UC-NRLF ^B 27fl 2bM 'm>:ty:'.[{ GIFT OF "^ JL<^^ ^^X^^^-^.^^^r-^'--^-^^^-^ Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/businessarithmetOObookrich BUSINESS ARITHMETIC BY C. M. BOOKMAN FORMERLY HEAD OF MATHEMATICS DEPARTMENT HIGH SCHOOL OF COMMERCE COLUMBUS, OHIO AMERICAN BOOK COMPANY NEW YORK CINCINNATI CHICAGO Copyright, 1914, by C. M. BOOKMAN. Copyright, 1914, in Great Britain. bookman's bus. arith. E. P. I >>:. PREFACE Strict conformity to modern conditions is the keynote of this Business Arithmetic. Through the elimination of useless material the complete subject is presented in a one- term course. Speed, accuracy, correct methods, — these are the demands of modern business and they have been fully met. Abundant oral and written problems, and vocational, agricultural, and manual training applications have been provided. Profit is the ultimate. goal of all business. Yet with all its systematizing, modern business, until recently, figured its profit on the cost of an article instead of on its selling price. The author believes that the direct methods of presenta- tion, the rapid calculation methods, the constant application of aliquot parts, the use of the equation in percentage calcu- lations, the combining of rules and explanations, and the recognition of the latest method of figuring profits make of the Business Arithmetic a distinctly valuable equipment which business men will not fail to discover and commend. Acknowledgments are due to I. A. Garbutt, of Cincinnati ; H. T. McMyler, of Cleveland; F. H. Hamm and W. C. Humpton, of Columbus, Ohio, for valuable material and criticisms; and to Treman, King & Co., of Ithaca, N. Y., for the Retail Merchants' Table. e%r\r%r\c:)ij TO THE PUPIL Keep these two things in mind : It is necessary to be acmi- rate ; it is essential to be rapid. Neither accuracy nor speed can be acquired without practice. First learn the method, then drill and drill until you know that your work is right. As you gain confidence in yourself yo\x will work faster. The exercises, drills, and -problems in this book are worth to you all the effort you will put on them ; they will not waste your time on what you already know. Work out the exercises, do the drill work, think out tlie problems. There are no tricks or puzzles to confuse you, and the problems are no harder than those you will have to solve later. Then, when you enter business, you may know that you are better fitted for it than the average person. Above all, don't be satisfied to do only fairly well what ought to be done very well. Some one is going to do it better than any one else ; why not you ? CONTENTS PAOK Addition 7 Subtraction 17 Multiplication . . . 23 Division 28 Miscellaneous Problems 30 Properties of Numbers .38 Fractions 43 Reduction of Fractions .44 Aliquot Parts 47 Addition of Fractions 51 Subtraction of Fractions 52 Multiplication of Fractions .... ... 53 Division of Fractions 58 Denominate Numbers . .63 Reduction of Denominate Numbers 73 Addition and Subtraction of Denominate Numbers . . .73 Multiplication and Division of Denominate Numbers . . 74 Denominate Numbers by Aliquot Parts 77 Graphs 79 Miscellaneous Problems 83 The Equation 88 Mensuration • 92 Practical Measurements 100 Special Methods 106 Differences in Time 106 Approximations used in Business 107 Application of Practical Measurements to Manual Training . 107 Miscellaneous Problems 109 5 6 ' . .'.*;•' CONTENTS .• , , ', ' '. '• • • - • PACK PERCENTAGfe* .':•': :• 117 Gain and Loss 120 Commercial Discount 123 Marking Goods 128 Wholesale and Retail Profits 130 Commission 133 Miscellaneous Problems 137 Interest 144 Common Interest 144 Exact Interest 151 Compound Interest 153 Sinking Funds 155 Banks and Banking 157 Bank Discount 164 Present Worth and True Discount 168 Partial Payments 169 Miscellaneous Problems 172 Taxes 180 Apportionment of Taxes 181 Indirect Taxes 183 Insurance 185 Fire Insurance 185 Life Insurance 189 Stocks and Bonds 192 Exchange 201 Domestic Exchange . . . 202 Foreign Exchange 209 Partnership 213 Railroad Rates 215 Parcel Post 219 Miscellaneous Problems 221 Review Problems 227 Appendix 237 The Metric System 237 Values of Foreign Coins 241 Square Root 242 BUSINESS ARITHMETIC ADDITION 1. Two things are important in addition : first, the figures must be plain; second, they must be arranged in straight columns or rows. Carelessness regarding these two details is the cause of many mistakes. Dictation Work. Write the following exercises from dictation, making the figures plain and arranging them in straight rows and columns, as for addition : 320615 487931 826704 593180 114329 607852 275016. 738548 2. The basis of rapid addition is the "grouping" of figures. By practice the eye can be trained to group or combine two, three, or four figures into sums which are recognized at sight, just as we recognize words at a glance without spelling out the letters. 3. Two-figure combinations. The following drill, exercises 1 to 5, contains all the possible groups or combinations of two figures each except 1 and.O, 1 and 1. In adding them, think results^ not separate numbers. Thus (first columns), think 9, 11, 7, 4, 10 ; not 1 and 8 are 9, 7 and 4 are 11, etc. Give results from left to right ; from right to left ; from top to bottom; from bottom to top; at random. 7 8 ADDITION r.iess. ( I 5' 3 3 6 7 Drill on these until all the results can be read in one minute or.less. 1. 17 '946384^ 5 4 899362884 9 275945 2. 793129142^7 5^ 8 7 53 418612443 9687753 :3 2 6 5 7 ....... 5 ? 17^84254^ 3. 31664629 1^6118347 4282657 58135_9j.92 4. 2887372915226284 23637866 7 48 5 3947 5. 17^84254^5683559 4. Add the results of the successive groups in rows 1 and 2; thus, 9, 20; 16, 26, etc. Add the results of rows 2 and 3 ; of rows 3 and 4 ; and of rows 4 and 5. 5. Add the results of rows 1, 2, and 3 ; of rows 1, 2, 3, and 4 ; of all five rows. 6. In adding, look for those combinations whose sum is 10 ; they are easily recognized and added. Drill on the following until all the results can be read in 40 seconds or less: 1. 7 16852943 3 9. 4258167 £^^^^3^5^ 2. 14 8" 9 3 6 52 7 677490317 962174583 ADDITION 9 3. 3 1 5. 2 6 9 8 4 7 4 7 8 9 3 5 1 2 6 6 3 2 1 7 5 9 ■ 8 4 4. 7 2 9 5 2 5 4 2 1 3 6 9 3 7 1 3 1 6 4 8 1 4. 1 5 2 4 4 1 1 & 3 1 8 9 5 5. 2 6 5 6 3 8- 7 4 3 5 1 3 7 8 2; 9 7 2 8 .7 7 1 5 9.' 1 6 9 a 4 8 9 5 8 5 3 7 7. Drill on the following groups, using two- figure com- binations and combinations of 10 ; the 60 combinations should be read in one and one half minutes or less. 1. 179463849589642 463869 5 66879568 394778558756^79 2. 788667 5 22678676 446647723 2 11476 241446387221245 3. 978853173935235 824798328788784 2225692 5 2447166 4. 129822738879933 499884869565643 699464523482179 10 ADDITION 8. Add the groups in rows 1 and 2, as suggested in § 4 ; in rows 1, 2, and 3 ; in rows 1, 2, 3, and 4. 9. Pick out, as indicated in the first column, the combina- tions of 10 in columns 2-10: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 7 3 4 27 795825 2 91 135687628 1) 7 5 2 5 2 5 7 8 7 51 6 4 7 4 9 3883 5 1 4 1 6 14 70 4 9 6 85577 2115 81 3 4 6 2 4 85 6 4 2J 75482 6576 61 3 6 5 116 9 15 4] 8 3 2 2 3 8 8 9 8 9 978785928 10. Add: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 8 4 3 5 9 2 6 1 7 5 2 3 7 4 4 7 2 2 6 8 8 2 5 8 4 8 3 5 7 6 8 3 1 5 9 5 1 3 2 3 3 6 3 5 3 4 2 4 7 9 2 3 4 8 6 5 9 6 9 6 1 5 6 2 7 4 2 8 2 1 8 7 5 9 4 5 7 8 8 3 5 6 5 4 5 6 2 7 8 7 5. 6 4 7 6 6 5 1 3 4 3 8 1 7 6 6 9 ADDITION 11 11. Read the results in the following. Watch for two- figure combinations and for combinations of 10. 1. 7 2 3 6 2 5 6 4 9 8 3 7 4 6 9 8 8 7 3 7 8 8 4 2 3 4 1 9 3 1 1 1 1 7 3 4 4 6 4 3 5 4 3 2 8 6 8 2. 5 8 6 2 5 1 7 6 6 2 6 2 2 8 9 8 3 5 3 3 2 2 3 9 8 4 7 7 9 9 2 9 4 3 1 5 • 7 1 4 2 4 3 9 2 9 9 9 4 8 3. 9 9 8 3 4 5 9 6 8 7 9 8 6 7 2 8 8 5 9 6 7 4 4 4 2 3 2 6 8 2 8 8 8 9 3 7 7 5 1 7 6 1 2 6 9 3 8 8 4. 1 4 6 7 5 2 3 4 7 8 3 2 5 5 8 7 9 1 6 2 8 8 4 9 8 5 8 3 5 9 8 2 3 2 9 3 1 7 8 3 8 9 8 4 3 7 1 4 5. 1 8 4 7 6 2 3 9 5 ^ 4 1 8 9 2 1 3 9 9 2 2 6 6 8 9 6 3 6- 4 7 6 8 3 1 6 7- 6 8 8 8 7 6 8. 9 5 8 2 7 2 The above results should be read in two minutes or less. 12 ADDITION 12. Checking is any means of proving the accuracy of the work. If the addition has been made downward, check by adding upward ; this is the best means of checking, and usually locates any error. 13. Many accountants use the following method in check- ing results : 7237 The sum of the units' column is 21 units The sum of the tens' column is 24 tens The sum of the hundreds' column is 28 hundreds The sum of the thousands' column is 20 thousands 1875 23061 {check) 23061 5641 2872 5436 14. The method of checking known as casting out nines is sometimes used. i^rA o Add the digits in each addend, dropping the nines as you do so. Drop 4 + 5 (9), and put down the 2. In the second ^^ ^ row drop 8 + 1, and put down (no remainder). In the third 885 3 row, 5 + 8 = 13, drop 9, leaving 4 ; 4 + 8 = 12 = one 9 and 3 763 7 over. The remainder in the fourth row is 7, and in the fifth, 0. (575 Q Adding the several remainders, we get 12 (one 9 and 3 over) ; 2(jgc Q dropping the 9's in the result gives a remainder 3. The addi- tion, therefore, is probably correct. 15. In writing or copying numbers, any error caused by transposing the figures of a number is divisible by 9 ; mis- takes may often be located in this way. Thus an error of # 90 might have been caused by writing |328 instead of #238 or vice versa ; writing 54 instead of 45 gives an error of 9, etc. WRITTEN WORK 16. Add the following problems by combinations of two figures ; remember always to look for sums which equal 10 ; check results by any method. ADDITION 13 1. 2. 3. 4. 5. 6. 7. 538 7622 68498 243967 942268 98254 820328 694 8431 71527 885354 239592 94893 538964 287 6691 42936 476932 873240 67868 932599 436 4424 22679 732369 952823 39675 813836 393 3739 39338 529437 842637 93464 376207 962 7385 78075 952546 749894 74649 933963 452 9461 68627 689475 376846 38473 670244 836 318 24496 396823 367298 72967 592683 ^■i'{ 8. 9. 10. 11. 12. 2468998 2369857 539863 6892576 6864939682 810773 784972 284006 380919 926784629 3106064 38648 186 6808 16930179 2958 414973 8675 8329727 8202904625 16476 8754 934 986235 623968234 286972 43692 681309 6809763 9813952975 3296498 57373 372691 4682792 9239392839 968634 865885 458 8257613 2895.12954 6976 16862 914 398458 6396832689 4163068 6197837 682789 2918975 2139323692 13. 14. 15. 16. 62534785 1211678.92 4519904 325 42768 4376.53 80022 279002 3426487 52678.21 3428 369001 546891 5S6M 319900 32673 63916294 23891.78 538 299751 "-^354689 996784.46 7723901 6867 552679 8228.77 47892 2871909 64738923 48935.25 72804 4572 634258 243.85 992367 70003 7354629 25364.48 734 247808 300030 114.15 63425 375803 34253645 65.65 6354745 8675391 14 ADDITION 17. 18. 19. 20. 258014675 334990800 2508146 4466820 39820017 100336472 567 30004 287941 5541763 268749 638914410 47190285 639014725 75271 36819304 832091748 472459016 33728451 591309247 47251635 61538697 163089 1648732 845361924 46573100 2537481 90057338 635127400 361022855 46275541 900036211 714257892 5326178 243885 11922347 364511 56640 273101 4457 38165243 88129934 7142386 553896452 3732450 632871 79573 2004893 992345515 3745106 26374810 7342888 5645 40009786 1118885 375642102 4994494 61195 836 20 437611 1589298 463702 4582901 634459011 2266839 8629815 33561 900026733 63825637 41432678 71280090 To THE Teacher. Inability to write or copy numbers accurately is the cause of frequent mistakes. Dictate the above numbers, and then cause the woik to be checked for accuracy and legibility. Make frequent use of dictation exercises of this kind. Note. In offices the expression to " foot-up," meaning to " add," is frequently heard ; the sum is called the " footing." 17. Horizontal addition. In invoices and in arrangements of numbers in tabular form, it is sometimes necessary to add numbers horizontally. Care should be taken to combine figures of the same order : units with units, tens with tens, etc. Do not attempt to add hoj'izontally if the numbers are very long ; place a dot over each figure as it is added. .1. Find (a) the total native parentage, (5) the total foreign or mixed parentage, (c) the foreign whites, {d) the ADDITION 15 total negro population, (e} the total population of each city. Check your work. 1910 Census for Cities of Ohio City Native Parentage Foreign OR Mixed Parentage Foreign Whites Negro Population Total Akron . Canton . Cincinnati Cleveland Columbus Dayton . Hamilton Lima Lorain . Newark . Springfield Toledo . . Youngstown Zanesville 37793 29470 154937 132314 116486 72301 21866 23465 8455 19090 30577 75114 25595 20885 17370 11798 132190 223908 35578 25559 9371 4445 9112 3914 8243 59383 26654 4145 13241 6848 56792 195703 16285 13847 3309 1614 10929 1602 3156 32037 24840 1602 657 291 19639 8448 12739 4842 725 978 375 1384 4933 1877 1936 1384 Total . . 2. Complete the following sales sheet. Add by columns and by rows, and check the work by adding the vertical and horizontal totals and comparing the two amounts. Summary for Week Ending July 25 Caki'ets Furniture Stoves Books Dishes Total Mon. $2436.15 $8654.72 $ 237.58 $ 972.15 $ 238.17 Tues. 754.13 2364.58 2364.25 764.73 1324.82 Wed. 1356.64 1655.18 1293.70 1215.14 2652.73 Thurs. 592.35 2736.63 75. 836.58 1736. Fri. 2317.59 9872.50 4378.56 72. 3642.75 Sat. 1654. 6375.25 1654.19 2315.04 1568.09 Total 16 ADDITION 3. The number of pupils in school was as follows, as indicated by buildings and by grades. How many were there in each grade ? in each building ? Check your work. GUADE Washing- ton Lincoln Jefferson Fbanklin NOETH Central Total 1 108 62 45 43 94 2 103 50 42 39 87 3 95 48 37 39 73 4 92 43 33 30 66 6 83 41 29 28 51 6 72 37 26 25 47 7 55 31 19 20 40 8 41 28 17 20 36 H. S. •834 Total. . • SUBTRACTION 18. The most rapid method in subtraction is illustrated as follows: suppose you wish to subtract 8615 from 9521. 9521 ^^y *° yourself: 5 and 6 (put down the 6) are 11, carry 1; on-, r 2 (1 + 1 carried) and (put down the 0) are 2 ; 6 and 9 (put ^ ' down the 9) are 15 ; 4 (3+1 carried) and 5 are 9. Put down S906 the 5. In other words you are to find that number which added to 3615 will give 9521. 19. Ease and rapidity in subtraction will come with prac- tice. Drill on the following, reading the differences at sight. The eiglity results should be read in a minute and a half. 1. 84596989738974798 23154744331360532 2. 11 16 13 13 10 11 14 15 17 14 12 13 19 5 ^ 7 5 J _J _8 _9 8 3 _9 _8 _3 3. 15 19 16 14 18 17 13 18 14 11 19 15 16 ^ 7 11 8 12 _5 11 _6 J _4 13 _6 13 4. 21 14 19 23 22 51 20 24 21 20 22 26 21 15 4 12 15 17 13 14 19 18 18 13 15 17 5. 38 35 41 37 25 42 51 47 81 62 93 46 87 29 26 38 18 19 26 17 39 79 45 47 32 16 6. 175 205 193 600 750 215 7C ) 195 219 351 514 68 42 151 480 514 155 57 ' 89 198 248 328 BUS, ARITH. 2 17 18 SUBTRACTION 20. Checking. The best way to check subtraction is to add (upward) the remainder to the subtrahend, checking tlie result by the figures in the minuend as you do so. Thus in § 18, 6 + 5 = 11 (check the 1), + 1 + 1 = 2 (check), 9 + 6= 15 (check), 5 + 1+3 = 9. 21. A parenthesis, ( ), signifies that all quantities within it are to be considered together. A vinculum — written over the num bers h as the same effect. For example, 17 — (6 + 4), or 17 — 6 + 4, means that the sum of 6 and 4 is to be sub- tracted from 17. 22. In making change, add to the amount of the purchase tlie amount necessary to equal the coin or bill tendered in payment. 1. If a man buys goods amounting to $2.53, and tenders a twenty-dollar bill, how will the cashier count out the change ? The cashier picks out, first 2^, then 2 dime.s, then a quarter, then a |2 bill, then a !$5 bill, then a $10 bill (not two 5's), making $20. The change is counted out piece by piece, thus: $2.53, $2.54, $2.55, $2.65, $ 2.75, $ 3, $ 5, $ 10, $ 20. Count out the change in the following : 2. 15 -*2.15 3. 110 -$1.73 4. no- 16.13 5. 120 -$11.42 Cost of the items purchased 10. 1.25, $8.25, $1.25 11. $.14, $1.52, $2.11 12. $21.25, $17.82, $16.54 23. To find the arithmetical complement of a number, sub- tract it from one unit of the next higher order. Thus, the 6. $2 -$.72 7. $1-$.14 8. $.75- $.52 9. $.50 -$.11 Amount tendered $10 $5 $100 SUBTRACTION <3 complement of 8 is 2 (10 — 8) ; the complement of 89 is 11 (100 - 89). Arithmetical complements are useful in getting the result in any problem which requires that one number be subtracted from the sum of other numbers. 1. Find the result of 764 minus 121 plus 263. Arrange as for addition, prefixing a minus sign to the ' ^^ quantity to be subtracted. Add, using the complement of the — 121 minus figure in each column; thus, 4 + 9 (the complement of 263 1) + 3 = 16 ; write 6, rejecting one 10, there being one minus ' QQg number. Continuing, 6 + 8 (complement) + 6 = 20 ; write 0, reject 10, carry 1. 8 + 9 + 2 = 19; write 9. (a) When the sum in any column, including the comple- ment, is less than 10, put down the entire sum, and add 1 to the minus figure in the next column before finding its complement. (5) The complement of is 10. 2. Find the result of 1360.40 minus 117.08 plus f 114.25. + 2 (complement of 8) + 5 = 7 ; write 7. Since 10 can- ^t'ooU.'lU jjQ^ ]jQ subtracted, add 1 to 0, the minus number in the next — 17.08 column, before finding its complement. 4 + 9 (complement 114.25 of + 1) + 2 = 15 ; reject 10; write 5. + 3 (complement $457 57 ^^ 7) + 4 = 7. 10 cannot be subtracted. 6 + 8 (comple- ment of 1 + 1) + 1 = 15; write 5. 3+1 = 4; write 4. There being no minus figure in this column, no 10 is rejected. 24. Solve the following by complementary addition. 1. 2. 3. 4. 5. 257 118.54 $854.25 328 $2116.45 196 7.52 - 75.93 -7 -.58 -318 54.85 156.55 421 36.71 254 -10.50 129.62 36 411.95 716 19.87 73.54 880 3246.78 119 5.52 254.76 706 21.16 20 SUBTRACTION 25. Balancing accounts. The following is taken from a bank ledger. It shows (1) each person's balance at the beginning of the day, (2) the amount drawn out by check, (3) the amount deposited. 1. By horizontal complementary addition determine each person's balance at the close of the day. Check by vertical addition. Depositor's Ledger Names Balance Checks Deposits Balanok Mr. A Mr. B Mr. C Mr. D Mr. E ' li H If )7 )8 )0 )6 )4 24 25 18 2i 1^ 1( JO }4 10 L2 )0 15 25 ] ] ] 56 29 10 148 M8 28 57 22 Total 2. When the debit and credit items of an account are given, this is a convenient method of determining the balance. This is important because of its wide use in bookkeeping. The debit side of the account is obviously the larger ; foot this account and write in the footing, .16698.04, for both debit and credit columns. Add the credit side thus :2 + 5+l + 2 + (4) = 14; put down the (4) and carry 1. Continuing, 1 (carried) + 7 + 7 + 5 + 9 + (1) = 30, etc. Check by adding the credit col- umn including the balance. Solve by the balancing account method : 3. Balance in bank June 1, 1914, $450. Checks from June 1st to June 30th, $25.35, $124.00, $17.62, $18.42, $42.54. What is the balance July 1st? Cash Dr. Cr. 2r ( li 2] )86 554 }64 142 J98 24 25 82 73 < 2t 15 1{ 168 )68 J56 254 )49 72 75 51 92 14 Bal. 6( 04 6( 598 04 SUBTRACTION 21 4. A man bought a farm for #8260. He built a house on it at a cost of $1850 and fences cost -1240. What was his gain if he sold it for 111000? 5. A man's salary is 1 1500 pe. ).iiu. it he requires for rent 1 300, for personal expenses |:!*r'-^>8, and for household expenses 1816.27, what amount^ wIIlc !iave left at the end of the year ? 