846 19 20 -48595 ^7297 24-29737 16-35143 20 21 -51567 ^5978 2578332 17-01121 21 22 -54598 -64684 27-29898 17-65805 22 23 ^7690 -63416 28-84496 18-29220 23 24 -60844 -62172 30-42186 18-91393 24 25 -64061 60953 32-03030 i9'52346 25 26 '67342 59758 33-67090 20-12104 26 27 -70689 58586 35-34432 2070690 27 28 -74102 57437 37-05121 21-28127 28 29 -77584 56311 38-79223 21-84438 29 30 '81136 55207 40-56808 22-39646 30 31 ^4759 54125 42-37944 22-93770 31 32 -88454 53063 44-22703 23-46833 32 33 -92223 52023 46-11157 23-98856 33 34 -96068 51003 48-03380 24-49859 34 35 '99989 50003 49-99447 24-99862 35 36 2-03989 -49022 51-99436 25-48884 36 37 2-08068 48061 54-03425 25-96945 38 2-I2230 47119 56-11494 26-44064 38 39 2-16474 -46195 58-23723 26-90259 39 40 2-20803 -45289 60-40198 27-35548 40 4i 2-2522O -444OI 62-61002 27-79949 4i 42 2-29724 -43530 64-86222 28-23479 42 43 2-343I9 -42677 67-15947 28-66156 43 44 2-39005 41840 69-50265 29-07996 44 45 2-43785 41020 71 '89271 29-49016 45 46 2-48661 -40215 74-33056 29-89231 46 47 2-53634 39427 76-81717 30-28658 47 48 2-58707 38654 79-35352 30-67312 48 49 2-63881 37896 81-94059 31-05208 49 50 2-69159 37153 84-57940 3 1 '4236 1 50 For explanation see pp. 8-13 (58) INTEREST TABLES 2% Years ONE POUND ONE POUND PEE ANNUM Years Amount | Present Value Amount Present Value SI 274542 -36424 87-27098 3178785 51 52 2-80033 *357io 90-01640 32-I4495 52 53 2-85633 -35 010 92-81673 32-49505 53 54 2-91346 34323 95'673O7 32-83828 54 55 2-97173 33650 98-58653 33-17479 55 56 3-03117 .32991 101-55826 33-50469 56 57 3-09179 32344 104-58943 33-82813 57 58 3-15362 31710 I07'68l2I 34-14523 58 $ 3-21670 3-28103 31088 30478 110-83484 114-05154 34-45610 59 34-76089 60 61 3-34665 29881 II7-33257 35-05969 6l 62 3-4I358 63 3-48186 29295 28720 120-67922 124-09280 35-35264 35-63984 62 63 6 4 3-55I49 28157 127-57466 35-92141 6 4 65 3 -62252 27605 131-12615 36-19746 65 66 3-69497 27064 13474868 36-46810 66 %> 3-76887 26533 138-44365 36-73343 67 68 3-84425 26013 142-21252 36-99356 68 69 3-92114 25503 146-05677 37-24859 69 70 3-99956 25003 I49-9779I 37-49862 70 71 4-07955 24513 I53'97747 3774374 71 72 4-16114 24032 158*05702 37-98406 72 73 4-24436 23561 l62'2l8l6 38-21967 73 74 4-32925 23099 166-46252 38-45066 74 75 4-41584 22646 17079177 38-67711 75 76 4-50415 22202 175-20761 38-89913 76 77 4-59424 21766 I797II76 39-11679 78 4-68612 21340 I84-30599 39-330I9 78 79 477984 20921 188-99211 39-53940 79 80 4-87544 205II I93-77I95 3974451 80 8 1 4-97295 2OIO9 198 '64739 39-94560 81 82 5-07241 I97I5 203-62034 40-14275 82 I 3 5-17385 19328 208-69275 40-33603 83 84 85 5-38288 18949 2I3-86660 18577 219-14394 40-5255I 4071129 84 85 86 5-49054 18213 224-52681 40-89342 86 87 5-60035 17856 230-01735 41-07198 87 88 5-71235 17506 : 235-61770 41-24704 88 89 5-82660 17163 241-33005 41-41867 89 90 5-94313 16826 247-15665 41*58693 91 6-06200 16496 253-09979 41-75189 oi 92 6-18324 -16173 259-16178 41-91362 92 93 6-30690 15856 , 265-34502 42-07217 93 94 6-43304 15545 271-65192 42-22762 94 95 6-56170 15240 278-08496 42-38002 95 96 6-69293 14941 284-64666 42-52943 96 97 6-82679 98 6-96333 14648 ; 291-33959 14361 298-16638 42-67591 97 42-81952 08 99 7-10259 14079 305-12971 42-96032 99 100 7-24465 13803 312-23230 43-09835 ioo See also Tables on pp. xx-xxxi (59) 21% INTEREST TABLES Years ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value I I -02250 97800 i -ooooo 0-97800 I 2 I-0455I -95647 2-02250 I '93447 2 3 1-06903 93543 3-0680I 2-86990 3 4 I -09308 91484 4-13704 3-78474 4 5 I-II768 89471 4-67945 5 6 1-14283 87502 6-34780 5-55448 6 7 1-16854 85577 7-49062 6-41025 7 8 1-19483 83694 8-65916 7-24718 8 9 I-22I7I 81852 9-85399 8-06571 9 10 I -24920 80051 II-0757I 8-86622 10 ii 1-27731 78290 12-32491 9-64911 ii 12 1-30605 76567 13-60222 10-41478 12 13 1-33544 74882 14-90827 11-16360 13 14 1-36548 73234 16-24371 11-89594 14 15 1-39621 71623 17-60919 12-61217 15 16 i -42762 70047 19-00540 13-31263 16 17 1-45974 68505 20-43302 13-99768 17 18 1-49259 66998 21-89276 14-66766 18 19 1-52617 65523 23-38535 15-32290 19 20 1-56051 64082 24-91152 15-96371 20 21 i -59562 62672 26-47203 16-59043 21 22 1-63152 61292 28-06765 17-20335 22 23 i -66823 59944 29-69917 17-80279 23 2 4 1-70577 58625 31-36740 18-38904 24 25 I744I5 '57335 33-073I7 18-96238 25 26 178339 56073 34-8I732 I9-523H 26 27 1-82352 54839 36-60071 20-07I50 27 28 1-86454 53632 38-42422 20-60783 28 29 i -90650 52452 40-28877 2I-I3235 29 30 1-94939 51298 42-19526 21-64533 | 30 31 I-99325 50169 44-14466 22-I4702 31 32 2-03810 49065 46-13791 22-63767 32 33 2-08396 47986 48-17602 23-ii753 33 34 2-13085 46930 50-25998 23-58683 34 35 2-17879 45897 52-39083 24-04580 35 36 2-22782 44887 54-56962 24-49467 36 2-27794 43899 56-79744 24-93366 37 38 2-32920 42933 59-07539 25*36299 38 39 2-38160 41989 6I-40457 25-78288 39 40 2-435I9 41065 63-78618 26-19352 40 4 1 2-48998 40161 66-22137 26-59513 41 42 2-54601 39277 68-71135 26-98790 42 43 2-60329 38413 7I-25735 27-37203 43 44 2-66186 37568 73-86064 27-74771 44 45 2-72176 36741 76-52251 28-11512 45 46 2-78300 35932 79-24426 28-47444 46 2-84561 35142 82-02726 28-82586 48 2-90^64 34369 84-87287 29-16955 48 49 2-97511 33612 87-78251 29-50567 49 50 3-04205 32873 9075762 29-83440 50 For explanation see pp. 8-13 INTEREST TABLES 2i/o Years ONE FOUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 3-11049 32149 9379966 30-I55 8 9 51 52 3-18048 31442 96-91016 30-47031 52 53 3-25204 30750 100-09064 3077781 53 54 3-32521 30073 103-34267 31-07854 54 55 3-40003 29412 106-66788 31-37265 55 56 3-47653 28764 110*06791 31-66030 56 57 : 3-55475 28131 113-54444 31-94161 57 58 3-63473 27512 117-09919 32-21673 58 59 3*71651 60 3-80013 26907 120-73392 26315 124-45043 32-48580 59 32-74895 60 61 3-88564 25736 128-25057 33-00631 61 62 3-97306 25169 132-13621 33-25800 62 63 4-06246 24616 136-10927 33-50416 63 64 4-I5386 24074 140-17173 33-74490 64 65 4-24733 23544 I44-32559 33*98034 65 66 4-34289 23026 148-57292 34-21060 66 6? 4-44061 22519 I52-9I58I 34-43580 67 68 4-54052 22024 157-35642 34-65604 68 69 4-64268 21539 161-89694 34-87143 69 70 4747H 21065 166-53962 35-08208 j 70 71 4-85395 20602 171-28676 35-28810 71 72 4-96317 20148 176-14071 35-48959 72 73 5-07484 19705 181-10388 35-68664 73 74 5-18902 19271 186-17871 35-87935 74 75 530577 18847 191-36774 36-06783 75 76 5-425I5 18433 196-67351 36-25215 76 ii 5-54722 5-67203 18027 202*09866 17630 207-64588 36-43242 77 36-60873 78 7? 579965 17242 213-31792 3678115 79 80 5-93015 16863 219-11757 36-94978 80 81 6-06357 16492 225-04771 37-11470 81 82 6 '20000 16129 231-11129 37-27599 82 83 6-33950 15774 237-31129 37-43373 83 84 6-48214 15427 243-65080 37-58800 84 85 6-62799 15088 250-13294 37-73888 85 86 677712 H756 25676093 37-88643 86 87 6-92961 I443I 263-53805 38-03074 87 88 7-08552 14113 270-46766 38-17187 88 89 7-24495 13803 277-553I8 38-30990 89 90 7-40796 13499 28479813 38-44489 90 91 7-57464 13202 292-20608 38-57691 91 92 774507 I29II 29978072 38-70602 92 93 7-91933 12627 307-52579 38-83230 93 94 8-09752 12349 315-44512 38-95579 94 95 8-27971 12078 323-54263 39-07657 95 96 8-46600 Il8l2 331-82234 39-19469 96 97 98 8-65649 8-85126 II552 11298 340-28834 348-94483 39-31021 97 39-42319 98 99 9-05041 11049 35779609 39-53368 99 zoo 9-25405 10806 366-84650 39-64174 100 See also Tables on pp. xx-xxxi (61) INTEBEST TABLES ONE POUND ONE POUND PEK ANNUM Years Years Amount Present Value Amount Present Value I I -02500 97561 I -00000 97561 I 2 I -05062 95181 2-O25OO I -92742 2 3 I '07689 92860 3-07562 2-85602 3 4 1-10381 90595 4-15252 376197 ! 4 5 1-13141 88385 5-25633 4-64583 5 6 1-15969 86230 6-38774 5-50812 6 7 1-18869 84127 7-54743 6-34939 7 8 1-21840 82075 8-73612 7-17014 8 9 I -24886 80073 9-95452 7-97087 9 10 I -28008 78120 11-20338 8-75206 10 ii 1-31209 76214 12-48347 9 -5*42 1 ii 12 1-34489 74356 1379555 10-25776 12 13 I-3785I 72542 15-14044 10-98318 13 14 1-41297 70773 16-51895 11-69091 M 15 I -44830 69047 17-93193 12-38138 15 16 1-48451 67363 19-38022 13-05500 16 % 1-52162 1-55966 65720 64117 20-86473 13-71220 22-38635 14-35336 11 19 I-59865 62553 23-94601 14-97889 19 20 I -63862 61027 25-54466 15-58916 : 20 21 1-67958 '59539 27-18327 16-18455 21 22 172157 28-86286 16-76541 22 23 1-76461 56670 30-58443 17-33211 23 24 1-80873 55288 32-34904 17-88499 24 25 1-85394 '53939 34-15776 18-42438 25 26 I -90029 -52623 36-01171 18-95061 26 27 1-94780 -51340 37-91200 19-46401 2 7 28 I -99650 -50088 39-85980 19-96489 28 29 2 -04640 48866 41-85630 20-45355 29 30 2-09757 -47674 43-90270 20-93029 30 3 1 2-I5000 46511 46-00027 21-39540 31 32 2-20376 '45377 48-15028 21-84918 32 33 2-25885 44270 50-35403 22-29188 33 34 2-3I532 43i9i 52-61289 22-72379 34 35 2-3732I 42137 54-92821 23-14516 35 36 2-43254 41109 57-30141 23-55625 36 37 2-49335 40107 5973395 23-95732 37 38 2-55568 39128 62-22730 24-34860 38 39 2-61957 38174 64-78298 24-73034 39 40 2-68506 37243 67-40256 25-10277 40 4i 2-75219 36335 70-08762 25-46612 4i 42 2-82100 35448 72-83981 25-82061 42 43 2-89152 34584 75-66081 26-16645 43 44 2-96381 33740 78-55232 26-50385 44 45 3-03790 32917 81-51613 26-83302 45 46 3-II385 32115 84-55403 27-15417 46 47 3-19169 3i33i 87-66788 27-46748 47 48 3-27149 30567 90-85958 2777315 48 49 335328 29822 94-13107 28-07137 49 50 3-437II 29094 97-48435 28-36231 50 For explanation see pp. 8-13 (62) INTEREST TABLES 2l/o Years ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value 51 3-52304 28385 100-92146 28-64616 51 52 3-6IIII 27692 104-44449 28-92308 52 53 370139 27017 108-05561 29-19325 53 54 379392 26358 III-75700 29-45683 54 55 3-88877 25715 115-55092 29-71398 55 56 3^8599 25088 119-43969 29-96486 56 4-08564 24476 123-42569 30-20962 57 58 4-18778 23879 I27-5II33 30-44841 58 59 4-29248 23296 131-69911 30-68137 59 60 4-39979 22728 I35-99I59 30-90866 60 61 4-50978 22174 140-39138 31-13040 61 62 4-62253 21633 144-90116 31-34673 62 63 4-73809 2II06 I49-52369 3I-55778 63 64 4-85654 20591 154-26179 3176369 64 65 4-97796 20089 159-11833 31-96458 65 66 5-10241 19599 164-09629 32-16056 66 67 5-22997 I9I21 169-19869 32-35177 67 68 5-36072 18654 174-42866 32-53831 68 69 5-49473 18199 17978938 3272030 69 70 5-63210 17755 185-28411 32-89786 70 7 1 577291 17322 190-91622 33-07108 71 72 5-91723 16900 196-68912 33-24008 72 73 6-06516 16488 202*60635 33-40495 73 74 6-21679 16085 208-67151 33-56581 74 75 6-37221 15693 214-88829 33-72274 75 76 6-53I5I I53IO 221-26050 33-87584 76 6-69480 14937 227-79201 34-02521 78 6-86217 14573 234-48681 34-17094 78 79 7-03372 14217 241-34898 34-31311 79 80 7-20957 13870 248-38271 34-45182 80 81 7-38981 13532, 255-59228 34-58714 81 82 7-57455 13202 262 -98209 3471916 82 83 12880 270-55664 34-84796 83 84 7-95801 12566 278-32056 34-97362 84 35 8-15696 12259 286-27857 35-09621 85 86 8-36089 11960 294'43553 35-21582 86 87 8-56991 11669 302-79642 35-3325I 87 88 878416 11384 311-36633 35-44635 88 89 9-00376 III06 320-15049 35-55741 89 90 9-22886 10836 329-15425 35-66577 90 9 1 9-45958 I057I 338-383II 3577148 gi 92 9-69607 10313 347-84269 35-87462 92 93 9-93847 10062 357-53875 35-97523 93 94 10-18693 09817 367-47722 36-07340 94 95 10-44160 09577 377-66415 36-16917 95 06 10-70264 09343 388-10576 36-26261 96 97 10-97021 09116 398-80840 36-35376 97 08 1 1 -24447 08893 409-77861 36-44269 98 99 11-52558 08676 421*02308 36-52946 99 100 11-81372 08465 432-54865 36-61410 100 bee also Tables on pp. xx-xxxi (63) INTEREST TABLES ONE POUND ONE POUND PEE ANNUM Years Years Amount Present Value Amount Present Value I I -02750 97324 I -00000 0-97324 I 2 1-05576 94719 2-02750 I -92042 2 3 I -08479 92184 3-08326 2-84226 3 4 1-11462 89717 4-16805 3*73943 4 5 1-14527 87315 5-28267 4-61258 5 6 1-17677 84978 6-42794 5-46237 6 7 1-20913 82704 7-60471 6-28941 7 8 I -24238 80491 8-81384 7-09431 8 9 1-27655 78336 10*05622 7-87768 9 10 I-3II65 76240 1 1 -33276 8-64008 10 ii 1-34772 74199 12-64442 9-38207 ii 12 138478 72213 I3-992I4 IO-I0420 12 13 I -42287 70281 15-37692 10-80701 13 14 1-46199 68400 1 6 79979 1 1 -49101 14 15 I-50220 -66569 18-26178 12*15670 15 16 i-5435i ' 6 4787 19-76398 12-80457 16 17 i -58596 -63053 21-30749 I3-435II J 7 !8 1-62957 -61366 22-89344 14-04877 18 19 1-67438 -59723 24-52301 14-64600 19 20 1*72043 -58125 26-19740 15-22725 20 21 I-76774 ^569 27-91783 15-79295 21 22 1-81635 -55055 29-68557 I6-34350 22 23 1-86630 -53582 31-50192 16-87932 23 24 1-91763 -52148 33-36822 17-40080 24 25 1-97036 -50752 35-28585 17-90832 25 26 2-02455 '49394 37-25621 18-40226 26 27 2-08022 -48072 39-28075 18-88297 28 2-13743 -46785 41-36098 I9-35083 28 29 2-19621 -45533 43-49840 19-80616 29 30 2-25660 -44314 45-69461 20-24930 30 31 2-31866 -43128 47-95121 20-68059 3 1 32 2-38242 -41974 50-26987 21-10033 3 2 33 2-44794 -40851 52-65229 21-50883 33 34 2-51526 -39757 55-10023 21-90641 34 35 2-58443 -38693 57-61548 22-29334 35 36 2-65550 -37658 60-19991 22-66992 36 2-72852 '36650 62-85541 23-03642 38 2-80356 -35669 65-58393 23-393II 38 39 2-88066 -34714 68-38749 23-74025 39 40 2-95987 ^3785 71-26815 24-07810 40 41 3-04127 -32881 74-22802 24-40691 4 1 42 3-12491 -32001 77-26929 24-72692 42 43 3-21084 -31144 80-39419 25-03837 43 44 3-29914 -30311 83-60504 25-34I47 44 45 3-38986 -29500 86-90417 25-63647 45 46 3-48309 28710 90-29404 25-92357 46 47 3-57887 27942 9377712 26-20299 47 48 3-67729 27194 97-35600 26-47493 48 49 3-77842 26466 101-03329 26-73959 49 50 3-88232 25758 104-81170 26-99717 50 For explanation see pp. 8-13 (64) INTEREST TABLES 23% Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 3-98909 25068 108-69402 27-24785 51 S 2 4-09879 24397 112-68311 27-49I83 52 53 4-2II50 23744 116-78189 27-72927 53 54 4-32732 23109 120-99340 27-96036 54 55 4-44632 22491 125-32071 28-18527 55 56 4-56859 21889 129-76703 28-40415 56 57 4-69423 21303 I34-33563 28-61718 57 58 4-82332 20733 139-02986 28-82451 58 59 60 4'95596 5-09225 20178 19638 I43-853I8 148-80914 29-02628 59 29-22266 60 61 5-23229 I9II2 I53-90I39 29-41378 61 62 5376l8 18601 I59-I3368 29*59979 62 63 5-52402 18103 164-50986 29-78082 63 64 5^7593 17618 170-03388 29-95700 64 65 5-83202 17147 17570981 30-12846 65 66 5-99240 16688 181-54183 30-29534 66 67 6-15719 16241 187-53423 30-45775 67 68 6-32651 15806 193-69142 30-61582 68 69 6-50049 15383 200-01793 30-76965 i 69 70 6-67926 14972 206-51843 30-91937 70 71 6-86294 I457I 213-19768 3106508 71 72 7-05167 14181 220-06062 31-20689 72 73 7-24559 13802 227-11229 3i-3449i 73 74 7-44484 13432 234-35788 31-47923 74 75 7^4957 13073 241-80272 31-60995 75 76 7-85994 12723 249-45229 31-73718 76 77 8*07609 12382 257-31223 31-86100 77 78 8-29818 12051 265-38832 31-98151 78 S 8-52638 8-76085 II728 11414 273-68649 282-21287 32-09880 79 32-21294 80 81 9-00178 III09 290-97373 32-32403 81 82 9-24933 10812 299-9755I 32-43214 82 83 9-50368 10522 309-22483 32-53737 83 84 9-76503 10241 318-72851 32-63977 84 85 10-03357 09967 328-49355 32-73944 85 86 10-30950 09700 338-52712 32-83644 86 87 10-59301 09440 348-83662 32-93084 87 88 10-88431 09188 359-42962 33-02271 88 89 11-18363 08942 370-31394 33-11213 89 90 II-49II8 08702 38I-49757 33-I99I5 90 9i 11-80719 08469 392-98876 33-28385 91 92 12-13189 08243 404-79595 33-36628 92 93 12-46552 08022 416-92783 33-44650 93 94 12-80832 07807 429-39335 33-52457 94 95 I3-I6055 07598 442-20167 33-60056 95 96 13-52246 07395 455-36221 33-67451 96 97 I3-89433 07197 468-88467 33-74648 97 98. 14-27642 07005 482-77900 33-81652 98 99 14-66902 06817 497-05542 33-88469 99 100 15-07242 06635 51172445 33-95 1 04 xoo See also Tables on pp. xx-xxxl (65) INTEEEST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I I -03000 97087 I -00000 97087 I 2 I -06090 94260 2-03000 1-91347 2 3 09273 9I5H 3-09090 2-82861 3 4 I255I 88849 4-18363 3-71710 4 5 15927 86261 5-30914 4*57971 6 19405 83748 6-46841 5-4I7I9 6 7 22987 '81309 7 -66246 6-23028 7 8 26677 78941 8-89234 7-01969 8 9 30477 76642 10-15911 7786II 9 10 34392 74409 1 1 -46388 8-53020 10 ii 38423 72242 12-80780 9-25262 ii 12 42576 -70138 14-19203 9-95400 12 13 46853 -68095 15-61779 10-63496 13 14 51259 66lI2 17-08632 1 1 -29607 14 15 '55797 64186 18-59891 H'93794 15 16 60471 62317 20-15688 12-56110 16 11 65285 70243 '60502 58739 21-76159 23-41444 13-16612 I37535I ii 19 75351 57029 25-11687 14-32380 19 20 80611 55368 26-87037 14-87748 20 21 86029 '53755 28-67649 15-41502 21 22 91610 52189 30-53678 15-93692 22 23 '97359 50669 32-45288 16-44361 23 24 2-03279 49193 34-42647 J 6'93554 24 25 2-09378 47761 36-45926 W3 1 S 25 26 2-15659 -46369 38-55304 17-87684 26 27 2-22129 "45019 40-70963 18-32703 27 28 2-28793 *437o8 42-93092 18-76411 28 29 2-35657 -42435 45*21885 19-18846 29 30 2-42726 "41199 47*57542 19-60044 30 31 2-50008 -39999 50-00268 20-00043 31 32 2-57508 -38834 52-50276 20-38877 32 33 2-65234 -37703 55-07784 20-76579 33 34 2-73191 36604 57-73oi8 21-13184 34 35 2-81386 35538 60-46208 21-48722 35 36 2-89828 34503 63'27594 21-83225 36 2-98523 33498 66-17422 22-16724 37 38 3-07478 32523 69*i5945 22-49246 38 39 3-16703 31575 72-23423 22-80822 39 40 3-26204 30656 75-40126 23-11477 40 4 1 3-35990 29763 78-66330 23-41240 41 42 3-46070 28896 82-02320 23-70136 42 43 3-56452 28054 85-48389 23-98190 43 44 3-67I45 27237 89-04841 . 24-25427 44 45 378160 26444 9271986 24-51871 45 46 3-89504 -25674 96-50146 24*77545 46 4-01190 24926 100-39650 25-02471 47 48 4-13225 24200 104-40840 25-26671 48 49 4-25622 -23495 108-54065 25-50166 49 50 4-38391 -22811 112-79687 25-72976 50 For explanation see pp. 8-13 (66) INTEKEST TABLES Years ONE POUND OflE POUND PEK ANNUM Years Amount Present Value Amount Present Value 51 4-5I542 22146 117-18077 25-95I23 51 52 4-65089 21501 121-69620 26-16624 52 53 4-79041 20875 126-34708 26-37499 53 54 4-934I2 20267 I3I-I3749 26-57766 54 55 5-082I5 19677 136*07162 26-77443 55 56 5-2346I 19104 I4I-I5377 26-96546 56 57 539165 18547 146-38838 27-15094 58 5-55340 18007 151-78003 27-33101 58 5-72000 17483 I57-33343 27-50583 59 60 5-89160 16973 163-05344 27-67556 60 61 6-06835 16479 168-94504 27-84035 61 62 6-25040 15999 175-01339 28-00034 62 63 6-43791 15533 181-26379 28-15567 63 64 6-63105 15081 187-70171 28-30648 64 65 6-82998 14641 194-33276 28-45289 65 66 7-03488 14215 20I-I6274 28-59504 66 67 7-24593 13801 208-19762 2873305 67 68 7-46331 13399 2I5-44355 28-86704 68 69 7-68721 13009 222-90686 28-99712 69 70 7-91782 12630 230-59406 29-12342 70 71 8T5536 12262 238-51189 29-24604 j 71 72 8-40002 11905 246-66724 29-36509 72 73 8-65202 H558 255-06726 29-48067 73 74 8-91158 'II22I 263-71928 29-59288 74 75 9-17893 10895 272-63086 29-70183 75 76 9-45429 10577 281-80978 29-80760 76 9-73792 10269 291-26407 29-91029 77 7 IO-03006 09970 301-00200 30-00999 78 79 10-33096 80 10-64089 09680 09398 311-03206 30-10679 79 321-36302 30-20076 80 81 10-96012 09124 332-00391 30-29200 81 82 1 1 -28892 -08858 342-96403 30-38059 82 83 11-62759 -08600 354-25295 30-46659 83 84 1 1 -97642 08350 365-88054 30-55009 84 85 12-33571 O8IO7 377-85695 30-63115 ! 85 86 12-70578 07870 390-19266 30-70986 86 87 13-08695 07641 402-89844 30-78627 87 88 I3-47956 07419 4I5-98539 30-86045 88 89 13-88395 07203 429-46495 30-93248 89 90 14-30047 06993 443-34890 31-00241 90 91 14-72948 06789 457^4937 3I-07030 QI 92 I5-I7I37 06591 472-37885 31 -13621 92 93 15-62651 06399 487-55022 31-20021 93 94 16-09530 062I3 503-17672 31-26234 94 95 16-57816 -06032 519-27203 31-32266 95 96 17-07551 -05856 535-85019 31-38122 96 97 I7-58777 '05686 552-92569 31-43808 97 98 18-11540 -05520 570-51346 31-49328 98 99 18-65887 -05359 588-62887 31-54687 09 100 19-21863 05203 607-28773 31-59891 i ioo See also Tables on pp. xx-xxxf (67) G 2 3l/o INTEREST TABLES ONE POUND ONE POUND PER ANNUM Years Years Amount Present Value Amount Present Value I I -03500 96618 I -00000 9 66l8 I 2 -07 1 22 93351 2-03500 1-89969 2 3 -10872 90194 3-10623 2*80164 3 4 'H75 2 87144 4-21494 3-67308 4 5 -18769 84197 536247 4-5I505 5 6 -22926 81350 6-550I5 532855 6 7 -27228 78599 777941 6-11454 7 8 -31681 75941 9-05169 6-87396 8 9 -36290 '73373 10-36850 7-60769 9 10 -41060 70892 H73I39 8-31661 10 ii '45997 68495 13-14199 9-00155 ii 12 -5HO7 66178 14-60196 9-66333 12 13 -56396 63940 16-11303 10-30274 13 14 '61869 61778 17-67699 10-92052 14 15 -67535 59689 19-29568 11-51741 15 16 '73399 57671 20-97103 12-09412 16 17 -79467 55720 22-70501 12-65132 17 18 -85749 53836 24-49969 13-18968 18 19 i -92250 52016 26-35718 13-70984 19 20 i -98979 50257 28-27968 14-21240 20 21 2-05943 48557 30-26947 14-69797 21 22 2-13151 46915 32-32890 15-16713 22 23 [ 2 -2O6l I 45329 34-46041 15-62041 23 24 2-28333 43796 36-66653 16-05837 24 25 2-36324 42315 38 -94986 16-48152 25 26 2-44596 40884 4I-3I3IO 16-89035 26 27 2-53I57 39501 43-75906 I7-28537 27 28 2-620I7 38165 46 -29063 1 7 -66702 28 29 2-7II88 36875 48-91080 18-03577 29 30 2-80679 35628 51-62267 18-39205 30 31 2-90503 34423 54-42947 18-73628 31 32 3-00671 33259 5733450 19-06887 32 33 3-IH94 32134 60-34121 19-39021 33 34 3-22086 31048 63-453I5 1970068 34 35 3-33359 29998 66-67401 20-00066 35 36 3-45027 28983 70-00760 20-29049 36 37 3-57I03 28003 73-45787 20-57053 38 3-69601 27056 77-02889 20-84109 38 39 3-82537 26141 80-72490 21-10250 39 4 3 -95926 25257 84-55028 2I-35507 40 41 4-09783 24403 88-50953 21-59910 41 42 4-24126 23578 92-60737 21-83488 42 43 4-38970 22781 96-84863 22-06269 43 44 4-54334 22OIO 101-23833 22-28279 44 45 4-70236 21266 105-78167 22-49545 45 46 4-86694 20547 110-48403 2270092 46 47 5-03728 19852 II5-35097 22-89944 48 5-21359 -I9l8l 120-38826 23-09125 48 49 5-396o6 18532 125-60184 23-27657 49 50 5 -58493 | -17905 130-99791 23-45562 50 For explanation see pp. 8-13 (68) INTEREST TABLES Years ' ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 5-78040 17300 136-58283 23-62862 51 5 2 5-9827I 16714 142-36324 2379577 52 53 6-I92II 16150 I48-34595 53 54 6-40883 15603 24-11330 54 55 6-63314 15076 160-94689 24-26405 55 56 6-86530 14566 167-58003 24-40971 56 57 7-I0559 14073 I74-44533 24-55045 57 5* 735428 13598 181-55092 24-68642 59 7-61168 I3I38 188-90520 24-81780 59 60 7-87809 12693 196-51688 24-94474 60 61 8-15382 12264 204-39497 25-06738 61 62 8-43921 11849 212-54879 25-18587 62 63 873458 I 1449 220-98800 25-30036 63 64 9-04029 11062 22972258 25-41097 64 65 935670 10688 23876287 25-5I785 65 66 9-68418 10326 248-11957 25-62III 66 % 10-02313 10-37394 09977 09640 257-80376 25-72088 267-82689 25-81728 3 69 10-73703 09314 278-20083 25-91041 69 70 11-11282 08999 288-93786 26-00040 70 71 11-50177 08694 300-05069 26-08734 71 72 1 1 -90434 08400 311-55244 26-17134 72 73 12-32099 O8ll6 323-45680 26-25251 73 74 12-75222 07842 335-77778 26-33092 74 75 13-19855 07577 348-53001 26-40669 75 76 13-66050 07320 361-72856 26-47989 76 ft 14-13862 I4-63347 07073 06834 375-38906 26-55062 389-52768 26-61896 79 15-14564 06603 404-16115 26-68498 79 80 I5-67574 06379 419-30678 26-74878 80 81 16-22439 06164 434-98252 26-81041 81 82 1679224 05955 451-20691 26-86996 82 83 I7-37997 05754 467-99915 26-92750 83 84 17-98827 05559 485-37912 26-98309 84 85 18-61786 05371 503-36739 27-03680 85 86 19-26948 05190 521-98525 27-08870 86 87 19-94391 05014 541-25474 27-I3884 87 88 20-64195 04845 561-19865 27-18729 88 89 21-36442 04681 581-84060 27-23409 j 89 00 22-11217 04522 603-20503 27-27932 90 9i 22-88610 04369 625-31720 27-32301 1 91 92 23-68711 04222 648-20330 27-36523 92 93 24-51616 04079 671-89042 27-40602 93 94 25*37423 03941 696-40658 27-44543 94 95 26-26233 03808 721-78082 27-4835I 95 96 27-18151 03679 748-04314 27-52029 96 97 28-13286 03555 775-22465 27-55584 97 98 29-11751 03434 803-35752 27-59018 98 99 30-13662 03318 832-47503 27-62337 99 100 31-19141 03206 862-6II66 I 100 3ee also Tables on pp. xx-xxxi (69) 4% INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM ! Years Amount Present Value Amount Present Value I I '04000 96154 i -ooooo 96154 I 2 I -08160 92456 2 -04000 I -88609 2 3 12486 88900 3-12160 277509 3 4 16986 85480 4-24646 3-62990 4 5 21665 82193 5'4 I 632 4-45182 5 6 26532 79031 6-63298 5-24214 6 7 31593 75992 7-89829 6-00205 7 8 36857 73069 9-21423 673275 8 9 42331 70259 10-58280 7-43533 9 10 48024 67556 12-00611 8*11090 10 ii '53945 64958 13-48635 8-76048 ii 12 60103 62460 15-02581 938507 12 13 66507 60057 16-62684 9-98565 13 14 73168 57748 18-29191 10-56312 *4 15 "80094 55526 20-02359 11-11839 15 16 -87298 53391 21-82453 1 1 -65230 16 17 -9^790 51337 23-69751 12-16567 17 l8 ; 2-02582 49363 25-64541 12-65930 18 19 2-I0685 47464 27-67123 I3-I3394 19 20 2-19112 45639 29-77808 I3-59033 20 21 2-27877 43883 31-96920 14-02916 21 22 2-36992 42196 34-24797 14-45112 22 23 i 2-46472 40573 36-61789 14-85684 2 3 24 2-56330 39012 39-08260 15-24696 24 25 2-66584 37512 4I-6459I 15-62208 25 26 2-77247 36069 44-3II74 15-98277 26 27 2-88337 34682 47-08421 16-32959 2 7 28 ; 2 -99870 33348 49-96758 16-66306 28 29 3-11865 32065 52-96629 16-98372 29 30 3-24340 30832 56-08494 17-29203 30 31 3373I3 29646 59-32834 17-58849 31 32 3-50806 28506 62-70147 I7-87355 32 33 3-64838 27409 66-20953 18-14765 33 34 379432 26355 69-85791 18-41120 34 35 3*94609 25342 73-65222 18-66461 35 36 4-10393 24367 77-5983I 18-90828 36 37 4-26809 23430 81-70225 19-14258 38 ! 4-43881 22529 85-97034 19-36787 38 39 4-61637 21662 90-40915 19-58449 39 40 4-80102 20829 95-02552 19-79277 40 4i 4-99306 20028 99-82654 I9-99305 4 1 42 5-19278 19257 104-81960 20-18563 42 43 5-40050 18517 IIO-OI238 20-37080 43 44 5-61652 17805 115-41288 20-54884 44 45 5-84118 17120 121-02939 2072004 45 46 6-07482 16461 126-87057 20-88465 46 47 6-31782 15828 I32-94539 2 1 -04294 47 48 6-57053 15219 139-26321 2I-I95I3 4 8 49 6-83335 -14634 I45-83373 21-34147 49 50 7-10668 -14071 152-66708 21-48219 50 For explanation >ee pp. 8-13 (70) INTEREST TABLES years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 7-39095 '!3530 15977377 21-61749 51 52 7-68659 13010 167-16472 21-74758 52 53 7-99405 1 2509 1 74 -85 1 3 1 21 -87268 53 54 8-31381 12028 182-84536 21-99296 54 55 8-64637 11566 191-15917 22-10861 55 56 8-99222 i 1 121 199-80554 22-21982 56 57 9'35 I 9 I - Io6 93 20879776 22-32675 57 58 9'72599 10282 218-14967 22-42957 58 lo 9 10-11503 10-51963 09886 227-87566 09506 237-99069 22-52843 22-62349 g 61 10-94041 09140 248-51031 22-71490 6l 62 1 1 -37803 08789 259-45073 22-80278 62 63 II-833I5 08451 270-82875 22-88729 63 64 12-30648 08126 282-66190 22-96855 64 65 12-79874 07813 294-96838 23-04668 ; 65 66 13-31068 07513 307-76712 23-12181 66 68 13-84311 14-39684 07224 06946 321-07780 334-92091 23-19405 23-26351 3 69 14-97271 06679 349-3I775 23-33030 69 70 15-57162 06422 364-29046 2339452 70 71 16-19448 06175 379-86208 23-45627 71 72 16-84226 05937 396-05656 23-5 1 564 72 73 17-51595 05709 412-89892 23-57273 73 74 18-21659 05490 430-41478 23-62763 74 75 18-94525 05278 448-63137 23-68041 75 76 19-70307 05075 467-57662 2373116 76 20-49119 04880 487-27969 2377996 78 21-31084 04692 507-77087 23-82689 78 79 22-16327 04512 529-08171 23-87201 79 80 23-04980 04338 551-24498 23-9I539 80 81 23-97I79 04172 574-29478 23-95711 81 82 24-93066 04011 598-26657 23-99722 82 83 25-92789 03857 623-19723 24-03579 83 84 26-96500 03709 649-12512 24-07287 84 85 28-04360 03566 676-09012 24-10853 85 86 29-16535 03429 704-I3373 24-14282 86 87 30-33I96 03297 733-29908 24-17579 87 88 3 i -54524 03170 763-63104 24-20749 88 89 32-80705 03048 795-17628 24-23797 89 90 34-II933 02931 827-98333 24-26728 90 OI 35-48411 02818 862-10267 24-29546 9 1 92 36-90347 02710 897-58677 24-32256 92 93 38-37961 02606 934-49024 24-34861 93 94 39-9I479 02505 972-86985 24-37367 94 95 02409 1012-78465 24-39776 i 95 96 43-17184 02316 1054-29603 24-42092 96 97 44-89872 02227 1097-46788 24-44319 97 98 46-69467 02142 1142-36659 24-46461 98 99 48-56245 02059 1189-06125 24-48520 99 ,100 50-50495 01980 1237-62370 24-50500 100 See also Tables on pp. xx-xxxi (71) 4107 2 /< INTEREST TABLES ONE POUND Years ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value I I -04500 -95694 I -00000 95694 I 2 I -09203 91573 2-04500 1-87267 2 3 1-14117 87630 3-13702 2-74896 3 4 1-19252 83856 4-27819 3-58753 4 5 1-24618 80245 5-47071 4-38998 5 6 i -30226 76790 671689 5-I5787 6 7 i -36086 73483 8-01915 5-89270 7 8 i -42210 70319 9-38001 6*59589 8 g 1-48610 67290 10-80211 7-26879 9 10 I-55297 64393 I2-2882I 7-91272 10 H 1-62285 61620 13-84118 8-52892 ii 12 1-69588 58966 15-46403 9-11858 12 I 3 , I-77220 56427 I7-I599I 9-68285 13 I4 ; 1-85194 '53997 18-93210 10-22283 T 4 15 1-93528 51672 2078405 io-73955 15 16 2-02237 '49447 2271933 1 1 -23401 16 ! 7 2-11338 47318 2474170 11-70719 17 18 ; 2-20848 45280 26-85508 12-15999 18 I9 2-30786 43330 29-06356 12-59329 T 9 20 2-41171 41464 3I-37I42 13-00794 20 21 2-52024 39679 33783H 13-40472 21 22 2-63365 37970 36-30338 13-78442 22 23 275217 36335 38-93703 14-14777 23 24 2-87601 34770 41-68919 14-49548 24 25 3-00543 33273 44-5652I 14-82821 25 2 6 3-14068 31840 47-57064 15-14661 26 27 3-28201 30469 50-71132 15-45130 27 28 3 -42970 29157 53-99333 15-74287 28 29 3-58404 27901 16-02189 29 30 3-74532 26700 61-00707 16-28889 30 31 3-9I386 25550 6475238 16-54439 31 32 4-08998 24450 68-66624 1678889 32 33 4-27403 23397 72-75622 17-02286 33 34 4-46636 22390 77-03026 17-24676 34 35 4-66735 21425 81-49662 17-46101 35 36 4-87738 20503 86-16396 17-66604 36 37 5 -09686 19620 91-04134 17-86224 37 38 5-32622 18775 96-13820 18-04999 38 39 5-56590 17967 101*46442 18-22966 39 40 5-81636 I7I93 107-03032 18-40158 40 41 6-07810 16453 112-84668 18-56611 41 42 6-35161 15744 118-92479 18-72355 42 43 6-63744 15066 125-27640 18-87421 43 44 6-93612 14417 131-91384 19-01838 44 45 7-24825 13796 138-84996 19-15635 45 46 7-57442 13202 146-09821 19-28837 46 47 7-91527 12634 153-67263 19-41471 47 48 8-27145 12090 161-58790 19-53561 48 49 8-64367 11569 I69-85935 19-65130 49 50 9-03264 11071 I78-50303 19-76201 So For explanation see pp. 8-13 (72) INTEREST TABLES 4107 2 /< ONE POUND ONE POUND PER ANNUM Years Years i Amount 1 Present Value Amount Present Value 51 9-43910 -10594 187-53566 I9-86795 51 9-86386 -10138 196-97477 ,19-96933 S 2 53 10-30774 -09701 206-83863 20-06634 S3 54 I077I59 -09284 217-14637 20-15918 54 55 11-25631 -08884 227-91796 20-24802 55 56 11-76284 -08501 239-17427 20-33303 56 57 12-29217 -08135 250-93711 20-41438 57 58 12-84532 -07785 263-22928 20-49224 58 59 13-42336 -07450 276-97459 20-56673 59 60 14-02741 -07129 289-49795 20-63802 60 61 14-65864 -06822 303-52536 20-70624 61 62 15-31828 06528 318-18400 20-77152 62 63 16-00760 06247 333-50228 20-83399 63 64 1672794 05978 349-50988 20-89377 64 65 17-48070 05721 366-23783 20-95098 65 66 18-26733 05474 38371853 21-00572 66 67 19-08936 05239 401-98586 21-05811 67 68 19-94838 05013 421-07523 . 21-10824 68 69 20-84606 04797 441-02362 21-15621 69 70 2178413 04590 461-86968 2I'2O2II 70 71 2276442 04393 483-65381 21-24604 7 1 72 23-78882 -04204 506-41823 2I-28808 72 73 24-85931 -04023 530-20706 21-32830 73 74 25-97798 -03849 555-06637 21-36680 74 75 27-14699 -03684 581-04436 21-40363 75 76 28-36861 03525 608-19136 21-43888 76 29-64520 -03373 636-55997 21-47262 78 30-97923 -03228 666-20517 21-50490 78 79 32-37329 -03089 697-18440 21-53579 79 80 33-83009 02956 729-55770 21-56534 80 81 35-35245 02829 763-38779 21-59363 81 82 36-9433I 02707 798-74024 21-62070 82 83 38-60576 02590 835-68355 21-64660 83 84 40-34302 -02479 874-28931 21-67139 84 85 42-15845 -02372 914-63233 21-69511 85 86 44-05558 -02270 956-79079 21-71781 86 87 46-03808 -02172 1000-84637 2173953 87 88 48-10980 -02079 1046-88446 21-76032 88 89 50-27474 -01989 10^4-99426 21-78021 89 90 52-537io -01903 1145-26900 21-79924 90 91 54-90127 -01821 1197-80611 21-81746 9 1 92 57-37i83 -01743 1252-70738 21-83489 92 93 59-95356 94 62-65147 01668 01596 1316-07922 1370-03278 21-85156 21-86753 93 94 95 65-47079 -01527 1432-68426 21-88280 95 96 68-41697 -01462 1498-15505 21-89742 96 97 71-49574 -01399 1566-57202 21-91140 97 98 7471305 -01338 1638-06777 21-92479 98 99 78-07514 -01281 1712-78082 21-93760 99 100 81-58852 -01226 1/90-85595 21-94985 100 See also Tables 011 pp. \.\ xxxi (73) 6% INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Yalue Amount Present Value I 05000 95238 i-ooooo 95238 I 2 10250 -9O7O3 2-05000 I '85941 2 3 15763 86384 3-I5250 2-72325 3 4 2I55I 82270 4-3IOI3 3 '54595 4 5 27628 78353 5-52563 4-32948 5 6 '34010 74622 6-80191 5-07569 6 7 -40710 71068 8-14201 5-78637 7 8 -47746 67684 9'549 11 6-46321 8 9 -55133 64461 11-02656 7-10782 9 10 -62889 61391 12-57789 7-72173 10 ii 71034 58468 14-20679 8-30641 ii 12 79586 55684 15-91713 8-86325 12 I 3 '88565 53032 1771298 9-39357 13 14 97993 50507 19-59863 9-89864 M 15 2-07893 48102 21-57856 10-37966 i5 16 2-18287 45811 23-65749 10-83777 16 3 2-29202 2-40662 43630 25-84037 41552 28-13238 11-27407 1 1 -68959 11 19 2-52695 '39573 30-53900 12-08532 19 20 2-65330 37689 33-06595 12-46221 20 21 278596 35894 3571925 12-82115 21 22 2-92526 34185 38-5052I 13-16300 22 23 3-07152 32557 41-43048 13-48857 23 24 3-22510 31007 44-50200 13-79864 24 25 3-38635 29530 4772710 14-09394 25 26 .V55567 28124 5 I ' II 345 I4-375I8 26 27 373346 26785 54-66913 14-64303 27 28 3-92013 25509 58-40258 14-89813 28 29 4-11614 24295 62-32271 15-14107 29 3 4'32I94 23138 66-43885 I5'37245 3 31 4-53804 22036 70-76079 15-59281 31 32 4-76494 20987 75-29883 15-80268 32 33 5-00319 19987 80-06377 16-00255 33 34 5-25335 19035 85-06696 16-19290 34 35 5-51602 18129 90-32031 16-37419 35 36 5-79182 17266 95-83632 16-54685 36 6-08141 16444 101-62814 16-71129 37 38 6-38548 15661 107-70955 16-86789 38 39 6-70475 I49I5 114-09502 17-01704 39 40 7-03999 14205 120-79977 17-15909 40 4 1 7-39I99 13528 127-83976 17-29437 4i 42 7-76159 12884 I35-23I75 17-42321 42 43 8-14967 12270 142-99334 I7-5459I 43 44 45 8-557I5 8-98501 11686 11130 151-14301 159-70016 17-66277 17-77407 44 45 46 9-43426 10600 168-68516 17-88007 46 47 9-90597 10095 178-11942 17-98101 47 48 10-40127 09614 188-02539 18-07716 48 49 10-92133 09156 198-42666 18-16872 49 50 1 1 -46740 08720 209-34800 18-25592 50 For explanation see pp. 8-13 (74) INTEKEST TABLES 5% Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 12-04077 08305 220-81540 I8-33898 j 51 5 2 12-64281 07910 232-85617 18-41807 52 53 I3-27495 07533 245-49897 18-49340 53 54 13-93870 07174 258-77392 18-56514 54 55 I4-63563 06833 272-71262 18-63347 55 56 15-36741 06507 287-34825 18-69854 56 16-13578 06197 30271566 1876052 57 58 16-94257 05902 318-85144 18-81954 58 59 17-78970 05621 335-79402 18-87575 59 60 18-67919 -05354 18-92929 60 61 19-61315 -05099 372-26290 18-98027 61 62 20-59380 -04856 391-87605 19-02883 62 63 21-62349 -04625 412-46985 19-07508 63 64 22-70467 04404 434'09334 19-11912 64 65 23-83990 04195 456-7980I 19-16107 65 66 25-03190 03995 480-63791 19-20102 66 67 26-28349 03805 505-66981 19-23907 67 68 27-59766 03623 53I-95330 19-27530 68 69 70 28-97755 30-42643 03451 03287 559-55096 588-52851 19-30981 69 19-34268 70 71 31-94775 -03130 618-95494 19-37398 7i 72 33-545I3 02981 650-90268 I9-40379 7 2 73 02839 684-44782 19-43218 73 74 36-9835I 02704 719-67021 19-45922 74 75 38-83269 02575 19-48497 75 76 40-77432 02453 795-48640 19-50949 7 6 42-81304 02336 836-26072 19-53285 77 78 44-95369 02225 879-07376 19-55510 78 79 47-20I37 02II9 924-02745 19-57628 79 80 49-56144 02018 971-22882 19-59646 80 81 52-0395I 01922 102079026 19-61568 81 82 54-64149 01830 1072-82978 19*63398 82 83 01743 1127*47126 19-65141 83 84 60-24224 Ol66o 1184-84483 19-66801 84 85 63-25435 01581 1245-08707 19-68382 85 86 66-41707 01506 1308-34142 19-69887 86 87 69-73792 01434 I374-75849 1971321 87 88 73-22482 01366 1444-49642 19-72687 88 89 76-88606 OI30I 1517-72124 19-73987 89 90 80-73037 01239 1594-60730 19-75226 90 91 84-76688 OIlSo I675-33767 19-76406 91 92 89-00523 OII24 1760-10455 1977529 02 93 93-45549 01070 1849-10978 I9-78599 93 94 98-12826 OIOI9 1942-56527 1979618 94 95 103-03468 00971 2040-69353 19-80589 95 96 108-18641 00924 2143-72821 19-81513 96 97 "3-59573 00880 2251-91462 19-82394 97 98 II9-27552 00838 2365-51035 19-83232 08 99 125-23929 00798 248478586 19-84030 99 100 131-50126 00760 2610-02516 19-84791 100 See also Tables on pp. xx-xxxi (75) 6% INTEREST TABLES ONE POUND Years ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I I -06000 94340 I -00000 94340 I 2 1-12360 89000 2-o6oOO I-83339 2 3 1-19102 83962 3-18360 2-67301 3 4 -26248 79209 4-37462 3-465II 4 5 '33823 74726 5-63709 4-21236 5 6 -41852 70496 6-97532 4-91732 6 7 -50363 66506 5-58238 7 8 -59385 62741 9-89747 6-20979 8 9 i -68948 59190 II-49I32 6-80169 9 10 1-79085 55839 13-18079 7-36009 10 ii 1-89830 52679 14-97164 7-88687 ii 12 2-OI22O 49697 16-86994 8-38384 12 13 2*13293 46884 I8-882I4 8-85268 13 14 2*26090 44230 2I-OI507 9-29498 14 15 2-39656 41727 23-27597 971225 15 16 2-54035 39365 25-67253 10-10590 16 17 2-69277 37136 28-2I288 10-47726 17 18 2-85434 35034 30-90565 10-82760 18 !9 3-02560 33051 33*75999 11-15812 19 20 3-207I4 31180 3678559 1 1 -46992 20 21 339956 29416 39-99273 1 1 -76408 21 22 3-60354 27751 43-39229 12-04158 22 23 3-8I975 26180 46*99583 12-30338 23 24 4-04893 24698 50-8I558 12-55036 24 25 4-29I87 23300 54-86451 1278336 25 26 4-54938 21981 59-I5638 13-00317 26 27 4-82235 20737 63-70577 13-21053 27 28 5*11169 19563 68-52811 13-40616 28 29 5-4I839 18456 73-63980 13-59072 29 30 574349 I74II 79-05819 I3-76483 30 31 6-08810 16425 84-80168 13-92909 31 32 6-45339 15496 90-88978 14-08404 32 33 6-84059 14619 97-343*6 14-23023 33 34 7-25103 13791 104-18375 14-36814 34 35 7-68609 I3OII 1 1 1 -43478 14-49825 35 36 8-14725 12274 119-12087 14-62099 36 37 8-63609 II579 127-26812 14-73678 37 38 9^5425 10924 135-90421 14-84602 38 39 970351 10306 145-05846 14-94907 39 40 10-28572 09722 154-76197 15-04630 40 41 10-90286 09172 165-04768 15-13802 41 42 11-55703 08653 I75-95054 15*22454 42 43 12-25045 08163 187-50758 15-30617 43 44 12-98548 07701 19975803 I5-383I8 44 45 1376461 07265 212-74351 I5-45583 45 46 14-59049 06854 226-50812 I5-52437 46 47 15-46592 06466 241-09861 15-58903 48 16-39387 O6l00 256-56453 15-65003 48 49 I7-37750 05755 272-95841 1570757 49 50 18-42015 05429 290-33590 15-76186 50 For explanation see pp. 8-13 (76) INTEREST TABLES 6/o Tears ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value 51 52 19-52536 -05122 20-69689 -04832 308-75606 328-28142 15-81308 51 15-86139 52 53 21-93870 -04558 348-97831 15-90697 53 54 23-25502 -04300 370-91701 I5-94998 54 55 24-65032 -04057 394-17203 I5-99054 55 56 26-12934 -03827 418-82235 16-02881 56 5 y 27-69710 -03610 444-95169 16-06492 57 58 29-35893 -03406 472-64879 16-09898 58 59 31-12046 -03213 502-00772 16-13111 59 60 32-98769 -03031 533-12818 16-16143 60 61 34-96695 -02860 566-11587 16-19003 j 61 62 37-06497 -02698 601-08282 16-21701 62 63 39-28887 -02545 638-14779 16-24246 63 64 41-64620 -02401 677-43666 16-26647 64 65 44-H497 -02265 719-08286 16-28912 65 66 46-79367 -02137 763-22783 16-31049 66 67 49-60129 -02016 810-02150 16-33065 67 68 52-57737 -01902 859-62279 16-34967 68 69 55-7320I -01794 912-20016 16-36792 69 70 59^7593 " Ol6 93 967-93217 16-38454 70 71 62-62049 '01597 1027-00810 16-40051 71 72 66-37772 -01507 1089-62859 16-41158 72 73 70-36038 -01421 1156-00630 16-42979 73 74 74-58200 -01341 1226-36668 16-44320 74 75 79-05692 -01265 1300-94868 16-45585 75 76 83-80034 -OII93 1380-00560 16-46778 7 6 % 88-82836 94-15806 OII26 01062 1463-80594 1552-63429 16-47904 77 16-48966 78 B 99-80754 I05-79599 OIOO2 00945 1646-79235 1746-59989 16-49968 16-50913 g 81 112-14375 -00892 1852-39588 16-51805 81 82 118-87238 -00841 1964-53964 16-52646 82 83 126-00472 00794 2083-41202 16-53440 83 84 133*56500 00749 2209-41674 16-54188 84 85 141-57890 00706 2342-98174 16-54895 85 86 150-07364 00666 2484-56065 16-55561 86 87 159-07806 00629 2634-63428 16-56190 87 88 168-72274 -00593 279371234 16-56783 88 89 178-74010 00559 2962-33508 16-57342 89 90 189-46451 00528 3141-07519 16*57870 90 9i 200-83238 00498 3330-53970 16-58368 9i 92 212-88232 00470 353i-372o8 16-58838 92 93 225-65526 -00443 3744-25441 16-59281 93 94 239-I9458 -00418 3969-90967 16-59699 94 95 253-54625 -00394 4209-10425 16-60093 95 96 268-75903 00372 4462-65050 16-60465 96 97 284-88457 00351 4731-40953 16-60816 97 98 99 100 301-97765 320-09631 339-30208 00331 00312 00295 5016-29411 5318-27175 5638-36806 16-61147 16-61460 16-61755 98 99 100 See also Tables on pp. xx-xxxi (77) / /O INTEKEST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I I-07000 93458 I'OOOOO 93458 I 2 14490 87344 2-O7OC)O I -80802 2 3 22504 81630 3-21490 2-62432 3 4 31080 76290 4*43994 3-38721 4 5 40255 71299 5-75074 4-10020 5 6 50073 66634 7-I5329 4-76654 6 7 60578 62275 8-65402 5*38929 7 8 71819 58201 10-25980 5-97I30 8 9 83846 '54393 11-97799 6-5I523 9 10 96715 50835 13-81645 7*02358 10 ii 2-10485 47509 15-78360 7-49867 ii 12 2-25219 44401 17-88845 7-94269 12 13 2-40985 41496 20-14064 8-35765 13 14 2-57853 38782 22-55049 8-74547 14 15 2-75903 36245 25-12902 9-10791 15 16 2-95216 -33873 27-88805 9-44665 16 '7 3-15882 -31657 30-84022 9-76322 17 18 3*37993 -29586 33-99903 10-05909 18 19 3-61653 -27651 10-33560 19 20 3-86968 -25842 40-99549 10-59401 20 21 4-14056 -24151 44-86518 10-83553 21 22 4-43040 -22571 49-00574 11-06124 22 23 4-74053 -21095 53-436I4 11-27219 23 24 5-07237 -19715 58-17667 II*46933 24 25 5-42743 -18425 63-24904 11-65358 25 26 5*80735 -17220 68-67647 11-82578 26 2 7 6-21387 -16093 74-48382 11-98671 2 7 28 6-64884 -15040 80-69769 12-13711 28 29 7-11426 -14056 87-34653 12-27767 29 30 7-61226 -13137 94-46079 12-40904 30 3 1 8-14511 -12277 102-07304 12-53181 31 32 8-71527 II474 110-21815 12-64656 32 33 932534 10723 II8-93343 12-75379 33 34 9-97811 10022 128-25876 I2-8540I 34 35 10-67658 09366 138-23688 12-94767 35 3-5 11-42394 08754 148-91346 I3-0352I 36 12-22362 O8l8l 160-33740 I3-II702 37 38 13-07927 07646 172-56102 I3*i9347 38 39 13-99482 07146 185-64029 13-26493 39 40 14-97446 06678 199-63511 IS'SS 1 ?! 40 4 1 16-02267 06241 214-60957 13-39412 41 42 17-14426 05833 230-63224 13*45245 42 43 18-34435 05451 247-77650 13-50696 43 44 19-62846 05095 266-12085 I3-5579 1 44 45 21-00245 04761 285-7493 1 13-60552 45 46 22-47262 04450 306-75176 13-65002 46 47 24-04571 04159 329-22439 13-69161 47 48 25-72891 03887 353-27009 13-73047 48 49 27-52993 03632 378-99900 13-76680 49 50 29-45703 -03395 406-52893 13-80075 50 For explanation see pp. 8-13 (78) INTEKEST TABLES 7/ Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 31-51902 03173 435-98595 I3-83247 51 52 33-72535 02965 467-50497 13-86212 52 53 36-08612 02771 501-23032 ; 13-88984 53 54 38-61215 02590 537-31644 13-91573 54 55 41-31500 02420 575-92859 I3-93994 55 56 44-20705 02262 617-24359 13-96256 56 57 47-30155 02114 661-45065 13-98370 58 50-61265 01976 70875219 14-00346 58 59 54-15554 01847 759-36484 14-02192 59 60 57-94644 01726 813-52038 14-03918 60 61 62-00267 01613 871-46681 14-05531 61 62 66-34286 01507 933-46949 14-07038 62 63 70-98686 01409 999-81235 14-08447 63 64 75-95594 01317 1070-79922 14-09764 64 65 81-27285 01230 1146-75516 14-10994 65 66 86-96195 01150 1228-02802 14-12144 66 67 93 -04929 01075 1314-98998 14-13219 67 68 99-56274 01004 1408-03928 14-14223 68 69 106-53213 00939 1507-60203 14-15162 69 70 113-98938 00877 i6i4'i34i7 14-16039 70 71 121-96864 00820 1728-12357 14-16859 7 1 72 130-50644 00766 1850-09222 14-17625 72 73 139-64189 00716 1980-59867 14-18341 73 74 149-41682 00669 2120-24058 14-19010 74 75 159-87600 00625 2269-65742 14-19636 75 76 171-06732 00585 2429-53344 14-20220 76 77 183-04203 78 195-85498 00546 2600-60078 14-20767 : 77 00511 2783-64283 14-21277 78 79 209-56483 00477 2979-49783 14-21755 79 80 224-23437 00446 3189-06268 14-22201 80 8l 239-93077 00417 3413-29707 14-22617 81 82 256-72592 00390 3653-22786 14-23007 82 83 274-69674 00364 3909-9538I 14-23371 83 84 293-92551 00340 4184-65058 14-23711 84 85 314-50029 00318 4478-57612 14-24029 85 86 336-5I53I 00297 4793-07645 14-24326 86 87 360-07139 00278 5129-59180 14-24604 87 88 385*27638 00260 5489-66323 14-24863 88 89 412-24573 00243 5874-93965 14-25106 89 90 441-10293 00227 6287-18543 I4-25333 I 9 91 471-98014 00212 6728-28841 I4-25545 Qi 92 505-OI875 00198 7200-26859 I4'25743 92 93 540-37006 00185 7705-28740 14-25928 93 94 578-I9596 00173 8245-6575I 14-26101 94 95 618-66968 00162 8823-85354 14-26262 95 96 661-97656 OOI5I 9442-52329 14-26413 96 97 708-31492 OOI4I 10104-49992 14-26555 97 98 757-89696 00132 10812-81491 14-26686 98 99 810-94975 00123 11570-71196 14-26810 99 100 867-71623 OOII5 12381-66179 14-26925 100 Bee also Tables on pp. xx-xxxi (79) 8% INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I I -OSOOO 92593 I 'OOOOO 92593 j 2 16640 85734 2-08000 1-78326 2 3 25971 79383 3 -24640 2-57710 ^ 4 36049 73503 4-50611 3-3I2I3 A 5 46933 68058 5-86660 3-99271 5 6 58687 63017 7-33593 4-62288 6 7 71382 '58349 8-92280 5-20637 7 8 85093 54027 10-63663 5-74664 8 9 I -99900 50025 12-48756 6-24689 9 10 2-15892 46319 14-48656 671008 10 ii 2-33164 42888 16-64549 7-I3896 ii 12 2-51817 397II 18-97713 7-53608 12 13 2-71962 36770 21-49530 7-90378 J 3 J 4 2-93719 34046 24-21492 8-24424 J 4 16 3-I72I7 31524 27-15211 8-55948 15 16 3-42594 29189 30-32428 8-85137 16 11 3-70002 3 -99602 27027 25025 3375023 37-45024 9-12164 9-37189 11 19 4-3I570 23171 41-44626 9-60360 19 20 4-66096 21455 4576196 9-8I8I5 20 21 5'03383 19866 50-42292 10-01680 21 22 5-43654 18394 55-45676 10-20074 22 23 5-87146 17032 60-89330 10-37106 23 24 6-34118 I577C 66-76476 10-52876 24 25 6-84848 14602 73 '! 594 10-67478 25 26 7-39635 13520 79-95442 10-80998 26 2 7 7-98806 12519 87-35077 10-93516 27 28 8-62711 II59I 95-33883 11-05108 28 29 9-31727 10733 103-96593 11-15841 29 30 10-06266 09938 113-28321 n-257'78 30 31 10-86767 09202 123-34587 1 1 -34980 31 32 11-73708 08520 134-21354 11-43500 32 33 12-67605 07889 145-95062 11-51389 33 34 13-69013 07305 158-62667 11-58693 34 35 I4-78534 06763 172-31680 n-65457 35 36 15-96817 06262 187-10215 11-71719 36 37 17-24563 05799 203-07032 11-77518 37 38 18-62528 05369 220-31595 1 1 -82887 38 39 20-11530 04971 238-94122 11-87858 39 40 21-72452 04603 259-05652 11-92461 40 4i 23 -46248 04262 280-78104 11-96723 4i 42 25-33948 03946 304-24352 12-00670 42 43 27-36664 03654 329-58301 12-04324 43 44 29-55597 03383 356-94965 12-07707 44 45 31-92045 03133 386-50562 12-10840 45 46 34-47409 02901 418-42607 12-13741 46 47 37-23201 02686 452-90015 12-16427 47 48 40-21057 02487 490-13216 12-18914 48 49 43-42742 02303 530-34274 12-21216 49 50 46-90161 02132 573-77016 12-23348 50 For explanation see pp. 8-13 (So) INTEREST TABLES ONE POUND ONE POUND PEE ANNUM Years Years Amount Present Value Amount Present Value 51 50-65374 01974 620-67177 12-25323 51 52 54-70604 01828 67I3255 1 I2-27I5I *2 53 59-08252 01693 726-03155 12-28843 54 63-80913 01567 785-11408 12-30410 ^4 55 68-91386 01451 848-92320 12-31861 55 56 74-42696 01344 917-83706 12-33205 56 80-38112 01244 992-26402 12-34449 ^7 58 86'8ll6l OII52 1072-64514 12-35601 58 g 9375654 IOI-257O6 01067 00988 1159-45676 12-36668 59 1253-21330 12-37655 60 61 I09-35763 00914 1354-47036 12-38570 61 62 118-10624 00847 1463-82799 12-39416 62 63 I27-55474 00784 1581-93423 12-40200 63 64 I37-759I2 00726 1709-48897 12-40926 64 65 148-77985 00672 1847-24808 12-41598 65 66 160-68223 00622 1996-02793 1 2 '422 2 1 66 67 I73-5368I 00576 2I56-7IOI6 I2-42797 67 68 187-41976 00534 2330-24698 12-43330 68 69 202-41334 00494 2517-66673 12-43824 69 70 218-60641 00457 2720-08007 12-44282 70 7i 236-09492 00424 2938-68648 12-44705 7 1 72 254-98251 00392 3174-78140 12-45098 72 73 275-38111 00363 3429-76391 12-45461 73 74 297-41160 00336 3705-14502 12-45797 74 75 321-20453 003II 4002-55662 12-46108 75 76 346-90089 00288 4323-76115 12-46397 76 77 374-65296 00267 4670-66205 12-46664 78 404-62520 00247 5045-31501 12-46911 78 79 436-99522 -00229 5449-94021 12-47139 79 80 47I-95483 00212 5886-93543 12-47351 80 81 5097II22 00196 6358-89026 12-47548 81 82 550-48812 00182 6868-60148 12-47729 82 83 594-527I7 00168 7419-08960 12-47897 83 84 642-08934 00156 8013-61677 12-48053 84 85 693'45649 00144 8655-70611 12-48197 85 86 748-9330I 00134 9349-16260 12-48331 86 87 808-84765 OOI24 10098-09561 I2-48455 87 88 873*55546 00114 10906-94326 12-48569 88 89 943*43990 OOI06 11780-49872 12-48675 89 oo 1018-91509 00098 12723-93862 12-48773 90 91 1100-42830 00091 13742-85370 12-48864 9 1 92 1188-46256 00084 14843-28200 12-48948 92 93 1283-53956 00078 16031-74456 12-49026 93 94 1386*22273 00072 17315-28413 12-49098 94 95 I497-I2055 00067 18701-50686 12-49165 95 06 1616-89019 OOO62 20198-62740 12-49227 06 97 1746-24141 00057 21815-51760 12-49284 97 98 1885-94072 00053 23561-75900 12-49337 98 99 2036-81598 00049 25447-69972 12-49386 99 100 2199-76126 00045 27484-51570 12-49432 100 See also Tables on pp. xx-xxxi (81) INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value I 09000 91743 I -00000 W43 I 2 I88l0 84168 2-09000 I-759II 2 3 29503 77218 3-27810 2-53129 3 4 41158 70843 4-573I3 3-23972 4 5 53862 64993 5-9847I 3-88965 5 6 67710 59627 7-52333 4-48592 6 7 82804 54703 9-20043 5-03295 7 8 99256 50187 1 1 -02847 8 9 2-17189 46043 13-02104 5-99525 9 10 2-36736 42241 15-19293 6-41766 10 ii 2-58043 38753 17-56029 6-80519 ii 12 2-8I266 '35553 20-14072 7-16073 12 J 3 3 -06580 32618 22-95338 7 -48690 14 3-34I73 29925 26-01919 7-78615 14 15 3-64248 27454 29-36092 8-06069 15 16 3-97031 25187 33-00340 8-31256 16 17 4-32763 23107 36-97370 8-54363 17 18 471712 21199 4I-30I34 875563 18 10 5-14166 19449 46-01846 8-95011 in 20 5-60441 17843 51-16012 9-12855 20 21 6-10881 16370 5676453 9-29224 21 22 6-65860 15018 62-87334 9'44243 22 23 7-25787 13778 69-539I4 9-58021 2 3 24 7-91108 12640 76-78981 9-70661 24 25 8-62308 11597 8470090 9-82258 25 26 9-39916 10639 93-32398 9-92897 26 27 10-24508 09761 102-72313 10-02658 28 11-16714 08955 112-96822 10-11613 28 29 12-17218 08215 I24-I3536 10-19828 ; 20 30 13-26768 07537 I36-30754 10-27365 30 31 14-46177 06915 I49-57522 10-34280 31 32 1576333 06344 164-03699 10-40624 32 33 17-18203 05820 179-80032 10-46444 33 34 1872841 05339 196-98234 10-51784 34 35 20-41397 04899 21571075 10-56682 35 36 22-25123 04494 236-12472 10-61176 36 24-25384 04123 25837595 10-65299 37 38 26-43668 03783 282-62978 10-69082 38 39 28-81598 03470 309-06646 10-72552 39 40 31-40942 03184 337-88245 1075736 40 4 1 34-23627 02921 369-29187 1078657 4 1 42 37-3I753 02680 403-52813 10-81337 42 43 40-67611 02458 440-84566 10-83795 43 44 44*33696 02255 481-52177 10-86051 44 45 48-32729 02069 525^5873 10-88120 45 46 52-67674 01898 574-I8602 10-90018 46 57'4i765 01742 626-86276 10-91760 48 62-58524 01598 684-28041 10-93358 48 49 68-21791 01466 746-86565 10-94823 49 50 74-35752 01345 815-08356 10-96168 50 For explanation see pp. 8-13 (82) INTEREST TABLES Years ONE POUND ONE POUND PER ANNUM Years Amount Present Value Amount Present Value 51 81-04970 01234 889-44108 10-97402 51 5 2 88-344I7 01132 970-49077 IO-98534 52 53 96-29514 01038 1058-83494 iQ'99573 53 54 104-96171 00953 1155-13009 11-00525 54 55 114-40826 00874 1260-09180 11-01399 55 56 12470501 00802 1374-50006 II-O22OI 56 135-92846 00736 1499-20506 11-02937 eg 148-16202 00675 I635-I3352 II-036I2 58 59 161-49660 00619 I783-29553 II-0423I 59 60 176-03129 00568 1944-79213 1 1 -04799 60 61 191-87411 00521 2120-82342 1 1 -05320 61 62 209-14278 00478 2312-69753 1 1 -05798 62 63 227-96563 00439 2521-84031 1 1 -06237 63 64 248-48253 00402 2749-80594 1 1 -06640 64 65 270-84596 00369 2998-28847 1 1 -07009 65 66 295-222IO 00339 3269-13444 11-07347 66 67 32179209 00311 3564-35654 11-07658 67 68 35075338 -00285 3886-14862 1 1 -07943 68 69 382-32118 00262 4236-90200 1 1 '08205 69 70 416-73009 00240 4619-22318 1 1 -08445 70 71 454-23579 00220 5035-95327 1 1 -08665 7i 72 495-11702 00202 5490-18906 1 1 -08867 72 73 539-67755 ; -00185 5985-30608 1 1 -09052 73 74 588-24853 00170 6524-98362 ir09222 74 75 641-19089 00156 7113-23215 1 1 ^9378 75 76 698-89807 00143 7754-42304 II-0952I 76 77 761 -79890 OOI3I 8453-32II2 ir09653 77 78 830-36080 00120 92I5-I2002 H-09773 78 79 905-09327 ooi 10 10045-48082 11-09883 79 80 986-55167 ooioi 10950-57409 1 1 -09985 80 81 1075-34132 00093 II937-I2576 II-I0078 81 82 1172-12204 -00085 13012-46708 II-IOI63 82 83 1277-61302 -00078 14184-58911 II-I024I 83 84 1392-59819 OOO72 15462-20213 II-I03I3 84 85 1517-93203 00066 16854-80033 11-10379 85 86 1654-54591 00060 1837273236 II-I0440 86 87 1803-45504 00055 20027-27827 11-10495 87 88 1965-76600 00051 2183073331 II-I0546 88 89 2142-68494 00047 23796-49931 11-10593 89 90 2335-52658 00043 25939-18425 II-I0635 90 91 2545-72397 00039 2827471083 II-I0675 91 92 2774-83913 00036 30820-43481 II-I07II 92 93 3024-57465 00033 33595-27394 11-10744 93 94 3296-78637 00030 36619-84859 11-10774 94 95 3593-49715 00028 399!6'63497 II-I0802 95 96 3916-91189 00026 435IO-I32II II-I0827 96 3 4269-43396 4653-68302 00023 00021 47427-04400 51696-47796 II-I085I II-IO872 97 08 99 5072-51449 00020 56350-16098 II-I0892 99 100 5529-04079 00018 61422-67547 II-I09IO 100 See also Tables on pp. xx-xxxi (83) D2 INTEEEST TABLES Years ONE POUND ONE POUND PER ANNUM 1 Years Amount Present Value Amount Present Value I 10000 90909 I -00000 90909 I 2 21000 82645 2-10000 1-73554 2 3 33100 75 I 3 I 3*3*000 2-48685 3 4 46410 '68301 4-64100 3-16987 4 5 61051 '62092 6-10510 379079 5 6 1-77156 -56447 77I56I 4-35526 6 7 1-94872 -51316 9-48717 4*86842 7 8 2-14359 -46651 5-33493 8 g 2-35795 -42410 I3-57948 575902 9 10 2-59374 -38554 I5-93742 6-14457 10 ii 2-85312 -35049 18-53117 6-49506 ii 12 3-13843 -31863 21-38428 6-81369 12 13 3-45227 -28966 24-52271 7-I0336 13 l| 3-79750 -26333 27-97498 7-36669 15 4-17725 -23939 3177248 7-60608 15 16 4-59497 -21763 35*94973 7-82371 16 3 5-05447 19784 17986 40-54470 45 '599 1 7 8-02155 8*20141 11 10 6*11591 I635I 5i '15909 8*36492 19 y 20 672750 14864 57-27500 8-5I356 20 21 7-40025 -13513 64*00250 8-64869 21 22 8-14027 -12285 71-40275 877154 22 23 24, 8-95430 9-84973 III68 IOI53 79-54302 88-49733 8-88322 8-98474 23 24 "T 25 10-83471 09230 98-34706 9-07704 25 26 11-91818 08391 109*18177 9-16095 26 13-10999 07628 121-09994 9-23722 27 o 14-42099 -06934 134-20994 9-30657 28 20 15-86309 06304 148-63093 9-36961 29 7 30 17-44940 05731 164-49402 9*42691 30 31 19-19434 05210 181-94342 9-47901 31 o 21-11378 -04736 201-13777 9-52638 32 33 23-22515 -04306 222-25154 9-56943 33 ^A 25*54767 'O3QI4 245 -47670 9-60857 34 OT 35 28-I0244 03558 271-02437 9-64416 35 36 30-91268 03235 299-12681 9*67651 36 34-00395 02941 330-03949 9*70592 37 38 37-40434 02673 364-04343 973265 38 39 41-14478 02430 401-44778 975696 39 *J" 40 45-25926 02209 442-59256 9-77905 40 41 4978518 O2OO9 487-85181 9-79914 41 T 42 54-76370 60-24007 01826 Ol66o 592-40069 9-81740 9-83400 42 43 44 45 66-26408 72-89048 01509 01372 652-64076 718-90484 9-84909 9-86281 44 45 46 80-I7953 01247 79I-79532 9-87528 46 T.W ! 88-19749 97-01723 106-71896 01134 01031 00937 871-97485 960-17234 1057-18957 9-88662 47 9-89693 48 9-90630 49 50 II7-39085 00852 1163-90853 9-91481 | 50 For explanation see pp. 8-13 (84) INTEREST TABLES Yean ONE POUND ONE POUND PEE ANNUM Years Amount Present Value Amount Present Value 51 129-12994 00774 1281-29938 9-92256 51 52 142-04293 00704 1410-42932 9-92960 52 53 156-24723 00640 1552-47225 9-93600 53 54 171-87195 00582 170871948 9-94182 54 55 189-05914 00529 1880-59142 9-947II 55 56 207 -96506 00481 2069-65057 9-95191 56 228-76156 00437 2277-61562 9-95629 58 251-63772 00397 2506-37719 9-96026 58 io 9 276*80149 304-48164 00361 00328 2758-01490 3034-81640 9-96387 9-96716 Io 9 61 334-92980 00299 3339-29803 9-97014 61 62 368-42278 00271 3674-22784 9-97286 62 63 405-26506 00247 4042 -65062 9-97532 63 64 445-79I57 00224 4447-91568 9-97757 64 65 490-37073 00204 4893-70725 9-97961 65 66 539-40780 00185 5384-07798 9-98146 66 67 59334858 00169 5923-48578 9-983I5 67 68 652-68344 00153 6516-83435 9-98468 68 69 717-95178 00139 7169-51779 9-98607 69 70 789-74696 OOI27 7887-46957 9-98734 70 7 1 86872165 00115 8677-21652 9-98849 71 72 955-59382 00105 9545'938l8 9^954 72 73 1051-15320 00095 10501-53199 9-99049 73 74 1156-26852 00086 11552-68519 9-99I35 74 75 1271-89537 00079 12708-95371 9-99214 75 76 1399-08491 00071 13980-84909 9-99285 76 77 1538-99340 00065 I5379-93399 9'99350 77 78 1692-89274 00059 16918-92739 9-99409 78 79 1862-18201 00054 1 86 1 1 -8201 3 9-99463 80 2048-40021 00049 20474 '00215 9-99512 80 81 2253-24024 00044 22522-40236 9*99556 81 82 2478-56426 00040 24775-64260 9-99597 82 83 2726-42069 00037 27254-20686 83 84 2999-06275 00033 29980-62754 9-99667 84 85 3298-96903 00030 32979-69030 85 86 3628-86593 00028 36278-65932 9-99724 86 2 7 399175253 00025 39907-52526 9-99749 87 88 4390-92778 00023 43899*27778 9-99772 88 89 4830-02056 OOO2I 48290-20556 9-99793 89 90 5313-02261 00019 53I20-226I2 9-99812 90 9 1 5844-32487 00017 58433*24873 9-99829 91 92 6428-75736 000l6 64277-57360 92 93 7071-63310 00014 70706-33096 9-99859 93 94 777879641 00013 77777-96406 9-99871 94 95 8556-67605 00012 85556-76046 9-99883 95 96 9412-34365 oooi i 94113-43651 9-99894 96 97 10353-57802 oooio 103525-78016 9-99903 97 08 II388-93582 00009 II3879-358I8 9-99912 98 99 12527-82940 OOOOS 125268-29400 9-99920 99 100 13780-61234 00007 137796-12340 9-99927 100 See also Tables on pp. xx-xxxi. For 15% see p. xl (85) INTEKEST TABLES AMOUNT OF ONE POUND AT END OF YEAK Years 1% li% u% lf% Years 10 20 30 4 50 10462 22019 34785 48886 64463 13227 28204 45161 64362 86102 1-16054 i -34686 i -56308 1-81402 2-10524 1-18944 1-41478 i -68280 2-00160 2-38079 10 20 30 40 50 00 70 80 00 100 10 20 30 40 50 1-81670 2-00676 2-21672 2-44863 2-70481 2-10718 2-44322 2-38590 2-83546 270149 3-29066 3-05881 3-81895 3-46340 4-43205 2-83182 3-36829 4-00639 4-76538 5-66816 60 Z 90 IOO 10 20 30 40 50 2% 2i% 2i% 2f% 1-21899 I -48595 1-81136 2-20803 2-69159 i -24920 i -28008 1-56051 1-63862 1-94939 2-09757 2-43519 ; 2-68506 3-04205 3-437II 1-31165 i -72043 2-25660 2-95987 3-88232 60 70 80 90 100 10 20 30 40 50 3-28103 3-99956 4-87544 5-943I3 7-24465 3-80013 474714 5-930I5 7-40796 9-25405 4-39979 5-63210 7-20957 9-22886 11-81372 5-09225 6-67926 8-76085 11-49118 15-07242 60 70 80 90 IOO 10 20 30 40 50 3Q/ /o 3i% 3i% 3f% 1-34392 i -806 1 1 2-42726 3-26204 4-3839I 1-37689 1-89584 2-61037 3-59420 4-94884 1-41060 I -98979 2-80679 3-95926 5-58493 i -44504 2-08815 3-01747 4-36038 6-30094 60 & go IOO 5-89160 7-91782 10-64089 14-30047 19-21863 6-81402 9-38219 12-91828 17-78711 24-49097 7 -87809 11-11282 I5-67574 22-11217 31-19141 9-10513 13-15732 19-01290 27-47448 39-70183 00 70 80 90 IOO For explanation see pp. 8-13 (86) INTEREST TABLES AMOUNT OF ONE POUND AT END OF YEAR Years 4% 4i% 4t% 4f% Years 10 1-48024 1-51621 1-55297 i -59052 10 20 2-19112 2-29891 2-41171 2-52977 20 30 3-24340 3-48564 3-74532 4-02366 30 40 4-80102 5-28497 5-81636 6-39972 40 50 7-10668 8-01315 9-03264 10-17892 50 60 10-51963 12-14965 14-02741 16-18982 00 70 I5'57i62 18-42148 80 23-04980 27-93091 21-78413 33-83009 2575030 40-95647 g 90 34-11933 42-34925 52-53710 65-14226 00 100 50-50495 64-21055 81-58852 103-61036 IOO 5% 5i% 6% 8i% IO i -62889 1-70814 i -79085 1-87714 10 20 2-65330 2-91776 3-20714 3-52365 20 30 4 '3 2 1 94 4-98395 5-74349 6-61437 30 40 7'03999 8-5I33I 10-28572 12-41607 40 50 1 1 -46740 14-54196 18-42015 23-30668 50 60 18-67919 24-83977 32-98769 43-74984 60 70 30-42643 80 49-56144 42-42992 72-47643 59-07593 105-79599 82-12446 ! 7O 154-15891 i 8O oo 80-73037 123-80021 189-46451 289-37746 90 100 131-50126 211-46864 339-30208 543-20I27 IOO 7% 8% 9% 10% 10 1-96715 2-15892 2-36736 2-59374 10 20 3-86968 4-66096 5-60441 6-72750 20 30 7-61226 IO-06266 13-26768 17-44940 30 40 I4-97446 21-72452 31-40942 45-25926 40 50 29-45703 46-90161 74-35752 117-39085 50 60 57-94644 101-25706 176-03129 304-48164 00 7O 113-98938 218-6064! 