6. In an election the votes for the candidates A and B in five wards were as follows : ABD A B 1 1261 832 2 793 1116 3 1030 755 4 1349 624 5 998 977 majority Which candidate has a majority? How large is the majority? 7. Arrange in proper form and find the balance for July 1st. Deposits: Jan. 1, i300; Feb. 3, 1250; March 2, 1150; June 28, 1250. Checks: Jan. 16, -f 125. 30; Feb. 7, 175.20; June 18, 195.18. 8. A cash register showed the following record of the daily sales of two clerks. Which sold the more goods, and B $ 27.61 126.13 81.35 134.25 84.16 194.68 how much? j^ Monday . $ 43.85 Tuesday . . 78.94 Wednesday . . . 90.09 Thursday . . . 148.72 Friday . . . . . 110.27 Saturday . . . . 213.50 22 SUBTRACTION Determine the balance in the following : — 9. 10. LI. Db. Cr. De. Or. Dr. Or. $ 236.97 14657.81 $ 421.07 $3118.72 $200. $5000. 2436.18 753.34 1872.56 550. 231.46 428.70 1846.90 624.83 396.54 27.81 61.69 1000. 115.00 524.65 2148.19 642.90 568.89 246.66 198.75 312.40 Bal. 940.07 168.17 Bat.. 301.01 1587.75 I Bal. 12. THE CITY NATIONAL BANK In Account wi ^ U ^ -. >.^^. - Date Withd rawn Deposited Balance (L^. / £:^A4L ■^" ^ f tr. ■L ?.,1 ^0 7 S- {T^ 7. / ,? 7 s . o J / ^ So o c6) + 8: = 44. fxj = |. 44 + |: = 44|. (J) When the integral parts are different. Multiply 41 by 6^. _6i iof(4 + 6)=3|. (4 X 6) + 3^ =27i. ^xl = ^. 27^^ = 27^ 27A MULTIPLICATION . 57 Application of aliquot parts. Multiply 625 by 625. ^'i 6| hundreds x 6^ hundreds = 39y\ ten thousands. 6^ ^\ of 10000 = 625. 625 annexed to 39 ten thousands 39 Jg = 390625 (390000) gives 390625. Notes. 1. When the answer ends in Jg, annex 0625 to the integers in the product. 2. When the answer ends* in j%, as in 8| x 8f, annex 9 times 0625, which is 5625, to the integers in the product. Multiply 966| by 9.66|. *^3 Express the | by as many 4's as there are 6's in _9J the two factors. Point off as in the multiplication 93| = 9344.44| of decimals. Note. When the decimal part is substituted for the fractional part, add as many numbers in the answer as were displaced by the aliquot part in both factors. (See 966| x 9.66|.) 81. 3^, 33J, 333J, etc., can be expressed by ^; remember that they are the aliquot parts of 10, 100, 1000, etc. Solve orally : 825 X 825 1025 bushels at 810.25 931 X 933| 875 doz. at $8.75 925 X .925 4.66f X 4.66f 825 X .425 1275 acres at 1127.5 325 rugs at f 9. 25 13. 350 X 350 14. 286 X 150 15. 476 X 175 1. 8i X 8-i 2. lOi X 101 3. 91 X 91 4. 8|x8f 5. 91 X 91 6. 4f x4f 7. 81x41 8. 12| X 12f 9. 3ix9i 10. 36| X 3f 11. 31 X 33J 12. 9JX9.3J 58 FRACTIONS DIVISION OF FRACTIONS 82. The process in the division of fractions differs from that in the multiplication of fractions in that we multiply by the reciprocal of the divisor. The reciprocal of any fraction is the fraction inverted; e.g.^ the reciprocal of f is |, the reciprocal of 3 (|) is ^, etc. 83. To divide a fraction by an integer, (a) Divide | by 4. (6) Divide .0042 by 7. OOOfi Place the point for the quotient directly above the ' point in the dividend. Dividing, 7 is contained in 0, 7). 004^ times; 7 in 0, times; 7 in 4, times; 7 in 42, 6 times. r Note. Observe carefully the position of the decimal point in the above problem. Divide (by inspection when possible) : 1. 14^17 2. lf-^15 4. ii^3 5. 1^5 6. .121 ^ 4 (aliquots) 7. .022-110 8. .00044-220 84. To divide a mixed number by an integer. When the mixed number is small, change it to an improper fraction and divide as in dividing a fraction by an integer ; 9. .75-5 10. .0033^3000 11. m^i2 12. .7500-^15 13. Mff-21 14. .881-5-24 15. .56^-18 16. .220122-13 7)6456| DIVISION 59 (a) Divide 6456f by 7. Q92 8_ When the mixed number is much larger than the 1^-- divisor, divide the integral part of the mixed number as if there were no fraction. 7 is contained in 6456, 922 times with a remainder g of 2; then the total remainder will be 2|. Dividing 21 2f by 7 gives ^\. (b) Divide 3.40236 by 52. .06543 52)3.40236 3 12 282 260 Follow the same method as in (b) § 83. 223 208 156 156 Note. Annex as many ciphers to the dividend as are needed; they have no value ; e.g., .5 has the same value as .500. In annexing ciphers be careful not to change the position of the decimal point; e.g., 2 = 2.00. Divide (by inspection when possible): 1. 4|-6 9. 448.71f^7 10. 7.6724^5 11. 24.66| ^ 8 12. 2874.5^100 13. 587.81^\ ^ 11 14. 34.121 ^ 8 15. 5.90^^ -^ 11 16. 48.376-^24 2. 8f^l0 3. 5|^7 4. 686J - 9 5. 8654f - 7 6. 956f -J- 4 7. 48341 - 11 8. 478.336 ^ 16 60 FRACTIONS 85. To divide any expression by a fraction. (a) Divide I by |. (6) Divide 216 by -i/. 14=1 ;sJ?xA=9o 2 . (c) Divide | of | by ^ of |. 3 ^279_Q5 Invert all the separate fractions composing 4 ^ ^ ^ ^ the divisor, and cancel. 2 (^) Divide 7J by if 2 5 5252 ^^ _ 1 A Reduce the mixed number to an improper fraction. ^ N T^- • 1 A14AO 1, -I TO ^^ove the decimal point in the (e) Divide .02408 by .172 ^.^.^^^ 3 p,^^^^ ^ j*;;" ^;^j,^ ^^ '^ make an integer of it. Therefore, jl72.}i 024.08 the point in the dividend must be 11 2 moved 3 places to the right. The n yo division is now performed in the same manner as dividing by an " ^^ integer. (See §83 6.) Divide (by inspection when possible) : 1. iV-i\ 9. 440.04-1.1 3. 25.26-1- jS^ 4. 25.6-^51.2 5. . 004 -^ .0002 6. ^^i 7. 31^.5 8. 625^2.5 10. .24^1.11 11. .0222 -5- .0111 12. .75 -.15 13. 48 -A 14. 8.5 H- .0017 15. (25ix,V)^(|xi) 16. (lof f)^(|of ,7,) DIVISION 61 86. To divide by a mixed number, (a) Divide 364 by 2^. 52 Cb) Divide 6.48^ by 1.3|. 1.3| 6.48J 12 12 16.5 77.80 The L.C.M. of 4 and 3 is 12. Multiplying ^''WS both dividend and divisor by 12, gives the new 16^5)77^8.0 dividend and divisor, 77.80 and 16.5. The divi- g(3Q sion results in a quotient of 4.7^\. (See § 83 b.) 1180" 1155 16 5 ¥¥ (0 Divide 8658.24i\V ^y .3|. .3f)8658.24J^V 2361 3.3l||| lil)25974i7.2^3^3^ 22_ 39 33 When the fraction in the dividend is too large to handle by example (b) multiply both dividend "' and divisor by the denominator of the divisor. ^b Divide as in (e) § 85. 14 11 37 83 -4 2 33 ^m=-\\'h ¥#^ii=iffi 62 FRACTIONS Divide : 1. 196f^6f 2. 42861^141 3. 86941^261 4. 638654if ^ .39-1 5. 64.95J^16 6. 83.65 ^1.7J 7. 6892752^1-191 8. 867^191 9. 9.37|H-.042f 10. 67.45^111 87. Special methods of division of fractions. (a) Divide 135 by .12|. 135 8 1080 .12| = |. Dividing by \ is the same as. multiplying by 8. (6) Divide 424 by 25. 4.24 4 16.96 25 is \ of 100. Pointing off two places divides the number 424 by 100. Divid- ing by 100 makes the quotient \ of what it should be, so multiply by 4. ((?) Divide 75 by J. 75 25 100 I lacks just ^ of itself of being 1. Then add I of the number to itself. (d) Divide 80 by f 80 60 f is just \ of itself larger than 1. Then subtract \ of the number from itself. 1. 864 -.16| 2. 264--.09J-J 3. 563 ^.16| 4. 6857^75 5. 4836^125 6. 935 ^.88| 7. 36.54-125 8. 125 --f 9. 217 -J 10. 3568^.901^ 16. 85.931^^6 11. 3568 --If 90^^ 12. 3568- 13. 50000-250 14. 9872 --4 15. 5893^.36-^^ DENOMINATE NUMBERS 88. A denominate number is a quantity used in measure- ments, the value of whose unit has been fixed ; e.g.^ 5 feet and 3 pounds are denominate numbers because the units, feet and pounds, are fixed by law. 89. Some of the subjects to which measurements apply are value, weight, length, area, capacity, time, etc. Note. The tables for the Metric System will be found in the Appendix. MEASURES OF VALUE 90. United States money. Table 10 mills (m.) = 1 cent (J^) 10 cents = 1 dime (d.) 10 dimes = 1 dollar (,|) 10 dollars = 1 eagle Note. The mill is not a coin. The following money is now authorized by the United States Government : — Coins : The copper one-cent piece and the nickel five-cent piece. The silver dime, quarter, half dollar, and dollar. The gold quarter eagle (12.50), half eagle (f 5), eagle ($10), and double eagle ($20). Note. Uncoined gold and silver is called bullion. Silver coins less than |1 are legal tender to the amount of 1 10; nickel and copper pieces to the amount of 25 cents. 63 64 DENOMINATE NUMBERS Paper Money : Silver certificates and gold certificates. United States notes (greenbacks). National bank notes. Treasury notes (not now issued but still in circulation). 91. Canadian money is the legal currency of Canada. Table 10 mills (in.) = 1 cent (f ) 100 cents = 1 dollar ($) Note. Canada also issues subsidiary coins, the silver 5^ piece, 10^ piece, 20j* piece, 25^ piece, and 50^ piece. 92. The unit of English money is the pound sterling ; its value in United States money is $4.8665. Table 4 farthings (far.) = 1 penny (d.) 12 pence = 1 shilling (s.) 20 shillings = 1 pound or sovereign (£) 93. The unit of French money is the franc ; its value in United States money is i.l93. Table 10 millimes (m.) = 1 centime (c.) 10 centimes = 1 decirae (dc.) 10 decimes = 1 franc (fr.) 94. The unit of German money is the mark ; its value in United States money is 1.238. Table 100 pfennigs (pf.) = 1 mark (M.) MEASURES OF WEIGHT 95. There are three kinds of weights used in the United States : Commercial, Troy, and Apothecaries'. 96. Commercial or avoirdupois weight is used for all com- mercial weighing, except for weighing precious stones. TABLES 65 Table 16 drams (dr.) 16 ounces 100 pounds 20 cwt. or 2000 lb. 112 pounds 2240 pounds = 1 ounce (oz.) = 1 pound (lb.) = 1 hundredweight (cwt.) = 1 ton (T.) = 1 long hundredweight = 1 long ton Notes. 1. The long ton is used in United States customhouses, and in wholesale transactions in coal and iron. 2. The commercial pound contains 7000 Troy grains. Commercial Table Showing pounds per bushel of various products, with exceptions. Pounds COiMMODITY U. S. Cus- Exceptions tomhouse States Barley 48 48 Ariz., 45; Ala., Ga., Ky., Pa., 47; Cal.,50. Beans 60 60 Ariz., 55; N.H., Vt., Me., 62. Buckwheat . . . 48 52 Cal., 40; Conn., Me., Mass., Mich., Miss., N.Y.. Pa., R.I., Vt., 48; Idaho, N. Dak., S. Dak., Okla., Ore., Tex., Wash., 42; Ind., Kan., Minn., N.J., N.C., Ohio, Tenn., Wis., 50. Clover seed . . . 60 60 N.J., 64. Corn (in ear) . . 70 70 Miss,, 72; Ohio, Ind., Ky., 68. Corn (shelled) . . 56 56 Mass., 50; Cal., 52 Corn meal . . • 48 50 Ala., Ark., Ga., Fla., 111.^ Miss., N.C., S.C, Tenn., 48. Oats 32 32 Md., 26 ; N. J., Va., 30; Ida., Ore., 36. Onions 57 57 Conn., Me., Mass., Minn., N. Dak., S. Dak., Okla., Vt., 52; Fla., Tenn., 56; Ind., 48; Mich., 54; Ohio, 55; Pa., R.I., 50. Peas 60 60 Potatoes .... 60 60 Md., Pa., 56. Rye 56 66 Colo., 54; Me., 60. " Timothy seed . . 45 45 Ark., 60; Okla., N. Dak., S. Dak., 42. Wheat 60 60 BUS. ARITH. 66 DENOMINATE NUMBERS Other Commercial Measures Beef — barrel 2001b. Butter— firkin 56 1b. Fish- quintal 1001b. Flour — barrel 196 1b. Grain — cental 100 lb. Nails — keg 1001b. Pork — barrel 2001b. Salt — barrel 2801b. Lime — cask" 2401b. 97. Gross weight is the total weight of the goods and the containing package, commonly called container. 98. Net weight is the weight of the goods alone. 99. Tare is the allowance made for the weight of the con- taining package. 100. Troy weight is used in weighing diamonds, gold, sil- ver, and other precious minerals. Notes. 1. The carat used in weighing diamonds is equal to 3.168 grains. 2. The term carat is also used to denote the Jineness of gold, and means ^\ part. Gold 18 K. (carats) fine is ^| pure. Table 24 grains (gr.) = 1 pennyweight (pwt.) 20 pennyweight = 1 ounce (oz.) 12 ounces = 1 pound (lb.) Table Diamond Weight 16 parts = 1 carat grain 4 carat grains = 1 carat (K.) 101. Apothecaries' weight is used by druggists and physi- cians in compounding and prescribing medicines. Note. Drugs, medicines, and chemicals are bought and sold at wholesale by commercial weight. TABLES 67 Table 20 grains (gr. xx) = 1 scruple (sc. or 3) 3 scruples (iij) = 1 dram (dr. or 5) 8 drams (viij) = 1 ounce (oz. or 3) 12 ounces (xij) = 1 pound (lb or #) Notes. 1. In writing quantities in apothecaries' weight, the charac- ters denoting denominations precede the figures, except in pounds. The quantities are usually expressed in Roman characters. 2. Fractions of a pound are generally used instead of ounces. LONG MEASURE 102. The statute mile of 5280 feet is the legal mile in the United States and England. 103. The inch and yard for common use are divided into halves, quarters, eighths, and sixteenths. At the United States customhouses they are divided into tenths, hun- dredths, etc. Table 12 inches (in. or ") =1 foot (ft. or ') 3 feet = 1 yard (yd.) 5^ yards or 16^ feet = 1 rod (rd.) 40 rods = 1 furlong (fur.) 320 rods or 5280 feet = 1 mile (mi.) Notes. 1. Dimensions are written: first, length ; then, width ; then, height or thickness. 2. The following abbreviations are used: a room 18 ft. long, 14 ft. wide, and 8 ft. 3 in. high may be written : a room 18' x 14' x 8' 3". Special Long Measure 1 size = I in. Used by shoemakers. 1 hand = 4 in. Used in measuring the height of a horse. 1 fathom = 6 ft. Used in measuring depths at sea. 1 knot (geog. mi.) = 1.1522 ly^.^ or 6086 ft. Used for measuring distances at sea. 3 knots = 1 league. 68 DENOMINATE NUMBERS 104. Sixrveyors* long measure is used in measuring the dimensions of land, etc. Notes. 1. The unit of measure is the Gunter's Chain, which is 4 rods, or 66 feet, long, divided into 100 links. 2. In measuring roads, etc., a tape or chain 100 feet long is used, each foot divided into tenths and hundredths. Table 7.92 inches = 1 link (1.) 25 links = 1 rod or pole (rd.) 40 rods or 100 1. = 1 chain (ch.) 80 chains = 1 mile (mi.) SQUARE MEASURE 105. Square measure is used in measuring the areas of surfaces, as land, boards, plastering, etc. Notes. 1. The area of a surface is found by multiplying the length by the breadth. 2. Paving, painting, etc., are estimated by the square of 100 square feet. Table 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30^ square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) GOVERNMENT LAND MEASURE 106. The public lands are surveyed by selecting a north and south line called a principal meridian, and an intersect- ing east and west line called a base line. 107. Range lines are lines running north and south on each side of the principal meridian, at intervals of 6 miles. The strips into which the land is thus divided are called ranges. TABLES 69 5 4 3 5* 2 f 4 3 ^I 1 Base 1 Lin ^ 2 3 4 1 1 ". 2 3 3 6 5 4 3 2 1 7 8 9 10 11 12 18 17 16 15 14 13 19 20 21 22 23 24 30 29 28 27 26 25 31 32 33 34 35 36 A Township divided into Sections 108. Townships are formed by running east and west lines parallel to the base line at intervals of 6 miles. Notes. 1. Townships are numbered north and south; ranges, east and west. 2. A township is divided into 36 sections, each 1 mile square. Each section contains 640 acres. 3. A section may be divided into halves or quar- ters, which are named according to their location in the section; thus, " E. (East) I of Sec. 20," " S. W. (South West) \ of Sec. 20." The halves and quarters may be similarly subdivided; thus, " N. W. i of N. W. I of Sec. 20." A Section N.W. }i of N.W. >^ Section 320 A. S. 3^of N.W. >^ S.W.1^ Section 160 A, CUBIC MEASURE 109. Cubic measure is used in measuring the contents or volumes of solids. Table 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 24| cubic feet = 1 perch (P.) 128 cubic feet = 1 cord (cd.) 1 cubic yard (of earth) = 1 load Notes. 1. A cord of wood is a pile 8' x 4' x 4'. 2. A perch of stone is 16^' x 1^' x 1'. 3. A cubic foot of water weighs 62| pounds. 70 DENOMINATE NUMBERS MEASURES OF CAPACITY 110. Liquid measure is used in measuring liquids. Table 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal.) Notes. 1. Barrels are of various sizes, but 31 ^ gallons is a technical barrel. 2. The unit of liquid measure is the gallon of 231 cubic inches. 3. A gallon of water weighs about 8^ pounds. 111. Apothecaries* fluid measure is used by druggists and physicians in compounding and prescribing liquid medicines. Table 60 minims (m.) = 1 fluid drachm (f 5) 8 fluid drachms = 1 fluid ounce (f 3 ) 16 fluid ounces = 1 pint (O.) 8 pints = 1 gallon (Cong. = 231 cu. in.) Note. The fluid gallon contains 231 cubic inches. 112. Dry measure is used in measuring grain, fruits, etc. Table 2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.) Notes. 1. The unit of measure is the Winchester bushel, which contains 2150.42 cubic inches ; it is used in measuring grain, sand, etc. 2. The heaped bushel contains 2747.71 cubic inches; it is used in measuring fruits, vegetables, etc. 3. Fruits and vegetables are often sold by the pound instead of by dry measure. 4. The gallon dry measure contains 268f cubic inches. TABLES 71 CIRCULAR MEASURE 113. Circular measure is used in measuring angles or arcs of circles. Table 60 seconds (") = 1 minute (') 60 minutes = 1 degree (°) 360 degrees = 1 circle (cir.) Notes. L The unit of circular measure is the degree, which is ■^Ijj of the circumference of a circle. 2. At the equator 1 degree is equal to 69^ statute miles, or 60 geographical miles or knots. TIME MEASURE 114. The length of the solar year is the exact time required by the earth to make one complete revolution around the sun, — 365 days, 5 hours, 48 minutes, 46 seconds (nearly 365^ days). 115. The solar year, divided into 365 days, is called a common year ; every fourth year (leap year) 1 day is added to the month of February. A little too much is allowed in this way, so the centennial years not divisible by 400 are excluded. (The year 1900 was not a leap year.) Table 60 seconds (sec.) = 1 minute (min.) 60 minutes = 1 hour (hr.) 24 hours = 1 day (da.) 7 days = 1 week (wk.) 100 years = 1 century (C). Commercial Table 30 days = 1 month (mo.) 12 months = 1 year (yr.) 72 DENOMINATE NUMBERS 116. Standard time is the time adopted by the railroads of the United States and Canada, and by nearly all the people of these countries. The country is divided into four time belts, each extending 1^- degrees east and west from the meridians 75, 90, 105, and 120, west of Greenwich. Since there is just a 15-degree, or 1-hour, difference between each meridian, a difference of 1 hour in time is made between each time belt. The time of the 75th meridian is called Eastern Time ; the 90th meridian. Central Time ; the 105th meridian, Mountain Time ; the 120th meridian. Western or Pacific Time. MISCELLANEOUS MEASURES 117. Counting. Table 12 units = 1 dozen (doz.) 20 units = 1 score 12 dozens = 1 gross (gro.) 12 gross = 1 great gross (gt. gro.) 118. Paper. Table 24 sheets = 1 quire (qr.) 20 quires = 1 ream (rm.) 2 reams = 1 hiindle (bdl.) 5 bundles = 1 bale (bl.) Note. Paper is often sold in " reams of 500 sheets." 119. Printers* measure makes use of two units, viz. : point and pica. Table A point = ^^ of an inch A pica = ^ of an inch The agate = 5^ points ADDITION AND SUBTRACTION 73 REDUCTION OF DENOMINATE NUMBERS 120. Descending reduction. Reduce £ 5 Is. Sd. 2 far. to farthings. £ s. d. far. 5 7 8 2 20 1075. (5x20) + 7 = 107.. 12 1292(^. 4 5170 far. (107 X 12) + 8 = 1292^/. (1292x4) +2 = 5170 far. 121. Ascending reduction. Reduce 59 pt. dry measure, to higher denominations. 2)59 8)29 qt. + 1 pt. , ^^^^f; f ^/ \ ^\^'' = \ ^^;) ' "^'^^ '' ^y ^ — ^ ^ 8 ; result, 3 pk., 5 qt., and 1 pt. 8 pk. + 5 qt. ADDITION AND SUBTRACTION OF DENOMINATE NUMBERS 122. (a.) Add: Add (upward) the farthings as fol- ^ «• ^- far. lows : 3 + 1 = 4, check because 4 far. 3 6 5 2 make Id. ; continuing, 1+2 = 3, write 4 GsJ 1 down 3. 