80 224-23437 471-95483 416-73009 986-55167 789-74696 70 2048 -4002 1 80 90 441-10293 1018-91509 2335-52658 5313-02261 oo 100 867-71623 2199-76126 5529-04079 13780-61234 ioo (87) INTEEEST TABLES I THE PRESENT VALUE OF ONE POUND DUE AT END OF YEAR Years 1% li% If % Years 10 90529 88318 86167 84073 IO 20 81954 7800I 74247 -70682 20 30 74192 68889 63976 59425 30 40 67165 60841 55126 49960 40 50 60804 '53734 47500 42003 50 60 55045 47457 40930 35313 60 70 49831 41913 35268 29689 70 80 45112 37017 30389 24960 80 90 40839 32692 26185 20985 90 100 36971 28873 22563 17642 ZOO 2o/ 70 I O i o/ O i o/ fcl 4 7O fj 2 7O 2f% 10 82035 '80051 78120 76240 zo 20 '67297 -64082 61027 58125 20 30 -55207 -51298 47674 '443 J 4 30 40 45289 -41065 37243 33785 40 50 -37153 -32873 29094 25758 50 60 -30478 -26315 22728 19638 60 70 -25003 -21065 80 -20511 -16863 17755 13870 14972 11414 70 80 90 -16826 -13499 10836 -08702 90 100 13803 -10806 08465 06635 zoo 307 7O v% 3i/ 03. Q/ 10 -74409 72627 70892 69202 zo 20 -55368 -52747 50257 -47889 20 30 -41199 38309 35628 -33140 30 40 -30656 -27823 25257 -22934 40 50 -22811 -20207 17905 -15871 50 60 16973 -14676 12693 -10983 60 7O 12630 -10658 08999 -07600 70 8O 09398 -07741 06379 -05260 , 80 00 06993 -05622 04522 '03640 oo ZOO 05203 04083 03206 '02519 zoo For explanation see pp. 8-13 (88) INTEREST TABLES THE PRESENT VALUE OF ONE POUND DUE AT END OF YEAB Years 4% 4i% 4i% 4f% Years 10 67556 65954 64393 62872 ZO 20 -45639 43499 41464 39529 20 3 -30832 28689 26700 24853 30 40 -20829 18922 17193 15626 40 50 -14071 12479 11071 09824 50 60 -09506 08231 07129 06177 60 70 -06422 05428 04590 03883 70 80 '04338 -03580 -02956 02442 80 90 -02931 -02361 -01903 -01535 90 100 01980 -01557 01226 00965 100 5% 5i% 6% 6i% 10 -61391 20 -37689 58543 34273 55839 -53273 31180 -28380 10 20 30 -23138 20064 17411 -15119 30 40 -14205 11746 09722 -08054 40 50 -08720 -06877 -05429 -04291 50 60 '53S4 -04026 -03031 -02286 60 70 -03287 -02357 -01693 -01218 70 80 -02018 -01380 -00945 -00649 80 90 -01239 -00808 -00528 -00346 90 100 00760 -00473 00295 -00184 100 7% 8% 9% 10% 10 50835 46319 -42241 38554 10 20 25842 21455 -17843 14864 20 30 13137 09938 -07537 05731 30 40 -06678 04603 -03184 -02209 4 50 -03395 -02132 -01345 -00852 50 60 01726 00988 00568 00328 60 g 00877 00446 00457 OO2 1 2 OO24O ooioi 00127 00049 70 80 00 00227 00098 00043 00019 90 100 00115 00045 00018 00007 100 For 15% seep, xl INTEREST TABLES THE AMOUNT OF ONE POUND PER ANNUM Years 1% 1% H% lf% Years 10 10-46221 10-58167 10-70272 10-82540 10 20 22-01900 22-56298 23-12367 23-70161 2O 30 34-78489 36-12907 37-53868 39-01715 30 40 48-88637 51-48956 54-26789 57-234I3 40 50 64-46318 68-88179 73-68283 78-90222 50 60 81-66967 88-57451 96-21465 104-67522 60 70 100-67634 110-87200 122-36375 135-33076 70 80 121-67152 136-11880 152-71085 171-79382 80 90 144-86327 164-70501 187-92990 215-16462 90 100 170-48138 197-07234 228-80304 266-75177 loo 2% 2i% 21% 2f % 10 10-94972 11-07571 1 1 '20338 11-33276 IO 20 24-29737 24-91152 25-54466 ! 26-19740 2O 30 40-56808 42-19526 43-90270 45-69461 30 40 60-40198 63-78618 67-40256 71-26815 4 50 84-57940 j 90-75762 97-48435 104-81170 50 60 114-05154 124-45043 1 35 '99 1 59 148-80914 60 70 80 149-97791 166-53962 19377195 219-11757 185-28411 206-51843 70 248-38271 282-21287 80 90 247-15665 284-79813 329-15425 381-49757 90 zoo 312-23230 366 -84650 432-54865 511-72445 IOO 3% 3i% 3i% 3f% 10 1 1 -46388 11-59675 ii'73 I 39 1 1 -86784 10 20 26-87037 27-56424 28-27968 29-01739 20 30 47-57542 49-54980 51-62267 5379924 30 40 75-40126 79-82158 84-55028 89-61010 40 50 112-79687 121-50263 130-99791 I4I-35837 50 60 163-05344 178-89303 196-51688 216-13690 60 70 230-59406 257-91354 288-93786 324-19515 70 80 321-36302 366-71643 419-30678 480-34408 80 90 443-34890 516-52651 603-20503 705-98614 90 IOO 607-28773 722-79916 862-61166 1032-04883 loo For explanation see pp. 8-13 (90) INTEEEST TABLES THE AMOUNT OF ONE POUND PER ANNUM Years 4 % I A / 4 P/ 4 / Years IO 1 2 'OO6l I 20 29-77808 30 56-08494 40 95-02552 50 152-66708 12-14622 30-56250 58-48553 100-82283 165-01525 I2-2882I 3I*37I42 61-00707 107-03032 I78-50303 12-43209 10 32-20563 20 63-65594 30 113-67841 40 193-24036 50 60 237-99069 70 364-29046 ! 80 551-24498 00 827-98333 ioo 1237-62370 262-34474 409-91711 633-66848 972-92354 1487-30697 289-49795 461-86968 729-55770 1145-26900 I790-85595 521-05885 70 841-18887 80 I350-36345 90 2160-21801 ioo 50/ /o 5i% 6 % UK 10 12-57789 20 33-06595 30 66-43885 40 120-79977 50 209-34800 12-87535 34-86832 72-43548 136-60561 246-21748 13-18079 3678559 79-058I9 15476197 290-33590 13-49442 10 38-82531 20 86-37486 30 175-63192 40 343-17967 50 60 353*58372 70 588-52851 80 971-22882 90 1594-60730 ioo 2610-02516 433*45037 753-27120 1299*57139 2232-73101 3826-70246 533-12818 967-93217 1746-59989 3141-07519 5638-36806 657-68984 60 1248-06867 70 2356*29087 8O 4436-57630 90 8341-55802 ioo 7% 8% 9% 10% 10 13*81645 20 40-99549 30 94-46079 : 40 199*63511 50 406-52893 14-48656 4576196 113-28321 57377016 15-19293 51-16012 136-30754 337-88245 815-08356 15-93742 10 57-27500 20 164-49402 30 442-59256 | 40 1163-90853 50 60 813-52038 70 1614-13417 80 3189-06268 90 6287-18543 ioo 12381-66179 1253-21330 2720-08007 5886-93543 12723-93862 27484-51570 1944-79213 4619-22318 10950-57409 25939-18425 61422-67547 3034-81640 6O 7887-46957 70 20474-00215 8O 53I20-226I2 OO 137796-12340 ioo 1 (91) INTEEEST TABLES THE PRESENT VALUE OF ONE POUND PER ANNUM DUE AT END OF YEAR Years 1% 14% li% 1 3. O/ *4 /O Years 10 9-47130 9-34553 9-22219 9'IOI22 10 20 18-04555 I7'59932 17-16864 1675288 20 3O 25-80771 24-88891 24-01584 23-I8585 30 40 32*83469 3I-32693 29-91585 28-59423 4 50 39-19612 37-01288 34-99969 33-I4I2I 50 60 44-95504 i 42-03459 39-38027 36-96399 60 7O 50-16851 46-46968 43-15487 40-17790 70 80 54-88821 50-38666 46-40732 42-87994 80 90 59-16088 53-84606 49-20985 45-15161 go 100 63-02888 56-90134 51-62470 47-06147 100 2% 2J% 24% 2f % 10 8-98258 8-86622 875206 8-64008 10 20 16-35143 15-96371 15-58916 15-22725 2O 30 22-39646 21-64533 20-93029 20-24930 30 40 27-35548 26-19352 25-10277 24-07810 40 50 3I-4236I 29-83440 28-36231 26-99717 50 60 34-76089 32-74895 30-90866 29-22266 60 70 37-49862 35-08208 32-89786 30-91937 i 70 80 39-7445I 36-94978 34-45182 32-21294 80 90 4I-58693 38-44489 35-66577 33-i99i5 90 ' 100 43-09835 39-64174 36-61410 33-95104 100 3% 3J% 34% 33. q/ 4 /O 10 8-53020 8-42240 8-31661 8-21279 IO 20 14-87748 14-53935 14-21240 13-89620 2O 30 19-60044 18-98192 18-39205 17-82925 30 40 23-11477 22-20843 21-35507 20-55099 40 50 25-72976 24-55176 23-45562 22-43449 50 60 27-67556 26-25366 24-94474 2373792 60 g 29-12342 30-20076 27-48970 28-38740 26-00040 2674878 24-63991 70 25-26411 80 90 31-00241 29-03937 27-27932 25-69607 oo too 31-59891 29-51288 27-65543 25 "99499 loo For explanation see pp. 8-13 (92) INTEREST TABLES THE PKESENT VALUE OF ONE POUND PEE ANNUM DUE AT END OF TEAE Years 4% 4i% 4*0/0 4f % Years IO 8-II090 8-01089 7-91272 7-81635 zo 20 I3-59033 I3-29437 13-00794 12-73067 2O 30 17-29203 1677902 16-28889 15-82042 30 40 1979277 19-07727 18-40158 17-76302 40 50 21-48219 20-59306 19-76201 18-98437 50 60 22 '62349 21-59278 20-63802 19-75227 60 70 80 2339452 23-9I539 22-25213 22-68700 21 -2021 1 2I-56534 20-23506 20-53861 g 00 24-26728 22-97381 2179924 20-72945 90 zoo 24-50500 23-16297 21-94985 20-84944 zoo 5% ft* 6% 61% zo 7-72173 7-53763 7-36009 7-18883 zo 20 12-46221 11 '95 O 38 11-46992 11-01851 20 30 15-37245 I4-53375 1376483 13-05868 30 40 17-15909 16-04612 15-04630 14-14553 40 50 18-25592 16-93152 1576186 1472452 50 60 18-92929 17-44985 16-16143 15-03297 60 g 19-34268 19-59646 I7-75330 16-38454 I7-93095 16-50913 15-19728 15-28482 g 00 zoo 19-75226 19-84791 18-03495 18-09584 16-57870 I6-6I755 15-33145 15-35629 90 zoo 7% 8% 9% 10% zo 7-02358 6-71008 6-41766 6-14457 zo 20 10-59401 9-81815 9-12855 8-51356 20 30 12-40904 11-25778 10-27365 9-42691 30 40 I3-33I7I 11-92461 10-75736 977905 40 50 13-80075 12-23348 10-96168 9-91481 50 60 I4'039l8 70 14-16039 80 14-22201 I2-37655 12-44282 12-47351 1 1 -04799 1 1 -08445 11-09985 9-96716 9-98734 9-99512 60 g 90 I4-25333 12-48773 11-10635 9-99812 90 ZOO 14-26925 12-49432 11-10910 9-99927 ioo See also Tables pp. xx-xxxi. For 15% see p. xl (93) INTEEEST TABLES THE PRESENT VALUE OF A PERPETUITY OF 1 PER ANNUM At per Cent. At per Cent. * s. d. *. rf. or O26 800-00000 cA or 526 19-51220 X 050 400-00000 "5i j 550 19-04762 8 > 076 266-66667 51 - 5 7 6 18-60465 '2 O IO O 200-00000 51 5 10 o 18-18182 | ,, 12 6 160-00000 5 ,, 5 12 6 17-77778 ? " o 15 o 133-33333 5t S i S O 17-39130 1 " o 17 6 114-28571 5| 5 17 6 17-02128 I ,, I O 100-00000 6 ,, o o o 16-66667 l 2 6 88-88889 6 626 16-32653 IT 5 o 80-00000 6 ,, 650 16-00000 if " 7 6 72-72727 6 676 15-68627 IO 66-66667 I 6| ,, 6 10 o 15-38462 if 12 6 61-53846 6 6 12 6 15-09434 If M 15 57-14286 6f ,, 6 15 o 14-81481 17 6 53-33333 6- > 6 17 6 H-54545 2 g ',! 2 O 50-00000 ; 7 700 14-28571 2 1 226 47-05882 7* 726 14-03509 2^ ,, 250 44*44444 7i 750 13-79310 2- , 42-10526 7 f ,, 7 7 6 I3-55932 2^ 2 IO 40-00000 7| ,, 7 10 o I3-33333 2jj 2 12 6 38-09524 j 7f ,, 7 12 6 13-11475 2! " 2 15 36-36364 7 f 7 15 o 12-90323 2! 2 17 6 34-78261 ; 7| ,, 7 17 6 12-69841 3 300 33-33333 8 55 800 12-50000 3f i. 326 32-00000 8^ ,, 826 12-30769 35 30-76923 8j 55 850 I2-I2I2I 3! " 3 7 6 29-62963 ' 8f ,, 876 1 1 -94030 3 10 o 28-57143 8| ,, 8 10 o II-7647I 3l > 3 12 6 27-58621 8 ,, 8 12 6 1 1 -59420 31 3 *5 26-66667 8? 8 15 o II-42857 3l 3 17 6 25-80645 SI 8 17 6 II-2676I 400 25-00000 9 " 900 II-IIIII 4* M 426 24-24242 1 9^ n 926 10-95890 2 450 23-52941 9| .. 950 IO-8I08I 4| 1! 476 22-85714 976 IO-66667 4 10 o 22-22222 9^ ,, 9 10 o 10-52632 4 4 12 6 21-62162 9$ ,, 9 12 6 10-38961 4i " 4 15 o 21-05263 9? ,, 9 !5 o 10-25641 41 4 17 6 20-51282 9^ ,, 9 17 6 IO-I2658 5 500 20-00000 10 ,, 10 10-00000 1 \\ For explanation see p. 1 3 (94) INTEKEST TABLES THE PRESENT VALUE OF THE EEVEESION OF A PERPETUITY OF 1 Years 1 o/ Deferred X /O li% Ii% 13 o/ Years 4" /O Deferred I 99-00990 2 98-02960 3 97-05901 4 96-09893 5 95-I4657 79-01235 78-03688 77-07347 76-12194 75-18217 65-68145 64-71079 63-75447 62-81229 61-88402 56-16006 I 55-19416 2 54-24488 3 53-31192 4 52-39500 5 6 . 94-20452 7 93-27181 8 92-34832 9 9I-43398 10 90-52870 74-25399 73-33727 72-43188 71-53766 70-65447 60-96948 60-06846 59-18074 58-30615 57-44448 51-49386 6 50-60822 7 49-73781 8 48-88237 9 48-04164 10 ii 89-63237 12 88-74492 I 3 i 87-86626 1 14 86-99630 15 86-13495 69-78220 68-92069 68-06982 67-22945 66-39945 56^9555 55-759I6 54-935I4 54-12329 53-32344 47-21537 ii 46-40331 12 45-60522 13 44-82085 14 44-04998 15 16 85-28213 17 84-43775 18 83-60173 19 82-77399 20 81-95445 65-5797I 64-77008 63-97045 63-18069 62-40068 52-5354I 51-75902 50-99411 50-24050 49-49803 43-29236 16 42-54778 17 41-81600 18 41-09680 19 40-38998 20 21 81-14302 22 80-33962 23 79-544I8 24 78-7566I 25 77-97684 61-63031 60-86944 60-11796 59-37577 58-64273 48-76653 48-04584 47-3358I 46-63626 45-94706 39-69531 21 39-01259 22 38-34161 ! 23 37-68217 24 37-03408 25 26 77-20480 27 76-44039 28 75'68356 29 74-9342I 3 74-I9229 57-9I875 57-20370 56-49748 55-79998 55-11109 45-26804 44-59905 43-93995 43-29059 42-65083 36-397I3 26 35-77113 27 35-I559I 28 34-55126 29 33-95701 30 31 73'4577I 32 7273041 33 72-01031 34 71*29733 35 70-59142 54-4307I 53-75873 53-09504 52-43954 51-79214 42 -02052 41-39953 40-78771 40-18494 39'59 I0 7 33-37298 3 1 32-79900 32 32-23489 33 31-68048 34 3i-i356i 35 36 69-89250 37 69-20049 38 68-51534 39 67-83697 40 67-16531 5I-I5273 50-52122 49-89750 49-28148 48-67307 39-00599 38-42954 37-86162 37-30209 36-75082 30-60011 36 30-07382 37 29-55658 3 8 29-04823 39 28-54863 40 41 66-50031 42 65-84189 43 65-18999 44 64-54455 45 63-90549 48-07216 47-47868 46-89252 46-31360 4574183 36-20771 35-67262 35-H544 34-62605 34-II433 28-05762 41 27-57506 42 27-10079 43 26-63469 44 26-17660 45 46 63-27276 47 62-64630 48 62-02604 49 61-41192 50 60-80388 45-17712 44-61938 44-06852 43-52446 42-98712 33-61018 33-II348 32-62412 32-14199 31-66698 25-72639 46 25-28392 47 24-84906 48 24-42168 49 24-00165 50 For explanation see pp. 13, 14. See also Tables on pp. xxxii-xxxix (95) INTEREST TABLES THE PRESENT VALUE OF THE REVERSION OF A PERPETUITY OF 1 Years Deferred 2o/ /o 2i% 2i% 2f% Years Deferred I 49-01961 43-46644 39-02439 35-39040 I 2 48-05844 42-50997 38-07258 34-44322 2 3 47-11612 4I-57454 37-I4398 33-52I38 3 4 46-19227 40-65970 36-23803 32-62421 4 5 45-28654 39-76499 3535417 31-75106 5 6 44-39857 38-88996 34-49188 30-90127 6 I 43-52801 42-67452 38-03419 37-19726 33-65o6i 32-82986 30-07423 29-26933 I 9 41-83776 36-37873 32-02913 28-48596 9 10 41-01742 35-57822 31-24794 2772356 10 ii 40-21315 34'79533 30-48579 26-98157 ii 12 39-42466 34-02966 29-74224 26-25944 12 13 38-65163 33-28084 29-01682 25-55663 13 14 37*89375 32-54850 28-30909 24-87263 T 4 15 37-15074 31-83227 27-61862 24-20694 15 16 36-42229 31-13181 26-94500 23-55907 16 \l 3570813 35-00797 30-44676 29-77678 26-28780 25-64664 22-92853 22-31487 3 X 9 34-32154 29-12154 25-02111 21-71764 19 20 33-64857 28-48073 24-41084 21-13639 20 21 32-98879 27-85401 23-8I545 20-57069 21 22 32-34195 27-24109 23-23459 2O-O2OI4 22 23 31-70780 26-64165 22-66789 19-48432 23 24 31-08607 26-05540 22-11501 18-96284 24 25 30-47654 25-48206 21-57562 I8-45532 25 26 29-87896 24-92133 21-04939 17-96138 26 27 29-29310 24-37294 20-53599 17-48067 2? 28 28-71873 23-83661 20-03511 I7-OI28I 28 29 28-15562 23-31209 19-54645 16-55748 29 30 27-60354 22-79911 19-06971 16-11434 30 3 1 27-06230 22-29742 18-60460 15-68305 31 S 2 26-53167 21-80677 18-15082 15-26331 32 33 26-01144 21-32691 17-70812 14-85481 33 34 25-50141 20-85761 17-27621 I4-45723 34 35 25-00138 20-39864 16-85484 14-07030 35 36 24-51116 19-94977 16-44375 13-69372 36 24-03055 19-51078 16-04268 I332722 3$ 23-55936 19-08145 I 15-65140 12-97053 38 39 23-09741 18-66156 15-26966 12-62339 39 40 22-64452 18-25092 14-89723 12-28554 40 4 1 22 -2005 1 17-84931 14-53388 II-95673 41 42 21-76521 I7-45654 I4-I7939 11-63672 42 43 21-33844 17-07241 I3-83355 11-32527 43 44 20-92004 16-69673 13-49615 11-02217 44 45 20-50984 16-32932 13-16698 10-72717 45 46 20-10769 15-97000 12-84583 IO-44007 46 47 I97I342 15-61858 12-53252 10-16065 47 48 19-32688 15-27489 12-22685 9-88871 48 49 I8-94792 14-93877 1 1 -92863 9*62405 49 50 18-57639 14-61004 11-63769 9-36647 50 For explanation see pp. 13, 14 (96) INTEREST TABLES THE PRESENT VALUE OF THE EEVEESION OF A PERPETUITY OF 1 Years O o/ Deferred O /Q 3i% 3i% 3f% Years Deferred I 32-36246 29-80071 27-60525 25-70281 I 2 31-41986 28-86267 26-67174 24-77380 2 3 30-50472 27-95416 25-76979 23-87836 3 4 29-61623 27-07425 24-89835 23-01529 4 5 | 28-75362 26-22203 24-05638 22*18341 5 6 27-91614 25-39664 23-24288 21-38160 6 7 27-10305 24-59723 22-45689 20-60877 7 8 26-31364 23-82298 21-69747 19-86387 8 9 25-54722 23-07311 20-96374 i9'H59o 9 10 i 24-80313 22-34683 20-25482 18-45388 10 ii 24-08071 21-64342 19-56988 17-78687 ii 12 i 23-37933 20-96215 18-90810 1 7 -.14398 12 13 22-69737 20-30233 18-26869 16-52431 13 14 22-03726 19-66327 17-65091 15-92705 M 15 21-39539 19-04433 17-05402 15-35137 15 16 20-77223 18-44487 16-47731 14-79650 16 17 20-16721 17-86428 15-92011 14-26169 18 19-57982 17-30197 15-38175 13-74621 11 19 19-00953 16-75735 14-86159 13-24936 19 20 18-45585 16-22988 14-35903 12-77047 20 21 ij-gi&si 15-71902 13-87346 12-30888 21 22 I73964I 15-22423 13-40430 11-86398 22 23 16-88972 14-74501 12-95102 ii-435i6 23 24 16-39779 14-28089 12-51306 11-02185 24 25 15-92018 13-83137 12-08991 10-62347 25 26 15-45649 13-39600 11-68108 10-23948 26 27 i 15-00630 12-97433 11-28606 9-86938 2? 28 14-56922 1 2 -56594 10-90441 9-51266 28 29 14-14487 12-17040 10-53566 9-16883 2 9 30 13-73289 11-78731 10-17938 8-83742 30 31 13-33290 11-41628 9-83515 8-51800 31 32 i 12-94456 1 1 -05693 9-50256 8-2IOI2 32 33 1 12-56754 10-70889 9-18122 7-9I337 33 34 12-20149 10-37181 8-87075 7-62734 34 35 11-84611 10-04534 8-57077 7-35i66 35 36 1 1 -50108 9-72914 8-28094 7-08593 36 37 11-16609 9-42289 8-00090 6-82982 37 38 10-84087 9-12629 7-73034 6-58296 38 39 10-52511 8-83902 7-46893 6-34502 39 40 10-21856 8-56080 7-21636 6-11568 40 41 9-92093 8-29133 6-97233 5-89463 41 42 ! 9-63197 8-03034 6-73655 5-68157 42 43 9-35I43 777757 6-50874 5-47621 43 44 9-07906 7-53276 6-28864 5-27828 44 1 45 8-81462 7-29565 6-07598 5-08750 ; 45 46 8-55788 7-06600 5-87051 4-90361 46 47 8-30862 6-84359 5-67199 4-72637 47 48 8-06662 6-62817 5-48018 4-55554 48 49 7-83167 6-41954 5-29486 4-39088 49 50 7-60357 j 6-21747 5-11581 4-23218 50 See also Tables on pp. xxxii-xxxix (97) INTEBEST TABLES THE PRESENT VALUE OF THE REVERSION OF A PERPETUITY OF1 Years Deferred 4% 4i% 5% 6% Years Deferred I 24-03846 21-26528 19-04762 15-72327 I 2 23-11391 20-34955 18-14059 14-83328 2 3 22-22491 19-47326 17-27675 I3-99366 3 4 21-37010 18-63469 I6-45405 13-20156 4 5 20-54818 17-83224 15-67052 12-45431 5 6 19-75786 17-06435 14-92431 i i "74935 6 7 18-99795 16-32952 14-21363 1 1 -08429 7 8 18-26725 15-62633 I3-53679 10-45688 8 9 17-56467 I4-95343 12-89218 9-86498 9 10 16-88910 14-30950 12-27827 9-30658 10 ii 16-23952 1 3 "69330 11-69359 8-77980 ii 12 15*61493 13-10364 11-13675 8-28283 12 13 15-01435 12-53937 10-60643 7-8I399 13 14 14-43688 11-99939 10-10136 7"37l69 14 15 13-88161 11-48267 9-62034 6-95442 IS 16 13*34770 10-98821 9-16223 6-56077 16 J 7 12-83433 10-51503 8-72593 j 6-18941 X 7 18 12-34070 10-06223 8-31041 5-83907 18 19 ' 11-86606 9-62893 7-91468 5-50855 19 20 11-40967 9-21428 7-53779 5-I9675 20 21 10-97084 8-81750 7-17885 4-90259 21 22 10-54888 8-43780 6-83700 4-62509 22 23 10-14316 8-07445 6-51143 436329 23 2 4 975304 772674 6-20136 4-11631 24 25 9*37792 7-39401 5-90606 3*88331 25 26 I 9-01723 7-07561 5-62482 3*66350 26 27 ! 8-67041 6-77092 5-35697 3*456i4 27 28 8-33694 6-47935 5-10187 3-26051 28 29 8-01628 6-20033 4-85893 3*07595 29 30 770797 5-93333 4-62755 2-90184 30 31 7-41151 5-67783 4-40719 2-73758 31 32 7-12645 5*43333 4-I9732 2-58263 32 33 6-85235 5*!9936 3*99745 2-43644 33 34 6-58880 4-97546 3-80710 2-29853 34 35 6-33539 476121 3-62581 2-16842 35 36 6-09172 4-55618 3-453I5 2-04567 36 5-85742 435998 3-28871 i -92989 37 38 5-63213 4-17223 3*13211 i -82067 38 39 5*4i55i 3-99256 2-98296 171760 39 40 5-20723 3-82064 2-84091 1-62037 40 4 1 5-00695 3-65611 2-70563 -52865 4 1 42 4-81437 3-49867 2-57679 44213 42 43 4-62920 3-34801 2-45409 36050 43 44 4-45116 3-20384 2-33723 28349 44 45 4-27996 3-06587 2-22593 21084 45 46 4-II535 2-93385 2-11993 1-14230 46 47 3*957o6 2-80751 2-01899 i -07764 47 48 3-80487 2-68661 I -92284 1-01664 48 49 3-65853 2-57092 1-83128 95910 49 50 2-46021 I -74408 90481 50 For- explanation see pp. 13, 14. See also Tables on pp. xxxii-xxxix (98) INTEEEST TABLES Tlie Present Value of the Perpetuity of One Year's Rent or Fine, Payable for Renewing Estates at Various Intervals and Rates of Interest YEARS' PURCHASE Years 3% 4% 5% 6% 8% 10% Years 2 16-4204 12-2549 9-7561 8-0906 6-0096 4-7619 2 o 107839 8-0089 6-3439 5-2350 3-8504 3-0211 3 4 7-9675 5-8872 4-6401 3-8098 2-7740 2-1547 4 I 6-2786 5-1533 4-6I57 3-7690 3-6I95 2-9403 2-9566 2-3894 2-1307 1-6380 1-7039 1-2961 1 7 4-3503 3-1652 2-4564 i -9856 1-4009 1-0541 7 10 2-9076 2-0823 1-5901 1-2646 8629 -6275 10 H 1-9509 I-3667 i -0205 793i 5162 -3575 M 20 i -2405 8395 6049 4531 2731 -1746 20 21 1-1624 7820 '5599 4167 2479 -1562 21 40 4421 2631 1656 1077 0483 -0226 40 Number of Years' Purchase for the Renewal of any Number of Years Expired in a TEN YEARS' LEASE Years 2% 2i% 3% 31% I 82034 78119 74409 70892 i 2 1-65710 1-58192 1-51051 I -44265 2 3 2-51059 2-40267 2-29992 2-20207 3 4 3-38115 3-24394 3-11301 2-98806 4 5 4-26912 4-10623 3-95049 3-80156 5 6 5-17485 4-99009 4-81310 4-64353 6 7 6-09870 5-89604 5-70159 5'5H97 7 8 7-04102 6-82464 6-61673 6-41692 8 9 8-00219 7-77645 7-55933 7-35043 9 10 8-98258 8-75206 8-53020 8-31661 10 4% 41% 5% 17'95 % i 67557 64393 61391 1919 i 2 1-37815 1-31683 1-25852 4182 2 3 2-10885 2-O2OO2 I -93536 6851 3 4 2-86876 2-75485 2-64604 I -OOOO 4 5 3-65908 3-52274 3-39225 I-37I4 5 6 4-48100 4-32519 4-I7578 i -8094 6 i 5-33581 5-16376 6-22481 6-04005 4-99848 5-86232 2-3261 2-9355 8 9 7-14936 6-95578 6-76935 3-6543 9 10 8-11090 7-91272 772173 4-5021 10 For explanation see pp. 14-16 (99) E2 INTEKEST TABLES Number of Years' Purchase for the Renewal of any Number of Years Expired in a TWENTY YEARS' LEASE Years 2 % 21% 3o/ 70 3i% Years I '67297 61027 55368 50256 I 2 I'35940 1-23580 1-12397 i -02272 2 3 2-05956 1-87696 1-71136 1-56108 3 4 2-77372 2-53416 2-31638 2-11828 4 5 3*50217 3-20778 2-93954 2-69499 5 , 6 4-24518 3*89825 3*58i4i 3-29188 6 7 5-00306 4-60598 4-24252 3-90966 7 8 577609 5-33140 4-92348 4*54906 8 9 6-56458 6-07495 5-62486 5-21085 9 10 7-36885 6-83710 6-34728 5*89579 10 ii 8-18919 7-61829 7-09137 6-60471 ii 12 9'02595 8-41902 7*85779 7*33844 12 13 9^7944 9-23977 8-64720 8-09786 *3 14 IO-75000 10-08103 9-46029 8-88385 J 4 15 II-63797 10-94333 10-29777 9-69735 15 16 12-54370 11-82719 11-16038 10-53932 16 i? i3*46755 12-73314 12-04887 11-41076 17 18 14-40987 13-66174 12-96401 12-31271 18 19 15*37104 14-61355 13-90661 13-24622 19 20 16-35143 15-58916 14-87748 14-21240 20 4% 4i% 5% 12'304% I -45639 41465 -37689 o 9 8 J 2 -93103 84795 77262 208 2 3 i -42466 i -30075 1-18814 332 3 4 i "93803 1*77393 i -62444 471 4 5 2-47194 2-26839 z -08255 628 5 6 3-02721 2-78511 2-56357 803 6 7 3-60468 8 4-20526 3*32509 3-88936 3-06864 3*59896 i-ooo I -221 I 9 4-82985 4-47902 4*15580 1-470 9 10 5*47943 5-09522 4*74048 1-749 10 ii 6-15500 573915 5-35439 2-062 ii 12 6-85758 6-41205 5-99900 2-414 12 13 7-58828 7-11524 6-67584 2-809 13 14 8-34819 7-85007 7-38652 3*253 14 15 9-I385I 8-61796 8-13273 3*751 15 16 9*96043 9-42041 8-91626 4-3ii 16 17 10-81524 10-25898 9*73896 4-940 17 18 1170424 11-13527 10-60280 5-646 18 19 12-62879 12-05100 1 1 -50983 6-439 19 20 13*59033 13-00794 12-46221 7'329 ^J For explanation see pp. 14-16 (100) INTEREST TABLES Number of Years' Purchase for the Renewal of any Number of Years Expired in a TWENTY-ONE YEARS' LEASE Years 2 % 2k % 3% 3i% Years I '65978 59539 "53754 48557 I 2 I-33275 i -20566 1-09122 98813 2 3 2-01918 1-83119 1-66151 i -50829 3 4 271934 2-47235 2 -24890 2 -04665 4 5 3-433SO 3-12955 2-85392 2-60385 5 6 4-16195 3-80317 3-47708 3-18056 6 7 4-90496 8 5-66284 4-49364 5-20137 4-11895 478006 377745 439523 I 9 6-43587 5-92679 5-46102 5-03463 9 10 7*22436 6-67034 6-16240 5-69642 zo ii 8-02863 7-43249 6-88482 6-38136 ii 12 8-84897 8-21368 7-62891 7 -09028 12 13 9-68573 9-01441 8-39533 7-82401 13 14 10-53922 9-83516 9-18474 8-58343 14 15 1 1 -40978 10-67642 9-99783 9-36942 15 16 12-29775 11-53872 10-83531 10-18292 16 17 13-20348 12-42258 11-69792 1 1 -02489 J 7 18 ; 14-12733 13-32853 12-58641 11-89633 18 19 15-06965 14-25713 I3'5oi55 12-79828 19 20 16-03082 15-20894 I4-444I5 I373J79 20 21 I7-OII2I 16-18455 15-41502 14-69797 21 4% 4i% 5% 11'564 % i -43883 39678 35894 100 I 2 -89522 81143 73583 213 2 3 , i -36986 1-24473 1-13156 338 3 4 i -86349 i -69753 i -54708 477 4 5 2-37686 2-17071 1-98338 633 6 2-91077 2-66517 2-44149 806 6 7 3-46604 3-18189 2-92251 I -000 7 8 4 -0435 i 3-72187 3-42758 1-216 8 9 4-64409 4-28614 3-95790 1-457 9 10 5-26868 4-87580 4-51474 1-726 10 ii 5-91826 5-49200 5-09942 2-026 ii 12 6-59383 6-13593 5-71333 2*361 12 13 7-29641 6-80883 6-35794 2734 *3 14 8-02711 7-51202 7-03478 3-i5i M 15 8-78702 8-24685 7-74546 3-616 15 16 9-57734 9-01474 8-49167 4-135 16 17 10-39926 18 1 1 -25407 9-81719 10-65576 9-27520 10-09790 4713 S'359 3 19 12-14307 11-53205 10-96174 6-079 19 20 13-06762 12-44778 1 1 -86877 6-882 20 21 14-02916 13-40472 12-82115 7779 21 (101) INTEREST TABLES Number of Years' Purchase for the Renewal of any Number of Years Expired in a FORTY YEARS' LEASE Years 2o/ O l o/ /o &~z /o 3% 31% * I 45289 -37243 30655 -25257 I 2 -91484 -75417 -62231 -51398 2 3 1-38603 I-H545 '94753 -78454 3 4 i -86664 * -54652 i -28252 i -06458 4 2-35686 1-95761 1-62755 I-3544I 5 6 2-85689 2-37898 1-98293 1-65439 6 7 3-36692 2-81089 2-34898 1-96486 7 8 3-88715 3*25359 2-72600 2-28620 8 9 4-41778 3-70737 3-ii434 2-61879 9 10 4-95902 4-17248 3-5I433 2-96302 10 ii 5-51110 4-64922 3-92631 3-3I930 ii 12 6-07421 5-I3788 4-35066 3-68805 12 13 6-64858 5-63876 4-78774 4-06970 13 14 7-23444 6-15216 5-23793 4-46472 14 15 7-83202 6-67839 5-70162 4-87355 15 16 8-44155 7-21778 6-17923 5-29670 16 17 9-06328 7-77066 6-67116 5-73466 17 18 9-69743 8-33736 7-17785 6-18794 18 19 10-34427 8-91822 7-69975 6-65710 19 20 1 1 -00405 9-51361 8-23729 7-14267 20 21 11-67702 10-12388 8-79097 7-64523 21 22 12-36345 10-74941 9-36126 8-16539 22 23 13-06361 1 1 -39057 9-94865 8-70375 23 24 1377777 12-04777 IO-55367 9-26095 24 25 14-50622 12-72139 11-17683 9-83766 25 26 15-24923 13-41186 11-81870 10-43455 26 2 7 16-00711 14-11959 12-47881 11-05233 2 7 28 16-78014 14-84501 13-16077 11-69174 28 29 17-56863 15-58856 13-86215 12-35352 29 30 18-37290 16-35071 I4-58457 13-03846 30 31 19-19324 17-13190 15-32866 I3-74738 31 32 20-03000 17-93263 16-09508 14-48111 32 33 20-88349 18-75338 16-88449 I5-24053 33 34 2175405 I9-59465 17-69758 16-02652 34 35 22-64202 20-45694 I8-53506 16-84002 35 36 23-54775 21-34080 I9-39767 17-68199 36 37 24-47160 22-24675 20-28616 18-55343 37 38 25-41392 23-I7535 21-20130 I9-45538 38 39 26-37509 24-12716 22-14390 20-38889 39 40 27-35548 25-10277 23-11477 21-35507 40 For explanation see pp. 14-16 (102) INTEREST TABLES Num Years \ )er of Years' Purchase for the Renewal of any Number of Years Expired in a FORTY YEARS' LEASE 4% 4i% 5% 8% Years I -20828 17192 14205 '04603 i 2 -42490 35159 29120 -09574 2 3 '65019 53934 44780 -14943 3 4 '88449 73554 61224 20742 4 5 1-12816 94057 78490 27004 5 6 1-38157 1-15482 96619 33768 6 7 I-645 12 1-37872 1-15654 -41072 7 8 1-91922 1-61269 1-35641 -48961 8 9 2-20428 1*85719 i -56628 57481 9 10 2-50074 2-11269 1-78664 66683 10 ii 2-80905 2-37969 2-01802 76620 II 12 3-12971 2-65871 2-26096 87353 12 *3 3-46318 2-95028 2-51606 98945 13 14 3-81000 3' 2 5497 278391 1-11463 14 15 4-17069 3-57337 3-06515 i -24983 IS 16 4'5458i 3-90610 3-36045 I-39585 16 i? 18 4-93593 5-34165 4-25381 4-61716 3-67052 3-99609 1-55355 17 i -72387 18 J 9 5-76361 4-99686 , 4-33794 1-90781 19 20 6-20244 5-39364 4-69688 2-10646 20 21 6-65883 5-80829 5-07377 2-32101 21 22 7-13347 6-24159 5-46950 2-55272 22 23 7-62710 6-69439 5-88502 2-80297 23 24 8-14047 7-16757 6-32132 3-07324 24 25 8-67438 7-66203 6-77943 3-365I3 25 26 9-22965 8-17875 7-26045 3-68037 26 27 9-80712 8-71873 7-76552 4-02083 27 28 10-40770 9-28300 8-29584 4-38853 28 29 30 1 1 -03229 11-68187 9-87266 10-48886 8-85268 9-43736 4-78565 5-21453 29 30 31 12-35744 11-13279 10-05127 5-67772 31 32 1 3 -06002 11-80569 10-69588 6-17797 32 33 1379072 12-50888 11-37272 6-71824 33 34 14-55063 13-24371 12-08340 7-30I73 34 35 1 5 '34095 14-01160 12-82961 7-93190 35 36 16-16287 14-81405 13-61314 8-61248 36 17-01768 15-65262 14-43584 9-3475I 38 17-90668 16-52891 15-29968 10-14135 38 39 18-83123 1 7 -44464 16-20671 10-99868 39 40 1979277 18-40158 17-15909 11-92461 40 (103) INTEREST TABLES The Percentage per Annum which each Number of Years' Purchase of Perpetuity allows the Purchaser Years PEE CENT. PEE ANNUM Years . a. (1. I 100 IOO O O I 2 50 50 o o 2 3 33-3 33 6 8 3 4 25 25 o o 4 5 20 20 5 6 16-6" 16 13 4 6 7 i4-2857 14 5 8* 7 8 I2'5 12 IO O 8 9 n-i II 2 2 : \ 9 10 10 IO O O IO ii 9-69 9 i 9| " 12 8-3 868 12 13 7-69236 7 13 io 13 14 7-14285 7 2 io* 14 15 6-6 6 13 4 15 16 6-25 650 16 3 5-88235 5'S 5 17 71 *7 5 ii IT '8 19 5-26316 5 5 3* *9 20 5 500 20 21 4-7619 4 15 2| 21 22 4-5 4 IO II 22 23 4 6 n* 23 24 4-16 434 24 25 4 400 25 26 3-846I5 3 16 ii 26 27 376 3 14 i 27 28 3 ii 5i 28 29 3-4483 3 8 n* 29 30 3-3 368 30 31 3-2258 3 4 6 31 32 3-125 326 32 33 3'3 3 o 7 33 34 2-9412 2 18 10 34 35 2-85714 2 17 if 35 36 2-7 2 15 6* 36 2-76 2 14 of 37 38 2-6316 2 12 7* 38 39 2-56416 2 ii 3| 39 40 2-5 2 10 40 41 2 -4396 2 8 9 41 42 2-38095 2 7 71 42 43 2-32558 2 6 6 43 44 2-2 7 2 5 5* . 44 45 2-2 2 4 5i 45 46 2-I739I 2 3 5! 46 9 2-I2766 2 2 6f 2-083 2 i 8 47 48 49 2-0408 209! 49 50 2-0 200 50 For explanation see p. 16 (104) INTEREST TABLES INTEREST, AMOUNT, AND DISCOUNT OF 1 IN A YEAR, NINE, SIX, AND THREE MONTHS Interest p . ^ per Annum Interest Amount Discount 1 % I year 9 months O it 3 M 01 0075 005 0025 I -01 1-0075 1-005 1-0025 009901 007444 004975 002494 11% I year 9 months O ii 3 ,i 015 I-OI5 OII25 I-OII25 0075 I -0075 00375 I -00375 014778 OIII25 007444 003736 If % i year 9 months 3 0175 I-OI75 013125 1-013125 00875 I '0 8 75 004375 1-004375 017199 012955 008674 004356 207 /o I year 9 months 6 M 3 .. 02 015 01 005 1-02 I-OI5 I'OI I'005 019608 014778 009901 004975 /I year 01 o/ J 9 months ^4 / 1 6 13 ,, 0225 i -0225 016875 1-016875 OII25 I'OII25 005625 I -005625 022005 016595 OIII25 005593 2i % - r I year 9 months 6 3 025 I -025 01875 1-01875 0125 1-0125 00625 1-00625 024390 018405 012346 006211 21% I year 9 months 3 0275 020625 01375 006875 I -0275 I -020625 I'OI375 I -006875 026764 020208 013563 006828 3 % I year 9 months 6 ,, 3 03 0225 015 0075 1-03 I -0225 I-OI5 1-0075 029126 022005 014778 007444 31% I year 9 months 6 3 ,i 035 02625 0175 00875 1-035 I '02625 I-OI75 I-00875 033816 025579 017199 008674 4 % ti year ] 9 months 6 3 >. 04 03 02 oi 1-04 1-03 I -O2 I -01 038462 029126 019608 009901 ( i year 4^% r,? ths is .. 045 03375 O225 OII25 1-045 I -03375 I -0225 1-01125 043062 032648 022005 011125 5 % / 1 year J 9 months 6 3 M 05 I -05 0375 1-0375 025 I -025 0125 I-OI25 047619 036145 024390 012346 For explanation see p. 16 (105) INTEREST TABLES SINKING FUND FOE THE REPAYMENT OF LOANS Years 1% li% li% If % Years I I -000000 I 'OOOOOO I -000000 I -000000 I 2 497512 -496893 496278 -495663 2 3 330022 -329202 328383 -327567 3 4 246281 '245361 244445 -243532 4 5 196040 -195062 194089 -193121 5 6 162548 -161534 160525 -159523 6 7 138628 -137589 136556 -I3553 1 7 8 120690 -119633 118584 -H7543 8 9 106740 -105671 104609 -103558 9 10 095582 -094503 093434 -092375 10 ii 086454 -085367 084294 -083231 ii 12 078849 -077758 076680 -075614 12 *3 072415 -071321 070240 -069173 J 3 J 4 066901 -065805 064723 -063656 T 4 15 062124 -061026 059944 -058877 15 16 057945 -056847 055765 -054700 16 17 054258 -053160 052080 '051016 17 18 050982 -049884 048806 -047745 18 19 048052 -046955 045878 -044821 J 9 20 045415 -044320 043246 -042191 20 21 043031 -041937 040866 -039815 21 22 040864 -039770 038703 "037656 22 23 038886 -037897 036731 -035688 -23 24 037073 035987 034924 -033886 24 25 035407 034322 033263 -032230 25 26 033869 -032787 031732 -030703 26 27 032446 031367 030315 -029291 2 7 28 031124 030049 029001 -027982 28 29 029895 028822 027779 -026764 29 30 028748 027679 026639 -025630 30 31 027676 026609 025574 024570 3 1 32 026671 025608 024577 023578 32 33 025728 024668 023641 022648 33 34 024840 023784 022762 021774 34 35 024004 -02295 1 021934 020951 35 36 023214 -022165 021152 020175 36 022468 021424 020414 019443 38 021762 -020720 019716 018750 38 39 021092 -020054 019055 018094 39 40 020456 019421 018427 017472 40 4 1 019851 018821 017831 016882 4i 4 2 019276 018249 017264 016321 42 43 018727 017705 016725 015787 43 44 018204 017186 016210 015278 44 45 017705 016690 015720 014793 45 46 017228 016217 015251 014330 46 47 016771 015764 014803 013888 47 48 016334 015331 014375 -013466 48 49 015915 014916 013965 -013061 49 50 015513 '014518 ' OI 357 2 -012674 50 For explanation see pp. 16, 17 (106) INTEREST TABLES SINKING FUND FOR THE REPAYMENT OF LOANS Years \ % 1 % ]i % If" % Years 51 -015127 014136 013195 -012303 51 52 -014756 013769 012833 011947 52 53 -014400 013416 012485 011605 53 54 -014057 013078 012151 011277 54 55 -013726 012751 011830 010961 55 56 -013408 012437 011521 010658 56 57 -013102 012135 011223 010366 57 58 -012806 011843 010937 010085 58 59 -012520 011562 010660 009814 59 60 '012244 011290 010393 009553 60 61 -011978 011028 010136 009302 61 62 -011720 010774 009888 009059 62 63 -011471 010529 009647 008825 63 64 -011230 010292 009416 008598 64 65 -010997 010063 009191 008379 65 66 -010771 009841 008974 008168 66 67 '010551 68 -010339 009626 009417 008764 008560 007964 67 007766 68 69 -010133 009215 008363 007575 69 70 -009933 009019 008172 007389 70 71 -009739 008829 007987 007210 71 72 -009550 008645 007808 007036 72 73 -009367 008466 007634 006868 73 74 -009189 008292 007465 006704 74 75 ! -009016 008123 007301 006546 75 76 -008848 007959 007141 006392 76 77 -008684 007800 006987 006243 , 78 -008525 007644 006836 006098 78 79 -008370 80 -008219 007493 007347 006690 006548 005958 005821 79 80 81 -008072 007203 006410 005688 81 82 -007929 007064 006276 005559 82 83 -007789 006929 006145 005434 83 84 -007653 006797 006018 005312 84 85 -007520 006668 005894 005194 85 86 -007390 006543 005773 005078 86 87 -007264 006420 005656 004966 87 88 -007141 006301 005541 004857 88 89 -007021 006185 005430 -004751 89 90 -006903 006071 005321 -004648 90 91 -006789 005961 0052 1 5~* -004547 91 92 -006676 005853 005112 '004449 92 93 -006567 005747 005011 -004353 93 94 -006460 005644 004913 -004260 94 95 -006355 005544 004817 -004169 95 96 -006253 005445 004723 -004081 96 97 -006153 005349 004632 -003995 97 08 -006055 005256 004543 003911 98 99 -005959 005164 004456 003829 99 100 -005866 005074 004371 -003749 100 (107) INTEREST TABLES SINKING FUND FOR THE REPAYMENT OF LOANS Years 2% 2i% 2*% 2f% Years I i -oooooo i -oooooo i -oooooo i -oooooo I 2 495049 -494438 493827 -493222 2 3 326755 -325945 325137 -324332 3 4 -242624 -241719 240818 -239920 4 5 192158 -191200 190247 -189298 5 6 -158526 '157535 156550 155571 6 7 -i345 12 -1335 132495 -131497 7 8 -116509 -115485 114467 -113458 8 9 -102515 -101482 100457 '099441 9 10 -091326 . -090288 089259 -088240 10 ii -082178 -081136 080106 '079086 ii 12 -074560 ^SSI? 072487 -071469 12 13 -O68ll8 -067077 066048 -065033 *3 14 ! -062602 -061562 060536 '059525 Z 4 15 | ^57825 -056789 055766 -054759 15 16 -053650 -052617 051599 -050597 16 17 -049970 -048940 047928 -046932 *7 18 -046702 045677 044670 -043681 18 19 -043782 042762 041760 -040778 T 9 20 '04II57 040142 039147 -038172 20 21 -038785 037776 036787 -035819 21 22 -036631 035628 034646 -033686 22 23 -034668 033671 032696 -031744 23 24 -032871 -031880 030913 -029969 24 25 -031221 -030236 029276 -028340 25 26 -029699 -028721 027768 -026841 ' 26 27 028293 -027322 026377 -025458 27 28 026990 026025 025088 -024177 28 29 025779 024821 023891 -022989 29 30 024650 023699 022777 -021884 30 31 -023596 022653 021739 020855 3 1 32 -022611 021674 020768 -019893 3 2 33 -021687 020757 019859 -018993 33 34 -020819 019897 019007 018149 34 35 -020002 019087 018205 017356 35 36 ; -019233 018325 017451 016611 36 37 -018507 017606 016741 015910 38 -017821 016928 016070 015248 38 39 017171 016285 015436 014623 39 40 016556 015677 014836 014032 40 4i 015972 015101 014268 013472 4i 42 015417 014554 013728 012942 42 43 014890 014034 013217 012439 43 44 014388 013539 012730 011961 44 45 013910 013068 012267 011507 45 46 013453 012619 011826 011075 46 47 013018 012191 oi 1407 -010664 47 48 012602 011782 011006 -010272 48 49 012204 -011392 010623 009898 49 50 -011823 011018 010258 009541 So , For explanation see pp. 16, 17 (108) INTEREST TABLES SINKING FUND FOE THE EEPAYMENT OF LOANS Years 2 % 2i% 2i% 2f% Years 51 '011459 010661 009909 009200 51 52 'on 109 010319 009574 008874 52 53 -010774 009991 009254 008563 53 54 010452 009677 008948 008265 54 55 010143 009375 008654 007980 55 56 009847 009085 008373 007706 56 57 009 56 1 008807 008102 007444 58 -009287 008540 007842 007193 58 g 009022 008768 008283 008035 007593 007353 006952 006720 8 61 008523 007797 007123 006498 6z 62 008286 007568 006901 -006284 62 63 008058 007347 006688 -006079 63 64 007839 007134 006482 -005881 64 65 007626 006929 006285 005691 65 66 007421 006731 006094 '005508 66 67 007223 006540 005910 005332 67 68 007032 006355 005733 005163 68 69 006847 006177 005562 005000 69 70 006668 006005 005397 004842 70 7 1 006494 005838 005238 004690 71 72 006327 005677 005084 004544 72 73 096165 005522 004936 004403 73 74 006007 005371 004792 004267 74 75 005855 005226 004654 004136 ! 75 76 005708 005085 004519 004009 76 77 78 005564 005426 004948 004816 004390 004265 003886 003768 * 8 005291 005161 004688 004564 004143 004026 003654 79 003543 80 81 005034 004444 003912 -003437 Si 82 004911 004327 003803 003334 82 83 004792 004214 003696 003234 83 84 004676 004104 003593 003137 84 85 004563 003998 003493 003044 85 86 004454 003895 003396 002954 86 87 004348 003795 003303 002867 87 88 004244 003697 003212 002782 88 89 004144 003603 003124 002700 89 90 004046 003511 003038 -002621 90 9 1 003951 003422 002955 002545 91 92 003859 003336 002875 -002470 92 93 003769 003252 002797 -002399 93 94 00368 i 003170 002721 -002329 94 95 003596 003091 002648 -002261 95 96 003513 003014 002577 002196 06 97 003432 002939 002507 002133 97 98 003354 002866 002440 00207 1 98 99 003277 002795 002375 002012 99 zoo 003203 002726 002312 001954 100 (109) INTEKEST TABLES SINKING FUND FOB THE BEPAYMENT OF LOANS ( Years 3o/ Q l o/ /o O^" /o 3i% 3- % Years I I -000000 I -000000 I -000000 I -000000 I 2 492611 492005 491400 490798 2 3 323530 322731 -321934 321140 3 4 239027 238137 237251 236369 4 5 188355 187415 186481 185552 5 6 ^54598 153630 -152668 151712 6 I 130506 -129522 112456 -111463 128544 110477 127574 109498 1 9 098434 -097436 096446 095465 9 10 -087231 -086231 085241 084261 10 ii -078077 -077079 076092 075115 ii 12 -070462 -069467 068484 067512 12 13 064030 -063039 062062 061096 13 14 058526 '057542 056571 055613 14 15 053767 -052789 051825 050876 15 16 049611 -048640 047685 046745 16 17 045953 '044990 -044043 043113 17 18 042709 -041754 -040817 039897 18 19 039814 -038868 -037940 037031 19 20 037216 -036279 -035361 034462 20 21 034872 -033944 033037 032149 21 22 032747 -031829 -030932 030055 22 23 030814 -029906 -029019 028153 23 24 029047 -028149 -027273 026419 24 25 027428 -026539 -025674 024832 25 26 025938 -025060 -024205 023375 26 27 024564 -023696 -022852 022033 2 7 28 023293 -022435 -021603 020795 28 29 022115 -021267 '020445 019650 29 30 021019 020182 -019371 -018588 30 31 019999 019172 -018372 -017600 31 32 019047 018230 -017442 016681 32 33 018156 ' OI 735 -016572 015824 33 34 017322 016526 -015760 015023 34 35 016539 015753 -014998 014273 35 36 015804 015028 -014284 013571 36 37 i -015112 014346 -013613 012911 37 38 014459 013704 '012982 012292 38 39 013844 013099 -012388 011709 39 40 013262 012528 011827 011159 40 41 012712 011988 011298 010642 41 42 012192 -011478 010798 010153 42 43 011698 010994 010325 009691 1 43 44 i -011230 010536 -009878 009254 44 45 010785 oioioi -009453 008841 45 46 010363 009688 -00905 1 008449 46 47 009961 009296 -008669 008078 47 48 009578 008923 -008306 007726 48 49 0092 i 3 008568 -007962 007392 49 50 008866 -008230 '007634 007074 So For explanation see pp. 16, 17 (no) INTEREST TABLES SINKING FUND FOE THE REPAYMENT OF LOANS Years 3% 3i% 31% 3J% Years 51 008534 007908 007322 006772 51 5 2 0082 1 7 007601 007024 006485 52 53 007915 007308 006741 006212 53 54 007626 007028 00647 I 005952 54 55 007349 006761 006213 005704 55 56 007085 006506 005967 005468 56 57 006831 006261 005732 005242 57 58 006588 006028 005508 005028 58 006356 005804 005294 004822 59 60 006133 005590 005089 004627 60 61 005919 005385 004892 004440 6l 62 005714 005188 004705 004261 62 63 005517 005000 004525 004090 63 64 005328 004819 004353 003927 64 65 005146 004646 004188 003771 65 66 004971 004479 004030 003621 66 67 004803 004320 003879 003478 67 68 004642 004166 003734 003341 68 69 004486 004019 003595 003210 69 70 004337 003877 003461 003085 70 tar* 004193 003741 003333 002964 71 72 004054 003610 003210 002849 72 73 003921 003484 003092 002738 73 74 003792 003363 002978 002633 74 75 003668 003247 002869 002531 75 76 003548 003135 002764 002434 76 77 003433 003027 002664 002340 77 78 003322 002923 002567 002250 78 003215 002823 002474 002164 80 003112 002727 002385 002082 80 81 003012 002634 002299 002003 81 82 002916 002545 002216 001926 82 83 002823 002459 002137 001853 83 84 002733 002376 002060 001783 84 85 002647 002295 001987 001716 85 86 002563 OO22I8 001916 001651 86 87 002482 002144 001848 001589 87 88 002404 002072 001782 001529 88 89 002329 002003 001719 001472 89 00 002256 001936 001658 001416 90 91 002185 001872 001599 001363 91 92 002117 001809 001543 001312 92 93 00205 l 001749 001488 001263 93 94 001987 001691 001436 001216 94 95 001926 001635 001385 001171 95 96 001866 001582 001337 001127 96 001809 001529 001290 001085 97 98 001753 001479 001245 001045 98 99 001699 001430 OOI2OI 001006 99 100 001647 001384 OOII59 000969 100 (III) INTEREST TABLES SINKING FUND FOE THE REPAYMENT OF LOANS i Years 1 i 4% 4i% 4i% 5% Years . i -oooooo I 'OOOOOO I '000000 i -oooooo I 2 490196 489596 488997 487805 2 3 320349 319559 318773 317209 O 4 235490 234615 233744 232012 4 s ; 184627 183707 182792 180975 5 6 150762 149817 148878 147017 6 7 126610 125652 124701 122820 7 8 108528 107565 106609 104722 8 9 ! 094493 093529 092575 090690 9 zo 083291 082330 081379 079505 10 II 074149 073193 072248 070389 ii 12 066552 065603 064666 062825 12 13 060144 059203 058275 056456 13 14 054669 053738 052820 051024 14 15 049941 049020 048114 046342 15 16 045820 044910 044015 042270 16 i? 042199 041300 040418 038699 *7 18 038993 038107 037237 035546- 18 19 036139 035264 034407 032745 19 20 033582 032720 031876 030243 20 21 031280 030431 029601 027996 21 22 029199 028362 027546 025971 j 22 23 027309 026486 025682 024137 23 24 025587 024776 023987 022471 24 25 024012 023215 022439 020952 25 26 022567 021783 02 102 I 019564 26 27 021239 020467 019719 018292 2 7 28 020013 019255 018521 017123 28 29 018880 018135 017415 016046 29 30 017830 017098 016392 015051 30 3 1 016855 016137 015443 014132 31 32 015949 015243 014563 013280 32 33 015104 014411 013745 012490 33 34 i oi43!5 013635 012982 011755 34 35 ! 013577 012910 012270 011072 35 36 012887 012232 011606 010434 36 37 012240 011597 010984 009840 37 38 011632 01 1002 010402 009284 38 39 011061 010444 009856 008765 39 40 010523 009918 009343 008278 40 41 010017 009424 008862 007822 4i 42 009540 008959 008409 007395 42 43 009090 008521 007982 006993 43 44 008665 008107 007581 006616 44 45 008262 007717 007202 006262 45 46 007882 007348 006845 005928 46 47 007522 006999 006507 005614 47 4 007181 006669 006189 005318 48 49 006857 006356 005887 005040 49 50 006550 006060 005602 004777 ! 50 ) For explanation see pp. 16, 17 (112) INTEREST TABLES SINKING FUND FOE THE EEPAYMENT OF LOANS I Years 4 % 4i % 4|% 5% Years 51 006259 -005779 005332 004529 51 52 005982 -005513 005077 004295 52 53 005719 -005261 004835 -004073 53 54 005469 -005021 004605 -003864 54 55 005231 -004793 004388 -003667 55 56 005005 -004577 004181 -003480 56 57 004789 -004371 003985 -003303 57 58 004584 -004175 003799 -003136 58 g 004388 -003989 004202 -003812 003622 -002978 59 003454 -002828 60 61 004024 -003643 003295 002686 61 62 003854 -003482 003143 002552 62 63 003692 -003329 002998 002424 63 64 003538 -003183 002861 002304 64 65 003390 '003044 002730 002189 65 66 003249 -002912 002606 -002081 66 67 003115 -002785 002488 -001978 67 68 002986 -002665 002375 -001880 68 69 002863 -002549 002267 001787 69 70 002745 -002440 002165 001699 70 71 -002633 '002335 002068 001616 71 72 -002525 -002234 001975 001536 72 73 -002422 -002139 001886 001461 73 74 002323 -002047 001802 001390 74 75 002229 -001960 001721 001322 75 76 -002139 001877 001644 001257 76 77 -002052 78 -001969 001797 001721 001571 001501 001196 77 001138 78 79 -001890 001648 001434 001082 79 80 -001814 001578 001371 001030 80 81 -001741 '001511 001310 000980 8 1 82 001672 001448 001252 000932 82 83 001605 001387 001197 000887 83 84 001541 001329 001144 000844 84 85 001479 001273 001093 000803 85 86 001420 001219 -001045 000764 86 87 001364 oou68 000999 000727 87 88 001310 001119 000955 000692 88 89 001258 001073 000913 000659 89 90 001208 001028 000873 000627 90 91 oon6o 000985 000835 000597 91 92 001114 000944 000798 000568 92 93 001070 000905 000763 000541 93 94 001028 000867 000730 000515 04 95 000987 -000831 000698 000490 95 96 000949 -000796 000667 000466 96 000911 000763 000638 000444 98 000875 000732 000610 000423 08 99 000841 000701 000584 000402 99 100 000808 000672 000558 000383 xoo ("3) F INTEKEST TABLES SINKING FUND FOB THE REPAYMENT OF LOANS Years 6% 7% 8% 10% Years I I '000000 I -000000 I -000000 I -000000 I 2 485437 -483092 480769 476190 2 3 ! -314110 -311052 308033 302115 3 4 -228591 225228 221921 215471 4 5 177396 173891 170456 163798 5 6 143363 139796 136315 129607 6 7 119135 115553 112072 105406 7 8 -101036 097468 094015 087444 8 9 ; -087022 083486 080079 .073641 9 10 -075868 -072377 069029 062745 I0 ii -066793 -063357 060076 053963 " 12 -059277 -055902 052695 046763 12 13 -052960 -049651 046522 040779 13 14 -047585 -044345 041297 035746 14 15 042963 039795 036829 031474 15 16 038952 035858 032977 027817 16 18 035445 -032425 032357 -029413 029629 026702 024664 17 021930 18 19 029621 -026753 024128 019547 19 20 027185 -024393 021852 017460 20 21 025005 -022289 019832 015624 21 22 023046 -020406 018032 014005 22 23 021278 018714 016422 012572 23 24 019679 017189 014978 OII3OO 24 25 018227 015811 013679 OIOI68 25 26 016904 014561 012507 009159 26 27 -015697 013426 011448 008258 27 28 -014593 012392 010489 007451 28 29 -013580 011449 009618 006728 29 30 012649 010586 008827 006079 30 31 011792 009797 008107 005496 3i 3 2 01 1002 009073 007451 004972 32 33 -010273 -008408 006852 004499 33 34 -009598 -007797 006304 004074 34 35 -008974 -007234 005803 003689 35 36 ! -008395 006715 005345 003343 36 37 ; -007857 006237 004924 003030 38 -007358 005795 004539 002747 38 39 006894 005387 004185 002491 39 40 006462 005009 003860 002259 40 4i 006059 -004660 003562 002050 4i 42 005683 -004336 003287 001860 42 43 005333 -004036 003034 001688 43 44 005006 -003758 002802 001532 44 45 OO47OI -OO3499 002587 OOI39I 45 46 004415 -003260 002390 001263 46 3 004148 -003037 003898 -002831 002208 002040 OOII47 OOIO4I 47 48 49 003664 -002639 001886 000946 49 50 003444 002460 001743 000859 50 For explanation see pp. 16, 17 ("4) INTEREST TABLES SINKING FUND FOR THE REPAYMENT OF LOANS Years 6% 7% 8% 10% Years 51 003239 002294 001611 000780 51 5 2 003046 002139 -001490 000709 52 53 002866 001995 -001377 000644 53 54 002696 001861 001274 000585 54 55 002537 001736 001178 000532 55 56 002388 001620 001090 000483 56 002247 001512 001008 000439 58 002116 001411 000932 000399 58 59 -001992- 001317 000862 000363 59 60 001876 001229 000798 000329 60 61 001766 001147 000738 000299 61 62 001664 001071 '000683 000272 62 63 001567 ooiooo -000632 000247 63 64 001476 '000934 -000585 000225 64 65 001391 -000872 -000541 000204 65 66 001310 -000814 -000501 000186 66 67 001235 000760 -000464 000169 67 68 001163 000710 -000429 000153 68 69 001096 -000663 -000397 000139 69 70 001033 -000620 -000368 000127 70 71 000974 000579 -000340 000115 71 72 000918 000541 -000315 000105 72 73 000865 000505 -000292 000095 73 74 000815 -000472 -000270 000086 74 75 000769 -000441 -000250 000079 75 76 000725 -000412 -000231 000072 76 000683 -000385 -000214 000065 78 000644 000359 000198 000059 78 79 000607 000336 000183 000054 79 80 000573 000314 -000170 000049 80 * 81 000540 000293 -000157 000044 81 82 000509 '000274 -000146 000040 82 83 000480 -000256 -000135 000037 83 84 000453 -000239 -000125 000033 84 85 000427 -000223 000116 000030 85 86 000402 -000209 000107 000028 86 87 000380 -000195 000099 000025 87 88 000358 -000182 000092 000023 88 89 000338 -000170 000085 OOOO2I 89 90 000318 -000159 000079 000019 90 pi 000300 000149 000073 000017 91 92 000283 000139 000067 000015 92 93 000267 000130 000062 000014 93 94 000252 OOOI2I 000058 000013 94 95 000238 000113 000053 OOOOI2 95 96 000224 000106 000049 OOOOII 96 97 0002 1 1 000099 000046 ooooio 97 08 000199 000092 000042 000009 98 99 000188 -000086 000039 000008 99 zoo 000177 -000081 000036 000007 100 (115) F2 INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 3 and 3?, PER CENT., and Replacing Capital when Invested at Lower Rates Yrs. 3&2% 3&2i% 3i*2% 3i&2i% 3|&3% Yrs. I 97087 97087 96618 96618 -96618 I 2 i -90458 I -90903 I -88662 I -89098 I -89534 2 3 2-80304 2-81582 2-76430 : 2-77672 2-78916 3 3-66806 3-69252 3-60200 3-62558 3-64928 4 5 4-50129 4-54036 4-40221 4-43957 4-47719 5 6 5-30431 5-36050 5-16727 5-22057 5-27433 6 7 6-07858 6-15402 5-89929 5-97031 6-04206 7 8 6-82548 6-92198 6-60023 6-68991 6-78167 8 9 7-54629 7-66537 7-27191 7-38242 7-49435 9 10 8-24222 8-385I3 7*9*599 8-04772 8-18126 10 ii 8-91441 9-08216 8-53403 8-68765 8-84349 ii 12 9-56392 975732 9-12745 9-30344 9-48208 12 13 10-19177 10-41143 9-69759 ; 9-89626 10-09800 13 M 10-79891 1 1 -04526 10-24569 10-46720 10-69217 14 15 11-38628 11-65957 10-77291 11-01729 11-26550 15 16 n-95455 12-25505 11-28030 11-54748 1 1 -8 1 88 1 16 17; 12-50471 12-83239 11-76881 12-05869 12-35292 17 18 13-03745 13-39224 12-23958 12-55176 12-86857 18 19 1 3 -55348 I3-93522 12-69329 ; 13-02751 13-36650 19 20 14-05349 14-46192 13-13082 13-48670 13-84740 20 21 14-53810 14-97290 I3-55293 13-93003 14-31193 21 22 15-00794 15-46872 13-96036 14-35820 14-76071 22 23 I5-46357 15-94988 I4-35377 14-77184 i5' J 9436 23 24 I5-90556 16-41690 14-73381 I5-I7I55 I5-6I343 24 25 16-33441 16-87025 15-10108 I5-55792 16-01848 25 26 16-75063 17-31040 I 5'456i3 15*93150 16-41004 26 27 17-15469 I7-73777 I 5"7995 I 16-29278 16-78860 27 28 17-54704 18-15279 16-13172 16-64227 17-15465 28 29 17-92810 I8-55588 16-45322 16-98045 17-50864 29 30 18-29828 18-94742 16-76448 17-30773 17-85100 30 3 I 18-65799 19-32778 17-06591 17-62456 18-18217 31 32 I9-00757 I9-69733 17-35791 17-93133 18-50254 32 33 19-34740 20-05640 17-64087 18-22842 18-81251 33 34 19-67781 20-40535 17-91515 18-51620 19-11243 34 35 19-99912 20-74448 18-18109 18-79502 19-40267 35 36 20-31164 21-07412 18-43900 19-06523 19-68357 36 20-61567 21-39454 18-68922 19-32707 19-95545 37 38 20-91150 21-70604 18-93202 19-58092 20-21863 38 39 21-19940 22-00890 19-16768 19-82705 20-47340 39 40 21-47962 22-30339 19-39648 20-06572 20-72007 40 4 1 21-75243 22-58975 19-61866 20-29721 20-95891 41 42 22-01804 22-86825 19-83446 20-52200 21-19018 42 43 22-27671 23-13910 20-04412 20-73962 21-41414 43 44 22-52864 23-40256 20-24786 20-95102 21-63105 44 45 22-77405 23-65883 20-44588 21-15618 21-84113 45 46 23-01315 23-90814 20-63838 21-35531 22-04462 46 47 23-24613 24-15069 20-82556 21-54862 22-24174 48 23-47317 24-38668 21-00759 21-73630 22-43270 48 49 23-69446 24-61630 21-18466 22-09863 22-61771 49 50 23-91017 24'83975 21-35693 22-09569 22-79696 50 For explanation see p. 18 (116) INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 3 and 3| PER CENT., and Replacing Capital when Invested at Lower Rates Yrs. 3&2% 3&2i% 3i&2% 3i&2i% 3i&3% Yrs. 51 24-12044 25-05719 21-52456 22-26740 22-97064 51 52 24-32552 25-26882 21-68770 22-42437 23-13894 52 53 24-52548 25-47479 21-84650 22-59657 23-30203 53 54 24-72049 25-67527 22-OOIIO 22-75417 23-46009 54 55 24-91071 25-87041 22-15164 22-90731 23-61327 55 56 25-09626 26-06038 22-29825 23-05612 23-76173 56 25-27729 26-24531 22-44105 23-20076 23-90563 58 25-45392 26-42536 22-58016 23-34134 24-04512 58 59 60 25-62628 25-79449 26-60065 26-77133 2271569 22-84776 23-47800 23-61086 24-18033 24-31140 8 61 25-95866 26-93751 22-97647 23-74003 24-43847 61 62 26-11891 27-09935 23-IOI93 23-86563 24-56167 62 63 64 26-27535 27-25694 26-42807 27-41041 23-22423 23-98777 24-10656 24-68111 63 24-79691 64 65 26-57719 27-55988 23-45973 24-22209 24-90920 65 66 26-72280 27-70545 23-573II 24-33446 25-01807 66 67 26-86500 27-84723 23-68369 24-44377 25-12365 67 68 27-00387 27-98533 23-79I55 24-55012 25-22603 68 69 27-13951 28-11985 23-89677 24-65358 25-32532 69 70 27-27200 28-25089 24-75424 25-42160 70 71 27-40142 28-37853 24-09960 24-85219 25-51498 71 72 27-52786 28-50289 24-19720 24-94751 25-60554 72 73 27-65140 : 28-62403 24-29275 25-04027 25-69338 73 74 27-772IO ' 28-74206 24*38587 25-13054 25-77857 74 75 27-89005 28-85705 24-47676 25-21840 25-86120 75 76 28-0053I 28-96908 24-56549 25-30392 25-94135 76 28-II795 29-07825 24-65212 25-38717 26-01910 78 28-228O5 29-18461 24-73670 25-46821 26-09451 78 8 2 8-33565 29-28826 28-44084 29-38925 24-81930 24-89996 25-54710 25-62391 26-16766 26-23863 B 81 28-54366 29-48767 24-97874 25-69869 26-30747 81 82 28-64418 29-58357 25-05568 25-77151 26-37425 82 83 28-74245 29-67704 25-13085 25-84241 26-43905 83 84 28-83854 29-768I2 25-20427 25-91145 26-50191 84 85 28-93249 29-85689 25-27601 25-98104 26-56289 85 86 29-02436 ; 29-94341 25-34609 26-04416 26-62206 86 87 29-11420 30-02773 25-41458 26-10792 26-67946 87 88 29-20206 30-10991 25-48150 26-17003 26-73516 88 89 29-28798 30-19002 25-54689 26-23052 26-78920 89 90 29-37201 30-26809 25-61081 26-28944 26-84163 90 91 29-45420 30-34420 25*67327 26-34683 26-89251 91 92 29-53460 ! 30-41838 25-73433 26-40274 26-94187 92 93 29-61324 ; 30-49069 25-79402 26-45720 26-98977 93 94 29-69017 30-56117 25^5236 26-51025 27-03625 94 95 29-76543 30-62988 25-90940 26-56194 27-08191 95 96 29-83905 30-69686 25-96517 26-61229 27-12512 96 97 29-91108 30-76216 26-OI97O 26-66135 27-16759 97 98 29-98156 30-82582 26-0730I 26-70916 27-20880 98 99 30-05052 30-88787 26-I25I5 26-75573 27-24880 99 loo 30-11799 30-94837 26-I76I3 26-80111 27-28761 100 ("7) INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 4 PER CENT., and Replacing Capital when Invested at Years 2% 2i% 3% 3i% *- I 96153 96153 96153 96153 I 2 1-86898 i -87326 1-87754 I-88l82 2 3 2-72662 2-73870 2-75080 2-76294 3 4 3-53827 3-56103 3-58388 3-60684 4 5 ! 4*30740 4-34316 4-37916 4*41538 5 6 5-03713 5-08777 5-13881 5-19027 6 I 5-73026 6-38938 5-79725 6-47386 5-86488 6-55925 5-933I5 7 6-64555 8 9 7-01678 7-11962 7-22367 7-32891 9 10 7*61514 7-73641 7-85975 7-98458 10 ii 8-18478 8-32598 8-46902 8-61390 ii 12 872908 13 9-24912 8-88990 9-42967 9-05288 9-61265 9-21562 12 9-798oi 13 14 974640 9-94663 10-14957 10-35513 14 IS 10-22229 10-44207 10-66478 10-89027 15 16 10-67804 10-91715 11-15936 1 1 -40448 16 '7 11-11483 11-37297 11-63433 11-89865 17 18 11-53374 11-81055 12-09063 12-37366 18 19 i 1 '93577 12-23083 12-52915 12-83033 19 20 12-32184 12-63470 12-95073 13-26945 20 21 12-69281 13-02298 13-35617 13-69177 21 22 13-04948 13-39646 13-74620 14-09799 22 23 I3-39260 24 13-72286 13-75584 14-10182 14-12152 14-48280 14-48880 23 14-86484 24 25 14-04091 14-43503 14-83066 15-22672 25 26 I4'34736 14-75606 15-16569 1 5 '575QI 26 27 I4-64277 15-06549 15-48846 15-91029 27 28 14-92767 15-36383 15-79948 16-23307 28 29 15-20257 15-65159 16-09926 16-54387 29 30 15-46792 15-92924 16-38827 16-84315 30 31 15-72417 16-19722 16-66696 17-13138 31 32 15-97173 16-45594 16-93577 17-40901 32 33 16-21099 16-70582 17-19509 17-67646 33 34 16-44232 16-94721 17-44532 i7-934ii 34 35 16-66605 17-18048 17-68681 18-18236 35 36 16-88252 17-40597 17-91993 18-42158 36 37 17-09204 17-62397 18-14499 18-65211 37 38 17-29488 17-83481 18-36232 18-87428 38 39 I7-49I34 18-03877 18-57222 19-08843 39 40 17-68167 18-23612 18-77498 19-29486 40 4i 17-86611 18-42711 18-97086 i9'49385 4i 42 18-04491 18-61201 19-16014 19-68571 42 43 18-21828 18-79103 19-34307 19-87068 43 44 18-38643 18-96440 19-51987 20-00000 44 45 18-54957 19-13234 19-69078 20-22104 45 46 18-70788 19-29505 19-85603 20-38691 46 47 18-86154 19-45272 20-01580 20-54688 47 48 19-01074 19-60554 20-17032 20-70116 48 49 19-15563 19-79522 20-31978 20-84998 49 50 19-29637 19-89731 00-46434 20-99354. 50 For explanation see p. 18 (nS) INTEKEST TABLES Value of an Annuity Yielding Interest on Capital at 4 PER CENT., and Replacing Capital when Invested at Years 2o/ To 24% 3% 3i% Years 51 I9-433I J 20-03658 20-60419 2I-I320I 51 52 I9-56599 20-17364 20-73949 21-26535 52 53 I9-695I5 20-30271 20-87042 21-39449 53 54 I9-82072 20-42985 20-99712 21-51884 54 55 19-94281 20-55321 21-11974 21-63883 55 56 20-06I56 20-67293 21-23842 2175460 56 57 20-I7707 20-78914 2I-3533 1 21-86631 57 58 20-28946 2O-9OI94 21-47867 21-97411 58 g 20-39882 2I-OII46 20-50526 2I-II78I 21-57221 22-07814 21-67648 22-17854 g 61 20-60887 21-22108 2177744 22-27544 61 62 20-70975 21-32139 21-87521 22-36896 62 63 20-80798 21-41882 21-96990 22-45923 63 64 20-90364 21-51348 22-06161 22-54635 64 65 20-99683 2I-60544 22-15045 22-63045 65 66 2I-08760 21-69480 22-23650 2271163 66 3 2I-I7605 2I-78l65 2I-26224 2I-86605 22-31987 22-40064 22-78999 22-86563 s 69 21-34624 21-94808 22-47891 22-93866 69 70 2I-428I2 22-02783 22-55472 23-00916 70 7 1 2I-50794 22-10536 22-62819 23-07722 71 72 21-58576 22-18074 22-69939 23-14293 72 73 2I-66l64 22-25403 22-76839 23-20638 73 74 2I-73565 22-32530 22-83527 23-26763 74 75 2I-80783 22-39462 22-90008 23-32677 75 76 2I-87824 22-46204 22-96291 23-38388 76 21-94693 22-52761 23-02380 23-43902 78 22-01394 22-59140 23-08283 23-49226 78 79 22-07933 22-65345 23-14006 79 80 22-I43I4 2271383 23-I9553 23-5933I 80 81 ! 22-20542 22-77257 23-24932 23-64125 81 82 i 22-26620 22-82973 23-30146 23-68755 82 83 ! 22-32555 22-88535 23-35202 23-73225 83 84 22-38348 22-93947 23-40105 84 85 22-44003 22-99215 23-44852 23-81711 85 86 22-49526 23-04342 23-49468 23-85737 86 87 22-54918 23-09333 23-53937 23-89626 87 88 22-60185 23-14191 23-58272 23-9338I 88 89 ! 22-65329 23-18919 23-62476 23-97008 89 90 2270353 23-23523 23-66552 24-00510 90 91 22-75260 23-28005 23-70506 24-03893 91 92 22-80055 23*32369 23-7434I 24-07160 92 93 22-84739 23-36618 2378061 24-10316 93 94 22-89315 23-40755 23-81668 24-13364 94 95 22-93787 23-44784 23-85168 24-16307 95 96 22-98157 23-48707 23-88562 24-19151 96 23-02427 23-52528 23-91854 24-21897 98 23-06601 j 23-56249 23-95049 24-24549 98 99 23-10680 23-59873 33-98147 24-27112 99 100 23-14668 23-63403 24-01153 24-29586 100 ("9) INTEBEST TABLES Value of an Annuity Yielding Interest on Capital at 5 PEE CENT., and Replacing Capital when Invested at Years 2% 2i% 3o/ 70 01 o/ 02 /o Years I 95238 95238 95238 -95238 I 2 i -83469 1-83882 i -84294 i -84706 2 3 2-65425 2-66570 2-67716 2-68865 3 4 3*41736 3-43858 3-45988 3-48127 4 5 4-12953 4-16239 4-I9543 4-22866 5 6 479557 4-84145 4-88764 4-934I7 6 7 5-41970 5-47959 5 '53997 5 -60085 7 8 6-00565 6-08024 6-I5550 6-23144 8 9 6-55671 6-64642 6-73701 6-82846 9 10 7-07581 7-18088 7-28701 7-394I9 10 ii 7-56556 7-68604 7-80778 7-93072 ii 12 8-02828 8-16412 8-30137 8-43996 12 13 8-46608 8-61710 8-76996 8-92367 *3 14 8-88083 9-04678 9-21435 9-38344 M 15 ; 9*27425 9-45478 9-63701 9-82076 15 l6 : 9-64784 9-84262 10-03907 10-23700 16 I? 10-00302 10-21161 10-42182 10-63342 J 7 18 10-34104 10-56300 10-78647 11-01117 18 19 10-66305 10-89792 11-13414 ii-37i35 19 20 10-97011 11-21740 11-46582 11-71495 20 21 11-26319 11-52242 11-78248 12-04288 21 22 11-54316 11-81382 12-08497 12-35604 22 23 II-8I082 12-09243 12-37411 12-65521 23 2 4 12-06693 12-35898 12-65063 12-94116 24 25 12-31217 12-61417 12-91524 13-21457 25 26 12-54717 12-85864 13-16858 13-47611 26 27 12-77252 13-09297 13-41126 13-72638 27 28 12-98875 13-31772 13-64382 13-96596 28 29 13-19638 13-53340 13-86680 I4-I9539 29 30 I3-39586 13-74048 14-08069 14-41518 30 31 13-58763 13-93942 14-28593 14-62578 31 32 1377209 14-13211 14-48297 14-82766 32 33 13-94962 14-31447 14-67220 15-02123 33 34 14-12057 14-49134 I4-85399 15-20689 34 35 14-28526 14-66156 15-02871 1 5 -38501 35 36 14-44401 14-82546 15-19669 I5-55593 I 36 14-59709 14-98332 1535824 15-72000 37 38 H74479 15-13544 15-51365 i5'87752 38 39 14-88734 15-28207 15-66321 16-02879 39 40 15-02500 1 5 -42347 15-80718 16-17409 40 4i 15-15797 I5-55988 15-94581 16-31369 41 42 15-28648 15-69150 16-07932 l6-447*3 ! 