3 4 j^ Add Id. (carried) +2 + 4 + 6 = 13 n 1 o q = Is. Id., check ; continuing, 1+5 = 6, ; write down 6. Perform the rest of the y io O o addition in a similar way. Result, £ 9 15s. M. 3 far. (6.) Subtract: Since 3 far. cannot be subtracted from 1 far., ^^ y ,. ^ borrow Id., which makes, in all, 5 far.; 5 f ar. — lb » d 1 g ^^^. ^ 2 far. Having borrowed Id., 2d. is left in O ^ ^ the minuend ; 2-2 = 0. Perform the rest of the 11 8 2 subtraction. Result :£ 11 8s. 2 far. £ s. d. far. 2 7 8 2 12 74 DENOMINATE NUMBERS MULTIPLICATION AND DIVISION OF DENOMINATE NUMBERS 123. (a). Multiply £2 78. M. 2 far. by 12. 2 far. X 12 = 24 far., or Qd. (12 x 8rf.)4- 6r/.= 102^/., or 85. 6^/. ; write 6 under the pence. Perforin the rest of the multiplication in a 2y ][2 6 similar way. Result: £28 V2s. Qd. (6). Divide £12 lis. 2d. by 9. Divide £12 by 9 = 1, with a remainder £ 8. d. far. of £3. Reduce the £3 to shillings; thus, * 9)12 11 2 (3 X 20) + 11 = 71. 7\s. -^9 = 7, rem. 85. 1 7 10 34 (8 X 12)+ 2 = 98, etc. Result: £1 7s. lOd. 3| far. EXERCISES 1. Change <£ 4 58. to United States money. 2. How many farthings are there in 200 marks ? 3. Divide £ 18 178. lid. by 15. 4. What is the cost of 7 bu. of cherries at 12^ a quart? 5. Find the cost of 2 lb. 10 pwt. of ore at 8^ per grain. 6. Multiply 24 bu. 3 pk. 5 qt. by 16. 7. Reduce 3 T. 5 cwt. 15 lb. 10 oz. to drams. 8. What is the value of a diamond weighing ^g of a carat at il25 per carat? 9. Reduce 38 lb. to grains, apothecaries' weight. 10. A farm is 24 ch. 15 1. long, and 32 ch. 14 1. wide. How many rods of fence will be required to inclose it ? 11. Add : 1 mi. 85 rd. 5 yd., 3 mi. 17 rd. 4 yd. 2 ft. 9 in., 4 mi. 17 rd. 1 ft. 10 in. 12. Read: S. 1 of S.E. 1 Sec. 33. MULTIPLICATION AND DIVISION 75 13. How many acres are there in a field 200 rd. long and 27 rd. wide ? 14. How many barrels of water can be contained in a tank 8' 3" x 3' 9" x 8|' ? 15. From a farm containing 45 A. 72 sq. rd., a lot 35' X 165' was sold. How much land was left? 16. A man wishing to travel abroad changed flOO to English money, |100 to French money, and flOO to German money. How much money of each kind did he receive ? 17. A man bought a farm located as follows : N. | of N.E. ^, Sec. 4, T. 15, North R. 5 E. How many rods of fence are required to inclose it? 18. Find the value in United States money of the follow- ing : Books Lodge of Edinburgh . . . Defoe's Robinson Crusoe . . Robert Burns Philosophical Works of Bacon Henley on Burns .... Early Printing Freemasonry ...... Postage Total d. 10 6 4 6 6 6 10 6 2 3 6 6 6 10 19. Extend and foot the following bill ^ oz. iodoform @ 1 lb. abs. cotton 70 30 1 pt. cresol comp. ^ lb. bismuth subnitrate \ lb. bismuth subgallate 50 60 60 Total 76 DENOMINATE NUMBERS 20. A man bought a portrait in Paris, paying 12114 francs 8 centimes for it. What was its value in United States money ? 21. How many barrels of flour can be made from 2000 bu. of wheat, if 1 bu. will make 42 lb. of flour ? 22. What is the value of an 18-carat gold case, weighing 50 pwt., at 80^ per pennyweight of pure gold ? 23. Together four men own 228f bu. of potatoes. If A owns 75 bu. 3 pk., B owns 52 bu. 3J pk., and C owns 17^ bu., how much does D own ? 24. Reduce £ 27 17«. Sd. 2 far. to farthings. 25. How much are £ 25 wortli in United States money ? 26. How many dollars are there in 30 marks ? 27. How many pounds sterling are there in 500 marks ? 28. A man bought 5 pairs of gloves at 5 francs per pair, and a hat for 15 francs. He tendered in payment £ 2. How many francs did he receive in change ? 29. How many pounds will 1000 silver dollars weigh, 1 dollar weighing 412J gr. ? 30. A coal dealer bought 1000 T. of coal at f 6 per long ton, and retailed it at $8 per short ton. What was his gain ? 31. A merchant bought goods amounting to X6000 8«. After selling part of the goods for X5000 6«. 6d., he found he had remaining one third of the original purchase. Did he gain or lose on the part sold, and how much ? 32. A pupil gets the following grades in his school work for the first term : English, 83 ; arithmetic, 89 ; history, 92 ; science, 84. Find the average grade of his work for the term. 33. Find the average yearly production of oats in the United States from 1900 to 1910, the figures given being millions of bushels : 809,. 736, 987, 784, 894, 953, 964, 754, 807, 1007, 1126. BY ALIQUOT PARTS 77 34. A grocer bought 50 qt. of cranberries at 9^ per quart, dry measure. He sold them at 11^ per quart, liquid measure. How much more did he gain than he would have gained had he sold them by dry measure ? 35. An automobile consumes, on the average, 1|- gal. of gasoline per day. If gasoline costs 18^ per gallon, find the cost of the gasoline consumed from Feb. 5th to Nov. 26th, if the machine is run 6 days out of every 7. 36. A farmer sold 3 loads of potatoes containing respec- tively 54 bu. 17 lb., 42 bu. 41 lb., and 60 bu. 28 lb. What did he receive at 80^^ per bushel ? 37. A farmer sold 5 loads of wheat, the weights in pounds of the various loads being as follows : Weight of Wagon Loaded Weight of Wagon 7625 3870 7308 3728 7000 3709 6968 4000 7628 3910 How many pounds did he sell ? DENOMINATE NUMBERS BY ALIQUOT PARTS 124. Grain is generally priced by the bushel, but sold by the pound. 1. Find the value of 24000 lb. of wheat at 95^ per bushel. There are 60 lb. in a bushel of wheat; then 60^ per bushel would be 1^ per pound. Point $240, value at 60^ per bushel ^^ two places in the number of 120, value at 30^ per bushel pounds to find the value at 60^ 20, value at _5^per bushel per bushel = 1240. | of $240 1380, value at 95^ per bushel ^^^^^^ ^^^^ ^^^ ^^^^^ ^^ ^ ^^ ^0^' or W per bushel; ^ of |120 would give the value at | of 30^, or o^ per bushel. 78 DENOMINATE NUMBERS 2. What is the value of 24000 lbs. of coal (retail) at 18 per ton ? 24.000 Point off 3 places to show the number of thousands of 4 pounds. Multiply by ^ the price, for f 8 per ton is ^4 |i96. P®^ ^^^^ pounds. 3. Extend and foot the following bill of feed : No. OF Lbs. Article Prick Value 84654 Hay ^ 14 per ton 12570 Bran $ 18 per ton 546570 Corn (in ear) 40j« per bushel 685470 Straw ^ 6 per ton 40020 Chop § 25 per ton 68400 Oats 30^ per bushel Total 4. Find the value of the following shipment : Produce Wheat . . Wheat . . Clover seed . Potatoes . . Onions . . Beans . . . Corn (shelled) Barley . . Timothy seed Rye ... Total Weight in Lbs. 76350 74000 36540 75640 32400 48600 78400 38000 48200 60000 Pbice per Be. 76j? 70j« $3.00 90j« W^ 85^ 30j^ J52.00 56j? Value GRAPHS 125. A graph is a diagram showing fluctuations, such as variations in temperature, rise and fall of prices, etc. The temperature chart shows variations in temperature from 6 A.M. to 6 p.m. The hour is indicated by the row A.M. 10 12 3 70 50 40 ^v :?: Temperature Chart of figures along the top ; the temperature is indicated by the vertical column at the left. Illustrate graphically : 1. The varying price of wheat for the years 1900 to 1911, the prices for the respective years being as follows : 1900, 611^; 1901, 631^; 1902,671^; 1903, 70|y ; 1904, 811^; 1905, 77|^; 1906, 69y ; 1907, 71^; 1908, 84|-^; 1909, 99y ; 1910, 891^ ; 1911, 83-iy. 2. The production of corn in the United States for the years 1900 to 1910, the figures given indicating millions of bushels : 1900, 2105 ; 1901, 1522 ; 1902, 2523 ; 1903, 2244 ; 79 80 GRAPHS 1904, 2407 ; 1905, 2707 ; 1906, 2927 ; 1907, 2592 ; 1908, 2668 ; 1909, 2772 ;* 1910, 3125. To THE Pupil. On a sheet of graph paper keep a daily record, after your work has been checked in class, of problems solved correctly. Problems missed should be worked after they have been explained in class. Then, by means of a dotted line, indicate the percentage of prob- lems so corrected. This line should not show much variation. 3. The following graph illustrates a record kept for three weeks : loo 90 70 50 40 20 10 M i 1 T 1 ' ' 1 Ti 1 1 1 1 111 1 / 1 (i t it j i: I [ it 2 an I-JL ■ T 7i v\ i /! ' 1 M 'A '/ 1 \1vA 1tI ! A 1 - t a t il 1 U t ' t ... I rJL It I X ti It -EI tit tl I t jt ■f'" t t t M t T r t "ii" h 1 H :; 1u h \^ ^ h r~i ^ Tl ^l^ T 1 " 11 ti xi t 1 n l~i tT |--j T"!^ ^4 1 + 1-^ li r1 it r 1 iT tj jI tl 3t tl jt It It It 11 \T ^r M ^ At I % -t i- - _ __ Week Day WORKKD MlSSKD Made Up % Madk Up Men. 10 Tues. 8 2 1 Wed. 9 1 1 50 Thurs. 6 4 2 100 Fri. 10 2 60 Mon. 7 Tues. 6 1 50 2 Wed. 8 2 1 100 Thurs. 9 1 2 100 Fri. 7 3 Mon. 7 3 3 75 Tues. 9 1 4 100 3 Wed. 8 2 1 100 Thurs. 8 1 50 Fri. 7 1 100 Explanation. On Monday, first week, no problems were missed, so the solid line starts at 100%. On Tuesday, 80% of the assign- ment was correct. On Wednesday, one prob- lem of those missed on Tuesday was made up (50 %). On Thursday, the remaining problem missed on Tuesday and the one missed on Wednesday were worked (100%), etc. GRAPHS 81 4. The following illustration shows in a graphical way the percentages of investment on an 80-acre farm : Land and Outbuildings Dwelling Stock . . Machinery and Iraplenaents 83i % of the total investment 2|% 5. The following is a graphical representation of the profits of Oregon farmers on farms of different size. '\TH \ 2^ \ 3^ \ A^ ^i^ ^^ 1 ^^ 8^ 9^ 10^ III lE^^I ■ ^^^^^ 1 ^^^^^^^" 5 to 20 A, 21 to 80 A, 81 to 160 A, 161 to 320 A OVER 320 A, 6. A farmer who keeps a careful estimate of the cost and returns on all his crops finds that wheat makes him 7% profit, corn 6 J %, oats 5 %, and apples 10 %. Illustrate his profits, graphically, as in example 5. BUS. ARITH. — 6 82 GRAPHS 7. Draw a graph similar to the one found in example 4, which will show approximately the following family expendi- tures. „ , , Heat and Rent Household Clothes Light Miscellaneous % of income 20 25 15 5 30 spent Is the balance which is saved, represented on the graph ? 8. On a farm of 3*20 acres the following percentages of in- vestment are made: Land and Outbuildings 75 % of total investment Dwelling 3% Stock 19% Machinery and Implements .... 3% Represent, approximately, the above percentages. 9. The following is a graphical representation of the " Mean Monthly Temperatures " for certain towns in Oregon as shown by the Oregon Agricultural College. ??< So z aS -b){S--c) = area. Ex. Find the area of a triangle if the three sides are 15 ft., 17 ft., and 18 ft. 5 = H15 + 17 + 18) or 25. \/25 X 10 X 8 X 7= 118.3+ sq. ft. ( X O = ^i"ea. 7*2 X TT = area. i>2 X i7r(|7r = .7854) = area. EXERCISES Find the area and perimeter of : 1. A rectangle, base 72 rd., width 30 rd. 2.. A square, base 25 rd., width 25 rd. 3. A rectangle, base 30 rd., width 42 rd. 4. A circle, radius 3 ft. 5. A circle, diameter 4 ft. 6. A circle, circumference 24 ft. 7. Find the area of a triangle whose sides are 15^ 16', and 17^ 8. Find the base of a right triangle whose hypotenuse is 10 ft. and one side 6 ft. 9. What is the hypotenuse of a right triangle whose other two sides are 9 ft. and 12 ft. ? 96 MENSURATION 10. Find the area of a right triangle, if its base and per- pendicular are 7 ft. and 8 ft. respectively. 11. In a right triangle the hypotenuse is 25 fl., the base 13 ft. What is its area ? 12. A rectangular field, is 70 rd. long and has an area of 40 A. What is its width ? 13. How many square feet in the floor of a room 40 ft. by 20 ft. ? 14. A yard is 75 ft. by 165 ft. What will it cost to fence it at 12J^ per foot? 15. If a walk 3 ft. wide is inside the fence of a rectangular garden, how much area does the walk cover, the garden being 30 ft. by 40 ft. ? 16. A square field containing 40 A. has a road 30' wide running completely around it outside the fence. Find the area of the road in acres and square rods. SOLIDS 148. A solid has three dimensions, — length, breadth, and thickness. 149. A prism is a solid whose ends or bases are any equal, similar, and parallel plane fig- ures, and whose lateral faces are parallelo- grams. Note. Prisms are named from the number of sides L forming their bases, — triangular prisms, quadrilateral prisms, etc. 150. A cube is a prism having all three dimensions equal. Quadrilateral Prism Cube SOLIDS 97 151. A circular cylinder is a solid having equal, parallel, circular bases, and its lateral surface a uniform curve. Circular Cylinder 152. A pyramid is a solid having a polygon for a base and triangles for sides. Pyramid 153. A circular cone is a solid having a circular base, and lateral surface tapering to a point. Circular Cone 154. The altitude of a solid is the perpendicular distance from its base to the highest point. 155. The slant height of a pyramid is the altitude of its triangular lateral surface. 156. The slant height of a cone is the shortest distance from the circumference of its base to its vertex. 157. The volume of a body is the number of cubic units it contains. 158. Additional abbreviations: K = area of lower k = area of upper St. ht. = slant height. BUS. ARITH. 7 98 MENSURATION 15&. Formulas for solid figures: 1. Pkism, (a) K X h = volume. (6) P X h= area of lateral surface. (c) (F X h) -\- k -^ K= total area. 2. Cylinder, (a) Kx A = volume. (h) P X h = area of lateral surface. (t?) (P X A) + A: -h K= total area. 3. Pyramid, (a) K X ^h = volume. (h) P X I 8t. Jit. = area of lateral surface. (c) (P X I 8t. ht.) 4- K= total area. 4. Cone, (a) K X I h= volume. (b) P X 1st. ht. = area of lateral surface. (c) (P X I 8t. ht. ) + ir= total area. Notes. 1. The prism and cylinder have like formulas. 2. The pyramid and cone have like formulas. 3. In formulas 1 (c) and 2 (c), A' = k. EXERCISES . Find the volume, lateral area, and total area of : 1. A rectanglar prism, sides of base 8 ft. and 4 ft., alti- tude 9 ft. 2. A triangular prism, sides of base 4 ft., altitude 9 ft. 3. A cylinder, diameter of base 5 in., altitude 10 in. 4. A cylinder, radius of base 2 in., altitude 8 in. SOLIDS 99 5. A pyramid, base a square 6 ft. on a side, altitude 4 ft., slant height 5 ft. 6. A cone, diameter of base 4 in., altitude 7 in. 7. A triangular prism, sides of base 4 in., 5 in., and 7 in., altitude 11 in. 8. A cube, 8 in. on a side. 9. How many gallons of water will a cylindrical cistern hold if its diameter is 8 ft. and depth 20 ft. ? (See § 110.) 10. The volume of a cylinder is 500 cu. in., and its base has a diameter of 10 in. What is its height ? 11. The volume of a prism is 320 cu. ft., and its base is a square, 4 ft. on a side. Find the altitude. 12. A cylinder 25 ft. high has a capacity of 1000 cu. ft. What is the diameter of its base ? 13. How many cubic yards of dirt will it take to make a fill 300 yd. long, 10 ft. high, and 30 ft. wide ? 14. What must be the diameter of a cylindrical gallon measure 7 in. high? 15. A has a cylindrical cistern, diameter 4^ depth 10'. What is the diameter of B's cistern of the same shape and depth, holding 8 times as much as A's? 16. The volume of a cube each edge of which is 6" is how many times as great as that of a cube each edge of which is 2'' ? 17. How many square yards of tin will be required tc make 42 cylindrical pails, without covers, 10^' in diameter and 12'^ deep, allowing 4 sq. ft. for seams and waste on each dozen pails ? 18. A rectangular swimming pool is 60 yd. long, 80 ft. wide, and 10 ft. deep. How long will it take to fill it with water to within 3 ft. of the top, if the water runs in at the rate of 8 cu. ft. per second ? PRACTICAL MEASUREMENTS 160. Papering is estimated by the roll, either single roll (18 ft. long by 18 in. wide), or by the double roll (48 ft. long by 18 in. wide). It is more economical to use double rolls on account of the saving in matching the pattern. Note. Imported papers vary in length and width. 161. Use the following rules for estimating the number of rolls required for any given room : 1. Deduct the width of all openings (doors and windows) from the perimeter of the room. Divide this result by the width of the paper to determine the number of strips required for the walls. The length of each strip will be the height of the room. 2. Divide the width of the ceiling (width of the room) by the width of the paper to determine the number of strips required for the ceiling. Each strip will be the length of the room. 3. Determine the number of strips (of each kind) that can be cut from a roll, and divide this into the number of strips required to determine the number of rolls required. Note. Spaces above and under doors and windows (not allowed for in the above calculations) can usually be covered with the strips left over in matching the pattern. 162. Painting and plastering are estimated by the square yard. Make allowance for openings, unless otherwise directed. Note. Contracts usually specify allowances for openings. 163. Carpet is sold by the linear (running) yard ; linoleum by the square yard. 100 PAPERING, PAINTING, PLA8Tj3RtS(^ '' tOlr Carpets vary in width ; this, as well as the matching of the pattern, must be taken into account in figuring the number of yards necessary for a given floor. The strips are laid the long way of the room. EXERCISES 1. Find the cost of plastering, papering, and carpeting a room 20 ft. long, 16 ft. wide, and 10 ft. high (20' x W x 10'). It has 5 windows, each 6' x 3', 2 doors 7' x 3^ and 1 door 7' X 6'. Paper costs $1.12J per double roll ; plastering costs 40 ^ per square yard ; the carpet is | yd. wide, at f 2 per yard. Plastering Area of walls = 2 x (20 x 10) + 2 x (16 x 10) = 720 Area of ceiling = 20 x 16 = 320 Total area 1040 sq. ft. Openings : 5 windows = 5 x (6 x 3) = 90 2 doors = 2 X (7 X 3) = 42 1 door =7x6 =42 174 sq.ft. 174 sq.ft. Area to be plastered 866 sq. ft. -8.|5. = number of square yards. 866x1.40 ^^ 3g^^g^ ^^^^ ^^ 40^ per square yard. Papering Perimeter of room = 2 x (20 -h 16) = 72 Width of 5 windows = 5 x 3 = 15 Width of 2 doors =2x3=6 Width of 1 door = _6 Total width to be deducted 27 ft. 27 45 ft. 45' -- 18" (I) = 30 strips, each 10' long, for the walls. 16' -^ I' = 10| or 11 strips, each 20' long, for the ceiling. '162.': •; . -. JPI^ACTICAL MEASUREMENTS As each roll is 48' long, 4 ten-foot strips or 2 twenty-foot strips can be cut from each roll. Hence, 30 -f- 4 = 7|-, or 8 rolls for the walls. 11-f- 2 = 5 J, or 6 rolls for the ceiling. Total required is 8 -f 6 or 14 rolls. 14x1 1.121- = '* 15.75. Carpeting As the room is 16' wide, as many strips of carpet will be required as | yd. (the width of the carpet) is contained in 16'. I yd. = 21'. 16 -5- 21 = 71 or 8 strips, each 20' long. 20 X 8 20 X 8 = number oifeet; ^^— - — - = number of yard%» o 2. At 20 j^ per square yard, how much will it cost to plaster the walls and ceiling of a room 18' x 15' x 7' 4", making allow- ance for 2 doors 7' 6" x 8' 6", and 3 windows 6J' x 3'? 3. A room is 15' x 12' x 9'. How much will it cost to paper it at 37 J ^ per double roll, allowing for 2 doors 8' x 4' and for 2 windows 6' 4" x 3' 3" ? 4. A wall is 16' long and 12' high. How many double rolls of paper will it take to paper it, no allowance being made for openings ? 5. A barn is 100' x 60' x 30', with gables 20' above the walls. If no allowance is made for openings, what will it cost to paint it at 5 ^ per square yard ? 6. How many yards of carpet 1 yd. wide will it take to cover a room 14' x 10', strips running lengthwise ? 7. How many yards of. carpet | yd. wide will it take to cover the library, dining room, and living room, in the 100' ROOFING AND FLOORING 103 v//////. KLTCHEN io'-irxi3-r LIBRARY 12-7" X 15-3" fir DININQ PsO^M I6'-7"X 13-2" ■3) II LIVING RO^M I I2-7"XI2-H" / / HALL 7- 3' XI 7-0" i i -r//////// (i>=p u=^ ///////}- ■^//////A accompanying floor plan, no allowance being made for match- ing patterns ? 8. How many yards of linoleum will it take to cover the kitchen ? 9. How much will the carpet in problem 7 cost at il.33 per yard ? 