42 43 15-41071 15-81856 16-20795 16-57677 43 44 15-53086 15-94124 I 6'33i9o 16-70071 44 45 15-64710 16-05974 16-45138 16-81989 ; 45 46 I5-75950 16-17423 16-56657 16-93449 46 47 16-86850 16-28487 16-67764 17-04472 47 48 I5-97397 16-39183 16-78478 17-15076 48 49 16-07615 16-55328 16-88814 17-25278 49 50 16-17515 16-59532 16-98788 17-35096 50 For explanation see p. 1 8 (120) INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 5 PER CENT., and Replacing Capital when Invested at Years 2% 2i % 3% 3-L % Years 51 16-27113 16-69206 17-08414 17*44544 51 52 16-36418 1678572 17-17706 I7-53639 52 53 54 16-45443 16-54198 16-87635 16-96411 17-26677 I7-35340 17-62394 53 17-70824 54 55 16-62693 17-04908 17-43707 1778941 55 56 16-70940 17-13138 17-51789 17-86757 56 16-78945 17-21110 1 7 '59599 17-94287 57 58 16-86720 17-28834 17-67144 18-01538 58 59 16-94271 17-36320 17-74436 18-08526 59 60 17-01607 17-43576 17-81485 18-15257 60 61 17-08736 17-50610 17-88298 18-21743 61 62 17-15667 17-57430 17-94886 18-27993 62 63 17-22401 17-64045 18-01256 18-34017 63 64 17-28951 17-70460 18-07416 18-39822 64 65 I7-35320 1776683 I8-I3374 18-45418 65 66 17-41516 17-82722 18-19138 18-50813 66 67 I7-47544 17-88583 18-24713 18-56013 67 68 I7-534IO 17-94269 18-30108 18-61028 68 69 17-59119 17-99789 18-35328 18-65862 69 70 17-64675 18-05148 18-40379 18-70524 70 7i 17-70085 18-10351 18-45268 18-75020 71 72 1775353 18-15404 18-50000 18-79355 72 73 17-80483 18-20311 18-54581 18-83537 73 74 17-85480 18-25077 18-59015 18-87570 74 75 17-90347 ' 18-29706 18-63309 18-91461 75 76 17-95090 18-34204 18-67466 18-95213 76 17-99711 18-38574 18-71492 18-98834 77 78 18-04215 18-42821 1875390 19-02326 78 79 18-08605 18-46948 18-79166 19*05696 79 80 18-12885 18-50959 18-82823 19-08947 80 81 18-17057 18-54858 18-86365 19*12084 81 82 18-21125 18-58648 18-89796 19-15112 82 83 18-25093 18-62333 18-93120 19-18033 83 84 18-28961 18-65916 18-96341 19-20851 84 85 18-32738 18-69400 18-99461 19-23572 85 86 18-36419 18-72788 19-02485 19-26197 86 87 18-40011 18-76083 19-05414 19-28731 87 88 89 18-43516 18-46937 18-79288 18-82405 19-08254 19-11005 19-31177 88 I933537 89 90 18-50275 18-85438 19-13671 19-35816 90 91 18-53533 18-88388 19-16257 19-38014 91 92 18-56714 18-91258 19-18762 19-40138 92 93 18-59819 18*94051 19-21190 19-42187 93 94 18-62850 18-96768 I9-23544 19-44166 94 95 18-65810 18-99413 19-25826 19-46076 95 06 18-68700 19-01986 19-28038 19-47919 96 97 1871523 19-04491 19-30183 19-49700 97 98 18-74280 19-06929 19-32262 19-51418 98 99 18-76972 19-09301 19-34279 19-53078 99 100 1879602 19-11612 19-36233 19-54680 100 (121) INTEREST TABLES Valu of an Annuity Yielding Interest on Capital at 6 PER CENT., and Replacing Capital when Invested at Years 207 70 2i% 3o/ 7O 3t% 4% Years I 94340 94340 94340 94340 94340 I 2 1-80164 I -80562 1-80959 i'8i357 1-81753 2 3 2-58562 2-59648 2-60736 2-61825 2-62916 3 4 3-30443 3-32427 3-344I8 3'364i6 3-38421 4 5 3-96577 3-99605 4-02649 4-05711 4-08786 5 6 4-576ii 4-61787 4-65988 4-70216 474469 6 7 5' 1 4io7 5-I9494 5-24918 5-30380 5-35877 7 8 5-66543 5-73I74 579858 5-86589 5-93373 8 9 6-15328 6-23220 6-31178 6-39198 6-47279 9 I0 6-60825 6-69976 6-79205 6-88511 6-97881 10 ii 7-03344 7-13745 7^4234 7-34797 7-45440 ii 12 7 '43 '63 7-5479I 7-66507 7-78307 7-90189 12 13 7-80530 7-93349 8-06257 8-19256 8-32335 I 3 14 8-15647 8-29628 8-43697 8-57846 8-72075 *4 15 l 8-48716 8-63811 8-78990 8-94254 9-09579 15 16 8-79894 8-96065 9-12317 9-28634 9-45001 16 17 9-09339 18 9-37I89 9-26544 9-43814 9-73624 9-61141 9-91896 9-78483 10-10172 18 19 9-63558 9-82704 10-01863 10-21033 10-40161 I 9 20 9-88562 10-08603 10-28637 10-48647 10-68582 20 21 10-12299 10-33197 10-54052 10-74841 10-95530 21 22 10-34865 10-56569 IO-78202 10-99723 11-21089 22 23 10-56323 10-78795 II-OII52 11-23356 i 1 "45357 2 3 24 10-76762 10-99953 1 1 -23002 1 1 -45830 1 1 -68402 24 25 10-96239 II -2OI22 II-43798 11-67215 1 1 -90306 25 26 11-14840 II-39367 1 1 -63630 11-87578 12-11138 26 27 11-32593 II-577I6 11-82536 12-06971 12-30936 2 7 28 n-49557 "75254 I2-0058I 12-25445 12-49797 28 29 11-65786 1 1 -92023 12-17805 12-43085 12-67748 29 30 ii-8i335 I2-08065 12-34278 12-59906 12-84852 30 31 1 1 -96229 I2-23406 I2-5OOI6 12-75966 13-01152 31 32 12-10493 12-38114 12-65070 12-91289 13-16673 32 33 12-24185 I2-522O7 1279492 13-05960 13-31487 33 34 12-37333 I2-657II 12-93293 I3-I9958 13-45623 34 35 12-49969 12-78691 13-06523 I3-33369 | 13-59120 35 36 12-62100 I2-9II39 13-19192 13-46185 13-71987 36 12-73772 13-03084 I3-3I345 13-58456 13-84275 38 12-85000 I3-I4579 13-4302! 13-70201 13-96024 38 39 12-95824 I3-25627 13-54206 13-81444 14-07242 39 40 13-06233 I336255 13-64964 13-92234 I4-I7977 40 45 I3-52997 I3-83757 14-12729 14-39823 I4-64944 45 50 13-92312 I4-23325 I4-52095 14-78546 i 15-02630 50 55 14-25659 I4-56579 14-84803 15-10277 15-33013 55 60 14-54165 14-84715 I5-I2I04 15-36358 I5-57584 60 65 14-78721 15-08637 I5-350I4 I5-57924 I5-77536 65 70 15-03895 I5-29I22 I5-543I6 I5-7577I 15-93752 70 15-18488 I5-46695 15-70648 15-90609 16-06968 75 80 15-34660 15-61865 I5-84485 16-02949 16-17756 80 90 15-61378 I5-86345 16-06271 16-21850 16-33773 90 TOO 15-82203 16-04827 I6-22I39 16-35082 16-44520 ioo For explanation see p. 18. INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 7 PEE CEHT., and Replacing Capital when Invested at Year 2 % 21% 3% 31% 4 % Year, I -93458 93458 -93458 93458 93458 i 2 176976 1-77359 1-77743 178126 178509 2 3 2-52045 2-53077 2-54110 2-55145 2'56l8l 3 4 3-I9873 3-21732 3-23596 3-25467 3 '27343 4 5 3-8i449 3-84250 3-87064 3-89892 3-9273I 5 6 437587 4-41404 4-45240 4-49099 4'52977 6 7 4-88969 4-93839 4-98738 5-03667 5-08621 7 8 5*36167 5-42102 5-48077 5-54087 5-60136 8 9 5-7966o 5-86658 5-93704 6-00795 6-07929 9 10 6-19863 6-27908 6-36007 6-44160 6-52354 10 ii 6-57125 6-66196 6-75324 6-84500 6-93727 ii 12 6-91754 7-01818 7-11936 7-22105 7-32322 12 13 7-24019 7-35035 7-46102 7-57220 7 -68380 13 14 7-54I3 6 7-66072 7-78053 7-90070 8-02124 M 15 7-82320 7 '95 * 27 8-07970 8-20850 8-33743 15 16 8-08734 8-22376 8-36044 8-49726 8-63409 16 17 8-33542 18 8-56883 8-47975 8-62418 8-72068 8-87241 8-76862 9-02389 8-91273 9-17490 17 18 19 8-78874 8-94775 9-10631 9-26441 9-42161 19 20 8-99628 9-16196 9-32697 9-49118 9-65419 20 21 9-I9244 9-36444 9-53543 9-70525 9*87362 21 22 9378I4 9-55603 9-73264 9-90766 10-08075 22 23 9-55402 973748 9-91926 10-09907 10-27654 23 24 9-72091 i 9-90953 10-09622 10-28035 10-46167 2 4 25 9-87937 10-07293 10-26399 10-45216 10-63694 25 26 IO-030I9 10-22830 10-42340 10-61515 10-80299 26 27 10-17366 10-37592 10-57485 10-76983 10-96023 27 28 10-31034 10-51657 1071892 10-91667 11-10951 28 29 10-44070 10-65065 10-85600 1 1 -05644 11-25113 29 30 10-56524 1 Q77853 10-98672 11-18931 11-38563 30 31 10-68422 10-90049 11-11123 11-31580 ii-5i344 31 3 2 1079785 11-01710 ! 11*23002 "43615 11-63481 32 33 10-90667 11-12855 n-34353 11-55108 n-75033 33 34 11-01091 11-23507 11-45187 1 1 -66045 1 1 -86029 34 35 1 1 -i 1086 11-33723 11-55548 1 1 76498 1 1 -96501 35 36 1 1 -20662 11-43498 11-65447 1 1 -86465 12-06462 36 37 1 1 -29854 11-52857 11-74922 11-95986 12-iqow 37 38 11-38680 11-61845 11-84006 12-05081 12-25010 38 39 11-47171 11-70467 1 1 '9269 1 12-13769 12-33639 39 40 11-55321 11-78745 12-01028 12-22091 12-41881 40 45 ii-9i753 12-15554 12-37854 12-58606 1277759 45 50 12-22150 12-45982 12.67974 12-88095 13-06336 50 55 12-47770 60 12-69551 1271391 12-92842 12-92775 13-13491 13-12112 13-29239 I33I753 I3-47673 g 65 12-88228 13-10874 13-30743 13-47927 13-62583 65 70 13-04325 13-26313 ; 13-45225 13-61267 13-74665 70 75 13-18305 80 13-30477 13-39513 13-57441 13-50877 13-67765 13-72326 13-84485 13-81502 13-92486 75 80 90 13-50512 13-69150 13-83968 I3'955i8 I4-04337 90 100 13-66064 13-82896 13-95732 14-05304 , 14-12270 100 INTEKEST TABLES Value of an Annuity Yielding Interest on Capital at 7 PER CENT., and Replacing Capital when Invested at Years Q/ 1 Q/ rs } & 70 ^"2 To 3% 3i% 4% Years I 93023 -93023 93023 93023 93023 i 2 1-75424 1-75800 176177 176554 I-76930 : 2 3 2-48908 2-49914 2-50922 2-51931 2-52941 3 4 3-14838 3-16638 3-18444 3-20255 3-22072 4 5 374310 3-77007 3-79716 3-82437 3-85168 5 6 4-28218 4-31872 4-35544 4-39236 4-42944 6 7 4-77300 4*81939 4-86604 4-91294 4-96007 Ml 8 5-22169 5-27796 5-33459 5-39I50 8 9 5-63333 5-69940 576588 5-83274 5-89995 9 10 6-01229 6-08794 6-16405 6-24060 6-31748 IO ii 6-36221 6-44720 6-53266 6-61848 6-70471 ii 12 6-68628 6-78026 6-87465 6-96942 7-06454 12 13 6-98724 7-08979 7-19269 7-29597 7-3995 2 13 14 7-26734 7-37811 7-48918 7 -60046 771194 IS 7-52870 7-64725 7-76597 7-88488 8-00378 15 16 7-77303 7-89896 8-02497 8-15096 8-27678 16 17 8-00192 8-13484 8-26768 8-40033 8-53250 17 18 8-21679 8-35631 8'49553 8-63431 8-77247 18 19 8-41876 8-56458 8-70974 8-85426 8-99774 19 20 8-60904 . 8-76063 8-91139 9-06117 9-20963 20 21 8-78850 ! 8-94558 9-10150 9-25609 9-40911 21 22 8*95809 9-12026 9-28100 9-44002 9-59702 22 23 9-11843 9-28540 9 '4554 9-61363 9-7743I 23 2 4 9-27033 9-44i7i 9-61104 9-77775 9-94164 24 25 9-4I433 9-68991 9-76296 9-93305 10-09979 25 26 9-55ii9 9-73066 9-90707 10-08014 10-24937 26 27 9-68120 9-86417 10-04379 10-21952 10-39080 27 28 9-80488 9-99121 10-17366 10-35165 10-52488 28 29 9^2270 i IO-II2I4 10-29707 10-47724 10-65190 29 30 IO-035I2 i 10-22735 10-41461 10-59648 1077238 30 31 IO-I4240 10-33709 10-52643 10-70985 10-88672 31 32 10-24475 IO-44I90 10-63298 10-81759 10-99519 32 33 10-34265 10-54196 10-73468 10-92037 1 1 -09829 33 34 10-43634 10-63751 10-83165 11-01807 11-19633 34 35 IO-52609 IO-72904 10-92431 11-11136 1 1 -28961 35 36 10-61199 10-81654 11-01273 1 1 -20022 11-37825 36 37 10-69439 10-90025 1 1 -09730 11-28503 1 1 -46263 37 38 10-77342 10-98056 11-17831 11-36596 11-54308 38 39 10-84940 11-05754 11-25568 11-44322 11-61967 39 40 10-92228 11-13139 11-32990 11-51715 11-69276 40 45 11-24733 11-45909 11-65705 11-84091 12-01028 ! 45 50 11-51769 11-72910 11-92378 12-10156 12-26242 50 55 n-74495 u-95400 60 H'93773 12-14285 12.14344 12-32544 I2 '3 I 33 12-46401 12-48611 12-62594 8 65 12-10273 12-30239 12-47723 12-62818 1275673 65 70 ! I2-2447O I2-43828 1 2 -60446 1274519 12-86256 70 75 12-36782 12-55430 I2-7II65 12-84208 12-94850 ; 75 80 12-47489 12-65406 I2-802I3 12-92240 13-01846 j 80 90 12-65086 12-81427 12-94398 13-04495 13-12198 90 100 12-78723 12-93460 13-04683 13-13042 13-19122 100 For explanation see p. 18. (I2IC) INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 8 PER CENT., and Replacing Capital when invested at Ye- 2% 2 % 3% 34% 4% Years I ^2593 ^2593 92593 92593 -92593 I 2 173898 1-74269 i -74639 1-75009 175378 2 3 2-45848 2-46830 2-47813 2-48797 2-49782 3 4 3-09958 3 -II 7o3 3-I3453 3-15208 3^6967 4 5 3-67434 3-70032 372641 3-75261 377890 5 6 4-19242 4-22744 4-26261 4-29797 4-33347 6 7 4-66174 4-70599 475046 4-795 1 5 4-84004 7 8 5-08883 5-14226 5-19599 5-24998 5-30425 8 9 5-479oo 5-54I49 5-60431 5-66745 573089 9 ' 10 5-83683 5-90811 5-97975 6-05177 6-12404 10 ii 6-16606 6-24586 6-32603 6-40648 6-48723 ii 12 6-46998 6-55794 6-64620 673473 6-82352 12 13 6-75137 6-84706 6-94300 7-03918 7-I3552 13 14 7-01252 7-11561 7-21886 7-32220 7-42561 15 7-25558 7-36563 7-47569 7-58581 7-7958o 15 : 16 7-48223 7-59884 7-71539 7-83177 7-94786 it 17 7-69408 7-81690 18 7-89253 8-02118 7-93947 8-14936 8-06172 8-18337 8-27698 8-40386 n 19 8-07872 8-21288 8-34627 8-47889 8-61037 19 20 8-25375 8-39299 8-53126 8-66844 8-80421 20 21 8-41857 8-56260 8-70534 8-84666 8-98634 21 22 8-57405 8-72250 8-86941 9-01453 9-15759 22 23 8-72083 8-87343 9-02413 9-17271 9-31888 23 24 8-85967 9-01607 9-17036 9-32201 9-47086 24 25 8-99111 9-I5II4 9-30856 9-46307 9-61428 25 26 9-II585 ! 9-279I9 9-43948 9-59647 974972 26 27 9-23421 9'40053 9-56352 9-72271 9-87762 2 7 28 9-34667 9-5I583 9-68120 9-84223 9-99870 28 29 9-45367 9*62547 9-79288 9-95570 10-11327 29 30 9-55566 9-72980 9-89913 10-06330 10-22181 30 31 9-65288 9-82907 lO'OOOIO 10-16549 10-32471 31 32 9-74554 9-92379 10-09622 10-26252 10-42220 32 33 9-83410 10-01412 10-18786 10-35497 10-51480 33 34 9-91877 10-10030 10-27517 10-44277 10-60277 34 35 9-9998o 10-18278 10-35851 10-52654 10-68639 35 36 10-07729 10-26157 10-43798 10-60625 10-76577 36 37 10-15156 10-33688 10-51392 10-68228 10-84128 38 : 10-22275 10-40908 10-58660 10-75477 10-91322 38 39 10-29114 10-47823 10-65598 10-82392 10-98165 39 40 10-35668 10-54452 1072248 10-89004 1 1 -04692 40 45 10-64849 ! 10-83811 11-01504 11-17905 11-32990 45 50 10-89052 11-07935 1 1 -25290 11-41110 11-55402 50 55 10-09348 11-27981 1 1 -44833 11-59918 1173282 60 10-26532 1 11-44780 1 1 -60995 11-75240 11-87620 60 65 11-41214 ; 11-58950 II74453 11-87818 11-99185 65 70 11-53828 11-71001 11-85719 11-98164 12-08532 70 75 11-64755 , 11-81279 1 1 -95200 12-06724 12-16116 80 11-74246 ! 11-90108 12-03196 12-13813 12-22285 80 90 11-89825 12-04268 12-15717 12-24620 12-31406 90 100 12-01880 ! 12-14890 12-24785 12-32149 12-37501 100 INTEREST TABLES Value of an Annuity Yielding Interest on Capital at 9 PER CENT., and Replacing Capital when Invested at Years 20/ /o 2i% 3% 3i% 4% Years I 91743 91743 91743 91743 91743 I 2 1-70926 1-71284 1-71641 1-71999 i -72356 2 3 2-39949 2-40884 2-41820 2-42757 2-43695 3 4 3-00640 3-02281 3-03926 3-05576 3-07229 4 5 3-54411 3-56828 3-59253 3-61689 3-64130 5 6 4-02372 4-05597 4 08834 4-12086 4-15348 6 7 4-45411 4-49448 4-53502 4-57574 4-61659 7 8 4-84240 4-89076 4-93935 4-98810 5-03707 8 9 5-19440 5-25053 5-30690 5-36348 5-42026 9 10 5-51493 5-57852 5-70643 5-77064 10 ii 5-80794 5-87869 5-94965 6-02076 6-09203 ii 12 6-07681 6-15434 6-23201 6-30979 6-38765 12 13 6-32439 6-40828 6-49224 6-57626 6-66027 13 14 6-55299 6-64293 6-73283 6-82263 6-91233 15 6-76476 6-86031 6-95570 7-05094 7-14587 15 16 6-96136 7 -06220 7-16276 7-26296 7-36269 16 17 7-14439 7-25016 735548 7-46029 7-56435 17 IS 7-31518 7-42556 7-53529 7-64427 7-75236 18 19 770333 7-81616 7-92776 19 20 7-62445 7-74311 7-86065 7-97696 8-09179 20 21 7-76488 7-88724 8-00820 8-12764 8-24538 21 22 7-89696 8-02272 8-14684 8-26911 8-38933 22 23 8-02130 8-15023 8-27719 8 -40202 8-52450 23 24 8-13862 8-27041 8-40004 8-52711 8-65149 24 25 8-24940 8-38392 8-51586 8-64499 8-77101 25 26 8-35429 8-49127 8-62530 8-75618 8-88360 26 27 8-45359 8-59276 8-72875 8-86116 8-98965 27 28 8-54774 8-68900 8-82667 8-96033 9-08983 28 29 30 8-63715 8-72220 8-78033 8-86706 8-91941 9-00747 9-05428 9-14319 9-18442 9-27386 29 30 31 8-80313 8-94943 9-09099 9-22748 9-35848 31 32 8-88013 9-02788 9-17036 9-30735 9-43850 32 33 8-95359 9-10258 9-24590 9-51439 33 34 9-02372 i 9-17372 9-3I775 9-45537 9-58635 34 35 9-09074 9-24172 9-38623 965465 35 36 9-15474 9-30657 9-45144 9-58917 9-71940 36 9-21600 9-36847 9-51366 9-65I34 978091 38 9-27463 9-42774 9-573I3 9-71044 9-83942 38 39 9-33088 9-48443 9-62983 9-76677 9-89501 39 40 9-5387I 9-68410 9-82058 9-94797 40 45 9-62371 9-77833 ! 9-92211 10-05500 10-17687 45 50 9 -82096 9-97427 10-11470 10-24233 iQ-35733 50 55 9-98572 10-13644 10-27232 10-39361 10-50078 60 10-12474 10-27190 10-40226 10-51646 10-61549 60 65 10-24317 10-38583 10-51016 10-61706 10-70778 65 , 70 10-34468 10-48251 10-60029 10-69965 10-78225 70 10-43242 10-56479 10-67600 10-76786 10-84258 75 80 10-50851 10-63536 10-73975 10-82427 10-89159 80 90 10-63309 10-74830 10-83940 10-91012 10-96395 90 100 10-72927 10-83283 10-91143 10-96984 11-01225 100 For explanation see p. 18. INTEREST TABLES Valut of an Annuity Yielding Interest on Capital at 10 PER CENT., and Replacing Capital when Invested at Year, 2 % 2i% 3o/ /o 3i% 4 % Years I -90909 90909 90909 90909 90909 I 2 i 1-68053 1-68399 1-68745 1-69090 1-69435 2 3 ' 2-34326 2-35218 2-36111 2-37004 2-37898 3 4 2-91865 2-93412 2-94962 2-96515 2-98071 4 5 3-42281 3-44534 3-46795 3-49063 3-51337 5 6 3-86808 3-89788 3-92776 3-95776 3-98785 6 7 4-26417 4-30117 4-33828 4-37533 4-41287 7 8 4-61875 4-66272 4-70686 4-75III 4-79552 8 9 4-9379I 4-98860 5-03946 5-09046 9 10 5-22668 5-28377 5-34100 5-39837 5-45580 10 ii 5-48914 5-55229 5-61555 5-67885 5-74221 ii 12 5-72869 5-79754 5-86641 5-93528 6-00413 12 13 5-94820 6-02236 6-09645 6-17048 6-24438 13 6-14999 6-22913 6-30811 6-38688 6-46542 14 15 6-33613 6-41989 6-50335 6-58653 6-66929 15 16 6-50830 6-59635 6-68400 6-77117 6-85777 16 11 6-66800 6-81654 6-76005 6-91228 6-85152 7-00727 6-94237 7-10142 7-03240 7-19461 11 19 6-95497 7-05418 7-15236 7-24953 7-34543 19 20 7-08431 7-18664 7-28778 7-38765 7-48604 2C 21 7-20539 7-31064 7-41444 7-51671 7-61731 21 22 7-31898 7-42688 7-53313 7-63755 7-74000 22 23 7-42567 7-53602 7 '64444 7-75080 7-85491 23 24 7-52610 7-63866 7-74911 7-857I3 7-96261 24 25 7-62073 7-73539 7-84757 7-95710 8-06374 25 26 7-71016 7-82669 7-94042 8-05121 8-15880 26 27 7-79466 7-91283 8-02800 8-13988 8-24817 27 28 7-87464 7-99437 8-11076 8-22348 8-33243 28 29 7-95045 8-07161 8-18900 8-30254 8-41184 29 30 8-02246 8-14485 8-26317 8-37724 8-48680 30 3i 8-09088 8-21429 ' 8-33340 8-44794 8-55761 31 32 8-15587 8-28034 8-40004 8-51484 8-62448 32 33 8-21781 8-34314 8-46339 8-57839 8-68780 33 34 8-27684 8-40287 8*52355 8-63856 8-74776 34 35 8-33320 8-4598 8-58082 8-69580 8-80460 35 3* 37 8-38694 8-43832 8-51419 8-63528 8-68719 8-75013 8-80181 8-85842 8-90948 36 38 8-48745 8-61549 8-73675 8-85097 8-95801 38 39 8-53454 8-66281 8-78395 8-89775 9-00406 39 40 8-57957 8-70807 8-82909 8-94238 9-04787 40 45 8-77886 8-90734 9-02649 9-I3634 9-23685 45 50 8-94270 9-06964 9-18561 9-29074 9-38526 50 55 9-07909 9-20353 9-3I54I 9-41504 9-50290 55 60 9-19388 9-31506 9-42214 9-5I574 9-59674 60 65 9-29144 9-40867 9-51059 9-59803 9-67211 65 70 9-37488 9-48794 9-58433 9-66548 9-73283 70 9-44688 9-55530 9-64618 9-72110 9-78196 75 80 9-50923 9-61298 9-69819 9-76706 9-82183 80 90 9-61113 9-70516 9-77938 9-83691 9-88064 90 100 9-68964 9-77402 9-83797 9-88543 9-91985 100 INTEREST TABLES NOMINAL AND EFFECTIVE KATES OF INTEREST Effective Annual Hate when Nominal Rate Interest is Convertible Nominal Rate (Annual) (Annual) Half-yearly Quarterly Monthly 01 OIOO25 010038 010046 -01 0125 012539 012559 012572 '0125 015 015056 015085 015104 -015 0175 017577 017615 017641 -0175 02 02OIOO 020151 020184 '02 0225 022627 022691 022733 '0225 025 025156 025235 025288 -025 0275 027689 027785 027849 '0275 03 03O225 030339 030416 -03 0325 032764 032898 032989 -0325 035 035306 035462 035567 -035 0375 037852 038031 038151 -0375 04 040400 040604 040742 -04 045 045506 045765 045940 -045 05 050625 050945 051162 -05 06 060900 061364 061678 -06 3 O7I225 081600 071859 082432 072290 -07 083000 -08 09 092025 093083 093807 -09 10 102500 103813 104713 -io Nominal Annual Rate when Effective Rate Interest is Convertible Effective Rate ( A.nnuil) Half-yearly Quarterly Monthly (Annual) oi 009975 009963 009954 oi 0125 012461 012442 012429 0125 015 014944 014916 014898 015 0175 017424 017386 017361 0175 02 019901 019852 019819 02 0225 022375 022313 022271 0225 025 024846 024769 024718 025 0275 027313 027221 027159 0275 03 029778 029668 029595 -03 0325 032240 032111 032026 -0325 035 034699 034550 034451 *035 0375 037155 036984 036871 -0375 04 039608 039414 039285 04 045 044504 044260 044098 -045 05 049390 049089 048889 -05 06 059126 058695 058411 -06 3 068816 078461 068234 077706 067850 '07 077208 -08 09 088061 087113 086488 -09 10 097618 096455 095690 -io For explanation see pp. 18, 19 (122) INTEREST TABLES Constant Factors for Converting Values and Amounts of Yearly Annuities into those of Annuities for One Year Payable HALF-YEAELY, QUARTERLY, AND MONTHLY Yearly Rates Half-yearly Factors Quarterly Factors Monthly Factors Yearly Rates 01 00249 I -00377 I -00460 oi 0125 00312 I -00469 I -00572 0125 015 00374 I -00563 1-00685 015 0175 00436 I -00656 I -00799 0175 02 00497 I -00747 1-00914 02 0225 00559 1-00841 I -01027 0225 O25 00621 1-00933 1-01142 025 0275 00683 I -01025 1-01254 0275 03 I -00744 1-01118 1-01368 03 0325 I -00806 I'OI2II 1-01482 0325 035 I -00867 1-01303 1-01594 035 0375 1-00929 I-OI395 1-01707 0375 04 1-00990 I-OI488 I-OI82O 04 045 I-OIII3 I-OI672 I -02046 045 05 1-01235 1-01856 I-0227I 'OS 06 1-01478 I -02223 I-0272I 06 07 08 I-OI720 1-01961 I -02588 I -02952 1-03169 1-03616 3 09 I-O22OI I-033I4 1-04061 09 10 I -02440 I -03676 I -04504 io Value of Annuity for Twenty-five Years at 4 PER CENT. Annuity Payable Interest Convertible Yearly Half-yearly Quarterly Monthly Yearly . Half-yearly . Quarterly . Monthly 15-62208 15-77677 15^5449 I5-90645 I5-55624 15-71180 15-78998 15-84223 15-52282 I5-67883 1575722 15-80963 I5-50035 I5-65665 I5-73520 15-78771 The Present Value of 1 due a Year hence (?), and the Discount on 1 for One Year (d) corresponding to Various Rates of Interest (i) ! ^ d=l-v I " = rb d = l-v oi -990099010 0125 -987654321 015 -985221675 0175 -982800983 009900990 012345679 014778325 017199017 03 035 04 045 970873786 966183575 961538462 956937799 029126214 033816425 038461538 043062201 02 -980392157 -019607843 O225 '977995 IIQ ' "022004890 025 ^75609756 -024390244 0275 -973236010 -026763990 3 08 io 952380952 943396226 925925926 909090909 047619048 056603774 074074074 090909091 .For explanation see pp. 19, 20 (123) INTEEEST TABLES The Number of Years in which an Amount is doubled by Accumulation at SIMPLE AND COMPOUND INTEREST Rate per Cent. At Simple Interest At Compound Interest Rate per Cent. I 100-00 69-66 I if 80-00 66-67 55-80 46-56 11 if 57-14 39-95 J l 2 50-00 35-00 2 2 ! 44-44 2r 40-00 28-07 3 2! 36-36 25-55 2f 3 t 33-33 23-45 3 30-77 21-67 3l 28-57 20-15 3f 26-67 18-83 4 25-00 17-67 4 4* 22-22 1575 41 5 2O'OO 14-21 5 6 16-67 II-90 6 7 I4-29 10-24 7 8 I2-50 9'OI 8 9 II'II 8-04 9 10 10-00 7*27 10 DECIMALS OF ONE YEAR Weeks Decimal of One Year Weeks Decimal of One Year Months 1 Decimal of One Year I 019231 27 519231 I 083333 2 038462 28 538462 2 166667 3 4 057692 076923 29 30 557692 576923 3 4 250000 '333333 5 096154 3 1 596154 5 416667 6 H5385 32 615385 6 500000 I I346I5 153846 33 34 634615 653846 7 8 666667 9 173077 673077 9 750000 10 192308 36 692308 10 833333 ii 12 211538 230769 37 38 7II538 730769 ii 12 916667 i -oooooo 14 250000 269231 39 40 750000 769231 Days Decimals of One Year 288462 307692 42 788462 807692 60 082192 164384 17 326923 43 826923 90 246575 18 346154 44 846154 120 328767 19 20 365385 384615 46 865385 884615 & 410959 -493I5I 21 403846 47 903846 210 -575342 22 423077 48 923077 240 657534 23 24 442308 461538 49 50 942308 961538 270 300 739726 821918 2 S 480769 980709 904110 26 500000 52 I OOOOOO 365 i -oooooo For explanation see p. 2 1 (124) DECIMALS OF 1 THE DECIMAL CORRESPONDING TO EVERY FARTHING IN THE Pence 0* Is. 2*. 3*. 4#. Pence ooooo 05000 10000 15000 20000 O oi 00104 05104 10104 15104 20104 ok o| 00208 05208 10208 15208 20208 o of 00313 05313 10313 I53I3 20313 o I 00417 05417 10417 I54I7 20417 I I* 00521 05521 10521 I552I 20521 l 3 00625 05625 10625 15625 20625 ji If 00729 05729 10729 15729 20729 I'l 2 00833 05833 10833 15833 20833 : 2 2$ 00938 05938 10938 15938 20938 2i 2 2 01042 06042 11042 16042 21042 2 2 2 4 01146 06146 11146 16146 21146 2f 3 01250 06250 11250 16250 21250 3 3j 01354 06354 '"354 16354 21354 3i 3"! 01458 06458 11458 16458 21458 31 3l 01563 06563 "563 16563 21563 3f 4 01667 06667 11667 16667 21667 4 4i 01771 06771 11771 16771 21771 ; 4}- 4s 01875 06875 11875 16875 21875 4 41 01979 06979 11979 16979 21979 4! 5 02083 07083 12083 17083 22083 5 Si 02188 07188 12188 17188 22188 Si Sh 02292 07292 12292 17292 22292 53- 5f 02396 07396 12396 17396 22396 51 6 02500 07500 12500 17500 22500 6 6 02604 07604 12604 17604 22604 6* 6ir * 02708 02813 07708 07813 12708 12813 17708 17813 22708 22813 ' i 7, 02917 07917 12917 17917 22917 7 7* 03021 08021 13021 18021 23021 7k 7 2 03125 08125 i3 J 25 18125 23125 7-2- 71 03229 08229 13229 18229 23229 71 8 03333 08333 13333 18333 23333 8 s 03438 08438 13438 18438 23438 8 8| 03542 08542 13542 18542 23542 85 8f 03646 08646 13646 18646 23646 8| 9 t 03750 08750 13750 18750 23750 9 9f 03854 08854 13854 18854 23854 9i 9a 03958 08958 13958 18958 23958 9k 9f 04063 09063 14063 19063 24063 91 10 04167 09167 14167 19167 24167 10 10* 04271 09271 14271 .19271 24271 Io i IO I 04375 09375 14375 19375 24375 105 I0| 04479 09479 14479 19479 24479 lOf II 04583 09583 14583 -19583 24583 ii III 04688 09688 14688 19688 24688 "i JI 2 04792 09792 14792 19792 24792 i Ilf 04896 09896 14896 -19896 24896 ixf For explanation see pp. 21-23 (125) G 2 DECIMALS OF l\ THE DECIMAL CORRESPONDING TO EVERY FARTHING IN THE Pence 5. 8*. 7s. 86. Qs. Pence O 25000 30000 35000 40000 45000 oj 25104 30104 35104 40104 '45 I0 4 oj of 25208 30208 35208 40208 45208 % 4 25313 30313 35313 40313 45313 of I 25417 30417 35417 40417 45417 i * 25521 30521 35521 40521 45521 i^ ij 25625 30625 35625 40625 45625 l If 25729 30729 35729 40729 45729 If 2 25833 30833 35833 40833 45833 2 2% 25938 30938 35938 40938 45938 2?. 2| 26042 31042 36042 41042 46042 2^ 2f 26146 31146 36146 41146 46146 2 4 3 x 26250 31250 36250 41250 46250 3 26354 31354 36354 41354 46354 ll 26458 31458 36458 41458 46458 a 26563 31563 36563 41563 46563 4 x 26667 31667 36667 41667 46667 4 x 26771 3I77I 36771 41771 -46771 4l 26875 31875 36875 41875 -46875 4^ 44 26979 31979 36979 41979 46979 4f 5 27083 -32083 37083 42083 47083 5 S f 27188 32188 37188 42188 47188 5| 5i 27292 32292 37292 42292 47292 5f 51 27396 32396 ^7396 42396 -47396 sf 6 27500 32500 37500 42500 -47500 6 6i 27604 32604 37604 42604 47604 6| 27708 32708 37708 42708 47708 6| 27813 32813 37813 42813 47813 "4 7 27917 32917 37917 42917 -47917 7 1 28021 33021 38021 43021 "48021 7f 28125 28229 33125 33229 38125 38229 43125 -48125 43229 -48229 1 8 28333 33333 38333 43333 '48333 8 8f 28438 33438 38438 43438 48438 8J 8^ 28542 33542 38542 43542 48542 Sk O;^ 28646 33646 38646 43646 48646 8f 9 28750 33750 38750 43750 48750 9 9i 28854 33854 38854 43854 48854 9i 28958 33958 38958 43958 48958 91 9? 29063 34063 39063 44063 49063 9f 10 29167 34167 39167 44167 49167 10 I0j 29271 34271 39271 44271 49271 zo| 29375 34375 39375 44375 49375 lof 29479 '34479 39479 '44479 '49479 , II 29583 34583 39583 44583 49583 ii 11 i 29688 34688 39688 44688 49688 "i 'I* 29792 34792 39792 44792 49792 iii nj 29896 34896 3 9 8 9 6 44896 49896 i if For explanation see pp. 21-23 (126) DECIMALS OF 1 THE DECIMAL CORRESPONDING TO EVERY FARTHING IN THE Pence 10*. Us. 12*. 13*. 14*. Pence O 50000 55000 60000 65000 70000 oi 50104 '55 I0 4 60104 65104 70104 ! oi 50208 55208 60208 65208 70208 of 50313 55313 60313 65313 70313 o| i 50417 55417 60417 65417 70417 I xi 50521 55521 -60521 65521 70521 li. If 50625 55625 60625 65625 70625 ji if 50729 55729 60729 65729 70729 if 2 50833 55833 60833 65833 70833 2 2 i 50938 55938 60938 65938 70938 2 i 2g 51042 56042 61042 66042 71042 2h 2f 51146 56146 61146 66146 71146 2f 3 51250 56250 61250 66250 71250 3 3i 51354 56354 61354 66354 71354 32 51458 56458 61458 66458 71458 3f 51563 56563 -61563 66563 71563 4 51667 56667 -61667 66667 71667 4 i 4? 5i77i 56771 -61771 66771 71771 4^ 5i875 56875 -61875 66875 71875 4i 4t W79 56979 61979 -66979 7i 9 7 9 4t 1 52083 52188 52292 52396 53 57292 57396 62083 62188 62292 62396 67083 67188 67292 67396 72083 72188 72292 72396 5 51 5t 6 52500 57500 62500 67500 72500 6 6 52604 57604 62604 67604 72604 61 6 52708 57708 62708 67708 72708 63 6f 52813 57813 62813 67813 72813 6f 7 52917 57917 62917 67917 72917 7 7* 53021 58021 63021 68021 73021 71 53125 58125 63125 68125 73125 7a 7! 53229 58229 63229 68229 73229 71 8 8| 53333 53438 58333 58438 63333 63438 68333 68438 73333 73438 8 8i 53542 58542 63542 68542 73542 s 8| 53646 58646 63646 68646 73646 8f 9 53750 58750 6375 68750 73750 9 9* 53854 58854 63854 68854 73854 9b 53958 58958 63958 68958 73958 91 54063 59063 64063 69063 74063 10 54167 59167 64167 69167 74167 10 IOj 54271 59271 64271 69271 74271 lOi- 3 '54375 '54479 '59375 "59479 64375 64479 69375 69479 74375 74479 lOf IX 54583 59583 64583 69583 74583 II XI i 54688 59688 64688 69688 74688 I3[ 4 "i 54792 59792 64792 69792 74792 Il iif 54896 59896 64896 69896 74896 III (127) DECIMALS OF THE DECIMAL CORRESPONDING TO EVERY FARTHING IN THE Pence 15*- 16*. 17* 18. 19* Pence o 75000 -80000 85000 90000 95000 Oj 75 IO 4 -80104 85104 -90104 95104 f o| 75208 80208 85208 90208 95208 of 75313 80313 85313 90313 95313 o| I 75417 80417 85417 90417 95417 I *i 75521 80521 85521 90521 95521 *i ji 75625 80625 85625 90625 95625 ii if 75729 80729 85729 90729 95729 T 4 2 75833 80833 85833 90833 95833 2 2 i 75938 80938 85938 90938 95938 2,\ 2 2 76042 81042 86042 91042 96042 ; 2^ 2f 76146 81146 86146 91146 96146 2-J 3 76250 81250 86250 91250 96250 3 ii 76354 76458 8i354 81458 86354 86458 91354 91458 96354 3i 96458 31 31 76563 81563 86563 91563 96563 3? 4 76667 81667 86667 91667 96667 4 a 4* 76771 81771 86771 91771 96771 4f 76875 86875 91875 96875 4^ 76979 81979 86979 91979 96979 4! 5 77083 82083 87083 92083 97083 5 77188 82188 87188 92188 97188 5k 77292 82292 87292 92292 97292 5^ si 77396 82396 87396 92396 97396 5t 6 77500 82500 87500 92500 97500 6 1 77604 77708 82604 82708 87604 87708 92604 92708 97604 97708 I 61 77813 | -82813 87813 92813 97813 6$ 7 77917 82917 87917 92917 97917 7 7i 78021 83021 88021 93021 98021 7s 7f 78125 78229 83125 83229 88125 88229 93125 93229 98125 98229 1 8 78333 83333 88333 '93333 98333 8 8i 78438 83438 88438 -93438 98438 8^ 8 78542 83542 88542 -93542 98542 8f 8 78646 83646 88646 93646 98646 8| 9 78750 83750 88750 93750 98750 9 78854 83854 88854 93854 98854 s 9-* 78958 83958 88958 93958 98958 9? 79063 84063 89063 94063 99063 9! 10 79167 84167 89167 94167 99167 10 IT 79271 84271 89271 94271 99271 io IO^ 79375 84375 89375 '94375 '99375 io lOf 79479 84479 89479 '94479 99479 iof II 79583 84583 89583 94583 99583 ii Hi 79688 84688 89688 94688 99688 lit 11- 79792 84792 89792 94792 99792 "a Ilf 79896 84896 89896 -94896 99896 Ilf For explanation see pp. 21-23 (128) MORTALITY TABLES SHOWING THE EXPECTATION OF LIFE AND THE NUMBERS SURVIVING EACH YEAR ACCORDING TO VARIOUS MORTALITY TABLES For explanation see pp. 23-25 1129) MOBTALITY TABLES THE EXPECTATION, OR AVERAGE DURATION, OF LIFE Com- pleted Age North- ampton Experience 1780 Carlisle Experience I8IS Equitable Society's Experience 1834 ' Seventeen Offices' ' Experience 1843 English Experience No. 3 (Males) 1864 Actuaries' HM. Healthy Males) Corn- Experience pleted Age 1869 Years Years Years Years Years Years 25-18 3872 ... 39-9I 5 40-84 5I-25 ... ... 49-71 ... 5 10 39-78 48-82 48-83 48-36 47-05 50-291 10 ii 39-14 48-04 48-02 47-68 46-3I 49-536 II 12 38*49 47-27 47-20 47-01 45'54 48733 12 13 37-83 46-5I 46-40 44-76 47-893 13 14 37-17 4575 45-60 45-64 43-97 47-032 14 15 36-5I 45-oo 44-81 44-96 43-18 46-161 15 1 6 35-85 44-27 44-04 44-27 42-40 45-292 16 11 35-20 34-58 43*57 42-87 42-52 43-58 42-88 41-64 40-90 44-438 43-609 11 19 33-99 42-17 4178 42-19 40-I7 42-8I7 19 20 33-43 41-46 41-06 41-49 39-48 42-06I 20 21 32-90 40-75 40-33 40-79 38-80 4I-326 21 22 32-39 40-04 39-60 40-09 38;i3 40-603 22 23 31-88 39'3 J 38-88 39-39 39'879 23 24 31-36 38-59 38-I6 38-68 36-79 39-I47 24 25 30-85 37-86 37-44 37-98 36-12 38-405 25 26 30-33 37'H 3673 37-27 35-44 37^8 26 2 7 29-82 36-41 36-02 34-77 36-908 2 7 28 29-30 35-69 35-33 35-86 34-10 36-162 28 29 28-79 35'OQ 34-65 35'i5 33-43 35-4I9 29 30 28-27 34-34 33-98 34-43 3276 34-681 30 31 2776 33-68 33-30 33*72 32-09 33-946 32 27-24 33-03 32-64 33-oi 31-42 33-2I3 32 33 26-72 32-36 31-98 32-30 30-74 32-481 33 34 26-20 31-68 SI'S 2 3I-58 30-07 3 J 74 8 34 35 25-68 31-00 30-66 30-87 29-40 31-016 35 36 25-16 30-32 30-01 30-15 2873 30-286 36 37 24-64 ; 29-64 2935 29-44 28-06 29-560 37 38 24-12 28-96 28-70 28-72 27-39 28-838 38 39 23-60 28-28 28-05 28-00 26-72 28-118 39 40 23-08 27-61 27-40 27-28 26-06 27-399 40 22-56 26-97 2674 26-56 25-39 26-679 42 22-04 26-34 26-07 25-84 2473 25-956 42 43 21-54 2571 25-40 25-12 24-07 25-233 43 44 21-03 25-09 24'75 24-40 23-41 24-511 44 9 20-52 20-02 24-46 23-82 24-10 23-69 22-97 22-76 22-11 23-792 23-079 9 47 I9-5I 23-17 22-78 22-27 21 '46 22-375 47 48 19-00 22-50 22-12 21-56 20-82 21-679 48 49 18-49 21 -81 21-47 20-87 20-17 20-989 49 For explanation see pp. 23-25 MORTALITY TABLES THE EXPECTATION, OR AVERAGE DURATION, OF LIFE North- Carlisle Equitable ' Seventeen! English Actuaries' HM. Com- pleted ampton Experience Experience Society's j Offices' ' Experience Experience Experience No. 3 (Males) (Healthy Males) Corn- Experience i pleted Age Age 1780 1815 1834 1843 1864 1869 Years Years Years Years Years Years 50 I7-99 21-11 20-83 20-18 19-54 20-306 50 52 53 17-50 I7-02 16-54 20-39 19-68 18-97 20-20 I9'50 I9-59 ! 18-82 19-00 18-16 18-90 19-627 18-28 18-951 17-67 18-281 51 52 53 54 1 6 -06 18-28 !8'43 17*50 17-06 17-618 54 55 I5-58 17-58 17-85 16-86 16-45 16-962 55 56 15-10 16-89 17-28 16-22 15-86 16*316 56 57 14-63 16-21 1671 15-59 I5*26 15-679 57 59 5 3 -68 15-55 14-92 16-15 15-60 14-97 I4-37 14-68 I4*IO 15*052 58 14-435 59 60 13-21 14-34 15-06 1377 13-53 13-830 60 61 1275 13-82 14-51 13-18 12-96 13*237 61 62 12-28 13-31 13-96 12-61 12-41 12-659 62 63 II-81 12-81 13-42 12-05 11*87 12-095 63 64 u-35 12-30 12-88 11-51 n-34 11-547 64 65 10-88 11-79 12-35 10-97 10-82 1 1 -012 65 66 10-42 11-27 11-83 10-46 10-32 10-489 66 s 9-96 1075 11-32 9.96 9-83 9-977 67 68 9-50 10-23 10-82 9'47 936 9-475 08 69 9'5 970 10-32 9-00 8-90 8-980 69 70 8-60 9-18 9-84 8-54 8-45 8*495 70 8-17 8-65 8-10 8-03 8*026 71 72 774 8-16 8-88 7-67 7*62 7*575 72 73 733 772 8-42 7-26 7-22 7*148 73 74 6-92 7-33 7-97 6-86 6*85 6*749 74 75 6'54 7-01 7*52 6-48 6-49 6*376 75 76 6*18 6-69 7-08 6*ii 6-15 6*017 76 77 5-83 6-40 6-64 576 5-82 5-674 77 78 5-48 6-12 6-20 5-42 5-51 5-344 78 79 5-n 5-80 578 5*09 5-21 5-025 79 80 475 5-5I 5-38 4-78 4-93 4719 80 81 4-41 5-21 5-00 4-48 4-66 4-433 81 82 4-09 4-93 4-63 4-18 4*41 4-171 82 83 3-8o 4-65 4-30 3-90 4*17 3-930 83 84 3-58 4-39 4-00 3-63 3-95 3713 84 85 3-37 4-12 373 3-36 373 3-511 85 86 3-19 3-90 3'5O 3-10 3-53 3-310 86 87 3-01 3'3i 2-84 3-34 3*101 87 88 2-86 3-59 3-11 2*59 2-884 88 89 2-66 3-47 2-91 2-35 3-00 2-634 89 90 2-41 3-28 2-65 2-II 2-84 2-357 90 91 2-09 3-26 2-36 I-8 9 2-69 2-077 91 92 175 337 2-03 I-6 7 2-55 1795 92 93 170 1-47 2-41 1-496 93 94 1*05 3-53 1-31 1-28 2-29 1-204 94 1 75 50 3-53 1-05 75 1*12 99 2-17 2-06 930 684 96 3-28 50 89 1-95 500 9 l 98 ... 3-07 ... 75 1-85 ... 98 99 ... 2-77 'So 176 ... 99 (131) MORTALITY TABLES ENGLISH LIFE TABLE, No. 3 Age at Number Living j Number Number Living at Beginning Age at Beginning of Year at Dying during Beginning of Year ; the Year 01 xear Beginning of Year Males Females 1,000,000 149,493 5^,745 488,255 I 850,507 53,680 428,026 422,481 I 2 796,827 28,238 400,505 396,322 2 3 768,589 18,456 386,290 382,299 3 4 750,133 I3,3i5 377,077 373,056 4 5 736,818 9,899 370,358 366,460 5 6 726,919 7,768 365,325 36i,594 6 7 719,151 8 712,592 6,559 36i,372 357,779 5,458 358,062 354,530 I 9 707,134 4,625 355,328 35i,8o6 9 10 702,509 4,028 353,031 349,478 10 ii 698,481 3,637 351,048 347,433 ii 12 694,844 3,431 349,272 345,572 12 13 691,413 3,382 347,606 343,807 13 14 688,031 3,468 345,969 342,062 14 15 684,563 3,66 9 344,290 340,273 15 16 680,894 3,957 342,509 338,385 16 17 676,937 18 672,620 4,317 340,581 4,720 338,469 336,356 334,151 11 19 667,900 5,i5o 336,149 33I.75I 19 20 662,750 5,583 333,6o8 329,142 20 21 657,167 5,668 330,844 326,323 21 22 651,499 5,748 328,043 323,456 22 23 645,751 5,820 325,207 320,544 23 24 639,931 5,886 322,339 317,592 24 25 634,045 26 628,095 5,950 319,442 314,603 6,009 316,516 3U,579 5 27 622,086 6,065 3^,562 308,524 2 7 28 6l6,02I 6,121 310,581 305,440 28 29 609,900 6,176 307,572 302,328 29 30 603,724 6,231 304,534 299,190 30 31 597,493 6,287 301,466 296,027 3i 32 591,206 6,343 298,366 292,840 32 33 584,863 6,404 295,232 289,631 33 34 578,459 6,466 292,061 286,398 34 35 571,993 6,533 288,850 283,143 35 36 565,460 6,601 285,596 279,864 36 37 558,859 6,678 282,296 276,563 37 38 552,181 6,756 278,944 273,237 38 39 545,425 6,841 275,538 269,887 39 40 538,584 6,93i 272,073 266,511 40 4 1 531,653 7,027 268,544 263,109 4i 42 524,626 7,127 264,948 259,678 42 43 5*7,499 7,236 261,280 256,219 43 44 510,263 7,348 257,534 252,729 44 45 502,915 7,467 253,708 249,207 45 46 495,448 7,592 249,796 245,652 46 47 487,856 7,722 245,795 242,061 47 48 480,134 7,857 241,700 238,434 48 49 472,277 7,997 237,508 234,769 49 For explanation see pp. 23-25 (132) MORTALITY TABLES ENGLISH LIFE TABLE, No. 3 Age at Beginning Number Living at Number Dying during Number Living at Beginning 1 of Year Age at Beginning of Year Beginning of Year the Year Males | Female8 | of Year 50 464,280 8,141 233,216 231,064 50 51 456,139 8,414 228,821 227,318 51 52 447,725 8,590 224,195 223,530 52 53 439,135 8,761 219,437 219,698 53 54 430,374 9,259 214,552 215,822 54 421,115 9,58-3 209,539 211,576 411,532 9,909 204,395 207,137 57 401,623 10,245 I99,H4 202,509 57 58 391,378 io,593 193,686 197,692 58 59 380,785 10,958 188,102 192,683 59 60 369,827 11,338 182,350 187,477 60 61 358,489 n,737 176,421 182,068 61 62 346,752 12,149 170,303 176,449 62 63 334,603 12,572 163,989 170,614 63 64 322,031 13,002 157,474 164,557 64 g 309,029 295,599 13,430 150,754 158,275 13,846 143,833 151,766 67 281,753 14,244 136,718 145,035 67 68 267,509 14,607 129,421 138,088 68 69 252,902 14,925 121,963 130,939 69 70 237,977 15,184 114,370 123,607 70 222,793 106,675 116,118 72 207,424 15^68 98,919 108,505 72 73 191,956 15,469 91,149 100,807 73 74 176,487 15,363 83,416 93,071 74 75 161,124 15,136 75,777 85,347 75 76 145,988 14,789 68,294 77,694 76 77 131,199 14,319 61,026 70,173 77 78 116,880 13,726 54,036 62,844 78 79 103,154 13,021 47,38i 55,773 79 80 90,133 12,214 4i,"5 49,018 80 81 77,919 11,320 35,283 42,636 to 82 66,599 10,358 29,922 36,677 82 83 56,241 9,352 25,060 31,181 83 84 46,889 8,324 20,71^ 26,178 84 S 38,565 31,265 7,3oo 6,298 16,877 13,549 21,688 17,716 11 87 24,967 5,346 10,709 14,258 87 88 19,621 4,459 8,325 11,296 88 89 15,162 3,653 6,360 8,802 89 90 11,509 2,933 4,770 6,739 90 8,576 2,310 3,5io 5,o66 91 92 6,266 1,781 2,53i 3,735 92 93 4,485 i,343 1,787 2,698 93 94 3,H2 989 1,234 1,908 94 95 2,153 96 1,440 713 500 833 548 1,320 892 P 97 940 342 352 588 97 98 598 228 220 378 98 99 ... 370 ... ... 99 (135) MORTALITY TABLES INSTITUTE OF ACTUARIES MORTALITY TABLE HEALTHY MALES (HM.) Age at Begin- Number Living ning at Beginning of of Year Year Number Dying during the Year Probable Number out of every 100 Alive at the Beginning of a Year Age at Begin- ning of Year who will Survive the Year who will Die during the Year I 2 3 4 5 6 10 100,000 490 99-5100 4900 10 II 99,5 10 397 99-6010 3990 ii 12 329 99-6681 3319 12 13 98^784 288 997085 2915 13 14 98,496 272 997238 2762 14 9 98,224 97,942 282 997129 99-6753 2871 3247 17 97,624 379 99-6118 3882 17 18 97,245 466 99-5208 4792 18 19 96,779 556 99*4255 '5745 19 20 96,223 609 99-3671 6329 20 21 643 993275 6725 21 22 94,971 650 6844 22 23 94,32i 638 99-3236 6764 23 24 93,683 622 99-336I 6639 24 2C 93,061 6i7 99*3370 6630 2 5 26 92,444 618 99-33I5 6685 26 27 91,826 634 99*3096 6904 27 28 91,192 654 99-2828 7172 28 29 90,538 673 99-2567 7433 29 30 89,865 694 99-2277 7723 30 31 89,171 706 99*2083 7917 31 32 33 88,465 87,748 717 727 99-1895 99-1715 8105 8285 32 33 34 87,021 740 99-1496 8504 34 86,281 757 99-1226 8774 35 85,524 779 99-0891 9109 36 37 84,745 802 99-0536 9464 37 38 83,943 821 99-0220 9780 38 39 83,122 838 98-9918 1-0082 39 40 82,284 848 98-9694 1-0306 40 81,436 854 98-9513 i -0487 42 80,582 865 98-9266 i -0734 42 43 79,717 887 98-8873 1127 43 44 78,830 911 98-8444 1556 44 $ 77,9i9 76,969 950 996 98-7808 98-7060 2192 2940 9 47 75,973 ,041 98-6298 3702 47 48 74,932 ,082 98*5560 4440 48 49 73,850 ,124 98-4780 5220 49 50 72,726 ,160 98-4050 5950 50 7i,566 ,193 98-3330 6670 52 70,373 ,235 98-2451 7549 52 53 69,138 ,286 98-1400 8600 53 54 67,852 ,339 98-0266 i'9734 54 For explanation see pp. 23-25 MORTALITY TABLES INSTITUTE OF ACTUARIES MORTALITY TABLE HEALTHY MALES (Hsi.) Age at Number Begin- Number Living ; Dying Probable Number out of every 100 Alive at the Beginning of a Year Age at Begin- mug of CiU XH2g.l.UUJ.,Ug of Year UlUJUUM the who will Survive who will Die mng of Year Year the Year during the Year Year I 2 3 4 5 6 55 66,513 !,399 97-8967 2-1033 55 56 65,114 1,462 97-7547 2-2453 56 57 63,652 1,527 97-6010 2-3990 57 58 62,125 i,592 97-4374 2-5626 58 59 60,533 1,667 97-2461 2-7539 59 60 58,866 i,747 97-0322 2-9678 60 61 1,830 96-7962 3-2038 61 62 55^89 96-5364 3-4636 62 63 53.374 2,001 96-2510 3-7490 63 64 5L373 2,076 95-9590 4-0410 64 66 49.297 47,156 2,141 2,196 95-343I 4-343I 4-6569 67 44,960 2,243 95-0111 4-9889 67 68 42,717 2,274 94-6766 68 69 40,443 2,319 94-2660 5-7340 69 70 38,124 2,371 93-78o8 6-2192 70 71 35,753 2,433 93-1950 6-8050 72 33,320 2,497 92-5060 7*4940 72 73 30,823 2,554 . 91-7140 8-2860 73 / J 74 28,269 2,578 90-8805 9-ii95 74 * 25,691 23,164 2,527 2,464 90-1639 89-3628 9-8361 10-6372 76 20,700 2,374 88-5314 11-4686 77 78 18,326 2,258 87-6787 12-3213 78 79 16,068 2,138 86-6941 13-3059 79 80 1 3,930 2,015 85-5348 14-4652 80 81 1,883 84-1964 15-8036 81 82 10,032 82-8648 17-1352 82 84 8,313 6,768 1^545 i,346 81-4147 80-1123 18-5853 19-8877 11 5 5,422 4,284 1,138 941 79-0115 78-0345 20-9885 21-9655 If 87 3,343 773 76-8770 23-1230 87 88 2,570 615 76-0700 23-9300 88 89 i,955 495 74-6804 25-3196 89 90 1,460 408 72-0548 27-9452 90 1,052 329 68-7263 3I-2737 92 723 254 64-8686 35-I3I4 92 93 469 195 58-4222 4I-5778 93 94 274 139 49-2700 50-7300 94 $ 135 49 86 40 36-2964 18-3673 63-7036 81-6327 96 97 9 9 00 -0000 100-0000 97 (135) MOETALITY TABLES CARLISLI : TABLE Age at Beginning of Year Number Living at Beginning of Year Number Dying during the Year Age at Beginning of Year Number Living at Beginning of Year Number Dying during the Year 10,000 i,539 50 4,397 59 I 8,461 682 51 4,338 62 2 7,779 505 52 4,276 65 3 7,274 276 53 4,211 68 4 6,998 201 54 4,143 70 5 6,797 121 55 4,073 73 6 6,676 82 56 4,000 76 8 6,594 6,536 58 43 P 3,924 3,842 82 93 9 6,493 33 59 3,749 106 10 6,460 29 60 3,643 122 ii 6,43i 61 3,52i 126 12 6,400 32 62 3,395 127 13 6,368 33 63 3,268 125 6,335 35 64 3,H3 125 ii 6,300 6,261 39 42 3,018 2,894 124 123 3 6,219 6,176 43 43 67 68 2,771 2,648 123 I2 3 19 6,i33 43 69 2,525 124 20 6,090 43 70 2,401 124 21 6,047 42 2,277 134 22 6,005 42 72 2,143 146 23 5,963 42 73 ,997 I 5 6 24 5,92i 42 74 ,841 1 66 25 5,879 43 75 ,675 1 60 26 5,836 43 76 ,515 156 28 5,793 5,748 45 50 77 78 ,359 ,213 146 132 2 9 5,698 56 79 ,081 128 30 5,642 57 80 953 116 31 5,585 57 81 837 112 32 5,528 56 82 725 102 33 5,472 55 83 623 94 34 5,417 55 84 529 84 35 5,362 55 85 445 78 36 5,307 56 86 367 37 5,251 87 296 64 38 5,194 58 88 232 51 39 5,136 61 89 181 39 40 5,075 60 00 142 37 5,009 69 91 105 30 42 4,940 71 92 75 21 43 4,869 71 93 54 14 44 4,798 7i 94 40 IO 46 4,727 4,657 70 69 $ 30 23 7 5 47 4,588 67 97 18 4 48 4,521 63 98 14 3 49 4,458 61 99 ii 2 For explanation see pp. 23-25 (136) TABLES COMBINING MORTALITY OF SINGLE LIVES AND INTEREST For explanation see pp. 25-28 (137) MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE NORTHAMPTON TABLE OF MORTALITY Age 3% 4% 5% 6% Age I 16-021 13-465 11-563 10-107 I 2 18-599 15-633 13-420 11724 2 3 19-575 16-462 14-135 12-348 3 4 2O-2IO 17-010 14-613 12769 4 5 20-473 17-248 14-827 12-962 5 6 20727 17-482 15-041 I3-I56 6 7 20-853 17-611 15-166 I3-275 7 8 20-885 17-662 15-226 I3-337 8 9 20-812 17-625 15-210 I3335 9 10 20-663 17-523 15-139 13-285 10 ii 20-480 17-393 15-043 13-212 ii 12 20-283 17-251 14-937 13-130 12 13 20-081 17-103 14-826 13-044 13 J 4 I9-872 16-950 14-710 12-953 14 15 I9-657 16791 14-588 12-857 15 16 I9'435 16-625 14-460 12-755 16 11 I9-2I8 I9-OI3 16-462 16-309 14-334 14-217 12-655 12-562 11 19 I8-820 16-167 14-108 12-477 J 9 20 18-638 16-033 14-007 12-398 20 21 I8-470 15-912 13-917 12-329 21 22 I8-3II 15-797 13-833 12-265 22 23 18-148 15-680 13746 12-200 23 24 I?^ 15-560 13-658 I2-I32 24 25 I7-8I4 15-438 13-567 I2-063 25 26 I7-642 15-312 13-473 1 1 -992 26 27 17-467 15-184 13-377 II-9I7 27 2b I7-289 15-053 13-278 II-84I 28 29 I7-I07 14-918 13-177 1 1 -763 29 30 I6-922 14-781 13-072 1 1 -682 30 31 I6-732 14-639 12-965 II-598 31 32 16-540 14-495 12-854 II-5I2 32 33 I6-343 14-347 12-740 1 1 -423 33 34 16-142 14-195 12-623 11-331 34 35 I5-938 14-039 12-502 1 1 -236 35 36 15729 13-880 12-377 11-137 36 37 38 I5-5I5 I5-298 13716 13-548 12-249 12-116 1 1 -035 10-929 39 I5-075 13-375 11-979 IO-8I9 39 40 14-848 13-197 11-837 IO-705 40 4 1 I4-62O 13-018 11-695 10-589 4i 42 I439I 12-838 11-551 10-473 42 43 I4-I62 12-657 11-407 10-356 43 44 13-929 12-472 11-258 10-235 44 45 13-692 12-283 II -105 lO'IIO 45 For explanation see pp. 25-27 (138) MORTALITY TABLES YALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE NORTHAMPTON TABLE OF MORTALITY Age 3% 4% 5% 6% Age 4 6 13-450 12-089 10-947 9-980 4 6 47 13-203 1 1 -890 10-784 9-846 48 12-951 11-685 10-616 9-707 48 49 12-693 "475 10-443 9-563 49 50 12-436 1 1 -264 10-269 9-417 50 51 12-183 11-057 10-097 9-273 51 S 2 11-930 10-849 9-129 52 53 1 1 -674 10-637 9-748 8-980 53 54 11-414 10-421 8-827 54 55 11-150 10-201 9382 8-670 55 56 10-882 9-977 9-193 8-509 56 10-611 9-749 8-999 8'343 58 10-337 9-5I6 8 -80 1 8-173 58 g 10-058 9777 9-280 9-039 8-599 8-392 7-999 7-820 80 61 9-493 8-795 8-181 7*637 61 62 9-205 8-547 7-966 7-449 62 63 8-910 8-291 7-742 63 64 8-611 8-030 7-5H 7-052 64 65 8-304 7-761 7-276 6-841 65 66 7-994 7-488 7-034 6-625 66 67 7-682 7-211 6-787 6-405 67 68 7367 6-930 6-536 6-179 68 69 7-051 6-647 6-281 5*949 69 70 6734 6-361 6-023 5-716 70 71 6-418 6-076 5-764 5-479 71 72 6-103 5790 5-504 5-241 72 73 5-794 5-507 5-245 5-004 73 74 5-49I 5-230 4-990 4-769 74 75 5" J 99 4-962 4-744 4-542 75 76 4-925 4-710 4-511 4326 76 4-652 4-457 4-277 4 'o2 9 78 4-372 4-197 4-035 3-884 78 g 4-077 3-781 3-921 3776 3-5I5 3-641 3-394 B 81 3-499 3377 3-263 3-156 81 82 3-229 3-122 3-020 2-926 82 83 2-982 2-887 2-797 2-713 83 84 2-793 2-708 2-627 2-551 84 85 2-620 2-543 2-471 2-402 85 86 2-462 2-393 2-328 2-266 86 87 2-312 2-251 2-193 2-138 87 88 2-185 2-131 2-080 2-031 88 89 2-013 1-967 1-924 i -882 89 90 1-794 1758 1-723 1-689 90 (139) H MORTALITY TABLES VALUE OF AN ANNUITY CARLISI 4% r ON A SINGLE LIFE ACCORDING TO ' ,E TABLE OF MORTALITY FHE i Age Age 3o/ /o 5% 6% 7o/ /o 8% I 20-085 16-556 13-995 12-078 10-605 9-439 I 2 21-501 17728 14-983 12-925 11-342 10-088 2 3 22-683 18717 15-824 13-652 1 1 -978 10-651 3 4 23-285 19-233 16-271 14-042 12-322 10-957 4 5 23-693 19-594 16-590 14-325 12-574 11-184 5 6 23-846 19-747 16735 14-460 12-698 1 1 -298 6 7 23-867 19-792 16-790 14-518 12-756 "354 7 8 23-801 19766 16786 14-526 12-770 11-371 8 9 23-677 19-693 16-742 14-500 12754 1 1 -362 9 10 23-512 19-585 16-669 14-448 12-717 n-334 10 ii 23-327 19-460 16-581 14-384 12-669 1 1 -296 ii 12 23-143 19-336 16-494 14-321 12-621 1 1 -259 12 J 3 22-957 19-210 16-406 14-257 12-572 11-221 X 3 *4 22-769 19-082 16-316 14-191 I2-522 II-I82 H 15 22-582 18-956 16-227 14-126 12-473 11-144 15 16 22-404 18-837 16-144 14-067 I2-429 ii-in 16 J 7 22-232 18723 16-066 14-012 12-389 11-081 J 7 18 22-058 18-608 15-987 13-956 I2-3 4 8 11-051 18 J 9 21-879 18-488 15-904 13-897 I2-305 11-019 19 20 21-694 18-363 15-817 13-835 12-259 10-985 20 21 21-504 18-233 15-726 13769 12-210 10-948 21 22 21-304 18-095 15-628 13-697 12-156 10-906 22 23 21-098 17-95! 15-525 13-621 ! 12-098 '; IO-86I 23 24 20-885 17-801 15-417 13-541 12-037 10-813 24 25 20-665 17-645 15-303 13-456 11-972 10-762 25 26 20 -442 17-486 15-187 13-368 11-904 10-709 26 2 7 2O-2I2 17-320 15-065 13-275 11-832 10-652 27 28 19-981 I7'I54 I4-942 I3-I82 II759 10-594 28 29 I976I 16-997 14-827 13-096 11-693 i 10-542 29 30 I9-556 16-852 14-723 13-020 1 1 -636 10-498 30 31 19348 16-705 14-617 12-942 11-578 10-454 31 32 I9-I34 16-552 14-506 12-860 II-5I6 10-407 32 33 18-910 16-390 14-387 1 12771 1 1 -448 iQ-355 33 34 I8-675 16-219 14-260 12-675 U'374 j 10-297 34 35 18-433 16-041 14-127 12-573 11-295 I0 ' 2 35 35 36 I8-I83 15-856 13-987 12-465 II-2II IO-I68 36 I7-928 15-666 13-843 12-354 11-124 10-098 38 17-669 15-471 13-695 12-239 11-033 10-026 38 39 I7-405 15-272 13-542 12-120 10-939 9-950 39 40 I7-I43 15-074 13-390 12-002 10-845 9-875 40 4i 16-890 14-883 13-245 1 1 -890 10757 9-805 4i 42 16-640 14-694 13-101 11779 10-671 9737 42 43 44 16-389 I6-I3O 14-505 14-308 12-957 12-806 11-668 ii-55i 10-585 10-494 9-669 9*597 43 44 45 I5-863 14-104 12-648 1 1 -428 10-397 9-520 45 46 I5-585 13-889 12-480 1 1 -296 10-292 9-436 46 47 I5-294 13-662 12-301 H-I54 10-178 9-344 47 48 14-986 13-419 12-107 10-998 10-052 9-241 48 49 14^54 I3"!53 1 1 -892 10-823 9-908 9-121 49 So I4-303 12-869 11-660 10-631 9-749 8-987 50 For explanation see pp. 25-27 (140) MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE CARLISLE TABLE OF MORTALITY Age 3% 4% 5 % 6% 7 % I 8 % Age 51 52 13-932 13-558 12-566 11-410 12-258 11-154 10-422 10-208 9-573 9-392 8-838 51 8-684 52 53 13-180 11-945 10-892 9-988 9-205 8-523 53 54 12-798 11-627 10-624 9-761 9-011 8-356 54 55 12-408 11-300 10-347 9-524 8-807 8-179 55 56 12-014 10-966 10-063 9-280 8-595 7-995 5 6 11-614 10-625 9-771 9-027 8-375 7-802 57 58 11-218 10-286 9-478 8-772 8-153 7 -606 58 S 10-841 10-491 9-963 9-663 9-199 8-940 8-529 8-304 7-940 7743 7-418 9 7-245 60 61 10-180 9-398 8-712 8-108 7-572 7-095 61 62 9-875 9-137 8-487 7-9I3 7-403 6-947 62 63 9-567 8-872 8-258 7-714 7-229 6-795 63 64 9-246 8-593 8-016 7-502 7-042 6-630 64 65 8-917 8-307 7765 7-281 6-847 : 6-457 65 66 8-578 8-010 7-503 7-049 6-641 6-272 66 67 8-228 7-700 7-227 6-803 6-421 6-075 67 68 7-869 6-941 6-546 6-189 5-866 68 69 7-499 7-049 6-643 6-277 5-945 5-643 69 70 7-123 6-709 6-336 5-998 5-690 5-410 70 71 6-737 6-358 6-015 5-704 5-420 5-160 71 72 6-373 6-026 57" 5-162 4-922 72 73 6-044 5725 5-435 5-170 4-927 4-704 73 74 5752 5-190 4-944 4-719 4-5I 1 74 75 5-512 5-239 4-989 4-760 4-549 4-355 75 76 5-277 5-024 4-792 4-579 4-382 4-200 76 I 5-059 4-838 4-825 4-622 4-609 4-422 4-410 4-238 4-227 4-067 4-056 3-908 78 4-592 4-394 4-210 4-040 3-883 79 80 4-365 4-183 4-015 3-858 3713 3-577 80 81 4-119 3-953 3*799 3-656 3-523 3-398 81 82 3-898 3-606 3-474 3-352 3-237 82 83 3-672 3-534 3-406 3-286 3-I74 3-069 83 84 3-454 3-329 3-211 3-102 2-999 2-903 84 85 3-229 3" JI 5 3-009 2-909 2-815 2-727 85 86 3-033 2-928 2-830 2739 2-652 2-571 86 87 2-873 2-776 2-685 2-599 2-519 2-440 87 88 2-776 2-683 2'597 2-5I5 2*439 2-366 88 89 2-665 2-577 2-495 2-417 2-344 2-276 89 90 2-499 2-416 2-339 2-266 2-198 2-133 90 9i 2-481 2-398 2-321 2-248 2-180 2-115 91 92 2-577 2-492 2-412 2-337 2-266 2-198 92 93 2-687 2-600 2-518 2-440 2-367 2-297 93 94 2736 2-650 2-569 2-492 2-419 2-350 94 95 2757 2-674 2-596 2-522 2-451 2-383 95 96 2-704 2-628 2-555 2-486 2-420 2-358 96 97 2-559 2-492 2-428 2-368 2-309 2-253 97 98 2-388 2-332 2-278 2-227 2-177 2-129 98 99 2-131 2-087 2-045 2-004 1-964 1-926 99 100 1-683 1-653 1-624 1-596 1-569 1-543 100 (141) H 2 MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE. Age 21% 3o/ /o 31% 4% 41 o/ t\ O/ > /o 1 o /o 1 Age 10 26-732 24-148 21-954 20-077 18-459 17-057 IO II 26-535 23-995 21-834 19-982 18-385 16-998 II 12 26-307 23-814 21-689 19-865 18-289 16-919 12 13 26-055 23-610 21-523 19-728 18-176 16-824 13 25-785 23-390 21-341 19-578 18-049 16-717 14 15 25-502 23-158 21-149 19-417 17-914 16-602 15 16 25-215 22-922 20-953 19-252 17-774 16-482 10 17 24-930 22-686 20-757 19-087 17-634 16-362 17 18 24-653 22-458 20-567 18-928 17-499 16-248 18 19 24-390 22-243 20-389 18-780 17-375 16-142 X 9 20 24-145 22-043 20-225 18-644 17-262 16-047 20 21 23-906 21-848 20-066 18-513 17-153 15-957 21 22 23-669 21-656 19-909 18-384 17-047 15-868 22 23 23-428 21-460 19-748 18-251 16-937 15-776 23 24 23-178 21-254 19-578 18-110 16-819 15-678 24 2 5 22-916 21-038 19-399 17-961 16-694 15-572 2 5 26 22-646 20-814 19-212 17-804 16-561 15-460 26 27 22-368 20-582 19-018 17-641 16-423 15-342 27 28 22-086 20-347 18-820 17-474 16-281 15-221 28 29 21-802 20-109 18-620 17-304 16-137 15-097 29 30 21-515 19-867 18-416 17-131 15-989 14-971 30 31 21-224 19-623 18-209 16-955 15-839 14-842 31 32 20-928 19-373 17-996 16-774 15-684 14-708 32 33 20-627 19-117 17-778 16-587 15-523 14-570 33 34 20-319 18-855 17-554 16-395 15-358 14-426 34 35 20-006 18-587 17-325 16-197 15-186 14-277 35 36 19-687 18-314 17-090 15-994 15-010 14-124 36 37 19-365 18-037 16-850 15-786 14-830 13-966 37 og 19-039 17-756 16-607 !5'575 14-645 13-805 38 39 18-708 17-469 16-358 I5358 14-455 13-638 39 4 18-371 17-176 16-103 I 5' T 35 14-260 13-466 40 4 1 18-026 16-876 15-840 14-904 14-056 13-287 42 17-672 16-566 15-568 14-664 13-845 13-099 42 43 17-311 16-248 15-288 14-417 13-625 12-903 43 44 16-943 15-924 15-001 14-162 13-398 12-701 44 $ 16-570 16-194 15-594 15-260 14-707 14-410 13-901 13-165 12-927 12-491 12-278 $ 47 15-816 14-923 14-110 13-366 I 12-686 12-061 47 48 15-437 14-585 13-806 13-094 : 12-441 1 1 -840 48 49 14-242 13-499 12-817 12-191 11-614 49 50 14-669 13-896 13-187 12-536 11-936 11-383 50 51 14-280 13-545 12-870 12-249 ! 11-676 11-146 51 52 13-885 13-188 12-547 11-955 11-408 10-902 52 53 13-486 12-826 12-218 11*655 H' I 34 10-651 53 54 13-086 12-462 11-885 11-351 10-856 10-396 54 For explanation see pp. 25-27. (142) MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 2i% 3% 3^% 4% 4i% 5% Age 12-683 12-094 H'549 1 1 -043 10-573 10-135 55 12-279 11-724 II-2IO 10731 10-286 9-871 56 57 11-875 i n'353 10-868 10-417 9-996 9-602 57 58 11-471 10-981 IO-525 10-100 9-702 9-330 58 59 11-067 10-608 lO'lSo 9780 9-405 9-054 59 60 10-665 10-236 9-835 9-459 9-107 8776 60 61 10-266 9-866 9-490 9-138 8-497 61 62 9-871 9-498 9-148 8-818 8-509 8-217 62 63 9-481 9-134 8-807 8-500 8-211 7-938 63 64 9-096 8-774 8-471 8-185 7-914 7-659 64 65 8716 8-418 8-136 7-870 7-619 7-381 65 66 8-340 8-064 7-803 7-557 7-323 7-102 66 68 7-966 7-594 7712 7-471 7-I39 6-928 7-026 6-728 6-821 6-538 68 69 7-221 7-007 6-804 6-610 6-426 6-251 69 70 7i 6-852 6-489 6-657 6-311 6-470 6-141 6-293 5-979 6-124 5-824 5-676 70 71 72 6-137 5-975 5-820 5-672 5-530 5-395 72 73 5-800 5*653 5-5I2 5-377 5-247 5' 12 3 73 74 5-482 5-348 5-220 5-097 4-979 4-866 74 76 5-183 4-892 5*061 4-945 4-676 4-833 4-574 4725 4-476 4-622 4-382 It g 4-611 4*339 4-512 4-249 4-416 4-162 4'324 4-079 4-235 3-998 4-149 77 3-921 78 79 4-073 3-992 3-9I4 3-838 3765 3-695 79 80 3-8I5 3742 3-672 3-604 3-539 3*475 80 81 3*572 3-507 3-444 3-382 3-323 3-266 81 82 3-348 3-233 3-178 3-125 3-073 82 83 3-142 3-089 3-038 2-989 2-941 2-894 83 84 2-955 2-908 2-862 2-818 2-774 2732 84 85 2-781 2739 2-698 2-658 2-619 2-581 85 86 2-608 2-570 2-534 2-498 2-464 2-430 86 87 2-425 2-393 2-361 2-330 2-299 2-270 | 87 88 2-234 2-206 2-178 2-152 2-125 2-100 88 89 2-010 1-987 i -964 | i -942 1-920 1-898 89 90 1758 1-740 1 722 1 704 1-686 i 1-669 9O 91 1-501 1-487 1-473 1-459 I-446 i 1-432 91 92 1-239 1-229 1-219 1-208 1-198 I-I88 92 93 958 951 "944 '937 -930 924 93 94 68 1 -677 673 668 664 660 94 Si 418 179 415 178 413 178 411 177 408 176 4 06 175 95 97 ooo ooo -ooo -ooo ooo ooo 97 (143) MOKTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE GOVERNMENT EXPERIENCE, 1883 MALES Age 24% 3% 34% 4% 5 % Age 2O 22-434 20-561 18-936 ... 2O 25 21-282 19-601 18-130 ... 25 30 20-079 18-588 17-271 ... 30 35 18-822 17-515 16-353 35 40 17-501 16-376 15-365 I4-454 12-883 40 4 1 17-227 16-138 15-158 14-273 12-743 4 1 42 16-950 15-897 14-947 14-088 12-599 42 43 16-670 15-653 14733 13-899 12-451 43 44 16-387 15-404 13-707 12-300 44 45 16*099 15-152 14-292 13-510 12-145 45 46 15-807 14-895 14-065 13-309 1 1 -986 46 8 15-209 14-633 14-365 I3-833 I3-595 13-103 12-891 1 1 -822 "653 $ 49 14-900 14-091 12-673 11-477 49 50 14-588 13-813 13-103 12-450 1 1 -298 50 5i 14-268 13-526 12-845 12-219 IITXO 51 52 13-941 13-233 12-582 1 1 -982 10-916 52 53 13-608 12-933 12-311 11-737 10-714 53 54 13-267 12-625 12-032 1 1 -484 10-506 54 55 12-919 12-309 11-746 1 1 -224 10-289 55 56 12-563 11-986 11-45! iQ-955 10-063 56 12-198 11-653 11-146 10-676 9-828 58 11-823 11-310 10-832 10-387 9-583 58 59 u-439 10-956 10-506 10-086 9-326 59 60 1 1 -054 10-601 10-178 9-783 9-065 60 61 10-678 10-254 9-857 9*485 8-808 61 62 10-314 9-916 9-543 9-194 8-556 62 63 9-948 j 9-577 9-228 8-900 8-300 63 64 9-586 9*239 8-913 8-605 8-041 64 65 9-225 8-902 8-597 8-309 7-781 65 66 8-875 8-573 8-289 8 -020 7-525 66 67 8-533 8-252 7-987 7736 7*273 67 68 8-196 7*936 7-689 7-455 7-023 68 69 7-858 7-617 7-171 6-768 69 70 7-521 7-299 7-087 6-886 6-512 70 7 1 7-191 6-986 6-790 6-604 6-257 71 72 6-864 6-675 6-495 6-323 6-003 72 73 6-546 6-373 6-208 6-050 5754 73 74 6-245 6-086 5'934 5-788 5-5I5 74 75 5-955 5-809 5-669 5-535 5-283 75 76 5-672 5-538 5-410 5-286 5-054 76 5-404 5-281 5-163 5-050 4-836 78 5-033 4-925 4-821 4-624 78 79 80 4-891 4-647 4-788 4-553 4-689 4-463 4-594 4-376 4-4I3 4-210 % For explanation see pp. 25-27 (H4) MORTALITY TABLES VALUE OF AN ANNUITY ON A SINGLE LIFE ACCORDING TO THE GOVERNMENT EXPERIENCE, 1883 FEMALES Age 21 o/ 2/0 3% 3i% 4% 5% Age 2O 24-479 22-292 20-409 20 25 23-397 21-415 19-695 ... ... 25 30 22-223 20-451 18-898 ... ... 30 35 20-939 19-380 18-001 35 40 I9-523 18-180 16-980 15-904 14-063 40 4 1 19-223 17-923 16758 15-712 13-920 41 42 18-915 17-658 16-529 15-514 13769 42 43 1 8-601 17-386 16-294 15-310 13-613 i 43 44 18-279 17-107 16-051 15-098 I3-45I 44 45 I7-950 16-820 15-801 14-879 13-281 45 46 I7-6I2 16-525 15-543 14-652 13-105 46 47 48 I7-266 16-911 16-221 15-910 15-276 15-000 14-416 14-173 12-920 47 12727 48 49 I6-552 I5-592 14719 13-923 12-528 49 50 16-190 15-271 14-434 13-669 12-325 50 5 1 I5-83I 14-952 14-149 13-415 12-121 $i 52 I5-465 14-626 13-859 13-155 II-9II 52 53 I5-09I 14-292 13-558 12-885 1 1 '692 53 54 I47I2 I3-95I 13-252 12-609 11-467 S4 55 14-329 13-607 12-942 12-328 1 1 -236 55 56 I3-936 13-252 12-620 1 2 -036 10-994 56 57 I3-538 I3-I38 12-891 12-527 12-292 11738 11-960 u-435 10-745 57 10-492 58 1 12735 12-333 12-160 11-791 11-625 11-128 11-287 10-818 10-233 59 9-971 60 61 11-925 U"4i7 10-943 IO-500 9700 61 62 11*523 1 1 -046 10-601 IO-I85 9-429 62 63 II -I2O 10-674 10-257 9-866 9-155 63 64 IO-7I3 10-297 9-907 9-541 8-873 64 65 IO-296 9-909 9-546 9-204 8-579 65 66 9-880 9-52I 9-183 8-865 8-282 66 67 9-463 9-I3I 8-818 8-523 7-980 67 68 9-052 8745 8-456 8-182 7-678 68 69 8-650 8-367 8-100 7-847 7-379 69 70 8-260 8-000 7-754 7-520 7-087 70 7 1 7-893 7'654 7-426 7-210 6-809 7 1 72 7-539 7-3*9 7-110 6-910 6*539 72 73 7-196 6-994 6 -80 1 6-617 6-274 73 74 6-863 6-677 6-500 6-331 6-014 74 75 6-537 6-367 6-204 6-048 5757 75 76 6 -220 6-064 5-9I5 5773 5-504 76 5-911 5769 5-613 5-483 5-633 5-502 5-359 5-240 5-256 77 5-015 78 79 5-323 5-205 5-092 4-983 4-777 79 80 5-044 4-937 4-834 4735 4-547 80 (145) MOETALITY TABLES SINGLE PAYMENT TO SECURE 1 AT DEATH ACCORDING TO THE CARLISLE TABLE OF MORTALITY Age 3o/ /o 4% 5% 6% 7% 8% Age 46641 41224 37700 35251 33421 32015 O I 38587 32483 28595 25974 24079 22674 I 2 34463 27976 23891 21179 19258 17867 2 3 31021 24173 19886 17065 15097 13696 3 4 29267 22187 17757 14857 12847 11430 4 5 28079 20800 16238 13255 11198 09748 5 6" 27633 202 1 1 15548 12491 10387 08904 6 7 27572 20038 15286 12163 10007 08489 7 8 27764 20137 15305 12117 09916 08363 8 9 28125 20419 12264 I002I 08430 9 10 28606 20833 15862 12558 10263 08637 10 ii -29145 2I3I3 16281 12921 10577 08919 ii 12 -29681 21789 16695 13277 10891 09193 12 13 -30222 22272 17114 13640 II2II 09474 ^3 14 -30771 22762 17543 14013 H538 09763 14 11 3i3i5 31833 23249 23706 17967 18362 14381 14715 II859 I2I47 10045 10289 Ii 17 32334 24150 18733 15026 12408 10511 17 18 -32841 24590 19110 15343 12677 10733 18 19 33362 25052 19505 15677 12958 10970 19 20 -33901 25532 19919 16028 13259 I 1222 20 21 '34455 26031 20352 16402 i -13579 II496 21 22 -35037 26562 20819 16809 -13933 II807 22 23 35637 27II5 21310 17240 -14312 I2I4I 23 24 36252 27690 21824 17692 I47II 12496 24 25 36808 28289 22367 18174 -15136 12874 25 26 -37548 28901 22919 18672 j -15581 13267 i 26 27 -38218 29538 23500 19198 -16052 13689 2 7 28 38890 30176 24086 19725 -16529 I4II9 28 29 39531 30781 24633 '202 1 1 -16962 14504 29 30 -40129 31338 25129 -20642 '17335 14830 30 31 '40734 -31903 25633 -21083 ! -17714 I5I55 31 32 -41357 32491 26l62 -21547 -l8l20 15504 32 33 42010 33H3 26729 ! -22051 -18564 15889 33 34 42694 33771 27333 -22594 19049 I63I9 34 35 '43399 '34457 27967 23172 19565 16778 35 36 44117 35*70 28633 23783 i -20115 17274 36 37 44870 35901 29319 24411 -20684 17793 37 38 45624 36649 30024 25062 -21279 18326 38 39 -46393 374i6 30752 -25736 i -21894 18889 39 40 47156 38178 31477 -26404 -22509 19444 40 4 1 47893 38911 32167 27038 -23085 19963 4 1 42 48621 39636 32852 27666 -23648 20467 42 43 49352 40364 33538 28294 I -24210 20971 43 44 50108 41120 34257 28957 -24805 21504 44 45 50885 41905 35oio 29653 -25440 22074 45 46 51694 42734 30400 -26127 22696 46 47 52542 43607 36662 -31204 : -26873 -23378 47 48 53439 44542 37586 -32087 -27697 24141 48 49 54406 45565 38610 -33077 -28639 25030 49 For explanation see pp. 27, 28 (146) MORTALITY TABLES SINGLE PAYMENT TO SECURE 1 AT DEATH ACCORDING TO THE CARLISLE TABLE OF MORTALITY Age 3% 4% 5o/ /o 6% 7% 8% Age 50 55429 46658 39714 -34164 29679 26022 50 51 56509 47824 40905 '35347 30831 27126 51 52 57598 49003 42124 36558 32015 28267 5 2 53 58699 50211 43371 37804 33238 29459 53 54 59812 51436 44648 39089 34507 30696 54 55 60948 52694 45967 40431 35842 32007 55 56 62096 53977 47319 41812 37229 -33370 56 57 63260 55286 48710 43243 38668 -34800 57 58 64413 56591 50105 44687 40121 36252 58 59 65512 57833 51433 46062 4I5H 37644 59 60 66531 -58987 52667 47336 42803 38926 60 61 67436 -60007 53752 48445 -43922 40036 61 62 68325 61012 54824 '49549 -45027 41133 62 63 69222 62033 55914 50676 46165 42259 63 64 70157 63103 57067 51875 47389 43481 64 65 71112 64203 58262 53126 48664 44763 65 ,. 