164. Roofing and flooring are usually measured by the square of 100 square feet. Flooring is sometimes measured by the 1000 board feet. 165. The most common roofing materials are : slate, tiling, shingles, and tin. The size of slate used is generally 12" x 6^ or 24" x 16^ Note. Contractors use a table for estimating the amount of slate to be used. The size of shingles used is generally 16" x 4", or 18" x 4". 16" x 4" shingles are laid with 4" exposed to the weather. 104 PRACTICAL MEASUREMENTS 166. Shingles are sold in bundles of 250 each. Allowing for waste, the usual estimate of the number of shingles per square is shown in the following table. Pakt exposed Number Shingles TO THE Weather PER SyllARE 4 " 1000 H" 900 5 " 800 5A" 700 Ex. A gable roof is 40' long and 20' on each side. How many shingles laid -i" to the weather must be bought to cover it ? 4 2 iPx^^x2 ^ ^Q squares, length x width x no. sides lipp * no. square ft. in a square 16 X 1000 = 16000 shingles (by table). 167. In flooring, a waste of about ^ of the total amount of lumber required is allowed for the "tongue and groove." Use cancellation when possible : 1. I wish to floor a room 20' x 16'. How much will the material cost at fSO per thousand square feet? 2. How many bundles of shingles 16" x 4" will be re- quired to cover a roof 120' x 40' ? 3. At $4: per thousand how much will it cost to shingle a roof 100' X 80', allowing 800 shingles to the square ? 4. Find the cost, at i40 per thousand square feet, of the tongued and grooved flooring for a room 30' x 20'. 168. Lumber is sold by the 1000 (M) board feet. A board foot is 1 ft. long, 1 ft. wide, and 1 in. thick. Note. Boards less than 1" thick are counted as 1" thick. 169. In making extensions in bills of lumber, point off 3 places and multiply by the price per 1000 feet, using aliquot parts and cancellation. WOOD, STONE, BRICKS 105 At $22 per M what is the cost of 60 pieces of hemlock 16' X 6" x2''? 5 16 X 6 X 2 X ^j3 X 22 ^ ^ 21 1^ Divide by 12 because the width 12 ' *^ is expressed in inches. Make the extensions in the following bill of lumber : 200 pieces 18' x 12" x 2" ft. 500 pieces 14' x 10" x 3" ft. 150 pieces 16' x 15" x 2" ft. 250 pieces 12' x 8" x 2" ft. 400 pieces 16' X 2' x 4" ft. 1000 pieces 16' x 4" x 2" ft. Total ft. @ $.33.00 per M .... 600 running feet 2" x 4" @ 33.33 per M . . . . 15000 board feet oak flooring @ 35.00 per M . . . . 20 M shingles (oj 4. .50 per M . . . . Total 170. Wood is measured by the cord. A cord of wood is 8 ft. long, 4 ft. wide, and 4 ft. high, and contains 128 cu. ft. Note. A cord foot is 1 ft. of the length of such a pile. Use cancellation : 1. How many cords of wood in a pile 40' x 20' x 8' ? 2. At 15 per cord, how much will it cost to fill with wood a shed 25' x 15' x 18'? 171. Stone is measured by the cubic yard, or by the perch (24|cu. ft.). 172. Bricks are estimated by the M. 22 common bricks laid in mortar are counted for each cubic foot of wall. Note. Allowance is always made for openings in ordering material and in making contracts. 106 PRACTICAL MEASUREMENTS SPECIAL METHODS 173. To find the number of bricks in a wall, multiply the number of cubic feet in the wall by 22. 174. To find the number of perches of stone, in a wall, divide the number of cubic feet in the wall by 24J. 1. How many perches of stone in a wall 15' x 8' x 8' ? 2. How many bricks will be required to erect the four walls of a flat building 60' x 40' x 20', an allowance of 200 cu. ft. being made for the openings and corners, and the walls being 12" thick ?• DIFFERENCES IN TIME 175. Two methods are employed in finding the difference in time between two dates : 1. Exact number of days. P'ind the exact number of days from Feb. 2, 1912, to June 4, 1912 29, number days in February 27, number days left in February 31, number days in March 30, number days in April 31, number days in May 4, number days in June 123 da. 2. Compound subtraction. What is the difference in time between Oct. 24, 1909, and May 8, 1911 ? Ye. Mo. Da. 1911 5 8 May is the 5th month in the year, October the 1909 10 24 10th month. The subtraction is performed by the 1 6 14 method of denominate numbers. (1 mo. = 30 days) APPLICATION TO MANUAL TRAINING 107 Find the difference in time between the following dates : 3. From Jan. 23 to Nov. 15 of the same year. (Not a leap year.) 4. From Dec. 13, 1910, to April 3, 1912. (Compound subtraction.) 5. From May 10, 1900, to Jan. 5, 1904. (Compound subtraction.) 6. From Jan. 1, 1913, to Dec. 25, 1913. APPROXIMATIONS USED IN BUSINESS 176. To find the number of bushels of grain in a bin, multiply the capacity in cubic feet by .8. 177. To find the number of heaped bushels of fruit or vegetables in a bin, multiply the capacity in cubic feet by .63. 178. To find the number of gallons in a cistern or reser- voir, multiply the capacity in cubic feet by 7.48. Find the approximate number of bushels of (a) grain, (6) apples, in the following bins: 1. 12^ X 10' X 8' 3. 16' X 8' 4" x 7' 2. 20' X 15' X 10' 4. 18' 3" X 15' 9" x 12' 4" Find the approximate number of gallons in the following: 5. A cylindrical cistern, diameter 4', depth 20'. 6. A cylindrical cistern, radius 3', depth 15'. 7. A reservoir, 100 rd. x 60 rd. x 50'. APPLICATION OF PRACTICAL MEASUREMENTS TO MANUAL TRAINING 1. A room 32' x 28' is laid off so as to accommodate 20 pupils in manual training. Allowing one fifth of the floor space for the teacher's use in demonstration work, how much floor space is allowed per pupil ? 108 PRACTICAL MEASUREMENTS 2. Find the total cost of the following manual training tools and supplies : Articlb Pkiot 4 augur bits \", \", f", 1'' . . .75 1 mallet 36 4 clamps 8.00 Material for bench 6.00 Miscellaneous 8.66 Article Peiob 1 block plane . $1.60 1 jack plane . 1.60 1 rip saw . . 1.60 1 mortise saw . 1.00 1 brace . . . .76 3. At 18 ^ per board foot, what will poplar lumber f thick cost for making the nail box shown in the illustration ? 4. What will the material cost for making the bread board shown in the illustra- tion, using white pine f thick, at 22 ^ per board foot ? Add expense of sanding at 2^ per board foot. ^^' 5. At 26 ^ per board foot, what will the material cost for making the table shown in the illustration? Add expense of sanding at 2 ^ per board foot for all lumber used. MISCELLANEOUS PROBLEMS 109 6. Find the cost of material and sanding in the following, quartered oak being 26 ^ per board foot, and pine and bass- wood being 32 ^ ; sanding is 2 ^^ per board foot. MANUAL TRAINING MILL BILL Order No School H. S. of Commerce Date 12/4/13 Name Walter Burkholz Gut by Project Music Cabinet Delivered Ordered by W. B. Cutter Kind of Wood Quartered oak Pine Bass All sanded Thickness Width Length 1" 1" 1" I" f" 18" 16" 17" 24" 21" 38" 28" 24" 17" Article Top Sides Door Shelves MISCELLANEOUS PROBLEMS Group 1 1. Find I in the equation 1= FET, if P = |300, i^ = .06, and T= {. 2. Find R in the equation PBT= J, if P = 1250, T= |, and 7= $6.25. 3. Solve for A in the equation A = 9 tt. 4. Find the area of a circle whose radius is 3. 5. Solve for c in the equation ( 11. 16|%, 66| %, and 5 % ^4. 40 % and 20 % ^^ 12. 25 %, 10 %, and 33^ % %5. 30% and 20% 13. 25 %, 20 %, and 16f % 6. 50 % and 40 % 14. 20 %, 20 %, and 12| % 7. 33J% and 33J% 15. 12^ %, 6J %, and 5 % 8. 33^ % and 15 % ^ 16. 40 %, 20 %, and 12J % 17. A firm gives its customers a discount series of 25 %, 20%, and 10%. What single discount does it allow ? \/18. Goods listed at $300 are sold subject to a discount series of 10%, 10%, and 5%. If the retail merchant sells at a profit of 20 % of the cost, what is his selling price ? MARKING GOODS 203. Merchants often use a private mark to indicate the cost and selling price of goods. Usually some word or phrase is selected, containing 10 different letters, to be used as a key. These letters repre- sent the 10 digits. When a figure is repeated some letter is used to represent this. Note. Some merchants have different keys for cost and selling prices. MARKING GOODS 129 204. Take for a key, "you saw them." 123456T890 Repeater yousawthem x Goods which cost 12.80 and sell for $3.55, would be marked, o.hm u.ax 205. To show 20 % profit. Goods are frequently bought by the dozen and sold by the piece, or bought by the gross and sold by the dozen. It is evident that if 10 articles are sold for the cost of 12, the profit is 2 articles (^ of 10) or 20%. Thus, if ties cost i5.00 per dozen, and 10 ties are sold for §5.00 (50 ^^ each), the profit will be 20%. Hence to make 20% profit, mark each article at -^^ the cost per dozen ; or mark each dozen at -^^ the cost per gross. The per cent of profit as computed is based on the cost. 206. To show more than 20 % profit. If 50^ each for the above ties is a gain of 20%, it is a selling price of 120%. To show a profit of 40%, there must be a selling price of 140%. This increase of 20% is ^ of 120 %. Then ^ of 50^ added to 50^ gives 5Sy (probably marked at 60^). 207. To show less than 20 % profit. Subtract the aliquot part. Mark the cost and selling price of each piece by the above key: 1. Cost i 12 per dozen, sold at a gain of 20 %. 2. Cost $18.50 per dozen, sold at a profit of 30 %. 3. Boots cost $ 26 per dozen, sold at a gain of 25 %. 4. Shoes cost $21.20 per dozen, sold at a gain of 25 %. 5. Shoes cost $17.50 per dozen, sold at a gain of 15 %. BUS. AllITH. — 9 130 PERCENTAGE 6. Pencils cost $5.00 per gross, sold at a gain of 10 % per dozen. 7. Mark the selling price of towels bought at i2.90 per dozen and sold at a gain of 55 %. 8. Knives bought at $3.60 per dozen are sold at 35 % profit. Mark the cost and selling price of each knife. 9. Mark shoes costing $ 3.90 per pair so as to gain 33 j %. 10. By selling a hat at $3.60, I gain 20%. What was the cost per dozen ? 11. A. merchant bought boots at $29.30 per dozen. He sold them at a profit of 20 % after allowing a discount of 10 % from the marked price. What was the marked price ? 12. A merchant buys silk marked at $1.20 per yard, and gets discounts of 25 % and 20 %. Mark the goods so that he will gain 25 %. 13. Caps are listed at $ 24 per dozen. The discounts al- lowed are 25, 20, and 16|. Mark a cap so as to gain 60 %. WHOLESALE AND RETAIL PROFITS 208. In most wholesale and retail businesses, capital is re- quired : (a) for the first cost of merchandise, (5) for the cost of doing business, including selling expenses, advertising, commissions for selling, and the like. 209. Profit is the difference between the total cost and the total selling price, which is in excess of the cost. 210. Percent of profit is a per cent of all money invested. Since it is not possible to determine all moneys invested until the goods shall have been sold, and since the cost of doing business, including commissions for selling, must be figured on the selling price, it is advisable to figure both profits and cost of doing business on the selling price. WHOLESALE AND RETAIL PROFITS 131 Note. In gain and loss the cost was used as the base, but in problems where cost of doing business must be figured, always use the selling price as the base. Illustration : An article cost $19.50, cartage 50 j^. If the cost of doing business is 15%, and a profit of 10 % is to be made, at what price must the article be sold ? Selling price 100 % Cost of doing business 15 % Profit desired 10 % Wholesale cost 100 % — 25 % = 75 % of selling price. 119.50 + .50 = $20, cost in money. 120 -f- .75 = 126.67, selling price. 211. The following Retail Merchants' Table is based upon the selling price. The numbers in the table are per cents. Retail Merchants' Table table for finding the selling price of an article Cost OF DOING Busi- ness Net Per Cent of Profit Desired 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 20 25 30 35 40 50 15% 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 65 60 55 50 45 35 16% 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 64 59 54 49 44 34 17% 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 63 58 53 48 43 33 18% 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 62 57 52 47 42 32 li>% 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 61 56 51 46 41 31 20% 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 60 55 50 45 40 30 21% 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 59 54 49 44 39 29 22% 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 58 53 48 43 38 28 23% 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 57 52 47 42 37 27 24% 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 56 51 46 41 36 26 25% 74 73 72 71 70 69 68 67 66 65 64 63 62 6l!60 55 50 45 40 35 25 132 PERCENTAGE Rule. Divide the cost (invoice price with freight added) by the figure in the column of "net per cent profit desired" on the line with per cent of " cost of doing business." Example : If a wagon costs $60.00 Freight 1.20 161.20 A net profit is desired of 5 per cent It costs to do business 19 per cent Take the number in column 5 on a line with 19, which is 76. 80.526 (selling price) i76)61 ^20.00 60 8 400 380 200 152 480 456 EXERCISES 1. An automobile cost $800 at the factory, freight i» 18.50; at what price must it be sold to show a profit of 25 % if it costs 20 % to conduct the business ? 2. One gross of brooms cost $26.50, with freight charges of $1.50. If it costs 15% to do business, and the jobber wishes to secure a profit of 15 %, at what price must he sell them per dozen ? 3. A car of coal cost, with freight added, $108. At what price must it be sold to pay expenses of 21 % and a profit of 7 % ? COMMISSION 133 4. A piece of farm machinery cost at the factory S 214. 50. At what price must it be sold to show a profit of 5 % and cover a selling expense of 17 % ? 5. A stove cost 118, freight 82. It was marked at a price sufficient to cover expenses of 15 % and show a profit of 35 %. If it was sold at a discount of 10 % from marked price, what was the selling price ? 6. A druggist buys toilet articles and rubber goods to the amount of f 100 each. For advertising purposes the toilet articles are sold at cost. If the selling expense of both is 15 %, at what per cent profit must the rubber goods be sold to realize 10 % on the entire transaction ? 7. Extend and foot the following bill: Dayton, Ohio, Jan. 16, 1914. The Kroger Company, Columbus, Ohio. In account with The E. C. Harley Company. 2001b. 1001b. 50 201b. 200 200 No. 6 coffee @ 30^ . . . Dayton roast coffee @ 25^ boxes laundry soap @ 95^ currants @ V2^ . . . . doz. canned goods @ $1.25 doz. canned goods @ 95/' At what price must each article be sold to realize a profit of 12% if the expense of doing business is 18%? COMMISSION 212. Commission or brokerage is the sum charged by an agent for transacting business for another. The agent is called the broker, commission merchant, or collector, according to the character of the business trans- 134 PERCENTAGE acted. The one for whom the business is transacted is called the principal. 213. A guaranty is an additional charge made by the agent for assuming the risk on credit sales, or for the quan- tity and quality of goods. 214. Merchandise sent by a principal (shipper or con- signor) is called a shipment. 215. Merchandise received by an agent (consignee) is called a consignment. 216. Gross proceeds is the total amount received by the agent for the goods. 217. Net proceeds is the amount remaining after all ex- penses have been deducted. 218. The prime cost is the actual cost of the merchandise. 219. The gross cost is the total cost, including expenses, etc. 220. An accoimt sales or account purchase is a statement itemizing the entire transaction. 221. Apply the principles of percentage. Gross proceeds or prime cost = base. Rate of commission = rate. Commission = percentage. Gross cost or gross proceeds = amount. Net proceeds = difference. Formulas : Gross proceeds or prime cost x rate of commission = com- mission, or ^^^^_ COMMISSION 135 Commission -f- rate = gross proceeds or prime cost, or R B. Commission -=- gross proceeds or prime cost = rate, or B B. Prime cost 4- commission = gross cost. Gross proceeds — commission = net proceeds. EXERCISES Supply the missing parts (by inspection) Gross Proceeds Rate of COMiMlSSION Commission Net Proceeds 1. $4500 n 2. 1800 12i — — 3. 1200 n — — 4. 1260 3 — — 5. 1600 H — — 6. 1800 16| — — 7. 7500 1500 — 8. 1400 — 400 — 9. 1500 — 600 — 10. 1800 — 400 — Supply the missing part : Gross Proceeds Kate of Commission Kate of Gifarantv Net Proceeds 11. $ 4500 2i 2 12. 1800 10 — 1530 13. 12000 — 2i 9700 14. 1350 5 1 — 15. 1200 121 — — 136 16. PERCENTAGE Account Sales 20000 lb. of coal .$4 per ton KJOOO lb. of coal $3,50 per ton — 40000 lb. of hay $ 12 per ton — 60 T. of hay $10 per ton — 3000 lb. of wheat 70^ perbu. — 7000 lb. of oats 60^ per bu. 1500 lb. of corn (shelled) Charges 80^ per bu. .__ Freig^ht, .$250; storage, $136 drayage, $60; insurance, -^10. • — Commission, 6% Net Proceeds — — 17. An agent's commissions were ^2500 in one month. If he transacted business on a 5% commission, how much busi- ness did he handle that month? 18. An agent sold 40000 lb. of wheat. After deducting his commission of 2%, he sent his principal -1490. For how much per bushel was the wheat sold ? 19. A manufacturer remits his agent f 3150 with which to buy cotton. How much does the agent invest if his com- mission is 5 % ? [Amount -f- (1 -|- rate) = investment.] 20. A commission mercliant remits #8000 to invest in wheat, after all expenses are paid. Charges were as follows: guaranty, 2%; drayage, $10; freight, flOO; commission, 2^%. Find the commission, and the amount actually in- vested in wheat. 21. A salesman for a wholesale house works on a commis- sion of 5%. On sales in excess of $100000 per year he gets an added 1 %. From the following report of his sales, figure his total commissions, and his net income above expenses. MISCELLANEOUS PROBLEMS 137 Month Sales Expenses Jan Feb $21673.85 27421.96 28316.40 18629.90 23718.06 30163.46 $521.60 608.35 March 560.25 July 389.40 August Sept 465.75 720.80 Totals 22. A salesman is guaranteed a salary of $2000 per year, with the understanding that he is to receive not less than 4% of his total sales. What is his income in cash in the following years ? What per cent of his sales for 1910 did he receive* as salary ? What per cent of his sales for the three years is his income for that time ? Year Sales Income 1910 $41675.00 52317.81 64500.28 1911 1912 Totals MISCELLANEOUS PROBLEMS Group 1 1. Give the fractional equivalent for the following per- centages : 5%, 6f%, 81%, 10%, 111%, 121%, 20%, 25%, 331%, 50%, 621%, 75%. 2. If ^=200 and E= .05, find P in the equation BR = P. .3. If ^=600 and P= 200, find R in the equation BR = P. 138 PERCENTAGE 4. A man bought a drug store for $ 6000 ; he gave a mort- gage for 60 % of it. What was the amount of the mortgage ? 5. A merchant failing in business was able to pay 85% of his debts. How much did he pay A, if he owed him f 4000 ? 6. A man's income is $1500 per year. His expenses are as follows : rent, $ 300 ; household, $ 500 ; heat, $ 50; light, $ 20 ; clothing, $ 200 ; miscellaneous, ilOO. What per cent of his salary does he save ? 7. A town lot is valued at -f 2000, caused by a 25 % rise in the value of real estate. If the owner valued it before the rise at 20 % more than he paid for it, what did it cost him ? 8. A house is sold for $ 10000, at a loss of 20 % of the cost. Had it been sold for $ 15000, what would have been the per cent of gain ? 9. A man bought a farm for $ 6000. Disregarding inter- est, he can pay for the property in 12 years by saving 20 % of his income. What is his income ? 10. A merchant's cost of doing business is 33J % of his gross sales ; his profits are 20% of his gross sales. If the gross sales for the year 1912 are i 50000, what per cent of his profits is his cost of doing business ? Group 2 In applying the principles of percentage to the solution of problems, as in Gain and Loss, Commission, etc., pick out B, R, and P before at- tempting to solve. 1. Supply the missing parts : Cost SEi.i.iNd Prick Gain Loss Ratk $2500 13000 15000 !|600 1 6000 20% 1 15000 6i% $2000 20% MISCELLANEOUS PROBLEMS 139 2. An article is sold for 50 j^, at a profit of 15 j^. What formula can be applied to the solution of this problem ? What two parts are given, and what is to be found? 3. Make up a problem, using the formula — = P. 4. A bought 50 hogs for i 325 ; he sold them so as to gain 16| % on the cost. How much did he receive for each hog ? 5. A trunk is manufactured at a cost of §4.75. It is sold at a profit of 40 % of the cost by an agent who charged a com- mission of 10 %. How much did the manufacturer get for it ? 6. A clotliing merchant sold a suit of clothes for f 25. If he gained 33J % on the cost, what was the cost of the suit ? 7. An automobile which cost, when new, $1350, was sold a year later for 1837.50. What was the per cent of loss ? 8. A manufacturer gained 115000 in 1911, and lost 16700 in 1912. If the capitalization was $75000, what was the per cent of gain for the two years ? 9. A commission merchant received a shipment of 6000 bu. of potatoes. He sold 16|% of them at $1.25 per bushel ; 331% at $1,121; 40% at $1.10 ; the remainder at cost. If they cost him $1 per bushel, how much did he gain? 10. A bought a stock of merchandise for $ 12000. He sold it at a gain of 20 % of the cost, but was unable to collect 20 % of the bill. What per cent of the cost did he make on the deal ? Group 3 1. Find the missing parts : List Price Net Price Discount Eate of Discount 1300 $18 $250 $50 50^ ^% $75 16|% 87 J^ 7% 140 PERCENTAGE 2. A dealer can buy the same line of goods from either of two wholesale houses. The first offers him discounts of 20% , 15%, and 5%; the second offers 25%, 10%, and 5%. Which offer is the better, and how much ? 3. A gas company offers a discount of 5^ per thousand cubic feet off the contract price of 85^ per thousand cubic feet on bills paid before the 10th of each month. What per cent of each bill is saved by taking advantage of the offer? 4. Which is greater, a discount series of 15%, 20%, and 5%, or a straight discount of 40 % ? 5. A merchant bought a bill of goods on terms 2%/10, net 30. He paid the bill 5 da. after its date, thereby saving 117. What was the face of the bill ? 6. A wholesaler sold ten bills of goods to customers, allowing on each discounts of 25%, 10%, and 5%. What were the discounts, if the bills were as follows: #135.68, #820, $56.70, 1301, 1827.32, #26.81, #443.49, #72.50, #625, #281.33? 7. The net proceeds of a bill on which discounts of 10 % and 5% had been allowed were #256*50. What was the face of the bill ? 8. An article listed at #1.20 cost a dealer 72^. If the first discount was 20 %, what was the second discount ? 9.- Goods listed at #50 are discounted 40% and 33 J % to a retailer. What discount must the retailer give off the list price in addition to 40% in order to gain 25% of the cost? 10. What is the net discount of the following bill, if paid on April 1 ? What would it have been, if paid March 1, anticipation being 1| % per month? MISCELLANEOUS PROBLEMS 141 Feb. 1, 1914. 0. J. yilLLER, Mt. GiLEAD, Ohio. In account with BURLEY & STEVENS, Inc. 2/30, net 60 Date April 1 18 18 16 20 12 pr. Boys' grade #8134 @ $2.15 pr. Boys' grade #8163 @ $2.40 pr. Boys' grade # 9143 @ 11.85 pr. Boys' grade #8163 @ $2.25 pr. Boys' grade #8143a @ |1.75 Group 4 1. Using the key in § 204, mark shoes costing $2.40 a pair so as to gain Q^^%. 2. The following price tag was put on a sweater : — '—^ . What per cent of the cost is the profit on the sweater? (Use key in § 204.) 3. Make up a key for marking goods similar to the one in § 204. Make a price tag showing cost per piece on an article costing f 24 per dozen, and a selling price per piece to gain 30%. (§206.) 4. A suit of clothes costing $6.50 is marked to sell at 'f 10, but is sold for $9.87. What per cent of the cost is sacrificed by selling below the marked price? 5. A merchant marked an article costing 50/ to sell at 75/, thinking he was making a net profit of 50%. If his cost of doing business is 20 %, at what should he have sold it in order to make actually 50 % profit ? 6. Property costing $4800 is sold to net the owner 20% profit after paying a commission for selling of 5%. For what price does it sell ? (§ 211.) 142 PERCENTAGE 7. The capital employed in a state's industries is 1 1,300,732,732, and the expense of operating is 1 1,282,845,514. What per cent of the capital is the operating expense ? 8. A farmer can buy machinery at the manufactory for $138, less 3% for cash, and it will cost him fl2 freight charges to ship it to his home. Is it better to buy at this price, or at $150 delivered at his home, less 3% for cash? 9. An agent purchased 250 bales of cotton at $12.02 per bale. What is his commission at 1| % ? 10. A real estate firm charges, as commission, 5 % of the first $2500 involved in any transaction, and 2% of any amount over the first $2500. What will it receive for sell- ing property for $4000? for $5300 ? for $1625? for $108000? for $17783.60? Group 5 1. A man bought 1000 bu. of wheat at $1.01i per bushel, and 5000 bu. of corn at 44| ^ per bushel. He sold the wheat for $1.02| per bushel, and the corn at 43 J ^ per bushel. How much was his gain or loss ? 2. An apartment building cost the owner $28000, and he estimates his yearly expenses as follows: taxes, $310; insurance, $60; water, $70; janitor, $300; fuel, $460; repairs, $120. What yearly rental must he get from each of 12 apartments to net him 6% on his investment? 3. A creditor agrees to settle a debt at 90 ^ on the dol- lar. He receives $5327.38, after paying a commission of 2 % for collecting. What was the amount of the debt ? 4. A commission merchant receives $42.18 in payment of a commission of 2% and expenses of $3.10. What was the amount of the sale ? MISCELLANEOUS PROBLEMS 143 5. A life innurance agent receives 30 % of all premiums on new business. If the average premium paid on his new business is #31.50, how many premiums will he have to secure to earn an income of f 1956.15? 6. For what must property be sold to net the owner $8730 after paying a commission of 3% for selling? 7. Property selling for 18250 pays the agent negotiating the sale 3|^% commission. If it nets the owner 12^ % profit on the cost, how much did it cost ? 8. Property costing 13100 sells for $3750. If the sell- ing agent receives a 3 % commission, what per cent of the gross profit goes to the selling agent ? 9. A retail merchant takes in $800 a month at an ex- pense of $200 a month. At what must he sell an article costing him 25 j^ in order to net 15 % ? 10. What is the total amount of commissions received by a professional shopper in a large city, who purchases tlie following goods : Bought for Article and Prick Amount Rate Com. Mrs. A 12 yd. silk @ $1.25 . . 8 yd. lace @ 87 ^ . . . 5% Mrs. B 1 brass bed, $32.50 . . 1 dresser, $21.75 . . . 1% 6% Mrs. C 6 pr. gloves @ $1.35 . . 6 pr. hose @ 85 ^ . . . 2doz. hdkfs. @ 35j^ each Mrs. D 1 umbrella @ $5.60 . . «% INTEREST 222. Interest is an allowance made for the use of money. 223. Three factors enter into interest calculations, viz., principal, rate per cent, and time. 224. Certain per cents are allowed by law. The legal rate ranges from 5% to 8% in the different states. Any charge above the rate allowed by law is called usury, and is prohibited under various penalties in different states. Note. Debts of all kinds are subject to interest from the time they become due, but not before, unless specified. 225. Interest is commonly computed on 360 da. to the year, 30 da. to the month, and 12 mo. to the year. This is called common interest. Time less than one year is found by counting the actual number of days. Long periods of time are found by compound subtractions. Hate is by the year, unless otherwise specified. 226. Interest formulas : Principal x rate x. tiipe (in years) = interest, or PIiT= I. Interest -^ (rate x, tin^e) = principal, or ■^-s^= P- Interest -f- (principal x time) = rate, or ^^= R- Interest -^ (principal x rate ) = time, or — — = T, JT til Principal + interest = amount, or P -f- PUT — A. 227. (a) Find the interest on $200 for 4 mo. at 6.%. Find the amount. PRT= J, where P = $ 200, R = .06, and T = \. 144 INTEREST 145 Substituting these values in the equation, we have 1200 X .06 X ^ = 14, interest. .$ 200 + I 4 = $ 204, amount. (b) What principal will amount to f 240 in 4 yr. at 5%? F + PET=A. A 1+RT 240 Factoring, P(\ + RT) = A, P= Substituting the values P = Solving, 240 -i- 1 . 2 = $ 200, principal. 228. Supply the missing parts : Principal Kate Time Interest Amount 1. $75 6% 3yr. — — 2. $150 4% Hyr. — — 3. $125 — lyr. $625 — 4. $300 7% — $84 — 5. — 5% Syr. $75 — 6. — H% 4 yr. — $1180 7. $ 1200 — 2 yr. 6 mo. $105 — 8. $1000 5% 1 yr. 4 mo. — — 229. Cancellation method. Find the interest on $ 350.50 for 1 yr. 2 mo. 11 da. at 6 %. 1 yr. 2 mo. 11 da. = 431 1350.50 ""lOO 481 '^360 = int. $350.50 x481 X0_ $151065.50 100 xm 60 6000 $151.0655- -^6 = $25.18 int. BUS. ARITH. — 10 da. ; this is reduced to years by dividing by 360. In ap- plying the formula PRT = I, cancel 6 into 360. In dividing by 6000, move the decimal point 3 places to the left and divide by 6. Hence, to Jind the interest at 6%, multiply the principal hy the number of days, move the decimal point 3 places to the left, and divide hy 6. 146 INTEREST Find the interest on f 7563 at 6 % for 197 da. \ im ^ \ 2521 The form here used is the most convenient 2 \ 197 ^^^ canceling and performing the other neces- yiTrTjq sary operations. Cancel 3 into 7563 and into 6; multiply 2521 by 197 without recopying; divide the result by 2, and point off 3 places 22689 2521 in the result. ) 496637 248.3185 $248.32, int. 230. To find the interest at any other rate than 6 %. Add or subtract the necessary aliquot part to the interest at 6 %. If the rate in the above problem had been 5 %, find the interest. 6 )$ 248.3185 41.3864 = int. at 1 % (1 % is J of 6 %). i 206.93 = int. at 5 % (Subtraction). Note. In all problems involving dollars and cents, carry the decimal places to the final result, then if the figure in mills is 5 or more, add 1 to the cents in the result; if less than 5, drop it. Many mistakes in bookkeeping and office work can be avoided by observing this rule. Find the interest : Principal Ratb % Time 1. i 300 6 3 yr. 3 mo. 5 da. 2. 450 4 7 mo. 6 da. 3. 248.25 5 2 yr. 9 mo. 4. 796.50 6 1 yr. 3 mo. 15 da. 5. 503.40 3 90 da. 6. 872 8 93 da. 7. 897.50 6 143 da. 8. 15000 5 3 yr. 5 mo. 17 da. 9. 5000 6 60 da. 10. 9000 4 35 da. INTEREST 147 231. eo-day method. 60 days is ^ of one year (860 da.), J of 6% = 1 %. The interest for 60 da. at, 6% is therefore 1% of the principal. The interest on |50 at 6% for 60 da. would be f0.50; therefore, to find the interest for 60 da. at 6 %, point off two places to the left of the decimal point. 232. If the per cent is other than 6 %, find the proper aliquot part of the interest at 6 %. 233. Time. If the time is other than 60 da., add or sub- tract the proper aliquot part of 60 da. Find the interest on 1750 at 5% for 80 da. $ 7.50 = interest for 60 da. at 6 % 2.50 = interest for 20 da. at 6% 6)tl0.00 = mterest for 80 da. at 6% 1.67 = interest for 80 da. at 1 % f 8.33 = interest for 80 da. at 5% Find the interest : 1. Pkinoipal 1 98 Kate % 6 Time 60 da, 2. 150 7 60 da. 3. 240 8 90 da. 4. 1450 ^ a less than 6%) 72 da. 5. 2380 61 33 da. 6. 868.40 4 120 da. 7. 1000 H 75 da. 8. 850.75 6 54 da. 9. 790 4 1 mo. 20 da. 10. 575.34 5 2 mo. 18 da. 148 INTEREST 234. Six per cent method. The interest on 11 at 6% for 1 yr. is 6^. Then it will be 1^ for 60 da., and 1 mill for 6 da. Why ? Find the interest on 12340.20 at 7 % for 2 yr. 2 mo. 15 da. 'f0.12 =mt.onilfor 2yr.at6%. .01 =int.onilfor 2mo.at6% (2mo. = J^ of 2yr.). .0025==int on $ 1 for 15da. at6 % ri5 (la. = j of 2 mo.). $0,132 5 = int. on^lfor 2 yr. 2 mo. 15 da. at 6%. 2340.20 265 00 5 300 39 75 265 6)310.076500 = int. on $2340.20 at 6 %. 51.6794 = int. on 12340.20 at 1%. 1361.7559 = $361.76, int. at 7 %. Find the interest and amount 1. Principal $758.12 Ratk % 6 2. 896.50 6 3. 3500. 4 4. 450.75 5 5. 185.54 6 6. 1000. 8 7. 3428. 6 8. 26250. 3 9. 7368.58 2 10. 596.33 H TlMB 1 yr. 2 mo. 12 da. 2 yr. 4 mo. 15 da. 3 yr. 4 mo. 18 da. 6 mo. 24 da. 1 yr. 5 mo. 6 da. 4 yr. 3 mo. 19 da. from Apr. 3 to July 25. from 5/20/09 to 11/24/12. from 2/10/04 to 5/18/06. from 1/10/11 to 12/21/12. INTEREST 149 235. Simple interest table. The accompanying table shows the inter- est on 11000 from 1 da. to 1 mo., and 1 mo. to 6 mo. at 3 % to 7%. For instance, 11000 will earn, in 20 da., 12.22 at 4%, and 12.77 at 5%. In 2 mo., 11 da., it will earn, at 7 %, 111.66 + 12.13, or ii 13.79. 236. To find what $100, $750, or any other aliquot part of $ 1000 will earn, deter- mine the amount for $1000 from the table, and take the necessary aliquot part of it. Thus: What will $275 earn in 5 mo. and 21 da. at 6 % ? $1000 earns $28.50. $ 250 earns J of this, or $7,125. DATS 3% 4% 5% 6% 1% 1 1.08 $.11 $.13 $.16 $.19 2 .16 .22 .27 .33 .38 8 .25 .33 .41 .50 .58 4 .33 .44 .55 .66 .11 5 .41 .55 .69 .83 .97 6 .50 .66 .83 1.00 1.16 7 .58 .77 .97 1.16 1.36 8 .66 .88 1.11 1.33 1.55 9 .75 1.00 1.25 1.50 1.75 10 .83 1.11 1.38 1.66 1.94 11 .91 1.22 1.52 1.83 2.18 12 1.00 1..33 1.66 2.00 2.33 13 1.08 1.44 1.80 2.16 2.52 14 1.16 1.55 1.94 2.33 2.72 15 1.25 1.66 2.08 2.50 2.91 16 1.33 1.77 2.22 2.66 3.11 17 1.41 1.88 2.36 2.83 3.30 18 1.50 2.00 2.50 8.00 3.50 19 1.58 2.11 2.63 3.16 3.69 20 1.66 2.22 2.77 3.33 3.88 21 1.75 2.83 2.91 3.50 4.08 22 1.83 2.44 3.05 3.66 4.27 23 1.91 2.55 3.19 3.83 4.47 24 2.00 2.66 3.33 4.00 4.66 25 2.08 2.77 3.47 4.16 4.86 26 2.16 2.88 3.61 4.33 5.05 . 27 2.25 8.00 3.75 4.50 5.25 28 2.83 3.11 3.88 4.66 5.44 29 2.41 3.22 4.02 4.83 5.63 Months 1 2.50 3.33 4.16 5.00 5.83 2 5.00 6.66 8.33 10.00 11.66 3 7.50 10.00 12.50 15.00 17.50 4 10.00 13.33 16.66 20.00 23.33 5 12.50 16.66 20.83 25.00 29.16 6 15.00 20.00 25.00 30.00 35.00 25 earns ^^ of $7,125, or $, .7125. $ 275 earns $7.125 + $.7125, or $7.84. 150 INTEREST EXERCISES Find the interest on : 1. 1300 for 18 da. at 5%. 2. $125 for 1 mo. 10 da. at 4 %. 3. $260 for 3 mo. 5 da. at 7 %• 4. $55 for 2 mo. at 6%. 5. $100 for 1 mo. at 2%. (2%isJof4%.) 6. 11000 for 15 da. at J %. 7. ilOOO for 23 da. at 3 J %. 8. $1500 for 4 mo. 19 da. at 41 %. 9. $825 for 6 mo. 21 da. at 51%. 10. $33.33 for 5 mo. 17 da. at 6^ %. 11. How much does a man lose if he allows $ 2000 to lie idle for 30 da., when money is worth 5 % ? 12. What is the earning power of $100 at 6% for 8 mo. 15 da.? 13. If $1800 lies idle for 1 mo. 20 da., what is the loss at 41%? 14. A man refuses to lend $ 50 at 7 % for 4 mo. What amount of interest does he sacrifice in refusing ? 15. A depositor allows $3725 to remain in the bank from May 4 to Nov. 4. If he had transferred the money to a savings account at 3^ %, how much would he have gained in interest ? 16. Find the interest on $3000 at 6% from Nov. 15, 1912, to May 10, 1913. 17. In Ohio, a Loan Co. may deduct 10 % of the loan and charge 8 % interest on the total amount. How much interest is received on a $100 loan for 4 months ? EXACT INTEREST 151 SPECIAL INTEREST METHODS 237. (a) Find the interest on $854.30 for 93 da. at 8%. Principal x time (in years) x rate = inter- \ ^854.30 est. As the time is expressed in days, divide ^^\ ^^ 31 this product by 360 (by 36 and move the deci- ^-\a \ g 2 '"^1 point 1 place to the left). Hence, divide C-H9 V ^1 ^ ^^® product of the principal, the number of ^ ^ days, and the rate, by 360. 1 <0860 Notice that the rate is per cent in pointing 51 2580 off decimal places in the result. In the illus- 3)52.96(360 tration, point off 5 places, 2 for the cents in the 1kl7 655 int principal, 2 for the hundredths in the rate, and 1 for canceling the in 360. (ft) Find the interest on $658 at 5% for 6 mo. The interest at 5 % for 6 mo. is the same as the 4)$ 65.80 interest at 10% for 3 mo. Hence, to find the interest $16.45 int. at 5%, point off 1 place to the left, and find the aliquot part ^ the time is of one yr. ((?) Find the interest on $ 300 at 8 % for 6 mo. $300 .04 Double the time and take | the rate, or double the rate and take h the time, as in (a). $ 12, int. (d) Find the interest on $212.56 for 2 mo. 18 da., at 6%. $ ^12. 56 g-j^pg ^j^g interest on ^ 1 at 6 % is I ^ per '01^ month, or |^ of a mill per day, one half the 63768 number of months, and one sixth the num- 2 12.56 ^^^ ^^ days may be written as the cents $2.76328 = $2.76, int. ^°^ ™^^^' ^^ *^'^ multiplier. EXACT INTEREST 238. Exact interest is computed on a basis of 365 days to the year. Exact interest is rarely used except in govern- ment calculations. 365 days is 5 days more than common 152 INTEREST interest. Five days is y^^ of 365, therefore, to find the exact interest, find the interest by any of the above methods and subtract y^^ of it. Find the exact interest : Principal Rati TiMR 1. i700 6% 80 da. 2. $800 4% 75 da. 3. $975 2% 15 da. 4. i 812.25 6% 144 da. 5. $7368.90 4% 13 da. 6. A savings bank pays 4% interest on its deposits. It lends money at 6%. If its deposits amount to #237458.50 and its loans amount to $ 192546, what is its gain per year ? (Exact interest paid yearly.) 7. A manufacturer ordered a bill of goods amounting to f 3548.60. The terms were 3 mo., 5 % off for cash. He paid cash. Find his gain, using 6 % simple interest. 8. A corporation is allowed 1 J % annual rate on its aver- age daily balance in a bank, the same to be credited every month. Fill in the allowance by simple interest. Month AvEBAOB Daily Balance Allowance Jan Feb March April May June July Aug Sept Oct Nov Dec $73210.90 61740.89 125608.34 53217.98 90020.07 70663.24 81210.37 53721.62 74889.75 96271.49 163618.52 181241.13 COMPOUND INTEREST 153 COMPOUND INTEREST 239. Compound interest is interest upon principal and added interest. Interest is added at stated periods, 3 months (quarterly), 6 months (semiannually), or 12 months annually). 240. Many transactions are computed by compound inter- est. Savings banks and insurance companies use this method, and returns on bond investments are reckoned by compound interest. 241. To find compound interest and amount. Find the compound interest on I 2000 for 3 yr., at 6 %, interest compounded yearly. Solution 1 $ 120, interest for the first year. I 2000 + I 120 = 12120, principal for second year. $2120 X 6% = $127.20, interest for second year. $2120 + i 127.20 = I 2247.20, principal for third year. •f 2247.20 X 6% = $134.83, interest for third year. $120 + $127.20 4- $134.83 = $ 382.03, compound interest. Solution 2 $2000 X 6% = $ 120, interest for first year. $ 120 X 6 % =$7.20, interest on interest. $ 120 + $ 7.20 = $ 127.20, interest for second year. $127.20 + $120 = $247.20, compound interest for two years. $247.20 X 6 % = $14.83, interest on interest. $120 4- $14.83 = $134.83, interest for third year. $120 4- $127.20 + $134.83 = $382.03, compound interest. Note. Solution 1 is generally used. 154 INTEREST 242. Compound interest is generally computed by using the compound interest table. Table showing Amount of $ 1 at Compound Interest for Any Number OF Years not exceeding Ten Yr. 2% 8% 8i% 4% c% 1 1.0200 0000 1.0300 0000 1.0350 0000 1.0400 0000 1.0600 000 2 1.0404 0000 1.0609 0000 1.0712 2500 1.0816 0000 1.1236 000 3 1. 