66 72103 65347 59510 54440 50012 46133 66 2 73122 74168 66539 67770 60824 62186 55832 57287 5I45I 52969 47593 49141 67 68 69 75246 69043 63605 58809 54565 50793 69 70 76340 70349 65067 60389 56234 52519 70 77465 71701 66595 62053 58000 54371 72 78525 72979 68043 63638 59687 56134 72 , 73 79483 74136 69357 65075 61225 57748 73 74 80334 75161 70524 66355 62586 59178 74 ; i 81033 81717 76004 76831 71481 72419 67396 68421 63698 64791 60333 61481 g 82352 77597 73291 -69377 65805 62548 78 82996 78378 74181 70351 66851 63645 78 79 83713 79256 75191 71472 68055 64919 79 80 84374 80066 76119 -72502 69167 66096 80 81 85090 80950 77148 -73645 70410 67422 81 82 85734 8i745 78067 -74675 71529 68615 82 83 86392 82561 79019 -75740 72693 69859 83 84 87027 83352 79948 -76781 73838 71089 84 85 87682 84173 80910 77874 75042 72393 85 86 88253 84891 81762 78836 76108 73548 86 87 88719 85477 82452 79628 76978 74496 87 88 89002 85833 82870 -80101 77502 75067 88 89 89325 86242 83357 -80658 79078 75733 89 90 89809 86861 84103 -81513 79196 76793 00 91 -89861 86929 84186 -81615 78634 76926 9 1 92 -89582 86569 83752 -81111 77973 76311 92 93 S '89261 86156 83248 -80528 77633 75578 93 94 89118 85962 83005 -80234 77512 75185 94 95 89057 85868 82876 -80064 77424 74941 95 06 89212 86047 83071 -80268 77626 75126 96 97 89633 86569 83676 -80936 -78352 -75904 97 98 90132 87184 84391 -81734 -79216 76822 98 99 90880 88127 85500 -82996 -80609 -78326 90 zoo 92185 89797 87505 '85306 -83193 -81163 | lob (147) MOKTALITY TABLES SINGLE PAYMENT TO SECURE 1 AT DEATH ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 2i% 3% 3i% 4% 4i% 5% ! Age 10 32361 26752 22378 18937 ' -16204 14015 10 II 32841 27198 22783 19299 -16524 14296 ii 12 33396 27726 23274 19750 -16937 14670 12 13 34012 28320 23836 20276 ^17425 15122 13 34672 28962 2445 20856 17970 15632 14 15 35360 29637 25099 21473 18553 16182 15 16 36060 30326 25764 22109 19156 16752 16 17 36757 31011 26427 22742 19758 17322 17 18 '37433 31677 27069 23354 20337 17869 18 19 38072 32302 27670 23924 20873 18371 19 20 38671 -32886 28226 24447 21361 18823 20 21 39254 -33451 28763 24950 21827 19254 21 22 3983 -34011 -29294 25446 22287 19676 22 | 23 -40418 '34584 29839 25957 22761 20113 23 i 24 -41030 -35183 30413 26499 23267 20582 24 i 25 i -41668 -35812 31019 27074 23808 21087 2 5 26 -42328 -36465 31652 27678 24378 21621 26 27 -43005 37139 32307 28306 24973 22182 27 28 -43691 37824 32975 28947 -25583 22758 28 29 44385 -38518 33653 29600 26205 23346 29 30 45086 -39221 '34343 30266 26840 23948 30 3 1 '45794 '39934 35044 30943 ! -27488 24563 31 3 2 46516 -40662 35762 31640 ; -28156 25199 32 33 47251 -41407 36499 32357 ; -28847 25858 33 34 48002 -42170 37256 33097 29561 26542 34 35 48766 '42950 38033 33858 30299 27251 35 36 '49543 '43745 38828 34639 31057 -27981 36 37 50329 -44553 39637 '35437 31834 -28731 38 45372 40461 36251 32629 29501 38 39 51933 46207 41303 37086 1 -33446 30294 39 40 52755 47060 42165 '37943 34289 31114 40 4 1 '53595 47935 43054 38831 35164 31969 42 '54457 48836 '43974 '39752 36076 32863 42 43 55340 49762 44921 40706 37023 33796 43 44 56236 50707 45892 41685 '37999 3476o 44 45 46 57147 58064 51669 52642 46884 47889 42690 43712 39004 40028 '35755 36772 3 47 58985 53621 48904 '44745 41067 378o6 47 48 59910 546o8 49930 '45792 42122 38858 48 49 60842 55605 50970 46856 43197 '39934 49 50 61782 56613 52023 47938 44293 -41033 50 62732 57635 53096 49043 45416 -42162 52 63695 58676 50174 j -46569 : -43326 52 53 64667 59729 55303 51327 -47748 j -44518 53 54 65645 60792 56428 52496 48947 '45735 54 For explanation see pp. 27, 28 (148) MOKTALITY TABLES SINGLE PAYMENT TO SECURE 1 AT DEATH ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 2i% 3o/ /o 3i% 4% 4i% 5% Age 55 66627 61863 ! -57566 53682 50166 -46975 55 56 67612 62939 -58712 54881 51401 -48235 56 57 68597 64020 -59866 56090 52651 -49513 57 58 69583 65103 -61026 57309 53915 '50809 58 59 70568 66190 -62193 58539 55193 -52122 59 60 71548 67274 63361 '59773 56478 -53446 60 6z 72522 -68353 64526 61007 57766 -54777 61 62 73485 -69424 65685 62237 59053 -56109 62 63 74437 70484 66835 63461 60337 -5744I 63 64 75375 71532 -67974 64675 61613 -58767 64 65 76302 72569 69104 65883 62886 -60092 65 66 77220 73600 70230 67089 64159 -61421 66 67 78132 74626 -71354 68297 65437 i '62758 67 68 79039 75650 -72478 69507 66721 "64105 68 69 79948 76678 j -73610 70729 68021 '65473 69 70 80849 77700 74738 71950 69323 -66845 70 8i734 78706 75852 73159 70615 -68210 7 1 72 82593 -79685 i -76937 74339 71879 -69549 72 73 83415 -80623 ' -77980 75475 73098 70841 73 74 84190 -81510 78967 76551 74254 72069 74 75 84919 -82345 -79897 77567 75347 73231 75 76 85628 -83159 -80806 78561 76418 74372 76 77 86313 j '83946 -81686 79525 77459 75482 77 78 86978 -84711 -82543 80466 78476 76569 78 79 87628 -85461 -83384 81392 79479 77643 79 80 88256 -86187 -84200 82291 80455 78690 80 81 88850 -86874 : -84974 -83145 '81383 79686 81 82 89394 -87506 -85686 83931 82238 80605 82 83 89899 88090 -86345 84659 83031 81458 83 84 90353 88617 86940 85317 83747 82228 84 85 90778 89110 87496 85932 84416 82948 85 86 91200 89601 88050 86545 85084 1 -83667 86 87 91645 90118 88635 87194 85792 84430 87 88 92113 90663 89252 87878 86541 85239 s ' 88 89 92659 91301 -89977 88686 87427 86198 89 90 93272 92020 90796 89600 88432 87290 90 93899 92756 91637 90541 89468 88417 9 1 92 94538 93508 92498 91507 90534 89579 92 93 95224 94317 93426 92549 91687 -90840 93 94 95899 95116 94344 93583 92834 92096 94 $ 96542 97124 95878 96568 95222 96018 '94575 '95475 93934 '94933 93304 94405 95 96 97 97561 | -97087 96618 95694 95238 97 (149) MOETALITY TABLES ANNUAL PAYMENT DURING LIFE TO SECURE 1 AT DEATH ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 2i% 3Q/ /o 3i% 4% 4i% 5% Age 10 01167 01064 00975 -00899 00833 00776 10 II 01193 01088 00998 -00920 -00852 00794 II 12 01233 01117 01026 -00947 -00878 00819 12 13 01257 01151 01058 -00978 -00909 00848 13 14 01295 01188 01094 -01014 00943 00882 14 1$ 01334 01227 01133 -01052 00981 -00919 15 16 01376 01268 01174 -01092 01020 00958 1 6 17 01418 01309 01215 -01132 01060 00998 17 18 01459 01350 01255 -01172 01099 01036 18 19 01499 01390 01294 OI2IO OII36 01072 19 20 '01538 01427 01330 -01245 OII70 OII04 20 21 "01576 01464 01365 -01279 '01202 OII35 21 22 '01615 01501 OI40I -01313 01235 OII66 22 23 01655 01540 01438 ; -01348 01269 01199 23 24 01697 01581 01478 I -01387 01306 "01234 24 2 5 01742 01625 -01521 01428 01346 01272 25 26 01790 01672 01566 01472 01388 01314 26 27 '01840 01721 01614 -01519 01433 "01357 2 7 28 01893 01772 01664 '01567 01480 01403 28 29 '01947 '01825 01715 -01617 OI529 01450 29 30 02003 -01880 01769 -01669 ! '01580 01499 30 31 '02o6l 32 '02I2I 01936 -01824 -01723 I -01632 01996 -01883 -01780 -01688 01550 01604 31 32 33 02185 02058 '01944 ; -01840 -01746 Ol66l 33 34 02252 02124 '02008 -01903 OI8O7 OI72I 34 35 02322 02193 -02076 -01969 01872 01784 35 36 02395 "02265 02146 02038 01940 01850 36 37 02471 02340 02221 -021 1 1 0201 1 01920 37 38 02551 02419 02298 -02187 02086 01993 38 39 02635 02502 02380 02267 02164 02069 39 40 02723 02589 02465 02352 02247 02151 40 02817 02682 02557 02442 02336 02238 41 42 02917 02780 02654 02538 02430 02331 42 43 03022 02885 i '02758 02640 02532 02431 43 44 03134 02996 -02868 02749 02639 -02537 44 45 03253 03114 "02985 02865 02754 02650 45 46 03377 03238 ; -03108 02987 02874 -02769 46 47 03508 03367 -03237 -03115 03001 -02895 47 48 03645 03504 I -03372 -03249 03134 i -03026 48 49 03790 03648 03515 -03391 03275 -03166 49 50 03943 03801 03667 03542 03424 ; -03314 50 04106 03963 03828 03702 03583 -03471 5 1 52 04279 04136 04000 03873 03753 -03640 52 53 04464 04320 04184 04056 03935 i -03821 53 54 04661 04516 04379 04250 04129 '04013 54 For explanation see pp. 27, 28 (IS*) MORTALITY TABLES ANNUAL PAYMENT DURING LIFE TO SECURE 1 AT DEATH ACCORDING TO THE INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Age 1 o/ Q o/ tl 2 /O I *^ 7u 3i% 4% 4i% 5% Age 55 04870 04725 04588 04458 04335 04219 55 56 05092 04946 04809 04678 04555 04437 S^ 57 05328 05182 05044 04913 04788 -04670 57 58 05580 05434 05295 05163 05038 04918 58 59 05848 05702 05563 05431 05304 05184 59 60 06134 05987 05848 05715 05588 '05467 60 61 06437 06291 06151 06018 05890 -05768 61 62 06760 06613 06473 06339 06211 -06087 62 63 07102 06956 06815 06680 06551 06427 63 64 07466 07319 07177 07042 06912 06787 64 65 07853 07705 07564 07427 07296 07170 65 66 08268 08120 07978 07841 07709 07581 66 67 08714 08566 08423 08286 08153 08025 67 68 09197 09049 08906 08767 08634 08504 68 69 09725 09576 09433 09294 09160 09030 69 70 10297 10148 10005 09866 09731 -09601 70 10914 10766 10622 10483 10348 -10218 71 72 II572 11425 11281 11142 11007 '11876 72 73 12267 12119 11976 11836 11701 '11569 73 74 12988 12840 12696 i -12556 12420 -12287 74 75 13734 13585 13440 -13299 13161 ! -13027 75 76 14532 14382 14236 -14094 13954 -13819 76 77 15382 15230 15083 14939 14798 -14660 77 78 16291 16138 15989 15843 15701 15561 78 79 17275 17121 16970 16823 16679 16538 79 80 18329 18174 18022 17873 17727 17584 80 81 19435 19277 19123 18972 18824 18679 81 82 20559 20399 20242 20089 19938 19790 82 83 21707 21543 21383 21225 21071 '20920 83 84 22844 22676 22510 22348 22189 '22032 84 85 24009 23834 23662 23493 23327 -23163 85 86 25279 25096 24916 24739 24565 -24393 86 87 26755 26563 26373 26187 26003 '25823 87 88 28485 28282 28081 27884 27689 '27498 88 89 30786 30570 30358 30149 29943 -29740 89 90 33813 33585 33360 33138 32919 32703 i 90 '37537 37294 37053 36816 36582 36351 : 9i 92 42217 41954 41694 41438 41185 40935 92 93 48624 48338 48055 47776 '47499 47226 93 94 57035 56719 56405 56095 55789 55486 94 Si 68105 82364 67748 8i954 67394 81546 67044 81144 66696 80742 66354 95 80350 96 97 97561 97087 96618 96154 95694 95238 97 (151) MORTALITY TABLES 1 PRESENT VALUE OF REVERSION TO A PERPETUITY AT DEATH OF A PERSON OF AGE STATED. GOVERNMENT EXPERIENCE, 1883 MALES Age 24% 3% 34% 4% 5% Age 2O 17-566 12-772 9-635 .. . 20 25 18-718 13-732 10-441 ... ... 25 30 19-921 14-745 11-300 ... ... 30 35 21-178 15-818 12-218 ... ... 35 40 22-499 16-957 13-206 10-546 7-II7 40 41 22-773 17-195 13-413 10-727 7-257 4 1 42 23-050 17-436 13-624 10-912 7-401 42 43 23-330 17-680 13-838 II-IOI 7*549 43 44 23-613 17-929 I4-057 11-293 7-700 44 45 23-901 18-181 14-279 11-490 7-855 45 46 24-193 18-438 14-506 11-691 8-014 46 % 24-489 24-791 18-700 18-967 I4-738 14-976 11-897 12-109 8-178 8-347 % 49 25-100 19-242 15-220 12-327 8-523 49 50 25-412 19-520 I5-468 12-550 8-702 50 51 25-732 19-807 15-726 12-781 8-890 51 52 26-059 20-100 15-989 13-018 9-084 S 2 53 26-392 2O-4OO 16-260 13-263 9-286 53 54 26-733 20-708 16-539 13-516 9-494 54 55 27-081 2I-O24 16-825 13776 9-711 55 56 27-437 21-347 17-120 I4-045 9-937 56 27-802 28-177 21-680 17*425 i4'3 2 4 10-172 22-023 17-739 14-613 10-417 1 59 28-561 22-377 18-065 14*914 10-674 60 28-946 22-732 18-393 15-217 iQ-935 60 61 29-322 23-079 18-714 I 5*5 I 5 11-192 61 62 29-686 23-417 19-028 15-806 11-444 62 63 30-052 23-756 19*343 16-100 1 1 -700 63 64 30-414 24-094 19-658 16-395 ii*959 64 65 30775 24'43i 19-974 16-691 12-219 65 66 31*125 24-760 20-282 16-980 12-475 66 67 31-467 68 31-804 25-081 20-584 20-882 17-264 I7-545 12-727 12-977 3 69 32-142 25*716 21-183 17-829 13-232 69 70 32-479 26-034 21-484 18-114 i3*488 70 71 32-809 26-347 21-781 18-396 13743 7 1 72 33-I36 26-658 22-076 18-677 I3-997 72 73 33-454 26-960 22-363 18-950 14-246 73 74 33755 27-247 22-637 19-212 14-485 74 75 34-045 27*524 22-902 19-465 14-717 75 76 34-328 27*795 23-161 19-714 14-946 76 34-596 28-052 23-408 19-950 15-164 78 34-855 28-300 23-646 20-179 15-376 78 79 35-109 28-545 23-882 20-406 I5-587 79 80 35*353 28-780 24-108 20-624 15-790 80 For explanation see p. 28 (152) MORTALITY TABLES PRESENT VALUE OF REVERSION TO A PERPETUITY AT DEATH OF A PERSON OF AGE STATED. GOVERNMENT EXPERIENCE, 1883 FEMALES Age 2i% 3o/ Ol o/ /O U2" /O 4% 5% Age 20 *5'S 21 II-O4I 8-I62 ... 20 25 16-603 II-9I8 8-876 ... ... 25 30 17777 12-882 9'673 ... ... 30 35 19-061 I3-953 IO-570 ... ... 35 40 20-477 11-591 9-096 5-937 40 4 1 20777 I5-4H II-8I3 9-288 6-080 4 1 42 21-085 15-676 I2-042 9-486 6-231 42 43 21-399 I5-947 12-277 9-690 6-387 43 44 21-721 I6-226 I2'520 9-902 6-549 44 45 22-050 I6-5I3 I2-770 10-121 6719 45 46 22-388 16-808 I3-028 10-348 6-895 46 47 22734 I7-II2 I3-295 10-584 7-080 47 48 23-089 I7-423 I3-57I IO-827 7-273 48 49 23-448 I774I I3-852 11-077 7-472 49 50 23-810 18-063 I4-I37 11-331 7-675 50 51 24-169 18-382 I4-422 II-585 7-879 51 52 24-535 18707 I47I2 II-845 8-089 52 53 24-909 19-041 I5-OI3 12-115 8-308 53 54 25-288 19-382 I53I9 I2-39I 8-533 54 55 25-671 19-726 15-629 I2-672 8-764 55 56 26 -064 2O-o8l I5-95I 12-964 9-006 56 57 26-462 20-443 I6-279 13-262 9-255 57 58 26-862 20-806 16-611 13-565 9-508 c8 27-265 2IT73 16-946 13-872 9-767 ! 59 60 27-667 2I-542 17-284 14-182 10-029 60 61 28-075 21-916 17-628 14-500 10-300 61 62 63 28-477 28-880 22-287 22-659 17-970 18-314 14-815 15-134 10-571 10-845 62 63 64 29-287 23-036 18-664 15-459 11-127 64 65 29-704 23-424 19-025 15796 11-421 65 66 30-120 23-8I2 19-388 16-135 11718 66 3 30-537 30-948 24-202 24-588 19753 20-115 16-477 16-818 1 2 -O2O I2-322 68 69 3I-350 24-966 20-471 I7-I53 12-621 69 70 31740 25-333 20-817 17-480 12-913 70 7 1 32-107 25-679 21-145 17790 I3-I9I 71 72 32-461 26-014 21-461 18-090 I3-46I 72 73 32-804 26-339 21770 18-383 13726 73 74 33-137 26-655 22-071 18-669 13-986 74 75 26-967 22-367 18-952 14-243 75 76 33780 27-269 22-656 19-227 14-496 76 34-089 27-564 22-938 19-498 14-744 77 78 34-387 27-850 23-212 19-760 14-985 78 79 34-677 28-I28 23-479 20-017 15-223 79 80 28-396 23737 20-265 I5-453 80 (153) MORTALITY TABLES Present Value of Reversion to a Perpetuity at Death of a Person of Age stated. NORTHAMPTON TABLE Age 3o/ /o 4% 5% 6% Age 5 12-860 7-752 5-173 3-705 5 10 12-670 7-477 4-861 3-382 10 15 13-676 8-209 5-412 3-810 15 20 14-695 8-967 5-993 4-269 20 25 15-519 9-562 6-433 4-604 25 30 16-411 10-219 6-928 4-985 30 35 17-395 10-961 7-498 5-431 35 40 18-485 1 1 -803 8-163 5-962 40 45 19-641 12-717 8-895 6-557 45 50 20-897 13-736 973 1 7-250 50 II 22-183 23-556 14-799 15-961 10-618 1 1 -608 7-997 8-847 II 65 25-029 17-239 12-724 9-826 65 70 26-599 18-639 13-977 10-951 70 75 28-134 20-038 15-256 12-125 75 80 29-552 21-357 16-485 13-273 80 85 30-713 22-457 17-529 14-265 85 90 31-539 23-242 18-277 14-978 90 95 33-091 24-760 19-762 16-431 95 CARLISLE TABLE Age 3% 4% 5% 6% Age 5 9-640 5-406 3-410 . 2-342 5 10 9-821 5-415 3-331 2-219 10 15 10-751 6-044 3-773 2-541 15 20 11-639 6-637 4-183 2-832 20 25 12-668 7-355 4-697 3-211 25 30 13777 8-148 5-277 3-647 30 35 14-900 8-959 5-873 4-094 35 40 16-190 9-926 6 -6 10 4-665 40 45 17-470 10-896 7352 5-239 45 50 19-030 12-131 8-340 6-036 50 II 65 20-925 22-842 24-416 13-700 15-337 16-693 9-653 1 1 -060 12-235 7-143 8-363 9-386 II 65 70 26-210 18-291 13-664 10-669 70 75 27-821 19-761 15-011 11-907 75 80 28-968 20-817 I5-985 12-809 80 85 30-104 21-885 16-991 I 375 8 85 90 30-834 22-584 17-661 14-401 90 95 30-576 22-326 17-404 H-HS 95 For explanation see p. 28 (154) TABLES COMBINING MORTALITY OF TWO AND THREE LIVES AND INTEREST PREMIUM CONVERSION TABLES 1'or explanation see pp. 29-39 (155) MOKTALITY TABLES TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the NORTHAMPTON TABLE Ages 3% 4% 5% Ages 32 44 20 70 6-790 40 45 12-869 60 95 2-458 5 80 4-175 20 75 5-298 40 50 n-955 60 loo 1-577 5 85 3'102 20 80 4-225 40 55 10-658 65 65 6-047 5 90 2-405 20 85 3-143 40 60 9-224 65 70 5-193 5 95 2-658 20 90 2-437 40 65 8-006 65 75 4-256 5 ioo 1-637 20 95 2-696 40 70 6-5I5 65 80 3-542 10 10 19-964 20 100 i -66 1 40 75 5-"5 65 85 2-719 10 15 19-409 25 25 16-915 40 80 4-102 65 oo 2-131 10 20 18-872 25 30 16-311 40 85 3-065 65 95 2-398 10 25 18-189 25 35 15-660 40 90 2-380 65 ioo 1-555 10 30 17-410 25 40 14-823 40 95 2-639 70 70 4-556 10 35 16-596 2 5 45 13-954 40 loo 1-641 70 75 3-804 10 40 15-605 25 So 12-793 45 45 12-371 70 80 3-228 10 45 14-601 25 55 1 1 -274 45 50 11-580 70 85 2-522 10 50 13-309 25 60 9-668 45 55 10-400 70 90 1 1-987 10 55 1 1 -667 25 65 8-329 45 60 9-063 70 95 2-248 10 60 9-957 25 70 6-736 45 65 7-910 70 100 1-513 10 65 8-537 25 75 5-263 ! 45 70 6-465 75 75 3-231 10 70 6-874 25 80 4-203 45 75 5-089 75 80 2-790 10 75 5-353 25 5 3-i3o 45 80 4-087 75 85 2-217 10 80 4-262 2 5 90 2-428 45 85 3-056 75 90 1758 10 85 3-167 25 95 2-688 45 90 2-375 75 95 I- 993 10 90 2-454 25 100 i -660 45 95 2-633 75 ioo 1-392 10 95 2714 30 30 15783 45 ioo 1-637 80 80 2-459 10 100 1-668 30 35 15-209 50 50 10-942 80 85 1-993 J 5 15 18-908 30 40 14-449 50 55 9-924 80 90 1-589 IS 20 18-423 30 45 13-649 50 60 8-729 80 95 806 15 25 17-793 30 50 12-551 50 65 7-691 80 100 316 15 30 17-064 30 55 1 1 -089 50 70 6-338 85 85 657 15 35 16-295 30 60 9-529 50 75 5-022 85 90 335 15 40 I5348 30 65 8-224 50 80 4-054 85 95 509 15 45 14-382 30 70 6-662 50 85 3-040 85 100 170 15 5o 13-131 30 75 5-213 50 90 2-365 90 90 088 15 55 11-528 30 80 4-168 50 95 2-629 90 95 217 15 60 9-852 30 85 3-107 50 100 1-639 90 100 979 15 65 8-458 30 90 2-411 55 55 9-103 95 95 383 i5 7o 6-818 30 95 2-670 55 60 8-098 95 ioo 072 15 75 53I4 30 100 1-651 55 65 7-219 100 100 991 15 80 4-235 35 35 14-720 For explanation see pp. 29-31 (157) I 2 MORTALITY TABLES TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883 TWO MALES TWO FEMALES Ages 2i% 3% 34% Ages 2i% 3o/ /O 3i% 2O 2O I7-438 16-239 I5-I74 ! 20 20 19-906 18-384 17-047 20 25 16-847 15-726 I4-727 20 25 19-348 I7-9I5 16-651 20 30 16-186 15-151 14-224 20 30 18-675 17347 16-169 20 35 15-445 14-505 13-658 20 35 17-867 16-661 15-584 20 40 14-617 13778 13-018 20 40 16-905 I5-835 14-872 20 45 13-687 12-957 12-289 20 45 15-760 14-837 H-OOO 20 50 12-632 12-014 11-444 20 50 14-394 13-625 12-922 20 55 1 1 -409 10-907 10-441 20 55 12-856 12-241 11-673 20 60 9-954 9-569 9-209 20 60 11-184 10-714 10-276 20 65 8-204 7-93I 7-673 20 65 9'335 8-998 8-680 20 70 6-584 6-399 6-222 20 70 7-503 7-275 7-058 20 75 5-141 5-021 4-905 20 75 i 5-742 i 5-598 5-460 20 80 3-833 3-759 3-688 20 80 j 4-263 4-177 4-093 20 85 2-786 2743 2-701 20 85 ! 3-002 2-953 2-906 20 9O 1-958 1-933 1-910 20 90 2-041 2-015 1-990 20 95 1-125 1-115 1-105 20 95 1-266 1-255 1-243 25 25 16-321 15-265 14-322 25 25 18-866 I7-505 16-300 25 30 15-724 I4-743 13-862 25 30 18-271 16-999 15-868 25 35 1 5 -046 14-149 I3-339 25 35 17-537 16-373 15-332 25 40 14-277 13-472 12-741 25 40 16-641 15-601 14-664 25 45 13-403 12-697 12-052 25 45 i5'552 14-650 13-831 25 50 12-399 11-799 11-247 25 50 14-233 13-479 12-789 2555 25 60 11-226 9-817 10-737 9-441 10-283 9-089 2555 25 60 12-735 1 1 -096 12-129 10-631 11-570 10-198 25 65 8-110 7-842 7-589 25 65 9-274 8-940 8-625 25 ?o 6-522 6-340 6-165 25 70 7-462 7-236 7-021 2575 25 80 5-102 3-809 4-983 3737 4-869 3-666 25 75 25 80 5-717 4-248 5-574 4-163 5-437 4-080 25 85 2-773 2-73 2-688 25 85 2-994 2-945 2-899 25 90 1-950 1-926 1-903 25 90 2-037 2 'OH 1-986 2 5 95 I-I22 l'H2 I*IO2 25 95 1-265 I -253 1-241 30 30 15-198 I4-279 I3'45I 30 30 17-763 16-564 ! 15-493 30 35 I4-593 13745 12-977 30 35 ; 17-121 16-011 15-016 30 40 I3-893 I3-I26 12-428 30 40 16-310 15-309 14-406 30 45 I3-083 I2-406 11-786 30 45 15-297 14-422 13-627 30 50 12-139 1 1 -560 1 1 -026 30 50 14-042 13-306 12-631 30 55 1 1 -022 IQ'547 10-106 30 55 12-595 I2-OOO 11-451 30 60 9-665 9-298 8-954 30 60 10-996 IO-538 10-112 30 65 8-005 7'743 7-495 30 65 9-206 8-876 8-565 30 70 6-452 6-273 6-101 30 70 7-418 7-194 6-981 30 75 5-058 4-940 4-828 30 75 5-689 5'547 5-4I2 30 80 3783 3711 3-641 30 80 4-232 4-147 4-065 30 85 2758 2-7I5 2-674 30 85 2-985 2-937 2-890 30 90 I-942 I-9I8 I-895 30 90 2-032 2-OO6 I-98I 30 95 1-118 I-I09 1-099 30 95 1-262 I-25I 1-239 For explanation see pp. 29-31 (158) MOKTALITY TABLES TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883 TWO MALES TWO FEMALES Ages 2i% 3% 31% Ages 2i% 3Q/ To 3i% 35 35 14-067 13-277 12-559 35 35 16-582 15-543 14-608 35 40 13-449 12-727 12-068 35 40 15-878 14-929 14-071 35 45 12-718 12-074 1 1 -483 35 45 14-965 14-127 13-363 35 50 1 1 -845 1 1 -290 10777 35 So 13-797 13-084 12-431 35 55 10-792 10-334 9-907 35 55 12-420 11-841 1 1 -304 35 60 9 '494 9-138 8-804 35 60 10-876 10-427 10-008 35 65 7-886 7-630 7-389 35 65 9-127 8-801 8-495 35 70 6-373 6-197 6-029 35 70 7-368 7-146 6-936 35 75 35 80 5-007 3753 4-892 3-682 478i 3-613 35 75 35 80 5-659 4-214 5-5i8 4-130 5-383 4-048 35 85 2-740 2-698 2-657 35 85 2-975 2-927 2-881 35 90 1-932 1-909 1-886 35 90 2-027 2-OOI 1-976 35 95 1-114 1-105 1-095 35 95 1-260 1-248 1-237 40 40 12-923 12-254 1 1 -642 40 40 15-296 14-418 13-619 40 45 12-285 11-681 11-126 40 45 14-510 I372I 13-001 40 50 11-501 10-975 10-487 40 50 13-459 I2-78I 12-156 40 55 10-529 10-090 9-680 40 55 12-183 1 1 -623 11-105 40 60 9-301 8-957 8-634 40 60 10-716 10-279 9-871 40 65 7753 7-504 7-269 40 65 9-025 8-706 8-406 40 70 6-284 6-112 5-948 40 70 7-306 7-088 6-880 40 75 1 4'95i 4-837 4-728 40 75 5-623 5^4 5-351 40 80 3718 3-648 3-58i 40 80 4-194 4-IIO 4-029 40 85 2720 2-679 2-638 40 85 2-964 2-9I7 2-871 40 90 1-921 1-898 1-875 40 90 2 -O2 1 1-995 1-971 40 95 I-IIO i-ioo 1-091 40 95 I-258 1-246 1-235 45 45 II753 11-200 10-689 45 45 I3-869 I3-H9 12-489 45 50 11-079 10-589 10-134 45 50 12-969 12-338 11757 45 55 10-210 9-795 9-407 45 55 1 1 -830 1 1 -302 10-812 45 60 9-074 8-744 8-434 45 6 10-477 10-059 9-667 4565 7-600 7-360 7-132 45 65 8-875 8-565 8-274 45 7o 6-184 6-016 5-856 4570 7-217 7-003 6-801 4575 45 80 4-887 3-680 4-776 3-611 4-669 3-544 45 75 45 80 5-574 4-168 5-437 4-085 5-306 4-005 45 85 2-698 2-657 2-617 45 85 2-951 2-904 2-858 45 90 I-909 1-886 1-863 45 90 2-014 1-989 1-964 45 95 I-I05 1-095 1-086 45 95 1-255 1-243 1-232 50 50 IO-532 10-088 9-675 50 50 12-245 1 1 -680 11-157 50 55 9795 9-412 9-053 So 55 1 1 -284 10-801 10-351 50 60 8-781 8-471 8-179 50 60 10-092 9-701 9*335 50 65 7-411 7-181 6-963 50 65 8-622 8-328 8-052 50 70 6-064 5-902 5747 50 70 7-061 6-856 6-660 5075 50 80 4-813 3-636 4-705 3-568 4-601 3-503 50 75 50 80 5-484 4-119 5-35I 4-037 5-223 3-959 50 85 2-672 2-632 2-592 50 85 2-926 2-880 2-835 5090 1-895 1-872 1-849 50 90 2-003 1-978 1-953 (159) MORTALITY TABLES TWO LIVES ~~ Value of" an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883 TWO MALES TWO FEMALES Ages 2i % 3% 3i% ** 2i % 3 % 3i % 50 95 i -099 1-090 i -080 50 95 1*250 1-239 1-228 ! 55 55 9-212 8-873 8-555 55 55 10-523 lo-ioo 9-704 ! 55 60 8-361 8-080 7-814 i 55 60 9-534 9-182 8-852 55 65 7-138 6-925 6-722 55 65 8-245 7-974 7-718 55 7o 5-8 9 8 5744 5-597 55 70 6-824 6-630 6-446 55 75 4-717 4-612 4-512 55 75 5-343 5-216 5-094 55 80 3-582 3'5 l6 3-453 55 80 4-038 3-959 3-883 55 85 2-642 2-603 2-564 55 85 2-882 2-837 2793 55 90 1-879 1-856 1-834! 5590 1-979 1-954 1-930 5595 1-093 1-083 | I '74 55 95 ! 1*239 ! 1-228 1-217 60 60 7-705 7-465 7-238 60 60 8-771 8-471 8-187 60 65 6-685 6-497 i 6-319 60 65 7-710 7-472 7-245 60 70 5-608 5-468 5-335 60 70 6-481 6-306 6-138 60 75 60 80 4-546 S'49 1 4-429 3-428 4-356 3-367 | 60 75 5T43 5*025 60 80 | 3-929 3-854 4-910 378i 60 85 2-596 2-558 2-520 60 85 2-826 2-783 2-740 60 90 1-857 1-835 1-813 ' 60 90 1-952 1-928 1-904 60 95 i -085 i i -076 i -066 60 95 1-229 1-217 1-206 6565 5-9ii 5-759 5-614 65 65 6-910 6-713 6-526 65 70 5-053 4-936 4-825 65 70 5-927 5777 5-633 i 6575 65 80 4-I75 3-262 4-091 3-206 4-010 3*152 65 75 4-793 65 80 3-722 4-688 3-654 4-587 3-587 6585 2-463 2-428 2-394 65 85 2-713 2-673 2-633 65 90 1-786 1-765 i-745 65 90 1-893 1-870 1-847 65 95 1-058 1-049 1-041 65 95 i -203 1-192 1-181 70 70 4-407 4-3I4 4-225 7070 5-206 5-086 4-971 70 75 3-7I9 3-649 3-582 70 75 4-3I3 4-226 4-141 70 80 2-963 2-915 2-869 70 80 3-427 3367 3-3io 70 85 2-276 2-245 2-215 70 85 2-549 2-512 2-476 70 90 1-676 1-657 1-638 70 90 i -806 1785 1-764 70 95 I -01 1 i -002 '994 70 95 1-165 1-154 1-144 75 75 75 80 3-215 2-625 3-161 3-108 2-586 2-548 75 75 75 80 3-671 2-997 3-604 2-949 3*539 2-903 75 85 2-063 2-036 2-OIO 75 85 2-287 2-256 2-226 7590 i-S5i i'534 I-5I8 75 9<> 1-657 1-639 1-620 75 95 -958 80 80 2-199 950 2-169 942 2T4I 75 95 80 80 1-094 2-523 1-084 2-486 1-075 2-451 80 85 1-773 1-752 1-732 80 85 1-985 1-960 1-936 80 90 1-367 1-353 1-340 80 90 1-478 1-462 1*447 80 95 ; -872 865 858 80 95 1-004 995 987 85 85 i -469 1-453 I-438 8585 1-617 1-599 1-581 85 90 1-164 i-i53 I -143 85 90 1-243 1-231 1-219 85 95 -772 766 760 85 95 877 870 863 90 90 949 941 932 90 90 988 '979 970 90 95 655 '651 646 9<> 95 725 719 714 95 95 485 -482 '478 95 95 557 '554 550 For explanation see pp. 29-3 1 (160) MOKTALITY TABLES TWO LIVES r Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883. MALE AND FEMALE FEMALE THE ELDER MALE THE ELDER Ages 2i% 3% 3i% Ages 2i% 3o/ /o 3i% M. F. F. M. 2O 20 18-580 17-235 16-047 2O 2O 18-580 I7-235 16-047 2O 25 18-124 16-848 I57I7 20 25 17-887 16-638 15-530 20 30 17-568 16-375 I5-3I3 20 30 17-114 15-971 14-952 20 35 16-890 15-797 14-817 20 35 16-258 15-229 14-304 I 20 40 16-067 15-087 14-202 2O 40 15-311 14-402 13-579 2045 15-066 14-211 13-434 20 45 14-263 13-479 12-763 20 50 13-842 13-122 12-463 20 50 13-092 12-435 11-831 20 55 20 60 12-436 10-880 11-854 10-431 11-316 IO-OI2 20 55 20 60 11-761 10-207 11-233 9-806 10-743 9-431 20 65 9-129 8-803 8-497 20 65 8-373 8-091 7-825 20 70 7-370 7-149 6-938 20 70 6-694 6-503 6-321 20 75 5-662 5-521 5-387 20 75 5-209 5-086 4-968 20 80 4-218 4-133 4-05I 20 80 3-872 3*797 3-725 20 85 2-977 2-929 2-883 20 85 2-809 2765 2722 20 90 2-028 2-002 1-977 20 90 1-969 1-945 1-921 20 95 1-261 1-249 I-238 20 95 1-129 1-119 I'lIO 2525 17-497 16-304 I5-242 25 25 17-497 16-304 15-242 25 30 17-014 I5-890 I4-886 25 30 16-790 15-689 14-705 25 35 16*41 1 I5-372 I4-439 25 35 I5-993 I4-995 14-098 25 40 15-659 I472I I3-873 25 40 15-097 14-211 13-408 25 45 14-726 13-903 I3-I54 25 45 14-093 13-324 12-623 25 50 13-566 I2-870 I2-232 25 50 12-959 12-313 11-719 25 55 12-221 11-655 II-I3I 25 55 : 11-659 11-139 10-655 25 60 I07I9 IO-28I 9-87I 25 60 10-133 9-736 9365 25 65 9-OI6 8-697 8-396 2565 8-322 8-043 7-779 25 70 7-296 7-078 6-871 25 7o 6-660 6-471 6-291 25 75 5-6l6 5-477 5*344 25 75 5-187 5-065 4-948 25 80 4-I90 4-106 4-025 25 80 3-859 3785 3-7I3 25 85 2-962 2-915 2-869 25 85 2-801 2758 2-715 25 90 2-O2O 1-995 I-970 25 90 1-965 1-941 1-918 25 95 1*257 1-246 1-234 25 95 1-128 1-118 1-108 30 30 I6-383 I5337 H'399 30 30 16-383 15-337 14399 30 35 I5-864 14-888 I4-008 30 35 15-660 14-704 13-842 30 40 I5-I97 I4-307 I3-50I 30 40 14-833 13-976 13-199 30 45 I4-344 I3-557 1 2 '840 30 45 13-887 I3-I39 12-456 30 50 I3-259 I2-589 1 1 '973 30 50 12-802 12-169 11-588 30 55 II-98l n-433 10-925 30 55 11-542 1 1 -030 io-555 30 60 10-539 10-112 9-7I4 30 60 10-049 9-658 9-292 30 65 8-889 8-577 8-283 30 65 8-266 7-990 7-729 30 70 7-212 6-998 6-794 30 70 6-623 6-435 6-257 30 75 30 80 5^4 4'l6o 5-427 4-077 5-296 3-996 30 75 30 80 5-164 3-845 5-043 377i 4-926 3-700 30 85 2-945 2-898 2-853 3085 2793 2-75 2-708 30 oo 2-OII 1-986 1-961 30 oo 1-961 !"937 1-913 3095 1-253 1-242 I-23I 30 95 1-126 1-116 1-106 For explanation see pp. 29-3 1 MORTALITY TABLES TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883. MALE AND FEMALE FEMALE THE ELDER MALE THE ELDER Ages 2^% 3% 31 o/ 2 /O Ages 21% 3o/ 70 3i% M. F. i F. M. 35 35 15-229 14-327 13-511 35 35 15-229 14-327 13*511 35 40 14-659 13-827 13-071 35 40 14-488 13-671 12-928 35 45 13-904 13-159 12-479 35 45 13-621 12-901 12-242 35 5o 12-909 12-269 11-680 35 50 12-603 1 1 -989 11-423 35 55 11-711 11-183 10-694 I 35 55 n-399 10-898 10-433 35 60 10-338 9-924 9-537 35 60 9-95 9-566 9-206 35 65 8-747 8-443 8-156 35 65 8-201 7-929 7-671 35 70 7-117 6-907 6-708 35 70 6-582 6-396 6-219 35 75 5-505 5-370 5-241 35 75 5-138 5-018 4-902 35 80 4-125 4-043 3-964 I 35 80 3-830 3757 3-686 35 85 2-926 2-880 2-835 35 85 2784 2741 2-699 35 90 2-001 1-976 I-95 1 35 90 1-956 1-932 1-909 35 95 1-249 1-237 1-226 35 95 1-124 1-114 1-104 40 40 I4-022 13-258 12-562 40 40 14-022 13-258 12-562 40 45 I3-379 12-687 12-052 j 40 45 13-256 12-574 11-949 40 50 12-497 11-893 1 1 '337 1 40 50 12-331 11742 11-199 40 55 11-399 10-895 10-427 40 55 1 1 -205 10721 10-270 40 60 10-109 9-710 9-337 40 60 9-820 9'445 9-093 40 65 8*587 8-292 8-013 40 65 8-119 7-852 7-598 4070 7-010 6-806 6-611 40 70 6-531 6-174 4075 40 80 c *A ^o 4-085 5-306 4-004 5-180 3*926 40 75 40 80 5-108 3-813 4*989 3-740 4-875 3-669 4085 2-904 2-858 2-814 40 85 2775 2732 2-690 40 90 1-989 1-965 1-940 40 90 I-95 1 1-927 1-903 40 95 1-244 1-232 I -221 4095 I-I22 I-II2 I -102 45 45 12736 12-108 II-529 4545 12-736 12-108 II-529 45 5 11-988 11-430 IO-9I4 45 50 II-932 II-38I IO-87I 45 55 11-017 10-544 IOT03 45 55 10-918 10-458 10-028 45 6 9-837 9-457 9'IQI 45 60 9-627 9-265 8-926 45 65 8-402 8-117 7-849 45 65 7-999 7739 7-493 45 70 6-889 6-691 6-502 4570 6-460 6-280 6-109 45 75 45 80 4-040 5-234 3-961 5'IIQ 3-884 45 75 45 80 5-067 3-79I 4-950 3718 4-837 45 85 2-879 2-834 2790 4585 2-763 2-720 2-679 45 90 1-976 1-952 I-927 45 90 1-945 1-921 1-898 45 95 1-238 1-226 I-2I5 45 95 I-II9 I'lIO i-ioo 50 50 11-331 10-833 10-370 50 50 n-33 1 10-833 10-370 50 55 50 60 10-516 9-482 10-084 9-127 9 -68l 8-795 50 55 50 60 10-465 9-309 10-040 8-970 8-651 50 65 8-169 7-643 So 65 7795 7-311 50 70 6744 6-553 6-370 50 70 6-332 6-159 5-994 50 75 50 80 5-276 3-990 3-912 5-030 3-837 50 75 50 80 4-992 3749 4-878 4-768 3-609 50 85 2-851 2-806 2763 50 85 2740 2-698 2-658 50 90 1-961 1-937 1-913 50 90 1-934 1-910 1-887 For explanation see pp. 29-31 (162) MORTALITY TABLES -TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the GOVERNMENT EXPERIENCE TABLE, 1883. MALE AND FEMALE FEMALE THE ELDER MALE THE ELDER Ages 2i% 3% 3t% Ages [ 2^ % 3o/ 70 3i% M. F. F. M. 50 95 I-23I 1-220 i -208 50 95 1-116 1-106 1-097 55 55 9-825 9-447 9-093 55 55 9-825 9-447 9-093 55 60 8-Q74 8-656 8-356 55 60 8-845 8-536 8-245 55 65 7-830 7-582 7-346 55 65 7-487 7-256 7-037 55 70 6-539 6-358 6-186 55 70 6-138 5-974 5-8i7 55 75 5-i6i 5-040 55 80 3-927 3-851 4-925 55 75 3778 55 80 4-873 4-763 4-658 3-679 3-610 3-544 55 85 2-818 2774 2-732 55 85 2-700 2-659 2-619 55 9o 1-944 1-920 1-896 55 90 1-912 i -888 i -866 5595 1-223 I -212 i '201 55 95 1-106 1-097 1-087 60 60 8-201 7-934 7-681 60 60 8-201 7'934 7-681 60 65 7-279 7-063 6-857 60 65 7-049 6-843 6-647 60 70 6-182 6-020 5-866 60 70 5-858 5-707 5-564 6075 60 80 4-955 4-844 3-818 3-747 4-737 60 75 3-678 60 80 4-706 3-586 4-603 3-520 4-504 3-457 60 85 2-766 2-724 2-683 60 85 2-651 2-611 2-572 60 90 1-920 i 1-897 1-874 60 oo I -887 I -864 1-842 60 95 1-214 1*203 1-192 60 95 I -098 I -088 1-079 6565 6-374 6-202 6-038 65 65 6-374 6-202 6-038 6570 5-528 5 '394 5-266 65 70 5 '394 5*264 S-HO 6575 65 80 4-524 3-554 4-428 3-491 4336 65 75 3-429 65 80 4-408 4-316 3-408 3-348 4-228 3-289 6585 65 90 2-619 1-844 2-581 1-822 2-543 65 85 i -800 s 65 90 2-549 1-832 2-511 1-810 2-475 1789 6595 1-182 1-171 1-161 I 65 95 1-076 1-066 1-057 70 70 4-781 4-675 4-574 7070 478i 4-675 4'574 7075 4-001 3'923 3-848 70 75 3-995 3-918 3-843 70 80 3-213 3' J 59 3-107 70 80 3-I52 3-100 3-049 70 85 2-415 2-381 2-348 70 85 2-399 2-366 2-333 70 90 1-727 1-707 1-688 70 90 I-75I I-73I 1711 70 95 1-125 1-115 1-105 7095 1-044 1-035 1-027 7575 75 80 3-430 2-829 3-370 2785 3-3ii 2-742 7575 75 80 3 '430 2-774 3-370 2-731 3'3ii 2-690 75 85 2-181 2-152 2-124 75 85 2-160 2-132 2-104 75 90 1-595 1-577 1-560 75 90 1-610 1-592 1*575 7595 1-063 1-054 1-045 7595 984 976 968 80 80 2-352 2-320 2-288 80 80 2-352 2-320 2-288 80 85 1-868 1-845 1-823 80 85 1-882 1-859 1-837 80 90 i -402 1-388 1-373 80 90 1-440 1-425 1-410 80 95 962 954 946 80 95 908 900 893 8585 I-540 1-524 1-507 8585 1*540 I-524 1-507 85 90 1-191 1-179 1-168 85 90 1-215 1-203 1-192 85 95 846 839 832 85 95 799 793 787 90 90 968 960 95i 90 90 968 960 951 90 95 712 707 702 90 95 666 661 657 95 95 | -519 515 512 95 95 519 515 512 (163) MOETALITY TABLES TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE A.jjea 3 % 3Jf% 4% Ages 3o/ /<) 3i% 4% 10 10 21-0079 19-3289 17-8656 20 60 9-6503 9-2849 8-9422 10 15 20-4046 18-8209 17-4348 20 65 8-0149 i 7-7544 7-5079 IO 2O 19-6575 18-1842 16-8879 - 20 70 6-3944 6-2197 6-0531 10 25 18-9794 17-6168 16-4105 20 75 4-8992 4-7883 4-6817 10 30 18-1217 16-8869 15-7863 ! 20 80 3-6458 3-5784 3-5132 10 35 17-1325 16-0360 15-0513 20 85 2-6828 2-6429 2 -6042 10 40 15-9913 15-0410 14-1806 20 00 1-7153 i -6974 I -6799 10 45 14-6570 13-8586 ; I3-I296 20 95 4122 4099 4076 10 50 13-1800 12-5312 j 11-9335 25 25 17-5703 16-3949 ! 15-3455 10 55 1 1 -5676 11-0611 i 10-5905 25 30 16-9261 15-8382 I4-862I 10 60 9-8667 9-4891 9-135 25 35 16-1390 15-1537 14-2645 10 65 8-1707 7-9025 7-6489 25 40 15-1822 14-3135 I3-524I 10 70 6-4997 6-3206 ! 6-1498 25 45 14-0130 13-2723 12-5945 10 75 4-9661 4-8528 47440 25 50 12-6787 12-0695 11-5075 10 80 3-6859 3-6I73 3-5509 25 55 11-1886 10-7083 10-2615 10 85 2-7056 2-6652 2-6259 25 60 9-5902 9-2291 8-8904 10 90 1-7242 I -7062 1-6885 25 65 7-9774 7-7191 7-4748 10 95 4129 4107 4084 25 70 6-3726 6-1990 6-0334 15 i5 19-8661 I8-3635 17-0435 25 75 4-8875 47771 i 4-6710 15 20 19-1866 I777 9 8 16-5386 25 80 3-6400 3-5728 I 3-5078 15 25 18-5708 17-2617 16-1006 25 85 2 -680 1 2-6404 2-60I7 15 30 17-7738 16-5811 15-5163 25 90 I-7I45 1-6967 I-6792 15 35 16-8405 15-7762 14-8192 25 95 4121 -4098 '4075 15 40 i575oi 14-8240 13-9848 ! 30 30 I6-3734 i I5-356I I4-4399 15 45 14-4623 13-6816 12-9684 30 35 I5-68IO I4-750I I3-9077 15 50 13-0271 12-3908 11-8045 ; 30 40 I4-8l62 13-9872 13-2324 15 55 1 1 -4524 10-9544 10-4915 30 45 I373I3 I3-OI82 12-3645 15 60 9-7844 9-4122 9-0633 30 50 12-4690 11-8779 11-3320 15 65 8-1160 7-8512 7-6007 30 55 11-0378 10-5688 10-1322 15 70 6-4676 6-2903 6-1213 30 60 , 9^55 9-1311 8-7984 i5 75 4-9502 ! 4-8378 4-7298 30 65 7-907I 7-6525 7-4117 15 80 3-6801 3-6II8 3-5459 30 70 6-3275 6-1559 5-9922 15 85 2-7055 2-6652 2-6260 30 75 4-8598 1 4-7503 4-6452 i5 90 1-7272 I -7092 1-6915 30 80 3-6234 3-5567 3-4922 15 95 4138 4115 4093 30 85 2-6705 2-6310 2-5925 2O 20 18-5817 I7'2554 16-0809 30 90 I-7I02 i -6925 1-6750 20 25 18-0385 167952 15-6891 30 95 4115 4092 4070 20 30 I73I49 16-1739 I5-I533 35 35 15-0950 14-2329 13-4496 20 35 16-4510 I5-4263 I4-5035 35 40 I4'3405 13-5632 12-8535 20 40 15-4240 I4-5274 13-7141 35 45 I3-3625 12-6859 12-0644 20 45 14-1936 i I3-4344 12-7402 35 50 ; 12-1954 11-6285 11*1041 20 50 12-8092 ! 12-1880 11-6153 35 55 10-8436 10-3896 j 9-9665 20 55 11-2791 10-7916 10-3381 35 o 93536 9-0080 8-6833 For explanation see pp. 29-3 1 (164) MOKTALITY TABLES- TWO LIVES Value of an Annuity for the Joint Continuance of Two Lives according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Agea 3 3i% 4% 35 6 5 7-8211 7-5714 7-3350 :ss 70 5-6627 5-5216 5-3865 35 70 6-2742 6-1050 5-9437 55 75 4-4616 4-3673 4-2764 35 75 4-8279 4-7197 4-6157 55 80 3-3947 3-3349 3-2770 35 80 3-6051 3-5389 3-4749 55 85 2-5429 2-5063 2-4706 35 85 2-66oo 2 -6207 2-5825. 55 90 i -6568 i -6398 1-6231 35 90 I 7058 I -688l i -6707 55 95 4051 4029 4007 35 95 4110 4087 4065 60 60 7-1988 6-9834 67787 40 40 13-7103 12-9996 12-3479 60 65 6-3213 6-1504 5-9872 40 45 12-8622 12-2343 "6557 60 70 5-3013 5'!755 5-0548 40 50 11-8177 II-284I i 10-7894 60 75 4-2332 4-1469 4-0638 4 55 10-5734 IO-I4O6 9-7366 60 80 3-2576 3-2018 3-1476 40 60 9-1705 8-8373 8-5241 60 85 2-4634 2-4285 2-3945 40 65 77034 7-4605 7-2304 60 90 i -6224 i -6059 1-5897 40 70 6-2029 6-0372 5-8790 60 95 4010 3987 3965 40 75 47868 4-6802 4-5777 6565 5-6519 5-5"5 5-3771 40 80 3-5821 3-5166 3-4533 65 70 4-8312 4-7242 4-6213 40 85 2 -6476 2 -6085 ; 2-5705 65 75 3-9266 3-8507 3-7775 40 90 I-7005 I -6828 1-6655 65 80 3-0687 3-0181 2 -9690 40 95 4103 4080 4058 6585 2-35H 2-3190 2-2873 45 45 I2-l6l9 11-5979 1 1 -0760 65 90 1-5719 l'556l I-5406 45 50 1 1 -2685 10-7807 10-3270 65 95 3944 3922 3901 45 55 IO-I663 97638 9-3873 70 70 4-2226 4-I378 4-0560 45 60 8-8855 8-5709 8-2747 70 75 3-5095 3-4470 3-3865 45 65 7-5I45 7-282I 7-0618 70 80 2-8014 2-7580 2-7159 45 70 6-0851 5'9249 57719 70 85 2-1880 2-1591 2T309 45 75 4-7I7I 4-6I32 ! 4-5132 70 90 i -4989 1-4841 1-4696 45 80 3-5425 3-4782 3-4160 70 95 3854 3833 -3812 45 85 2-6257 2-5872 2-5497 75 75 2-9876 2-9395 2-8928 45 90 I-69I7 I -6742 1-6570 75 80 2-4424 2-4077 2-3739 45 95 4094 4071 4049 75 85 i -9508 i -9265 I -9028 50 50 IO-5428 IO-II23 9-7103 75 90 1-3791 i -3659 I-3530 So 55 50 oo 9-6109 8-4864 9-2481 8-1970 8-9078 7-9240 7595 80 80 3684 2 -0488 3663 2-0225 3643 9969 50 65 7-2447 7-0270 ' 6-8204 80 85 I '6761 i -6569 6381 50 70 5-9I48 5-7624 5-6167 80 oo I-23I9 i -2206 2096 50 75 4-6152 4-5I52 i 4-4189 80 95 3467 3448 -3429 50 80 3-4839 3-42I4 3-3609 8585 I -4025 I-3877 -3732 50 85 2-5929 2-555I 2-5183 85 90 I -0676 i -0583 0491 50 90 1-6776 I -6603 i '6433 8595 3172 3155 3138 50 95 4076 4053 4031 90 90 8693 8625 8557 55 55 8-8676 8-5546 8-2598 90 95 2850 2835 2820 556o 7-93IO 7^749 7-4327 95 95 1321 I3H 1308 55 65 6-8562 6-6590 6-47I3 1 (165) MORTALITY TABLES TWO LIVES ingle Payment to secure 1 at the Death of either of Two Lives according to the NORTHAMPTON TABLE Ages 3 % 3% Ages 3 % 15 15 5273 30 55 6991 i 50 75 8406 IS 20 5439 30 60 7269 50 80 8730 15 25 5564 30 65 7587 So 85 9013 15 30 5708 30 70 7949 50 oo 9218 15 35 5878 30 75 8321 5095 9640 i5 40 1545 6080 30 80 6305 30 85 8681 -8986 5555 55 60 7471 7644 15 So 6563 30 90 9205 5565 7864 15 55 6840 30 95 9639 55 70 8138 15 60 7149 35 35 6294 55 75 8442 1565 7496 35 4 6443 55 80 8750 15 70 7884 35 45 6615 55 85 9025 1575 8278 35 50 6822 55 90 9224 15 80 8654 35 55 7049 55 95 9641 1585 8970 35 60 7312 60 60 7785 20 20 5592 35 65 7618 60 65 7970 20 25 5706 35 70 7970 60 70 8212 20 30 20 35 5839 '5997 3575 35 80 8688 6075 60 80 8489 8778 2O 40 6186 5 85 8990 60 85 9040 20 45 6398 35 90 9207 60 90 -9231 20 50 6644 35 95 9639 60 95 -9641 20 55 6908 40 40 6574 65 65 8115 20 60 7205 40 45 6727 65 70 8316 20 65 7541 40 50 6915 65 75 8 55 6 2O 70 20 75 79i8 40 55 8302 40 60 7125 65 80 737i 65 85 8817 9061 20 80 8669 40 65 7661 65 90 9241 20 85 8980 40 70 7999 65 95 9642 20 9O 9202 40 75 8353 70 70 8468 25 25 5811 40 80 8698 70 75 8660 25 30 5932 40 85 8996 70 80 8881 25 35 6079 40 90 9210 7085 9098 25 40 6256 40 95 9640 70 90 9259 2545 6457 4545 6861 70 95 9643 25 50 2555 6692 6946 4550 4555 7028 7216 7575 75 80 8802 8973 25 60 7234 45 60 7442 75 85 9154 25 65 7562 45 65 77i3 75 90 9289 2570 7932 45 70 8034 75 95 9645 2575 25 80 8311 8675 4575 45 80 8375 8711 80 80 80 85 9091 9230 25 85 8983 4585 9003 80 90 9330 25 90 9204 45 90 9213 80 95 9648 2595 9639 4595 9640 85 85 9327 30 30 6042 50 50 7170 85 90 9396 3035 6175 5055 7334 8595 9654 30 40 6339 50 60 7536 00 00 9436 30 45 6527 So 65 7783 90 95 9657 | 30 50 6749 i 50 70 8083 9595 9691 For explanation see pp. 29-31 (166) MORTALITY TABLES -TWO LIVES Single Payment to secure 1 at the Death of either of Two Lives according to the CAELISLE TABLE Ages 3% Ages 3Q/ /o Ages 3% 15 15 15 20 4202 4343 30 55 30 60 6479 6933 50 75 50 80 8246 8528 15 25 4526 30 65 7313 50 85 8823 15 30 '4739 30 70 7768 50 oo 9020 1535 4963 3075 8190 5095 8943 15 40 15 45 5238 5520 30 80 3085 8495 8804 5555 5560 7057 7350 1550 5884 30 90 9006 5565 7606 1555 15 60 6351 6839 3095 3535 542! 55 70 5575 7956 8307 15 65 7245 3540 -5617 55 80 8567 15 70 7723 35 45 5826 55 85 8846 1575 15 80 8161 8475 35 50 3555 6122 6528 55 90 9037 8959 1585 8792 3500 6968 60 60 7584 2O 20 4468 35 65 7338 60 65 7790 20 25 4635 35 70 7784 60 70 8088 20 30 4831 35 75 8200 60 75 8399 20 35 5039 35 80 8501 60 80 8632 2O 40 5302 3585 8807 60 85 8890 20 45 5571 35 90 9009 60 oo 9068 20 50 5924 3595 8933 60 95 8993 ^g 20 60 6380 6860 40 40 40 45 5782 5961 6565 65 70 7948 8196 20 65 7259 40 50 6227 6575 8469 20 70 7731 4 55 6604 65 80 8677 20 75 20 80 8166 8478 40 60 40 65 7022 7377 6585 65 oo 8917 9088 20 85 8793 4070 7811 65 95 9010 20 00 8999 4075 8219 7070 8382 25 25 25 30 4782 4958 40 80 40 85 8514 8816 70 75 7080 8601 8769 2535 5148 40 oo 9015 70 85 8974 25 40 5391 40 95 8940 70 oo 9130 25 45 5644 4545 6105 7095 9054 25 50 25 55 25 oo 5983 6425 6893 45 So 45 55 45 60 6336 6680 7069 7575 758o 75 85 8768 8896 9063 25 65 7283 45 65 7405 75 90 9197 25 70 7747 4570 7826 75 95 9128 25 80 8176 8484 4575 45 80 8226 8518 80 80 80 85 8992 9128 25 85 8797 45 85 8819 80 90 9246 25 90 9002 45 90 9017 80 95 9183 25 95 8926 4595 8942 8585 9226 30 30 5111 50 50 6522 85 90 9320 30 35 5279 50 55 6818 8595 9269 30 40 5500 50 60 7166 90 oo 9392 30 45 5733 5065 7469 9095 9354 30 So 6053 50 70 7863 9595 9306 For explanation sec pp. 29-31 (167) MORTALITY TABLES TWO LIVES Single Payment to secure 1 at ths Death of either of Two Lives according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3Q/ 70 3i% 4% Ages 3% 3i% 4% 10 10 35900 31256 27439 20 70 78463 75586 72872 10 15 37657 32974 29096 20 75 82818 80426 78147 10 20 39833 '35125 31200 20 80 86469 84518 82641 10 25 41808 '37045 33036 20 85 89273 87681 86138 10 30 44306 -39514 35437 20 90 92091 90878 89693 10 35 47187 -42391 38263 20 95 95887 95232 94586 10 40 505" 45756 41612 25 25 45912 -41177 37132 10 45 '54397 49754 45655 25 30 47788 -43060 38991 10 50 58699 54243 50255 25 35 50081 : -45375 41290 10 55 63396 59214 55421 25 40 52868 -48216 44137 10 60 68350 6453 61019 25 45 56273 '51737 47713 10 65 73289 69895 66735 25 50 60159 -55804 10 70 78156 75245 72500 25 55 64499 '60407 -56686 10 75 82623 -80208 77907 25 60 69155 s '65409 61960 10 80 86352 84386 82496 25 65 73852 -70515 67404 10 85 89207 87606 86054 , 25 70 78527 75656 72948 10 90 92065 90849 -89659 25 75 82852 -80464 78188 10 95 95885 95230 -94583 25 80 86486 84537 82662 15 i5 39225 34520 -30601 25 85 89281 87690 86147 15 20 41205 36494 32543 25 90 92094 90881 89695 ; 15 25 42998 38246 34228 25 95 95887 95233 94586 15 30 45319 40548 36475 30 30 49398 44690 40615 15 35 48038 43270 39156 30 35 5I4I5 46739 42662 15 40 51214 46488 42365 30 40 '53934 49319 45259 15 45 54965 50353 46275 ;; 30 45 57094 52596 48597 15 50 59H5 547i8 50751 ! 30 50 60770 56452 52569 1555 63731 '59575 -55801 30 55 64939 60879 57183 15 60 68589 64790 -61295 30 60 69460 65741 62313 15 65 73449 70069 -66920 30 65 74057 70741 67647 15 70 78250 75347 -72610 30 70 78658 75802 73107 i5 75 82669 80259 -77962 30 75 82933 80555 78287 15 80 86369 84405 -82516 30 80 86534 -84591 82722 15 85 89207 87606 -86054 30 85 89309 87721 86183 i5 90 92057 90839 -89648 30 90 92106 90895 89711 15 95 95882 95227 -94580 30 95 95889 95235 94588 20 20 42966 | -38268 -34303 35 35 53122 48488 44424 20 25 44548 -39824 -35810 35 40 55319 50753 46717 20 30 46656 -41925 ; -37871 35 45 58168 i -53720 49752 20 35 49172 44453 -40370 35 50 61567 -57295 53446 20 40 52163 -47493 -43407 35 55 '65504 61485 57821 20 45 "55747 -51189 -47152 35 6 69844 66157 62756 ; 20 50 '59779 '55403 '5H79 35 65 74308 : 71015 67942 20 55 64236 -60126 -56391 35 70 78813 -75974 73293 20 60 68980 -65221 -61760 35 75 83026 ! -80658 78401 20 65 73743 70396 -67277 | 35 80 86587 '84651 82789 For explanation see pp. 29-31 (168) MORTALITY TABLES -TWO LIVES Single Payment to secure 1 at the Death of either of Two Lives according to the INSTITUTE OF ACTUAEIES HEALTHY MALES TABLE Ages 3o/ /o 3i% 4% Ages 3% 3i % : 4 % 35 85 89340 87756 86220 55 75 84093 81850 79706 35 90 92119 -90910 89728 55 80 -87200 -85341 -83550 35 95 95890 -95236 94590 55 85 -89681 -88143 86651 40 40 57155 -52659 48661 55 90 i -92262 -91073 -89911 40 45 59625 -55247 51324 55 95 '959o8 I -95256 94613 40 50 62667 58460 54656 60 60 -76120 73003 70082 40 55 66291 62327 58705 60 65 -78676 75820 73126 40 60 70377 66734 63368 60 70 -81647 79117 76712 40 65 74650 71390 68344 60 75 I -84758 -82595 80524 40 70 79021 76203 73542 60 80 -87599 -85791 84048 40 75 83145 80792 i 78547 60 85 -89913 -88406 86944 40 80 86654 84727 -82872 60 90 i -92362 -91188 90039 , 40 85 89376 87797 -86267 60 95 '959 i 9 -95270 i -94629 , 40 90 92135 I -90928 89748 65 65 80626 -77981 -75472 40 95 95892 1 -95239 '94593 65 70 83016 -80643 78379 45 45 61665 -57399 '53553 65 75 -85651 -83597 81625 45 50 64267 -60162 56434 65 80 -88150 -86412 84734 45 55 67477 -63601 -60048 65 85 -90239 -88776 87356 45 60 71207 -67635 64328 05 90 ^2509 -91356 90228 45 65 75201 71993 -68993 65 95 '95939 -95292 94653 45 70 79364 76583 73954 70 70 -84789 82626 80554 4575 45 80 83348 -81018 78795 70 75 -86866 -84962 86770 '84857 -83015 70 80 -88928 -872Q2 83129 85708 45 85 89440 -87870 -86347 70 85 -90715 89317 87958 45 90 -92160 90957 -89781 70 90 92722 91600 90501 45 95 '95895 95242 -94596 70 95 95965 95322 94688 50 50 -66380 62423 -58806 75 75 -88386 -86678 85028 50 55 -69095 65345 -61893 75 80 89974 88477 87023 50 60 -72370 68899 -65677 75 85 91405 90104 88835 50 65 -75986 72856 -69921 75 90 93071 91999 90950 50 70 79863 77132 -7455I 75 95 96014 95380 94753 50 75 '83645 81350 79158 80 80 91120 89779 88473 50 80 -86940 -85049 -83227 80 85 -92206 91015 89853 50 85 89535 , -87978 -86468 80 90 '93499 92491 91501 50 90 92201 -91004 -89833 80 95 96078 95452 94835 So 95 95900 -95248 ; -94603 8585 93002 91926 90872 55 55 71260 67690 '64385 ! 85 90 93978 93040 92119 55 60 73988 70665 '67566 85 95 96164 95552 94947 55 65 77118 74100 -71264 90 90 '94555 93702 92863 55 70 80594 77947 75436 90 95 96257 95660 95069 9595 96703 96174 95651 (169) MORTALITY TABLES Two LIVES Annual Payment during the Joint Continuance of Two Lives to secure 1 at the First Death according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages ; 3 % 3i % 4 % Ages 3 % 3i% 4% 10 IO i 'Ol6 015 015 30 55 054 '053 05 1 IO 20 -019 018 017 30 60 066 065 064 10 30 , -023 022 021 30 70 -107 106 105 10 40 -030 -028 027 30 80 187 186 184 10 50 -041 -040 039 30 90 340 338 '335 10 60 063 -062 060 35 35 033 032 031 10 70 104 -103 101 35 40 036 035 034 10 80 184 i -183 181 35 45 040 039 038 10 90 338 -336 333 35 50 047 045 044 J 5 X 5 019 -018 017 3555 055 054 053 15 20 020 '019 019 35 6o 067 066 065 1525 15 30 *O22 'O2I 024 '023 020 022 35 70 35 8o 108 188 107 186 106 184 15 35 027 -026 025 35 90 340 338 336 15 40 031 -029 028 40 40 039 038 036 15 45 036 -034 033 40 45 043 042 041 15 5o 042 -041 040 40 So 049 048 046 i5 55 051 -050 049 40 55 057 056 55 15 60 064 -062 06 1 40 60 069 068 067 15 70 105 -103 102 40 70 no 108 107 15 80 185 -183 181 40 80 189 188 186 15 90 338 -336 333 40 90 341 339 337 20 20 O22 ] 'O2I 020 45 45 047 046 044 20 25 O23 'O22 021 45 50 052 051 050 20 30 025 -024 023 45 55 060 059 058 20 35 028 -027 O26 45 60 072 071 069 2O 40 032 -031 O29 45 70 112 in 109 20 45 '37 035 '34 45 80 191 189 188 20 50 043 042 041 45 90 342 340 338 20 55 052 051 050 50 50 058 056 055 20 60 065 063 062 So 55 06 5 064 062 20 70 106 105 103 50 60 076 075 074 20 80 186 I8 5 183 50 70 'US 114 113 2O 90 '339 '337 335 50 80 194 192 191 25 25 025 024 023 50 90 344 342 340 i 25 30 027 026 025 55 55 072 071 070 I 25 35 029 028 027 55 6 o 083 08 1 080 25 40 "033 031 030 55 70 121 120 118 25 45 037 036 035 558o I 9 8 I 9 7 195 25 5o 044 043 041 55 90 347 345 '343 2555 25 60 053 065 052 064 050 063 60 60 60 70 093 130 091 128 090 126 25 7o 107 105 104 00 80 206 204 203 25 80 186 185 183 60 oo 352 350 348 25 90 339 337 '335 70 70 162 161 159 30 30 028 027 026 70 80 234 232 231 30 35 031 030 029 70 90 372 369 366 30 40 034 033 032 80 80 299 297 295 30 45 039 038 036 80 90 419 416 414 30 50 045 044 043 90 90 471 468 465 For explanation see pp. 29-31 (170) MORTALITY TABLES TWO LIVES Value of an Annuity during the Continuance of either of Two Lives according to the NORTHAMPTON TABLE Ages 3o/ /o 4% 5% 6% Ages 15 15 24-015 20-171 17-216 14-954 15 15 15 25 23-241 I9-599 16-831 14-665 15 25 15 35 22-444 19-043 16-435 14-368 15 35 15 45 21-662 18-467 16-003 14-027 1545 15 55 20-957 I7-9I5 15-567 I3-674 i5 55 15 65 20-364 17-425 15-155 I3343 1565 1575 19-945 17-058 14-837 13-069 i5 75 20 20 23-*43 I9-53I 16-782 14-640 20 20 20 30 22-274 18-941 16-372 14-348 20 30 2O 40 21-390 18-306 15-907 14-003 20 40 20 50 20-551 17-667 15-415 13-620 20 50 2O 60 19-818 17-077 14-936 13-228 2O 6O 2O 7O 19-223 16-568 14-498 12-852 2O 70 20 80 18-850 16-233 14-197 12-578 20 80 2525 22-245 18-932 16-370 14-382 2525 2535 21-289 18-260 15-894 I3-979 25 35 2545 20-342 17-561 15-368 13-569 2545 2555 25 65 19-480 18748 16-885 16-279 14-833 14-324 13-142 12-719 25 55 2565 25 75 18-214 15-811 13-915 12-369 2575 30 30 21-255 18-249 15-889 14-004 30 30 30 40 20-202 17-488 15-333 I3-592 30 40 30 50 30 60 19-198 I8-32I 16-724 16-018 14-745 14-172 I3-I33 12-665 3050 30 60 30 70 I7'6l3 '5-4I3 13-653 12-218 3070 30 80 I7'I73 15-018 13-297 11-895 30 80 35 35 20-154 17-466 15-324 13-557 35 35 3545 19-008 16-616 14-686 13-070 3545 35 55 17-957 15-792 14-035 12-547 35 55 35 65 I7-065 I5-053 13-414 12-024 3565 35 75 I6-4I7 14-485 12-919 11-614 35 75 40 40 I8-932 I6-574 14-658 13-088 40 40 40 50 17-694 40 60 16-600 15-627 14-746 13-929 13-214 12-520 n-935 40 50 40 60 40 70 i 15711 13-987 12-562 n-374 40 70 40 80 I5-I60 I3-49I 12-116 10-969 40 80 45 45 I7-608 I5-576 13-898 12-463 4545 4555 45 65 I6-285 I5-I46 I4-536 I3-59I 13-076 12-283 11-809 11*252 4555 45 65 45 75 i i4'3" 12-859 11-643 10-594 45 75 So So 50 60 16-158 14752 I4-447 I3-3I4 13-016 12-093 1 1 -804 1 1 -048 50 50 50 60 50 70 I 3 -588 12-319 1 1 -238 10-311 50 70 50 80 12-855 1 1 -660 10-644 9-772 50 80 55 55 I4'6l9 13-223 12-029 10-965 55 55 5565 I3-I20 11-976 10-983 10-100 55 65 55 75 11-999 10-992 10-120 9-342 55 75 6060 12-948 11-852 10-896 10-061 60 60 60 70 60 80 11-372 IO-36I 10-500 9-590 9-735 8-9I5 9-058 8-3I5 60 70 1 60 80 J For explanation see pp. 31, 32 (170 MORTALITY TABLES-TWO LIVES Value of an Annuity during the Continuance of either of Two Lives according to the CARLISLE TABLE A & es 3 % Ages 3% Ages 3% Ages 3% 5 5 27-570 ! 15 80 22712 35 40 21-528 55 55 15715 5 10 27-332 15 85 ; 22-663 35 45 20-965 55 60 14-802 5 *5 26-986 15 90 22-640 35 50 ! 20-423 55 65 14-107 5 20 26-665 15 95 22-639 35 55 19-924 55 70 13-513 525 26-343 20 20 25-398 35 60 19-515 55 75 13-107 5 30 26-032 j 20 25 24-941 3565 19-211 55 80 12-854 5 35 25-737 ' 20 30 24-505 35 70 18-949 55 85 12-677 540 25-444 20 35 i 24-098 3575 18767 55 90 12-600 5 45 25-174 20 40 J 23-707 35 80 18-651 55 95 I2 '59i 5 50 24-902 20 45 23-351 35 85 18-567 60 60 13-688 5 55 24-638 20 50 23-003 35 90 18-530 60 65 12-820 5 60 24-411 20 55 22-676 35 95 18-527 60 70 \ 12-050 565 24-238 j 20 oo ; 22-404 40 40 20-803 60 75 11-506 5 70 24-079 20 65 : 22-201 40 45 20-137 60 80 11-161 5 75 23-961 20 70 22-029 40 50 19-490 60 85 10-909 580 23-883 i 20 75 21-909 40 55 18-893 60 oo 10-791 585 23-820 li 20 80 21-835 Ji 40 60 18-409 60 95 1 10-790 5 90 23-786 20 85 21782 40 65 18-054 65 65 11-788 5 95 23-792 20 90 21-757 40 70 17-750 65 70 10-847 10 IO 27-060 20 95 21756 4 75 I7-540 65 75 '0-I73 10 15 26-685 25 25 24-417 40 80 17-406 65 80 9-740 10 20 26-335 1 25 30 23-912 40 85 17-306 65 85 ! 9-428 10 25 25-989 25 35 23-440 40 oo 17-261 65 90 i 9-285 10 30 25-659 25 40 22-986 40 95 17-261 65 95 9-277 10 35 25'35o 25 45 22-575 45 45 I9-355 7 70 9-691 10 40 25-049 25 50 22-176 45 50 18-585 70 75 j 8-831 10 45 10 50 24774 24-505 2555 25 60 21-801 21-489 4555 45 60 17-871 70 80 8-259 17-292 i! 70 85 7-830 10 55 24-253 2565 21-255 45 65 16-870 70 90 7*635 10 60 24-046 25 70 21-054 45 70 16-521 70 95 7-633 10 65 10 70 23-892 23761 25 75 25 80 20-915 20-827 45 75 45 80 16-286 ! 75 75 16-140 75 80 7-793 7-086 10 75 23-671 25 85 20-765 45 85 16-036 ; 75 85 6-524 10 80 23-614 25 90 20-737 45 90 15-987 ! 75 90 6-253 10 85 23-575 25 95 20-735 4595 15-987 j 75 95 6-276 10 90 23-557 30 30 23-33 50 50 17-662 80 80 6-271 j o 95 23-555 30 35 22-782 50 55 16-787 80 85 5-601 J 5 J 5 26-256 30 40 22-251 |j 50 60 16-064 80 90 5-274 15 20 25-855 30 45 21-771 50 65 15-528 80 95 5-315 15 25 25-456 30 50 21-308 50 70 15-088 85 85 4-802 1530 1535 25-075 24721 30 55 30 60 20-877 20-519 50 75 50 80 14-792 14-613 85 oo 4-393 85 95 4'478 i5 40 24-377 30 65 20-251 50 85 14-491 oo oo 3-909 i5 45 24-062 30 70 20-018 50 90 14*436 oo 95 4-039 15 So 23753 30 75 19-856 5095 14-430 95 95 4-131 15 55 23-463 30 80 19753 15 60 23-221 ! 30 85 19-679 i5 65 23-041 30 oo 19-645 i5 7o 22-887 30 95 19-644 i5 75 22779 35 35 22-148 For explanation see pp. 31, 32 (172) MOKTALITY TABLES TWO LIVES Value of an Annuity during the Continuance of either of Two Lives according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3o/ /o 34% 4% A = es : 3o/ 70 34% 4% 10 10 27-2889 24-5789 22-2874 30 55 20-9234 J 9'3953 18-0413 10 20 26-5334 23-9943 21-8324 30 60 20-6178 19-1192 17-7915 10 30 25-8941 23-4826 21-4211 30 70 20-1964 18-7300 17-4317 10 40 25-3333 23-0155 21-0306 i 30 80 19-9864 18-5311 17-2430 10 50 24-8647 22-6101 20-6790 30 90 19-8971 18-4448 17-1598 10 60 24-5176 22-2995 20-4005 35 35 22-0792 20-4161 18-9440 10 70 24-3052 22-1036 20-2197 ; 35 40 21-4228 19-8639 18-4780 10 80 24-2049 22-0088 20-1299 35 45 20-8181 I9-3458 18-0329 10 90 24-1641 21-9694 20-0919 35 50 20-2880 18-8834 17-6287 15 15 26-4501 23-9351 217903 35 55 I9-8373 18-4834 17-2729 15 20 26-0140 23-5941 21-5221 35 60 19-4694 18-1512 16-9725 15 25 25-6252 23-2862 21-2770 35 70 18-9694 17-6898 16-5461 15 30 25-2517 22-9838 21-0315 35 8o 18-7244 I7-4578 16-3262 J 5 35 ; 24-9047 22-6976 20-7945 1 35 o 18-6212 i7'358i 16-2300 15 40 24-5842 22-4279 20-5668 40 40 20-6421 19-2056 17-9215 15 45 24-2893 22-1749 20-3490 40 45 19-9075 J 8-5755 I7-3795 15 50 24-0273 21-9459 20-1484 40 50 19-2548 18-0059 16-8813 15 55 23-7995 21-7434 19-9680 40 55 18-6966 17-5105 16-4407 15 60 23-6096 21-5718 19-8126 40 60 18-2416 17-1000 16-0696 15 70 23-3470 21-3293 19-5886 40 70 17-6298 16-5357 1 5 '5487 15 80 23-2204 21-2097 19*4753 ! 40 80 I7-3365 16-2582 15-2857 15 90 23-1708 21-1618 1 9 -4293 40 o 17-2156 16-1415 I5-I73I 20 20 25-5033 23-1938 21-2067 45 45 19-0251 17-8165 16-7250 20 25 25-0419 22-8280 20-9154 45 50 18-2213 17-1139 16-1095 20 30 24-5950 22-4663 20-6214 45 55 17-5210 16-4919 I5-5558 2035 24-1786 22-1228 20-3371 45 60 16-9439 15-9710 15-0848 2O 40 23-7947 21-7998 20-0644 45 70 16-1649 15-2526 14-4216 20 4 5 23-4424 21-4974 19-8041 45 80 I5-7934 14-9012 14-0888 20 50 23-1296 21-2240 19-5645 i 45 90 15-6417 I4-7547 I3-9474 20 55 22-8572 20-9815 19-3483 50 50 17-2498 16-2625 15-3617 20 00 22-6281 207744 19-1606 50 55 16-3792 15-4878 14-6708 20 70 22-3046 20-4752 18-8837 50 60 15-6458 14-8251 14-0710 20 80 22-1391 20-3184 18-7349 50 70 14-6380 13-8953 13-2123 2O 00 22-0671 20-2489 18-6678 50 80 14-1548 13-4382 12-7794 25 25 24-5055 22-4023 ; 20-5759 50 90 I3-9586 13-2488 12-5966 25 30 i 23-9792 21-9760 i 20-2295 55 55 15-3200 14-5424 13-8254 2 5 35 ; 23-4860 21-5694 19-8930 55 60 H3987 13-7083 13-0689 25 40 i 23-0319 21-1877 I9-57I3 55 70 13-0876 12-4972 11-9491 25 45 22-6184 20-8335 19-2667 55 80 12-4415 1 1 -8858 1 1 -3699 25 50 22-2555 20-5165 18-9892 55 90 12-1769 1 1 -6304 11-1234 2 5 55 21-9431 20-2388 18-7418 60 60 I3'2730 12-6860 12-1393 25 60 21-6836 20-0042 i 18-5293 60 70 11-5911 11-1295 10-6972 25 70 21-3218 19-6699 | 18-2203 60 80 10-7207 10-3051 9-9I57 25 80 21-1403 19-4980 ' 18-0572 60 90 10-3534 9-9505 9-5732 25 90 21-0633 19-4236 17-9854 70 70 9-0904 8-8028 8-5300 30 30 23-3614 21-4751 19-8219 70 80 7-5975 73845 7-1814 30 35 22-7735 20-9900 19-4200 70 oo 6-8975 6-7079 6-5273 30 40 22-2274 20-5310 19-0332 80 80 5-436o 5"3 2I 9 5-2117 30 45 21-7296 20-1046 18-6669 80 90 4-2504 4-1733 4-0986 3050 21-2947 19-7251 18-3349 j 90 90 2-6105 2-5809 2-5521 For explanation see pp. 31, 32 (173) K 2 MORTALITY TABLES TWO LIVES Single Payment to secure 1 at the Death of the Last of Two Lives according to the NORTHAMPTON TABLE Ages 3% Ages 3o/ /o Ages 3o/ Yo 20 20 2968 15 15 -2693 35 55 '4479 21 21 3019 15 20 -2824 35 60 4615 22 22 3070 15 25 2939 35 65 4738 23 23 3122 15 30 3055 35 70 4844 24 24 *3 I 75 15 35 3172 35 75 4927 25 25 26 26 3230 3285 15 40 15 45 3288 '3399 35 80 -4986 40 45 -4378 27 27 15 50 3506 40 50 '4555 29 29 '3399 3458 J 5 55 '3 6o 5 15 60 -3696 40 55 40 60 4720 4874 30 30 3518 15 65 '3777 40 65 -5013 31 31 358o 15 70 -3846 40 70 5133 32 32 33 33 3642 3707 15 75 '3899 15 80 -3937 40 75 40 80 5226 5293 34 34 '3772 20 25 -3094 45 50 '4779 35 35 3839 20 30 -3221 45 55 -4965 36 36 3907 20 35 -3350 45 60 -5139 38 38 3977 4048 20 40 20 45 '3479 3603 4565 45 70 5297 '5434 39 39 4121 20 50 3723 45 75 5540 40 40 4195 20 55 3833 45 80 5617 41 41 4270 20 60 3936 50 55 i -5213 4242 4346 20 65 4029 50 60 5412 43 43 4422 20 7O 4110 50 65 '5593 4444 4501 20 75 4173 50 70 *575i 4646 4580 20 80 4662 25 30 4218 3368 50 75 -5875 50 80 -5964 47 47 '4745 25 35 3508 55 60 -5678 4829 25 40 -3648 55 65 -5887 49 49 4916 25 45 3784 55 70 -6070 50 50 5003 5090 2550 25 55 4035 5575 55 80 6214 6318 52 52 5178 25 60 4H7 60 65 6181 53 53 5267 25 65 4248 60 70 6396 54 54 5358 25 70 '4335 60 75 6567 55 55 5451 2575 4403 60 80 6691 56 56 '5545 25 80 -4453 6570 6721 57 57 58 58 5641 5738 30 35 -3671 65 75 30 40 -3825 65 80 6928 7081 5959 5837 30 45 '3974 7070 7027 60 60 '5937 30 50 -4117 7075 7281 61 61 6039 30 55 -4250 70 80 7474 62 62 63 63 6142 30 60 -4372 6248 30 65 -4483 75 75 75 80 7587 7829 64 64 -6355 30 70 4579 8080 8124 65 65 -6465 30 75 66 66 -6575 30 80 4653 4707 80 85 80 90 8323 8451 67 67 -6687 35 40 4008 8585 8564 6868 6800 35 45 4172 85 90 8736 6969 6913 35 50 4332 9090 8937 For explanation see pp. 31, 32 (174) MORTALITY TABLES TWO LIVES Single Payment to secure 1 at the Death of the Last of Two Lives according to the CARLISLE TABLE Ages 3 % A*. 3 % A ^ s 3 % IS 15 2061 30 40 3228 50 60 '5030 1520 2178 30 45 3368 50 65 -5186 1525 2294 30 50 3503 50 70 -5314 15 30 2405 30 55 3628 50 75 -5400 1535 2508 30 60 3732 50 80 -5453 15 40 2609 30 65 3810 50 85 -5488 1545 2700 30 70 3878 50 90 -5504 15 50 2790 30 75 3926 50 95 -5506 '555 15 60 2875 2945 30 80 30 85 '3955 55 55 W2 '3977 55 60 -5398 1565 2998 30 90 3987 55 65 -5600 15 70 3043 3095 3987 55 70 '5773 1575 15 80 3074 3094 35 35 35 40 3258 '3439 55 75 -5891 55 80 -5965 1585 3108 3545 3602 55 85 -6016 15 90 3115 35 50 376o 55 90 -6039 15 95 20 20 3115 2311 3555 35 60 3906 55 95 -6041 4025 60 60 -5722 20 25 2444 3565 -4113 6065 -5975 20 30 2571 3570 4190 60 70 -6199 20 35 20 40 2690 2804 3575 35 80 4243 60 75 -6358 4276 60 80 -6458 20 45 2908 35 85 4301 60 85 -6531 20 50 3009 35 90 '43 1 2 60 90 -6566 2055 3104 3595 4313 60 95 -6566 20 60 3183 40 40 3650 65 65 -6275 20 65 3242 40 45 3844 65 70 -6550 2O 70 3293 40 50 4032 65 75 -6746 20 75 3328 40 55 4206 65 80 -6872 20 80 3349 40 60 '4347 65 85 6963 20 85 3364 40 65 4450 65 90 7004 20 90 3372 40 70 '4539 65 95 7007 20 95 3372 40 75 4600 70 70 6886 2525 2530 2597 2744 40 80 40 85 4639 4668 70 75 70 80 7137 7303 25 35 -2882 40 90 4681 7085 7428 25 40 '3i4 4<>95 4681 70 90 7485 25 45 '3134 4545 4071 7095 7486 25 50 -3250 45 50 4296 7575 7439 25 55 '3359 45 55 4504 75 80 7645 25 60 3450 45 60 4672 75 85 7809 2565 35i8 45 65 '4795 75 oo 7887 25 70 '3577 45 70 4897 75 95 7881 25 75 25 80 3617 3643 45 75 458o 4965 5008 8080 80 85 7882 8077 25 85 3661 45 85 5038 80 90 8i73 25 90 3669 45 90 5052 80 95 8161 25 95 3669 45 95 5052 8585 8310 30 30 2914 50 50 4564 85 90 -8429 3035 3073 | 50 55 4819 8595 8405 For explanation see pp. 31, 32 (175) MORTALITY TABLES TWO LIVES Single Payment to secure 1 at the Death of the Last of Two Lives according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3o/ /o 3i% 4% Ages 3% 3i% 4% 10 10 -1761 1350 1043 30 55 3615 3103 2676 10 20 "1981 '1548 1218 30 60 3703 3196 2773 10 30 -2167 -1721 1376 30 70 3826 3328 2911 ic 40 2330 1879 -1527 30 80 3888 3395 2983 10 50 2467 2016 -1662 30 90 3914 3424 3015 10 60 2568 2121 1769 35 35 3278 2758 2329 10 70 2630 2187 -1838 35 40 3469 2945 2508 10 80 2659 -2219 1873 35 45 3645 3120 2680 10 90 2671 2233 1888 35 50 3800 -3276 2835 15 15 2005 1568 -1235 35 55 '393 1 "34" 2972 15 20 2132 -1683 1338 35 60 4038 j 3524 3088 15 25 2245 1787 1432 35 70 4184 i -3680 3252 15 30 2354 1890 1526 35 80 4255 '3758 3336 15 35 2455 -1986 1618 35 90 4285 -3793 3373 15 40 2548 -2088 1705 40 40 3697 3167 2723 IS 45 i * 26 34 -2163 1789 40 45 3911 338o 2931 15 50 -2711 -2241 1866 4050 4101 '3573 3123 15 60 2777 -2309 2832 -2367 1935 1995 40 55 40 60 4263 4396 3740 3879 3292 '3435 15 70 2909 -2449 2081 40 70 '4574 4070 3635 15 80 2946 -2489 2125 40 80 4659 4164 3736 J 5 90 2960 '2506 2143 40 90 4694 -4203 ! -3780 20 20 2281 -1819 1459 45 45 4167 i -3637 s -3183 20 25 2515 -1942 -1571 45 50 4402 -3875 3419 | 20 30 2545 -2064 1684 4555 4606 -4085 3632 20 35 -2666 -2181 1794 45 60 4774 1 -4261 3814 20 40 2778 229O 1898 45 70 5001 -4504 4069 20 45 2881 2392 1998 45 80 5109 -4623 4197 20 50 2972 2485 2091 45 90 5153 '4 6 72 4251 20 55 3051 2567 2174 50 50 4685 : -4162 3707 20 60 3118 -2637 2246 5055 4938 -4424 3973 20 70 -3212 2738 2352 50 60 5152 4648 4203 20 80 3260 2791 2410 50 70 '5445 4963 4534 20 90 3281 2814 2435 50 80 5586 -5211 4700 25 25 2571 2086 1702 50 90 5643 5182 4771 25 30 2725 1 -2230 1835 55 55 5247 '4744 4298 25 35 2868 -2368 1964 55 oo 5515 5026 4589 25 40 3000 -2497 2088 55 70 5897 5436 .5020 25 45 '3i2i I -2617 2205 55 80 6085 5642 5242 25 50 -3227 -2724 2312 1 55 90 6162 5729 '5337 25 55 -3318 i -2818 2407 60 60 5843 5372 4946 25 60 -3393 : -2897 2489 60 70 6333 -5898 55oi 25 70 -3498 '3 010 '2608 60 80 6586 '6177 5802 25 80 -3551 -3068 -2670 60 90 6693 6297 '5933 25 90 '3574 -3093 '2698 70 70 7061 6685 6335 30 30 -2905 -2400 1991 70 80 ' 7496 7165 6853 3 35 P 376 -2564 -2146 70 90 7700 7393 7105 30 40 -3235 -2719 -2295 80 80 1 -8l2 5 7862 7611 30 45 '3380 -2863 30 50 -3506 -2992 2436 2564 80 oo j 90 90 '8471 8 94 8 8231 87*9 8039 8634 For explanation see pp. 31, 32 (176) MOKTALITY TABLES TWO LIVES Annual Payment during the Continuance of either of Two Lives to secure 1 at the Last Death according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3% 3i % 4 % || Ages 3 % 31 % 4% 10 IO 0062 0053 0045 30 55 0165 0152 0141 10 20 0072 0062 0053 30 60 0171 0159 0148 10 30 0081 0070 0061 30 70 -0181 0169 0158 10 40 0088 0078 0069 30 80 0185 0174 0164 10 50 0095 0085 0077 30 oo 0187 0176 0166 10 60 oioi 0091 0083 35 35 0142 0129 0117 10 70 0104 0095 0087 35 40 0155 0141 0129 IO 80 0105 0096 0089 35 45 0167 oi53 0141 10 00 0106 0097 0090 35 50 0178 0165 0152 15 15 0073 0063 -0054 35 55 0189 0175 0163 15 20 0079 0068 -0059 35 60 0197 0184 0172 15 25 0084 0074 0064 35 70 -0209 0197 0185 15 30 0090 0079 0069 35 80 0216 0204 0193 15 35 0095 0084 0074 35 90 0218 0207 0196 15 40 oioo 0089 0079 40 40 0171 0157 0144 15 45 0104 0093 0084 40 45 0187 0173 0160 15 50 0108 -0098 0088 40 50 0203 0188 0175 15 55 oi 1 2 | -0102 -0092 40 55 0216 0202 0189 15 60 0115 0105 -0096 40 60 0228 0214 020 1 15 70 0120 ono oioi 40 70 0246 02 3 2 0220 15 80 0122 01 12 -0104 i 40 8O 0254 0241 0229 15 oo 0122 "0113 -0105 40 90 0258 0245 0234 20 20 0086 -0075 -0066 4545 0208 0193 Ol8o 20 25 OO93 '0082 '0072 45 50 0229 O2I4 0200 20 30 0099 -0088 -0078 4555 0249 0234 0219 20 35 'OIO6 'OO94 -0084 45 60 0266 0251 0237 20 40 01 12 '0100 -0090 45 70 0291 0277 0264 20 45 oi 18 0106 -0096 45 80 0304 0291 0278 20 50 0123 01 12 '0102 45 90 0310 0297 0284 20 55 0128 0117 -0107 1 50 50 0257 O24I 0227 20 60 0132 oi2i -oi 1 1 50 55 0284 0268 0254 2O 70 0138 -0127 -oi 18 ! 50 60 0310 0294 0279 20 80 OI4I '0131 'OI22 50 70 -0348 0333 0319 20 90 0142 -0132 j -0124 50 80 j -0369 0354 0341 25 25 oioi -0089 0079 50 90 0377 0364 0351 25 30 OIO9 -OO97 0086 5555 0322 0305 0290 25 35 0117 -0105 0094 55 60 0358 0342 0326 25 40 0125 -0113 oioi 55 70 0419 0403 0388 25 45 0132 -0120 0109 55 80 -0453 0438 0424 25 50 0139 -0127 -0116 55 90 -0468 0454 0440 25 55 0145 -0133 0122 60 60 -0409 0393 0376 25 60 0150 '0138 0127 60 70 -0503 0486 0470 25 70 0157 -0146 '0136 60 80 -0562 0546 0532 25 80 0160 -0150 -0140 60 90 "0590 0575 0561 25 90 0162 '0152 0142 70 70 -0700 0682 0665 30 30 0119 -0107 -0096 70 80 -0872 08 55 0838 30 35 0129 -0117 '0105 70 90 -0975 0959 0944 30 40 0139 | -0126 ! 'on 5 80 80 -1262 1244 1225 30 45 0149 ; -0136 -0124 80 90 -1613 1595 1577 3050 0157 -0144 -0133 oo 90 -2478 2454 2431 For explanation see pp. 31, 32 (177'; MOETALITY TABLES TWO LIVES 1 Value of the Reversion to a Perpetuity on the Death of the FIRST of Two Lives Ages NORTHAMPTON HEALTHY MALES Acres 3% 4% 5% 3% 34% 4% Ages 15 IS 18-113 11-589 8*036 13-467 10-208 7-957 15 15 20 20 19-200 12-465 8-768 14-752 11-316 8-919 20 20 25 25 19-950 ; 13*056 9-236 15-763 12-176 9-654 25 25 30 30 20-744 13-687 9-745 16-960 13-215 10-560 30 30 3535 21-611 . 14-388 10-320 18-238 14-338 11-550 35 35 40 40 22-569 15*180 10-984 19-623 15-572 12-652 40 40 45 45 1 23-557 : 16-010 | 1 1 -688 21-171 16-974 13-924 45 45 50 50 24-619 16-919 12-478 22-791 18*459 15-290 50 50 55 55 25-652 17-821 13-265 24-466 20-017 16-740 60 60 26-727 18-774 14-112 26-134 21-588 18-221 60 60 65 65 27-862 19-799 15-040 27-681 23-060 19-623 6565 70 70 29-072 20-913 16-070 29-111 24-434 20-944 70 70 75 75 30-219 80 80 31-211 21-985 22-932 17-083 17-982 30-346 31-285 25-632 26-549 22-107 23-003 7575 80 80 85 85 32-024 23-661 18744 31-931 27-184 23-627 8585 Value of the Reversion to a Perpetuity on the Death of the LAST of Two Lives Ages NORTHAMPTON HEALTHY MALES Ages 30/ /o 4% 5% 3% 34% 4% 15 15 9-318 4-829 2-784 6-883 4-636 3-210 15 15 20 20 10-190 5-469 3-218 7-830 5-378 3-793 2O 2O 25 25 1 1 -088 6-068 3-630 8-828 6-169 4-424 25 25 30 30 12-078 6751 4-111 9-972 7-096 5-178 30 30 35 35 13-179 7-534 4-676 11-254 8-155 6-056 35 35 40 40 14-401 8-426 5-342 12-691 9-366 7-078 40 40 4545 15-725 9-424 6-102 14-308 10755 8-275 45 45 So 50 17-175 io-553 6-984 16-084 12-309 9-638 50 50 60 60 18714 20-385 11-777 13-148 7-971 9-104 18*013 20*060 14-029 15-885 11-175 12-861 55 55 60 60 6565 22-196 14-639 10-408 22-149 17-810 14-637 6565 70 70 24-126 16*365 1 1 -884 24-243 19769 16-470 70 70 80 80 26 -049 27-893 18*053 19-782 13-429 14-988 26-198 27-897 21-622 18-228 23-250 19788 7575 80 80 8585 29-402 21-253 16-314 29-258 24-564 21-058 85 85 For explanation see p. 32 MORTALITY TABLES TWO LIVES Value of an Annuity during the Life of y after the Death of x NORTHAMPTON CARLISLE HEALTHY MALES Age of Age of X y 3% 3% 3% 3i% 4% 45 20 7-271 7-487 7-849 6-79 5-904 45 25 6-650 6711 7-025 6-126 5-366 45 30 5-998 5-906 6-136 5-397 4-766 45 35 5-315 5-102 5-225 4-639 4-132 45 40 4-612 4-275 4-314 3-868 3-479 60 20 10-042 11-912 12-392 10-940 9-702 60 30 8-544 10-027 10-382 9-284 8-332 60 35 7-711 9-023 9-233 8-316 7-513 60 40 6-822 7-919 8-006 7-265 6-6n 60 50 4-975 5 '574 5-410 4-990 4-612 75 30 12-157 14-343 15-008 13-665 12-486 75 40 10-191 12-028 12-389 11-422 10-557 75 75 7-964 9-281 5-588 5-993 9-281 6-003 8-672 8-117 5-688 5-395 75 70 3*135 3'3i9 3'i47 3-023 2-906 Value of an Annuity during the Life of ;/, who is to be nominated at the Death of x A rro r\i Age of 91 at NORTHAMPTON CARLISLE HEALTHY MALES ATG 01 X y &\i Death of x 3o/ /o 3% 3% 3i% 4% 45 10 12-393 12-473 12-994 10-762 8-998 45 25 10-763 11-024 11-387 9-564 8-094 45 30 10-253 10-460 10-782 9-103 7-740 45 35 9-690 9-888 10-120 8-59I 7-341 45 40 9-066 9-232 939I 8-018 6-888 60 10 14-863 16-308 I6-9I8 14-544 12-598 60 30 12-296 13-676 I4-038 12-302 10-837 60 35 11-621 12-929 I3-I77 11-610 10-279 60 40 10-873 12-071 12-228 10-836 9*644 60 50 9-218 10-181 10-021 8-989 8-091 75 10 I775I 19-863 20-708 18-340 16-348 75 75 30 So 14-685 1 1 -010 16-657 12-400 I7-I83 12-266 15-512 n-335 14-063 10-499 75 60 8-831 9-311 9-252 8-657 8-113 75 70 6-338 6-582 6-305 5-968 5-657 For explanation see p. 33 (179) MORTALITY TABLES-TWO LIVES Single Payment to secure 1 at the Death of x provided he dies before ?/, according to the NORTHAMPTON TABLE Ages 3% Ages 3 % jj A * es 3% x y x y x y 15 15 26366 50 20 47767 1 65 35 59587 20 10 30838 50 30 45221 65 40 57855 2O 2O 27962 50 40 41378 65 45 55766 25 15 31846 50 50 -35853 65 50 53073 25 25 29054 , 55 i5 53896 65 55 i 49904 30 10 36038 ! 55 25 51226 65 60 45822 30 20 32987 55 35 -48319 65 65 40576 30 30 30210 55 45 -43830 70 10 71527 35 15 -37643 55 55 '37357 70 15 70284 35 25 -34755 60 10 60306 70 20 68822 35 35 i -31473 60 20 57287 70 25 68087 40 10 -42717 60 30 55136 70 30 67236 40 20 '39579 60 40 W34 7 35 66139 40 30 36815 60 50 46567 7 40 64650 40 40 32868 60 60 38923 70 45 62843 45 15 45053 65 10 65695 70 50 60461 45 25 42208 65 15 64308 70 55 57691 45 35 38980 65 20 62784 70 60 54027 45 45 34306 65 25 61920 70 65 49029 50 10 50891 05 30 60899 70 70 42338 Single Payment to secure 1 at the Death of x provided he dies before ?/, according to the CARLISLE TABLE Ages 3 % Ages 3 % Ages 3% x y . , x y i 15 15 2101 50 20 4681 65 35 6236 20 10 '2503 50 30 4400 65 40 6088 20 20 -2234 50 40 -3965 65 45 5940 25 15 -2705 50 50 -3260 65 50 5644 25 2 5 2391 55 15 -5409 65 55 5137 30 10 3190 55 25 -5211 65 60 4534 30 20 2928 55 35 493i 65 65 3973 30 30 - 2 556 55 45 -4454 70 10 7276 35 15 '3427 55 55 -3528 70 15 7205 35 25 3136 60 10 -6147 7O 20 7161 35 35 2710 60 20 -5986 70 25 7082 40 10 3959 60 30 -5766 70 30 6986 40 20 3733 60 40 -5472 70 35 6908 40 30 40 40 3388 2891 60 50 60 60 4917 3792 70 40 7<> 45 6788 6692 45 15 -4 26 2 65 10 6673 70 50 6475 45 25 1 45 35 4018 65 15 -6592 70 55 3636 65 20 -6531 70 60 6034 5464 45 45 3052 65 25 -6439 70 65 4956 50 10 4880 i 65 30 -6332 70 70 4190 For explanation ee p. 34 (i8oj MOKTALITY TABLES TWO LIVES Single Payment to secure 1 at the Death of .? provided he dies before y, according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3% 3i% 4% Ages 3% 3i% 4% x y x y 15 15 1961 -1726 1530 45 15 4483 4091 3746 15 25 1638 1467 1322 45 20 '4343 3969 3638 15 35 1318 1204 1105 4525 4211 3856 3540 15 45 1014 0944 0882 45 30 4022 3693 3399 1555 0730 0690 0655 4535 3778 3480 3213 15 70 0359 0347 0336 45 40 3466 3207 2975 20 15 2326 '2IOI 1831 45 45 3083 2870 2678 20 20 2148 -1913 1715 45 55 -2217 2094 1982 20 30 1785 1 -1619 1475 45 70 -1068 1033 1000 2O 40 1412 i -1306 1212 50 15 -5045 4655 4307 20 50 I 06 1 '0999 0943 50 20 -4917 4541 4205 20 60 0744 -0713 068 3 ' 50 25 -4808 '4445 4120 20 7O 0476 -0461 0447 50 30 -4647 4303 3995 25 15 2662 -2358 2101 50 35 ; '4433 4115 3828 25 20 2482 -2209 1979 50 40 -4146 -3861 3603 25 25 2296 -2059 1857 50 45 3769 3524 3302 25 35 1860 -1697 1556 50 50 i -3319 i -3121 2940 25 45 1416 ! -1318 1231 50 60 -2303 -2196 2097 25 55 IOII 0959 0911 50 70 1388 1342 1300 2570 0520 0504 4 89 i 55 i5 5643 -5268 4925 30 15 3057 2720 2434 55 20 5524 -5160 4828 30 20 2881 -2574 2312 55 25 '5439 -5082 4758 30 25 2697 -2422 -2187 55 30 -5304 -4961 ! -4649 30 30 2470 -2234 2O3I 55 35 '5124 -4800 -4505 30 40 1955 -1799 1662 55 40 '4877 4579 ! -4305 30 50 1430 -1342 1262 55 45 4531 4266 4023 30 60 0970 i -0927 0886 55 50 -4092 -3868 -3661 30 70 0603 0585 0567 55 55 3563 -3384 i -3219 35 15 35 20 3486 3321 3123 2983 28II 2693 55 70 60 15 1850 -1790 6264 -5911 1734 5588 35 25 35 30 3148 -2841 2922 -2650 2573 2412 6O 20 "6154 60 25 -6086 5809 '5747 '5493 5436 35 35 2656 -2424 2221 60 30 -5976 5647 '5345 35 45 2039 1892 1762 60 35 "5832 -5516 5226 35 55 1426 1349 1277 60 40 -5630 5331 5057 35 70 -0705 -0683 0662 60 45 5332 5060 4808 40 15 '3956 40 20 -3804 3574 '3443 3243 3129 60 50 60 60 '4934 3806 4694 3650 447i 3504 40 25 -3651 33H 3019 60 70 i -2484 2409 2336 40 30 -3438 3132 -2864 70 20 7370 7098 6840 40 35 W4 -2905 2669 70 30 7263 6995 6744 40 40 -2858 2633 2433 70 40 7058 6803 '6563 4O SO -2121 -1986 40 60 -1408 -1342 1863 1280 70 50 ; '6598 70 60 -5681 6371 5503 6i55 '5335 40 70 -0844 i -0817 0791 70 70 -4239 -4131 '4028 For explanation see p. 34 (181) MORTALITY TABLES THREE LIVES Value of an Annuity for the Joint Continuance of Three Lives of Equal Ages according to the NORTHAMPTON TABLE Ages 4 % || Ages 4% Ages 4% IO IO IO 12-200 3O 30 3O 9-221 50 50 50 6-317 II II II 12-043 3i 31 3 1 9-099 5i 5 1 5i 6-161 12 12 12 11-865 32 32 32 8-975 52 52 52 6-on 13 13 13 1 1 -678 33 33 33 8-848 53 53 53 5-859 14 I 4 I 4 II-48I 34 34 34 8-718 54 54 54 5-705 15 15 15 1 1 -274 35 35 35 8-585 55 55 55 5-550 io 16 16 1 1 -056 36 36 36 8-448 c6 c6 56 5-393 17 17 17 10-845 37 37 37 8-309 57 57 57 5-235 18 18 18 10-656 38 38 38 8-165 58 58 58 5-076 19 19 19 IO-490 39 39 39 8-017 59 59 59 4-916 20 20 20 IO-342 40 40 40 7-865 60 60 60 4-755 21 21 21 IO-222 41 41 41 7-714 61 61 61 4-593 22 22 22 IO-II8 42 42 42 7-567 62 62 62 4-432 23 23 23 IO-OI2 43 43 43 7-423 63 63 63 4-263 24 24 24 9-905 44 44 44 7-276 65 65 65 3-9I4 26 26 26 27 27 27 9-796 9 -685 9-572 45 45 45 46 46 46 47 47 47 7-126 6-972 6-813 70 70 70 80 80 80 2-995 2-119 1-400 28 28 28 9*457 48 48 48 6-650 85 85 85 782 29 29 29 9'340 49 49 49 6-482 90 90 90 -563 Value of an Annuity for the Joint Continuance of Three Lives according to the CARLISLE TABLE Ages 3 % Ages 3 % A ^ es 3Q/ /o 025 3 I 26 31 8-460 9-684 25 50 55 ; 7-959 50 75 80 26 51 56 7-689 51 76 81 2-499 2-349 2 27 32 10-257 27 52 57 7-411 52 77 82 2-220 3 28 33 10-726 28 53 58 7-133 53 78 83 2-086 4 29 34 10-930 29 54 59 6-870 54 79 84 I-942 5 3 35 1 1 -056 30 55 60 6-626 55 80 85 I-796 6 31 36 1 1 -063 31 56 61 6-405 56 81 86 1-652 7 32 37 1 1 -009 32 57 62 6-183 57 82 87 530 8 33 38 10-910 33 58 63 5-959 58 83 88 437 9 34 39 10-780 34 59 64 5-734 59 84 89 334 io 35 40 ii 36 41 10-632 10-479 35 60 65 36 61 66 5-519 60 85 90 5-318 61 86 91 184 109 12 37 42 10-331 37 62 67 5-112 62 87 92 095 13 38 43 10-182 38 63 68 4-900 63 88 93 117 14 39 44 10-029 39 64 69 4-673 64 89 94 in 15 40 45 16 41 46 9-877 40 65 70 4-439 65 90 95 -064 9-732 41 66 71 4-192 ! 66 91 96 -055 17 42 47 9-588 42 67 72 3-953 67 92 97 070 18 43 48 9-438 43 68 73 3729 68 93 98 100 19 44 49 9-270 4469 74 3-520 69 94 99 08 1 20 45 50 21 46 5i 9-088 8-887 46 71 76 3-336 70 95 100 3-145 71 96 101 -946 756 22 47 52 23 48 53 8-676 8'454 47 72 77 2-971 | 72 97 102 48 73 78 2-806 73 98 103 509 230 24 49 54 8-215 49 74 79 2-637 i For explanation see p. 35 (182) MORTALITY TABLES THREE LIVES Value of an Annuity for the Joint Continuance of Three Lives of Equal Ages according to the INSTITUTE OF ACTUARIES HEALTHY MALES TABLE Ages 3% 34% 4% Ages 3 % 34 % 1 4 % u-534 10-633 9-850 50 8-621 8-320 8-036 I 16-013 14-760 13*669 51 8-312 8-030 7-764 2 I7-358 16-004 14-824 52 8-004 7-740 7-492 3 18-100 16-696 I5-470 53 7-696 7-45I 7-219 . 4 18-534 17-107 I5-859 54 7-389 7-l6l 6-945 e 18-833 17-393 16-134 55 7-085 6-873 6-673 6 19-006 17-567 16-305 56 6783 6-401 17 19-072 17-642 16-386 6-483 6-303 6-131 19-046 17-633 16-391 58 6-187 6-021 5-862 9 18-946 17-555 16-332 59 5-895 5-742 5-597 10 18-787 17-424 16-222 60 5-607 5-468 5-334 ii 18-589 17-257 16-079 6z 5325 5-197 5-075 12 18-361 17-060 15-910 62 5-048 4-931 4-820 13 18-110 16-843 15-720 63 4-777 4-671 4-569 14 17-846 16-612 64 4-416 4324 15 17-572 16-372 15-305 8 4-254 4-167 4-084 16 17-300 16-132 15-093 66 4-004 3-925 3-850 11 1 7 -030 16-773 15-895 15-669 14-884 14-683 67 68 376o 3-525 3-690 3-462 3-622 3-401 19 16-526 15-452 14-492 69 3-297 3-241 3-186 20 16-293 15-248 14-312 70 3-078 3-028 2-979 21 16-073 15-055 14-142 71 2-868 2-823 2-779 22 15-861 14-870 i3'979 72 2-665 2-626 2-587 23 15-656 14-691 13-823 73 2-472 2-437 2-402 24 15-453 14-514 13-668 74 2-287 2-256 2-226 25 15-251 14-337 I3'5i3 75 2'III 2-083 2-057 26 15-046 14-159 I3-356 76 1-943 1-919 896 27 I4-837 28 14*623 13-976 13-787 13-194 13-028 77 -784 78 -634 764 616 743 598 29 1 4 -404 13-593 12-857 79 492 476 460 30 I4-I79 13-394 12-681 80 358 '344 '33 1 31 I3-947 13-189 12-497 81 232 220 208 32 13-710 12-978 12-309 82 114 104 094 33 13-467 12-761 12-114 83 1-004 995 987 34 13-218 12-538 11-914 84 901 894 886 12-964 12-309 1 1 -708 85 806 '799 793 12-704 12-075 11-497 86 717 711 706 37 12-439 11-836 11-280 87 635 630 626 38 12-167 11-590 11-057 88 '559 *555 '55 1 39 1 1 -892 "339 10-829 89 490 486 483 40 11-612 1 1 -084 10-596 00 425 423 420 11-327 10-824 10-358 ! 91 368 366 363 42 1 1 -037 iQ-559 10-115 92 317 315 3i3 43 10-746 10-291 9-868 93 266 264 263 44 10-449 10-018 9-616 94 226 225 224 45 10-150 9-742 9-360 95 187 186 185 46 9-847 9-462 9-101 96 157 157 156 47 9-543 9-180 8-839 97 146 145 145 48 9-237 8-895 8-573 98 112 '112 | -III 49 8-930 8-608 8-305 99 087 086 -086 100 -015 015 015 For explanation see p. 35 MORTALITY TABLES THREE LIVES Value of an Annuity during the Longest of Three Lives according to the NORTHAMPTON TABLE Ages 3% 4% Ages 3% 4% 10 10 10 26-642 21-938 20 40 40 22-762 19-259 10 10 30 25-812 2 1 -400 2O 40 60 21-697 18-582 10 10 50 25-340 20-835 20 45 45 22-008 18741 10 10 70 25-007 20-78I 20 45 65 21-123 18-134 10 2O 2O 25707 2I-263 20 50 50 21-396 18-380 10 20 40 24-645 2O '606 20 50 70 20-594 17704 10 20 60 24-292 20-333 20 55 55 20-948 18-013 10 25 25 25-077 20-944 20 55 75 20-273 i 17350 10 25 45 24-401 20-49I 20 00 60 20-491 17-671 10 25 65 23-905 20-077 20 65 65 19-983 17-242 10 30 30 24785 20-635 20 70 70 19-606 16-916 10 30 50 23-780 2O -O2 1 30 30 30 23-266 19-625 10 30 70 23-472 19746 30 30 50 21-896 18793 10 35 35 24-217 20-380 30 30 7 21-376 18-357 10 35 55 23-251 19-628 30 35 35 22-485 19-250 10 35 75 23-029 I9-426 30 35 55 21-141 18-233 10 40 40 23-746 19-851 30 35 75 20-713 17-887 10 40 60 22-878 I9-35I 30 40 40 21-814 18-628 10 45 45 23-271 I9-495 30 40 60 20-570 17-815 10 45 65 22-462 I9-035 30 45 45 21-062 18-241 10 50 50 22-647 I9-202 30 45 65 19-902 17-298 10 50 70 22-028 18-664 30 50 50 20-227 17-585 10 55 55 22 '34i 18-958 30 50 70 19-267 16-783 J o 55 75 21768 18-484 ! 30 55 55 19-670 17-164 10 60 60 22-004 18705 30 55 75 18-651 16-263 10 65 65 21-464 18-225 30 60 60 19-107 16708 10 70 70 21-308 18-110 30 65 65 18-251 i5'97i 15 25 25 24773 20-776 30 70 70 18-045 15-805 15 25 45 23-932 20-192 40 40 40 20-909 17-996 i5 25 65 23-375 19723 40 40 60 19-414 16-997 15 35 35 23-738 20-078 40 45 45 20-011 I7'50I i5 35 55 22-687 19-263 40 45 05 18-601 16-364 15 35 75 22 -407 19-007 40 50 50 19-020 16-731 *5 45 45 22-681 19-114 40 50 70 17-817 15736 i5 45 65 21783 18-581 40 55 55 18-291 16-174 15 55 55 21-639 18-508 40 55 75 17-264 ! 15-303 15 55 75 15 65 65 2I-032 207I 17-984 ! 17-800 40 60 60 40 65 65 17-567 15-590 16-583 14-747 20 20 20 25-I52 20-836 40 70 70 16-237 14-464 20 20 40 23-941 20-185 50 50 50 17-913 15-866 20 20 60 23-372 19-740 50 50 70 16-358 i 14-633 20 25 25 24-430 20-557 50 55 55 16-953 15-165 20 25 45 20 25 65 23-488 22-867 19-904 19-369 So 55 75 50 60 60 15-618 14-040 15-994 14-394 20 30 30 23-980 20-116 50 65 65 14-823 13-398 20 30 50 22-795 19-390 So 70 70 14-269 12-935 20 30 70 22-390 19-045 60 oo 60 14-602 I3" r 94 20 35 35 23-282 19782 60 65 65 13-163 12-065 20 35 55 22-129 18-900 60 70 70 12-280 11-319 20 35 75 21-805 18-602 70 70 70 10-540 9-817 For explanation see p. 35 (184) CONVERSION TABLES Single Premium Conversion Table for Finding by Inspection the Present Value of 1 due at Death from the Value of an Annuity for Life Value of 1 at Death Value of Annuity 2k % 3% 3i / 2 /O 4% 5% 97561 97087 96618 96154 95238 I 95122 94175 93237 92308 -90476 2 92683 91262 89855 88462 -85714 3 90244 88350 -86473 84615 -80952 4 87805 85437 -83092 80769 -76190 5 85366 82524 -79710 76923 -71429 6 82927 79612 -76329 73077 -66667 7 80488 76699 -72947 69231 -61905 8 78049 73786 -69565 65385 -57143 9 75610 70874 -66184 61538 -52381 10 73171 67961 -62802 57692 -47619 ii -70732 65049 -59420 53846 -42857 12 68293 62136 '56039 50000 -38095 13 65854 59223 -52657 46154 -33333 14 63415 563" *49275 42308 -28571 !5 60976 53398 -45894 38462 -23810 16 58537 50485 -42512 34615 -19048 17 56098 47573 -39130 30769 -14286 18 53659 44660 '35749 26923 -09524 19 51220 41748 32367 23077 -04762 20 48780 38835 -28986 19231 -ooooo 21 46341 35922 -25604 15385 22 43902 33010 -22222 11538 23 41463 30097 -18841 07692 2 4 39024 27184 -15459 03846 3 36585 34146 24272 -12077 21359 -08696 ooooo 27 31707 18447 -053 H ... 28 29268 15534 -01932 ... 2 9 26829 I262I ! ... Difference (subtractive) of Value of 1 at Death Difference of Annuity 2i% 3% 3i% 4% 5% I -00244 -0029! 00338 00385 00476 2 -00488 -00583 -00676 00769 00952 '3 -00732 -00874 -OIOI4 01154 01429 4 -00976 -01165 01353 01538 01905 '5 -01220 '01456 01691 01923 02381 6 '01463 -01748 02029 02308 02857 7 -01707 -02039 02367 02692 03333 8 -01951 -02330 02705 03077 03810 9 o2io<; -02621 03043 03462 04286 For explanation see pp. 35-39 (185) CONVEESION TABLES Annual Premium Conversion Table for Finding by Inspection the Annual Premium to secure 1 at Death from the Value of an Annuity for Life. INTEEEST 3 PEK CENT. Value of Annuity Annual Premium Decimals of Value of Annuity o I 2 '3 '4 5 6 7 8 9 o- 0-9 -9709 8800 8042 7401 -6852 6375 '5959 559i 5264 4972 I- i '9 '4709 4471 4254 -4057 ! -3875 3709 3555 3412 3280 '3*57 2- 2'9 '3042 2935 -2834 2739 -2650 2566 2487 2411 2340 2273 3_ 3-9 -2209 2148 -2090 -2034 -1981 -1931 1883 1836 1792 1750 4- 4*9 -I 709 1670-1632 -1596 -1561 -1527 1494 1463 1433 "1404 5- 5'9 * I 375 1348 -1322 1296 -1271 1247 1224 1201 1179 ' -1158 6- 6-9 -1137 III7 -1098 -1079 *i 060 -1042 1025 1007 -0991 i -0975 7- 7-9 '0959 0943 0928 0914 i -0899 -0885 0872 0858 0845 -0832 8- 8-9 -0820 0808 0796 0784 -0773 -0761 0750 0740 0729 0719 9- 9*9 '0709 0699 0689 0680 -0670 0661 0652 0643 0635 0626 10-10-9 -0618 O6l0 O6O2 0594 i -0586 0578 0571 0563 0556 0549 11-11*9 '0542 0535 0528 0522 -0515 i -0509 0502 0496 0490 0484 12-12 '9 1 '0478 0472 0466 0461 ; -0455 0449 0444 0439 0433 0428 I3-I3'9 '4 2 3 0418 0413 0408 -0403 0398 0394 0389 0384 0380 14-14-9 | -0375 0371 0367 0362 0358 0354 0350 0346 0342 0338 I 5- I 5'9 0334 0330 0326 0322 0318 0315 0311 0308 -0304 0300 16-16*9 0297 0294 0290 0287 0283 0280 0277 0274 -0271 0267 17-17-9 0264 O26l 0258 0255 -0252 0249 0246 0243 0241 0238 18-18-9 0235 O232 0230 0227 O224 O222 0219 O2l6 0214 02 1 1 19-19-9 0209 0206 0204 O2OI 0199 0197 0194 OI92 0190 0187 20-20-9 Ol8 5 Ol8 3 Ol8o 0178 0176 -0174 0172 OI7O 0167 0165 21-21-9 0163 0161 0159 0157 0155 -0153 0151 0149 0147 0145 22-22-9 0144 0142 0140 -0138 0136 -OI34 0132 0131 0129 -0127 23-23-9 0125 OI24 -OI22 -OI2O OII9 -OH7 0115 0114 01 12 -OIIO 24-24-9 OIC9 OIO7 OIO6 -OIO4 OIO2 "OIOI 0099 0098 0096 j -0095 25-25-9 0093 0092 0090 -0089 0088 -0086 0085 0083 0082 -0080 +J *J S 26-26-9 0079 0078 0076 -0075 0074 -0072 0071 0070 -0068 i -0067 27-27-9 0066 0065 0063 OO62 006l '0060 0058 0057 0056 0055 28-28-9 0054 OO52 0051 0050 0049 -0048 0047 0045 0044 0043 29-29-9 0042 OO4I -0040 0039 -0038 i -0037 0036 0034 0033 0032 30-30-9 0031 OO3O 0029 -0028 ! -0027 -0026 0025 OO24 0023 0022 3i-3!*9 0021 002O -0019 -0018 -0017 -0016 -0015 0015 0014 0013 32-32-9 0012 OOII *OOIO '0009 -0008 -0007 -0006 0005 0005 0004 33-33'9 0003 0002 '0001 -OOOO ! For interest at I I* i-l if per cent. add 0192 0168 0143 0119 For interest at 2 2i l 2f add 0095 0071 0047 0024 For interest at 3 3* 3^ 3f subtract oooo 0024 0047 0070 For interest at 4 4* 41 4t subtract 0093 oi 16 0139 0162 For interest at 5 6 7 8 subtract 0185 0275 0363 0449 For explanation see pp. 35-39 (186) RATES FOE ANNUITIES AND ASSURANCES CHAKGES BY GOVERNMENT AND BY BRITISH LIFE OFFICES For explanation see pp. 39, 40 187 POST OFFICE ANNUITIES COST OF IMMEDIATE LIFE ANNUITIES OF 1 Age Age Next Birth- Males Females Next Birth- Males Females day day s. d. 5. d. s. d. \ *. d. 6 25 19 o 27 12 6 4 6 16 9 ii 18 6 9 7 25 15 I 27 9 i 47 16 4 2 1800 8 25 ii i 27 5 8 48 15 18 3 17 13 2 9 25 7 o 27 2 2 49 15 12 3 17 6 i 10 25 2 ii 26 18 8 50 15 6 i 16 18 ii ii 24 18 10 26 15 i 51 14 19 ii 16 ii 9 12 24 14 9 26 ii 6 52 H 13 6 16 4 7 13 24 10 6 26 7 10 53 14 7 i 15 17 4 M 24 6 4 26 4 i 54 i 14 o 5 15 9 ii 15 24 2 i 26 o 4 55 13 13 8 15 2 4 Id 23 17 10 25 16 6 56 13 6 9 14 14 9 11 23 13 6 23 9 i 2 5 12 7 i 57 12 19 8 25 8 8 58 12 12 5 14 6 ii 13 19 o 19 20 23 4 9 23 o 4 25 4 8 59 12 4 ii 13 ii i 25 o 8 60 ii 17 4 13 3 i 21 22 15 10 24 16 6 61 ii 9 8 12 15 i 22 22 II 4 24 12 4 62 ii 2 2 12 7 o 23 22 6 9 24 8 i 63 10 14 ii ii 19 o 2 4 22 2 3 24 3 10 64 10 7 8 ii ii o 25 21 17 7 23 19 5 i 65 IOO6 II2II 26 21 12 II 23 15 o 66 9 13 4 10 14 7 27 21 8 3 23 10 6 67 964 10 6 4 28 21 3 6 23 5 ii 68 8 19 7 9 18 i 29 20 18 9 23 i 3 69 8 12 10 9 9 10 30 20 13 II 22 l6 6 70 862 9 i 10 31 20 9 I 22 II 8 7i 7 19 5 8 14 2 32 20 4 2 22 6 9 72 7 12 10 8 6 10 33 19 19 2 22 I 9 73 764 7 19 10 34 19 14 2 21 16 7 74 7 o i 7 13 o 35 19 9 2 21 ii 5 75 6 14 i 764 36 19 4 I 21 6 2 76 684 6 19 10 ii 18 18 ii 18 13 9 21 9 20 15 3 8 628 5 17 4 6 13 7 6 7 5 39 40 18 8 6 20 9 7 18 3 2 20 3 ii B 5 12 3 572 6 i 6 5 15 9 4i 17 17 10 19 18 o 81 42 17 12 4 19 12 i or 524 5 10 3 43 17 6 10 19 5 ii over 44 17 i 4 18 19 8 45 16 15 8 18 13 3 | For explanation Bee pp. 39, 40 (189) POST OFFICE ANNUITIES COST OF DEFEEEED LIFE ANNUITIES. Money Eeturnable Age Next Birthday Years Deferred Annual Payment Single Payment Males Females Males Females s. d. s. d. s. d. s. d. 10 10 I 16 II 202 17 19 7 19 II I IO 20 15 3 l6 10 12 12 7 13 18 7 IO 30 o 7 ii o 8 10 8 13 2 9 12 7 IO 4 045 o 4 ii 5 14 o 6 6 3 10 50 025 028 3 9 i 3 16 7 15 10 i 15 i i 18 5 17 i 10 18 14 6 15 2O o 14 4 o 15 ii ii 17 6 13 3 4 15 3<> 074 082 8 o i 8180 15 40 o 3 ii 044 5 i n 5 12 8 15 50 020 023 2 18 4 3 4 10 20 IO I I 3 2 i 16 7 16 3 4 17 16 7 20 20 o 13 5 o 14 ii ii i 7 12 6 6 20 30 068 075 760 8 i 7 20 35 o 4 10 054 5 15 4 6 7 5 20 40 o 3 5 o 3 10 4 8 5 4 18 o 20 45 025 028 360 3 13 5 25 10 i ii 3 i 14 7 15 4 o 16 17 o 25 20 o 12 5 o 13 9 10 4 10 ii 7 10 25 25 086 095 8 5 2 9 2 10 25 30 060 067 6 10 6 742 25 35 042 048 500 5 10 ii 25 40 o 2 ii o 3 3 3 H 8 4 3 o 30 10 192 i 12 5 H 3 9 15 15 6 30 15 o 17 4 o 19 4 ii ii 9 12 17 9 30 20 o ii 4 O 12 6 9 6 10 10 6 10 30 25 078 085 777 8 3 i 30 30 052 059 5 13 2 6 5 5 30 35 036 o 3 ii 446 4 13 ii 30 40 o 2 5 028 3 i ii 3 7 9 35 10 i 6 ii i 9 ii 13 2 3 14 ii 7 35 15 o 15 10 o 17 6 10 ii 4 II 14 35 20 10 I II 2 870 946 35 25 068 074 680 7 i ii 35 30 045 o 4 ii 4 15 7 5 6 3 35 35 2 II 033 3 10 o 3 16 8 40 IO i 4 7 i 7 2 II 19 2 13 4 10 40 i5 O 14 2 o 15 8 9 8 ii 10 8 9 40 20 089 099 7 4 10 807 40 25 o 5 7 063 5 8 2 603 40 30 038 040 3 19 3 469 45 10 I 2 i 4 3 10 13 9 ii 16 3 45 i5 12 3 o 13 7 8 3 10 9 i 8 45 20 075 083 624 6 16 o 45 25 048 o 5 i 498 4 18 i 50 10 o 19 i i i i 955 10 5 6 5 15 o 10 5 o ii 6 6 18 5 7 13 ii 50 20 062 069 5 i 5 5 ii o 55 IO o 16 i o 17 ii 7 16 8 8 14 i IS 087 095 5 H 9 6 5 7 60 10 o 13 4 o 14 7 6 9 10 7 2 i For explanation see pp. 39, 40 (190) POST OFFICE ANNUITIES COST OF DEFERRED LIFE ANNUITIES. Money not Returnable Age Next Birthday Years Deferred Annual Payment Single Payment Males Females Males Females *. (I. *. d. *. d. s. d. 10 10 I 15 I i 18 6 16 ii 10 18 6 7 10 20 o 13 7 o 15 4 10 9 8 12 I 2 10 30 065 076 650 7 " 3 zo 40 031 o 3 10 386 4 8 i 10 50 015 I 10 I 12 9 2 4 II 15 IO I I 3 I i 16 9 15 ii 10 17 8 8 15 20 12 6 o 14 5 9 ii 10 ii 46 15 30 059 o 6 10 5 10 i 6 16 3 15 40 028 034 2 l6 II 3 15 o 15 50 I I o i 5 I 4 2 i H 5 20 10 I II I i 14 10 14 10 ii 16 9 6 20 20 o ii 6 o 13 4 8 13 5 10 6 8 20 30 050 o 6 i 4 15 i 603 20 35 034 042 372 479 20 40 022 029 254 3 i 4 20 45 OI4 019 i 8 7 204 25 10 I 8 II I 12 9 13 9 4 15 8 10 25 20 o 10 4 12 2 7 H 7 976 25 25 068 080 5 13 o 7 i 4 25 30 044 054 3 19 10 532 25 35 029 035 2 13 ii 3 12 i 2 5 40 o i 8 022 i 13 ii 274 30 10 i 6 9 i 10 6 12 6 10 14 6 5 30 15 o 15 i o 17 6 9 5 i II I 2 30 20 093 O IO II 6 15 4 869 30 25 059 070 4 15 8 6 i 8 30 30 037 045 347 4 5 o 30 35 022 029 208 2 15 10 30 40 012 o i 7 i 3 o i 13 7 35 10 i 4 5 i 8 o 1136 I 3 2 I 35 '5 o 13 6 o 15 9 8 3 4 9 17 7 35 20 080 096 5 15 6 742 35 25 o 4 10 o 5 10 3 18 o 59 35 30 O 2 IO 036 2 9 i 3 6 2 35 35 o i 6 020 i 7 9 i 19 9 40 10 I 2 i 5 3 9 19 2 ii 15 3 40 15 O II IO o 13 10 7 o 10 8 ii 8 40 20 069 080 4 15 i 600 40 25 o 3 10 048 2 19 10 3 18 10 40 30 020 027 i 13 10 274 45 10 o 19 4 122 8 13 7 10 5 6 45 15 10 II 8 5 17 2 737 45 20 054 065 3 13 9 4 H 4 45 25 029 035 2 I 8 2 16 8 50 IO o 16 7 o 18 ii 7 6 3 8 13 o 50 15 080 095 4 12 o 5 13 8 50 20 o 3 n o 4 10 2 12 3 8 3 55 IO o 13 5 o 15 5 5 16 5 6 19 o g 15 10 o 5 ii 10 072 II 10 359 446 435 5 3 " For explanation see pp. 39, 40 (190 POST OFFICE ASSURANCES SINGLE PREMIUMS FOR LIFE ASSURANCE FOR 100 Age at Entry Sum Assured Payable Age at Entry At Death In 10 Years In 15 Years In 20 Years .s. rf. . d. s. d. *. rf. 16 37 5 o 80 4 6 71 13 o 64 7 o 16 I? 18 37 19 6 38 13 6 80 5 6 80 6 6 71 14 6 71 16 6 64 9 6 64 12 o \l 19 39 6 6 80 7 6 71 17 6 64 13 6 19 20 39 J 9 o 80 8 o 71 18 6 64 15 o 20 21 40 ii o 80 8 o 71 19 o 64 16 o 21 22 | 41 3 80 8 6 71 19 6 64 17 o 22 23 41 15 80 8 6 72 o o 64 17 6 23 24 42 7 6 80 8 6 72 o 6 64 19 o 24 25 43 i o 80 9 o 72 i o 65 o o 25 26 43 H 6 80 9 6 72 2 o 65 i 6 26 27 44 8 6 80 10 o 72 3 o 65 3 6 27 28 45 2 6 80 10 6 72 4 o 6 5 5 o 28 29 45 17 o 80 ii o 72 5 o 65 7 o 29 30 46 ii 6 80 ii 6 72 6 o 65 8 6 30 3i 47 6 o 80 ii 6 72 7 o 65 10 6 31 32 48 i o 80 12 6 72 8 o 65 12 6 S 2 33 48 16 o 80 13 o 72 9 6 65 15 o 33 34 35 49 ii 6 50 7 6 80 13 6 80 14 o 72 10 6 72 12 65 17 o 66 o o 34 35 36 5i 3 6 80 14 6 72 13 6 66 2 6 36 51 19 6 80 15 o 72 15 o 66 5 6 37 38 52 16 o. 80 16 o 72 16 6 66 8 6 38 39 53 13 80 16 6 72 18 6 66 ii 6 39 40 54 10 o 80 17 6 73 o 6 66 15 6 40 4 1 55 7 o 80 18 o 73 2 6 66 19 o 4 1 42 56 5 o 80 19 o 73 5 o 67 3 6 42 43 57 3 o 81 o 6 73 7 6 67 8 6 43 44 58 i 6 8l 2 73 I0 6 67 14 o 44 45 59 o 6 81 3 o 73 *4 o 67 19 6 45 46 59 19 6 81 5 o 73 17 o 68 6 o 46 47 60 18 6 81 6 6 74 i o 68 12 6 47 48 61 17 6 81 8 o 74 5 o 68 19 6 48 49 62 17 o 81 10 o 74 9 o 69 7 o 49 50 63 16 6 8l 12 74 13 6 69 14 6 50 51 64 16 o 81 14 o 74 18 6 70 3 o 5i 52 65 16 o 81 16 6 75 4 o 70 12 6 52 53 66 16 o 81 19 o 75 9 6 71 2 o 53 54 67 16 o 82 2 75 16 o 71 12 6 54 55 68 16 6 82 5 o 76 3 o 72 4 o 55 56 69 16 6 ... 56 i 70 17 o 71 17 6 ::: ::: ... 58 72 18 o 73 18 o ::: ::: ::: g 61 74 18 o .. . ... 61 62 75 18 o 62 63 76 18 o ... ... 63 64 77 17 o .. ... ... 64 65 78 16 6 ... ... 65 For explanation see pp. 39, 40 (192) POST OFFICE ASSURANCES SINGLE PREMIUMS FOR LIFE ASSUBANCE FOR 100 Age at Entry Sum Assured Payable Age at Entry In 25 Years In 30 Years In 35 Years In 40 Years s. d. a ** 1,030 1,040 1,050 21 9 2 21 13 4 21 17 6 25 15 o 26 o o 26 5 o 30 o 10 30 6 8 30 12 6 34 6 8 34 13 4 35 o o 38 12 6 39 o o 39 7 6 I, O60 22 I 8 26 10 o 30 18 4 35 6 8 39 15 1,070 1,080 22 5 10 22 10 22 14 2 26 15 o 27 o c 27 5 o 3i 4 2 31 10 o 3i 15 10 35 13 4 36 o o 36 6 8 40 2 6 40 10 o 40 17 6 I,IOO 22 l8 4 27 10 o 32 i 8 36 13 4 41 5 o 1,110 23 2 6 | 27 15 o 32 7 6 37 o o 41 12 6 1,120 21 6 8 28 o o 32 13 4 37 6 8 42 o o 1,130 j 23 10 10 28 5 o 32 19 2 37 13 4 42 7 6 1,140 1,150 23 15 o 23 19 2 28 10 o 28 15 o 33 5 o 33 10 10 38 o o 38 6 8 42 15 o 43 2 6 1,160 24 3 4 29 o o 33 16 8 38 13 4 43 1 1,170 24 7 6 29 5 o 34 2 6 39 o o 43 17 6 1,180 24 ii 8 29 10 o 34 8 4 39 6 8 44 5 1,190 24 15 10 29 15 34 14 2 39 13 4 44 12 6 1,200 25 o o 30 o o 35 o o 40 o o 45 o o I,2IO 25 4 2 30 5 o 35 5 10 40 6 8 45 7 6 I,22O 25 8 4 30 10 o 35 ii 8 40 13 4 45 15 o 1,230 25 12 6 30 15 o 35 17 6 41 o o 46 2 6 1,240 25 16 8 3100 36 3 4 41 6 8 46 10 o 1,250 26 o 10 31 5 o 36 9 2 4i 13 4 46 17 6 I,26O 26 5 o 31 10 o 36 15 42 o o 47 5 o 1,270 26 9 2 31 J 5 o 37 o i 42 6 8 47 12 6 1,280 26 13 4 32 o o 37 6 8 42 13 4 48 o o 1,200 26 17 6 i 32 5 o 37 12 6 43 o o 48 7 6 1,300 27 i 8 32 10 o 37 18 4 43 6 8 48 15 o I,3IO 27 5 10 32 15 o 38 4 2 43 13 4 49 2 6 1,320 27 10 o 33 o o 38 10 o 44 o o 49 10 o 1,330 27 14 2 33 5 o 38 15 10 44 6 8 49 17 6 1,340 27 18 4 33 10 o 39 i 8 44 13 4 50 5 o 1,350 28 2 6 33 15 o 39 7 6 45 o o 50 12 6 1,360 28 6 8 34 o o 39 13 4 45 6 8 51 o o 1,370 28 10 10 34 5 39 19 2 45 13 4 5i 7 6 1,380 28 15 o 34 10 o 40 5 o 46 o o 51 15 o 1,390 28 19 2 34 15 40 10 10 46 6 8 52 2 6 1,400 29 3 4 35 o o 40 16 8 46 13 4 52 10 o 1,410 29 7 6 35 5 41 2 6 47 o o 52 17 6 1,420 29 ii 8 35 10 o 41 8 4 47 6 8 53 5 o 1,430 29 15 10 35 15 o 41 14 2 47 13 4 53 12 6 1,440 30 o o 36 o o 42 o o 48 o o 54 o o 1,450 30 4 2 36 5 o 42 5 1 48 6 8 54 7 6 1,460 30 8 4 36 10 o 42 ii 8 48 13 4 54 15 o 1,470 30 12 6 36 15 o 42 17 6 49 o o j 55 2 6 1,480 30 16 8 37 o o 43 3 4 49 6 8 55 10 o 1,490 31 o 10 37 5 o 43 9 2 49 13 4 55 17 6 1,500 3i 5 o 37 10 o 43 15 o 50 o o 56 5 o For explanation see p. 40 (202) INCOME TAX TABLES 1,510 2,000 Income TAX THEREON AT PER 5d. Qd. Id. Bd. Qd. s. d. *. d. 5. d. *. d. *. d. 1192 37 15 o 44 o 10 50 6 8 56 12 6 1^520 1,530 1,540 O s 31 13 4 31 17 6 32 i 8 38 o o 38 5 o 38 10 o 44 6 8 44 12 6 44 18 4 50 13 4 51 o o 51 6 8 57 o o 57 7 6 57 15 o 32 5 10 38 15 o 45 4 2 51 13 4 58 2 6 1,560 1,570 32 10 o 32 14 2 39 o o 39 5 45 10 o 52 o o 45 15 i 52 6 8 58 10 o 58 17 6 u/ 1,580 32 18 4 39 10 o 46 i 8 52 13 4 59 5 o 1,590 1, 600 33 2 6 39 15 o 33 6 8 40 o o 46 7 6 46 13 4 53 6 8 59 12 6 60 o o 1,610 33 10 10 40 5 o 46 19 2 53 13 4 60 7 6 1,620 33 15 o 40 10 o 47 5 o 54 o o 60 15 o 1,630 33 19 2 40 15 47 10 10 54 6 8 61 2 6 1,640 34 3 4 41 o o 47 16 8 54 13 4 61 10 o 1,650 34 7 6 4i 5 o 48 2 6 55 o o 61 17 6 1,660 34 ii 8 41 10 o 48 8 4 55 6 8 62 5 o 1,670 34 15 10 4i 15 48 14 2 55 13 4 62 12 6 1,680 35 o o j 42 o o 49 o o 56 o o 63 o o 1,690 35 4 2 i 42 5 o 49 5 i 56 6 8 63 7 6 1,700 35 8 4 42 10 o 49 ii 8 56 13 4 63 15 o 1,710 35 12 6 42 15 o 49 17 6 57 o o 64 2 6 1,720 35 16 8 43 o o 5 3 4 57 6 8 64 10 o 36 o 10 43 5 5 9 2 57 13 4 64 17 6 IJ740 36 5 o 43 10 o 50 15 o 58 o o 65 5 o 36 9 2 43 15 o 51 o 10 58 6 8 65 12 6 1,760 1,770 36 13 4 36 17 6 44 o o 44 5 5i 6 8 51 12 6 58 13 4 59 o o 66 o o 66 7 6 1,780 37 i 8 44 10 o 51 18 4 59 6 8 66 15 o 1,790 37 5 10 44 15 52 4 2 59 13 4 67 2 6 1,800 37 10 45 o o 52 10 o 60 o o 67 10 o 1,810 1,820 37 14 2 37 18 4 45 5 o 45 10 o 52 15 10 53 i 8 60 6 8 60 13 4 67 17 6 68 5 o 1,830 38 2 6 45 15 o 53 7 6 6100 68 12 6 1,840 38 6 8 46 o o 53 13 4 61 6 8 69 o o 1,850 38 10 10 46 5 o 53 19 2 61 13 4 69 7 6 1,860 38 15 o 46 10 o 54 5 62 o o 69 15 1,870 3 8 19 2 46 15 o 54 10 10 62 6 8 70 2 6 1,880 39 3 4 47 o o 54 16 8 62 13 4 70 10 o 1,890 39 7 6 47 5 o 55 2 6 63 o o 70 17 6 1,900 39 ii 8 47 10 o 55 8 4 63 6 8 7i 5 o 1,910 39 15 10 47 15 o 55 14 2 63 13 4 71 12 6 1,920 40 o o 48 o o 56 o o 64 o o 72 o o 1,930 1 40 4 2 48 5 o 56 5 10 64 6 8 72 7 6 1,940 40 8 Ji 48 10 o 56 ii 8 64 13 4 72 15 o i,950 40 12 48 15 o 56 17 6 65 o o 73 2 6 1,960 40 16 8 49 o o 57 3 4 65 6 8 73 10 o 41 o 10 49 5 57 9 2 65 13 4 73 17 6 1,980 4i 5 o 49 10 o 57 15 66 o o 74 5 1,990 41 9 2 49 15 o 58 o 10 66 6 8 74 12 6 2,000 4i 13 4 50 o o 58 6 8 66 13 4 75 o o (203) INCOME TAX TABLES 2,050-5,000 Income TAX TI IEREON AT PER 5d. 6d. Id. Sd. Qd. & s. d. i. sothat i+/= 1-03583 = log 0-0152899 (p. 320) = log 0-0152899 x 22 = log -3363778 987= log 2 -9943 1 72 =l g 2-9943172 (p. 264) I-03583 22 x 987 = log Present Value of On p. 10 we showed that v= l , where v is the present value of i, and "=(- \ , where n represents the term. Hence to obtain the present value of i due at the end of any number of years we subtract the log of (i+/) w from the log of i". Thus, suppose we require to know the present value of i due at the end of 20 years at 5%, we have (i +/')" = i-o5 20 = log -021189 x 20 = log 0-42378 to be subtracted from i" = log o-oooooo. Now log o-oooooo log 0*42378 = log 1-57622 = -3769, this agreeing with the result given in the interest tables on p. 74. The log of (i +*)" is obtained from the columns headed log r" on p. 299, and by sub- tracting the logarithm there given from the log of i we obtain the logarithm of the present value of i due at the end of n years. Further examples are appended. What is the present value of i due at the end of 22 years at 4l%? From p. 298 we see that log (i + t)"= log f" 0-4547834. v n =- l --\ =log o-ooooooo - log o-4547834 = log 7-5452166 What is the present value of i due at the end of 47 years at 2|%? This equals log o'ooooooo log 0-4791140 (p. 278)=log 1-5208860 = -33181. What is the present value of i due at the end of 30 years at ? (218) ANNUITY WHICH i WILL PURCHASE This rate of interest is equivalent to 3-0625, and is not tabulated, so we must find from the table on p. 230 the logarithm of 1-030625, multiply by 30, and subtract it from the logarithm of i. i = log o'oooooo i -0306253 = log -0131007 X3o = log -393021 5,= log r 606979 =^-40456 What is the present value of i due at the end of 25 years at 3$%? This rate of interest also is not tabulated, but the logarithm corresponding to i + / when / is at the rate of 3-?; % is given in the column log r, p. 320. It is there seen to be 0-0163368. Multiplying this by 25 we have log 0-40842, which, subtracted from log i, leaves log 1-59158, corresponding to '39046. Annuity which i will Purchase On pp. 1 6 and 17 we explain the Sinking Fund Tables given on pp. 106-115. It is there shown that the Sinking Fund is obtained by dividing unity by the amount of i per annum. It is, however, further explained (p. 17) that in this table no provision is made for paying interest on the capital. If this has to be done, the amounts given in the Sinking Fund Table must be increased each year by the annual interest on i. Thus, if the Sinking Fund required to replace i in ten years at 4 % is ^-083291 per annum, we must add the annual interest on ^i = -o4 to this amount, in order to obtain the annuity which i will purchase for ten years at 4 %. The result of this addition is (-083 291 + -04=) -123291, the logarithm of which is 1-090931, which is the logarithm given in the column headed a" on p. 291. M. Thoman uses the symbol a" to represent this quantity, but in modern notation it is more usually expressed by the symbol . It will, moreover, be noticed that in M. Thoman's tables the index of the logarithm is given as 9 instead of i, as given above. The reason of this is that some people think it more convenient to avoid the negative characteristics of logarithms by adding 10 to the index, subtracting the negative index, when it occurs, from this 10, and so always dealing with a positive index. The 10 that has been added is subsequently deducted from the index, and thus the same result is arrived at. The more usual and, we think, the more convenient plan is not to employ this artifice, but to (219) N COMPOUND INTEREST deal with negative characteristics, whenever they occur, in the manner already explained. Another point to be noticed in M. Thoman's logarithmic tables is that he puts a comma between the index and mantissa, and a decimal point between the 5th and 6th decimal places. It is more in accordance with modern English custom to put the decimal point between the index and mantissa of the logarithm, while there is nothing to be gained by putting any mark at all between the 5th and 6th decimal places. Thus 0,17033-34 in Thoman=o-i 703334 in modern notation ; and in regard to negative characteristics 9, 09093- 1 2 in Thoman= 1-09093 12 in modern notation, and so on throughout wherever the index is seen by inspection, as it readily can be, to have had 10 added to it. From what has already been said, it will be seen that in dealing with annuities there are four things to be considered. One is the sum to which an annuity will amount in any number of years ; another is the present value of an annuity for any number of years ; the third is the annuity for any number of years which i or any other given amount will purchase ; and the fourth is the sinking fund which will redeem a debt in a given number of years. The third and fourth of these only differ by the amount of the interest on the debt for one year or one period, as has just been explained. It is the third of these for which the logarithm is given in M. Thoman's tables on pp. 269-316 in the column headed a". The fourth is tabulated in natural numbers under the head of Sinking Fund on pp. 106-115. Dealing with the third of these first, namely the annuity which i \ will purchase for any number of years, we have to notice that it is the reciprocal of the present value of i per annum tabulated in natural numbers on pp. 50-85. Obviously if the present value of an annuity of i per annum for 20 years at 4 % is 13*59033 (p. 70) an annuity for 20 years at 4 %, of which the present value is ;i, is equivalent to - of^i. This 3 59 33 equals ^'0735817,^6 logarithm of which is 2-866770, thus agreeing with the logarithm given on p. 291, where, however, the logarithm is stated as 8,86677-02. This difference in the method of stating the logarithm has already been explained. As another example we may take the present value of an annuity for 26 years at 2j %. This is ^"18-40226 (p. 64), and taking the reciprocal of this amount we have -05434115 = ^ 2-735129, which agrees with the logarithm given on p. 281. Thus to find the annuity which i will purchase, we have only to take the natural number corresponding to the logarithm given on pp. 269-316 under the heading log a n . (220) ANNUITY WHICH i WILL PURCHASE A few examples may be added. What annuity for 27 years will buy at 3 J % ? Ans. (p. 285) log For 86 years at 5^ % ? Ans. (p. 300) log For 7 years at 3 % ? Ans. (p. 283) log i'2054922 = -i6o5o6 = -130506 + 'o$(seep.no). If we require to know the annuity which any amount other than i will purchase, we have simply to multiply the annuity which i will purchase by the amount. This is readily done by taking the logarithm of the amount, adding it to the logarithm of the annuity which i will purchase, and taking the natural number corresponding to the logarithm. Take, for example, the annuity for 27 years at 3^ % that may be pur- chased for 3,927. 3927=log 3-594061 (p. 241) The annuity which i will purchase=log 2-749704 (p. 285) 3927 =log 2-343765 ^220-68. What annuity for 68 years may be purchased for 5,737, reckoning interest at 4^ % ? 5 737=log 3758685 (p. 249) The annuity which i will buy=log 2-675548 (p. 295) 5737 =log 2-434233= 2 7i-79. The annuity that may be bought for i at rates not given in the table may be calculated from the formula = /'* j"*' = log /+log(i +/)" log [(i +/)" i]. What annuity for 30 years will i purchase at 5% ? / =. -05 = log 2-6989700 (p. 318) (i + /)* =1-053 = log 0-0211893 x 3 = log 0-6356790 = 4-32 194 i (i + *)* '05 x 1-053 =log 1-3346490 (i +/)"-! = 4-32194-1 =log 0-5213918 i (i + *')*__ -05 x 1-053 (I +/)"-! 3-32I94 This is the figure given on p. 299, save that the last figures of the logarithm are 70 instead of 72, a difference that is inappreciable. (221) S2 COMPOUND INTEREST What annuity for 10 years will 683 purchase at 4-1 %? z = -041 = log 2-6127839 (p. 319) + /)*=ro4i IO = log 0-01745073 x io = log 0-1745073= 1-49454 /(i+/) n = -041 x i -04 1 10 =log (i + /)"i = 1-49454 i = log 1-6942014 i (\ + iY '041 x ro4i 10 <,+^-i --49454 = 683 = lOg 2-8344207 Annuity 683 will buy for 10 years = log 1-9275105 = 84-6273 Present Value of i per Annum We have just seen that the present value of an annuity is the reciprocal of the amount of the annuity which i will purchase for the same period at the same rate of interest. In other words, the annuity which i will purchase and the present value of an annuity multiplied together produce unity the period and the rate of interest, of course, being the same in both cases. The logarithms of the annuity which i will purchase are given in the column headed a", on pp. 269-316. By subtracting this tabulated logarithm from o, which is the log of i, we obtain the logarithm of the present value of an annuity of i. What is the present value of an annuity of i per annum for 43 years at 3 J- % ? i =logo'ooooooo Annuity i will purchase for 43 years at 3} % . . = log 2-6824736 (p. 290) Present value of i per annum for 43 years at 3^ % . =log 1-3175264 = 20-7743 What is the present value of i per annum for 30 years at 5 % ? i=logo"ooooooo The annuity which i will purchase for 30 years at 5 % . . = log 2*8132570 (p. 299) Present value of i per annum for 30 years at 5 % .=log 1^867430=^15-37245 This result may be seen in the table on p. 74. Although the present values of annuities are given in natural numbers on pp. 50-85, it is often convenient to have the logarithms of the values rather than the natural numbers, Thus, suppose we want to know (222) PRESENT VALUE OF i PER ANNUM the present value of an annuity of ,47-25 per annum for 30 years at 5 %. To obtain the result we must multiply the value of i per annum by 47*25, and this, as has been already explained, can be most readily done by the addition of the logarithms of the two numbers. Present value of i per annum for 30 years at 5 % . = log 1-186743 (p. 299) 47-25 =log 1-674402 (p. 245) 47'25 =log 2-861145=^726-35, which is the present value of an annuity of ^47*25 per annum for 30 years at 5%. What is the present value of an annuity of ^8642 for 68 years 8642 = log 3-9366143 (p. 260) Value of annuity of \ (log o -log 2-5269372) . = log i 473 o6 28 (p. 282) Value of annuity of ^8642 for 68 years at 2|% . . = log 5-4096771=^256849. The value of an annuity for some other rate of interest than is given in the tables may sometimes be needed, and we must therefore explain how the value may be arrived at. We have already shown (p. 221) that the present value of an annuity is the reciprocal of the annuity that i will purchase, and that the annuity which i will purchase may be obtained from id -I- /V* the formula -. ^ * . Hence the formula for finding the (i +t) n i present value of an annuity is / >~ == ^g[( I + *)"" T ]~lg * -log (i +/)". We may repeat the example already dealt with. What is the present value of i per annum for 30 years at 5 % ? (i 4. /)" = ro5 3 = log o'o2i 1893 x 3o = log 0-6356790=4-32194 (i +/)" 1=4-32194-1 =3-32^94 = log 0-5213918 /= -05 =log 2-6989700 (i + t)"=ro$ =log 0-6356790 /(i +/)"= -05 x i -053 = log "1-3346490= log 1-3346490 =1 1-18628- -05 x i -05 (223) =1 1-1867428-1^71 * & ^ COMPOUND INTEREST If the logarithm here found is added to the logarithm found in the converse problem on p. 221, we have log 1*1867428 log 2-8132572 log o '0000000= i thus showing that the answers are reciprocals of each other. What is the present value of i per annum for 75 years at 37%? ro37 75 =log 0*0157788 x 75 = log 1-1834100 = 15*255 I-037 73 1= 14-255 =log 1-1539672 037 =log 2-5682017 i*o37 7S =log 1*1834100 log 1-7516117 ""^ =ilog r 4 2 3555 =^25-2555. The Amount of i per Annum Another calculation that we sometimes require to make is the sum to which an annuity will amount in a given number of years at a specified rate of interest. If we know the present value of the annuity, and if we know also the sum to which 1. will amount in the given period, we can, by multiplying the present value by the amount of 1, obtain the sum to which the annuity will amount in the period. Thus, suppose we wish to ascertain the amount of i per annum for 20 years at 5 ( %. Turning to p. 74,- we see that the present value of i per annum is 12-46221, and on the same page we see that the amount of i in 20 years is 2*6533. Multiplying these two amounts together we have 33*066, which agrees with the amount of i per annum given on the same page. The reason of this connection is plain, for since the possession of an annuity of i for 20 years at 5% is mathematically equi- valent to having ^1 2*46221 in hand now, and as the sum to which ^"12-46221 will amount in 20 years is the amount of i in 20 years multiplied by 12-46221 (= 2-6533 x 12-46221 = 33-066), this must also be the sum to which an annuity of i will amount in 20 years at 5 % This result may very easily be obtained by logarithms from the tables on pp. 269-316. In the column headed a n we have, as already explained, the reciprocal of the present value of an annuity, and in the column headed r n we have the amount of i> and we (224) SINKING FUND make use of these two tables in the following way to obtain, as in the example just given, the amount of i per annum in 20 years at 5%. Turning to p. 299, we have Value of annuity = (log o log 2*9044049=) log 1*0955951 Amount of i log 0*4237860 Amount of annuity in 20 years at 5% = log 1-5193811 = ^33'o66, thus agreeing with the result previously obtained. Some additional examples are appended. What is the amount of i per annum at the end of 63 years at 3 i%? Value of annuity =log 1-4259707 (p. 285) Amount of i = log 0-8750738 (p. 285) Amount of annuity =log 2-3010445 = 200-007. What is the amount of .735 per annum at the end of 34 years at 2 J % ? Value of annuity = log 1-3327200 (p. 282) Amount of i =log 0-4185348 (p. 282) 735 = log 2-8662873 (p. 2 54) Amount of ^735 p.a. in 34 years = log 4-6175421 =^41,451-68. It will be noticed that the logarithm of the annual payment is added to the other two logarithms, thus conveniently effecting the necessary multiplication. Sinking Fund A reference to the remarks on pp. 16, 17, and 219 will show the connection between the sinking fund and the annuity which i will purchase , it will be seen that it is only necessary to deduct the rate of interest from the annuity which i will purchase to obtain the sinking fund. Thus the sinking fund which will redeem a debt of i in 25 years at 4 % is obtained by taking from p. 291 the annuity which i will purchase = log 2*8062612 = -064012, and subtracting from this amount the rate of interest "04 : whence we have -024012, which is the sinking fund given on p. 112. Further examples as obtained by logarithms are appended. What annual payment will redeem a debt of ^"i in 65 years at 4%? (2251 COMPOUND INTEREST The annuity i will purchase (p. 292) = 2-6479998 = -044463 Subtract the interest for i year =-04125 Sinking fund = 003713 What is the annual sinking fund that will amount to ^337 in 43 years at 2 % ? Annuity i will buy = ^2*5918772 (p. 280) 337 =iog 2-5276299 (p. 238) Annuity 337 will buy =log 1-1195071 = 13-16760 Deduct interest on 337 for i year = 33 7 x : - = 8*84625 o X IOO Sinking fund to redeem 337 in 43 years = 4-32135 Or the calculation may be made in a slightly different way : Annuity i will buy = ^2-5918772 = '039073 Sinking fund to redeem i = '039073 '02625 = log 2-1079896 = -012823 337= log 2-5276299 Sinking fund to redeem 337 = log 0-6356195 = ^"4-32135 Annuities for which the Rate of Interest on Capital is Different from the Rate for Sinking Fund As explained on p. 18, we require for this calculation to know the annual sinking fund that will amount to i in a given period at the lower rate of interest, and to know also the annual interest upon i. The present value of an annuity equal to the addition of these two is i, and the present value of an annuity of i is the reciprocal of the present value just mentioned. What annuity must be paid during 29 years to repay a debt of i by accumulation at 3^ % and to pay interest on the loan at 4^ %? The annuity which will amount to i in 29 years at 3j% is obtained by multiplying the annuity which i will purchase for 29 years by the present value of i due at the end of 29 years. Annuity i will purchase (p. 285) = log "2 7305 144 Present value of^i (p. 285) = log 1-5971883 Annuity to amount to i in 29 years = log 2*3277027 = -021267 Annual interest on i = -045 Annual payment required = log 2*8212973 = -066267 (226) LOGARITHM OF THE RATE OF INTEREST If, on the other hand, we want to know the present value of an annuity of i for 29 years on the condition that interest on the loan is being paid at 4^ %, and the principal is being replaced by accumulation at 3^ %, we must take the reciprocal of the above amount. This is log 0*0 log 2*8212973 = 1*1787027 = ^15*0905. What is the value of an annuity of i for 50 years yielding interest on capital at 5 %, and replacing capital when invested at Annuity i will purchase (p. 283) = ^2-5895642 Present value of i (p. 283) = log 1*3581388 Annuity to amount to i in 50 years = log 3*9477030 = '0088655 Annual interest on . i ='050 Annuity to pay i and interest = log 27698608 = -0588655 Required value of annuity = log o'o log 27698608 = log 1-2301392 = ^16-98788, which agrees with the amount given on p. 1 20. As in other cases, the values or amounts of annuities other than ;i may be obtained by the addition of the logarithms. Logarithm of the Rate of Interest The Tables on pp. 318-320 give the logarithm of the rate of inte- rest under the heading /. This is in modern notation represented by the symbol /. On p. 318 this is given to 10 places of decimals for every rate given in M. Thoman's first Table (pp. 269-316). On p. 319 it is given for every -^th % up to 10 %, and on p. 320 for every ^th % also up to 10 %. This Table is convenient for such calculations as the present value of i per annum, as may be seen from the first example on p. 222. It has several times been pointed out that the more decimals are taken in the logarithm the more nearly exact will be the results. This is especially the case when the logarithm has to be multiplied. Logarithm of the Amount of I in i Period This logarithm is given to 7 places of decimals on pp. 269-316 in the column r", but on p. 318 the logarithm is given to 10 places of decimals. As has just been said, the use of 10 places gives more nearly exact results than 7 places, though for most purposes 7 places are sufficient. (aar) COMPOUND INTEREST As an example of a fairly large difference, as differences go, take the amount of i for 90 years at 2 J % : i'O2875 9 (see p. 216) = log 0*0123098482 (p. 318^ x qo = log 1-1078863380= 12-8199544. ro2875 9 = log 0-0123098 x 90 = log 1-1078820= 12-8198265. This only gives a difference of 25 shillings in the amount of ^10,000 in 90 years, thus showing that 7 places are usually ample. Even this difference does not occur if we take the logarithm from p. 282, where it is seen to be log 1-1078863= 12-8199533, giving a difference of i in the amount of one million pounds in 90 years. The lo-figure logarithms are useful, however, for the construction of a table of (i +i) n (or r"\ as in pp. 269-316, where the multiplica- tion is worked to 10 places, and the nearest 7 places are printed. This accounts for the smaller variation when (i+/) 9 is taken from p. 282. The tables on pp. 319 and 320 give log (i+/), or log ^, as M. Thoman called it, for every T \,th and ^th %, and it is more convenient to take these logarithms from this table than from the table of logarithms on pp. 230-266. The Logarithms of Log r Under the heading of 'log 2 r' we have the logarithm of 'log r? Thus at \ % 'log r* = 0*00216606 ; and from p. 235 we see that this number = log 3*33567, which agrees with the value of 'log 2 r" on p. 318. We sometimes find it convenient to multiply a logarithm by taking the logarithm of the logarithm and adding the logarithm of the multiplier. This gives us a logarithm of the second order, as it were (log 2 ), and the number corresponding to this log 2 is the log we require. Thus to get the logarithm of (i -fz) 87 when / = -04, we have log 2 r= log 2-2312998 (p. 318) 87= log i'9395i93 log (i -\-if 7 = log 2 0-1708191 = log 1-48190, thus agreeing with the figure given on p. 291 and with log (i -H) x87 by ordinary multiplication. TABLE OF THE LOGARITHMS OF THE NATURAL NUMBERS FROM 1 TO 10,000 For explanation see pp. 207-215 (220) LOGARITHMS Log. 000. NO. 100. No. 1 o 3 4 Diff. 100 000000 000434 000868 001301 001734 433 IOZ 004321 004751 i 005181 ; 005609 006038 429 102 008600 009026 009451 009876 010300 425 103 012837 013259 013680 014100 014521 421 104 017033 oi745i 017868 018284 018700 416 105 021189 021603 022016 022428 022841 412 106 025306 025715 026125 026533 026942 409 107 029384 029789 | 030195 : 030600 031004 405 108 033424 033826 034227 034628 035029 401 109 037426 037825 038223 038620 039017 397 no 041393 041787 042182 042576 042969 393 III 045323 045714 046105 046495 046885 390 112 049218 049606 049993 050380 050766 387 "3 053078 053463 053846 054230 054613 383 114 056905 057286 057666 058046 058426 380 "5 060698 061075 061452 061829 062206 377 116 064458 064832 065206 : 065580 065953 374 117 068186 068557 068928 ; 069298 069668 370 118 071882 072250 072617 072985 073352 367 119 075547 075912 076276 076640 077004 364 120 079181 079543 079904 080266 080626 361 121 082785 083144 083503 083861 084219 358 122 086360 086716 087071 087426 087781 355 123 089905 090258 090611 090963 091315 352 124 093422 093772 094122 094471 094820 349 125 096910 097257 097604 097951 098298 347 126 100371 100715 101059 101403 101747 344 127 103804 104146 104487 104828 105169 341 128 107210 I0 7549 107888 108227 108565 338 129 1 10590 110926 111263 111599 111934 336 130 113943 114277 114611 i i 4944 115278 333 131 117271 117603 II7934 118265 118595 330 132 120574 120903 121231 121560 121888 328 133 123852 124178 124504 124830 125156 326 134 127105 127429 127753 128076 128399 323 135 130334 130655 130977 131298 131619 321 136 133539 133858 I34I77 134496 134814 3i9 137 136721 137037 137354 I3767I 137987 3i6 138 139879 140194 140508 140822 141136 3U 139 143015 H3327 143639 I4395I 144263 312 140 146128 146438 146748 147058 147367 310 141 149219 H9527 149835 150142 ; 150449 307 142 152288 152594 152900 153205 i535!o 305 143 155336 155640 155943 156246 156549 33 144 158362 158664 158965 159266 159567 3 01 *45 161368 161667 161967 162266 162564 299 146 164353 164650 164947 165244 165541 297 147 167317 167613 167908 168203 168497 295 148 I 70262 170555 170848 171141 171434 293 149 173186 173478 173769 174060 174351 291 For explanation see pp. 207-215 (230) OF NUMBERS Log. 175. No. 149. No. 5 6 7 8 9 1 Difl. 100 101 002166 006466 002598 006894 003029 007321 003461 003891 007748 | 008174 431 427 102 010724 011147 OII57O ; 011993 012415 423 103 014940 015360 015779 016197 Ol66l6 419 104 019116 019532 019947 020361 020775 415 105 023252 023664 024075 024486 024896 411 100 027350 027757 028164 028571 028978 407 107 031408 031812 032216 032619 033021 403 108 035430 035830 036230 036629 037028 399 109 039414 039811 040207 040602 040998 396 ZIO 043362 043755 044148 044540 044932 392 III 047275 047664 048053 ; 048442 048830 389 112 051153 051538 051924 052309 052694 385 "3 054996 055378 055760 056142 056524 382 114 058805 059185 059563 059942 060320 379 115 062582 062958 063333 063709 064083 375 116 066326 066699 067071 067443 067815 372 117 070038 070407 070776 07H45 071514 369 118 073718 074085 074451 074816 075182 366 119 077368 077731 078094 078457 078819 363 120 080987 081347 081707 082067 082426 360 121 084576 084934 085291 085647 086004 357 122 088136 088490 088845 089198 089552 354 123 091667 092018 092370 092721 093071 35i 124 095169 095518 095866 096215 096562 348 125 098644 098990 099335 099681 100026 345 126 I0209I 102434 102777 103119 103462 343 127 I055IO 105851 106191 106531 106871 340 128 108903 109241 109579 109916 110253 337 129 112270 112605 112940 H3275 113609 335 130 115611 H5943 116276 Il66o8 116940 332 131 118926 119256 119586 H99I5 120245 329 132 122216 122544 122871 123198 123525 3 2 7 133 125481 125806 126131 126456 126781 325 134 128722 129045 129368 129690 130012 322 135 I3J939 132260 132580 132900 I332I9 320 137 I35I33 138303 I3545I 138618 135769 138934 136086 139249 136403 139564 3i8 315 138 141450 I4I763 142076 142389 142702 313 139 H4574 144885 145196 H5507 145818 3" 140 147676 H7985 148294 148603 148911 309 141 150756 151063 151370 151676 151982 306 142 153815 154120 154424 154728 155032 304 143 156852 I57I54 157457 157759 . 158061 302 144 159868 160168 160469 160769 161068 300 $ 162863 165838 163161 166134 163460 166430 163758 166726 164055 167022 298 296 M7 168792 169086 169380 169674 169968 294 148 171726 172019 172311 172603 172895 292 149 174641 174932 175222 175512 175802 290 (231) LOGARITHMS Log. 176. No. 150. No. 1 2 3 4 Diff. I50 176091 176381 176670 176959 177248 28 9 151 178977 179264 179552 179839 180126 287 152 181844 182129 182415 182700 182985 285 153 184691 184975 185259 185542 185825 283 154 187521 187803 188084 188366 188647 28l 155 190332 190612 190892 191171 19145! 279 156 193125 193403 193681 193959 194237 2 7 8 *57 195900 196176 196453 196729 197005 2 7 6 158 198657 198932 199206 199481 199755 274 159 201397 201670 201943 202216 202488 273 160 204120 204391 204663 204934 205204 271 161 206826 207096 207365 207634 207904 26 9 162 209515 209783 210051 210319 210586 268 163 212188 212454 212720 212986 213252 266 164 214844 215109 215373 215638 215902 264 165 217484 217747 218010 218273 218536 263 166 220108 220370 220631 220892 221153 261 167 222716 222976 223236 223496 223755 260 168 225309 225568 225826 226084 226342 258 169 227887 228144 228400 228657 228913 257 170 230449 230704 230960 231215 231470 255 171 232996 233250 233504 233757 234011 254 172 235528 235781 236033 236285 236537 252 173 238046 238297 238548 238799 239049 251 174 240549 240799 241048 241297 241546 249 175 243038 243286 243534 243782 244030 2 4 8 176 245513 245759 246006 246252 246499 246 $ 247973 250420 248219 250664 248464 250908 248709 248954 251395 245 244 179 252853 253096 253338 253580 253822 242 180 255273 255514 255755 255996 256237 241 181 257679 257918 258158 258398 258637 240 182 26007 I 260310 260548 260787 261025 238 183 262451 262688 262925 263162 263399 237 184 264818 265054 265290 265525 265761 236 185 267172 267406 267641 267875 268110 234 186 269513 269746 269980 270213 270446 233 187 271842 272074 272306 272538 272770 232 188 274158 274389 274620 274850 275081 231 189 276462 276692 276921 277151 277380 229 190 278754 278982 279211 279439 279667 228 191 281033 281261 281488 281715 281942 227 192 283301 283527 283753 283979 284205 226 193 194 285557 287802 285782 288026 286007 288249 286232 288473 286456 288696 225 224 195 290035 290257 290480 290702 290925 222 196 292256 292478 292699 292920 293141 221 197 294466 294687 294907 295127 295347 22O 198 296665 296884 297104 297323 297542 219 199 298853 299071 299289 299507 299725 218 For explanation see PP- 207-215 (232) OF NUMBERS Log. 300. No. 199. No. 5 6 7 8 9 Diff. ISO 177536 177825 178113 178401 178689 288 151 180413 180699 180986 181272 181558 286 152 183270 183555 183839 184123 184407 284 153 186108 186391 186674 , 186956 187239 283 154 188928 189209 189490 189771 190051 28l 155 191730 192010 192289 192567 192846 279 156 194514 194792 195069 195346 195623 277 197281 197556 197832 198107 198382 275 200029 200303 200577 200850 201124 274 159 202761 203033 j 203305 203577 203848 272 160 205475 205746 206016 206286 206556 270 161 208173 208441 208710 208979 209247 269 162 210853 2III2I 211388 211654 211921 267 163 213518 213783 214049 214314 214579 265 164 216166 216430 216694 216957 217221 264 165 218798 219060 219323 219585 219846 262 166 221414 221675 221936 222196 222456 260 . 