0012 0800 1.0927 2700 1.1087 1787 1.1248 6400 1.1910 160 4 1.0824 3210 1.1255 0881 1.1475 2300 1.1698 5856 1.2624 770 5 1.1040 8080 1.1592 7407 1.1876 8631 1.2166 52J)0 1.3382 256 6 1.12016242 1.1940 5230 1.2292 5533 1.26.53 1902 1.4185 191 7 1.1480 8567 1.2298 7387 1.2722 7926 1.3159 3178 1.5036 303 8 1.1716 5038 1.2667 7008 1.3168 0904 1.3685 6905 1.6938 481 9 1.1950 9257 1.3047 7318 1.3628 9735 1.4233 1181 1.6894 790 10 1.2189 9442 1.3439 1638 1.4105 9876 1.4802 4428 1.7908 477 Note. This is only a small sectiou of a compound interest table. Tables giving all per cents for a long period of time can be secured at any savings bank. 243. To find compound interest by the table : 1. Payable annually, multiply the principal by the amount (shown in the table under the proper rate and time) less f 1. 2. Payable semiannually, take J the rate and twice the time, less f 1. 3. Payable quarterly, take J the rate and four times the time, less $ 1. Note. ^1 is subtracted to find the compound interest; the table gives the compound amount. 244. If the time should be any time not shown in the table, multiply the amounts for the proper aliquot parts of the time ; e.g.^ to compute the compound interest for 20 yr. at 6 %, multiply 1.7908477 by itself, giving 3.2071355. SINKING FUNDS 155 Find the compound interest on JB^tOO for 5 yr. at 3J %. See compound interest table, § 242. The amount in the 3^% cohimn opposite the 5th year is $1.18768631. Since this is the amount, the compound interest on $ 1 is 1.18768631. Then the com- pound interest on $400 will be 400 times 1 .18768631, or $75.07. 400 X $.18768631 = $75.07 Find the compound interest (by table) Pbincipal Rate Time 1. 1 600 3% 8 yr. 2. $1500 6% 4 yr. 3. $ 500 4% 3 yr. (semiannually) 4. 11240 8|-% 2 yr. 5. $ 350 4% 3 yr. (quarterly) 6. $ 590 2% 8yr. 7. $ 800 6% 5 yr. (quarterly) 8. 11000 81% 9yr. 9. $2370 8% 4yr. 10. $5760 6% 6 yr. (semiannually) 11. $8320 4% 2 yr. 12. $5980 2% 7yr. SINKING FUNDS 245. A sinking fund is a sum set aside each year, at com- pound interest, sufficient to meet a certain obligation at its maturity. Cities often make public improvements by bor- rowing money and issuing bonds therefor. Tiie bonds are payable in 5, 10, 15, or more years, as the case may be. To meet these bonds at maturity a sinking fund is estab- lished. A series of equal payments is called an annuity. 156 INTEREST 246. Table showing annuity of $ 1 at the end of each year from 1 to 10 yr. : Period 8% 4% 5% 6% 1 1. 1. 1. 1. 2 2.03 2.04 2.05 2.06 3 3.0909 3.1216 3.1625 3. 1886 4 4.183627 4.246464 4.310125 4.374616 5 6.309136 6.416323 5.526a31 6.637093 6 6.468410 6.632976 6.801913 6.976319 7 7.662462 7.898294 8.142008 8.393838 8 8.892336 9.214226 9.M9109 9.897468 9 10.169106 10.582796 11.026564 11.491816 10 11.463879 12.006107 12.677893 13.180796 247. To find an annuity: 1. A certain city makes improvements at an expense of #300,000 and sells municipal bonds maturing in 10 yr. To pay for them, at 3 % interest, what sum must be set aside each year to meet the bonds at maturity ? An annuity of $ 1 for 10 yr. at 3 % is $ 11.463879. Then it will require as many dollars to amount to ^300,000 as ^11.463879 is contained times in $300,000, or $20169.16 Ans. 2. City bonds to the amount of #500,000, maturing in 10 yr., were issued. A sinking fund earning 5% was provided. What should be the annual investment in the sinking fund ? 3. For the erection of a city hall §100,000 municipal bonds, payable in 8 yr., are issued. What amount must be laid aside each year at 4% compound interest to redeem the bonds^ at maturity ? 4. A steel company sells 8500,000 worth of 10-yr. bonds, and #100,000 worth of 20-yr. bonds. The sinking fund earns 4%. What amount must be provided each year to retire both issues at maturity? BANKS AND BANKING 248. Practically all business is done, directly or indirectly, through banks ; they are the money and credit centers of the community. Their most important functions are : (1) To receive funds for deposit. (2) To make loans. (3) To transfer funds. (See Exchange, p. 201.) By " funds " is meant money, checks, or any other form of credit. The depositor really buys bank credit which he can order transferred as he wishes. The credit department, which handles the loans, is one of the most important departments in a bank. In this depart- ment a complete record is kept of the applicant's solvency, viz. : (1) An application blank, filled in by the applicant, stat- ing his financial condition. (2) The depositor's average balance in the bank, which helps to determine the amount of the loan. (3) The applicant's liabilities, both as maker or endorser of notes. 249. Although a bank is organized by individuals, its business is of such a nature that it is subject to very care- ful regulation by law, both as to its organization and its methods of doing business. There are six kinds of banks, viz. : (a) National banks are chartered by tlie federal govern- ment. They are authorized to issue money (bank notes), and are limited as to the kinds of loans they may make. 167 158 BANKS AND BANKING (6) Federal reserve banks are central banks in the national banking ^\stem. They are authorized to issue money (fed- eral reserve notes), and most of their business is transacted with other banks. (c?) State banks are organized under state laws ; in many details they are like national banks. (^d) Savings banks receive money in small amounts, and usually pay interest on deposits. (g) Private banks are companies or individuals doing a banking business under a private name. (/) Trust companies generally have two departments: (1) a banking department doing a general banking business ; (2) a trust department which acts as executor of estates, guardian of minors, etc. 250. Banks receive for safe-keeping valuables such as stock certificates, bonds, insurance policies, and the like. Valu- ables of this kind are usually kept in safety deposit boxes which are rented to individuals. 251. The character of the bank is indicated by its name, as First National, Kent Savings, City Trust and Savings, First State, etc. 252. Deposits. An individual may deposit funds in a bank by (1) opening an account, and (2) taking out a certificate of deposit. (1) A checking account is one in which the funds on de- posit are subject to withdrawal by check. The depositor fills out a deposit slip, and the amount de- posited is entered by the bank clerk (teller) in the bank or pass book carried by the depositor. This entry is a record of the transaction for the depositor. The bank, however, opens an account for the depositor in its ledger, and keeps a daily record of deposits and withdrawals. The amount on deposit is called the depositor's balance. BANKING 159 Deposit Slip FIDELITY TRUST COMPANY DEPOSITED BY Canj Bros. St. Louis, Mo., Mar. 1915 PLEASE LIST EACH CHECK SEPARATELY Dollars Cents Currency 121 Gold Silver A. a Co. CHECKS 31.26 13 20 A. a Co. 20.15 M. L. T. 108.26 F. Hall 7.60 167 Total 27 801 47 A savings ac- count is one in which the funds on deposit draw inter- est at an agreed rate (usually 3 or 4%), and are sub- ject to withdrawal only on presenta- tion of the pass book. Accompanying is a form of pass book used in opening a savings account : It will be no- ticed that with- drawals as well as The Security Savings Bank Co. Withdrawals Deposits Balance L^^. f Jlc oo Sl -) o fV" i&^, (Ely^ CHIti^^na ^aimnal iBank AmtiltimitHi Total A»iHlii$Clutt Bnl rant font |53 I \i 3jif_r_\ X/a-rrv**^ (Jryp*,^ The " stub " of the check is for the convenience of the depositor in keeping a record of his transactions with the bank. When would the balance, as shown on the stub, differ from that in the bank's ledger ? 254. Unless withdrawn, interest is allowed on savings de- posits twice a year, on Jan. 1 and on July 1 ; thus com- pound interest is paid. No interest is paid on parts of a dollar, nor usually on any money not left during the entire interest period. Savings banks may demand 30 days' notice of the with- drawal of funds. 1. In the savings account of Louis Cooper, p. 159, enter the proper interest due him at 3% on July 1, 1918, and on Jan. 1, 1914, and compute his balance on Feb. 6, 1914. 2. The City Railway and Light Co.'s balance in the Fourth National Bank on Dec. 9 is 134,786.49. The com- pany makes a deposit of i 18,726.12, and draws a check for its weekly pay roll for $20,112.47. What is the company's balance at the opening of the bank on Dec. 10 ? 3. What is the value of a certificate of deposit for $350 dated Feb. 23, 1912, bearing interest at 3%, on Dec. 23, 1912? What is its value on June 15, 1912? June 15, 1913? 255. An indorsement is anything written on the back of a commercial paper, which refers to the paper itself. BUS. ARITII. — 11 162 BANKS AND BANKING 256. Checks, certificates of deposit, and other forms of commercial paper may be transferred from one person to another by indorsement, unless drawn to the contrary ; they are called negotiable paper. The omission of the words " or order," or "to the order of," makes paper nonnegotiable. Such indorsements may read : " Pay to the order of ," " Pay to or order," " Pay to bearer," etc. The follow- ing indorsements, supposed to be written on the back of the check on p. 161, show (on the left) the indorsement used in cashing the check ; (on the right) the indorsement used in transferring the money to Charles Elwert. Henry Hawkins Pay to Charles Elwbrt or order Henry Hawkins 257. Postal savings banks have been established by the United States government at certain post offices. Postal savings certificates are issued in denominations of f 1, 12, 85, f 10, 820, and 150, each bearing the name of the depositor and other necessary information. Deposits up to 8100 monthly are allowed to any one person. Interest at 2 % annually is paid on each certificate left on deposit for a full year. Compound interest is not allowed. United States bonds, bearing interest at 2J%, to any amount not exceeding 8500 to one person, will be issued to a depositor upon surrender of certificates. 258. Loans and discounts. Banks lend money on notes, the payment of which is secured by some valuable assigned as security or collateral. Loans are made on ''collateral notes," on "judgment notes," and the like. Forms of notes differ for different kinds of business. LOANS 163 Notes may be secured in the following ways : 1. By the indorsement of one or more persons who thus become liable for payment. 2. By the deposit of collateral. 3. By the mortgaging of property. 'H^.-y'f ^^yv Ji^_ ^itt^ "^^^yo y y/^^yi^y^f^//:^^yy^pfi>iZ^J/^//^j^^ PROTEST WAIVED Q)zye ^^^^^^^^Ld Jj^mi^ ^^/ ^^'^^ ^^^-y Form of Note 260. Loans may be classified as follows : {a) Investment loans, made upon collateral security which can readily be turned into cash. (5) Industrial loans, made to manufacturers, merchants, and farmers for discounting bills, extending trade, moving crops, etc. (c) Capital loans, made to manufacturers and merchants who want permanent capital for starting a business and ex- pect to repay the loans from the earnings of the business. (c?) Mortgage loans, made usually on real estate as security. 261. Most banks make short-time loans, the notes usually falling due in 30, 60, or 90 days; or demand loans which may be called in (payment demanded) at any time. Long-time loans are made by savings banks and by trust companies. Most of the money lent on mortgage security is lent b}^ individuals or by insurance companies. 164 BANKS AND BANKESTG 262. Organizations known as Building and Loan Associa- tions make loans on real estate, especially for building pur- poses. In order to secure such a loan one must become a stockholder in the association, the payments for stock and the repayment of the loan being made in weekly or monthly installments. 263. The date on which a note or obligation becomes due and payable is called the date of maturity. BANK DISCOUNT 264. Bank discount is an amount deducted from the face of a note as a consideration for the use of the money before matuiity. If the note bears interest, the discount is deducted from the face of the note plus the interest. 265. The proceeds is the amount left after the discount has been deducted. 266. Time of discoimt is the actual time from the date the note is discounted to the day of maturity. 267. Interest is figured by calendar years, months, or days, according to the wording of the note or draft. Bank discount is reckoned on actual time for parts of a year, not counting the day of discount. Arkansas, Mississippi, Oklahoma, Soutli Dakota, South Carolina, and Texas allow 3 days of grace beyond the date of maturity on notes and drafts; Massachusetts, Minnesota, New Hampshire, and Rhode Island on sight drafts. (See Exchange, p. 201.) Note. Problems in bank discount are based upon percentage and common interest 'No days of grace are considered in this text. BANK DISCOUNT 165 EXERCISES 1. Find the bank discount and proceeds of the following note, which was discounted Jan. 6, 1913, at 8%. ^^Tz^^^^y&rada- "^^ > /^'-^ J^_ C/^t^^v^ -rr.t-,.jt-^ c^/4Cfr(////eYtfiiikMffmfe//^aHiue^/raef'/^ idL- ^om/Je^/r^/i/zy /<'/%/?.{m^z^ /y '*^'^^"*^ — — ^-"/^- ^^-y -^ "^^^^ ^-7^^. '^^^ " -^ • Q)^h£m PROTEST WAIVED^^,^^ Solution Nov. 1, 1912 + 4 mo. = March 1, 1913, date of maturity. Time of Discount Iktf.kest 31 $5680.10, principal 6 56.804, interest 60 da. , ^ ^^ :| 25 da. in Jan. 56.804, interest 60 da 29 da. in Feb. $5794.01, amount to be discounted 1 da. in March. 55 da. $57.94, discount for 60 da. at 6% 4.828 , discount for 5 da. at 6% 53.112, discount for 55 da. at 6% 17.704 , discount for 55 da. at 2% 70.82, discount for 55 da. at 8% $5794.01 - $70.82 = $5723.19, proceeds. Find the discount and proceeds of : 2. $1500 with interest at 4% for 6 mo. from April 10, discounted June 8 at 6%. 3. 8875 with interest at 6% for 90 da. from Jan. 3, dis- counted Feb. 5 at 7%. 166 BANKS AND BANKING 4. 83100 without interest for 1 yr. from July 7, 1914, discounted Dec. 10, 1914, at 6%. 5. 14750 with interest at 41 % for 120 da. from June 11, discounted Aug. 1 at 7 %. 269. Hankers make use of a table for finding tlie number of days between dates. Time Table From Jan. Feu. Mar. Apr. May To JiNE Jilt Acq. Sept. Oct. Nov. Dec. Jan. 365 31 69 90 120 151 181 212 243 273 304 3:^ Feb. 334 365 28 59 89 120 150 181 212 242 273 303 Mar. 306 337 366 31 61 92 122 153 184 214 245 275 Apr. 275 306 334 365 30 61 91 122 153 183 214 244 May 245 276 304 335 365 31 61 92 123 163 184 214 June 214 245 273 304 334 365 30 61 92 122 153 183 July 184 216 243 274 304 335 365 31 62 92 123 153 Aug. 153 184 212 243 273 304 334 365 .31 61 92 122 Sept. 122 153 181 212 242 273 303 334 365 30 61 91 Oct. 92 123 161 182 212 243 273 304 335 365 31 61 Nov. 61 92 120 151 181 212 242 273 304 334 .365 30 Dec. 31 62 90 121 151 182 212 243 274 304 335 305 Explanation of Table. From Jan. 10 to Jan. 10 is 365 da.; from Jan. 10, 1912, to Jan. 24, 1913, is 36.5 da. + 14 da. ; from June 6 to Nov. 30 is 177 da. (24 + 153). Note. When banks discount a paper, they often charge for their serv- ices a certain per cent, ranging from ^^ % ^o i %, on the face of the paper, or the face phis the interest; there is usually a minimum charge of 10^-. This charge is called collection. The bank discount plus the collection charge is the total charge. BANK DISCOUNT 167 EXERCISES Find the bank discount and proceeds on the following. Use the table (§ 269) for finding the number of days. Face Date Date Due Kate Date Discounted Ratk Discounted 1. 1 700 1/ 2/13 7/ 2/13 5% 3/ 4/13 6% 2. 1460 9/ 3/11 11/ 3/11 6 10/21/12 6 3. 1500 7/ 5/12 1/ 5/13 7 10/12/12 6 4. 50 10/31/12 11/30/12 6 11/ 5/12 ^ 5. 3146.75 1/24/13 5/24/13 6 3/20/13 8 6. 8154.09 2/27/13 10/27/13 4 6/12/13 6 7. 321.44 3/15/13 4/15/13 5 4/10/13 7 8. 750 5/22/13 8/22/13 H 7/31/13 ^ 9. 1000 1/2/12 1/ 2/14 6 11/24/13 6 10. 150 2/ 3/12 2/ 3/13 8 1/ 6/13 7 11. The following note was discounted Jan. 1, 1913, at fo ; collection, ^ %, computed on the face of the note. Find the bank discount and proceeds after allowing for collection. 6 $3259 Nashville, Tenn., Dec. 1, 1912. Sixty days after date, for value received, we promise to pay Wm. A. Pierson or order, Thirty-two hundred fifty-nine no/100 dollars, at the Traders' National Bank, in Nashville, Tenn., with interest at the rate of eight per cent per annum after maturity until paid. Carroll Bros, and Co. 12. Find the proceeds on a 3 mo. note for 8175, interest at 8 % from Oct. 5, discounted Oct. 16 at 10 % ; collec- tion, 1%. 13. A 90-da. draft for f!350 was discounted Jan. 3, 1913, the day of acceptance, at 6%; collection, ^%. Find the proceeds. 168 BANKS AND BANKING PRESENT WORTH AND TRUE DISCOUNT 270. The present worth of a debt is the sum which, put at interest, will produce the value of the debt at maturity. 271. The true discount is the difference between the amount due at maturity and the present worth. Note. Bank discount is rapidly replacing present worth and true discount. 1. Find the present worth and true discount of a debt of $500, due in 6 mo., if the rate of discount is 6%. il, with int. at 6% for 6 mo., will amount to il.03. If 'f 1 amounts to $1.08 in 6 mo. at 6%, it will take as many dollars to amount to 1500 in that time as $1.03 is con- tained in 1500, or 485.44. Then $485.44 is the present worth. $500 - $485.44 is the true discount, $14.56. Find the present worth and true discount of : 2. $1700 for 3 mo. at 4% 3. $2500 for 4 mo. at 5% 4. $5000 for 10 mo. at 6% 5. $900 for 2 yr. and 6 mo. at 8% 6. What is the difference between true discount and bank discount on a note for $1000 for 8 mo. at 8%? 7. Find the simple interest, true discount, and bank dis- count on a note for $8000 for 6 mo. at 6%. 8. A dealer's price on an automobile is $1200, 4 mo. time, or $1150 cash. At what per cent does he figure money ? 9. A bill of goods is invoiced at $2500 on 3 mo. credit. For how much must a note be drawn with interest at 6 % to cancel the debt? PARTIAL PAYMENTS 169 10. What note at 6% interest must be given March 1 to cancel the following bill at maturity? New York, N.Y., 2/18/12. C. H. Garrjson Detroit, Mich. Salesman C. H. Order taken 8/30. In account with 2/10, net 60 March 1 dating PHILLIPS^ONES COMPANY Ul 3 doz. @ 4.50 each 0U3 1 6/12 " @ 4.50 " 898 4 6/12 " @ 4.50 " 898 B 1 6/12 " @ 4.25 " BR H91 1 3/12 " @ 8.50 " SEl 1 9/12 " @ 8.50 " B VC61 1 3/12 " @ 8.50 " Total PARTIAL PAYMENTS 272. Partial payment is part payment on a note, draft, or other form of obligation. When a payment is made, an indorsement is entered on the back of the paper, somewhat after the following form : Rec'd on the within note Jan. 1, 1914, 150 March 2, 1914, .