167 224015 224274 224533 224792 225051 259 " 1 68 226600 226858 227115 227372 227630 257 169 229170 229426 229682 229938 230193 2 5 6 170 231724 231979 232234 232488 232742 254 171 234264 234517 234770 235023 235276 253 172 236789 237041 237292 237544 237795 251 173 239299 239550 239800 240050 240300 250 174 241795 242044 242293 242541 242790 249 175 244277 244525 244772 245019 245266 247 176 246745 246991 247237 247482 247728 2 4 6 249198 249443 249687 249932 250176 244 178 251638 25I88I 252125 252368 252610 243 179 254064 254306 254548 254790 255031 242 1 80 256477 256718 256958 257198 257439 240 181 258877 259116 259355 259594 259833 239 182 261263 26I50I 261739 261976 262214 238 183 263636 263873 264109 264346 264582 2 3 6 184 265996 266232 266467 266702 266937 235 185 268344 268578 268812 269046 269279 234 186 270679 270912 271144 271377 271609 233 187 273001 273233 273464 273696 273927 231 1 88 275311 275542 275772 276002 276232 230 189 277609 277838 278067 278296 278525 229 190 279895 280123 280351 280578 280806 228 191 282169 282396 282622 282849 283075 226 192 284431 284656 284882 285107 285332 225 193 286681 286905 287130 287354 287578 224 194 288920 289143 289366 289589 289812 22 3 195 291147 291369 291591 291813 292034 222 196 293363 293584 293804 294025 294246 221 197 198 295567 297761 295787 297979 296007 298198 296226 298416 296446 298635 2 2O 218 199 299943 300l6l 300378 300595 300813 217 (233) LOGARITHMS Log. 301. NO. 200. No. 1 2 3 4 Diff. 200 301030 301247 301464 301681 301898 217 201 303196 303412 303628 303844 304059 216 202 305351 305566 305781 305996 306211 215 203 20 4 307496 309630 307710 309843 307924 310056 308137 310268 308351 310481 214 213 205 311754 311966 312177 312389 312600 212 206 313867 314078 314289 314499 314710 211 207 315970 316180 316390 316599 316809 210 208 318063 318272 318481 318689 318898 2O9 209 320146 320354 320562 320769 320977 208 210 322219 322426 322633 322839 323046 207 211 324282 324488 324694 324899 325105 206 212 326336 326541 326745 326950 327155 205 213 328380 328583 328787 328991 329194 204 2I 4 330414 330617 330819 331022 331225 203 215 332438 332640 332842 333044 333246 202 2X6 334454 334655 334856 1 335057 335257 2O I 217 336460 33666o 336860 337060 337260 200 2X8 338456 338656 338855 339054 339253 199 219 340444 340642 340841 341039 341237 198 220 342423 342620 342817 343014 343212 197 221 344392 344589 344785 344981 345178 I 9 6 222 346353 346549 346744 346939 347135 195 223 348305 348500 348694 348889 349083 194 22 4 350248 350442 350636 350829 351023 194 225 352183 352375 352568 352761 352954 193 226 354io8 354301 354493 354685 354876 192 227 356026 356217 356408 356599 356790 191 228 357935 358125 358316 358506 358696 190 229 359835 360025 360215 360404 360593 190 230 361728 361917 362105 362294 362482 I8 9 231 363612 363800 363988 364176 364363 188 232 365488 365675 365862 366049 366236 187 233 367356 367542 367729 367915 368101 186 234 369216 369401 369587 369772 369958 185 235 371068 371253 37H37 371622 371806 185 236 372912 373096 37328o 373464 373647 184 2 37 374748 374932 375^5 375298 375481 183 238 376577 376759 376942 377124 377306 182 239 378398 378580 378761 378943 379124 182 240 380211 380392 380573 380754 380934 181 2 4 I 382017 382197 382377 382557 382737 180 242 383815 383995 384174 384353 384533 179 243 385606 385785 385964 386142 386321 179 244 387390 387568 387746 387923 388101 178 245 389166 389343 389520 389698 389875 177 2 4 6 390935 391112 391288 391464 391641 176 247 392697 392873 393048 393224 393400 176 2 4 8 394452 394627 394802 394977 395^2 175 249 396199 396374 396548 396722 396896 174 For explanation see pp. 207-215 (234) OF NUMBERS Log. 397. NO. 249. No. 5 6 7 8 9 Diff. 200 302114 302331 302547 302764 302980 216 2O I 304275 304491 304706 304921 305136 215 202 306425 306639 306854 307068 307282 214 203 308564 308778 308991 309204 309417 213 204 310693 310906 311118 311330 3H542 212 205 312812 313023 313234 313445 313656 211 206 314920 3I5I30 315340 315551 315760 210 207 317018 317227 317436 317646 317854 209 208 319106 319522 319730 319938 208 209 321184 321391 321598 321805 322012 207 210 323252 323458 323665 323871 324077 206 211 3253! 325516 325721 325926 326131 205 212 327359 327563 327767 327972 328176 204 2I 3 329398 329601 329805 330008 3302II 203 2I 4 331427 331630 331832 332034 332236 202 215 333447 333649 333850 334051 334253 201 216 335458 335658 335859 336059 336260 2OO 217 337459 337659 337858 338058 338257 I 99 218 339451 339650 339849 340047 340246 199 219 34H35 341632 341830 342028 342225 I 9 8 220 343409 3436o6 343802 343999 344196 197 221 345374 345570 345766 345962 346157 I 9 6 222 347330 347525 347720 347915 348110 22 3 349278 349472 349666 34986o 350054 194 22 4 351216 35i4io 351603 351796 351989 193 225 353147 353339 353532 353724 353916 192 226 355068 35526o 355452 355643 355834 192 227 356981 357172 357363 357554 357744 191 228 358886 359076 359266 359456 359646 190 22 9 360783 360972 361161 361350 361539 189 230 362671 362859 363048 363236 363424 188 231 364551 364739 364926 365H3 365301 187 232 366423 366610 366796 366983 367169 187 233 368287 368473 368659 368845 369030 1 86 234 370143 370328 370513 370698 370883 185 37I99I 372175 372360 372544 372728 184 373831 374015 374198 374382 374565 183 237 375664 375846 376029 376212 376394 183 238 377488 377.670 377852 378034 378216 182 239 379306 379487 379668 379849 380030 181 240 381115 381296 381476 381656 381837 180 241 382917 383097 383277 383456 383636 180 242 243 244 384712 386499 388279 384891 386677 388456 385070 386856 388634 385249 387034 388811 385428 387212 388989 179 178 177 $ 390051 390228 391993 390405 392169 390582 392345 390759 392521 177 176 247 393575 393751 393926 394101 394277 *75 248 395326 3955 01 395676 395850 396025 175 249 397071 397245 397419 397592 397766 174 1 (235) LOGABITHMS Log. 397. NO. 250. No. 1 2 3 4 DHL 250 397940 398114 398287 398461 398634 173 251 399674 399847 400020 400192 400365 173 252 401401 401573 401745 401917 402089 172 253 403121 403292 403464 403635 403807 171 254 404834 405005 405176 405346 4Q55 1 7 171 255 406540 406710 406881 407051 407221 170 256 408240 408410 408579 408749 408918 169 257 409933 410102 410271 410440 410609 169 2 5 8 411620 411788 411956 412124 412293 1 68 259 413300 413467 413635 413803 413970 167 260 414973 415140 415307 415474 415641 167 26l 416641 416807 416973 4I7I39 417306 1 66 262 418301 418467 418633 418798 418964 165 263 419956 420121 420286 420451 420616 165 264 421604 421768 421933 422097 422261 164 26 5 423246 423410 423574 423737 423901 163 266 424882 425045 425208 425371 425534 163 267 426511 426674 426836 426999 427161 162 268 428135 428297 428459 428621 428783 162 269 429752 429914 430075 430236 430398 161 270 43*364 431525 431685 431846 432007 160 271 432969 433130 433290 433450 4336io 160 272 434569 434729 434888 435048 435207 '59 273 436163 436322 436481 436640 436799 159 274 437751 437909 438067 438226 438384 158 9 439333 440909 439491 441066 439648 441224 439806 441381 439964 441538 157 157 277 442480 442637 442793 442950 443106 156 278 444045 444201 444357 444513 444669 156 279 445604 445760 445915 446071 446226 155 280 447158 4473 i 3 447468 447623 447778 155 281 448706 448861 449015 449170 449324 154 282 450249 450403 450557 4507H 450865 154 283 451786 451940 452093 452247 452400 153 284 453318 453471 453624 453777 453930 153 285 454845 454997 455150 455302 455454 152 286 456366 456518 456670 456821 456973 152 287 457882 458033 458184 458336 458487 151 288 459392 459543 459694 459845 459995 151 289 460898 461048 461198 461348 461499 150 290 462398 462548 462697 462847 462997 149 291 463893 464042 464191 464340 464490 149 292 465383 465532 465680 465829 465977 148 293 466868 467016 467164 467312 467460 148 294 468347 468495 468643 468790 468938 147 295 469822 469969 470116 470263 470410 H7 296 471292 471438 471585 471732 471878 146 472756 472903 473049 473195 473341 146 298 474216 474362 4745o8 474653 474799 146 299 475671 475816 475962 476107 476252 145 For explanation see pp. 207-215 (236) OP NUMBERS Log. 476. NO. 299. No. 5 6 7 8 9 Diff. 250 398808 398981 399154 399328 399501 173 25 1 400538 400711 400883 401056 401228 173 252 402261 402433 402605 402777 402949 172 2 53 403978 j 404149 404320 404492 404663 171 254 405688 405858 406029 406199 406370 171 2 55 407391 407561 407731 407901 408070 170 256 409087 409257 409426 409595 409764 I6 9 2 57 410777 ! 410946 411114 411283 411451 I6 9 258 412461 412629 412796 412964 413132 168 259 414137 414305 414472 414639 414806 167 260 415808 415974 416141 416308 416474 167 261 417472 417638 417804 417970 418135 1 66 262 419129 419295 419460 419625 419791 165 263 420781 420945 421110 421275 421439 165 264 422426 422590 422754 422918 423082 164 265 424065 424228 424392 424555 424718 163 266 425697 ; 425860 426023 426186 426349 163 267 427324 427486 427648 427811 427973 162 268 428944 429106 429268 429429 429591 162 269 430559 430720 430881 43 i 042 431203 161 270 432167 ! 432328 432488 432649 432809 160 271 433770 433930 434090 434249 434409 1 60 272 435367 I 435526 435685 435844 436004 159 273 436957 437n6 437275 437433 437592 159 274 438542 438701 438859 439017 439175 158 275 440122 440279 440437 440594 440752 157 276 441695 441852 442009 442166 442323 157 9 443263 444825 443419 444981 443576 445137 443732 445293 443889 445449 156 156 279 446382 446537 446692 446848 447003 155 280 447933 448088 448242 448397 448552 155 281 449478 449633 449787 449941 450095 154 282 451018 451*72 451326 45H79 45 l6 33 154 283 452553 452706 452859 453012 453^5 '53 284 454082 454235 454387 454540 454692 i53 3 4556o6 457125 455758 457276 455910 457428 456062 457579 456214 45773 1 152 152 287 458638 458789 458940 459091 459242 151 288 460146 460296 460447 460597 460748 150 289 461649 461799 461948 462098 462248 150 290 463146 463296 463445 463594 463744 149 291 292 464639 466126 464788 466274 464936 466423 465085 466571 465234 466719 149 148 293 467608 467756 467904 468052 468200 148 294 469085 469233 469380 469527 469675 H7 295 470557 470704 470851 470998 47H45 H7 296 472025 472171 472318 472464 472610 146 473487 473633 473779 473925 474071 146 298 474944 475090 475235 47538i 475526 146 299 476397 476542 | 476687 476832 476976 145 (237) o a LOGARITHMS Log. 477. No. 300. No. 1 2 3 4 Diff. 300 477121 477266 477411 477555 477700 H5 301 478566 478711 478855 478999 479143 144 302 480007 480151 480294 480438 480582 144 303 481443 481586 481729 481872 482016 J 43 304 482874 483016 483159 483302 483445 143 305 484300 484442 484585 484727 484869 142 306 485721 485863 486005 486147 486289 142 307 487138 487280 487421 487563 487704 141 308 488551 488692 488833 488974 489114 141 309 489958 490099 490239 490380 490520 140 310 491362 491502 491642 491782 491922 140 3" 492760 492900 493040 493179 493319 139 312 494155 494294 494433 494572 494711 139 313 495544 495683 495822 49596o 496099 138 314 496930 497068 497206 497344 497483 138 I 315 498311 498448 498586 498724 498862 138 316 499687 499824 499962 500099 500236 137 317 501059 501196 501333 501470 501607 137 3i8 502427 502564 502700 502837 502973 136 319 503791 503927 504063 504199 504335 136 320 505150 505286 505421 505557 505693 136 321 506505 506640 506776 506911 507046 135 322 507856 507991 508126 508260 508395 135 323 509203 509337 509471 509606 509740 134 324 510545 510679 510813 510947 511081 134 325 511883 512017 512151 512284 512418 133 326 513218 5I335I 513484 513617 513750 133 5H548 514681 5H8i3 514946 515079 133 328 515874 516006 516139 516271 516403 132 329 517196 517328 517460 517592 517724 132 330 518514 518646 518777 518909 519040 131 33i 519828 519959 520090 520221 520353 131 332 521138 521269 521400 521530 521661 131 333 522444 522575 522705 522835 522966 130 334 523746 523876 524006 524136 524266 130 335 525045 525174 525304 525434 525563 129 336 526339 526469 526598 526727 526856 129 337 527630 527759 527888 528016 528145 129 338 528917 529045 529174 529302 529430 128 339 530200 530328 530456 530584 530712 128 340 53H79 531607 531734 531862 531990 128 34i 532754 532882 533009 533136 533264 127 342 534026 534153 53428o 534407 534534 127 343 535294 535421 535547 535674 5358oo 126 344 536558 536685 5368ii 536937 537063 126 345 537819 537945 538071 538197 538322 126 346 539076 539202 539327 539452 539578 125 $ 540329 541579 540455 541704 540580 541829 540705 541953 540830 542078 125 125 349 542825 54295 543074 543199 543323 124 For explanation see pp. 207-215 (233) OF NUMBERS Log. 543. No. 349. ! No. 5 6 7 8 9 Diff. 300 477844 477989 478133 478278 478422 145 301 479287 47943 J 479575 479719 479863 144 302 480725 480869 481012 481156 481299 144 303 482159 482302 482445 482588 482731 143 304 4835*7 483730 483872 484015 484157 143 305 485011 485153 485295 485437 485579 142 306 486430 486572 486714 486855 486997 142 307 487845 487986 488127 488269 488410 HI 308 489255 489396 489537 489677 489818 141 309 490661 490801 490941 491081 491222 140 310 492062 492201 492341 492481 492621 '39 3" 493458 493597 493737 493876 494015 139 312 494850 494989 495128 495267 495406 139 313 496238 496376 496515 496653 496791 138 314 497621 497759 497897 498035 498173 138 315 498999 499137 499275 499412 499550 138 316 500374 500511 500648 500785 500922 137 317 501744 501880 502017 502154 502291 137 3i8 503109 503246 503382 503518 503655 136 319 504471 504607 504743 504878 505014 136 320 505828 505964 506099 506234 506370 136 321 507181 507316 507451 507586 507721 135 322 508530 508664 508799 508934 509068 135 323 509874 510009 510143 510277 510411 134 324 511215 5"349 511482 511616 511750 134 325 512551 512684 512818 512951 513084 133 326 513883 514016 5!4i49 514282 514415 133 327 515211 515344 515476 515609 515741 133 328 516535 516668 516800 516932 517064 132 329 517855 517987 518119 518251 518382 132 330 519171 519303 519434 5*9566 519697 131 331 520484 520615 520745 520876 521007 131 332 521792 521922 522053 522183 522314 '3i 333 523096 523226 523356 523486 523616 130 334 524396 524526 524656 524785 524915 130 335 525693 525822 525951 526081 526210 129 336 526985 527"4 527243 527372 527501 129 337 528274 528402 528531 528660 528788 129 338 529559 529687 529815 529943 530072 128 339 530840 530968 531096 531223 531351 128 340 532117 532245 532372 532500 532627 128 34i 533391 533518 533645 533772 533899 127 342 534661 534787 5349H 535041 535167 127 343 535927 536053 536180 536306 536432 126 344 537189 537315 537441 537567 537693 126 345 538448 538574 538699 538825 538951 126 346 539703 539829 539954 540079 540204 125 347 540955 541080 541205 541330 541454 125 348 542203 542327 542452 542576 542701 125 349 543447 543571 543696 543820 543944 124 (239) LOGARITHMS Log. 544. NO. 350. No. 1 2 3 4 Diff. 350 544068 544192 544316 544440 544564 124 351 545307 545431 545555 545678 545802 124 352 546543 546666 546789 546913 547036 123 353 547775 547898 548021 548144 548267 123 354 5493 549126 549249 549371 549494 123 355 550228 550351 550473 550595 550717 122 356 55H50 55'572 55 l6 94 551816 551938 122 357 552668 552790 5529H 553033 553155 121 358 553883 554004 554126 554247 554368 121 359 555094 555215 555336 555457 555578 121 360 556303 556423 556544 556664 556785 1 2O 361 557507 557627 557748 557868 557988 1 2O 362 558709 558829 558948 559068 559188 1 2O 363 559907 560026 560146 560265 560385 119 364 561101 561221 561340 561459 561578 II 9 365 562293 562412 562531 562650 562769 II 9 366 563481 563600 5637i8 563837 563955 119 564666 564784 564903 565021 565139 118 368 565848 565966 566084 566202 566320 118 369 567026 567H4 567262 567379 567497 118 370 568202 568319 568436 568554 568671 117 37i 569374 569491 569608 569725 569842 117 372 570543 570660 570776 570893 571010 117 373 571709 571825 571942 572058 572174 116 374 572872 572988 573104 573220 573336 116 375 574031 574H7 574263 574379 574494 116 575188 575303 575419 575534 575650 H5 377 576341 576457 576572 576687 576802 "5 378 577492 577607 577722 577836 577951 "5 379 578639 578754 578868 578983 579097 114 380 579784 579898 580012 580126 580241 114 38i 580925 581039 58H53 581267 581381 114 382 582063 582177 582291 582404 582518 114 383 583199 5833 12 583426 583539 583652 "3 384 584331 584444 584557 584670 584783 H3 385 585461 585574 585686 585799 585912 "3 386 586587 586700 586812 586925 587037 112 387 5877U 587823 587935 588047 588160 112 388 588832 588944 589056 589167 589279 112 389 589950 590061 590173 590284 590396 112 390 591065 591176 591287 591399 59I5 10 III 39i 592177 592288 592399 59 2 5 J o 592621 III 392 593286 593397 593508 5936i8 593729 III 393 594393 594503 594614 594724 594834 110 394 595496 5956o6 595717 595827 595937 1 10 395 596597 596707 596817 596927 597037 110 396 597695 597805 5979H 598024 598i34 no 397 598791 598900 599009 599119 599228 109 398 599883 599992 600101 600210 600319 109 399 600973 601082 601191 601299 601408 109 For explanation see pp. 207-215 (240) OP NUMBERS Log. 601. No. 399. No. 5 6 7 8 9 Diff. 350 544688 544812 544936 545060 545183 124 351 5459 2 5 546049 546172 546296 546419 124 352 547159 547282 547405 547529 547652 123 353 354 548389 549616 548512 548635 548758 548881 123 549739 54986i 549984 550106 123 355 550840 550962 551084 ! 551206 551328 122 356 552060 552181 552303 552425 552547 122 357 553276 553398 553519 553640 553762 121 358 554489 i 554610 554731 554852 554973 121 359 555699 ! 555820 555940 556061 556182 121 360 556905 361 558108 557026 557H6 558228 558349 557267 557387 120 558469 | 558589 120 362 559308 559428 , 559548 559667 559787 120 363 560504 560624 560743 560863 i 560982 119 364 561698 561817 561936 562055 562174 II 9 365 562887 563006 563125 563244 563362 1 19 366 564074 564192 564311 564429 564548 119 367 565257 565376 565494 565612 565730 118 368 566437 566555 566673 566791 566909 118 369 567614 567732 567849 567967 568084 118 370 568788 568905 569023 569140 i 569257 117 37i 569959 570076 570193 570309 570426 117 372 571126 571243 571359 57H76 571592 117 373 572291 572407 572523 572639 572755 1x6 374 573452 573568 573684 5738oo 573915 116 9 574610 574726 575765 575880 574841 575996 574957 575072 576111 576226 116 US 377 576917 577032 577M7 577262 577377 "5 378 578066 578181 578295 578410 578525 "5 379 579212 579326 579441 579555 579669 114 380 580355 580469 580583 580697 580811 114 381 581495 581608 581722 581836 581950 114 382 582631 383 583765 582745 i 582858 583879 583992 582972 584105 583085 584218 114 IM 384 584896 585009 585122 585235 585348 | 113 385 586024 586137 586250 586362 586475 H3 386 587149 587262 587374 587486 587599 H2 387 588272 588384 588496 588608 588720 112 388 589391 589503 589615 589726 589838 112 389 590507 590619 590730 590842 590953 112 390 591621 591732 591843 591955 592066 III 39i 592732 592843 592954 593064 593175 III 392 593840 593950 594061 594i7i 594282 III 393 394 594945 595055 596047 596157 595165 596267 595276 595386 596377 596487 110 I IO 395 597M6 597256 597366 597476 597586 110 396 598243 598353 598462 598572 598681 no 397 599337 599446 599556 599665 599774 109 398 600428 600537 600646 600755 600864 1 09 399 601517 601625 601734 601843 601951 109 LOGARITHMS Log. 602. NO. 400. No. 1 2 3 4 -i Diff. 400 602060 602169 602277 602386 602494 108 4OI 603144 603253 603361 603469 603577 1 08 4O2 604226 604334 604442 604550 604658 1 08 403 605305 605413 605521 605628 605736 1 08 404 606381 606489 606596 606704 606811 107 405 607455 607562 607669 607777 607884 107 4 06 608526 608633 608740 608847 608954 107 407 609594 609701 609808 609914 610021 107 408 610660 610767 610873 610979 6uo86 1 06 409 611723 611829 611936 612042 612148 106 410 612784 612890 612996 613102 613207 106 411 613842 613947 614053 614159 614264 106 412 614897 615003 615108 615213 6i53 I 9 IO 5 413 615950 616055 616160 616265 616370 105 414 617000 617105 617210 6I73I5 617420 105 4 J 5 618048 618153 618257 618362 618466 105 416 619093 619198 619302 619406 619511 104 417 418 620136 621176 620240 621280 620344 621384 620448 621488 620552 621592 104 104 419 622214 622318 62242 i 622525 622628 104 420 623249 623353 623456 623559 623663 103 421 624282 624385 624488 624591 624695 103 422 625312 625415 625518 625621 625724 103 423 626340 626443 626546 626648 626751 103 424 627366 627468 627571 627673 627775 102 425 628389 628491 628593 628695 628797 102 426 629410 629512 629613 629715 629817 102 427 630428 630530 630631 630733 630835 I O2 428 631444 631545 631647 631748 631849 101 429 632457 632559 632660 632761 632862 101 430 633468 633569 633670 633771 633872 101 634477 634578 634679 634779 634880 101 432 635484 635584 635685 635785 635886 IOO 433 636488 636588 636688 636789 636889 IOO 434 637490 637590 637690 637790 637890 IOO 435 638489 638589 638689 638789 638888 IOO 436 639486 639586 639686 639785 639885 IOO 437 640481 640581 640680 640779 640879 99 438 641474 641573 641672 641771 641871 99 439 642465 642563 642662 642761 642860 99 440 643453 643551 643650 643749 643847 98 441 644439 644537 644636 644734 644832 98 442 645422 645521 645619 645717 645815 98 443 646404 646502 646600 646698 646796 98 444 647383 647481 647579 647676 647774 98 445 648360 648458 648555 648653 648750 97 446 649335 649432 649530 649627 649724 97 447 650308 650405 650502 650599 650696 97 448 651278 651375 651472 651569 651666 97 449 652246 652343 652440 652536 652633 97 For explanatipri see pp. 207-215 (242) OF NUMBERS Log. 653. No. 449, No. 5 6 7 8 9 Diflf. 400 602603 602711 602819 602928 603036 108 401 603686 ; 603794 603902 604010 604118 1 08 402 604766 604874 604982 605089 605197 1 08 43 605844 605951 606059 606166 606274 1 08 404 606919 607026 607133 607241 607348 107 405 607991 608098 608205 608312 608419 107 406 609061 609167 609274 609381 609488 107 407 6IOI28 610234 610341 610447 610554 107 408 6III92 611298 611405 611511 611617 106 409 612254 612360 612466 612572 612678 1 06 410 6I33I3 613419 613525 613630 613736 106 411 614370 614475 614581 614686 614792 106 4 I2 615424 615529 615634 615740 615845 105 4*3 616476 616581 616686 616790 616895 105 414 617525 617629 617734 617839 617943 105 4*5 618571 618676 618780 618884 618989 105 416 619615 619719 619824 619928 620032 104 417 620656 620760 620864 620968 621072 104 418 621695 621799 621903 622007 622110 104 419 622732 622835 622939 623042 623146 104 420 623766 623869 623973 624076 624179 103 421 624798 624901 625004 625107 625210 103 422 625827 625929 626032 626135 626238 103 423 626853 626956 627058 627161 627263 103 424 627878 627980 628082 628185 628287 102 425 628900 629002 629104 629206 629308 I O2 426 629919 630021 630123 630224 630326 102 427 630936 631038 63H39 631241 631342 102 428 631951 632052 632153 632255 632356 IOI 429 632963 633064 633165 633266 633367 IOI 430 633973 634074 634175 634276 634376 IOI 43 1 634981 635081 635182 635283 635383 IOI 432 635986 636087 636187 636287 636388 IOO 433 636989 637089 637189 637290 637390 IOO 434 j 637990 638090 638190 638290 638389 IOO 435 1 638988 639088 639188 639287 639387 IOO 436 639984 640084 640183 640283 640382 IOO 437 640978 641077 641177 641276 641375 99 438 641970 642069 642168 642267 642366 99 439 642959 643058 643156 643255 643354 99 440 643946 644044 644143 644242 644340 98 441 644931 645029 645127 645226 645324 98 442 645913 646011 646110 646208 646306 98 443 646894 646992 647089 647187 647285 98 444 647872 647969 648067 648165 648262 98 445 ! 648848 648945 649043 649140 649237 97 446 64982 i 649919 650016 650113 650210 97 i 650793 650890 650987 651084 651181 97 448 651762 651859 651956 652053 652150 97 449 652730 652826 652923 653019 653116 97 (243) LOGARITHMS Log. 653. No. 450. No. 1 2 3 4 Diff. 450 653213 653309 653405 653502 653598 96 451 654177 654273 654369 i 654465 654562 96 452 655138 655235 655331 655427 655523 96 453 656098 656194 656290 656386 656482 9 6 454 657056 657152 657247 657343 657438 96 455 1 658011 658107 658202 658298 658393 95 456 658965 659060 659155 659250 659346 95 457 659916 660011 660106 660201 660296 95 458 660865 660960 661055 661150 661245 95 459 661813 661907 662002 662096 662191 94 460 662758 662852 662947 663041 663135 94 461 663701 663795 663889 663983 664078 94 462 664642 664736 664830 664924 665018 94 463 665581 665675 665769 665862 665956 94 464 666518 666612 666705 666799 666892 94 465 667453 667546 667640 667733 667826 93 466 668386 668479 668572 668665 668759 93 467 669317 669410 669503 669596 669689 93 468 670246 670339 670431 670524 670617 93 469 671173 671265 671358 67H5I 671543 93 470 672098 672190 672283 672375 672467 92 47i 673021 673113 673205 673297 673390 92 472 673942 674034 674126 674218 674310 92 473 674861 674953 675045 675137 675228 92 474 675778 675870 675962 676053 676145 92 476 676694 677607 676785 677698 676876 677789 676968 677881 677059 677972 9i 9i 478 678518 679428 678609 679519 678700 679610 678791 679700 678882 679791 9i 9i 479 680336 680426 680517 680607 680698 9i 480 681241 681332 681422 . 681513 681603 90 481 682145 682235 682326 682416 682506 90 482 683047 683137 683227 683317 683407 90 483 683947 684037 684127 684217 684307 90 484 684845 684935 685025 685114 685204 90 485 685742 685831 685921 686010 686100 90 486 686636 686726 686815 686904 686994 89 487 687529 687618 687707 687796 687886 89 488 688420 688509 688598 688687 688776 89 489 689309 689398 689486 689575 689664 89 490 690196 690285 690373 690462 690550 89 491 691081 691170 691258 691347 691435 88 492 691965 692053 692142 692230 692318 88 493 692847 692935 693023 693111 693199 88 494 693727 693815 693903 693991 694078 88 495 694605 694693 694781 694868 694956 88 496 695482 695569 695657 695744 695832 87 497 696356 696444 696531 696618 696706 87 498 697229 697317 697404 697491 697578 87 499 698101 698188 698275 698362 698449 87 For explanation see pp. 207-215 (244) OF NUMBERS Log. 698. NO. 499. No. 5 6 7 8 9 Diff. 450 653695 653791 653888 653984 654080 9 * 451 654658 654754 654850 654946 655042 96 452 655619 655715 655810 655906 656002 96 453 656577 656673 656769 656864 | 656960 9 A 454 657534 657629 657725 657820 657916 9 6 1 658488 659441 658584 659536 658679 659631 658774 659726 658870 659821 95 95 660391 660486 660581 660676 660771 95 458 661339 661434 661529 661623 I 661718 95 459 662286 662380 662475 662569 1 662663 94 460 663230 663324 663418 663512 663607 94 461 664172 664266 664360 664454 664548 94 462 665112 665206 665299 665393 665487 94 463 666050 666143 666237 666331 666424 94 464 666986 667079 667173 667266 667360 94 465 667920 1 668013 668106 668199 668293 93 466 668852 668945 669038 669131 669224 93 467 669782 669875 i 669967 670060 670153 93 468 670710 670802 670895 670988 671080 93 469 i 671636 671728 671821 671913 672005 92 470 672560 672652 672744 672836 672929 92 47i 673482 673574 673666 673758 673850 472 674402 674494 i 674586 674677 674769 92 473 675320 675412 675503 675595 675687 92 474 676236 676328 676419 676511 676602 92 475 677151 677242 s 677333 677424 677516 9 1 476 678063 678154 678245 i 678336 678427 9i 477 678973 679064 679155 679246 679337 9i 478 679882 679973 680063 680154 680245 i 9 1 479 680789 680879 680970 681060 681151 9i 480 681693 681784 681874 681964 682055 90 481 682596 682686 682777 682867 682957 90 482 683497 683587 683677 683767 683857 90 483 684396 684486 684576 684666 684756 90 484 685294 685383 685473 685563 685652 90 485 686189 686279 686368 686458 686547 90 486 687083 687172 687261 687351 687440 89 487 687975 i 688064 688153 688242 688331 89 488 688865 688953 689042 689131 689220 ! 9 489 689753 689841 689930 690019 690107 8 9 490 690639 690728 690816 690905 690993 8 9 491 691524 691612 691700 691789 691877 88 492 692406 692494 692583 692671 692759 88 493 693287 693375 693463 693551 693639 88 494 694166 694254 694342 694430 694517 88 495 695044 695*31 695219 695307 695394 88 496 695919 696007 696094 696182 696269 87 497 696793 696880 696968 697055 697142 87 498 697665 697752 697839 697926 698014 87 499 698535 698622 698709 698796 698883 87 (245) LOGARITHMS Log. 698. NO. 500 No. 1 2 3 4 Diff. 500 698970 699057 699144 ! 699231 699317 87 501 699838 699924 700011 700098 700184 87 502 700704 700790 700877 700963 701050 86 503 701568 701654 701741 701827 701913 86 504 702431 702517 702603 702689 702775 86 505 703291 703377 703463 703549 703635 86 506 704151 704236 704322 704408 704494 86 507 705008 705094 705179 705265 705350 i 86 508 705864 705949 706035 ; 706120 706206 85 509 706718 706803 706888 706974 707059 85 510 707570 707655 707740 707826 707911 85 511 708421 708506 708591 708676 708761 85 512 709270 709355 709440 709524 709609 85 513 7IOII7 710202 710287 710371 710456 85 710963 711048 711132 711217 711301 84 515 516 711807 712650 711892 712734 711976 712818 712060 712902 712144 84 712986 84 517 713491 713575 713659 713742 713826 84 518 714330 714414 7H497 714581 714665 84 519 715167 715251 715335 7154*8 715502 84 520 716003 716087 716170 716254 716337 83 521 716838 ! 716921 717004 717088 717171 83 522 7I767I 717754 717837 717920 718003 83 523 718502 718585 718668 718751 718834 83 524 7I933I 719414 719497 719580 719663 83 5 2 5 720159 720242 720325 720407 720490 83 526 720986 721068 j 721151 721233 721316 83 527 72l8ll 721893 i 721975 722058 722140 82 528 722634 722716 ! 722798 722881 722963 82 529 723456 723538 723620 723702 723784 82 530 724276 724358 724440 724522 724604 82 531 725095 725176 725258 725340 725422 82 532 725912 725993 726075 726156 726238 82 533 726727 726809 i 726890 726972 727053 81 534 727541 727623 727704 727785 727866 81 535 728354 728435 728516 728597 728678 81 536 729165 729246 729327 729408 729489 81 537 729974 730055 i 730136 730217 730298 81 538 730782 730863 730944 731024 73U05 81 539 731589 731669 731750 731830 73I9H 81 54 732394 732474 732555 732635 732715 80 54 1 733197 733278 733358 733438 733518 80 542 733999 734079 734160 734240 734320 i 80 543 734800 734880 734960 735040 735120 ; 80 544 735599 735679 735759 735838 735918 80 545 736397 736476 736556 736635 736715 80 54 6 737193 737272 737352 737431 7375" 79 547 737987 738067 738146 738225 738305 79 548 738781 738860 738939 739018 739097 79 549 739572 739651 739731 739810 739889 79 For explanation see pp. 207-215 (246) OF NUMBERS Log. 740. No. 549. 5 6 7 8 9 DifE. 500 699404 69949I 699578 | 699664 699751 87 501 700271 700358 700444 700531 700617 87 502 701136 701222 701309 701395 701482 86 53 701999 702086 702172 702258 702344 86 504 702861 702947 703033 703119 i 703205 86 505 703721 703807 703893 703979 I 704065 86 506 704579 704665 704751 704837 704922 86 57 705436 705522 705607 705693 705778 86 508 706291 706376 706462 706547 706632 85 509 707144 707229 7073 i 5 707400 707485 85 510 707996 708081 708166 708251 708336 85 5" 708846 708931 709015 709100 709185 85 5 709694 709779 709863 709948 710033 85 710540 710625 710710 710794 710879 85 514 711385 711470 7H554 711639 711723 84 515 712229 712313 712397 712481 712566 84 516 713070 713154 713238 713323 713407 84 517 713910 713994 518 7H749 714833 714078 714916 714162 715000 714246 715084 84 84 5i9 715586 715669 715753 715836 715920 84 520 716421 716504 716588 716671 716754 ; 83 521 717254 717338 717421 717504 717587 83 522 718086 718169 718253 718336 718419 83 523 718917 719000 719083 719165 719248 83 524 719745 719828 719911 719994 720077 83 525 720573 526 721398 720655 721481 720738 721563 720821 721646 720903 721728 83 83 527 722222 722305 722387 722469 722552 82 528 723045 723127 723209 723291 723374 82 529 723866 723948 724030 724112 724194 82 530 724685 724767 724849 72493 1 725013 82 53i 725503 725585 725667 725748 725830 82 532 726320 726401 726483 726564 726646 82 533 727134 727216 727297 727379 727460 81 534 727948 728029 728110 728191 728273 Si 535 728759 728841 728922 729003 729084 81 536 729570 729651 729732 729813 729893 81 537 730378 730459 730540 730621 730702 81 538 731186 731266 731347 731428 731508 81 539 73I99 1 732072 732152 732233 732313 Si 540 732796 732876 732956 733037 733117 So 733598 733679 733759 733839 733919 So 542 734400 73448o 73456o 734640 734720 80 543 735200 735279 735359 735439 735519 80 544 735998 736078 736157 736237 736317 80 545 736795 736874 736954 737034 80 546 737590 737670 737749 737829 737908 79 547 738384 738463 738543 738622 738701 79 548 739177 739256 739335 7394H 739493 79 549 739968 740047 740126 740205 740284 79 (247) LOGARITHMS Log. 740. No. 550 No. 1 2 3 4 DifiE. 550 740363 740442 740521 740600 740678 79 551 741152 741230 741309 741388 741467 79 552 741939 742018 742096 742I7S 742254 79 553 742725 742804 742882 742961 743039 78 554 743510 743588 743667 743745 743823 78 555 744293 744371 744449 744528 744606 78 556 745075 745 r 53 745231 745309 745387 78 557 745855 745933 746011 746089 746167 78 558 746634 746712 746790 746868 746945 78 559 747412 747489 747567 747645 747722 78 560 748188 748266 748343 748421 748498 77 56i 748963 749040 749118 749195 749272 77 562 749736 749814 749891 749968 750045 77 563 750508 750586 750663 750740 750817 77 564 751279 75 J 356 75*433 75i5io 751587 77 565 752048 752125 752202 752279 752356 77 566 752816 752893 752970 753047 753123 77 567 753583 75366o 753736 753813 753889 77 568 754348 754425 754501 754578 754654 76 569 755112 755189 755265 755341 755417 76 570 755875 75595 1 756027 756103 756l8o 76 57i 756636 756712 756788 756864 756940 76 572 757396 757472 757548 757624 757700 76 573 758155 758230 758306 758382 758458 76 574 758912 758988 759063 759139 759214 76 575 759668 759743 759819 759894 759970 75 576 760422 760498 760573 760649 760724 75 577 761176 761251 761326 761402 761477 75 578 761928 762003 762078 762153 762228 75 579 762679 762754 762829 762904 762978 75 580 763428 763503 763578 763653 763727 75 58i 764176 764251 764326 764400 764475 75 582 764923 764998 765072 765H7 765221 75 583 765669 765743 765818 765892 765966 74 584 766413 766487 766562 766636 766710 74 585 767156 767230 767304 767379 767453 74 586 767898 767972 768046 768120 768194 74 587 768638 768712 768786 768860 768934 74 588 769377 769451 769525 769599 769673 74 589 770115 770189 770263 770336 770410 74 590 770852 770926 770999 771073 771146 74 59i 771587 771661 771734 771808 771881 73 592 772322 772395 772468 772542 772615 73 593 773055 773128 773201 773274 773348 73 594 773786 77386o 773933 774006 774079 73 595 774517 774590 774663 774736 774809 73 596 775246 7753 J 9 775392 775465 775538 73 597 775974 776047 776120 776193 776265 73 598 776701 776774 776846 776919 776992 73 599 777427 777499 777572 777644 777717 72 For explanation see pp. 207-215 (248) OF NUMBERS Log. 778. NO. 599. No. 5 6 7 8 9 Diffi. 550 740757 740836 740915 740994 741073 79 551 741546 741624 741703 741782 741860 79 552 742332 742411 742489 742568 742647 79 553 743118 743196 743275 743353 743431 78 554 743902 743980 744058 744136 744215 78 555 744684 744762 744840 744919 744997 78 556 745465 745543 745621 745699 745777 78 557 746245 746323 746401 746479 746556 78 558 747023 747101 747179 747256 747334 78 559 747800 747878 747955 748033 748110 78 560 748576 748653 748731 748808 748885 77 56i 749350 749427 749504 749582 749659 77 562 750123 750200 750277 750354 750431 77 563 750894 750971 751048 75"25 751202 77 564 751664 75i74i 751818 751895 751972 77 565 752433 752509 752586 752663 752740 77 566 753200 753277 753353 75343 753506 77 567 753966 i 754042 754119 754195 754272 77 568 754730 754807 754883 75496o 755036 76 569 755494 755570 755646 : 755722 755799 ; 76 570 756256 756332 756408 756484 756560 76 57i 757016 757092 757^8 757244 757320 76 572 757775 757851 757927 758003 75 8 079 76 573 758533 758609 758685 758761 758836 76 574 759290 759366 759441 759517 759592 76 3* 760045 760799 760121 760875 760196 760272 760347 75 760950 761025 761101 75 577 761552 761627 761702 761778 761853 75 578 762303 762378 762453 | 762529 762604 75 579 763053 763128 763203 763278 763353 ! 75 58o 763802 763877 763952 764027 764101 75 58i 764550 764624 764699 764774 764848 75 582 765296 765370 765445 765520 765594 75 583 766041 766115 766190 766264 766338 74 584 766785 766859 766933 767007 767082 74 585 767527 767601 767675 767749 767823 74 586 768268 768342 768416 768490 1 768564 74 769008 769082 769156 769230 769303 74 588 769746 769820 769894 769968 770042 74 589 770484 770557 770631 770705 770778 74 590 1 771220 771293 771367 771440 77I5H 74 59i 771955 772028 772102 772175 772248 73 592 772688 772762 772835 772908 772981 73 593 773421 773494 773567 773640 773713 73 594 774152 774225 774298 774371 774444 73 595 774882 774955 775028 775100 775173 73 596 775610 775683 775756 775829 775902 73 597 776338 776411 776483 776556 776629 73 598 777064 777137 777209 777282 777354 73 599 777789 777862 777934 778006 778079 72 '249) LOGAKITHMS Log. 778. No. 600. No. 1 2 3 4 Diff. 600 778151 778224 778296 778368 778441 72 601 778874 778947 779019 779091 779163 72 602 779596 779669 779741 779813 779885 72 603 780317 780389 780461 780533 780605 72 604 781037 781109 781181 781253 781324 72 605 781755 781827 781899 781971 782042 72 606 782473 782544 782616 782688 782759 72 607 783189 783260 783332 783403 783475 71 608 783904 783975 784046 784118 784189 71 609 784617 784689 784760 784831 784902 7i 610 785330 785401 785472 785543 785615 7i 611 786041 786112 786183 786254 786325 7i 612 786751 786822 786893 786964 787035 71 613 787460 787531 787602 787673 787744 7i 614 788168 788239 788310 788381 788451 7i 6i5 788875 788946 789016 789087 789157 7i 616 789581 789651 789722 789792 789863 70 6i7 790285 790356 790426 790496 790567 70 618 790988 791059 791129 791199 791269 70 619 791691 791761 791831 791901 791971 70 620 792392 792462 792532 792602 792672 70 621 793092 793162 793231 793301 793371 70 622 793790 793860 793930 794000 794070 70 623 794488 794558 794627 794697 794767 70 624 795185 795254 795324 795393 795463 70 625 795880 795949 796019 796088 796158 69 626 796574 796644 796713 796782 796852 69 627 797268 797337 797406 797475 797545 69 628 797960 798029 798098 798167 798236 69 629 798651 798720 798789 798858 798927 69 630 799341 799409 799478 799547 799616 69 631 800029 800098 800167 800236 800305 69 632 800717 800786 800854 800923 800992 69 633 801404 801472 801541 801609 801678 69 634 802089 802158 802226 802295 802363 69 635 802774 802842 802910 802979 803047 68 636 637 803457 804139 804208 803594 804276 803662 804344 803730 804412 68 68 638 804821 804889 804957 805025 805093 68 639 805501 805569 805637 805705 805773 68 640 806180 806248 806316 806384 806451 68 641 806858 806926 806994 807061 807129 68 642 807535 807603 807670 807738 807806 68 643 808211 808279 808346 808414 i 808481 67 644 808886 808953 809021 809088 i 809156 67 645 809560 809627 809694 809762 809829 67 646 810233 810300 810367 810434 810501 67 647 810904 810971 811039 811106 811173 67 648 811575 811642 811709 811776 811843 67 649 812245 812312 812379 812445 812512 67 For explanation see pp. 207-215 (250) OF NUMBERS Log. 812. No. 649. No. 5 6 7 8 9 Diff. 600 778513 778585 778658 77873 ! 778802 72 601 779236 779308 779380 , 779452 779524 72 602 779957 780029 780101 780173 780245 72 603 780677 780749 780821 780893 780965 72 604 781396 781468 781540 781612 781684 72 605 782114 782186 782258 782329 782401 72 606 782831 782902 782974 783046 783117 72 607 783546 783618 783689 783761 783832 71 608 784261 784332 784403 784475 784546 71 609 784974 785045 785116 785187 785259 71 610 785686 785757 785828 785899 785970 71 611 786396 786467 786538 786609 786680 71 612 787106 787177 787248 7873^ 787390 71 613 787815 787885 787956 788027 788098 71 614 788522 788593 788663 788734 788804 71 615 789228 789299 789369 789440 789510 71 616 789933 790004 790074 790144 790215 70 617 790637 790707 790778 790848 790918 70 6x8 791340 791410 791480 791550 791620 70 619 792041 792111 792181 792252 792322 70 620 792742 792812 792882 792952 793022 70 621 793441 793511 793581 793651 793721 70 622 794139 794209 794279 794349 794418 70 623 794836 794906 794976 795045 795H5 70 624 795532 795602 795672 795741 70 625 796227 796297 796366 796436 796505 69 626 796921 796990 797060 797129 797198 6 9 627 797614 797683 797752 797821 797890 69 628 798305 798374 798443 798513 798582 69 629 798996 799065 799134 799203 799272 69 630 799685 799754 799823 799892 799961 69 631 800373 800442 800511 800580 800648 69 632 801061 801129 801198 801266 801335 69 633 801747 801815 801884 801952 80202 1 6 9 634 802432 802500 802568 802637 802705 6 9 635 803116 803184 803252 803321 803389 68 636 803798 803867 803935 804003 804071 68 637 804480 804548 804616 804685 804753 68 638 805161 805229 805297 805365 805433 68 639 805841 805908 805976 806044 8o6lI2 68 640 806519 806587 806655 806723 806790 68 641 807197 807264 807332 807400 807467 68 642 807873 807941 808008 808076 808143 68 643 808549 808616 808684 808751 808818 67 644 809223 809290 809358 809425 809492 67 645 809896 809964 810031 810098 810165 67 646 810569 810636 810703 810770 810837 67 3 811240 811910 811307 8ii977 811374 812044 811441 812111 811508 812178 67 67 649 812579 812646 812713 812780 812847 67 (251) LOGARITHMS Log. 812. No. 650. No. 1 2 3 4 Diff. 650 812913 812980 813047 813114 813181 67 651 813581 813648 813714 813781 | 813848 67 652 814248 814314 814381 814447 814514 67 653 814913 814980 815046 8i5"3 8I5I79 66 654 815578 815644 815711 8i5777 815843 66 655 816241 816308 816374 816440 816506 66 656 816904 816970 817036 817102 817169 66 657 817565 817631 817698 817764 817830 66 658. 818226 i 818292 818358 818424 818490 66 659 818885 818951 819017 819083 819149 66 660 819544 819610 819676 819741 819807 66 661 820201 820267 820333 820399 820464 66 662 820858 820924 820989 821055 821120 66 663 821514 ! 821579 821645 821710 821775 65 664 822168 822233 822299 822364 822430 65 665 822822 822887 822952 823018 823083 65 666 823474 823539 823605 823670 823735 65 667 824126 824191 824256 824321 824386 65 668 824776 824841 824906 824971 825036 65 669 825426 825491 825556 825621 825686 65 670 826075 826140 826204 826269 826334 65 671 826723 | 826787 826852 826917 826981 65 672 827369 827434 827499 827563 827628 65 673 828015 828080 828144 828209 828273 64 674 828660 828724 828789 828853 828918 64 675 676 829304 829947 829368 830011 829432 830075 829497 830139 829561 830204 64 64 677 830589 830653 830717 830781 830845 64 678 831230 831294 831358 831422 831486 64 679 831870 831934 831998 832062 832126 64 680 832509 832573 832637 832700 832764 64 681 833H7 833211 833275 833338 833402 64 682 833784 833848 833912 833975 834039 64 683 834421 834484 834548 834611 834675 64 684 835056 835120 835183 835247 8353io 63 685 835691 835754 835817 835881 835944 63 686 836324 836387 836451 836514 836577 63 687 836957 837020 837083 837146 837210 63 688 837588 837652 837715 837778 837841 63 689 838219 838282 838345 838408 838471 63 690 838849 838912 838975 839038 839101 63 6^1 839478 839541 839604 839667 839729 63 692 840106 840169 840232 840294 840357 63 693 840733 840796 840859 840921 840984 63 694 841359 841422 841485 841547 841610 63 695 841985 842047 842110 842172 842235 62 842609 842672 842734 842796 842859 62 697 843233 843295 843357 843420 843482 62 698 843855 843918 843980 844042 844104 62 699 844477 844539 844601 844664 844726 62 For explanation see pp. 2?7-2i5 (252) OF NUMBERS Log. 845. No. 699. No. 5 6 7 8 9 Diff. 650 813247 813314 813381 813448 8I35H 67 651 813914 813981 814048 814114 814181 67 652 814581 814647 814714 814780 i 814847 67 653 815246 815312 815378 815445 815511 66 654 815910 815976 816042 816109 816175 66 655 816573 816639 816705 816771 816838 66 656 817235 817301 817367 817433 817499 66 657 817896 817962 818028 818094 818160 66 658 818556 818622 818688 818754 818820 66 659 819215 819281 819346 819412 819478 66 660 819873 819939 820004 820070 820136 66 661 820530 820595 820661 820727 820792 66 662 821186 821251 821317 j 821382 821448 66 663 821841 i 821906 821972 822037 822103 65 664 822495 822560 822626 822691 822756 65 665 823148 823213 823279 823344 823409 65 666 823800 823865 823930 823996 824061 65 667 824451 824516 824581 824646 824711 65 668 825101 825166 i 825231 825296 825361 65 669 825751 825815 825880 825945 826010 65 670 826399 826464 ! 826528 826593 826658 65 671 827046 827111 827175 827240 827305 65 672 827692 827757 827821 827886 827951 65 673 828338 828402 828467 828531 8 2 8<;9<; 64 674 828982 829046 829111 829175 829239 64 675 829625 829690 829754 829818 829882 64 676 830268 830332 ! 830396 830460 830525 64 677 830909 830973 831037 831102 831166 64 678 831550 831614 831678 831742 831806 64 679 832189 832253 832317 832381 832445 64 680 832828 832892 832956 833020 833083 64 681 833466 833530 833593 833657 833721 64 682 834103 834166 834230 834294 834357 64 683 834739 834802 834866 834929 834993 64 684 835373 835437 835500 835564 835627 63 S 836007 836641 836071 836704 836134 836767 836197 836830 836261 836894 63 63 687 837273 837336 837399 837462 837525 63 688 689 837904 838534 837967 838597 838030 838660 838093 838723 838156 838786 63 63 690 839164 839227 839289 839352 839415 63 691 839792 839855 839918 839981 840043 63 692 840420 840482 840545 840608 840671 63 693 841046 841109 841172 841234 841297 63 694 841672 841735 841797 841860 841922 63 ^95 842297 842360 842422 842484 842547 62 696 842921 842983 843046 843108 843170 62 697 843544 843606 843669 843731 843793 62 698 844166 844229 844291 844353 844415 62 699 844788 844850 844912 844974 845036 62 (253) P 2 LOGARITHMS Log. 845. No. 700. No. 1 o o 4 Difl. 700 845098 845160 845222 845284 845346 62 701 845718 845780 845842 845904 845966 62 702 846337 846399 846461 846523 846585 62 703 846955 847017 847079 847141 847202 62 704 847573 847634 847696 847758 847819 62 705 848189 848251 848312 848374 848435 62 7 06 848805 848866 848928 848989 849051 6l 707 849419 849481 849542 849604 849665 61 7 08 850033 850095 850156 850217 850279 61 709 850646 850707 850769 850830 850891 61 710 851258 851320 851381 851442 851503 6l 711 712 851870 852480 851931 852541 851992 852602 852053 852663 852114 852724 61 61 713 853090 853150 853211 853272 853333 61 853698 853759 853820 853881 853941 61 715 716 854306 854913 854367 854974 854428 855034 854488 855095 854549 855156 61 61 717 718 855519 856124 855580 856185 855640 856245 855701 856306 855761 856366 61 60 719 856729 856789 856850 856910 856970 60 720 857332 857393 857453 857513 857574 60 721 857935 857995 858056 858116 858176 60 722 858537 858597 858657 858718 858778 60 723 859138 859198 859258 859318 859379 60 724 859739 859799 859859 859918 859978 60 725 860338 860398 860458 860518 860578 60 726 860937 860996 861056 861116 861176 60 727 861534 861594 861654 861714 861773 60 728 862131 862191 862251 862310 862370 60 729 862728 862787 862847 862906 862966 60 730 863323 863382 863442 863501 863561 59 731 863917 863977 864036 864096 864155 59 732 864511 864570 864630 864689 864748 59 733 865104 865163 865222 865282 865341 59 734 865696 865755 865814 865874 865933 59 735 866287 866346 866405 866465 866524 59 736 866878 866937 866996 867055 867114 59 737 867467 867526 867585 867644 867703 59 738 868056 868115 868174 868233 868292 59 739 868644 868703 868762 868821 868879 59 740 869232 869290 869349 869408 869466 59 869818 869877 869935 869994 870053 59 742 870404 870462 870521 870579 870638 58 743 870989 871047 871106 871164 871223 58 744 871573 871631 871690 871748 871806 58 746 872156 872739 872215 872797 872273 872855 872331 872913 872389 872972 58 58 873321 873379 873437 873495 873553 58 748 873902 873960 874018 874076 874134 58 749 874482 874540 874598 874656 874714 58 For explanation see pp. 207-215 (254) OF NUMBERS Log. 875. No. 749. No. 5 6 7 8 9 Diff. 700 845408 845470 845532 845594 845656 62 701 846028 846090 846151 846213 846275 62 702 846646 846708 846770 846832 846894 62 703 847264 847326 847388 847449 847511 62 704 847881 847943 848004 848066 848128 62 705 848497 848559 848620 848682 848743 ! 62 7 06 849112 849174 849235 849297 849358 6 1 707 849726 849788 849849 84991 i 849972 6 1 7 08 850340 850401 850462 850524 850585 61 709 850952 851014 851075 \ 851136 85H97 61 710 851564 851625 851686 851747 851809 61 711 852175 852236 852297 852358 852419 61 712 852785 852846 852907 ; 852968 853029 61 713 853394 853455 853516 853577 853637 61 7M 854002 854063 854124 854185 854245 61 715 854610 854670 854731 854792 854852 61 7l6 855216 855277 855337 855398 I 855459 61 717 7 l8 855822 856427 855882 855943 856487 856548 856003 856608 856064 856668 61 60 719 857031 857091 857152 857212 857272 60 720 857634 857694 857755 857815 857875 60 721 858236 858297 858357 858417 858477 60 722 858838 858898 858958 859018 \ 859078 60 723 859439 859499 859559 859619 859679 60 724 860038 860098 860158 860218 860278 60 i 860637 861236 860697 860757 861295 861355 860817 86I4I5 860877 861475 60 60 861833 861893 861952 862012 862072 60 728 862430 862489 862549 862608 862668 60 729 863025 863085 863144 863204 863263 60 730 863620 863680 863739 863799 863858 59 731 864214 864274 864333 864392 864452 59 732 864808 864867 864926 864985 865045 59 733 865400 865459 865519 865578 865637 59 734 865992 866051 866IIO 866169 866228 59 735 866583 866642 866701 866760 866819 59 736 867173 867232 867291 867350 , 867409 59 3 867762 868350 867821 868409 867880 868468 867939 867998 59 868527 868586 59 739 868938 868997 869056 869114 869173 59 740 869525 869584 869642 869701 869760 59 74i 870111 870170 870228 870287 870345 59 742 870696 870755 870813 870872 870930 i 58 743 871281 871339 871398 871456 871515 58 744 871865 871923 871981 872040 872098 58 9 872448 873030 872506 873088 872564 873146 872622 873204 872681 873262 58 58 747 873611 873669 873727 873785 873844 58 748 874192 874250 874308 874366 874424 58 749 874772 874830 874888 874945 875003 58 (255; LOGARITHMS Log. 875. No. 750. No. 1 2 3 4 750 875061 875"9 875177 875235 875293 58 751 875640 875698 875756 875813 875871 5 8 752 876218 876276 876333 876391 876449 58 753 876795 876853 876910 876968 877026 58 754 877371 877429 877487 877544 877602 58 755 877947 878004 878062 878119 878177 57 756 878522 878579 878637 878694 878752 57 757 879096 879153 879211 879268 879325 57 758 879669 879726 879784 879841 879898 57 759 880242 880299 880356 880413 880471 57 760 880814 880871 880928 880985 881042 57 761 881385 881442 881499 881556 881613 57 762 881955 882012 882069 882126 882183 57 763 882525 882581 882638 882695 882752 57 764 883093 883150 883207 883264 883321 57 765 883661 883718 883775 883832 883888 57 766 884229 884285 884342 884399 884455 57 767 884795 884852 884909 884965 885022 57 768 885361 8854X8 ! 885474 885531 885587 57 769 885926 885983 | 886039 886096 886152 56 770 886491 886547 886604 886660 886716 56 771 887054 887III 887167 887223 887280 56 772 887617 887674 887730 887786 887842 56 773 888179 888236 888292 888348 888404 56 774 888741 888797 888853 888909 888965 56 775 889302 889358 i 889414 889470 889526 56 776 889862 889918 889974 890030 890086 56 777 890421 890477 890533 890589 890645 56 778 890980 891035 891091 891147 891203 56 779 891537 891593 891649 891705 891760 56 780 892095 892150 892206 892262 892317 56 781 892651 892707 892762 892818 892873 56 782 893207 893262 893318 893373 893429 56 783 893762 893817 893873 893928 893984 55 784 894316 894371 894427 894482 894538 55 785 894870 894925 894980 895036 895091 55 786 895423 895478 895533 895588 895644 55 787 895975 896030 896085 896140 896195 55 788 896526 896581 896636 \ 896692 ! 896747 55 789 897077 897132 897187 897242 897297 55 790 897627 897682 897737 897792 897847 55 791 898176 898231 898286 898341 898396 55 792 898725 898780 898835 898890 898944 55 793 899273 899328 899383 899437 899492 55 794 899821 899875 899930 899985 900039 55 795 900367 1 900422 900476 900531 900586 55 796 900913 900968 9OIO22 901077 901131 55 797 901458 90I5I3 901567 901622 901676 54 798 902003 902057 902112 902166 9O222I 54 799 902547 902601 902655 902710 902764 54 For explanation see pp. 207-215 (256) OF NUMBERS Log. 903. NO. 799. No. 5 6 7 | 8 9 Diff. 750 875351 875409 875466 875524 875582 58 751 875929 875987 876045 876102 j 876160 58 752 876507 876564 876622 876680 ! 876737 58 753 877083 877141 877199 877256 ! 877314 58 754 877659 877717 877774 877832 877889 58 755 878234 878292 878349 878407 878464 57 756 878809 878866 878924 878981 879039 57 757 879383 758 8799 S6 879440 880013 879497 880070 879555 880127 879612 880185 57 57 759 880528 880585 880642 880699 1 880756 57 760 881099 881156 881213 881271 881328 57 761 881670 881727 881784 881841 881898 57 762 i 882240 882297 882354 882411 882468 57 763 i 882809 882866 882923 882980 883037 57 764 883377 883434 883491 883548 883605 57 765 883945 884002 884059 884115 884172 57 766 884 SI 2 884569 884625 884682 884739 57 767 885078 885135 885192 885248 885305 57 768 885644 885700 885757 885813 885870 57 76 9 886209 886265 886321 886378 886434 56 770 886773 886829 886885 886942 886998 56 771 887336 887392 887449 887505 1 887561 56 772 887898 887955 888067 888123 56 773 888460 888516 888573 888629 888685 56 774 889021 889077 889134 889190 889246 56 775 889582 889638 889694 889750 889806 56 776 890141 890197 890253 890309 890365 56 777 890700 890756 890812 890868 890924 56 778 891259 891314 891370 891426 891482 56 779 891816 891872 891928 891983 892039 56 780 892373 892429 892484 892540 892595 56 781 892929 892985 893040 893096 893151 56 782 893484 893540 893595 893651 893706 56 783 894039 894094 894150 894205 894261 55 784 894593 894648 894704 894759 894814 55 785 895146 895201 895257 8953 1 2 895367 55 786 895699 895754 895809 895864 895920 55 787 896251 896306 896361 896416 896471 55 788 896802 896857 896912 896967 897022 55 789 897352 897407 897462 897517 897572 55 790 897902 897957 898012 898067 898122 55 791 898451 898506 898561 898615 898670 55 792 898999 899054 899109 899164 899218 55 793 899547 899602 899656 899711 899766 55 794 900094 900149 900203 900258 900312 55 795 900640 900695 900749 900804 900859 55 796 901186 901240 901295 901349 901404 55 797 901731 901785 901840 901894 901948 54 798 902275 902329 902384 902438 902492 54 799 902818 902873 902927 902981 903036 54 LOGARITHMS Log. 903. No. 800. No. 1 2 3 4 Diff. 800 903090 903144 903199 903253 903307 54 801 903633 903687 903741 903795 903849 54 802 904174 904229 904283 904337 904391 54 803 904716 904770 904824 904878 904932 54 804 905256 905310 905364 905418 905472 54 805 905796 905850 905904 905958 906012 54 806 906335 906389 906443 906497 906551 54 807 906874 906927 906981 907035 907089 54 808 907411 907465 907519 907573 907626 54 809 907949 908002 908056 908110 908163 54 810 908485 908539 908592 908649 908699 54 811 909021 909074 909128 909181 909235 54 812 909556 909610 909663 909716 909770 53 813 910091 910144 910197 910251 910304 53 814 910624 910678 910731 910784 910838 53 815 911158 911211 911264 911317 911371 53 8x6 911690 911743 911797 911850 911903 53 8i z 912222 912275 912328 912381 912435 53 818 912753 912806 912859 912913 912966 53 819 913284 913337 913390 913443 913496 53 820 913814 913867 913920 913973 914026 53 821 914343 914396 914449 914502 914555 53 822 914872 914925 914977 915030 915083 53 823 915400 915453 915505 915558 915611 53 824 915927 915980 916033 916085 916138 53 825 916454 916507 916559 916612 916664 53 826 916980 917033 917085 917138 917190 53 827 917506 917558 917611 917663 917716 52 828 918030 918083 918135 918188 918240 5 2 829 918555 918607 918659 918712 918764 S 2 830 919078 919130 919183 919235 919287 52 831 919601 919653 919706 919758 919810 5 2 832 920123 920176 920228 920280 920332 52 833 920645 920697 920749 920801 920853 52 834 921166 921218 921270 921322 921374 52 835 921686 921738 921790 921842 921894 52 836 922206 922258 922310 922362 922414 52 837 922725 922777 922829 922881 922933 5 2 838 923244 923296 923348 923399 923451 52 839 923762 923814 1 923865 923917 | 923969 52 840 924279 924331 924383 924434 924486 52 841 924796 924848 924899 924951 i 925003 52 842 925312 925364 925415 925467 925518 S 2 843 925828 925879 ! 925931 925982 926034 51 844 926342 926394 j 926445 926497 926548 5i 845 926857 926908 926959 927011 927062 5i 846 927370 927422 927473 927524 927576 5i 847 927883 927935 927986 928037 928088 51 848 928396 928447 928498 928549 928601 51 849 928908 928959 929010 i 929061 929112 Si For explanation see pp. 207-215 (258^ OF NUMBERS Log. 929. NO. 849. No. 5 6 7 Q 9 Diff. 800 903361 903416 903470 903524 903578 54 801 903904 903958 904012 904066 904120 54 802 904445 904499 904553 904607 904661 54 803 904986 905040 905094 i 905148 905202 54 804 905526 905580 905634 905688 905742 54 805 906066 906119 906173 906227 906281 54 806 906604 906658 906712 906766 906820 54 807 907143 907196 907250 907304 907358 54 808 907680 97734 907787 907841 907895 54 809 908217 908270 908324 908378 908431 54 810 908753 908807 908860 908914 908967 54 811 909289 909342 909396 909449 909503 54 812 909823 909877 909930 909984 910037 53 813 910358 910411 910464 910518 910571 53 814 910891 910944 910998 911051 911104 53 815 911424 911477 9"530 9"584 911637 53 816 911956 912009 912063 912116 912169 53 817 912488 912541 912594 912647 912700 53 818 913019 913072 913125 913178 913231 53 819 913549 913602 913655 913708 913761 53 820 914079 914132 914184 914237 914290 53 821 914608 914660 9H7I3 9H766 914819 I 53 822 915*36 915189 915241 915294 915347 53 823 915664 915716 915769 915822 915875 53 824 916191 916243 916296 916349 | 9I640I 53 825 916717 916770 916822 916875 916927 53 826 917243 917295 : 917348 917400 917453 53 827 917768 917820 917873 917925 917978 52 828 918293 918345 918397 918450 918502 52 829 918816 918869 918921 918973 919026 5 2 830 919340 919392 919444 919496 919549 5 2 831 919862 919914 919967 920019 ! 920071 52 832 920384 920436 920489 i 920541 920593 52 833 920906 920958 921010 921062 921114 52 854 921426 921478 921530 921582 921634 i 52 835 921946 921998 922050 922102 922154 52 830 922466 922518 922570 922622 922674 52 837 922985 923037 ; 923089 923HO 923192 52 838 923503 923555 923607 923658 923710 52 839 924021 924072 924124 924176 i 924228 52 840 924538 924589 924641 924693 924744 52 841 925054 925106 925157 925209 925261 52 842 925570 925621 925673 925725 925776 52 843 926085 926137 926188 926240 926291 5i 844 926600 926651 ! 926702 926754 926805 5i 845 927114 927165 927216 927268 927319 5i 846 927627 927678 927730 927781 927832 51 847 928140 928191 928242 928293 928345 51 848 928652 928703 928754 928805 928857 51 849 929163 929215 929266 929317 929368 51 (259J LOGARITHMS Log. 929. No. 850. No. 1 2 3 4 Diff. 850 929419 929470 929521 929572 929623 5i 851 929930 929981 930032 930083 i 930134 5i f52 930440 930491 930542 930592 I 930643 5i 8 53 930949 931000 931051 931102 93 "53 5i 854 931458 931509 931560 931610 931661 5i 8 55 931966 932017 932068 932118 932169 5i 856 932474 932524 932575 932626 932677 5i 857 932981 933031 933082 933133 933i83 5i 858 933487 933538 933589 I 933639 933690 5i 859 933993 934044 934094 934145 934195 5i 860 934498 934549 934599 934650 934700 50 861 935003 935054 935104 935154 935205 50 862 935507 935558 9356o8 935658 935709 50 863 936011 936061 936m 936162 936212 50 864 936514 936564 936614 936665 936715 50 865 937016 937066 937H7 937167 937217 5o 866 937518 937568 937618 937668 937718 50 867 938019 938069 938119 938169 938219 50 868 938520 938570 938620 938670 938720 5o 869 939020 939070 939120 939170 939220 50 870 939519 939569 939619 939669 939719 50 871 940018 940068 940118 i 940168 940218 50 872 940516 940566 940616 940666 940716 5o 873 941014 941064 94III4 941163 941213 5o 874 94I5U 94I56I 941611 941660 941710 5o 875 942008 942058 942107 942157 942207 5o 876 942504 942554 942603 i 942653 942702 50 877 943000 943049 943099 943148 943198 49 878 943495 943544 ! 