^75 Note. The ordinary practice, especially with banks, is to take sepa- rate notes for whatever payments are agreed upon at the time the loan is made. Thus, if a borrower wishes to borrow ^150 for 3 mo., and repay f 50 a month, the bank would probably take 3 notes for $ 50 each, one due in 30 da., one in 60 da., and one in 90 da. 273. The two methods in general use in computing partial payments are the United States Rule and the Merchants' Rule. 170 BANKS AND BANKING 274. The United States Rule is authorized by the United States Supreme Court, and is used when the partial pay- ments are made on interest-bearing notes having 1 j^r. or more to run. (a) Interest must not be paid on interest. ' (6) Accrued interest must be paid before the payment can reduce the amount of the debt. 1. What was the balance due on a note for 82000 dated June 10, 1911, to run 1 yr. with interest at 6%, the fol- lowing payments having been made: Aug. 3, 1911, 1500; Dec. 15, 1911, $25; Feb. 3, 1912, $500? (Compound time is always used.) Solution Face of note $ 2000. Int. from June 10, 1911, to Aug. 3, 1911 17.6 7 Amount due Aug. 3, 1911 2017.67 Payment Aug. 3, 1911 500. Balance due Aug. 3, 1911 1517.67 Int. from Aug. 3, 1911, to Dec. 16, 1911 . . . . $33.39 As this amount (833.39) exceeded the amount of the payment, int. and payment must be carried over to the next payment Int. from Dec. 15, 1911, to Feb. 3, 1912 .... 12.14 Total int. due 45..53 Amount due Feb. 3, 1912 1663.20 Total payment (825 + $500) 525. Balance due Feb. 3, 1912 1038.20 Int. from Feb. 3, 1912, to June 10, 1912 12.98 Amount due at settlement 81060.18 Find the balance due on each of the following notes : Datk Face TiMK TO Run Rate Payments 2. 3. Sept. 1, 1909 Feb. 5, 1900 $10000 • 82000 4yr. 2yr. 6% 4% March 1, 1910, 8300 Dec. 1, 1910, 850 Junel, 1911, 8400 May 1, 1900,8200 Aug. 1, 1901, 8 10 _ PARTIAL PAYMENTS 171 275. The Merchants' Rule, while not a strict rule of law, is generally used when the interest-bearing note runs 1 jr. or less. (a) The note bears interest until date of settlement. (6) Each payment bears interest from its date until date of settlement. Note. Some business men use exact time, while others use compound subtraction. 1. Face of note,.ilOOO; time, 9 mo. from Jan. 1; rate, 6%. Indorsements: Feb. 1, 1100; June 1, $200. What amount was due at maturity? (Compound time.) Condensed Form of Solution Date Face 'JiME Kate Interest Amount Jan. 1 flOOO 9 mo. 6% 145 00 .| 1045 Feb. 1 100 8 mo. 0% 4.00 $104 June 1 200 4 mo. «% 4.00 204 Balance due 787 1 1045 f 1045 Find the balance due on each of the following, using com- pound subtraction to find the time in the 2d and 3d, and exact time in the 4th and 5th. ' Date Face Time Eate Indorsements 2. Feb. 1, 1912 $4000 10 mo. 6% April 3, 1912, $500 June 1, 1912, 100 Oct. 10, 1912, 200 3. Jan. 25, 1910 1500 7 mo. 7% Feb. 18, 1910, 150 July 2, 1910, 350 4. Aug. 9, 1908 850 5 mo. 6% Sept. 28, 1908, 75 Nov. 5, 1908, 60 Jan. 1, 1909, 100 5. Dec. 10, 1903 2000 9 mo. 5% Jan. 20, 1904, 200 Feb. 25, ie04, 300 172 BANKS AND BANKING MISCELLANEOUS PROBLEMS Group 1 1. From the equation PRT= /, find R, 2. By applying the formula, find / in the following : PR T $260. 6% lyr. 720. 4% 6 mo. 8400. 6% 3 mo. 568.72 7% 90 da. 85.60 8% 4 mo. 3. By the cancellation method find the interest on the following $98.60 for 72 da. at 6% $321.05 for 90 da. at 5% $426.17 for 35 da. at 7% $1260.09 for 63 da. at 6% $815. for 3 mo. at 8% 4. By the following : 60-da. method find the interest on the $621.50 for 4 mo. at 6% $283.17 for 5 mo. at 5% $12620.70 for lyr. at 4J% $84.62 for 75 da. at 3%" $161.13 for 112 da. at 3J % 5. By the 6% method find the interest on the following $378.50 from Feb. 2, 1913, to April 10, 1913, at 6% $216.06 from 11/3/12 to 2/1/13 at 8% $7615.83 from Oct. 23, 1912, to Jan. 13, 1913, at 5% $70 from 1/3/13 to 4/19/13 at 7% $169.69 from 1/15/13 to 2/28/13 at 4 % MISCELLANEOUS PROBLEMS 173 6. By the interest table, p. 149, find the interest on the folio wmg : ^^^^^ ^^^ g ^^^ g ^^^ ^^ ^1 ^^ 1300 for 3 mo. at 6% f 279 for 1 mo. 15 da. at 5% 11628 for 1 yr. 2 mo. 11 da. at 5^% $65 for 36 da. at 7% 7. Find the exact interest (p. 151) on : 11427 for 48 da. at 6% 1216.60 for 37 da. at 6^% i98.54 for 3 mo. 12 da. at 5 % 1627.43 for 1 mo. 15 da. at 41% f 13261.82 for 1 yr. 2 mo. 27 da. at 7 % 8. Find, by the most convenient method for each, the interest on the following : #3726.81 from April 5, 1911, to June 3, 1913, at 6% 1281.54 from Oct. 13, 1912, to Jan. 5, 1913, at 7% $2200 from July 3, 1910, to Aug. 6, 1914, at 8% •$75 for 7 mo. 8 da. at 2^% $125 for 9 mo. 22 da. at 4% 9. A man lent X 2159 5s. Qd. at 6%. Find the interest yearly. 10. How much money must I invest at 5% in order to receive a semiannual income of $1268.50? Group 2 1. A man builds a house costing $3200. He pays $1400 cash and gives three equal notes for the balance due, payable in 1, 2, and 3 yr. respectively, with interest at 5%. If he pays all interest due at the end of each year, what amount does he pay at the end of each year in paying off the in- debtedness ? 174 BANKS AND BANKING 2. A merchant bought a bill of goods on the following terms : 3 % cash, net 90 da. At what rate can he afford to borrow .money in order to pay cash ? 3. A bank pays 3% interest on deposits amounting to 11628,453.27; its loans average $1,462,817.61 at 5%, and 11,316,478.55 at 6%. What is the bank's yearly profit? 4. A city's bonded debt is $1,031,000. At 4%, what interest does it pay annually ? 5. A merchant bought #5000 worth of goods, terms net 60 da. At the end of the 60 da. he had sold 75% of the goods at a profit of 20 % on the cost, and the rest of them at cost. How much did he gain ? 6. A gave his 60-da. note to a bank for $200 at 6% interest. If the bank deducts the interest in advance, how much does he receive for the note ? 7. On April 1, 1910, A bought a bill of goods amounting to $1500. He gave his note for the amount, interest at 5%. How much did he pay at settlement, Nov. 15, 1910 ? 8. A company bought 1000 bales of cotton at $11.91 per bale, giving a 30-da. 5J % note in payment. How much interest did it pay at maturity ? 9. A farmer bought an 80-acre farm for $50 per acre. He paid $800 down, and gave four equal notes for the balance due, payable in 1, 2, 3, and 4 yr. respectively, interest at 6%, payable annually. How much did he pay at the end of each year until all the notes were paid ? 10. A railroad company buys 1000 gondola cars at $1000 each, giving in payment 20 series of 50 notes to each series, all dated July 1, 1913. One series matures at the end of each 6 months, and all bear interest at 6% per annum from date, interest payable semiannually. What amount must the company pay at the end of the first 6 months ? at the end of the second 6 months ? MISCELLANEOUS PROBLEMS 175 Group 3 1. A city authorizes the issuance of 1350,000 10-yr. bonds at 4% for the purpose of building a viaduct. What amount must be paid to a sinking fund earning 3| % in order to redeem the bonds at maturity? (Use table, page 156.) 2. A depositor has $ 1000 in the savings bank at 3 % interest. He draws out the money and buys a lot which he sells 6 mo. later for i)1100. If he pays il5 taxes on the lot, and #20 selling commission, what per cent does he make on his $1000 in excess of what it would have earned for him if left in the bank? 3. An electric light company borrows, on a 5-J% bond issue, #100,000 for extensions and improvements. What interest does it pay annually on the debt, and what amount must it deposit with the trustee of the sinking fund earning 4| % to redeem the bonds in 5 yr. ? 4. What is the difference between a checking and a savings account at a bank ? 5. The bank clearings in New Orleans on a certain day were 11,841,109, as against 11,524,060 for the corresponding day the year before. What was the percentage of increase ? 6. A coupon certificate of deposit for |600, drawing interest at 3%, is dated Oct. 28, 1912. If all the coupons are left attached, what is the value of the certificate on Aug. 3, 1913 ? 7. A cotton dealer sold 700 bales of cotton at $12.08 per bale, and accepted in payment a 90-da. note bearing interest at 5%. If he discounts the note at his bank at 5%, how much does he receive for it ? / 8. A bank discounts a 60-da. draft at 6%, allowing 5 da. for collection and return. If the face of the draft is $675.84, what are the proceeds, there being no charge for 176 BANKS AND BANKING collection ? (Time for collection and return must be added to time of draft.) 9. A jobber buys goods from a manufacturer to the amount of r^ 27,600, and gives his note in payment for 4 mo. at 5%. The jobber sells the goods to customers at a profit of 12 J % on the cost, taking 60- da. 6% notes in payment. At the end of 60 da., receiving the money on his customer's notes, he discounts his note to the manufacturer at 6 %. What is his profit on the transaction ? 10. A, holding B's 7 % 60-da. note for 1 1200, has it dis- counted at the bank for the full time at 6%. At the end of 30 da., having idle funds, A buys the note back from the bank, discounting it at 6%. What net amount does A receive in interest ? Group 4 1. A retail merchant sold out a stock of goods and in- vested 70 % of the money in a farm which paid him a yearly rental of $600. If the rate of income on his farm invest- ment is 8J %, for what amount did he close out his stock ? 2. The profits of a manufacturing business the first year are 40% of the capital employed; 75% of this gain is rein- vested in the business for the 2d year. The 2d year shows a profit of 45 % on the capital employed, and all this profit is allowed to remain in the business for the 3d year. What per cent of the original capital does the business start with for the 3d year ?, 3. What rate of commission is charged for selling goods for f 562.25, the net proceeds of the sale being 1541.17? 4. A bought a bill of goods to the amount of $640, terms 3%/10, net 30. In order to secure the 10-da. discount he discounted his 60-da. note at the bank at 6%. Find the face of the note. MISCELLANEOUS PROBLEMS 177 5. Find the difference between the simple interest and true discount on 12500 for 90 da. at 5%. Find the dif- ference between simple interest and bank discount. 6. If the John F. Price Co. accepted Frank Mueller's 60-da. note in payment of the following bill, for what amount could it be discounted at the bank, interest being at the rate of 6 % ? Sept. 20, 1914. Frank Mueller Ogden, Utah. In account with The JOHN F. PRICE CO. suit doz. hdkfs. @ 2 for 25^ pr. sacks @ 3 pr. for $ 1 shirts @ $1.76 each . ties @ $ 4 per dozen 7. What is the difference between the true and bank discount on 1 3000 for 150 da. at 6 % ? 8. Find the balance due at maturity by United States Rule on the following note : Face of note, $3500; date, Jan. 10, 1913; time to run, 2 yr. 6 mo. ; rate of interest, 6 %. Indorsements are as follows : 9/25/13, 1400; 11/1/13, 1500; 2/8/1914, |200; 6/15/14 •11000. 9. On his son's 11th birthday, a man deposited in a savings bank a sum sufficient to amount to tf 3000 on the son's 21st birthday. If the bank credits 4 % interest annu- ally, how much was deposited ? (§ 242.) 10. Find the interest on £> 200 10s. bd. for 2 mo. 15 da., at 6 %. BUS. ARITH. — 12 178 BANKS AND BANKING Group 5 1. A contractor agrees to build a bridge for f 15000. He employs 15 men for 120 da. at $2 per day each, 1 engineer for 108 da. at $5 per day, 2 teams for 123 da. at §4.50 per day each. Materials are billed to him at a discount of 2|-%, the bills calling for $^7186.20. In order to pay his men promptly, and to discount his bills, the contrac- tor borrows money from the bank at 6 % as follows : $ 2500 for 1 mo., 12500 for 2 mo., and 13000 for 3 mo. His surety bond for the safe completion of his contract costs him $225. What is the profit on tlie contract? 2. A man borrowed $50 and agreed to pay back $10 a month for 6 mo. Ignoring interest on the monthly pay- ments, at what rate does he pay interest on the loan ? 3. A man invested $5000 on Jan. 15, buying stocks which he sold later for $5300. He reinvested this amount, and sold out on May 2-4 at an advance of 2 % on his in- vestment. What rate of income lias his money earned ? 4. A jobber gives a customer a discount of 10 % from list prices, with an additional discount of 2 % for cash. What was the amount of the bill at list prices if the cus- tomer paid $ 2364.85 cash ? 5. A bill for $2534.20 was due a manufacturer Jan. 2. He carried the account until May 15 without interest. If money is worth 5 %, this was equivalent to what discount ? 6. A farmer owns a farm worth $ 15000 with its stock and implements. His accounts for a year are as follows : Dr. Cb. $1000, labor, self and wife $ 1400, sale of wheat 420, living expenses 280, sale of stock 112, extra help 150, sale of corn 150 , taxes and incidentals 321, sale of other products What rate of income does the farm pay above expenses ? MISCELLANEOUS PROBLEMS 179 7. A man gave his note Feb. 15, 1909, for 11250.75, at 7 %. Some time afterward he canceled the note by paying 11354.56 in full. What was the date of cancellation? 8. On March 29, 1908, J. R. Anderson, of Fort Worth, Tex., bought of Scott Freeman 42 head of cattle at f 42.50 a head, and gave in payment an 8% 90-da. note payable at the Citizens' National Bank of Fort Worth, J. F. Baker becoming his security. Write the note. 9. Scott Freeman discounted the above note at the bank on April 7 at 6 %. What were the proceeds ? 10. A city contracts for paving as follows : 3000' brick paving on A St., 36' wide, at $1.68 per square yard. 1600' asphalt paving on B St., 30' wide, at $1.80 per square yard. 7500' macadam paving on C St., 24' wide, and 8" deep, at $2 per cubic yard. 13800' curbing on C St., at 51 ^ per foot. To pay for the paving the city issues $50,000 5-yr. 4% bonds. Any balance left out of the $50,000 after paying for the paving is to be deposited in a bank at 2^ %, interest to be paid semiannually and to be applied to the bond charges each six months. What amount must the city ap- propriate to meet the interest and sinking fund needs each year if the sinking fund earns 3J % ? TAXES 276. Taxes are sums of money charged against persons or property for public purposes. 277. Taxes are of two kinds, direct and indirect. 278. Direct taxes are sums levied upon persons (income tax), property (property tax), or business (license fee). The nature of some direct taxes is indicated by the name, such as " Inheritance," " Corporation," " Income Tax," etc. 279. Indirect taxes are duties levied upon imported goods (called tariffs), or licenses charged on the manufacture of liquor or tobacco products (called excise or internal revenue). 280. Taxes are generally assessed and made payable in money, except road taxes which are often made payable in day's work. The value at which property is assessed is determined by officials called assessors. 281. In solving tax problems use tlie principles of per- centage. The assessed valuation is the base. The tax rate is tlie rate. The tax is the percentage. 282. Formulas: Assessed valuation x rate = tax, or BR = T. T Tax -¥- rate = assessed valuation, or — = ^. M T Tax -^ assessed valuation = rate, or — = R, 180 APPORTIONMENT OF TAXES 181 283. The tax rate may be expressed in two ways ; by a per cent, as I^^q %, or by so much on $100, as il.30 per flOO. Find the tax on property valued at 12000 at a rate of 1^ %. If BR = T, then 12000 x .012 = $24, tax. Fill in the missing parts : Valuation Tax Rate Tax 1. 2 $ 5500 1 1500 $ 12000 $ 6250 .0126 0/, .014 o/„ 3. 4. 5. 6. 7. 8. $ 93.75 $112.62 $ 187.50 $420. $ 56.32 .020/0 $36000 .022% APPORTIONMENT OF TAXES 284. Direct taxes are apportioned in the following way : Suppose the property value in a state is $2,000,000,000; the valuation of X county is $25,000,000, and of the city of Y $7,000,000. Suppose also that the amount of money to be raised, exclusive of licenses, permits, etc., is $14,000,000 for state purposes. X county must pay its proportionate part of this $14,000,000, or such a part of it as $25,000,000 is of $2,000,000,000. $25000000 25 1 1 ^ . .u i. 1 .. — = =H% of the whole amount. $2000000000 2000 ^^ 114,000,000 X .01| = $ 175000, amt. to be raised by X county. Further, if $25,000 is needed for county purposes, then X county must raise a total of $200,000. 182 TAXES Similarly, the city of Y, with a valuation of $ 7,000,000, must raise of the amount to be raised by the county, 25000000 ^ ^ or 2^ of 8200,000 = 856000, Y's share of the county tax. If the city of Y must raise 844000 for city expenses, its total tax will be 856000 + 844000, or 8100,000 for all purposes. To find the rate of taxation, divide 8100,000, the amount to be raised, by 87,000,000, the total valuation of the town's property. ^^^^^^^ 87000000 = 1| %, the rate. 1. A property has an assessed valuation of 810,000. What is the tax at the rate of 8.001 on a dollar? 2. If the assessed valuation is 85700 and the tax rate 1|%, what is the tax? 3. What is the tax on 85000 at the rate of 8-80 per 8100 ? 4. A corporation paid taxes as follows : a corporation tax (fee) of ^5^ 1| % on real estate assessed at 8 37,250, and an income tax of 837.50. What was its total tax? 5. A man paid 8230 taxes on real estate at 1|%. At what amount was his property assessed ? 6. An owner paid 8201.31 taxes on property assessed at 88750. What was the rate of taxation ? 7. An estate pays to the state 87240.60 as an inheritance tax at 1.5 %. On what amount is the tax levied ? 8. The total property valuation of a county is 833,264,780, and the amount to be raised by taxation is 8650,000. What is the tax on property valued at 84500? 9. A farmer owns property, real and personal, assessed at 85235. His poll tax is 81, property tax 875, and he is assessed 84 road tax. What per cent of his property valuation must he set aside for taxes ? INDIRECT TAXES 183 INDIRECT TAXES 285. Customs or duties are levied by the government for two reasons : 1. For protection of American industries. 2. For raising revenue. 286. Customs or duties are of two kinds, — specific and ad valorem. 287. A specific duty is a fixed sum of money levied upon each article regardless of its value. 288. An ad valorem duty is a certain per cent levied upon the market value of the article in the countrj^ from which it is imported. 289. Allowances for the weight of boxes, etc. (called tare), and for leakage and breakage, are made before esti- mating duties. The long ton of 2240 lb. is used in reckoning import duties. 290. A tariff is a list of dutiable articles with their legal rate. 291. A free list is a list of articles on which no duty is charged. 292. The following t^ble is taken from the Tariff Act of 1913. Import Duties Ahticle Specific Ditty Ad Valoeem Duty Bicycles Butter Cotton cloth, unbleached Cotton clothing, ready-made . . . Leather "glac6 " gloves, ladies' 14 in. long or less ladies' 17 in. long Oilcloth Woolen clothing, ready-made . . . 2^^ per pound $ 1 per dozen $1.75 per dozen 25% 30% 25% 35% 184 TAXES 293. To find a specific duty. What is the duty on 175 doz. ladies' gloves, 14 in. long ? 175 X $1 = $175, specific duty. Using the rates given above, find the duty on : 1. 200 doz. ladies' leather gloves, 12 in. long. 2. 500 doz. ladies' leather gloves, 17 in. long. 3. 1500 lb. of butter. 294. To find an ad valorem duty. What is the ad valorem duty on imported merchandise, valued at £ 300 10«., if the duty is 25 % ? <£300 10«=X300.5. $4.8665 X 300.5 = $1462.38, value in United States money. I of $1462 = $365.50 ad valorem duty. Note. The duty is reckoned on the nearest dollar. Find the duty on : 1. 300 yd. of oilcloth, invoiced at <£ 6 8«. lOd. 2. Woolen clothing invoiced at <£ 510. 3. A merchant imported merchandise valued at .£8000. The duty was 50 %. What was the total cost in U. S. money ? 