943593 943643 943692 49 879 943989 944038 944088 944137 944186 49 880 944483 944532 944581 944631 944680 49 881 944976 945025 945074 945124 945173 49 882 945469 9455 i 8 945567 945616 945665 49 883 94596i 946010 946059 946108 946157 49 884 946452 946501 946551 946600 946649 49 885 946943 946992 947041 947090 947140 49 886 947434 947483 947532 94758i 947630 49 887 947924 947973 948022 948070 948119 49 888 948413 948462 948511 948560 948609 49 889 948902 948951 948999 949048 949097 49 890 949390 949439 949488 949536 949585 49 891 949878 949926 949975 950024 950073 49 892 950365 950414 950462 9505" 950560 49 893 950851 950900 950949 ! 950997 951046 49 894 951338 951386 951435 95H83 95!532 49 895 951823 951872 951920 951969 952017 48 896 ! 952308 952356 952405 952453 952502 48 897 95 2 792 952841 952889 ; 95293 8 952986 48 898 953276 9533 2 5 953373 953421 953470 48 899 95376o 9538o8 953856 953905 953953 40 Eor explanation see pp. 207-215 (260) OF NUMBEES Log. 954. No. 899 I No. 5 6 7 8 9 Diff. 850 929674 929725 929776 929827 929879 51 851 93o l8 5 930236 930287 930338 930389 51 852 930694 930745 930796 930847 930898 51 853 931204 931254 931305 931356 931407 51 854 931712 931763 931814 931865 93I9I5 51 855 932220 932271 932322 932372 932423 51 856 932727 932778 932829 932879 932930 51 857 933 2 34 933285 933335 933386 933437 51 858 933740 933791 933841 933892 933943 51 859 934246 934296 934347 934397 934448 5 1 860 934751 934801 934852 934902 934953 50 861 935 2 55 935306 935356 935406 935457 50 862 935759 935809 935860 9359io 935960 50 863 936262 936313 936363 936413 936463 50 864 936765 936815 936865 936916 936966 50 865 937267 937317 937367 937418 937468 5 866 937769 937819 937869 937919 937969 5 867 938269 938320 938370 938420 938470 50 868 938770 938820 938870 938920 938970 i 5 869 939270 939320 939369 939419 939469 | 50 870 939769 939819 939869 939918 939968 | 50 871 940267 940317 940367 940417 940467 5 872 940765 940815 940865 940915 940964 50 873 941263 941313 941362 941412 941462 50 874 941760 941809 941859 941909 941958 50 875 942256 942306 942355 942405 942455 5o 876 942752 942801 942851 942901 942950 So 943247 943297 943346 943396 943445 49 878 943742 943791 943841 943890 943939 49 879 944236 944285 944335 944384 944433 49 880 944729 944779 944828 944877 944927 49 881 945222 945272 945321 945370 945419 49 882 945715 945764 9458i3 945862 945912 49 883 946207 946256 946305 946354 946403 49 884 946698 946747 946796 946845 946894 49 885 947189 947238 947287 947336 947385 49 886 947679 947728 947777 947826 947875 49 887 948168 948217 948266 948315 948364 49 888 948657 948706 948755 948804 948853 49 889 949146 949195 949244 949292 949341 49 890 949634 949683 949731 949780 949829 49 891 950121 950170 950219 950267 950316 49 892 950608 950657 950706 950754 950803 49 893 951095 95H43 951192 951240 951289 49 894 95i58o 951629 951677 951726 951775 49 895 952066 952114 952163 952211 952260 48 896 952550 952599 952647 952696 952744 48 897 953034 953083 953*31 953i8o 953228 48 898 9535i8 953566 953615 953663 9537" 48 899 954001 954049 954098 954146 954194 48 (26IJ LOGABITHMS Log. 954. NO. 900. No. 1 2 3 4 Diff. 900 954243 954291 954339 954387 954435 48 901 954725 954773 954821 954869 954918 48 902 955207 955255 955303 955351 955399 48 903 955688 955736 955784 955832 95588o 48 904 956168 956216 956265 956313 956361 48 905 956649 956697 956745 956793 956840 48 906 957128 957176 957224 957272 957320 48 907 957607 957655 957703 957751 957799 48 908 958086 958181 958229 958277 48 909 958564 958612 958659 958707 958755 48 9IO 959041 959089 959137 959185 959232 48 911 959518 959566 959614 959661 959709 48 912 959995 960042 960090 960138 960185 48 913 960471 960518 960566 9606 i 3 960661 48 914 960946 960994 961041 961089 961136 47 9*5 961421 961469 961516 961563 961611 47 916 961895 961943 961990 962038 962085 47 917 962369 962417 962464 962511 962559 47 918 962843 962890 962937 962985 963032 47 919 963316 963363 963410 963457 963504 47 920 963788 963835 963882 963929 963977 47 921 964260 964307 964354 964401 964448 47 922 964731 964778 964825 964872 964919 47 923 965202 965249 965296 965343 965390 47 924 965672 965719 965766 965813 965860 47 925 966142 966189 966236 966283 966329 47 926 966611 966658 966705 966752 966799 47 927 967080 967127 967173 967220 967267 47 928 967548 967595 967642 967688 967735 47 929 968016 968062 968109 968156 968203 47 930 968483 968530 968576 968623 968670 47 93i 968950 968996 969043 969090 969136 47 932 969416 969463 969509 969556 969602 47 933 969882 969928 969975 970021 970068 47 934 970347 970393 970440 970486 970533 46 935 970812 970858 970904 970951 970997 46 936 971276 971322 971369 971415 971461 46 937 971740 971786 971832 971879 971925 46 938 972203 972249 972295 972342 972388 46 939 972666 972712 972758 972804 972851 46 940 973128 973174 973220 973266 973313 46 941 973590 973636 973682 973728 973774 46 942 974051 974097 974H3 974189 974235 46 943 974512 974558 974604 974650 974696 46 944 974972 975018 975064 975110 ; 975^6 46 945 975432 975478 975524 975570 9756i6 46 946 975891 975937 975983 976029 i 976075 46 947 976350 ! 976396 976442 976488 976533 46 948 976808 i 976854 976900 976946 976992 46 949 977200 i 977312 977358 977403 977449 46 For explanation see pp. 207-215 (262) OP NUMBERS Log. 977. NO. 949. No. 5 6 7 8 9 Diff. 900 954484 954532 954580 954628 954677 48 901 954966 955 OI 4 955062 955^0 955158 48 902 955447 955495 955543 955592 955640 48 903 955928 S 955976 956024 956072 956120 48 W 956409 956457 956505 956553 956601 48 90S 956888 956936 956984 957032 957080 48 906 957368 957416 957464 957512 957559 48 907 957847 957894 957942 957990 958038 48 908 958325 958373 958421 958468 958516 48 909 958803 958850 958898 958946 : 958994 48 910 95928o 959328 959375 959423 959471 48 911 959757 959804 959852 959900 959947 48 912 960233 960280 960328 960376 960423 48 913 960709 960756 960804 960851 960899 48 914 961184 961231 961279 961326 96i374 47 915 916 961658 962132 961706 962180 961753 962227 961801 962275 961848 962322 47 47 9i7 962606 962653 962701 962748 962795 47 918 963079 963126 963174 963221 963268 47 919 963552 963599 963646 963693 963741 47 920 964024 964071 964118 964165 964212 47 921 964495 964542 964590 964637 964684 47 922 964966 965013 965061 965108 965155 47 923 965437 965484 965531 965578 965625 47 924 965907 965954 966001 966048 966095 47 925 966376 966423 966470 966517 966564 47 926 966845 966892 966939 966986 967033 47 927 967314 967361 967408 967454 967501 47 928 967782 967829 967875 967922 967969 47 929 968249 968296 968343 968390 968436 47 930 968716 968763 968810 968856 968903 47 931 969183 969229 969276 969323 969369 47 932 969649 969695 969742 969789 969835 47 933 970114 970161 970207 970254 970300 47 934 970579 970626 970672 970719 970765 46 935 971044 971090 971137 971183 971229 46 936 971508 971554 971601 971647 971693 46 937 971971 972018 972064 972110 972157 46 938 972434 972481 972527 972573 972619 46 939 972897 972943 972989 973035 973082 46 940 973359 973405 973451 973497 973543 46 941 973820 973866 9739U 973959 974005 46 942 974281 974327 974374 974420 974466 46 943 974742 974788 974834 974880 974926 46 944 975202 975248 975294 975340 975386 46 945 975662 975707 975753 975799 975845 46 946 976121 976167 976212 976258 976304 46 947 976579 976625 976671 976717 976763 46 948 977037 977083 977129 977175 977220 46 949 977495 977541 977586 977632 977678 46 (263) LOGARITHMS Log. 977. No. 950. No. 1 2 3 4 Diff. 950 977724 977769 977815 977861 977906 46 951 978181 978226 978272 978317 978363 46 952 978637 978683 978728 978774 978819 46 953 979093 979138 979184 979230 979275 46 954 979548 979594 979639 979685 97973 46 955 980003 980049 980094 980140 980185 45 956 980458 980503 980549 980594 980640 45 958 980912 981366 980957 981411 981003 981456 981048 981501 981093 98i547 45 45 959 981819 981864 981909 981954 982000 45 960 982271 982316 982362 982407 982452 45 961 982723 982769 982814 982859 982904 45 962 963 983175 983626 983220 983671 983265 983716 983310 983762 983356 983807 45 45 964 984077 984122 984167 984212 984257 45 965 984527 984572 984617 984662 984707 45 966 984977 985022 985067 985112 985157 45 967 985426 985471 985516 985561 985606 45 968 985875 969 | 986324 985920 986369 985965 986413 986010 986458 986055 986503 45 45 970 986772 986817 986861 986906 986951 45 971 987219 987264 987309 987353 987398 45 972 987666 987711 987756 987800 987845 45 973 988113 988157 988202 988247 988291 45 974 988559 988604 988648 988693 988737 45 975 989005 989049 989094 989138 989183 45 976 989450 989494 989539 989583 989628 44 978 989895 990339 989939 990383 989983 990428 990028 990472 990072 990516 44 44 979 990783 990827 990871 990916 990960 44 980 991226 991270 991315 991359 991403 44 981 991669 991713 991758 991802 991846 44 982 992111 992156 992200 992244 992288 i 44 983 992554 992598 992642 992686 992730 44 984 992995 993039 993083 993127 993172 44 985 993436 99348o 993524 993568 993613 1 44 986 993877 993921 993965 994009 994053 44 987 9943 i 7 99436i 994405 994449 994493 44 988 994757 994801 994845 994889 994933 44 989 995196 995240 995284 995328 995372 44 990 995635 995679 995723 995767 995811 44 991 996074 996117 996161 996205 996249 ! 44 992 996512 996555 996599 996643 996687 44 993 996949 996993 997037 997080 997124 44 994 997386 997430 997474 9975 i 7 997561 44 995 997823 997867 997910 997954 997998 44 996 998259 998303 998347 998390 998434 44 997 998695 998739 998782 998826 998869 44 998 999131 999174 999218 999261 999305 44 999 999565 999609 999652 999696 999739 43 For explanation see pp. 207-215 (264) OF NUMBEKS Log. 999. No. 999 No. 5 6 7 8 9 ' Diff. 950 977952 977998 ! 1 978043 978089 ' 978135 46 951 978409 978454 978500 978546 978591 46 952 978865 978911 978956 979002 979047 46 953 979321 979366 979412 979457 979503 46 954 979776 979821 979867 979912 979958 46 1 980231 980685 980276 980730 980322 980776 980367 980821 980412 980867 45 45 981139 981184 981229 981275 981320 45 958 981592 981637 981683 981728 981773 45 959 982045 982090 982135 982181 982226 45 960 982497 982543 982588 982633 982678 45 961 982949 982994 983040 983085 983130 45 962 963 983401 983852 983446 983897 983491 983942 983536 983987 983581 984032 45 45 964 984302 984347 984392 984437 984482 45 9^5 984752 984797 984842 984887 984932 45 960 985202 985247 985292 985337 985382 45 967 985651 985696 985741 985786 985830 45 968 986100 986144 986189 986234 986279 45 969 986548 986593 986637 986682 986727 45 970 986996 987040 987085 987130 987175 45 971 987443 987488 987532 987577 987622 45 972 987890 987934 987979 988024 988068 45 973 988336 988381 988425 988470 988514 45 974 988782 988826 988871 988916 988960 45 975 989227 989272 989316 989361 989405 45 976 989672 989717 989761 989806 989850 44 978 990117 990561 990161 990605 990206 990650 990250 990694 990294 990738 44 44 979 991004 991049 991093 991137 991182 44 980 991448 991492 991536 991580 991625 44 981 991890 991935 991979 992023 992067 44 982 992333 992377 992421 i 992465 992509 44 983 992774 992819 992863 992907 992951 44 984 993216 993260 993304 993348 993392 44 985 993657 993701 993745 993789 993833 44 986 994097 994141 994185 994229 994273 44 987 994537 994581 994625 994669 994713 44 988 994977 995021 995065 995108 995152 44 989 i 995416 995460 | 995504, 995547 995591 44 990 995854 995898 995942 995986 996030 44 991 996293 996337 996380 996424 996468 44 992 996731 996774 996818 996862 996906 44 993 997168 997212 ! 997255 997299 997343 44 994 997605 997648 997692 997736 997779 44 995 998041 998085 998129 998172 998216 44 998477 998521 998564 998608 998652 44 997 998913 998956 999000 999043 999087 44 998 999348 999392 999435 999479 999522 44 999 999783 999826 999870 9999 i 3 999957 43 (265) LOGARITHMS OF NUMBERS No. Log. No. Log. No. Log. No. Log. I OOOOOO 51 707570 101 004321 151 178977 2 301030 52 716003 102 008600 152 181844 3 ! 477121 53 724276 103 012837 153 184691 4 602060 54 732394 IO4 017033 154 187521 5 698970 55 740363 105 021189 155 190332 6 778151 56 748188 106 025306 156 193125 7 845098 57 755875 107 029384 157 195900 8 903090 58 763428 108 033424 158 198657 9 954243 IO OOOOOO g 770852 778I5I 109 no 037426 041393 IS 201397 204120 II 041393 61 785330 iii 045323 161 206826 12 079181 62 792392 112 049218 162 209515 13 113943 63 799341 113 053078 163 212188 14 146128 64 806180 114 056905 164 214844 15 176091 65 812913 115 060698 165 217484 16 204120 66 819544 116 064458 166 220108 17 230449 67 826075 117 O68l86 167 222716 18 255273 68 832509 118 071882 168 225309 19 ; 278754 69 838849 119 075547 169 227887 20 301030 70 845098 120 079I8I 170 230449 21 322219 7 1 851258 121 082785 171 232996 22 342423 72 857333 122 086360 172 235528 23 361728 73 ! 863323 123 089905 173 238046 24 380211 74 869232 124 093422 174 240549 25 397940 75 875061 125 096910 175 243038 26 414973 76 880814 126 100371 176 245513 3 431364 447158 77 886491 78 892095 127 103804 177 247973 128 I072IO 178 250420 29 462398 79 897627 129 H0590 179 252853 30 477I2I 80 903090 130 H3943 180 255273 31 491362 81 908485 131 II727I 181 257679 32 505150 82 913814 132 120574 ! 182 260071 33 518514 83 919078 133 123852 183 262451 34 53H79 84 924279 134 I27I05 184 264818 35 544068 85 929419 135 130334 185 267172 36 556303 86 934498 136 133539 186 269513 568202 87 939519 137 136721 187 271842 38 579784 88 944483 138 139879 188 274158 j 39 591065 89 949390 139 I430I5 189 276462 40 602060 90 954243 140 146128 190 278754 4 1 612784 OI 959041 141 I492I9 191 281033 42 623249 92 963788 142 152288 192 283301 43 633468 93 968483 143 155336 193 285557 44 643453 94 973128 144 158362 194 287802 45 653213 95 977724 145 161368 195 290035 46 662758 96 982271 I 4 6 1 64353 196 292256 47 672098 97 986772 167317 197 294466 48 681241 98 991226 148 170262 198 296665 49 690196 99 995635 149 173186 199 ! 298853 50 698970 loo OOOOOO 150 176091 j 2OO 30I03O For explanation see pp. 207-215 (266) LOGARITHMIC TABLES OF COMPOUND INTEREST AND ANNUITIES BY FEDOR THOMAN TABLE I. SHOWING (A) The Logarithms of the Amount of jCi at the end of any number of years from i to 100 years. Log >- ( B) The Logarithms of the Annuity a per annum which \ will purchase for any number of years from i to 100 years. Log a n . In the notation used in the explanation on pages 216-228, the symbol ( i -f- /)" is employed instead of M. Thoman's symbol r"; and instead of his symbol a 11 . For explanation see pp. 216-228 (267) COMPOUND INTEREST AND ANNUITIES Table 1. Shewing: 1st Logarithm 1 2nd the Logarithm of the annuity of the amount of l. at the end of 7J 0. per annum which l. will pur- any number of years. chase for any number of years. Years Log. r*. Log. a". Log. a. Log. r". Years 1 0,00216-61 0,00216-61 8,34757-77 0,11046-91 51 2 0,00433-21 9,70221-77 8,34018-12 0,11263-52 52 3 0,00649-82 9,52720-73 8,33294-45 0,11480-13 53 4 0,00866-42 8,32^86-16 0,11696-73 54 5 0,01083-03 9,3075174 8,31892-67 0,11913-34 55 6 0,01299-64 9,22941-43 8,31213-45 0,12129-95 56 I 0,01516-24 0,01732-85 9,16354-47 9,10662-90 8,30547-99 8,29895-81 0,12346-55 0,12563-16 Q 0,01049-46 9,05655-18 8,20256-45 0,12779-76 59 10 0,02 v 66-06 9,01186-88 8,28629-48 0,12996-37 60 (1 12 0,02382-67 0,02^99-27 8,971 54-97 8,93483-38 8,28014-49 8,27411-08 0,13212-98 0,13429-58 61 62 '3 0,02815-88 8,90114-35 8,26818-87 0,13646-19 63 '4 '5 0,03032-49 0,03249-09 8,87002-97 8,84113-64 8,26237-52 8,25666-70 0,13862-80 0,14079-40 64 65 16 0,03465-70 8,81417-67 8,25106-05 0,14296-01 66 n 0,03682-30 8,78891-61 8,24555-30 0,14512-61 67 18 0,03898-91 8,76515-97 8.24014-12 0,14729-22 68 1 9 0,04115-52 8,74274-50 8,23482-25 0,14945-83 69 20 0,04332-12 8,72153-41 8,22959-42 0,15162-43 70 21 12 23 24 0,04548-73 0,04765-34 0,04981-94 0,05198-55 8,70140-94 8,68226-97 8,66402-73 8,64660-57 8,22445-35 8,21939-82 8,21442-58 8,20953-39 0,15379*04 0,15595-64 0,15812-25 0,16028-86 7 1 72 73 74 2 0,05415-15 0,05631-76 8,62993-79 8,61396-47 8,20472-05 0,16245-46 0,16462-07 2 7 28 0,05848-37 o, of 064 -97 8,59863-34 8,58389-75 si 19532-05 8,19073-01 0,16678-68 0,16895-28 \ 29 0,06281-58 8,56971-49 8,18621-02 0,17111-89 30 0,06498-19 8,55604-81 8,18175-89 0,17328-49 80 31 32 0,06714-79 0,06931 -40 8,54286-33 8,53012-96 8.17305-56 0,17545-10 0,17761-71 8l 82 33 0,07148-00 8,51781-95 8,16880-04 83 34 0,07364-61 8,50590-74 8,16460-73 0,18194-92 84 35 0,07581-22 8,49437-03 8,16047-48 0,18411-52 8 30 0,07797-82 8,48^18-69 ! 8,15640-16 0,18628-13 86 3 0,08014-43 0,08231-03 8,47233-78 8,46180-52 8,15238-61 8,14842-72 0,18844-74 0,19061-34 Si 39 40 0,08447-64 0,08664-25 8,45! 57-26 , 8,44162-47 8,1445^-35 8,14067-37 0,1 9277'95 0,19494-56 89 90 41 0,08880-85 8,43194-75 8,13687-67 0,19711-16 91 42 0,09097-46 8,42252-77 8,13313*12 0,19927-77 92 43 0,09314-07 8,41335*33 8,12943-61 0,20144-37 93 44 0,09530-67 8,40441-31 ! 8,12579-04 0,20360-98 94 45 0,09747-28 8,39569-62 | 8,12219-29 0,20577-59 47 0,09963-88 0,10180-49 8,3 7 '9-30 ; 8,37889-42 8,11864-27 8..II5I3-86 0,20794-19 0,21010-80 97 48 49 5 0,10397-10 0,10613-70 0,10830-31 8,37079-11 j 8,36287-57 8,35514-03 8,11167-99 8,10826-55 8,10489-45 0,21227-41 0,21444-01 0,21660-62 98 99 TOO 7,69897-00 Perp For explanation see pp. 216-228 (269) Q2 LOGAEITHMIC TABLES OF JL Per Cent. Years Log. r*. Log. a". Log. a". Log. r. Years I 0,00432-14 0,00432-14 8,40013-73 0,22039-01 51 2 0,00864-27 9,70544-67 8,39368-10 0,22471-14 52 3 0,01296-41 9.53i5o-7i 8,38738-20 0,22903-28 53 4 0,01728-55 9,40871-66 8,38123-39 0,23335-42 54 1 0,02160-69 0,02592-82 9,23691-09 8,^6936-88 0,23/67-56 0,24199-69 55 56 I 9 0,03024-96 0,03457-10 0,03889-24 9,17210-14 9,11624-34 9,06722-10 8,36364-13 8,35804-40 0,24631-83 0,25063-97 0,25496-11 57 58 59 10 0,04321-37 9,02359-02 8,34722-17 0,25928-24 60 ii J2 0^05185-65 8,98432-06 8,94865-15 8,34198-82 8,33686-80 0,26360-38 61 62 '3 0,05617-79 8,91600-53 8,33185-73 0^2 72 24-65 63 14 0,06049-92 8,88593-30 8,32695-27 0,27656-79 64 15 0,06482-06 8,85807-85 8,32215-04 0,28088-93 65 j 20 0,06914-20 0*07778-47 0,08210-61 0,08642-75 8,83215-49 8,80792-76 8,78520-21 8,76381-54 8,74362-98 8^31284-06 8,30832-70 8,30390-41 8,29956-8-7 0,28r2l-07 0,28953-20 0,29385-34 0,29817-48 0,30249-62^ 66 67 68 69 70 21 0,09074-88 8,72452-77 8,29531-85 0,30681-75 7 1 22 0,09507-02 8,70640-81 8,29115-10 0,31 1 13-89 72 23 24 0,09939-16 0,10371-30 8,68918-31 8,67277-62 8,28706-38 8,28305-45 0,31546-03 0,31978-17 73 74 25 0,10803-43 8,65712-04 8,27912-12 0,32410-30 75 26 0,11235-57 8,64215-65 8,27526-16 0,32842-44 76 3 0,11667-71 0,I20 99 -8 8,62783-20 8,61410-00 8,27147-36 8,26775-54 0,33274-58 0,337o6-72 ? 2 9 0,12531-98 8,60091-87 8,26410-51 0,34I38-85 79 30 0,12964-12 8,58825-06 8,26052*10 0,34570-99 80 ." 0,13396-26 8,57606-17 8,25700-14 0,35003-13 81 33 0,13828-40 0,14260-53 8,56432-14 8,55300-19 8,25354-42 8,25014-80 0,35435-27 0,35867-40 82 83 34 0,14692-67 8,54207-78 8,24681-18 0,36299-54 84 P 37 0,15124-81 0,15556-95 0,15989-08 8i52i32-52 8,51145-62 8,24353-36 8,24031-21 8,23714-56 0,36731-68 0,37163-81 0,37595-95 85 86 87 38 0,16421-22 8,50190*10 8,23403-34 0,38028-09 88 39 40 0,16853-36 0,17285-50 8,49264-30 8,48366-72 8,23097-39 8,22796-52 0,38460-23 0,38892-36 89 90 42 43 0,17717-63 0,18149-77 0,18581-91 8,47495-92 8,46650-62 8,45829-59 8,22500-72 8,22209-81 8,21923-68 0,39324-50 0,39756-64 0,40188-78 9' 92 93 44 0,19014-04 0,19446-18 0,19878-32 8,45031-70 8,44255-89 8,43501-17 8,21642-22 8,21365-35 8,21092-93 0,40620-91 0,41053-05 0,41485-19 94 % 0,20310-46 0,20742-59 8,42766-63 8,42051-42 8,20824-89 8,20561-12 0,419! 7'33 0,42349-46 97 (, 98 49 50 0,21174-73 0,21606-87 8,41354-69 8,40675-69 8,20301-53 8.20046-04 0,42781-60 0,43213-74 99 100 8,00000-00 Perr For explanation see pp. 216-228 270 COMPOUND INTEREST AND ANNUITIES 11 2 Per Cent. Years Log. r\ Log. cr. Log. a". Log. -. Years j 0,00646-60 0,00646-60 8,45016-73 0,32976-82 51 2 3 0,01293-21 0,01939-81 9,70865-71 9,53577*87 8,44455-80 8,439*0-15 0,33623-42 0,34270-02 52 53 4 0,02586-42 9,41404-49 8,43379"!9 0,34916-63 54 I 7 0,03233-02 0,03879-63 0,04526-23 9,32033-19 9,24433-95 9,18057-36 8,42862-34 8,42359-09 8,41868-90 0,35563-23 0,36209-84 0,36856-44 I 8 9 0,05172-83 0,05819-44 9,12575-45 9,07776-69 8,41391-32 8,40925-87 0,37503-04 0,38149-65 59 10 0,06466-04 9,03516-62 8,40472-13 0,38796-25 60 ii 0,07112-65 8,99692-23 8,40029-69 0,39442-86 6l 12 13 14 0,07759-25 0,08405-85 0,09052-46 8,96227-45 8,93064-52 8,90158-54 8,39177-13 8,38766-27 0,40089-46 0,40736-07 0,41382-67 62 63 15 0,09699-06 0,10345-67 8,87473-89 8,84981-90 8,38365-27 8,3797378 0,42029-27 0,42675-88 65 66 il 0,10992-27 0,11638-88 8,826^9-08 8,80486-00 8,3759i'50 8,37218-13 0,43322-48 0,43969-09 67 68 10 0,12285-48 8,78446-37 8,36853-40 0,44615-69 69 20 0,12932-08 8,76526-42 0,45262-30 70 21 0,13578-69 8,74714-37 8,36148-74 0,45908-90 71 22 0,14225-29 8,73000-10 8,35808-32 0,465 5 5 -50 72 23 2 4 0,14871-90 0,15518-50 8,71374-88 8,69831-03 8,35475-53 8,35150-12 0,47202-11 0,47848-71 73 74 11 0,16165-11 0,1681171 8,68361-84 8,66961-41 8,34831-89 8,34520-62 0,48495-32 0,49141-92 9 27 0,17458-31 8,65624-46 8,34216-13 0,49788-52 7 l 28 29 0,18104-92 0,18751-52 8,64346-33 8,63122-84 8,33918-21 8,33626-68 0,50435-13 0,51081-73 78 79 30 o,i9398-i3 8,61950-22 8,3334i-34 0,51728-34 80 31 0,20044-73 8,60825-10 8,33062-05 0,52374-94 81 32 0,20691-34 8,59744-40 8,32788-65 o,5302i-55 82 33 0,21337-94 8,58705-33 8,32520-95 0,53668-15 03 34 u 37 0,21984-54 0,22631-1(5 0,23277-75 0,23924-36 8,57705-37 8,56742-20 8,5581371 8,32258-81 8,32002-07 8,31750-61 8,31504-28 0,54314-75 0,54961-36 0,55607-96 0,56254-57 1 87 38 0,24570-96 8*54053-14 8,31262-96 0,56901-17 88 39 40 0,25217-56 0,25864-17 8,53217-62 8,52409-87 8,31026-49 0,57547-78 0,58194*38 89 90 41 0,26510-77 8,51628-49 8,30567-71 0,58840-98 9' 42 0,27157-38 8,50872-18 8,30345-14 0,59487-59 92 43 0,27803-98 8,50139-68 8,30126-97 0,60134-19 93 44 0,28450-59 8,49429-90 8,29913-08 0,60780-80 94 45 0,29097-19 8,4874178 8,29703-39 0,61427-40 95 46 0,29743-79 8,48074-32 8,29497-78 0,62074-01 96 47 0,30390-40 8,47426-61 8,29296-14 0,62720-61 97 48 0,31037-00 8,46797*79 8,29098-41 0,63367-21 98 49 0,31683-61 8,46187-03 8,28904-46 0,64013-82 99 50 0,32330-21 8,45593*57 8,28714-24 0,64660-41 IOO 8,17609-13 ierp. (271) LOGARITHMIC TABLES OF Per Cent. Years Log. r. Log. a". Log. a". Log. r-. Years I 2 3 0,00700-06 0,01400-11 0,02100-17 0,00700-06 9,70945-67 9,53684-22 8,46228-76 8,45687-59 8,45161-58 0,35702-85 0,36402-90 0,37102-96 51 52 53 4 0,02800-22 9,41537-09 8,44650-12 0,37803-02 54 5 0,03500-28 9,32191-89 8,44152-64 0,38503-07 55 6 0,04200-34 9,24618-62 8,43668-64 0,39203-13 56 7 0,04900-39 9,18267-86 8,43i97-57 57 8 0,05600-45 9,12811-63 8,42738-97 0,40603-24 58 9 0,06300-50 9,08038-42 8,42292-39 0,41303-30 59 10 0,07000-56 9,03803-76 8,41857-38 0,42003-35 60 11 0,07700-61 9,00004-66 8,41433-55 0,42703-41 61 12 0,08400-67 8,96565-02 8,41020-47 0,43403-46 62 13 0,09 100-73 8,93427-09 8,40617-81 0,44103-52 63 0,09800-78 8,90545-97 8,40225-20 0,44803-58 64 15 0,10500-84 8,87886-05 8,39842-30 0,45503-63 65 16 0,11200-89 8,85418-64 8,39468-79 0,46203-69 66 7 0,11900-95 8,83120-29 8,39104-37 0,46903-74 67 18 0,12601-01 8,80971-52 8,38748-73 0,47603-80 68 '9 0,13301-06 8,78956-07 8,38401*59 0,48303-85 69 zo 0,14001-12 8,77060-16 8,38062-69 0,49003-91 70 21 0,14701-17 8,75272-00 8,37731-79 0,49/03-97 71 22 0,15401-23 8,73581-51 8,37408-61 0,50404-02 7 2 23 0,16101-28 8,71979-91 8,37092-93 0,51104-08 73 24 0,16801-34 8,36784-51 0,51804-13 74 25 0,17501-40 8^69013-73 8,36483-15 0,52504-19 75 26 0,18201-45 8,67636-51 8,36188-64 0,53204-25 76 27 0,18901-51 8,66322-65 8,35900-78 0,53904-30 77 28 0,19601-56 8,65067-47 8,35619-36 0,54604-36 78 29 0,20301-62 0,21001-68 8,63866-80 8,62716-86 8,35344-2.3 0,55304-41 0,56004-47 g 31 0,21701-73 8,61614-29 8,34812-05 0,56704-52 8. 32 33 0,22401-79 0,23101-84 8,60555-99 8, 59539 -20 8,34554-67 8,34302-89 0,57404-58 0,58104-64 82 83 34 35 0,23801-90 0,24501-96 8,58561-38 8,57620-21 8,34056-55 8,33815-50 0,58804-69 o,5954'75 Is 36 0,25202-01 8,56713-59 8,33579-6o 0,60204-80 86 37 0,25902-07 8,55839-57 8,33348-74 0,60904-86 87 38 0,26602-12 8,54996-37 8,33122-74 0,61604-92 88 39 0,27302*18 8,54182-32 8,32901-50 0,62304-97 89 40 0,28002-23 8,53395-9! 8,32648-89 0,63005-03 90 41 0,28702-29 8,52635-74 8,32472-80 0,63705-08 9 1 42 0,29402-35 8,51900-48 8,32265-12 0,64405-14 92 43 0,30102-40 8,51188-94 8,32061-72 0,65105-19 93 44 0,30802-46 8,50499-97 8,31862-48 0,65805-25 94 45 46 47 0,31502-51 0,32202-57 0,32902-63 8,49832-51 8.49185-59 8,48558-30 8,31667-34 8,314/6-15 8,31288-83 0,66505-31 0,67205-36 0,67905-42 96 97 48 0,33602-68 8,47949-75 8,31105-32 0,68605-47 98 49 0,34302-74 8,47359' I 5 8,30925-47 0,69305-53 99 0,35002-79 8,46785-72 8,30749-23 0,70005-59 100 8,2io85'34 Perp. For explanation see pp. 216-228 (272) COMPOUND INTEREST AND ANNUITIES is 4 Per Cent. Years Log. r". Log. a". Log. a-. Log. t-. fews 2 0,00753-44 0,01506-88 0,00753-44 9,71025-53 8,47425-55 8,46903-59 0,38425-53 51 52 3 0,02260-33 9,53790-40 8,46396-64 o,39932-4' 53 4 0,03013-77 9,41669-43 8,45904-12 0,40685-86 54 5 0,03767-21 9,32350-26 8,45425-46 0,41439-30 55 6 0,04520-65 9,24802-86 8,44960-11 0,42192-74 56 7 0,05274-09 9,18477-83 8,44507-55 0,42946-18 57 8 9 0,06027-53 0,06780-98 9,13047-18 9,08299-40 8,44067-34 8,43639-01 0,43699-62 0,44453-07 58 10 0,07534-42 9,04090-03 8,43222-12 0,45206-51 60 u 0,08287-86 9,00316-04 8,42816-25 o,45959-95 6l 12 '3 14 0,09041-30 0,09794-74 0,10548-19 8,96901-39 8,93788-29 8,90931-86 8,42421-04 8,42036-10 8,41661-07 o',47466-83 0,48220-27 62 63 64 '5 0,11301-63 8,88296-48 ^,41295-62 0,48973-72 65 16 0,12055-07 0,12808-51 8,85853-47 8,83579-35 8,40939-42 8,40592-18 0,49727-16 0,50480-60 67 20 o,i356i-95 0,14315-39 0,15068-84 8,81454-67 8,7759 I "4 8,40253-58 8,39923-37 8,39601-25 0,51234-04 0,51987-48 69 21 22 23 0,15822-28 0,16575-72 0,17329-16 8,75826-56 72581 '33 8,39287-02 8,38980-37 8,38681-08 o,53494-37 0,54247-81 0,55001-25 7 1 72 73 24 2 0,18082-60 0,18836-04 0,19589-49 0,20342-93 0,21096-37 8,71084-18 8,69661-43 8,68307-13 8,67016-03 8,65783-49 8,38388-95 8,38103-74 8,37825-25 8,37553-26 8,37287-63 o,55754-69 0,56508-13 0,57261-58 0,58015-02 0,58768-46 74 8 11 29 0,21849-81 8,64605-30 8,37028-14 0,59521-9 P 30 0,22603-25 8,63477-70 8,36774*59 0,60275-34 So 31 32 0,23356-70 0,24110-14 8,62397-31 8,61361-06 8,36526-83 8,36284-73 0,61028-78 0,61782-23 81 82 33 0,24863-58 8,60366-17 8,36048-09 0,62535-67 83 34 0,25617-02 8,59410-10 8,35816-78 0,63289-11 84 35 0,26370-46 8,58490-54 8,35590*63 0,64042-55 85 36 0,27123-90 8,57605-41 8,35369-49 o,64795-99 86 37 38 0,27877-35 0,28630-79 8,5675271 8,55930-68 8,35*' 53 -28 8,34941-82 0,65549-44 0,66302-88 I 39 0,29384-23 8,55137-67 8,34734-99 0,67056-32 89 40 8,54372-16 8,34532-67 0,67809-76 9 4 42 0,30891-11 0,31644-56 8,53632-73 8,52918-09 8,34334-75 8,34141-12 0,68563-20 0,69316-64 92 43 44 0,32398-00 o,33i5i-44 8,52227-03 8,51558-38 8i33/66-23 0,70070-09 0,70823-53 93 94 45 0,33904-88 8,50911-12 8,33584-77 0,71576-97 95 46 0,34658-32 8,50284-25 8,33407-18 0,72330-41 r> 4 0^36165-21 8,49676-86 8,49088-08 8,33 2 33-34 8,33063*19 0,73083-85 0,73837-30 97 98 49 0,36918-65 8,48517-10 8,32896-56 o,74590-74 99 5 0,37672-09 8,47963-16 8,32733-42 100 8,24303-80 Perp (273) LOGAKITHMIC TABLES OF 17 8 Per Cent. Y*ars Log. r". Log. a". Log. a". Log. r. Tears I 0,00806-76 0,00806-76 8,48607-21 0,41144-87 5 2 0,01613-52 9,71105-27 8,48103-92 0,41951-63 S 2 3 0,02420-29 9,53896-40 8,47615-50 0,42758-40 53 4 0,03227-05 9,41801-54 8,47141-35 0,43565-16 54 I 0,04033-81 0,04840-57 9,32508-31 9,24986-69 8,46680-90 8,46233-64 0,44371-92 0,45178-68 11 I 9 10 0,05647-34 0,06454-10 0,07260-86 0,08067-62 9,18687-27 9,13282-10 9,08559-62 9,04375-38 8,45799-04 8,45376-62 8,44965-94 8,44566-57 o,45985-44 0,46792-21 0,47598-97 0,48405-73 I- e ii 0,08874-38 9,00626-40 8,44178-08 0,49212-49 61 12 3 0,09681-15 0,10487-91 8,97236-58 8,94148-14 8,43800-08 8,43432-22 0,50019-25 0,50826-02 62 M 0,11294-67 8,91316-21 8,43074-13 0,51632-78 64 '16 0,12101-43 0,12908-19 8,88705-19 8,86286-36 8,42725-47 8,42385-95 o,5 2 439'54 0,53246-30 66 >7 0,13714-96 8,84036-28 8,42055-23 0,54053-07 67 18 0,14521-72 0,15328-48 8,8i935-49 8,79067-69 8,41419-08 0,54859-83 0,55666-59 68 69 20 0,16135-24 8,78119-14 8,41113-08 0,56473-35 70 21 22 . 0,16942-01 0,17748-77 8,76378-05 8,40814-80 8,40524-00 0,157280-11 0,58086-88 72 23 0,18555-53 8,73179-16 8,40240-42 0,58893-64 73 24 ? 29 30 0,19362-29 0,20169-05 0,20975-82 0,21782-58 0,22589-34 0,23396-10 0,24202-87 8,71704-94 8,70304-95 8,68973-27 8,67704-65 8,66494-41 8,65338-36 8,64232-76 8,39963-85 8,39694-07 8,39430-88 8,39174-08 8,38923-47 8,38678-87 8,38440-11 o,597oo-40 0,60507-16 0,61313-92 0,62120-69 0,62927-45 0,63734-21 0,64540-97 74 P g 31 0,25009-63 8,63174-21 8,38207-02 0,65347-74 81 32 33 0,25816-39 0,26623-15 8,62159-65 8,61186-28 8,37979-41 8,37757"!6 0,66961-26 82 83 34 0,27429-91 8,60251-60 8,37540-09 0,67768-02 i 4 35 0,28236*68 8,59353-27 8,37328-06 0,68574-78 85 36 0,2904-3-44 0,29850-20 8,58489-19 8,37120-95 8,36918-60 0,69381-55 0,70188-31 86 87 3 0,30656-96 8^568^6-14 8,36720-89 o,7o995-o7 88 39 0,31463-72 8,56083-74 8,36527-70 0,71801-83 89 40 0,32270-49 8,5533871 8,36338-88 0,72608-60 90 41 0,33077*25 8,54619-59 8,36154-34 0,73415-36 9 42 43 0,33884-01 0,34690-77 s'53254-oi 8,35973-95 8,35797-6i 0,74222-12 0,75028-88 92 93 44 ? 0,35497-54 0,36304-30 0,37111-06 0^38724-58 8,52605-23 8!s i 370'37 8,50782-39 8,50212-85 8,35625-21 8,35456-66 8,35291-82 8,35130-63 8,34072-98 o'76642-4i 0,77449-17 0,78255-93 0,79062-69 94 95 96 97 98 49 O 39531 "3, S 8,49660-98 8,34818-80 0,79869-45 99 5 oUo338-u 8,49126-01 8,34667-98 0,80676-22 100 8,27300-13 Perp. For explanation see pp. 216-228 (274) COMPOUND INTEREST AND ANNUITIES ^J Per Cent. Years Log. r". Log. a". Log. a". Log. r". Year." , 0,00860-02 0,00860-02 8,49773-88 0,43860-88 5' 2 3 4 0,01720-03 0,02580-05 0,03440-07 9,71184-90 9,54002-23 9,41933-40 8,49288-73 8.48818-28 8,48361-96 0,44720-89 0,45580-91 0,46440-93 52 53 54 i 0,04300-09 0,05160-10 9,32666-02 9,25170-10 8,479/9-18 8,47489-44 0,47300-94 0,48160-96 56 7 0,06020-12 9,18896-21 8,47072-20 0,49020-98 57 8 0,06880-14 9,13516-38 8,46667-00 0,49881-00 58 9 0,07740-15 9,08819-08 8,46273-38 0,50741-01 59 10 0,08600-17 9,04659-87 8,45890-93 0,51601-03 60 u 0,09460-19 0,00935-71 8,45519-19 0,52461-05 61 12 '3 0,10320-21 0,11180-22 8^94506-63 8,45157-82 8,44806-42 0*54181 -08 62 63 1 4 0,12040-24 8,91699-05 8,44464-66 0,55041-10 64 0,12900-26 8,89112-17 8,44132-18 0,55901-12 J>5 6 0,13760-27 8,86717-35 8,43808-68 0,56761-13 66 '9 0,14620-29 0,15480-31 0,16340-33 8,84491-09 8,82413-95 8,80469-66 8,43493-85 8,431-87-38 8,42889-01 0,57621-15 0,58481-17 67 68 69 20 0,17200-34 8,78644-42 8,42598-47 0,60201-20 7o 21 22 23 0,18060-36 0,18920-3-8 0,19780*40 8,76926-48 8,75305-73 8,73773-40 8,42315-50 8,42039-86 8,41771-31 0,61061-22 0,61921-24 0,62781-25 72 73 24 0,20640-41 8,72321-83 8,41509-63 0,63641-27 14. 3 0,21500-43 0,22360-45 8,70944-33 8,69634-97 8,41254-59 8,41006-01 0,64501-29 0,65361-31 $ 27 0,23220-46 8,68388 -so 8,40763-67 0,96221-32 77 28 0,24080-48 8,67200-24 8,40527-39 0,67081-34 78 2 9 0,24940-50 8,66066-02 8,40296-99 0,67941-36 79 30 0,25800-52 8,64982-07 8,40072-29 0,68801-37 80 31 0,26660-53 8,63945-01 8,39853-11 0,69661-39 8. 32 33 0,27520-55 0,28380-57 8,62951-77 8,61999-58 8,39639-29 8,39430-69 0,70521-41 0,71381-43 82 83 34 0,29240-58 0,30100-60 0,30960-62 8,61085-89 8,60208-40 8,59364-99 8,39227-14 8,39028-51 8,38834-65 0,72241-44 0,73101-46 0,73961-48 84 38 0,31820-64 0,32680-65 8,58553-72 8,57772-80 8,38645-44 8,38460-72 0,74821-49 0,75681-51 87 88 39 0,33540-67 8,57020-59 8,38280-38 0,76541*53 89 40 0,34400-69 8,56295-56 8,38104-31 o,7740i 55 90 4i 0,35260-70 8,55596-32 8,37932-39 0,78261-56 91 42 0,36120-72 8,54921-53 8,37764-48 0,79121-58 92 43 44 0,36980-74 0,37840-76 8,54270-02 8,53640-61 8,37600-50 8,37440-34 0,79981-60 0,80841-61 93 94 0,38700-77 8,53032-30 8,37283-88 0,81701-63 95 46 o,3956o-79 8,52444-06 8,37131-04 0,82561-65 96 47 48 0,40420-81 0,41280-82 8,51874-97 8,51324-20 8,36981-72 8,36835-82 0,83421-67 0,84281-68 97 98 49 50 0,42140-84 0,43000-86 8,50790-93 8,50274-40 8,36693-25 0,85141-70 0,86001-72 99 100 8,30103-00 Perp. (275) LOGARITHMIC TABLES OF Jig Per Cent. Years Log. r". Log. a-. Log. a". Log. r". Years 2 0,00913-21 0,01826-41 0,00913-21 9,71264-41 8,50925-70 8,50458-14 o,46573-55 0,47486-76 5* 52 3 4 0,02739-62 0,03652-83 9,54107-89 9,42065-01 8,50005-14 8,49566-10 0,48399-97 o,493*3"*8 53 54 5 0,04566-03 9,32823-42 8,49140-45 0,50226-38 55 6 0,05479-24 9,25353*10 8,48727-66 0,51139-59 56 I 9 0,06392-45 0,07305-66 0,08218-86 9,19104-63 9,13750-04 9,09077-79 8,48327-23 8,47938-67 8,4756i-55 0,52052-80 0,52966-00 0,53879-2* 59 10 0,09132-07 9,04943-46 8,47195-41 0,54792-42 60 ii 12 0,10045-28 0,10958-48 9,01244-01 8,97903-37 8,46839-85 0,55705-62 0,56618-83 61 62 '3 O, I 1871 -69 8,04863-78 8',46i 58-98 0.57532-04 63 14 0,12784-90 0,13698-10 0,14611-31 8,00080-3$ 8,89517-46 8.87146-43 8,45832-92 8,45516-00 8,45207-90 0,58445-24 o,59358-45 0,60271-66 18 0,15524-52 0,16437-73 8,84943-79 8,82890-09 8,44908-33 8,44616-96 0,61184-87 0,62098-07 I '9 20 o,i735o-93 0,18264-14 8,80969-06 8,79166-90 8,44333-55 8,44057-81 0,63011-28 0,63924-49 69 70 21 >*9!77-35 8,77471-88 8,43789-5 0,64837-69 7* 22 0,20090-55 0,21003-76 8*74364-08 8,43528-36 8,43274-17 0,65750-90 0,66664-1 1 72 73 2 4 0,21916-97 8,72934-89 8,43026*70 0,67577-31 74 2 5 0,22830-17 8,7*579-57 8,42785*75 0,68490-52 75 26 11 29 3o 0,23743-38 0,24656-59 0,25569-79 0,26483-00 0,27396-21 8,70292-24 8,69067-61 8,67901-02 8,66788-30 8,65725-67 8,42551-09 8,42322-54 8,42099-91 8,41883-00 8,41671-66 0,69403-73 0,70316-94 0,71230-14 0,72143-35 0,73056-56 76 2 e 31 0,28309-42 8,64709-75 8,4*465-70 o,73969-76 81 32 0,29222-62 8,63737-48 8,41264-97 0,74882-97 82 33 34 0,30135-83 0,31049-04 8,62806-09 8,61913-02 8,41069-32 8,40878-59 0,75796-18 0,76709-38 83 84 36 0,31962-24 0,32875-45 8,61056-00 8,60232-86 8,40692-63 8,40511-31 0,77622-59 0,78535-80 86 37 0,33788-66 8,59441-70 8,40334-50 0,79449-00 87 3 0,34701 -86 8,58680-73 8,40162-05 0,80362-21 88 39 40 0,35615-07 0,36528-28 8,57948-28 8,57242-85 8,39093-86 8,39829-79 0,81275-42 0,82188-63 89 90 41 0,37441-48 8,56563-03 8,39669-74 0,83101-83 9 1 42 0,38354-69 8,395* 3 '59 0,84015-04 92 43 44 0,39267-90 0,40181-11 8;s4664-6o 8,39361-23 8,39212-54 0,84928-25 0,85841-45 93 94 45 0,41094-31 8,54075-03 8,39067-46 0,86754-66 95 46 0,42007-52 8,53505-38 8,38925-85 0,87667-87 96 48 0,42920-73 8,52954-74 8,52422-22 8,38/87-63 8,38652-73 0,88581-07 0,89494-28 97 98 49 50 0,44747-14 0,45660-35 8,51907-05 8,51408-44 8,38521-04 8,38392-46 0,90407-49 0,91320-70 99 100 8,32735-89 Perp For explanation see pp. 216-228 (276) COMPOUND INTEREST AND ANNUITIES 4 Per Cent. Years Log. r". Log. a". Log. a". Log. r-. Years 2 0,00966-33 0,01932-66 0,00966-33 9>7i343'8i 8,52062-79 8,51612-32 0,49282-92 0,50249-25 51 52 3 0,02899-00 9,54213*37 8,51176-23 0,51215-58 53 4 0,03865-33 9,42196-39 8,50753-94 0,52181-91 54 5 0,0483 1 -66 9,32980-50 8,50344-87 0,53148-24 55 6 7 0,05797-99 0,06764-32 9^5535-68 9,19312-53 8^49564-32 0,54114-57 0,55080-91 56 57' 8 0,07730-65 9,13983-07 8,49191-85 0,56047-24 58 9 0,08696-99 9,09335-76 8,48830-64 0.570I3-57 59 10 0,09663-32 9,052*26- 1 7 8,48480-26 o,57979-90 60 1 1 12 0,10629*65 0,11595-98 9,01551-27 8,98235-00 8,48140-31 8,47810-38 0,58946*23 0,59912-56 61 62 3 0,12562-31 8,95219-58 8,47490-13 0,60878-90 63 14 0,13528-64 8,92460-13 8,47179-18 0,61845-23 64 0,14494-98 o, 15461-31 8,09931*03 8,87573-61 8,46877-22 8,46583-92 0,62811-56 0,63777-89 65 66 7 0,16427-64 8,85394-38 8,46298-99 0,64744-22 67 18 o,i7393-97 8,83363-92 8,46022-11 0,65710-55 68 '9 0,18360-30 8,81465-92 8.45753-02 0,66676-89 69 20 0,19326-63 8,79686-61 8,45491-46 0,67643*22 70 21 0,20292-97 8,78014-23 8,45237-16 0,68609-55 7' 22 0,21259-30 8,76438-69 8,44989-91 0,69575-88 72 23 0,22225-63 8,74951-19 8,44749-44 0,70542-21 73 24 0,23191 -96 8,73544-10 K.445'5'54 0,71508-54 74 25 0,24158-29 8,72210-71 8,44288-00 0,72474-88 75 26 27 0,25124-62 0,26090-96 8,70945-09 8,69742-01 8,44066-62 8,43851-20 0,73441-21 0,74407-54 76 77 28 0,27057-29 8,68596-79 8,43641-53 o,75373-87 78 29 o, 28023*62 8,6750^-22 8,43437-47 0,76340-20 79 30 0,28989-95 8,66463-57 8,43238-82 o,773o6-53 80 3 0,29956-28 8,65468-47 8,43045-41 0,78272-87 81 32 33 0,30922-61 0,31888-95 8,64516-82 8,63605-86 8,42857-08 8.42673-69 0,79239-20 0,80205-53 82 83 34 35 0,32855-28 0,33821-61 8,62733-05 8,61896-08 8,42495-08 8,42321-10 0,81171-86 0,82138-19 84 85 36 0,34787-94 8,61092-85 8,41151-63 0,83104-52 86 37 0,35754-27 8,60321-40 8,41986-:; 3 0,84070-86 87 38 0,36720-60 8,59579-96 8,41825-66 0,85037- 19 88 39 0,37686-94 8,58866-87 8,41668-90 0,86003-52 89 40 0,38653-27 8,58180-61 8,41516-13 0,86969-85 90 41 0,39619-60 8,57519-79 8,41367-26 0,87936-18 gi 42 0.40585-93 8,56883-09 8,41222-14 0,88902- ;i 92 43 0,41552-26 8,56269-29 8,41080-69 0,89868-85 93 44 0,42518-59 8,55677-28 8,40942-79 0,90835-18 94 0,43484-93 8,55106-01 8,40808-36 0,91801-51 46 0,44451-26 8,54554-47 8,40677-28 0,92767-84 96 48 0,45417-59 0,46383-92 8,54021-77 8,535 7'03 8,40549-46 8,40424-83 0,93734-17 0,94700-50 98 49 0,47350-2; 0,48316-58 8,53009-45 8,52528-28 8,40303-28 8,40184-73 0,95666-84 0,96633-17 99 100 8,35218-25 Perp (277) LOGARITHMIC TABLES OF 23 8 Per Cent. Years Log. r*. Log. a\ Log. a". Log. r\ Years l 0,01019-39 0,01019-39 8,53185-29 0,51988-97 51 2 3 0,02038-78 0,03058-17 9,71423-09 9,54318-69 8,52751-40 8,52331-72 0,53008-36 0,54027-75 52 53 4 0,04077-57 9,42327-52 8,51925-65 0,55047-14 54 5 0,05096-96 8,51532-64 0,56066-53 55 6 0,06116-35 9! 25 7 1 7-86 0,57085-92 56 7 0,07135-74 9,19519-91 8! 50783-67 0,58105-31 57 8 0,08155-13 9,14215-48 8,50426-73 0,59124-71 58 9 0,09174-52 9,09592-97 8,50080-89 0,60144-10 59 10 0,10193-91 9,05508-01 8,49745-71 0,61163-49 60 ii 12 0,11213-31 0,12232-70 9,01857-51 8,98565-46 8,49420-78 8,49105-72 0,62182-88 0,63202-27 61 62 7 0,13252-09 0,14271-48 0,15290-87 0,16310-26 0,17329-66 8,95574-04 8,92838-40 8,90322-91 8,87998-90 8,85842-88 8,48800-16 8,48503-75 8,48216-16 8,47937-06 8,47666-16 0,64221-66 0,65241-05 0,66260-45 0,67279-84 0,68299-23 63 65 66 67 18 0,18349-05 8,83835-42 8,47403-17 0,69318-62 68 20 0,19368-44 0,20387-83 8,81960-24 8,80203-55 8,47147-80 8,46899-81 0,70338-01 69 21 0,21407-22 8,78553-60 8,46658-92 0,72376-80 71 22 0,22426-61 8,77000-26 8,46424-91 72 23 0,23446-00 8,75534-79 8,46197-53 o,' 74415-58 73 24 11 0,24465-40 0,25484-79 0,26504-18 8,74149-52 8,72837-75 8,7i593-57 45761 -83 8,45553-o8 0,75434-97 0,76454-36 0,77473-75 74 27 0,27523-57 8,70411-73 8,45350-14 0,78493-14 77 28 0,28542-96 8,69287-154 8,45152-83 0,79512-54 78 2 9 30 0,29562-35 0,30581-74 8,68216-82 8,67195-84 8,44960-94 8,44774' 3 0,80531-93 0,81551-32 31 0,31601-14 8,66221-19 8,44592-81 0,82570-71 81 32 0,32620-53 8,65289-81 8,44416-24 0,83590-10 82 33 0,33639*92 8,64398-93 8,44244-45 0,84609-49 83 34 0,34659-31 8,63546-00 8,44077-30 0,8^628-88 84 35 0,35678-70 8,62728-74 8,43914-65 0,86648-28 36 0,36698-09 8,61945-00 8,43756-35 0,87667-67 86 0,37717-48 8,61192-87 8,43602-29 0,88687-06 87 39 40 0,38736-88 o,39756-27 0,40775-66 8,60470-55 8,59776-41 8,59108-91 8,43452-32 8,43306-33 8,43164-21 0,89706-45 0,90725-84 88 89 90 41 42 0,41795-05 0,42814-44 8,58466-66 8,57848-34 8,43025-82 8,42891-07 0,92764-62 0,93784-02 92 43 44 0,43833-83 0,44853-23 8,57252-74 8,56678-76 8,42759-85 8,42632-05 0,94803-41 0,95822-80 93 94 4 I 46 0,45872-62 0,46892-01 8,56125-31 8,55591-44 8,42507-58 8,42386-35 0,96842-19 0,97861-58 3 49 0,47911-40 0,48930-79 0,49950-18 8,55076-19 8,54578-74 8,54098-27 8,42268-24 8,42153-20 8,42041-11 0,98880-97 0,99900-37 1,00919-76 9 99 5 0,50969-57 8,53634-03 8,41931-90 1,01939-15 100 8,37566-36 }Vrp For explanation see pp. 216-228 (278) COMPOUND INTEREST AND ANNUITIES 2 2 PerCit. Years Log. ,-. Log. fl n . Log. a". Log. i-. Years l 0,01072-39 0,01072-39 8,54293-36 0,54691-71 51 2 0,02144-77 9,71502-27 8,53875*55 0,55764-10 5 3 0,03217-16 9,54423-83 0,56836-49 53 4 0,04289-55 9,42458-42 8^53081-40 0,57908-87 54 I 0,05361-93 0,06434-32 9! 25899-62 8,52703-92 S-52338-78 0,58981-26 0,60053-65 7 0,07506-71 9,19726-80 8,51985-48 0,61126-03 57 8 9 10 0,08579-09 0,0965 i -48 0,10723-87 9,14447-26 9,09840-45 9,05788-95 8,'5i3i 2 -52 8,50991-99 0,62198-42 0,63270-81 0,64343-19 58 g ii 12 0,11796-2:; 0,12868-64 9,02162-73 8,98894-73 8,50681-53 8,50380-78 0,65415-58 0,66487-97 61 62 13 0,13941-03 8,95927-i7 8,50089-34 0,67560-35 63 '4 0,15013-41 8,93215-16 8,49806-90 0,68632-74 64 0,16085-80 8,90723-11 8,49533-10 0,69705-13 65 '9 0,17158-18 0,18230-57 0,19302-96 0,20375-34 8,88422-30 8,86289-29 8,84304-63 8,82452-04 8,49267-63 8,49010-20 8,48760-50 8,48518-27 0,70777-51 0,71849-90 0,72922-28 0,73994-67 66 67 68 69 20 0,21447-73 8,80717-72 8,48283-24 0,75067-06 70 21 22 0,22520-12 0,23592-1,0 8,79089-94 8,77558-57 8,48055-17 8,47833-80 0,76139-44 0,77211-83 7' 72 2 3 0,2466-4-89 8,76114-85 8,47618-91 0,78284-22 73 2 4 0,25737-28 8,74751*14 8,47410-29 o,79356-6o 74 It, 0,26809-66 0,27882-05 8,7346o-72 8,72237-68 8,47207-72 8,47010-99 0,80428-99 0,81501-38 2? 28 0,28954-44 0,30026-82 8,71076-77 8,60973-31 8,46819-91 8,46634-31 0,82573-76 0,83646-15 $ 2 9 30 0,31099-21 0,32171-60 8,68923-13 8,67922-47 8,46453-99 8,46278-79 0,84718-54 0,85790-92 g 31 0,33243-98 8,66967-94 8,46108-53 0,86863-31 8. 32 0,34316-37 8,66056-49 8,45943*08 0,87935-70 82 33 0,35388-76 8,65185-33 8,45782-26 0,89008-08 83 34 0,36461-14 8,64351-93 8,45625-94 0,90080-47 84 o,37533"53 0,38605-92 0,39678-30 8,63553-99 8,62789-39 8,62056-18 8-45473-97 8,45326-23 8,45182-56 0,91152-86 0,92225-24 0,93297-63 gg 87 3 0,40750-69 8,61352-59 8,45042-85 0,94370-02 88 39 0,41823-08 8,60676-98 8,44906-99 0,95442-40 89 40 0,42895-46 8,60027-83 8,44774-84 90 41 0,43967-85 8,59403-72 8,44646-31 0,97587-18 9 1 42 0,45040-23 8,58803-36 8.44521-27 0,98659-56 92 43 0,46112-62 8,58225-53 8,44399-64 o,9973i-95 93 44 0,47185-01 8,57669-11 8,44281-29 ,00804-33 94 45 46 0,48257-39 0,49329-78 8^5661 6-35 8,44166-15 8,44054-10 ,01876-72 ,02949-11 ? 0,50402-17 o,5i47f55 8,56118-12 8,43945-07 8,43838-95 ,04021-49 ,05093-88 49 0,52546-94 8,55173-04 8,43735-68 ,06166-27 99 8,54725-84 8,43635*16 ,07238-65 100 8,39794-0 Petp. (279) LOGARITHMIC TABLES OF 5 g Per Cent. Years Log. r*. Log. a". Log. a". Log. r". Yean , 0,01125-32 0,01125-32 8,55387-14 o,5739i'i7 5 1 a 0,02250-63 9,7i58i-33 8,54984-90 0,58516-48 52 3 0,03375-95 9,54528-79 8,54596-51 0,59641-80 S3 4 0,04501-27 9,42589-07 8,54221-36 0,60767-12 54 I 0,05626-59 0,06751-90 9,33449-80 9,26080-97 8,53858-90 8 ; 53508-61 0,61892-44 0,63017-75 I 0,07877-22 0,09002-54 9,19933-16 9,14678-41 8,53169-96 8,52842-49 0,64143-07 0,65268-39 1 9 0,10127-85 9,10105-19 8,52525*77 0,66393-70 59 10 0,11253-17 9,06069-03 8,52219-35 0,67519-02 60 ii 0,12378-49 9,02466-94 8,51922-83 0,68644-34 61 12 0,13503-80 8,99222-85 8,51635-83 0,69769-65 62 13 0,14629-12 8,96278-97 8,51357-98 0,70894-97 63 4 0,15754-44 8,93590-42 8,51088-94 0,72020-29 64 0,16879-76 8,QII2I-6l 8,50828-38 0,73145-61 6? ID 0,18005-07 8,88843-83 85(50575-97 0,74270-92 66 '7 0,19130-39 8.86733-61 8,50331-43 0,75396-24 67 18 '9 0,20255-71 0,21381-02 8,84771-55 8,82941-31 8,50094-45 8,49864-78 0,76521-56 0,77646-87 68 69 20 0,22506-34 8,81229-15 8,49642-15 0,78772-19 70 21 22 0,23631-66 0,24756-97 8,79623-30 8,78113-65 8,49426- 29 8,49217-00 0,79897-51 0,8lO2?'82 7 72 23 0,25882-29 8,76691-42 8,49014-01 0,82148-14 73 24 0,27007-61 8,75348-99 8,48817-13 0,832*73-46 74 It, 0,28132-93 0,29258-24 8,74079-64 8,72877-45 8,48626-14 8,48440-84 0,84398-78 0,8.^24-09 ? % 0,30383-56 0,31508-88 8,71737-17 8,70654-14 8,48261-04 8,48086-55 0,86649-41 0,87774-73 29 0,32634-19 8,69624-17 8,47917-20 0,88900-04 79 30 o,33759'5i 8,68643-52 8,47752-80 0,90025-36 80 32 0,34884-83 0,36010-14 8,67708-78 8,66816-90 8,47593-21 8,47438-26 0,91150-68 0,92275-99 81 82 33 0,37135-46 8,65965-11 8,47287-81 0,93401-31 83 34 9 0,38260-78 0,39386-10 0,40511-41 8,65 1 150-88 8,64371-89 8,63626-03 8,47141-70 8,46999-80 8.46861-98 0,94526-63 0,95651-95 0,96777-26 84 8$ 37 0,41636-73 8,62911-38 8,46728-10 0,97902-58 87 38 0,42762-05 8,62226-13 8,46598-05 0,99027-90 88 39 0,43887-36 8,61568-65 8,46471-69 1,00153-21 89 40 0,45012-68 8,60937-42 8,46348-91 1,01278-53 90 4 I 0.46138-00 8,60331-05 8,46229-62 1,02403-85 9' 42 0,47263-31 8,59748-22 8,46113-68 1,03529-16 92 43 0,48388-63 8,59187-72 8,46001-01 1,04654-48 93 44 0,49513-95 0,50639-27 0,51764-58 8,58648-42 8,58129-29 8,57629-35 8,45891-50 8,45785-06 8,45681-59 1,05779-80 1,06905-12 1,08030-43 94 95 96 47 0,52889-90 8,57147-65 8,45581-00 1,09155-75 97 49 0,54015-22 0,55140-53 8,56683-36 8,56235-68 8,45483-22 8,45388-13 1,10281-07 1,11406-38 98 99 50 0,56265-85 8,55803-84 8,45295-69 1,12531-70 100 8,41912-93 Peri* For explanation see pp. 216-228 (280) COMPOUND INTEREST AND ANNUITIES 2 4 Per Cent. Years Log. r. Log. a*. Log. a". Log. -. Yean I 0,01178-18 0,01178-18 8,56466-78 0,60087-34 5' 2 0,02356-37 9,71660-28 8,56079-64 0,61265-52 S* 3 0,03534-55 9,54633-59 8,557o6-i5 0,62443-70 53 4 0,04712-73 9,42719-49 8,55345*71 0,63621-88 54 5 0,05890-92 9>336o5 -59 8,54997-78 0,64800 op 55 6 0,07069-10 9,26261-92 8,54661-81 0,65978-25 56 1 9 10 0,08247-28 0,09425-46 0,10603-65 0,11781-83 9,20139-02 9,14908-96 9,10360-17 9,06348-24 8,54337-31 8,54023-81 8,53720-85 8,53428-02 0,67156-43 0,68334-62 0,69512-80 0,70690-98 k ii 0,12960-01 9,02770-14 8,53144-91 0,71869-17 61 12 '3 0,14138-20 0,153*16-38 8,9Q549-79 8,96629-44 8,52871-14 8,52606-34 0,73047-35 0,74225-53 62 63 '4 0,16494-56 8,93964-19 8,52350-17 0,75403-72 64 15 16 0,17672-75 0,18850-93 8,91518-44 8,89263-51 8,52102-30 8,51862-41 0,76581-90 0,77760-08 \l '9 20 0,20029-11 0,21207-29 0,22385-48 0,23563-66 8,87175-80 8.85236-18 8,83428-09 8,8i737-85 8,51630-21 8,51405-41 8,51187-74 8,50976-93 0,78938-26 0,80116-45 0,81294-63 0,82472-81 Si 69 70 21 22 0,24741-84 0,25920-03 0,27098-21 8,80153-69 8,78665-49 8,77264-51 8' 505 74-95 8,50383-30 0,83651-00 0,84829-18 0,86007-36 7 72 73 24 0,28276-39 8,75943-09 8,50197-59 0-87185-55 74 *5 0,29454-58 8,74694-52 8,50017-61 0,88363-73 75 26 0,30632-76 8,73512-89 8,49843-16 0,89541 -91 7$ 28 0,31810-94 0,32989-13 8,72392-96 8,7i330-05 8,49674-05 8,49510-10 0,90720-00 0,91898-28 7! 29 30 0,34167-31 0,35345-49 8,70319-98 8,69359-00 8,49351-12 8,49196-96 0,93076-46 0,94254-64 3> 32 33 0,36523-67 0,37701 -86 0,38880-04 8,68443-72 8,67571-08 8,66738-32 8,49047-45 8,48902-44 8,48761-76 0,96611-01 0,97789-10 8. 82 83 34 0,40058-22 8,65942-89 8,48625-28 0,98967-38 84 35 0,41236-41 8,65182-48 8,48492-87 ,00145-56 85 36 0,42414-59 8,64455-00 8,48364-40 ,01323-74 86 37 38 0,43592-77 0,44770-96 8,63758-51 8,63091-21 8,48239-72 8,48118-72 ,02501-93 ,03680-11 87 88 39 0,45949' J 4 8,62451-47 8,48001-29 ,04858-29 89 0,47127-32 8,61837-77 8,47887-30 ,06036-47 90 4' 42 0,48305-51 0,49483-69 8,61248-72 8,60682-99 8,47776-64 8,47669-23 ,07214-66 ,08392-84 9' 92 43 44 0,50661-87 0,51840-05 8,60139-40 8,59616-81 8,47564-94 8,47463-68 ,09571-02 ,10749-21 93 94 47 o,c 3018-24 0,54196-42 0,55374-60 8,59114-17 8,58630-51 8,58164-91 8,4736535 8,47269-87 8,47177-15 ,11927-39 ,13105-57 ,14283-76 96 97 8 S.STT'w'S 1 8,47087-10 ,15461-94 98 49 0,57*7 30*97 8,57284-52 8,46999-64 ,16640-12 99 0.58909-15 8,56868-18 8,46914-69 ,17818-31 100 8,43933' 2 7 Perp. (281) LOGARITHMIC TABLES OF 2 17 8 Per Cent. Years Log. ,-. Log. a". Log. a". Log. T*. Years I 0,01230-98 0,01230-98 8,57532-41 0,62780-23 51 2 3 4 0,02461-97 0,03692-95 0,04923-94 9,71739-12 9,54738-21 9,42849-66 8,57159-90 8,56800-85 8,56454-64 0,64011-21 0,65242-20 0,66473-18 52 53 54 5 0,06154-92 9,33761-07 8,56120-75 0,67704-17 6 0,07385-91 9,26442-45 8,55798-62 0,68935-15 50 I 9 10 0,08616-89 0,09847-88 0,11078-86 0,12309-85 9,20344-38 9,15138-89 9,10614-43 9,06626-59 8,55487-76 8,55187-72 8,54898-03 8,54618-27 0,70166-13 0,71397-12 0,72628-10 0,73859-09 $ g ii 12 13 0,13540-83 0,14771-82 0,16002-80 0,17233-79 0,18464-77 9,03072-33 8,99875-58 8,96978-60 8,94336-46 8,91913-59 8,54348-06 8,54086-99 0,75090-07 0,76321-06 0,77552-04 0,78783-03 0,80014-01 61 62 64 16 0,19695-76 8,89681-29 8153127-28 0,81245-00 66 Is 0,20926-74 0,22157-73 8,87616-09 8,85698-54 8,52906-89 8,52693-72 0,82475-98 0,83706-97 6 '9 0,23388-71 8,83912-38 8,52487-51 0,84937-95 69 20 0,24619-70 8,82243-82 8,52288-00 0,86168-94 21 0,25850-68 8,80681-12 8,52094-94 0,87399-92 71 22 0,27081-67 8,79214-13 8,51908-09 0,88630-91 72 23 0,28312-65 8,51727-23 0,89861-89 73 24 li 27 0,29543-64 0,30774-62 0,32005-61 o,33230-59 8i?6533;45 8,74144-05 8,73044-16 8,51552-14 8,51382-63 8,51218-47 8,51059-50 0,91092-88 0,92323-86 0,93554-85 0,94785-83 74 P 28 29 30 0,34467-57 0^30929-54 8,72001-06 8,71010-58 8,70068-95 8,50905-53 8,50756-38 8,50611-90 0,96016-82 0,97247-80 0,98478-79 78 31 0,38160-53 8,69172-80 8,50471-90 0,99709-77 81 32 0,3939! '5 1 8,68319-07 8,50336-25 ,00940-76 82 33 34 0,40622-50 0,41853-48 8,50204-80 8,50077-41 ,02171-74 ,03402-72 83 84 0,43084-47 8,65985-83 8,65276-36 8,49953-92 8,49834-22 ,04633-71 ,05864-69 85 86 38 0,45546-44 0,46777-42 8,64597-66 8,63947-92 8,49718-19 8,49605-69 ,07095-68 ,08326-66 87 88 39 40 0,48008-41 0,49239-39 8,63325-52 8,62728-96 8,49496-62 8,49390-86 ,09557-65 ,10788-63 89 90 4i 0,50470-38 8,62156-81 8,49288-30 ,12019-62 9 1 42 0,51701-36 8,61607-79 8,49188-83 ,13250-60 92 43 0,52932-35 8,61080-69 8,49092-36 ,14481-59 93 44 0,54163-33 8,60574-36 8,48998-80 ,15712-57 94 45 o, 55394-32 8,60087-79 8,48908-04 ,16943-56 95 46 0,56625-30 8,59619-98 8,48820-00 ,18174-54 96 49 0,57856-29 0,59087-27 0,60318-26 8,59170-02 8,58737-06 8,58320-31 8,48734-59 8,48651-73 8,48571-34 ,19405-53 ,20636-51 ,21867-50 99 50 0,61549-24 8,57918*99 8,48493-33 ,23098-48 100 8,45863-78 Perp. For explanation see pp. 216-228 (282) COMPOUND INTEREST AND ANNUITIES Pr Cent. Years Log. r*. Log. a". Log. a. Log. r. Yean i 0,01283-72 0,01283-72 8,58584-21 0,65469-85 51 2 3 0,02567-44 0,03851-17 9,71817-84 9,54842-67 8,58225-86 8,57880-78 0,66753-57 0,68037-29 5 2 53 4 0,05134-89 9,42979*59 8,57548-32 0,69321-01 54 t 0,06418-61 0,07702-33 9,33916-23 9,26622-58 8,57227-98 8,56919-22 0,70604-74 0,71888-46 55 56 7 0,08986-06 9,20549-22 8,56621-52 0,73172-18 57 8 0,10269-78 9,15368-19 8,56334*42 0,74455-90 58 9 to o,ii553*50 0,12837-22 9,10867-95 9,06904-07 8! 55790*35 o,75739-63 o,77023*35 g II 13 0,14120-95 0,15404-67 0,16688-39 9,03373*5* 9,00200-22 8,97326-43 8,55532*53 8,55283*67 0,78307-07 0,79.590-79 0,80874-52 61 62 63 M 0,17972-11 8,94707-25 8^5481 1 -42 0,82158-24 64 0,19255-84 8,92307-08 8,54587-36 0,83441-96 65 *7 0,20539-56 0,21823-28 8,90097-23 8,88054-22 8,5437o-93 8,54161-83 0,84725-68 0,86009-41 66 67 18 0,23107-00 8,86158-64 8,53959*78 0,87293-13 68 ! 9 0,24390-73 8,84394 1 8 0,88.576-85 69 20 0,25674-45 8,82747-08 8!53575*76 0,80860-57 70 21 0,26958-17 8,81205-58 8,53393*29 0,91144-30 7' 22 0,28241-89 8,79759-57 8,53216-86 0,92428-02 9* 23 2 4 11 0,29525-62 0,30809-34 0,32093-06 8,78400-29 8,77120-09 8,75912-27 8,74770-92 8,53046-27 8,52881-27 8,52721-68 8,52567-30 0,93711-74 0,94995-46 0,96279-19 0,97562-91 73 74 ? % 29 0,34660-51 0,35944-23 0,37227-95 0,38511-67 8,73690-79 8,72667-20 8,71696-00 8,7o773*4i 8,52417-94 8,52273*41 8,52133-56 8,51998-21 0,98846-63 1,00130-35 1,01414-08 1,02697-80 e 31 0,39795*40 8,69896-07 8,51867-20 1,03981-52 81 32 33 34 0,41079-12 0,42362-84 0,43646-56 8,69060-91 8,68265-15 8,67506-27 8,51740-38 8,51617-61 8,51498-76 1,05265-24 1,06548-97 1,07832-69 82 83 84 35 0,44930-29 8,66781-98 8,51383-67 1,09116-41 85 36 % 0,46214-01 0,47497-73 0,48781-45 8,66090-15 8,65428-85 8,64796-30 8,51272-22 8,51164-30 1,10400-13 1,11683-85 1,12967-58 86 87 88 39 0,50065-18 8,64190-86 50958*53 1,14251-30 89 40 0,51348-90 8,63611-04 8,50860-46 i>i5535"02 90 4" 0,52632-62 8,63055-41 8,50765-46 1,16818-74 91 42 0,53916-34 8,62522-68 8,50673-42 1,18102-47 92 43 0,55200-07 8,62011-63 8,50584-25 1,19386-19 93 44 0,56483*79 8,61521-17 8,50497*85 1,20669-91 94 8,61050-23 8,50414-14 1,21953-63 95 46 0^59051-23 8,60597-85 8,50333-02 1,23237-36 96 47 0,60334-96 8,60163-10 8,50254-40 1,24521-08 97 48 0,61618-68 8,59745-14 8,50178-22 1,25804-80 98 49 0,62902-40 8,59343*i6 8,50104-37 1,27088-52 99 5 0,64186-12 8,58956-42 8,50032-80 1,28372-25 ICO 8,477*2-13 Ptrp (283) LOGARITHMIC TABLES OF O s Per Cent. Year Log. r\ Los. a\ Log. a". Log. r. Years I 0,01336-40 0,01336-40 8,59622-33 0,68156-20 51 2 0,02672-79 9,71896-45 8,59277-69 0,69492-60 52 3 0,0400(9-19 9,54946-96 8,58946-09 0,70829-00 53 4 0,05345-58 9,43109-29 8,58626-95 0,72165-39 54 1 0,06681-98 0,08018-38 9,34071-08 9,26802-30 8,58319-69 8,58023-81 0,73501-79 0,74838-18 i 0,10691-17 9.20753-57 9,15596-89 8,57738-8i 8,57464-21 0,76174-58 0,77510-98 12 9 10 0,12027-57 0,13363-96 9,11120-74 9,07180-68 8! 5 6944-5 2 o,78847-37 0,80183-77 8 ii 12 3 14 0,14700-36 0,16036-75 0,18709-55 9,03673-69 9,00523-70 8,97672-96 8,950/6-56 8,56698-59 8,56461-45 8,56232-71 8,56012-06 0,81520-17 0,82856-56 0,84192-96 0,85529-35 61 62 63 64 '5 16 0,20045-94 0,21382-34 8,92698-91 8,90511-32 8,'S5593'69 0,86865-75 0,88202-15 65 66 17 0,22718-73 8,88490-32 8,55395-39 0,89538-54 67 la 0,24055-13 8,86616-47 8,55203-95 0,90874-94 68 '9 0,25391-53 8,84873-51 8,55019-12 0,92211-34 69 20 0,26727-92 8,83247-65 8,54840-62 0,93547-73 21 0,28064-32 8,81727-12 8,54668-24 0,94884-13 71 22 23 0,29400-72 8,80301-83 8,78963-02 8,54501-74 8,54340-89 0,96220-52 72 73 24 0,32073-51 8,77703-03 8,54185-47 0198893-32 74 o, 33409-90 8,76515-18 8,54035-30 1,00229-71 75 26 0,34746-30 8,75393-54 8,53890-17 1,01566-11 76 27 0,36082-70 8,74332-87 8,53749-9' 1,02902-50 77 28 0,37419-09 8,73328-5i 8,53614-32 1,04238-90 78 29 0,38755-49 8,72376-27 8,53483-25 1-05575-30 30 0,40091-88 8,71472-42 8,53356-52 1,06911-69 80 3 0,41428-28 8,70613-55 8,53233-99 1,08248-09 81 32 0,42764-68 8,69796-63 8,53 ii 5"5 1,09584-49 82 33 0,44101-07 8,69018-87 8,53000-90 1,10920-88 83 34 35 36 0,45437-47 0,46773-87 0,48110-26 8,68277-75 8,67570-97 8,66896-42 8,52890-07 8,52782-86 8,52679-16 1,12257-28 i> 13593 -67 1,14930-07 84 85 86 37 0,49446-66 8,66252-16 8,52578-84 1,16266-47 87 38 39 40 0,50783-05 0,52119-45 o,53455-85 8,6^636-44 8,65047-58 8,64484-10 8,52481-77 8,52387-86 8,5229698 1,17602-86 1,18939-26 1,20275-65 88 89 90 41 0,54792-24 8,63944-58 8,52209-04 1,21612-05 91 42 0,56128-64 8,63427-75 8,52123-93 1,22948-45 92 43 0,57465-03 8,62932-37 8,52041-56 1,24284-84 93 44 0,58801-43 0,60137-83 8,62457-34 8,62001-62 8,51961-84 8,51884-67 1,25621-24 1,26957-64 94 1 0,61474-22 0,62810-62 0,64147-02 8,61564-23 8,61144-26 8,60740-86 8,51809-97 8, 5 i 73 7 -66 8,51667-65 1,28294-03 1,29630-43 1,30966-82 1 49 0,65483-41 8,60353-23 8,51599*87 1,32303-22 99 SO 0,66819-81 8,59980-62 8,51534-25 8,49485-00 IOO Perp For explanation see pp. 216-228 (284) COMPOUND INTEREST AND ANNUITIES 3 4 Per Cent. Years Log. f. Log. a". Log. a". Log. r-. Yean I 0,01389-01 0,01389-01 8,60646-92 0,70839-31 51 2 0,02770-01 9,71974-96 8,60315-55 0,72228*31 3 0,04167*02 9,55051-08 8,59997-00 0,73617*32 53 4 0,05556-02 9,43238-76 8,59690-69 0,75006-33 54 5 0,06945-03 9,34225-60 8,59396-07 o, 76395 -33 55 6 0,08334-04 9,26981-63 8,59112-62 0,77784-34 56 I 0,09723-04 0,11112-05 9,20957-41 9,15824-98 8,58839*84 o,79'73-34 0,80562-35 57 58 9 10 0,12501-05 0,13890-06 9,11372-80 9,07456-43 8] 58324*47 8,58081*02 0,81951*36 0,83340-36 59 60 11 12 13 0,15279-07 0,16668-07 0,18057-08 9,03972-87 9,00846-04 8,98018-18 8,57846*52 8,57620-62 8,57402-93 0,84729*37 0,86118-37 0,87507-38 61 62 63 0,19446-08 8,95444*39 0,88896-39 64 ! | 0,20835-09 8,93089-08 8!56990'9o 0,90285-39 65 16 i7 0,22224-10 0,23613-10 8,909 2 .V57 8,88924-38 8,56607-92 0,91674-40 0,93063-40 66 67 18 0,25002-11 8,87072-07 8,56426-61 0,94452*41 68 '9 0,26391-11 8,85350*37 8,56251-72 0,95841-42 69 20 0,27780-12 8,83745-5i 8,56083*01 0,97230-42 21 0,29169-13 8,82245-73 8,55920*23 0,98619-43 7' 22 23 0,30558-13 8,80840-92 8,79522-32 8^55611-56 1,00008*43 1,01397-44 72 73 24 0,33336*14 8,78282-30 8,55465-23 1,02786-45 74 11, 0,36114-16 8,77114*14 8,76011*94 IfffSf-S 1,04175-45 1,05564*46 27 0,37503*16 8,74970*45 8,55055-96 1,06953-46 77 28 29 30 0,38892-17 0,41670-18 8,73985-oo 8,73051*44 8,72165-99 8, 54806*03 8,54687-46 1,08342-47 1,09731-48 1,11120-48 g 31 0,43059-19 8,71325-29 8,54572*89 1,12509-49 81 32 0,44448-19 8,70526-28 8,54462*24 82 33 0,45837-20 8,69766-18 8,54355-34 1,15287-50 83 34 0,47226-21 0,69042*48 8,54252-05 1,16676-51 84 1 0,48615-21 0,50004-22 8,68352-86 8,67695-24 8,54152-24 8,54055-79 1,18065*51 1,19454-52 8 0,51393-22 0,52782-23 8,67067-67 8,66468-37 8,53962*59 8,53872-51 1,20843-52 1,22232-53 Is 7 39 0,54171-24 8,65895-73 8,53785-45 1,23621*54 8 9 40 0,55560-24 8,65348-21 8,53701*28 1,25010*54 90 41 0,56949-25 8,64824-42 8,53619*93 1,26399*55 9' 42 43 44 0,58338-25 0,59727-26 0,61116-27 8,64323-07 8,63842-97 8,63382*97 ^53465;23 1,27788-5-5 1,29177*56 1,30566*57 92 93 94 0,62505-27 0,63894-28 0,65283-28 8,62942*06 8,62519-25 8,62113-63 8,53320-63 8,53251-89 8,53185*41 l 'V9SS'S7 i'34733-58 S 97 48 0,66672-29 8,61724-36 8,53121*14 1,36122*59 98 49 0,68061-30 8,61350-65 8,53058-96 1,37511*60 99 0,69450-30 8,60991*73 8,52908-83 1,38900-60 100 8.51188*34 Perp. (285) K 2 LOGARITHMIC TABLES OF 3 g Per Gent. Years Log. r. Log. a". Log. a". Log. r. Years i 0,01441-55 0,01441-55 8,61658-14 0,73519-17 51 2 0,02883-10 8,61339-61 0,74960-72 52 3 4 0,04324-66 0,05766-21 9'55i55-02 9,43367-98 8,61033-67 8,60739-76 0,76402-27 0,77843-82 53 5-4 I 0,07207-76 0,08649-31 0,10090-87 0,11532-42 9,27160-56 9,21160-74 9,16052-46 8,60457-33 8,60185-85 8,59924-85 0,79285-37 0,80726-93 0,82168-48 0,83610-03 if 9 9 0,12973-97 9,11624-14 8',59432-4i 0,85051-58 59 10 0,14415-52 9,0773 !*34 8,59200-13 0,86493-14 60 ii 12 0,15857-07 0,17298-63 9,04271-06 9,01167-24 8,58976-61 8,58761-47 0,87934-69 0,89376-24 61 62 13 0,18740-18 8,98362-11 8,58554-37 0,90817-79 63 M 19 20 0,20181-73 0,21623-28 0,23064-84 0,24506-39 0,25947-94 0,27389-49 0,28831-05 8,95810-76 8,93477-62 8,91333-99 8,89356-40 8,87525-43 8,85824-80 8,84240-71 8,58354-97 8,58162-94 8,57977-98 8,57799-81 8,57628-15 8,57462-75 0,92259-34 0,93700-90 0,95142-45 0,96584-00 0,98025-55 0,99467-11 1,00908-66 64 67 68 69 70 21 22 0,30272-60 0,31714-15 8,82761-44 8,81376-87 8,57149-67 8,57001-56 ,02350-21 ,03791-76 72 23 0,33155-70 8,80078-24 8,56858-74 ,05233*31 73 24 o,34597-25 0,36038-81 0,37480-36 8,78857-90 8,77709-16 8,76626-12 8,56721-04 8,56588-25 8,56460-18 ,06674-87 ,08116-42 74 I 0,38921-91 0,40363-46 8:74636-72 8,56336-65 8,56217-50 : 10999-52 ,12441-08 I 29 30 0,41805-02 0,43246-57 8:72854-17 8,56102-52 8,55991-60 ,13882-63 ,15324-18 32 0,44688-12 0,46129-67 8,72031-32 8,71249-89 8,55884-57 8,55781-29 ,16765-73 ,18207-29 81 82 33 0,47571-22 8,70507-13 8,55681-61 ,19648-84 83 34 0,49012-78 8,69800-50 8,55585-40 ,21090-39 84 o,50454-33 8,69127-71 8,55492-53 ,22531-94 85 36 0,51895-88 8,68486*66 8,55402-88 ,23973-49 86 39 0,53337*43 o,54778-99 0,56220-54 8,67875-41 8,67292-19 8,66735-37 8:55152-12 ,25415-05 ,26856-60 ,28298-15 89 40 0,57662-09 8,66203-45 8,55074-23 ,29739-7 90 4 i 0,59103-64 8,65695-01 8,54999-00 ,31181-26 9' 42 0,60545-19 8,65208-77 8,54926-35 ,32622-81 92 43 44 45 0,61986-75 0,63428-30 0,64869-85 8,64743-53 8,64298-18 8,63871-66 8,54856-21 8,54788-44 8,54723-01 ,34064-36 ,35505-9! ,36947-46 93 94 46 0,66311-40 8,63463-02 8,54659-79 ,38389-02 96 48 49 0,67752-96 0,69194-51 0,70636-06 8,63071-35 8,62695-79 8,62335-56 8,54598-73 8,54539-76 8,54482-77 :4I272'I2 ,42713-67 97 98 99 5 0,72077-61 8,61989-91 8,54427-70 ,44155-23 IOO 8,52827-38 Perp. For explanation see pp. 216-228 (286) COMPOUND INTEREST AND ANNUITIES 3 2 Per Cent - Yean Log. i*. Log. a". Log. a". Log. r-. Yeart I 0,01494-03 0,01494-03 8,62656-17 0,76195-78 51 2 0,02988-07 9,72131-63 8,62350-03 0,77689-82 52 3 4 5 0,04482-10 0,05976-14 0,07470-17 9*34533 -72 8,62056-28 8,61774-35 8,61503-66 0,79183-85 0,80677-89 0,82171*92 53 54 6 7 8 9 0,08964-21 0,10458-24 0,11952-28 0,13446-31 9,21363-59 9,16279-32 9,11874-74 8,61243-73 8,60994-06 8,60754-19 8,60523-67 0,83665-96 0,86^54-03 0,88148-06 59 (0 0,14940-35 9,08005-39 8,60302-11 0,89642-10 bo ii 0,16434-38 9,04568-27 8,60089-11 0,91136-13 61 12 0,17928-42 9,01487-30 8,59884-30 0,92630-17 62 13 14 ',1 0,19422-45 0,20916-49 0,22410-52 0,23904-56 8,98704-74 8,96175-67 8,93864-51 8,9(742-58 8!s9497;87 8,59140-20 0,94124-20 0,95618-24 0,97112-27 0.98606-31 65 66 17 0,25398-59 8,89786-42 8,58971-42 1,00100-34 67 18 0,26892-63 8,87976-57 8,58808-95 1,01594-38 68 19 0,28386-66 8,86296-78 8,58652-57 1,03088-41 69 20 0,29880-70 8,84733-25 8,58502-01 1,04582-45 21 o,3i374-73 8,83274-26 8,58357-02 1,06076-48 71 22 23 0,32868-77 0,34362-80 8,81909-67 8,80630-76 8,58217-40 8,58082-92 ',07570-52 1,09064-55 72 73 24 0,35856-84 8,79429-86 8,57953-39 1,10558-59 74 25 o,3735o-87 8,78300-29 8,57828-60 1,12052-62 75 26 0,38844-91 8,77236-13 8,57708-38 1,13546-66 76 30 0,40338-94 0,41832-98 0,43327-01 0,44821-05 8,76232-15 8,75283-67 8,74386-54 8,73536-99 8,57592-53 8,57480-89 8,57373-3i 8,57269-61 1,15040-69 i,i6534-73 1,18028-76 1,19522-80 g 3* 0,46315-08 0,47809-12 8,72731-67 8,71967-52 8,57169-65 8,57073*29 1,21016-83 1,22510-87 81 82 33 0,49303-15 8,71241-75 8,56980-39 1,24004-90 83 34 t o,50797-i9 0,52291-22 0,53785-26 8, 7055 '-87 8,69895-57 8.69270-74 8,56890-83 8,56804-46 8,56721-18 1,26992-97 1,28487-01 84 0,55279-29 8,68675-46 8,56640-87 1,29981-04 87 38 8.68107-96 8,56563-41 1,31475-08 88 39 0,58267-36 8,67566-61 8,56488-71 1,32969-11 89 40 0,59761-40 8,67049-89 8,56416-65 1,34463*15 90 4' 42 43 0,61255-43 0,62749-47 0,64243-50 8,66556-43 8,66084-92 8,65634-16 8,56347-14 8,56280-09 8,56215-41 1,37451-22 1,38945-25 9' 92 93 44 0.65737-54 8,65203-04 8,56153-00 1,40439-29 94 45 46 0,67231-57 0,68725-61 8,64790-53 8,64395-66 8,56092-79 8,56034-69 1,43497*36 $ 2 49 0,70219-64 0,71713-68 0,73207-71 8,64017-52 8,63655-27 8,63308-11 8,55978-64 8,55924-54 1,44921-39 1,46415-43 1,47909-46 97 98 99 50 8,62975-31 8,55821-96 1,49403-50 00 8,54406-80 Perp (287) LOGARITHMIC TABLES OF 35 8 Per Cent. Years Log. T- Log. a-. Log. a". Log. r". Years I 2 3 0,01546-45 0,03092-91 0,04639-36 0,01546-45 9,72209-80 9,55362-44 8,63641-15 8,63347-00 8,63065-02 0,78869-17 0,80415-63 0,81962-08 5* 53 4 0,06185-82 9,43625-72 8,62794-62 0,83508-54 54 I 0,07732-27 0,09278-73 9,34687-31 9,27517-19 8,62535-28 8,62286-45 0,85054-99 0,86601-44 1 I 9 10 0,10825-18 0,12371-63 0,13918-09 0,15464-54 9,21565-94 9,16505-60 9,12124-62 9,08278-59 8,62047-69 8,61818-52 8,61598-50 8,61387-22 0,88147-90 0,89694-35 0,91240-81 0,92787*26 I ii 0,17011-00 9,04864-47 8,61 184-31 0,94333*72 61 12 o,i8557*45 9,01806-22 8,60989-39 0,95880-17 62 13 0,20103-91 8,99046-07 8,60802-13 0,97426-62 63 14 11 0,21650-36 0,23196-82 0,24743-27 8,96539-11 8,94249-77 8,92149-36 8,60622-17 8,60449-21 8,60282-94 0,98973*08 1,00519-53 1,02065-99 64 17 0,26289-72 8,90214-42 8,60123-11 1,03612-44 67 18 19 0,278.^6-18 0,29382-63 8,88425-49 8,86766-32 8,59969-41 8,59821-61 1,05158-90 1,06705-35 68 69 20 0,30929-09 8,85223-13 8,59679-46 1,08251-81 70 21 0,32475-54 8,83784-18 8,59542-71 1,09798-26 7 l 22 0,34022-00 8,82439-36 8,59411-16 1,11344-71 72 23 0,35568*45 8,81179-91 8,59284-57 1,12891-17 73 24 25 0,37114-90 0,38661-36 8,79998-20 8,78887-52 8,59162-77 1,14437-62 1,15984-08 74 7S 26 0,40207-81 8,77841-97 8,58932-74 i,i7530-53 76 28 0,41754-27 0,43300-72 8,76856-32 8,75925*90 8,58824-15 8,58719-61 1,19076-99 1,20623-44 9 2 9 0,44847-18 8,58618-97 1,22169-89 79 30 0,46393*63 8^74214-50 8,58522-07 1,23716-35 80 31 32 0,47940-09 0,49486-54 8,73426-39 8,72679-19 8,58428-77 8,58338-91 1,25262-80 1,26809-26 81 82 33 0,51032-99 8,71970-10 8,58252-38 ,28355*7i 83 34 o,52579*45 8,71296-62 8,58169-04 1,29902-17 84 0,54125-90 8,70656-48 8,58088-76 1,31448-62 85 1 39 40 0,55672-36 0,57218-81 0,58765-27 0,60311-72 0,61858-17 8,70047*54 8.69467-89 8,68915-74 8,68389-49 8,67887-63 8,58011-44 8,57796*03 8,57729-41 1,32995-07 1,34541*53 1,36087-98 1,37634-44 1,3918089 86 87 88 89 90 41 0,63404-63 8,67408-76 8,57665-23 1,40727-35 9 1 42 0,64951-08 8,66951-59 8,576o3-37 1,42273-80 92 43 0,66497-54 8,66514-94 8,57543*75 1,43820-26 93 44 47 0,68043-99 0,69590-45 0,71136-90 0,72683-35 8,66097-69 8-65698-79 8,65317-20 8,64952-28 8,57486-30 8,5743o-94 8,57377*57 8,57326-15 1,45366-71 1,46913-16 1,48459-62 1,50006-07 94 9 97 48 49 0,74229-81 0,75776-26 8,64602-92 8,64268-44 8,57276-57 8,57228-78 ^^(JS 98 99 50 0,77322-72 8,63948-08 8,57182-71 1^54645-44 too Perp. For explanation see pp. 216^228 (288) COMPOUND INTEREST AND ANNUITIES 4 Per Cent. Years Log. i*. Log. a*. Log. a". Log. r". Vears 2 3 0,01598-81 0,03197*62 0,04796-43 0,01598-81 9,72287-86 9,55465-88 8,64613-25 8,64330-69 8,64060-06 0,81530-34 0,83138-15 0,84736-96 51 S 2 53 4 0,06395-24 9.43754-25 8,63800-81 0,86335-77 54 0,07994-05 9,34840-59 8,63552-38 0,87934-58 6 0,09592-86 9,27694-92 8,63314-26 0,89533-39 56 i 0,11191-67 0,12790-48 9,21767-79 9,16731-26 8,63085-99 8,62867-09 0,91132-20 0,92731-01 j$ 9 10 0,14389-29 0,15988-11 9!o855o- 9 4 8,62657-14 8,62455-74 0,94329-82 0,95928-63 59 DO ii 0,17586-92 9,05159-7! 8,62262-50 0,97527-44 61 12 0,19185-73 9,02124-02 8,62077-05 0,99126-25 62 '3 0,20784-54 8,99386-12 8,61899-06 1,00725-06 63 M 0,22383-35 8,96901-11 8,61728-18 1,02323-87 64 ii 0,23982-16 0,25580-97 8,94633-40 8,92554-32 8,61564-11 8,61406-56 1,03922-69 1,05521-50 1 7 0,27179-78 8,90640-40 8,61255-26 1,07120-31 67 18 0,28778-59 8,88872-20 8,61109-89 1,08719-12 68 20 0,30377-40 0,31976-21 8,87233-45 8,85710-38 8,60970-26 8,60836-09 Mi9i6-74 69 70 21 o,33575'02 8,84291-25 8,60707-15 1,13515-55 7' 22 23 24 0^36772-64 0,38371-45 8,82965-95 8,81725-72 8,80562-03 8,60583-2? 8,60464-16 8,60349-67 1,15114-36 1,16713-17 1,18311-98 72 73 74 Ii 0,39970-26 0,41569-07 8,79470-89 8,78443-69 8,60239-62 8,60133-80 1,19910-79 1,21509-60 76 27 0,43167-88 8,77476-09 8,60032-05 1,23108-41 77 28 0,4^766-70 8,76563-43 8,59934-21 1,24707-22 78 29 0,46365-5! 8,59840-11 1,26306-03 79 30 0,47964-32 8^74886-70 8,59749-60 1,27904-84 80 32 33 0,49563-13 0,51161-94 0,52760-75 8,74115-52 8,73384-95 8,72692-23 8,59662-54 8,595/8-79 8,59498-22 1,29503-65 1,31102-46 1,32701-27 81 82 83 34 35 o,54359-56 o,55958;37 8,72034-85 8,71410-50 8,59420-71 8,59346-13 1,34300-09 1,35898-90 84 85 36 8,70817-10 8,59274-37 i,37497-7i 86 37 o59 T 55'99 8,70252-72 8,5920.5-31 1,39096-52 87 38 0,60754-80 8,69715-60 8,59138-85 1,40695-33 88 39 0,62353-61 8,69204-10 8,59074-89 1,42294-14 89 40 0,63952-42 8,68716-73 8,590'3'33 1,43892-95 90 4i 0,65551-23 8,68252-09 8,58954-08 1,45491-76 9 1 42 43 0,67150-04 0,68748-85 8,67808-90 8,67385-97 8,58897-05 8,58842-14 1,47000-57 1,48689-38 92 93 44 0,70347-66 8,66982-19 8,58789-29 1,50288-19 94 0,71946-47 8,66596-52 8,58738-41 1,51887-00 95 46 8,66228-01 8,58689-42 i,53485-8i 96 48 0^75 1 44- 10 0,76742-91 8,65875-75 8,65538-91 8,58642-26 8,58596-86 1,55084-62 1,56683-43 97 98 49 0,78341-72 8,65216-69 8.58553-13 1,58282-24 99 50 8,64908-37 8,58511-03 1,59881-05 100 8,57403-i3 Perp. (289) LOGARITHMIC TABLES OF 3 f Per Cent Years Log. i-. Log. a". Log. a\ Log. r-. Years 2 0,01651-10 0,03302-21 0,01651-10 9,72365-81 8,65572-64 8,65301-26 0,84206-29 0,85857-39 5 5* 3 4 0,04953-31 0,06604-41 JfjJ8?-M 8,65041-60 8,64793-08 0,87508-50 0,89159-60 53 54 I 0,08255-52 0,09906-62 9.34993-56 9,27872-24 8^64327-35 0,9081070 0,92461-81 8 0,1155773 0,13208-83 9,21969-15 9,16956-32 8,64109-16 8,63900-14 0,94112-91 0,95764-01 5 Z 58 9 10 0,14859-93 0,16511-04 9,12622-23 9,08822-45 8,63699-86 8,63507-92 0,97415-12 0,99066*22 g DO ii 12 13 0,18162-14 0,19813-24 0,21464-35 0*24766-56 0,20417-66 9.05453-96 9,02440-60 8,99724-88 8,97261-65 8,95015-42 8,92957-49 8,63323-94 8,63147-56 8,62078-43 8,62816-23 8,62660-65 8,62511-40 1,00717-32 1,02368-43 1,04019-53 1,05670-64 1,07321-74 1,08972-84 61 62 63 65 66 ! 7 0,28068-76 8,91064-39 8,62368-20 1,10623-95 67 18 0,29719-87 8,8931672 8,62230-79 1,12275-05 68 '9 o,3i37o-97 8,87698-17 8,62098-91 1,13926-15 69 20 0,33022-07 8,86195-01 8,61972-33 1,15577-26 7o 21 0,34673-18 8,84795-47 8,61850-82 1,17228-36 7i 22 23 0,36324-28 8,83489-44 8,82268-19 8,61734-17 8,61022-15 1,18879-46 1,20530-57 72 73 24 0^39626-49 8,81124-08 8,61514-59 1,22181-67 74 25 0,41277-59 8,80050-41 8,61411-30 1,33832-78 75 26 0,42928-70 8,79041-29 8,61312-08 1,25483-88 76 27 28 0,44579-80 0,46230-90 8,78091-47 8,77196-29 8,61216-79 8,61125-24 1^28786-09 9 2 9 0,47882-01 8,76351-60 8,61037-30 1,30437-19 79 30 0.49533' 11 8,75553-66 8,60952-79 1,32088-29 80 3 1 0,51184-21 8,74799-08 8,60871-60 ^33739-40 81 32 33 0,52835-32 0,54486-42 8,74084-85 8,73408-17 8,60730-58 8,60718-60 1^37041-61 82 83 34 9 o,56i37-53 0,57788-63 0,59439-73 8,72766-54 8,72157-69 8,60646-54 8,60577-28 8,60510-72 1,38692-71 1,40343-81 1,41994-92 84 11 9 39 40 0,61090-84 0,62741-94 0,64393-04 0,66044-15 8^71030-06 8,70507-60 8,70010-51 8,69537-26 8,60446-73 8,60385-22 8,60326-08 8,60269-23 1,43646-02 1,45297-12 1,46948-23 '*48599*33 11 89 90 42 43 44 0,67695-25 0,69346-35 0,70997-46 0,72648-56 0,74299-67 8,69086-51 8,68656-93 8,68247-36 8,67856-68 8,67483-87 8,60214-55 8,60162-00 8,60111-46 8,60062-86 8,60016-13 1,50250-43 ii53552-64 1.5520375 1.56854-85 9i 92 93 94 47 o,75950-77 0,77601-87 8,67127-97 8,66788-07 8,59971-18 8,59927-96 1.58505-95 1,60157-06 97 48 49 5 > 79252 -98 0,80904-08 0,82555-18 8,66463-35 8,66153-02 8,658/6-35 8,59886-40 8,59846-42 8,59807-96 1,61808-16 1,63459-26 1,65110-37 98 99 IOO 8,58827-17 Perp. For explanation see pp. 216-228 (290) COMPOUND INTEREST AND ANNUITIES 4 Per Cent. Years Log. r\ Log. a". Log. a". Log. r". Years , 0,01703-33 0,01703-33 8,66510-48 0,86870-03 51 2 3 0,03406-67 0,05110-00 9,72443-6; 9.55672-28 8,66258-90 8,66009-81 0,9027670 5* 53 4 3 0,06813-34 0,08516-67 0,10220-00 944010-59 9,35146-22 9,28049-16 8,65771-64 8,65543-85 8,65325-96 0,91980-03 0,93683-37 0,95386-70 54 1 i 9 0,11923-34 0,13626-67 9,22170-01 9,17180-78 9, 1 2869-97 8,65117-45 8,64917-91 8,64726-91 0,97090-03 0,98793-37 1,00496-70 i> 9 10 oil 7033-34 9,09093-12 8,64544-04 1,02200-04 60 11 0,18736-67 9,05747-23 8,64368-93 i,03903-37 61 12 0,20440-01 9,02756-23 8,64201-22 1,05606-70 62 >3 0,22143-34 9,00062-38 8,64040-56 1,07310-04 63 '4 0,23846-68 8,97620-77 8.63886-64 1,09013-37 64 0,25550-01 8,95395-82 8.63739-16 1,10716-71 * '7 18 0,2:253-34 0,28956-68 0,30660-01 8,93358-85 8,91486-40 8,89759-04 8,63597-82 8,63462-35 8,63332-48 1,12420-04 1,14123-37 1,15826-71 g ig 0,32363-34 8.88160-50 8,63207-97 1,17530-04 69 20 0,34066-68 8,86677-02 8,63088-59 i,i9233-38 70 21 o,35770'oi 8,85296-84 8,62974-11 1,20936-71 7' 22 23 24 o,37473-35 0,39176-68 0,40880-01 8,84009-86 8,82807-35 8,8i68r-66 8,62864-32 8,62759-01 8,62657-90 1,22640-04 1,26046-71 72 73 74 25 26 0,42583-35 0,44286-68 8.80626-12 8.79634-80 8,62561-08 8,62468-09 1,27750-04 ? z 29 0,45990-02 0,47693*35 0,49396-68 8,78702-48 8,77824-52 8,76996-73 8.62378-89 8,62293-26 8,622U-II 1^31 156-71 1,32860-05 79 30 0,51100-02 8,76215-40 8,62132-25 1,36266-71 80 32 0,52803-35 0,54506-69 8,75477'M 8,74778-92 8,62056-56 8,61983-91 1,37970-05 i,39673-38 81 82 33 34 $ 0,56210-02 o,579i3-35 0,59616-69 o,6i32o-o->. 8,74117-97 8,73491-80 8,72898-10 8,72334-80 8,61914-16 8,61847-21 8,61782-92 8,61721-20 1,41376-72 1,43080-05 I$4867J 8.3 84 85 86 H 0,63023-30 0,64726-69 8, 7 '799-95 8,71291-83 8,61661-94 8,61605-03 1,48190-05 87 88 39 0,66430-02 8,70808-79 8,61550-38 1,51596-72 89 40 0,68133-36 8,70349-33 8,61497-89 1,53300-05 90 4 1 0,69836-69 8,69912-09 8,61447-48 1,55003-39 9 1 42 43 44 0,71540-03 0,73243-36 0,74946-69 8,69495-78 8,60099-20 8,68721-27 8,61399-08 8,61352-58 8,61307-91 1,56706-72 1,58410-06 1,60113-39 92 93 94 0,76650-03 8,68360-94 8,61265-01 1,61816-72 95 46 0,78353-36 8,68017-27 8,61223-80 1,63520-06 90 47 oi8oo56-69 8,67689-37 8,61184-21 1,65223-39 97 48 0,81760-03 8,67376-39 8,61146-18 1,66926-73 98 49 0,83463-36 8,67077-56 8,61109-64 1,68630-06 99 SO 0,85166-70 8,66792-16 8,61074-53 8.60206-00 too Perp (291) LOGARITHMIC TABLES OF 4 Per Cent. Years Log. T-. Log. a". Log. a". Log. r". Years 2 0,01755-50 O,035 1 ! '0 o,OT755-5o 9,72521-38 8,67453-95 8,67203-78 0,89530-57 0,91286-07 51 52 3 4 0,05266-50 0,07022-OI 9,55775-22 9,44138-41 8,66964-88 8,66736-68 0,93041-58 0,94797-08 53 54 I 0,08777-51 0,I0533-01 9,35298-56 9,28225-70 8,66518-65 8,66310-27 0,96552-58 0,98308-08 H I 0,I2288-5I 0,14044-01 9,22370-38 9,17404-65 8,66111-09 8,6^920-66 1,00063-58 1,01819-08 tl 9 o, 1 5 799-51 9,13116-98 8,65738-54 i,03574-58 59 10 O, 1 7555-01 9,09362-95 8,65564-36 1,05330-09 60 ii 0,I93IO-52 9,06039-52 8,65397-73 1,07085-59 61 12 O,2I066'02 9,03070-66 8.65238-31 1,08841-09 62 13 0,22821-52 9,00398-60 8,65085-75 1,10596-59 63 '4 0,24577-02 8,97978-44 8,649.^9-74 1,12352-09 64 !* 0,26332-52 0,28088-02 8'9375cS-43 8,64799-98 8,64666-16 1,14107-59 1,15863-10 ll '7 0,29843-52 8, 9*1 906-43 8,64538-04 1,17618-60 67 18 0,31509*03 8,90199-19 8,64415-35 1,19374-10 68 *9 0,33354*53 8,88620-44 8,64297-84 1,21129-60 69 20 0,35110-03 8,87156-42 8,64185-29 1,22885-10 70 21 0,36865-53 8,85795-38 8,64077-48 1,24640-60 7 1 22 0,38621-03 8,84527-23 8,63974-18 1,26396-10 72 23 0,40376-53 8,83343-21 8,63875-20 1,28151-61 73 24 2 5 26 0,42132-03 0,43887-54 0,45643-04 8,82235-70 8,81198-01 8,80224-25 8,63780-36 8,63689-47 8,63602-38 1,29907-11 1,31662-61 1,33418-11 74 \l 27 0,47398-54 8,79309-17 8,63518-88 1,35173-61 77 28 0,49154-04 8,78448-13 8,63438-84 1,36929-11 78 29 0,50909-54 8,77636-97 8,63362-11 1,38684-61 30 0,52665-04 8,76871-95 8,63288-56 1,40440-12 80 31 0,54420-54 8,76149-70 8,63218-03 1,42195-62 81 32 0,56176-05 8,75467-20 8.63150-40 1,43951-12 82 33 o,5793 * '55 8,74821-68 8-63085-55 1,45706-62 83 34 0,59687-05 8,74210-64 8,63023-37 1,47462-12 84 39 0,61442-55 0,63198-05 0,64953-55 0,66709-05 0,68464-56 8,73631-76 8,73083-04 8,72562-48 8,72068-34 8,71599-02 8,62963-73 8,62906-52 8,62851-67 8,62799-04 8,62748-56 1,49217-62 1,50973-12 1,52728-63 1,54484-13 1,56239-63 11 1 40 0,70220-06 8,71153-00 8,62700-13 i, 5799S'i3 90 41 0,71975-56 8,70728-94 8,62653-67 i,59750-63 9i 42 o,7373i-o6 8,70325-53 8,62609-10 1,61506-13 92 43 0,75486-56 8,69941-61 8,62566-34 1,63261-63 93 44 0,77242-06 8,69576-03 8,62525-32 1,65017-14 94 * 0,78997*56 0,80753-07 8,69227-85 8.68896-05 8,62485-95 8,62448-18 1,66772-64 1,68528-14 8 47 0,82508-57 8,68579-77 8,62411-93 1,70283-64 97 48 0,84264-07 8,68278-17 8,62377-15 1,72039-14 98 49 0,86019-57 8,67990-48 8,62343-77 1,73794-64 99 50 o,87775*o7 8,67715-96 8,62311-74 1,75550-14 roo 8,61542-40 Perp For explanation see pp. 216-228 (292) COMPOUND INTEREST AND ANNUITIES 4 4 Pr Cent. Years Log. r. Log. a". Log. a". Log. r". Years I 0,01807-61 0,01807-61 8,68376-19 0,92187-92 51 2 3 4 0,03615-21 0,05422-82 0,07230-43 0,09038-03 0,10845-64 9,72599-01 9,55878-01 9,44266-01 9,35450-62 9,28401-84 8,68136-08 8,67907-02 8,67688-42 8,67479-75 8,67280-54 o,93995-53 0,95803-14 0,97610-74 0,99418-35 1,01225-96 52 53 54 7 0,12653-24 9,22570-26 8,67090-29 1,03033-56 57 ft o, 1 4460 - 8 ^ 9,17627-92 8,66908-58 1,04841-17 58 9 0,16268-46 9,13363-29 8,66735-01 1,06648-78 10 0,18076-06 9,09631-94 8,66569-14 1,08456-38 00 ii 0,19883-67 9,06330-85 8,66410-64 1,10263-99 61 12 0,21691-28 9,03383*97 8,66259-14 1,12071-59 62 M 0,23498-88 0,25306-49 9,00733-55 8,98334-69 8,66114-32 8,65975-84 1,13879-20 1,15686-81 64 15 0,27114-10 8,96151-80 8,65843-43 1,17494-41 65 .6 0,28921-70 8,94156-22 8,65716-79 1,19302-02 66 12 19 0,30729-31 0,32536-9! 8,92324-48 8,90637-17 8,89078-01 8,65595-66 8,65479-78 8,65368-92 1,21109-63 1,22917-23 1,24724-84 2 69 20 0^36152-13 8,87633-24 8,65262-84 1,26532-45 70 21 22 0,37959-73 8,86291-12 8,85041-55 8,65161-33 8,65064-18 1,28340-05 1,30147-66 72 23 24 o,4' 5 74'95 0,43382-55 8,83875-80 8,82786-22 8,64971-21 8,64882-20 i!337&'87 73 74 26 29 30 0,45190-16 0,46997-77 0,48805-37 0,50612-98 0,52420-58 0,54228-19 8,81766-13 8,80809-65 8,799ii-55 8,70067-16 8,78272-34 8,64796-99 8,64715-40 8,64637-30 8,64562-51 8,64490-89 8,64422-30 ii37378-o8 1,39185-69 1,40093-30 1,42800-90 1,44608-51 11 g 31 0,56035-80 8,76816-83 8,64356-61 1,46416-12 8. 32 0,57843-40 8,76149-75 8,64293-68 1,48223-72 82 33 34 0,59651-01 0,61458-62 0,63266-22 8,75519-36 8,74923-i3 8,74358-80 8,73824-30 8,64233-41 8,64175-69 8,64120-37 8,64067-38 i,5oo3i-33 1,51838-93 1,53646-54 i,55454-i5 83 84 8s 86 39 40 ',68689-04 0,70496-65 0,72304-25 8,733i7-68 8,72837-21 8,72381-26 8,71948-36 8,64016-61 8,63967-97 8,63921-36 8,63876-70 1,57261-75 1,59069-36 1,60876-97 1,62684-57 87 88 89 90 4i 0,74111-86 8,71537-12 8,63833-91 1,64492-18 9' 42 0,75919-47 8,71146-29 8,63792-80 1,66299-79 92 43 o,77727-o7 8,7o774-66 8,63753-58 1,68107-39 93 44 0,79534-68 8,70421-13 8,63715-92 1,69915-00 94 45 0,81342-29 8,70084-71 8,63679-81 1,71722-60 95 46 0,83149-89 8,69764-42 8,63645-21 i,7353o-2i 96 47 0,84957-50 8,69459-41 8,63612-04 i,75337-82 97 48 0,86765-11 8,69168-82 8,63580-26 1,77145-42 9" 49 50 0,88572-71 0,90380-3* 8,68891-89 8,68627-91 8, 63520-58 8,628.38-80 1,78953-03 1,80760-64 99 100 Perp. (293) LOGARITHMIC TABLES OF 43 & Per Cent. Years Log. r". Log. a". Log. " Log. r". Years I 0,01859-65 0,01859-65 8,69286-38 0,94842-09 S 1 2 0,03719-30 9,72676-52 8,69055-98 0,96701-74 5 2 3 4 3 0,05578-95 0,07438-60 0,09298-24 0,11157-89 9,55980-63 9-44393*37 9,35602-35 9,28577-58 8, 6862 7 -02 8,68427-38 8.68236-96 0,98561-39 1,00421-04 1,02280-69 1,04140-34 53 54 I 9 10 0,13017-54 0,14877-19 0,16736-84 0,18596-49 9,22769-65 9,17850-60 9,13608-89 9,09900-10 8,68055-30 8,67881-98 8,67716-57 8,67558-67 1,05099-98 1,07859-63 1,09719-28 1,11578-93 i g ii 12 '3 0,20456-14 0,22315-79 0,24175-44 9,06621-22 9,03696-18 9,01067-23 8,67407-93 8,67263-99 8,67126-54 i,i3438-58 1,15298-23 1,17157-88 61 62 63 M 0,26035-08 8,98689-51 8,66095-25 1,19017-53 64 15 0,27894-73 8,96527-40 8,66869-85 1,20877-18 in 0,29754-38 8,94552-24 8,66750-03 1,22736-82 66 Is 0,31614-03 0,33473-68 8,92740-58 8,91073-00 8,66635-55 8,66526-14 1,24596-47 1,26456-12 68 '9 0.35333-33 8,89533-21 8,66421-58 1,28315-78 69 20 0,37192-98 8,88107-48 8,66321-63 1,30175-42 70 21 0,39052-63 8,86784-06 8,66226-11 1,32035-07 7 1 22 0,40912-27 8,85552-85 8,66134-77 72 23 0,42771-92 8,84405-12 8,66047-44 t>35754'37 73 2 4 0,44631-57 8.83333*23 8,65063-94 1,37614-01 74 25 0,46491-22 8,82330-50 8,65884-09 ! 39473-66 26 0,48350-87 8,81391-05 8,65807-72 76 2 7 0,50210-52 8,80509-64 8.65734-67 1,43*19 2 -96 77 28 29 0,52070-17 0,53929-82 8,79681-64 8,78902-88 8,65664-81 8,65597-98 r,45052-6l 1,46912-26 78 79 30 0.55789-47 8.78169-64 8,65534-05 1,48771-91 80 32 33 0,57649-11 0,59508-76 0,61368-41 8,77478-56 8,76826-60 8,76211-02 8,65472-89 8,65414-36 8,65358-36 1,50631-56 I,5249I-2I I,54350-85 81 82 83 34 0,63228-06 8,75629-31 8,65304-78 I,562IO-50 84 1 0,65087-71 0,66947-36 0.68807-01 8,75079-21 8,74558-62 8,74065-64 8,65253-53 8,65204-46 8,65157-50 1,58070-15 1,59929-80 1,61789-45 85 86 87 38 0,70666-66 8,73598-50 8,65112-55 1,63640-10 88 39 40 0,72526-31 8:72735-50 8,65069-54 8,65028-37 1,6550875 1,67368-40 89 90 41 0,76245-60 8,72336-76 8,64988-95 1,69228-05 9 1 42 0,78105-25 8,71958-14 8,64951-24 1,71087-69 92 43 44 0,79964-90 0,81824-55 8,71598-45 8,71256-62 8,64915-13 8,64880-56 1,72047-34 1,74806-99 93 94 0,83684-20 8,70931-63 8,64847-46 1,76666-64 49 0,85543-85 0,87403-50 0,89263-14 0,91122-79 8,70622-51 8,70328-41 8,70048-49 8,69781-98 8,64815-78 8,64785-44 8,64756-40 8,64728-59 1,78526-29 1,80385-94 1,82245-59 1,84105-24 99 0,92982-44 8,69528-17 8,64701-96 1,85964-88 IOO 8,64097-81 Prjx For explanation see pp. 216-228 (294) COMPOUND INTEREST AND ANNUITIES 4 2 Per Cent. Years Log. r-. Log. a". Log. a". Log. r". Yean 1 2 3 0,01911-63 0,03823-26 0,05734-89 0,01911-63 9^56083-09 8,70184-69 8,69963-65 8,69753-17 0,97493-08 0,99404-71 1,01316-34 51 52 53 4 0,07646-52 9,44520-50 8,69552-71 1,03227-97 54 5 6 0,09558-15 0,11469-77 9*35753-78 9,28752-94 8,69361-74 8,69179-78 1,05139-60 1,07051-23 55 56 7 0,13381-40 9,22968-56 8,69006-37 1,08962-86 57 fi 0,15293-03 9,18072-68 8,68841-06 1,10874-48 58 9 0,17204-66 9,13853-79 8,68683-47 1,12786-11 59 10 0,19116-29 9,10167-43 8,68533-19 1,14697-74 60 ii 0,21027-92 9,06910*61 8,68389-87 1,16609-37 61 12 0,22939-55 9,04007-27 8,68253-16 1,18521-00 62 '3 0,24851-18 9,01399-67 8,68122-74 1,20432-63 63 4 0,26762-81 8,99042-91 8,67998-31 1,22344-26 64 15 0,28674-44 8,96901-41 8,67879-57 1,24255-89 65 16 0,30586-06 8,94946*50 8,67766-24 '1,26167-52 66 17 0,32497-69 8,93154-73 8,67658-07 1,28079-15 67 18 0,34409-32 8,91506-67 8,67554-80 1,29990-78 68 '9 20 0,36320-95 0,38232-58 8,80986-07 8,88579-16 8,67456-22 8,67362-09 1,31902-40 1,33814-03 69 70 21 0,40144-21 8,87274-21 8,67272-20 1,35725-66 7i 22 23 24 0,42055-84 0,43967-47 0,45879-10 8,86061-13 8,84931-18 8,83876-74 8,67186-36 8,67104-37 8,67026-06 1,37637-29 1,39548-92 1,41460-55 73 73 74 i 0,47790-73 0,49702-36 0,51613-98 8,82891-13 8,81968-46 8,81103-49 8,66951-25 8,66879-78 8,66811-51 1,43372-18 1,45283-81 1,47195-44 28 0,53525-61 8,80291-60 8,66746-27 1,49107-07 78 29 30 0,55437-24 o,57348-87 8,79528-63 8,78810-85 8,66683-93 8,66624-36 1,51018-69 1.52930-32 e 3* 0,59260-50 0,61172-13 8,78134-92 8,77497-81 8,66567-43 8,66513-02 1,54841-95 !> 567 53 -58 81 82 33 0,63083-76 8,76896-74 8,66461-02 1,58665-21 83 34 0,64995-39 8,76329-26 8,66411-32 1/0576-84 84 0,66907-02 0,68818-65 8,75793-06 8,75286-08 8,66363-81 8,66318-40 1,62488-47 1,64400-10 86 37 38 0,70730-27 0,72641-90 8,74806-41 8,66274-98 8,66233-48 1,66311-73 1,68223-36 87 88 39 40 0,74553-53 0,76465-16 8,' 73922 -14 8,73514-48 8,66193-80 8,66155-86 1,7013498 1,72046-61 89 90 4 1 0,78376-79 8,73127-91 8,66119-59 1,73958-24 9i 42 0,80288-42 8,72761-18 8,66084-91 1,75869-87 92 43 0,82200-05 8,72413-12 8,66051-74 1,77781-50 93 44 0,84111-68 8,72082-64 8,66020-04 94 0,86023-31 8,71768*73 8,65989-71 1,81604/76 46 0,87934-94 8,71470-45 8,65960-71 1,83516-39 96 47 0,89846-57 8,71186-91 8,65932-98 1,85428-02 97 48 49 0,91758-19 0,93669-82 8,70917-31 8,70660-87 8,65906-46 8,65881-10 i,87339 <6 5 1,89231-28 98 99 5 8,70416-90 8,65856-85 1,91162-90 100 8,65321-25 Perp (295) LOGARITHMIC TABLES OF 4: s Per Cent. Years Log. r". Log. a". Log. 9748-94 1,33016*61 66 \l 0,34261-85 0,36277-26 8,93977-i9 8,92367-61 8,69652-44 8,69560-54 1,35032-01 i-37047"4i 68 '9 20 0,38292-66 0,40308-06 8,90884-76 8,89514-88 8,69472-97 8,69389-54 1,39062-82 1,41078-22 69 70 21 22 2 3 24 % 3 0,42323-47 o,44338-87 0,46354-27 0,48369-68 0,50385-08 0,52400-48 0,54415-89 0,56431-29 8,88246-23 8,87068-74 8,85973*67 8,84953-41 8,84001-27 8,83111-39 8,82278-54 8,81498-08 8,69310-05 8,69234-29 8,69162-10 8,69093-28 8,69027-69 8,68965-17 8,68905-56 8,68848-74 1,45109-03 1,47124-43 1,49139-83 1,51155-24 1,53170-64 1,55186-04 1,57201-45 7' 72 73 74 P 29 30 0,58446-69 0,60462-09 8,80765-87 8,80078-20 8,68794-56 8,68742-90 1,59216-85 1,61232-25 1 3' 0,62477-50 8,7943171 8,68693-64 1,63247-66 8. 32 33 34 0,64492-90 0,66508-30 0,68523-71 8,78823-40 8,78250-53 8,77710-58 8^68601 -87 8,68559*15 1,65263-06 1,67278-46 1,69293-87 1 0.70539-" 8,77201-31 8,68518*40 1,71309-27 8; 36 o,72554-5i 8,76720-63 8,68479-55 86 37 0,74569-92 8,76266-67 8,68442-47 i ', 75340-07 87 38 0.76585-32 8,75837*68 8,68407*12 '.77355-48 88 39 40 0,78600-72 0,80616-13 8,75432-06 8,75048-34 8,68373*39 8,68341*22 '.79370-88 1,81386-28 89 90 4' 0,82631-53 8,74685*14 8,68310*52 1,83401-69 9' 42 0,84646-93 8,74341-23 8,68281*24 1,85417-09 92 43 44 0,86662-34 0,88677-74 8,74015-43 8,73706-68 8,68253-31 8,68226-66 1,87432-49 1,89447-90 93 94 45 0,90693-14 8,73413-95 8,68201-23 1,91463-30 95 46 0,92708-55 8, 73 '36 \33 8,68176*97 1,93478-70 96 47 o,94723-95 8,72872-94 8,68153-83 1,95494-11 97 48 49 0,96739-35 8,72622-99 8,72385-71 8,68131-74 8,68110*67 i!99524*9i 98 99 50 1,00770-16 8,72160*37 8,68090-56 2,01540*32 oo ' 8,67669-36 erp (297) LOGARITHMIC TABLES OF 4 K Pr Ceau Year Log. r*. Log. a". Log. a". Log. r". Year* l 0,02067-20 0,02067-20 8,72810-03 1,05427-07 51 2 3 4 I 7 0,04134-39 0,06201-59 0,08268-79 0,10335-99 0,12403-18 0,14470-38 9,72985-50 9,56389-48 9,44900-52 9,36206-24 9,29276-63 9,23562-38 8,72615-06 8,72429-97 8,72254-20 8,72087-27 8,71928-69 8,71778-03 i.,07494-26 1,09561-46 1,11628-66 1,13695-86 1,15763-05 1,17830-25 52 53 54 8 9 (O 0,16537-58 0,18604-78 0,20671-97 9,18735-42 9,14584-26 9,10964-48 8,7^34-85 8,71498-77 8,71369-41 1,19897-45 1,21964-65 1,24031-84 s ii 0,22739-17 9,07773-07 8,71246-42 1,26099-04 61 12 0,24806-37 8,71129-47 1,28166-24 62 13 0,26873-57 9,02389-47 8,71018-25 1,30233-44 63 14 0,28940-76 9,00094-66 8,70912-46 1,32300-63 64 11 0,31007-96 8,98013-97 8,96118-75 8,70811-83 8,70716-10 ^364^-03 17 0,35142-36 8,94385-53 8,70625-00 I,'38502-22 67 l8 19 0,37209-55 0,39276-75 8,92794-91 8,91330-63 8,70538-33 8,70455-84 1,40569-42 1,42636-62 68 69 20 0,41343-95 8,89978-94 8,70377-33 1,44703-82 70 21 0,43411-15 8,88728-13 8,70302-61 1,46771-01 7i 22 o,45478-34 o,47545'54 8,87568-10 8,86490-12 8,70231-47 8,70163-75 1,48838-21 72 73 2 4 0,49612-74 8,85486-59 8,70099-29 1^5297261 74 25 o,5i679'93 8,84550-83 8,70037-90 1,55039 '8 75 26 0,53747-13 8,83676-96 8,69979-44 1,57107-00 76 3 0,57881-53 8,82859-78 8,82094-66 8,69923-78 8,69870-77 1,59174-20 1,61241-40 29 0,59948-72 8,8i377-44 8,69820-29 1,63308-59 79 30 0,62015-92 8,80704-41 8,69772-21 I ,65375"79 80 31 0,64083-12 8,80072-24 8,69726-41 1,67442-99 81 32 33 0,66150-32 0,68217-51 8,79477-9i 8,78918-68 8,69682-78 8,69641-23 1,69510-19 82 83 34 0,70284-71 8,78392-07 8,69601-64 i> 73644-58 84 8,77895-82 8,69563-93 1,75711-78 85 37 o, 74419- ii 0,76486-30 8,77427-86 8,76986-30 8,69528-00 8,69493-77 1,77778-97 i,79846;i7 86 87 38 39 0,785,53-50 0,80620-70 8,76569-40 8,76i75-59 8,69461-16 8,69430-07 1^83980-57 88 89 40 0,82687-90 8,75803-37 8,69400-47 1,86047-76 90 42 43 0,84755-09 0,86822-29 0,88889-49 8,75451-40 8,75118-42 8,74803-29 8,69372-25 8,69345-36 8,69319-74 1,88114-96 1,90182-16 1,92249-36 9i 92 93 44 1 0,90956-68 0,93023-88 0,95091-08 0,97158-28 0,99225-47 8,74504-91 8,74222-31 8,73954-54 8,73700-75 8,73460-12 8,69295-32 8,69272-05 8,69249-8^ 8,69228-74 1*96383-75 i,9845o-95 2,00518-15 2,02585-34 94 ?8 49 1,01292-67 8,73231-93 8^69189-40 2,04652-54 99 50 1,03359-87 8,73015-45 8,69171-11 2,06719-74 oo 8,68797-46 erp. For explanation see pp. 216-228 (298) COMPOUND INTEREST AND ANNUITIES i ) PerCent. Years Log. r. Log. a". Log. 504*92 8^92261-82 8^75072-08 1,60441-97 1,62767-22 69 70 21 22 23 24 0,488.30-17 0,5 11 "55 -41 0,5348^66 0,55805-00 8,91096-99 8,00021-00 8,80025-13 8,88101-82 S^l?^ 8,74916-81 8,74870-46 1,65092-46 1,67417-71 1,69742-96 1,72068-20 7i 72 73 74 25 0,58131-15 8,87244-38 8,74826-57 1,74393*45 I 0,60456 -40 0,62781 -64 8,86446-99 8,85704-46 8,85012-16 8,74785-02 8,74745-66 8,74708-39 1,76718-69 i,79043-94 1,81369-18 1 29 0,67432-10 8,84365-98 8,74673-09 1,83694-43 79 30 8,83762-25 8,74639-67 1,86019-68 80 31 0,72082-62 ! 8,83197-62 8,74608-00 1,88344-92 ll 3* 0,74407-87 8,82669-14 8,74578-00 1,90670-17 82 33 0,76733-12 8,82174-07 8,74549* 60 1,92995-41 83 34 0,79058-36 8,81709-96 8,74522-68 1,95320-66 84 35 0,81383-61 8,81274-58 8,74497-18 1,97645*91 85 36 083708-85 8,80865-88 8,74473-04 1,99971-15 86 37 0,86034*10 8,80482-02 8,74450-16 2,02296-40 87 38 0,88359*35 8,80121-27 8,74428-49 2,04621-64 88 39 0,90684-59 8,79782-07 8,74407-95 2,06946-89 89 40 0,93009-84 8,79462-99 8,74388-49 2,09272-14 90 41 0,95335-08 8,79162-68 8,74370-06 M 1597*38 9 1 42 43 44 0,97660-33 0,99985-58 1,02310*82 878879-93 8,78613-62 8,78362-69 8j4336-o5 8,74320-36 2,13922-63 2,16247-87 2,18573-12 92 93 94 45 1,04636-07 8,78126-17 2,20898-37 95 47 1,06961-31 1,09286*56 8,77903-16 8,77692-83 8,7429 1*44 8,74278-10 2,23223-61 2,25548-86 96 97 4* 1,11611-81 8,77494-41 8,74265-45 2,27874-10 98 49 ",'3937-05 1,16262-30 8,77307-16 8,77130-41 8,74253-48 8,74242-13 2,'32 524-60 99 100 8,74036-27 [p er> (303) LOGARITHMIC TABLES OF 5 8 Per Cent. Years Log. ,-. Log. tt. Log. a". Log. r". Years I 0,02376-67 0,02376-67 8,77762-42 1,21210-28 5 2 3 4 0,07130-02 0,09506-69 9,73445-76 9,56997-88 9,45654-42 8,77611-49 8,77469-07 8,77334-67 1,23586-95 1,25963-63 1,28340-30 52 53 54 5 0,11883-36 9,37103-04 8,77207-81 1,30716-97 55 6 0,14260-03 8,77088-05 1,33093-64 5" I 0,16636-71 0,19013-38 9,24737-08 9,20045-16 8,76974-98 8,76868-19 1,35470-32 1,37846-99 <$ 9 0,21390-05 9,16026-45 8,76767-32 1,40223-66 59 10 0,23766-72 9>* 2536-53 8,76672-05 1,42600-33 60 ii 12 13 M 0,26143-39 0,28520-07 0,30896-74 9,09472-42 9,06758-06 9,04335-76 9,02160-62 8,76582-04 8,76497-00 8,76416-63 8,76340-69 1,44977-00 1,47353 ;68 1,52107-02 61 62 63 64 0,35650-08 9,00197-10 8,76268-91 1,54483-69 16 0,38026-76 8,98416-55 8,76201-06 1,56860-37 66 \l 0,40403-43 0,42780-10 8,96795-54 8,95314-68 8,76136-92 8,76076-29 I.59237-04 1,61613-71 67 68 19 0,45156-77 8,93957-74 8,76018-97 1,63990-38 69 20 0,47533-44 8,92711-00 8,75964-76 1,66367-05 21 0,49910-12 8,91562-74 8,75913-51 1,68743-73 71 22 0,5*286-79 8,90502-91 8,75865-03 1,71120-40 72 23 24 0,5466^-46 0,57040-13 8,89522-82 8,88614-87 8,75819-18 8,75775-84 i,73497-o7 73 74 ? 0,59416-80 0,61793-48 0,64170-15 8..87772-4I 8,86989-61 8,86261-26 8,75734-84 8,75696-05 8,75659-36 i, 78250-41 1,80627-09 1,83003-76 77 29 0,66546-82 0,68923-49 8,85582-80 8,84950-08 8,75624-66 8,7559* -83 1,85380-43 1,87757-10 78 Z9 30 0,71300-17 8,84359-43 8,7556o-77 1,90133-78 80 31 0,73676-84 8,83807-55 8,7553^38 1,92510-45 81 32 0,76053-51 8,83291-44 8,75503-57 1,94887-12 82 33 0,78430-18 8,82808-40 8,75477-27 1,97263-79 83 34 0,80806-85 8,82356-00 8,75452-38 1,99640-46 84 1 0,83183-53 0,85560-20 0,87936-87 8,81931-97 8,81534-31 8,81161-15 8,75428-84 8,75406-54 2,02017-14 2,04393-81 2,06770-48 & 39 0,90313-54 0,92690-22 8,80810-80 8,80481-69 75346-62 2,09147-15 2,11523-83 88 89 40 0,95066-89 8,80172-38 8,75328-74 2,13900-50 90 42 0,97443-56 0,99820-23 8,79881-56 8,79608-02 8,75311-84 8,75295-82 2,16277-17 2,18653-84 9 1 92 43 44 1,02196-90 i,04573-58 1,06950-25 1,09326-92 8,7935o-62 8,79108-33 8,78880-18 8,78665-27 8,75280-68 8,75266-34 75239-93 2,21030-51 2,23407-19 2,25783-86 2,28160-53 93 94 8 % i, "703-59 1,14080-27 8,78462-79 8,78271-96 8,75227-77 8,75216-27 2*32913-88 <$ 49 1,16456-94 8,78092-06 8,75205-38 2,35290-55 99 So i,i8833-6i 8,77922-42 2,37667-22 100 75012-25 Perp. For explanation see pp. 216-228 (304) COMPOUND INTEREST AND ANNUITIES 5 > 4 Per Cent Years Log. i-. Log. " Log. a". Log. r. Years I 0,02428-04 0,02428-04 8,78551-08 1,23829-92 51 2 0,04856-08 9,73522-09 8,78406-54 1,26257-96 3 0,07284-11 9,57098-71 8,78270-30 1,28685-99 53 4 0,09712-15 8,78141-86 1,31114-03 54 5 0,12140-19 9^3725 1 -46 8,78020-75 1,33542*07 55 6 7 0,14568-23 0,16996-26 9^4931-21 8,77906-53 8,77798-80 i^Wo-n 56 57 8 0,19424-30 9,20261-44 8, 77697 'i8 1,40826-18 58 9 10 0,21852-34 0,24280-38 9,16264*41 9,i2795-72 8,77601-30 8,77510-82 I,432?4-22 1,45682-26 g ii 0,26708-41 9,09752-37 8,77425-45 1,48110-29 61 12 0,29136-45 9,07058-33 8,77344-86 1,50538-33 62 13 0,31564-49 9,04655-88 8,77268-80 1,52966-37 63 14 o,33992-53 0,36420-56 9,02500-15 9,00555-60 8,77196-99 8,77129-19 1,55394-41 1,57822-44 64 ID 0,38848-60 8,98793*^6 8,77065-18 1,60250-48 66 \l 0,41276-64 0,43704-68 8,97190-62 8,95727-42 8,77004-74 8,76947-06 1,62678-52 1,65106-56 67 68 19 20 0,46132-71 0,48560-75 8,94387-69 8,76893-75 8,76842-84 1,67534-59 1,69962-63 69 70 21 22 23 0,50988-70 0,53416-83 0,55844-86 8,92025-8? 8,90981-98 8,90017-44 8,76794-75 8,76749-32 8,76706-41 1,72390-67 1,74818-71 1,77246-74 73 73 2 4 0,58272-90 0,60700-94 0,63128-98 8,89124-64 8,88296-93 8,87?28-47 8,76665-86 8,76627-57 1,79674-78 1,82102-82 1,84530-86 74 29 30 0,65557-02 0*67985-05 0,70413-09 0,72841-13 8,868i4'io 8,86149-22 8,85529-71 8,84951-92 8i76557-i8 8,76524-86 8,76494-34 8,76465-49 1,86958-90 1,89386-93 1,91814-97 1,94243-01 k 31 32 0,75269-17 0,77697-20 8,84412-52 8,83908-53 8,76438-23 8,76412-47 1,96671-05 1,99099-08 Si 83 33 34 $ 0,80125-24 0,82553-28 0,84981-32 0,87409-35 8,83437-28 8,82906-30 8,82583-38 8,82196-48 8,76388-11 8,76365-10 8^76322-79 3,01527-12 2,03955-16 2,06383-20 2,08811-23 83 84 85 8 11 39 40 0,89837-39 0,92265-43 o,94693-47 0,97121-50 8,81833-77 8,81493-54 8,81174-25 8,80874-47 8,76303-36 8,76284-98 8,76267-63 8,76251-21 2,11239-27 3,13667-31 3,16095-3? 2,18523-38 s i 88 89 90 4 42 0,99549-54 ,oi977-58 8,80592-87 8,80328-26 8,76235-70 8,76221-04 2,20951-43 2,23379-46 92 43 ,04405-62 8,80079-50 8,76207-18 2,25807-50 93 44 ,06833-65 8,79845-58 8,76104-08 2,28235-53 94 2 ,09261-69 ,11689-73 8,79625-54 8,79418-47 8,76181-68 8,76160-07 2,30663-57 2,33091-61 $ 1 ,14117-77 ,16545-81 8, 79040-07 8,76158-89 8,76148-42 2,35519-65 ^37947-68 $ 49 So ,18973-84 ,21401-88 8,78867-2? 8,78704-46 8,76138-53 8,76129-17 8,75966-78 2,40375-72 2,42803*76 99 00 (305) LOGARITHMIC TABLES OF i ' 7 > 8 Per Cent. Years Log. r-. Log. a". || Log. a". Log. r". Years I 2 0,02479-34 0,04958-68 0,02479-34 8,79329-68 8,79191-28 1,26446-46 1,28925-80 52 3 0,07438-03 9.57199-39 8, 79060-96 1,31405-14 53 4 0,09917-37 9.45903-94 8,78938-24 1,33884-49 54 1 7 0,12396-71 0,14876-05 9.37399-59 9.30656-36 9,25124-87 8,78822-64 8,78713-74 8,78611-13 1,36363-83 1,38843-17 1,41322-51 it, 57 8 0,19834-74 9,20477-14 8,78514-44 1,43801-86 58 9 0,22314-08 9,16501-70 8,78423-30 1,46281-20 59 10 0,24793-42 9,13054-11 1,48760-54 60 ii 0,27272-77 9,10031-41 8,78256-43 1,51239-88 61 12 0,29752-11 9,07357-53 8,78180-09 1,53719-22 62 13 0,32231-45 9,04974-79 8,78108-10 1,56198*57 63 0,34710-79 9,02838-32 8,78040-22 1,58677-91 64 H 0,37190-13 9,00912-55 8,99168-88 8,77976-21 8,77915-82 1,61157-25 1,63636-59 65 66 17 0^42148-82 8,97583*85 8,77858-88 1,6611^-94 67 l8 0,44628-16 8,96138-11 8,77805-15 1,68595-28 68 19 2O 0,47107-50 0,49586-85 8,94815-41 8,93602-05 8,77754-48 8,77706-67 1,71074-62 69 21 0,52066-19 8,92486-34 8,7766i-55 1,76033-31 7i 22 23 0,54545-53 0,57024-87 8,91458-22 8,90:509-02 8,77618-98 8,77578-81 1,78512-65 1,80991-99 72 73 24 $ 0,59504-22 0,61983-56 0,64462-90 8,89631-13 8,88817-915 8,88063-62 8,77540-91 8,77471-40 1^85950-67 1,88430-02 74 % 2 9 0,66942-24 0,69421-59 0,71900-93 8,87362-99 8,86711-46 8,86104-93 8,77439-53 s! 77381 -08 1,90909-36 1,93388-70 1,95868-04 2? 30 0,74380-27 8,85539-73 8,77354-29 1.98347-39 80 31 0,76859-61 8,85012-57 8,77328-99 2,00826-73 81 32 0,79338*95 8,84520-46 2,03306-07 82 33 34 0,81818-30 0,84297-64 8,84060-73 8,83630-93 8,71282-59 8,77261-31 2,05785-41 2,08264-76 84 0,86776-98 8,83228-85 8,77241-23 2,10744-10 85 36 0,89256-32 8,82852-47 8,77222-27 2,13223-44 86 $ 39 40 0,94215-01 0,96694-35 0,99173-69 8,82499-95 8,82169-59 8,81859-85 8,81569-33 8,77204-36 8,77187-47 8,77i7i-5i 8,77156-43 2,15702-78 2,18182-13 2,20661-47 2,23140-81 87 88 89 90 42 ,01653-04 ,04132-38 8,81296-69 8,81040-74 8,77142-22 8,77128-79 2,25620-15 2,2*099-49 92 43 ,06611-72 8,80800-37 8,77116-11 2,30578-84 93 44 ,09091-06 ,11570-40 ,14049-75 8-80574-57 8,80362-35 8,80162-87 8,77104-12 8,77092-81 8,77082-14 2,33058-18 2i38ci6-86 94 * 49 ,16529-09 ,19008-43 ,21487-77 8!79798-87 8,79632-87 8,77072-06 8,77062-54 2,40496-21 2,42975'55 2,45454-89 99 5 ,23967-12 8,79476-69 8, 77045 -05 2,47934-23 00 8,76900-79 crp. For explanation see pp. 216-228 (306) COMPOUND INTEREST AND ANNUITIES O Per Cent. Years Log. r-. Log. a". Log. a. Log. r-. Yean I 0,02530-59 0,02530-59 8,80098-36 ,29059-91 5- 2 0,05061-17 9,73674-45 8,79965-87 ,31590-50 3 0,07591-76 9,57290-90 8,79841-25 ,34121-09 53 4 0,10122-35 0,12652-93 0,15183-52 9,46028-35 9.37547-41 9,30827-11 8,79723-99 8,79613-68 ,36651-67 ,39182-26 ,41712-85 54 I 9 10 0,17714-11 0,20244-69 0,22775-28 0,25305-87 9,25318-05 9,20692-28 9,16738-30 9,13311-71 8i794i2-i5 8,79320-16 8,79152-02 ,44243-43 ,46774-02 ,49304-61 ,5i835-i9 1 8 ii 12 0,27836-45 0,30367-04 9,10309-50 9,07655-68 8, 70002 -93 ;54j6s;78 61 62 13 0,32897-62 0,35428-21 o,37958-8o 9,05292-52 9,03175-13 9,01268-01 8,78934-82 8,78870-67 8,78810-23 ,'59426-95 '61957-54 ,64488-12 64 10 0,40489-38 8,99542-52 8,78753-29 ,67018-71 66 19 0,43019-97 o,4555o-56 0,48081-14 8,97975-23 8,96546-77 8,95240-91 8,78699-65 8,78649-09 8,78601-46 ,69549-30 ,72079-88 ,74610-47 8 69 2O 0,50611-73 8,94043-96 8,78556-56 ,77141-06 70 21 0,53142-32 8,92944-22 8,78514-26 ,79671-64 7' 22 23 0,55672-90 0,58203-49 8,91931-64 8,90997-56 8,78474-38 8,78436-80 ,82202-23 ,84732-82 73 73 24 0,60734-08 8,90134-39 8,78401-37 ,87263-40 74 0,63264-66 s! 88595 -09 8,78367-97 8,78336-49 .89793-99 ,92324-58 \l 0^68325 -84 0,70856-42 8,87907-97 8,87269-55 8,78306-81 8,78278-83 ,94855-16 ,97385-75 78 29 30 0^7591 7 -60 8,86675-75 8,86122-91 8,78252-45 8,78227-58 ,99916-34 2,02446-92 i 31 0,78448-18 8,85607-74 8,78204-13 2,04977-51 81 32 33 0,80978-77 0,83509-36 8,8^127-26 8,84678-81 8,78182-01 8,78161-17 2,07508-10 2,10038-68 82 83 34 0,86039-94 8,84250-95 8,78141-51 2,12569-27 84 9 0,88570-53 0,91101-12 8,83868-45 8,83502-33 8,78122-97 8,78105-48 2,15099-86 2,17630-44 8 % 39 0,93631-70 0,96162-29 0,98692-87 8,83159-74 8,82839-00 8,82538-58 8,78088-99 8,78073-45 8,78058-78 2,20161-03 2,22691-61 2,25222-20 U SQ 40 1,01223-46 8,82257-04 8,78044-95 2,27752-79 90 41 1,03754-05 8,81993-11 8,78031-91 2,30283-37 oi 42 1,06284-63 8,81745-57 8,78019-62 2,32813-96 92 43 44 45 1,08815-22 1,11345-81 1,13876-39 8,81513-34 8,81295-38 8.81090-77 8,78008-01 8,77997-o8 8,77986-75 2.35344-55 2,37875-13 2,40405-72 93 94 95 46 1,16406-98 8,80898-60 8,77977-02 2,42936-31 90 i,i8937-57 1,21468-15 8,80718-09 8,80548-49 8,77967-84 8,77959'i8 2,45466-89 2,47997-48 9 l 98 49 i,23998-74 8,80389-09 8,7795 I 'i 2,50528-07 99 50 1,26529-33 8,80239-25 8,77943*31 2,53058-65 IOO Perpu (307) LOGARITHMIC TABLES OF 6 \ Per Cent. Years Log. f. Log. . Log. a". Log. r. Years i 0,02632-89 0,02632-89 8,81606-66 ,34277'59 51 2 3 4 3SR! 0,10531-58 9,73826-39 9,57500-48 9,46276-53 8,81485-28 8,81371-35 8,81264-40 ,36910-48 ,39543-38 ,42176-27 52 53 54 i 0,13164-47 o,i5797-36 0,18430-26 9,37842-19 9,31167-48 9,25703-02 8,81163-97 8,81069-66 8,80981-10 ,44809-16 ,47442-06 ,50074-95 1 8 0,21063-15 9,21120-86 8,80897-90 ,52707-84 58 9 10 0,23696-04 0,26328-94 9,17209-49 9,13824-52 8,80819-75 8,80746-32 ,55340-74 ,57973-63 8 ii 0,28961-83 9,10862-97 8,80677-32 ,60606-53 61 12 0,31594-73 9,08248-81 8,80612-48 ,63239-42 62 3 0,34227-62 9,05924-36 8,80551-55 ,65872-31 63 0,36860-51 9,03844-73 8,80494-27 ,68505-21 64 i5 0,39493-41 9,01974-43 8,80440-43 ,71138-10 65 16 0,42126-30 9,00284-80 8,80389-82 ,73771-00 66 i7 0,44759-20 8,98752-47 8,80342-25 ,76403-89 67 18 19 20 0,47392-09 0,50024-98 0,52657-88 8^96085 -3 1 8,94920-58 8,80297-51 8,80255-45 8,80215-91 ,79036-78 ,81669-68 ,84302-57 69 70 21 0,55290-77 8,93852-19 8,80178-72 ,86935-46 7 1 22 23 24 a 0^57923-67 0,60556-56 0,63189-45 0,65822-35 0,68455-24 8,92870-11 8,91965-64 8,91131-26 8,90360-33 8,89647-05 8,80143-7$ 8,80110-86 8,80079-93 8,80050-84 8,80023-47 ,89568-36 ,92201-25 ,94834-15 1,97467-04 2,00099-93 72 73 74 ii 27 0,71088-13 8,88986-21; 8,79997-74 2,02732-83 77 28 29 0,7372 1 ;o3 8,88373-38 8,87804-36 8,79973-53 8,79950-76 2,05365-72 2,07998-62 79 30 0^78986-82 8,87275-53 8,79929-33 2,10631-51 80 32 0,81619-71 0,842152-60 8,86783-63 8,86325-70 8,79909-18 8,79890-22 2,13264-40 2,15897-30 81 82 33 34 0,86885-50 0,89518-39 0,92151-29 0,94784-18 0,97417-07 8,85899-07 8,85501-33 8,85130-29 8,84783-92 8,84460-46 8,79872-38 8,79855-61 8,79839-82 8,79824-97 8,79810-09 2,18530-19 2,21163-09 2^26428-87 2,29061-77 83 86 87 38 1,00049-97 8,84158-20 8,79797-84 2,31694-66 88 39 40 1,02682-86 1,05315-75 8,83875-63 8,83611-35 8,79785-47 8,79773-83 2,34327-55 2,36960-45 89 90 41 1,07948-65 8,83364-09 8,79762-88 2,39593-34 9 1 42 1,10581-54 8,83132-63 8,79752-57 2,42226-24 92 43 1,13214-44 8,82915-93 8,79742-87 2,44859-13 93 44 1,15847-33 8,82712-95 8,79733-75 2,47492-02 94 ? 1,18480-22 1,21113-12 8,82522-77 8,82344-54 8,79725-16 8,79717-08 2,50124-02 * 49 SO 1,23746-01 1,26378-91 1,29011-80 1,3.1644-69 8,82177-45 8,82020-77 8,8i873-'84 8,81736-00 8,79709-48 8,79702-32 8,79695-59 8,79689-25 849588-00 a!sg39o-7' 2,58023-60 2,60656-49 2,63289-39 99 IOO Perp. For explanation see pp. 216-228 (308) COMPOUND INTEREST AND ANNUITIES 6 \ Per Cent. /ears Log. r". Log. a". Log. a". Log. f. Years 1 0,02734-96 0,02734-96 8,83077-22 ,39483-00 51 2 0,05469-02 9,73977-92 8,82966*09 ,42217*96 5.2 3 0,08204-88 9,57700-41 8,82862-00 ,44952-92 53 4 8 0,10939-84 0,13674-80 0,16409-76 9,46523-82 9,38135-80 9,31506-37 8,82764-50 8,82673-15 8,82587-53 ^50422-84 ,53157-80 54 g I 9 10 0,19144-73 0,21879-69 0,24614-65 0,27349-61 9,26086-14 9,21547-18 9,17677-99 9,14334-18 8,82507-31 8,82432-11 8,82361-62 8,82295-53 ^64097 -65 il g ii 0,30084-57 9,11412-77 8,82233-58 ,66832-61 61 12 0,32819-53 9,08837-77 8,82175-48 ,69567-57 62 13 14 0,35554-49 0,38289-45 9,06551-46 9,04509-01 8,82121-00 8,82069-90 ,72302-53 | 15 0,41024-41 9,02674-88 8,82021-99 '77772-45 65 1 6 0,43759-37 9,01020-48 8,81977-04 ,80507-41 66 \l 0,46494-33 0,49229-29 8,99522-41 8,98161-30 8,81934-88 8,81895-33 ,83242-37 ,85977-33 8 9 0,51964-25 8,96920-96 8,81858-22 ,88712-29 69 20 0,54699-22 8,95787-72 8,81823-41 ,9 I 447 2 5 70 21 0,57434-18 8,94749-91 8,81790-75 ,94182-22 71 22 0,60169-14 8,93797-5o 8,81760-10 ,96917-18 72 23 24 11 11 29 0,62904-10 0,65639-06 0,68374-02 0,71108-98 0,73843-94 0,76578-90 0,79313-86 0,82048-82 8,92921-85 8,92115-41 8,91371-58 8,90684-56 8,00049-21 8,09460-99 8,88915-82 8,88410-09 8^81 704-36 8,81679-04 8,81655 27 8,81632-98 8,81612-05 8,81592-41 ,99652-14 2,02387-10 2,05122-06 2,07857-02 2,10591-98 2,13326-94 2,16061-00 2,18796-86 73 74 F S 31 32 0,84783-78 0,87518-74 8,87940-52 8,87504-19 8,81556-67 8,81540-43 2,21531-82 2,24266-78 81 82 33 34 0,90253-71 0,92988-67 8,87098-44 8,86720-87 8,81525-19 8,81510-88 2,27001-74 2,29736-71 i 35 36 0,95723-63 0,98458-59 8,86369-31 8,86041-78 8,81497-44 8,81484-84 2,32471-67 2,35206-63 u 11 i,oii93-55 8,85736-47 8,85451-74 8,81473-01 8,81461-89 2,37941-59 2,40676-55 8 Z M 39 40 i!o666v47 1,09398-43 8,85186-07 8,84938-09 8,81451-47 8,81441-67 2,43411-51 2,46146-47 8 9 90 41 1,12133-39 8,84706-52 8,81432-48 2,48881-43 9 42 1,14868-35 8,84490-21 8,81423-86 3,51616-39 92 43 44 1,17603-31 1,20338-27 1,23073-24 8,84288-08 8,84099-13 8, 83922 '46 8,81415-75 8,81408-16 8,81401-02 2is7o86-3i 2,59821-27 93 94 i 1,2(5808-20 1,28543-16 I.31278-L2 8,83757-23 8,83602-65 8,83458-00 8,81394-32 8,81388-02 8,81382-12 2,62556-23 2,65291-20 2,68026-16 97 98 49 5 1,340I3-08 1,36748-04 8,83322-62 8,83195-89 8,81376-57 8,81371-36 2,70761-12 99 IOO 8.81291-34 Peru (309) LOGARITHMIC TABLES OF 6 s 4 Per Cent. Years Log. r-. Log. a". Log. a". Log. r*. Years ! 0,02836-79 0,02836-79 8,84511-27 1,44676-21 51 2 0,05673-58 9,74129-03 8,84409-58 1,47513-00 52 3 0,08510-37 9,57899-71 8,84314-55 1,50349-78 53 4 5 0,11347-15 0,14183-94 9,46770-23 9,38428-23 8,84225-70 8,84142-64 1,53186-57 1,56023-36 54 55 6 0,17020-73 9,31843-76 8,84064-98 1,58860-15 56 9 10 , '9857-52 0,22694-31 0,2 3I -10 0,28367-88 9,26467-41 9,21971-27 9,18143-83 9,14840-71 8,'83Q24-43 8,83860-89 8,83801-46 1,61696-94 i,64533-73 1,67370-51 1,70207-30 11 g n 0,31204-67 9,11958-96 8,83745-86 1,73044-09 61 12 0,34041-46 9,09422-^8 8,83693-84 i,7S88o-88 62 3 0,36878-25 9,07173-86 8,83645-16 1,78717-67 63 0,39715-04 9,05167-97 8,83599-62 1,81554-46 IS 0,4255^83 9,03369-43 8,83557-00 1,84391-24 65 16 0,45388-61 9,01749-60 8,83517-10 1,87228-03 66 X 7 0,48225-40 0,00285-12 8,83479-77 1,90064-82 67 18 0,51062-10 8,98956-65 8,83444-82 1,92901-61 68 J 9 0,53898-98 8,97747-98 8,83412-11 1,915738-40 69 20 0,56735-77 8,96645-47 8,83381-49 I 9^575' I 9 70 21 22 23 24 0,62409-34 0,65246-13 0,68082-92 94713-96 8,93866-31 8,93086-99 8,83352-83 8,83325-99 8,83300-87 8,83277-36 2,01411-97 2,04248-76 2,07085-55 2,09922-34 72 73 74 0,7091971 8,92369-42 8,91707-81 8,83255-33 8,83234-70 2,12759-13 9 11 oi76S93-29 0,79430-07 8,91097-05 8,90532-59 8,83215-40 8,83107-32 2,18432-70 2,21269-49 3 29 30 0,82266-86 0,85103-65 8,90010-40 8,89526-87 8,83180-40 8,83164-55 2,24106-28 2,26943-07 31 0,87940-44 8,80078-74 8,83149-70 2,29779-86 81 32 0,90777-23 8,88663-09 8,83135-80 2,32616-65 82 33 0,93614-02 8,88277-31 8,83122-78 2,35453-43 83 34 i* 0,96450-80 0,99287-59 ,02124-38 8,87919-00 8,87586-01 8,87276-38 8,83110-58 8,83099-17 8,83088-48 2,38290-22 2,41127-01 2,43963-80 84 ii 37 ,04961-17 8,86988-30 8,83078-47 2,46800-59 87 38 39 ,07797-96 ,10634-75 8,86720-17 8,86470-49 8,83069-09 8,83060-30 2,49637-38 2,52474-16 89 40 ,1347! '53 8,86237-90 8,83052-08 2,55310-95 90 41 ,16308-32 8,86021-12 8,83044-37 2,58147-74 91 42 ,I9I45-II 8,85819-04 8,83037-15 2,60984-53 92 43 ,21981-90 8,85630-58 8,83030-39 2,63021-32 93 44 ,24818-69 8,85454-78 8,83024-06 2,66658-11 94 ,27655-48 ,30492-27 8,85290-74 8,85137-63 8,83018-13 8,83012-57 2,69494-90 2,72331-68 955 2 8-59 2,61985-49 70 21 0,78595-65 9,03187-94 8,955 '9'96 2,65728*14 7' 22 23 0,82338-30 0,86080-95 9,02491*64 9,01862-51 8,95512-06 8,95504-80 2,69470-79 2,73213-43 72 73 24 0,89823-60 9,01293-22 8,95498-14 2,76956-08 74 25 0,93566-24 9,00777*44 8,95492-04 2,80698-73 7 2 26 0,97308-89 9,00309-57 8,95486-44 2,84441*38 76 27 ,01051-54 8,99884*72 8,95481-29 2,88184-03 n 28 2 9 30 ,04794-19 ,08536-84 ,12279-49 3,'99i47'30 8,98827-51 8,95476-59 8,95472-26 8,95468-29 2,91926-68 2,95669-33 2,99411*98 78 79 80 3* ,16022*14 8,98536-18 8,95464-65 3,03154-63 81 32 ,19764-79 8,98270-62 8,95461-32 3,06897-28 82 33 ,23507-44 8,98028-40 8,95458-26 3,10639-93 83 34 ,27250-09 8,97807-36 8,95455-45 3,14382-58 84 ,30993-74 ,34735*39 8,97605-57 8,97421*25 8,95452-87 8,95450-5 3,18125-23 3,21867-88 11 38 ,38478-04 ,42220-69 8,97252-83 8,97098-90 8,95448-34 8,95446-35 3,25610-53 3,29353-18 88 39 40 U9705 '99 8,96958-15 8,96829*43 8,95444-52 8,95442*85 3.33095-83 3,36838-48 89 90 4 1 ,53448-64 8,96711-67 8,95441*31 3,40581-13 9* 42 ,57191-29 8,96603-91 8,95439-9i 3,44323-78 92 43 ,60933-94 8,96505-28 8,95438-61 3,48066-43 93 44 ,64676-59 8,96415*00 8,95437*42 3,51809-08 94 ,68419-24 ,72161-89 8,96332*33 8,96256-63 8,95436-34 8,95435*34 3,5555*73 47 ,75904'54 8,96187-29 8,95434-43 3^63037-03 97 48 ,79647*19 8,96123-78 8,95433-58 3,66779-68 98 49 ,83389*84 8,96065-59 8,95432-81 3,70522*33 99 50 ,'87132-49 8,96012-28 8,9=;432-ii 3,74264-98 oo 8,95424*25 Perp. For explanation see pp. 216-228 (3H) COMPOUND INTEREST AND ANNUITIES 10 PerCent. Yea*. Log. T-. Log a". Log. a". Log. T-. Yeara I 2 3 0,04139-27 0,08278-54 0,12417-81 0,04139-27 9,76056-60 9,60435-01 9,00337-03 9,00306-83 9,00278-85 2,11102-69 2,15241-96 2,19381-23 5* 53 4 0,16557-07 9,49895-92 9,00253-42 2,23520-50 54 0,20696 34 0,24835-61 9,42127-07 9,36098-59 9,00230-32 9,00209-33 2,27659-77 2,31790-04 3 7 0,28974-88 9,31261-21 9,00190-26 2,35938-31 5 l 8 0,33114-15 9,27287-16 9,00172-93 2,40077-57 58 9 10 0,37253-42 0,41392-69 9,23965-11 9,21150-87 9,00157-18 9,00142-87 2,44216-84 2,48356-11 e u 0,45531-95 9,18741-68 9,00129-86 2,52495-38 61 12 13 0,49671-22 0,53810-49 9,16661-75 9,14853-64 9,00118-04 9,00107-30 2,56634-65 2,60773-92 62 0,57949-76 9,13272-77 9,00097-53 2,64913-19 64 15 0,62089-03 9,11883-91 2,69052-45 65 ID 0,66228-30 9,10658-73 9,00080-59 2,73191-72 66 17 0,70367-57 9,00574-15 9,00073-26 2,77330-99 67 18 1 9 20 0,74506-83 0,78646-10 0,82785-37 9,08611-14 9^06988-86 9,00066-59 9,00060-53 9,00055-03 2,81470-26 2,85600-53 2,89748-80 68 69 70 21 0,86924-64 9,06304-95 9,00050-03 2,93888-06 71 22 23 0,91063-91 0,95203-18 9,05692-41 9,05142-97 9,00045-47 9,00041-34 2,98027-33 3,02166-60 72 73 24 0,99342-44 9,04649-44 9,00037-57 3,06305-87 74 2 1,03481-71 1,07620-98 1,11760-25 1,15899-52 9,04205-57 9,03805-97 9,03445-86 9,03121-05 9,00034-16 9,00031-05 9,00028-23 9,00025-66 3,10445-14 3,14584-41 3,18723-68 3,22862-94 '4 11 29 1,20038-79 9,02827-87 9,00023-33 3,27002-21 I 9 30 1,24178-06 9,02563-04 9,00021-21 3,31141-48 80 31 1,28317-32 9,02323-69 9,00019-28 3,35280-75 81 32 1,32456-59 9,02107-23 9,00017-53 3,39420-02 82 33 i, 36595 '86 9,01911-38 9,00015-93 3,43559-29 83 34 M0735-I3 9,01734-10 9,00014-48 3,47698 -56 I 4 $ 1,44874-40 1,49013-67 9,' 573-56 9,01428-13 9,00013-17 9,00011-97 3,5>837-82 3,55977-09 8 5 86 a 39 i,53i52-94 1,57292-20 1,61431-47 9,01296-35 9,01176-88 9.01068-57 9,00010-88 9,00009-89 9,00009-00 3,60116-36 3,64255-63 3,68394-90 87 88 89 40 i,65570-74 9,00970-32 9,00008-17 3>72534- 1 7 9 4i 1,69710-01 9,00881-21 9,00007-43 3,76673-43 9' 42 1,73840-28 9,00800-36 9,00006-76 3,80812-70 92 43 44 1,77988-55 1,82127-81 9,00726-99 9,00660-40 9,00006-14 9,00005-58 3,84951-97 3,89091-24 93 94 1,86267-08 1,90406-35 9,00599-94 9,00545-06 9,00005-08 9,00004-61 3,93230-51 3,97369-78 9 47 1,94545-62 9,00495-22 9,00004-19 4,01509-05 n 48 1,98684-89 9,00440-07 9,00003-81 4,05648-31 98 49 So 2,02824-16 2,06963-43 9,00408-87 9><37i-54 9,00003-47 9,00003-15 4,09787-58 4,13926-85 99 100 ^,00000-00 Perp. (315) LOGARITHMIC TABLES -L^ Per Cent. Years| Log. T-. Log. a". Log. a". Log. r. Years I 2 0,04921-80 0,09843-60 0,049:11-80 9,772JiO-O2 9,08052-50 9,08038-09 2,51011-92 2,55933-72 51 5 2 3 0,14765-41 9,61945-76 9,08025-22 2,60855-52 53 4 I 0,19687-21 0,24609-01 0,29530-81 0,34452-62 9*4431 2-1 7 9,38600-95 9,34067-76 9,30384-99 9,08013-73 9,08003-48 9,07994-32 9,07986-15 9,07978-86 2,65777'32 2,70699-12 2,75620-93 2,80542-73 2,85464-53 54 9 10 0,44296-22 0,49218-02 9*07966-53 2,90386-33 2,95308-14 59 00 ii 12 0,54139*82 0,59061-63 9,22638-18 9,20800-26 9,07961-35 9,07956-71 3,00229-94 3,05151-74 61 62 13 0,63983-43 0,68905-23 9,19222-50 9,17860-65 9,07952-59 9,07948-88 3,10073-54 63 64 i! 0,73827-03 0,78748-84 9,16679-78 9,15651-89 9^07942-64 3!i99Tri5 3,24838-95 :* 0,83670-64 0,88592-44 9,14754-25 9,13968-18 9,07940-02 3,29760-75 3,34682-55 67 68 '9 0,93514-24 9,13278-15 9'o7935-58 69 20 0,98436-05 9,12671-17 3^44526- 16 70 21 22 i'o279-65 9,12136-31 9,11664-26 9,07932-04 3,49447-96 3*54369-76 71 23 24 1,13201-45 1,^8123-25 9,11247-08 9,10877-96 9,0792Q-.2l 9,07928-03 3,5929! '57 3,64213-37 73 74 3 1,23045-06 1,27066-86 9,10551-01 9,10261-16 9,07926-97 9,07926-01 3,69135-17 3,74056-97 9 % 1,32888-66 1,37810-46 9,10003-99 9,07925-17 9,07924-42 3,78978-77 3,83900-58 2 9 1,42732-27 9^09572-78 9,07923-75 3,88822-38 79 30 M7654"07 9,09392-45 9,07923-14 3,93744*18 80 31 1*52575-87 9,09232-07 9,07922-60 3,98665-98 81 32 1*57497-67 9,09089-38 9,07922-12 4,0358779 82 33 34 1,62419-47 1,67341-28 1,72263-08 9,08962-36 9,08849-27 9,08748-55 9,07921-70 9,07921-31 9,07920-97 4*08509-59 4,i343i-39 4,18353-19 8| 1 39 40 1,77184-88 1,82106-68 1,87028-49 1,91950-29 1,96872-09 9,08658-81 9,08578-84 9*08507-57 9,08444-03 9,08387-38 9,07920-67 9,07920-39 9,07920-15 9,07919-93 9,07919-74 4*23274-99 4,28196-80 4,33118-60 4,38040-40 4,42962-20 86 87 88 89 90 41 2,01793-89 9,08336-86 9,79 I 9-57 4,47884-01 9 1 42 2,06715-70 9,08291-80 9,07919-41 4,52805-81 92 43 2,11637-50 9,08251-61 9,07919-27 4,57727-61 93 44 2,16559-30 2,21481-10 9,08215-76 9,08183-77 9,07919-15 9,07919-04 4,62649-41 4,67571-22 94 46 48 2,26402-90 2,31324-71 2,36246-51 9,08155-23 9,08129-76 9,08107-04 9,07918-94 9,07918-86 9,07918-78 4,72493-02 4,77414-82 4,82336-62 i 49 50 2,41168-31 2,46090-11 9,08086-76 9,08068-66 9,07918-71 9,07918-65 4,87258-42 4,92180-23 99 100 9,07918-12 Perp. For explanation see pp. 216-228 TABLE II. SHOWING A. For every rate contained in the preceding table the logarithms, to 10 and 7 decimals, of /, t being the interest of i per annum or the rate ; of r, r being 1 increased by interest for one year ; and the logarithm of log 2 r. B. For every rate between o and 10 per cent., proceeding by loths, the logarithms of t and r. C. For every fractionary rate between o and TO per cent., pro- ceeding by i2ths, the logarithms of t and r. The rate of interest which M. Thoman calls t is in modern notation denoted by /, and the amount of i in i period is now expressed by i + / instead of by r. LOGARITHMIC TABLES OF Table II This table shews the Logarithms of (*), (r), and (Log 2 .r), t being the rate of interest per cent, and r 1 increased bj its interest for one year. Kate per Cent Log.*. Log. r. Log 8 , r. Kate Cent Va 7,69897-00043 0,00216-60618 7,33567-o8 V. i 8,00000-00000 0,00432-13738 7,63562-18 it 8,17609-12591 8,21085-33653 8,24303-80487 8,27300-12721 0,00646-60422 0,00700-05586 0,00806-70217 7,81063-85 7,84513-27 7,87704-97 7,9o674-55 1 $ 2 8,30102-09957 0,00860-01718 7,9345o-7i 2 2 V. 2/ 4 8,32735-89344 8,35218-25181 8,37566-36140 0,00913-20695 0,00966-33167 0,01019-39148 7,96056-92 7,98512-62 8,00834-10 2 fa 2 Vl 2% 8,39794-ooo87 8,41912-93077 8,43933*26938 0,01072-38654 0,01125-31701 0,01178-18305 8,03035-14 8,05127-49 8,07121-28 ll 2 % 2 '/ 8,45863-78490 0,01230-98482 8,09025-27 4 ! 3% 8,47712-12547 8,49485-00217 8,51188-33610 8,52827-37772 0,01283-72247 0,01336-39616 0,01389-00603 0,01441-55226 8,10847-11 8,12593-52 8,14270-41 8,15883-04 it 1 8,54406-80444 8,55930-80109 8,57403-12677 0,01494-03498 0,01546-45436 0,01598-81054 8,17436-08 8,18933-71 8,20379-70 ii 3 V. 8,58827-17068 0,01651-10368 8,21777-43 4 8,60205-99913 0,01703-33393 8,23129-98 4 4 V. 4J 8,61542-39529 8,62838-89301 8,64097-80574 0,01755-50144 0,01807-60636 0,01859-64885 8,24440-12 8,25710-39 8,26943-10 il Jy! 8,65321-25138 0,01911-62904 8,28140-36 4 Va ii 8,66511*17371 8,67669-36096 8,68797-46200 0,01963-54710 0,02015-40316 0,02067-19738 8,29304-13 8,30436-19 8,31538-19 4 % 5 8,69897-00043 0,02118-92991 8,32611-66 5 5V. 8,70969-38697 0,02170-60088 8,33658-00 5V. ll 8,72015-93034 8,73037-84686 0,02222-21045 0,02273-75876 8,34678-52 8,35674-44 5 l /4 5% 5 y, 8,74036-26895 0,02325-24596 8,36646-89 5 V. ii 8,75012-25268 8,75966-78447 8,76900-78709 0,02376-67220 0,02428-03760 0,02479-34233 8,37596-93 8,38525-54 8,39433-65 5 % -6 8,77815-12504 8,79588-00173 8,81291-33566 8,82930-37728 0,02530-58653 0,02632-89387 0,02734-96078 0,02836-78837 8,40322-11 8,42043-34 8,43695-11 8,45282-69 6 6$ 7 8,84509-80400 0,02938-37777 8,46810-76 7 7 V. 8,87506-12634 0,03140-84643 8,49704-67 7V. 8 8,90308-99870 0,03342-37555 8,52405-51 8 9 8,95424-25094 0,03742-64979 8,57317-92 9 10 9,00000-00000 0,04139-26852 8,61692-36 10 ii 9,07918-12460 0,04921-80227 12 For explanation see pp. 227, 228 COMPOUND INTEREST AND ANNUITIES Table II This table shews the Logarithms of t and r, t being the rate of interest per cent, and r being 1 increased by its interest for one year. Bate Bat* per Cent. Log. r. Log. t. Log. t. Log. r. J.O 0,00259-79807 8,74818-80 0,02366-39182 r 91 i 0,00302-94706 0,00346-05321 7i84509'8b 7,90309-00 8,75587-49 8,76342-80 0,02407-49873 0,02448-56677 5 2* 5% V.O 0,00389-11662 7,95424-25 8,77085-20 0,02489-59601 5 Vio I 0,00432-13738 8,00000-00 0,02530-58653 6 ' Vie 1 V.o 0,00475-11556 0,00518-05125 8,04139-27 8,07918-12 8,78532-98 8,79239-i7 0,02571-53839 0,02612-45167 rt i V 0,00560-94454 0,00603-79550 8,11394-34 8,14612-80 8,79934-05 8,80618-00 0,02653-32645 0,02694-16280 A I /" 0,00646-60422 8,17609-13 8,81291-34 0,02734-96078 1 / n 0,00689-37079 8,20412-00 8,81954-39 0,02775-72047 6 "/io i V.o 0,00732-09529 8,23044-89 8,82607-48 0,02816*44194 6 '/ie ' /,. i Vio 0,00774-77780 0,00817-41840 8,25527-25 8,27875-36 8,832^0-89 8,83884-91 0,02857-12527 0,02897-77052 Sfc 2 0,00860-01718 8,30103-00 8,84509-80 0,02938-37777 2 Vie 0,00902-57421 8,32221-93 8,85125-83 0,02978-94708 7 Vio 1 $j 0,00945-08958 0,00987-56337 0,01029-99566 8,34242-27 8,36172-78 8,38021-12 8,85733-25 8,86332-29 8,86923-17 0,03019-47854 0,03100-42814 7 'A. 7 A. 7 4 /,. 2 Vio 0,01072-38654 8,39794-00 8,87506-13 0,03140-84643 7 */! 2 Ae 0,01114-73608 8,41497-33 8,88081-36 0,03181-22713 7 / 2 Vio 0,01157-04436 8,43136-38 8,88649-07 0,03221-57033 7 7 A 2 /ie 0,01199-31147 8,44715-80 8,89209-46 0,03261-87609 7 'A. 2Ao 0,01241-53748 8,46239-80 8,89762-71 0,03302-14447 7 V.o 3 0,01283-72247 8,47712-13 8,90309-00 8 3 Vie 0,01325-86653 8,49136-17 8,90848-50 0,03382-56940 f Vio 3 Vio 0,01367-96973 8,5005-00 8,91381-39 0,03422-72608 8 *A 3 'A. 3 4 Ao 0,01410-03215 0,01452-05388 8,51851-39 8,53147-89 8,91907-81 8,92427-93 0,03462-84566 0,03502-92822 1> 3 7io 0,01494-03498 8,54406-80 8,92941 -89 0,03542-97382 8 % 2 / 3 7 0,01535-97554 0,01577-87564 8,55630-25 8,56820-1,7 8,93449-85 8,9395i-93 0,03582-98253 0,03622-95441 IP 3 V.'o 3 'Ao 0,01619-73535 0,01661-55470 8,59106.46 8,94448-27 8,94939-00 0,03662-88954 0,03702-78798 It 4 0,01703-33393 8,60206-00 8,95424-25 0,03742-64979 9 4 Vie 4 */! 0,01745-07295 0,01786-77190 8,61278-3,9 8,62324-93 8,95904-14 8,96378-78 0,03782-47506 0,03822-26384 9V,o 9 Vie 4 > 0,01828-43084 8,6334685 8,96848-29 0,03862-01619 9V.o 0,01870-04987 8,64345-27 8,97312-79 0,03901-73220 9 4 Ao i*/" 4 /io 0,01911-62904 0,01953-16845 8,65321-25 8,66275-78 8,97772-36 8,98227-12 0,03941-41192 0,03981-05541 9 > 4%e 0,01994-66817 8,67209- 79 8,98677-17 0,04020-60276 9 Ao 0,02036-12826 8,68124-12 8,99122-61 0,04060-23401 9 Vie 4*fc 0,02077-54882 8,69019-61 8,99563-52 0,04099-76924 9 V.o 5 0,02115-92991 8, 6980 , -oo 9,00000-00 0,04139-26852 10 (319) LOGARITHMIC TABLES Table II This table shews the Logarithms of t and r, t being the rate of interest per cent, and r being 1 increased by its interest for one year. Kate Log. r. Log. *. Log. t. Log. r. Bate per Cent r i *L ,, '?' if 3 i 3 Via 4 2r j), 4 I/u 4 0,00036-17614 0,00072-32216 0,00144-52409 0,00180-58009 0,00252-60240 0,00288-56882 0,00360-41243 0,00396-28971 0,00467-95548 0,00503-74407 0,00575-23289 0,00610-93322 0,0071 0,00788-99599 0,00824-52110 0,00895-48427 0,00930-92241 0,01001-71208 0,01037-06368 0,01107-68069 0,01142-94610 0,01213-39136 0,01248-57115 0,01353-93980 0,01424-04391 0,01459-05355 0,01528-98826 0,01563-91343 0,01633-67963 0,01668-52074 0,01738-11923 0,01772-87670 0,01842-30828 0,01876-98249 0,01946-24798 0,01980-83934 0,02049-93951 6,92081-88 7,22184-87 7,52287-87 7,61978-88 7,76591-68 7,82390-87 7,92081-88 7,96221-14 8,03476-21 8,06694-68 8,12493-87 8,15126-77 8,19957-24 8,22184-87 8,26324-14 8,28254-66 8,31875-88 8,33579'2i 8^83^-68 8,41218-04 8,42596-87 8,45229-77 8,48902-05 8,50060-24 8,52287-87 8,53360-26 8,55428-72 8,56427-14 8,59291-66 8,61101-48 8,61978-88 8,63682-21 8,64509-46 8,66118-14 8,66900-68 8,70614-86 8,71321-04 8,72699-87 8,73373-21 8,74689-36 8,75332-77 8,76591-68 8,77207-71 8,78414-16 8,79005-05 8,80163-23 8,80730-95 8,81844-58 8,82390-87 8,83463-26 8,83989-68 8,85023-77 8,85531-72 8,86530-14 8,87020-88 8,87986-01 8,88460-66 8,89394-66 8,89854-24 8,90759-05 8,91204-48 8,92081-88 8,92514-01 8,93365-60 8,93785-21 8,94612-46 8,95020-25 8,95824-53 8,96221-14 8,97003-68 8!98i5i-66 8,98527-67 8,99270-08 8,99636-57 0,02153-38405 0,02187-81089 0,02256-58279 0,02290-92705 0,02359-53688 0,02393-80075 0,02462-24749 0,02496-43045 0,02564-71576 0,02598-81820 0,02666-94283 0,02700-96512 0,02768-92984 0,02802-87236 0,02870-67791 0,02904-54103 0,02972-18816 0,03005-97225 0.03073-46170 0,03107-16713 0,03174-49962 0,03208-12676 0,03275-30303 0,03308-85224 0,03375-87300 0,03409-34464 0,03476-21063 0,03509-60505 0,03576-31697 0,03609-63453 0,03676-19309 0,03709-43415 0,03775-84005 0103875-25890 0,03908-34800 0,03974-45068 0,04007-46432 0,04073-41642 0,04106-35495 For explanation see pp. 227, 228 (320) IMPORTANT BOOKS ON VALUATION. Just Published. Demy 8vo, cloth, 334 pages. 7s. 6d. net. Valuation of Real Property. A Guide to the Principles of Valuation of Land and Buildings, &c., for Various Purposes, including the Taxation of Land Values. By CLARENCE A. WEBB, P.A.S.I., Valuer and Rating Surveyor, Author of ' The Law and Practice of Rating and Assessment,' Joint Author of ' Rates and Taxes.' Third Edition, Revised and Enlarged, By ALFRED RUNNINGS, F.S.I., Rating Surveyor to the Hackney Borough Council, &c. ' The book will prove a capital vade-mecum to all who are called upon to value land or buildings, as well as to owners or stewards of real estate It is a valuable contribution to a difficult and intricate subject.' Property Market Review. Demy 8vo, cloth, 168 pages. 7s. 6d. net. The Valuation of Mineral Property Ru!es and By T. A. 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