4. Find the total cost to the importer of the following shipment of gloves, the import duty on ladies' gloves being $1 per dozen, and on the men's gloves, $2.50 per dozen, the freight being $18.20. No. AnxicLB Price Amt. Duty Total 140 pr. 14" ladies' 170 pr. men's $1.45 1.10 • Total Freight Total cost INSURANCE 295. Insurance is an agreement by one party, for a con- sideration, to indemnify (pay) another party in case of loss. The loss may be from any cause stipulated in the agree- ment, and the different kinds of insurance take their names from the various causes. Fire insurance is insurance against loss by fire ; life insurance is insurance against loss of life ; accident, against injury from accident ; etc. Other kinds of insurance are marine, burglary, plate glass, automobile, hail, liability, etc. 296. The agreement between the two parties is called the policy. The amount paid for insurance is the premium. 297. Fire and life insurance are the most important ; and a consideration of these two kinds will furnish the general basis for calculating any kind of insurance. Hence, only these two will be treated in this book. FIRE INSURANCE 298. Fire insurance covers loss or damage to property by fire, water, smoke, and chemical extinguishers. 299. Two kinds of insurance are in general use : valued policies and open policies. 300. A valued policy states the amount to be paid in case of loss. 301. An open policy leaves the amount to be paid in case of loss open to evidence. This form of policy is generally used. 185 186 INSURANCE 302. Tlie value of the policy, or the amount of risk as- sumed, is the base. The rate of premium is the rate. The premiimi is the percentage. 303. The rate of premium is sometimes stated as a per cent of the amount insured, and sometimes as a certain rate on each ilOO of insurance. 304. To find the premiimi. A house is insured for 'f 3000 at 1^% premium. Find the cost of insurance. 11% of #3000 = !^45, premium. Find the premium on each of the following policies: ] Faok of Policy Rati of PRRMtuM 1. $ 3800 i% 2. $ 5600 \1o 3. $48200 \1o 4. #12000 30^ perl 100 5. $ 7400 mo 6. #60500 42^ peri 100 7. #18300 21^ peri 100 8. #51200 1% 9. #17100 3J% .0. #25500 60/ per $100 305. The insurable value of buildings is roughly esti- mated by the following method : Dwellings from 5^ up per cubic foot. Barns from 2^ to 3^ per cubic foot. Deduct one third for depreciation and owner's risk. FIRE INSURANCE 187 303. What is the insurable value of a dwelling 30' x 25' x 28', estimated to have cost 8^ per cubic foot? 30 X 25 X 28 = 21000 cubic feet SI il680 Less 1 560 $ 1120, insurable value. 307. The premium rate is liigher for a short term than for a long; it is called the short rate. If a policy is canceled by the insured, the company will return to him the difference between the premium paid and the premium already expired, reckoned at the short rate. If the company cancels the insurance, it will return an amount equal to the premium for the unexpired time reckoned at the regular rates. Short-rate tables may be secured from any insurance company. 308. Ordinarily, an insurance company will limit its liabil- ity to loss on any one property, except in cases of " preferred " risks, where there is small chance of loss. Hence, it is cus- tomary to divide the insurance up among several companies. In such cases, any loss less than the full amount of the insur- ance is divided pro rata among the companies interested. 309. When the policy contains a coinsurance clause, the company pays only such part of any loss as the face of the policy bears to the value of the property, or to a stipulated per cent of its value. Property valued at $12000 is insured for $8000. A loss of $7500 is sustained. What amount would be paid by the company if the policy contained a coinsurance clause ? 12 0T0 ~ 3 I of $ 7500 = $5000, amount paid. What amount would be paid under an ordinary policy? 188 INSURANCE 310. A stock of merchandise is insured as follows : In Company A for $3000. In Company B for S2000. In Company C for i^ 1000. What would each company pay in the event of a loss of ^''''' 13000 2000 1000 $ 6000, total insurance f of 13000 = f 1500, amount Company A pays, f of i3000 = ilOOO, amount Company B pays. J of f 3000 = I 500, amount Company C pays. EXERCISES 1. A dwelling 30' x 60' x 25', costing 10^ per cubic foot, is insured for 5 yr. at a rate of il.35 per 1 100. Find the insurable value and the premium. Note that the rate is for five years, not for one year. 2. A barn 40' x 100' x 40', costing 3^ per cubic foot, is in- sured for 3 yr. at a rate of i 1 per $ 100. What is the insurance company's net loss if the barn is totally destroyed by fire? 3. A house is insured in three companies. One fourth the insurance is carried by Company A, at 20^ per $100; five eighths is carried by Company B at 1 J % ; and the remainder is carried by Company C at 1J%. What is the total cost of insurance if the insurable value of the house is $10,000? 4. A building is insured for 1 yr. at 45^ per flOO, insurable value $15000. How much of the premium must be returned by the company if the insurance is canceled at the expiration of four months (1) by the company? (2) by the insured? (The short rate for 4 mo. is 70% of the annual premium.) LIFE INSURANCE 189 5. A house 50' x 40' x 40', costing 10 ^^ per cubic foot, with an addition 14' x 16' x 10', costing 5^ per cubic foot, was insured for 1 yr. at 50 fi per f 100. At the end of 60 da., the policy was canceled by the owner. What amount was returned to the insured ? (The short rate for 60 da. is 30 % of the annual premium.) 6. A house valued at $10,000 is insured in one company for 13000, in another for $2000. A loss of $8000 is sus- tained. Under a coinsurance clause, how much loss must be borne by the owner? 7. A company carries insurance on its stock of merchan- dise, valued at $25,000, to the amount of $12,500 under a policy containing the coinsurance clause. In the event of a $4850 loss, what will the company receive from the insurance company ? LIFE INSURANCE 311. In life insurance, the contingency insured against is the death of the insured. The policy may, however, agree to pay a fixed sura at the expiration of some specified time. On the death of the insured, the amount of the policy is paid to some one named in the policy, called the beneficiary. 312. Life insurance policies may be classified as whole- life, term, and endowment. 313. In whole life policies the face of the policy is payable at the death of the insured. 314. In term policies the sum insured is payable only if death occurs within a stated period ; after this period the policy lapses. 315. An endowment policy provides for the payment of a stated sum to the insured at the expiration of a stated period, if he is then living ; or to his beneficiary in case of death before that time. 190 INSURANCE 316. liiites for ilOOO insurance. Whole-life Endowment Age Ordinary Life lO-pavinent Life 20-i)avinent Life 10 Years 15 Years 20 Years 21 •S 10.16 47.26 20.22 103.01 66.34 47.73 22 10.56 47.08 20.66 103.10 65.04 47.83 23 10.08 48.72 30.13 103.10 66.04 47.94 2i 20.42 40.48 30.64 103.29 66.15 48.06 25 20.88 60.27 31.14 103.39 66.26 48.18 26 21.36 61.00 31.67 103.49 66.38 48.31 27 21.87 51.06 32.24 103.60 66.50 48.45 28 22.41 52.83 32.81 103.73 66.63 48.61 29 22.08 53.72 33.30 103.86 66.78 48.78 30 23.68 54.66 34.01 103.00 66.04 48.06 31 24.21 66.62 34.66 104.13 67.11 49.16 32 24.88 66.63 35.32 104.20 67.29 49.37 33 26.50 57.66 36.01 104.46 67.48 40.60 34 26.34 58.73 36.73 104.64 67.69 40.86 35 27.13 50.85 37.40 104.84 67.92 50.12 36 27.00 61.00 38.28 106.06 68.17 60.42 37 28.86 62.10 30.11 105.28 68.44 60.76 38 20.70 63.43 30.08 105.63 68.73 51.11 39 30.78 64.71 40.87 106.80 69.06 61.61 40 31.83 66.03 41.83 106.09 69.41 61.96 The above is taken from the rate book of one of the large companies. It is advisable to secure sample policies for examination of cash values, extended insurance, etc. EXERCISES 1. Find the annual cost of an ordinary whole-life policy for ^3000 at the age of 25 yr. According to the table the rate per 1 1000 at age 25 is $20.88. On 13000 the premium (cost) is 3 x $20.88, or $62.64. LIFE INSURANCE 191 . 2. What is the annual cost of a 110,000 policy on the life of a man 30 yr. of age on the ordinary whole-life plan ? 3. A man, age 33, insures for 15000 on the 15-year endow- ment plan. At the expiration of the period, how much more than the face of the policy will he have paid the company in premiums ? 4. How much would the payments in the preceding problem amount to at 2% compound interest? 5. A man 30 yr. of age took two policies ; one for $1000 on the 20-payment life plan, the other for 11000 on the 20-year endowment plan. At the expiration of the 20 yr. the value of the 20-payment life policy was $555 ; the value of the endowment policy was flOOO. As an investment, which was the better policy if money was worth 3% per year? (Use Annuity table, page 156.) 6. A merchant 34 yr. old took out $10,000 of ordinary life insurance as a means of protection to his creditors. What premium does he pay ? 7. A 15-yr. endowment policy for $2000, written on the life of a man 37 yr. old, is deposited as collateral for a loan of $-100 at 7 %. What is the cost of premium and interest annually ? 8. A man 29 yr. old pays a premium of $207.72 on a 10-yr. endowment policy, and $133.56 on a 20-payment life policy. How much insurance does he carry ? STOCKS AND BONDS STOCKS 317. Stock companies are associations of persons authorized by law to transact business as one individual. They are called incorporated companies, or corporations. 318. Stocks represent the capital, property, etc., which a company invests in a business under the law of the state. 319. A share represents a certain equal part of the capital stock. Shares are of any value assigned to them, as $25, 150, 1100. 320. A stock certificate is a printed statement, signed by the officers of an incorporated company, stating the number of shares owned, the par value of each, etc., to which the holder is entitled. 321. The par value is the value assigned to the stock by the corporation. 322. The market value is the value for which stock can be sold. It depends upon the dividends paid, security of the business, business conditions, etc. The market value is the quoted value, and may be par^ above par, or below par. Thus, par being 8100, a stock quoted at 123 is above par; at 76 it is below par. 323. A dividend is a certain amount of profit, based upon the par value of the stock, divided among stockholders. 324. An assessment is a sum levied upon stockholders to make up losses, to make improvements, etc. 192 STOCKS 193 325. Preferred stock is stock to which some preference has been given, over other stock issued by a corporation. It A Certificate of Stock receives the first profits distributed, sometimes at a guar- anteed rate per cent. Note. There are so many different kinds of stock issued that inves- tigation of the constitution and by-laws of the corporation is the only safe guide for anyone investing in its stock. 326. Common stock is stock generally issued by companies, and carries with it no guarantee of dividends. 327. A stockbroker is a person who makes a business of buying and selling stocks for others ; he usually charges, as commission, or brokerage, ^ of 1 % of the par value of the stock on each transaction. In some small exchanges the charge is ^ of 1 will he taken as the charge in all problems in this book unless otherwise stated. BUS. abith. — 13 194 STOCKS AND BONDS EXERCISES 1. A manufacturing company capitalized at $ 12000 declares a dividend of 16| %. Find the dividends of a stockholder who bought 20 shares of stock at the par value of $100. 162%=!. 20 X i 100 = .1^2000, stockholder's investment, iof i2000 = $333J. 2. An investment of ^i 112,420 was made in Northern Pacific at 127|. The stock pays regular dividends of 7 %. Find the ' 127 1 + i (brokerage) = 127|, cost per share. 112,420-1271 = 880 shares, f 100 X 880 X .07 = 16160, dividends. (Dividends are always figured on the par value.) 3. A man invests in Amalgamated Copper at 83, includ- ing brokerage. If this stock pays 5 %, what per cent of in- come will he get from an investment of $1992 ? 1992 -5- 83 = 24 shares. f 100 X .05 = $5, dividend per share. $5 X 24 = $120, income. 120^-1992 = 6/^%. Find the investment in each of the following, par value being $100 and brokerage being |^ of 1 % on the par value. Quantity Stock Pbicb Cost Com. Total Cost 4. 40 Ches. & Ohio 69J $2770 $6 $2776 00 5. 60 Mo. K. & T. 271 6. 120 Union Pac. 169| 7. 74 Erie R. R. 33| 8. 150 Gen. Elec. 160 9. 24 Erie 2 pfd. 42 10. 200 U. S. Steel 70 11. 31 Nat'l Bis. 130 12. 8 Amal. Copper 78J 13. 65 Am. C. & F. 54 STOCKS 195 14. A stock of par value of $25 pays a yearly dividend of $4.28 per share. What is the rate of income from this stock ? 15. What can I afford to pay for a stock paying annual dividends of §7.35 per share in order to net 5| % on the investment? (No brokerage.) Fill in the necessary amounts in the following : Quantity Stock Price Cost Com. Total Cost 16. 50 Amer. Can 4U _ _ 17. — Diamond Match 107 15350 — — 18. — People's Gas 1171 — $2.50 — 19. 100 Kan. C. & S. — — — 82637 50 20. — 111. Cent. 128f 1543 50 — — 21. — N. & W. — 3227 3.60 — 22. 35 C. M. & St. P. — — — 3731 88 23. — West. Union — — 12.50 6137 50 24. — Quaker Oats 375 — — 45015 25. — D. L. & W. — 6932 — 6934 26. Find the income on *n investment of 1^4340 in Balti- more & Ohio R. R. at 108|, brokerage |^, if the stock pays 5% dividends. 27. If the money in problem 4 was borrowed through a bank at 6 %, what was the income ? 28. A man buys 50 shares of Union Pacific common at 172|^, and sells them at 175|. If the broker charges ^% on all transactions through his office, what was the man's gain ? 29. If P., C, C, & St. L. pays 7% dividends, what in- vestment, through a broker, at 109|, brokerage | %, will pay an annual income of f 2350 ? 30. A broker owns 300 shares of National Biscuit Co. stock which pays 8% annual dividends. He sells at 137|- 196 STOCKS AND BONDS and invests the proceeds in U. S. Steel pfd., paying t)| %, at 111|. Is his income increased or diminished and how much ? (No brokerage.) 31. Find the cost, inchiding brokerage, of 450 shares of stock paying 5% dividends on a par value of {^100 per share, if the income from the investment is 4%. 32. An investor can buy Pullman Co. stock paying 12%, at ItjOJ, or Pittsburgh Coal pfd. paying 8%, at 90|. He chooses 500 shares of the former stock. Is his income more or less, and how much, than it would be on 500 shares of Pittsburgh Coal, brokerage ^ % on each transaction ? BONDS 328. A bond is an obligation to pay a certain sum of money at a stated time, with a fixed rate of interest payable at regular intervals. Interest payments are usually made on Jan. 1 and July 1. Bonds are named for the government, corporation, city, etc., issuing them ; for the time they are run, as lO-yr., 20-yr., etc. ; for the security they offer, as first-mortgage, extension, refunding, etc. Spanish War 3's were bonds issued by the govern- ment during the Spanish War, bearing 3% interest. Other titles, indicating the kind of bond, are : Panama Canal 2's, Cleveland City 4's, Denver Gas 5's, Valley Traction 5's, etc. 329. A coupon bond is a bond hav- ing certificates or Coupon from a CotftoN Bond ^ coupons attached, THE OHIO GRAVEL AND SANO COMPANY. No.. December 1,1912. The Ohio Gravel and Sand Company, on the first day of Decem- ber. 1917. will pay to bearer seventeen dollars and fifty cents, ($17.50), in Gold coin of the United States, of the standard existintr July 1, 1901. at the office of The Citizens Trust and Savings Uank. Columbus. Ohio, being six months interest then due on its seven (7) per centum first mortcage bond, all terms and conditions of which are made part hereof. 'r Oin!^ Sn. For value received, The Ohio Gr, . ■ : ;- ! ,~ : i ' r:ipany, a coiporation duly oroanized under the laws of the ISP this bond shall be registered as hereinafter provided, then registered owner hereof,' on or before the I si day of December. 1917, Five Hundred ($500.00) Dollars in Gold coin of the United Sutes, of the present standard of weight and fineness, with interest thereon in like gold coin, from the first day of December, 1 9 1 2, at the rate of seven (7) per centum per annum, payable semi-annually, on the I St day of June and December, of each year, to the bearer of the annexed coupons. The principal and interest of this bond are payable at the office of The Citizens Trust and Savings Banlc, ender of this bond and the annexed coupons as they severally mature. This bond is ate and amount, numbered consecutively from one ( 1 ) to fifty (50), Columbus, Ohio, upon ttie one of a ^lies of finy (50) bonds, all of like tenor both inclusive, all of which, wjth interest coupons attached, without preference distinction between principal and interest, are secured by a certain first morlgagi ized, executed and delivered by The Ohio Gravel and Sand Company to Lowry F. Sater, as Trustee, to said Lowry F. Saler, certain lands and properties therein referred to and described, in trust, ment of all said bonds and ' ir pnority among them, and witiK>u( first mortgage of even date herewith, duly audior- novided in said mortgage deed, and subject ( lumbers, commencing with the lowest numb< 1 or before the first day of December, 1917. : the p»y- I interest aforesaid. Said bonds are entitled to the benefit of a tinkmg hmd redemption either from the sinking fund or otherwis< outstanding, at any interest bearing period. < All redemptions prior to December I, 1917, at the rates and premiums aforesaid, shall be optional with said promisor and shall be made only upon its written direction given and delivered to the trustee at least two (2) months before the date of the redemption next following such notice, and thereafter, the sinking hmd shall be applied by the trustee to the redemption of bonds at their face value and accrued interest without such written direction. If any default shall be made in any of the payments of interest on tliis bond, or in the payments into the sink- ing fund as provided in said mortgage;,pr in the pa)in<*iJ of any taxes pi" assessments lawfully made or levied upon the whole or any part of the property itude ietUrity lie?«for, md if any such default «hall continue for a period of six (6) months after written notice thereof to i»i(ia xofclfe^jhy said trostee. or by the holder of this bond, or of any of its interest coupons thenduer and .iln6iy,f(b«B(i4ff in, ahy'siicheveBt,' at the'option of the holder hereof, this bond and accriied interest ,fha1l theVeupoi .ftcoipK (iJiV. ^ t)ayablc. This bond may be registered in the owrtef s name oji ^ihe boob of 'siid Tile Ohio Gravel and Sand Company, at the Hartman Building, in the" City of Columbus, Ohio, such.regirtry to be Bofcd oh the bond by the company's registration agent, after which no transfer will \x valid 'ufl«* made on the books of Said company by the registered owner or his attorney, and similarly noted on this bond, but the same may be discharged from registry by being duly transferred to bearer, afler which it shall be transferable by delivery, and it shall continue subject to successive registrations and transfers to bearer as aforesaid, at the option of each holder. Such registry of this bond shall not restrain or affect the negotiability of the attached interest coupons by delivery merely, but unredeemed conpons may be surrendered at any tim*. and the insullments of interest made payable thereafter Only to the registered owner of tliis bond, such surrender to be noted on the bond by the company's registration agent This bond shall be con- tidoed iuued oiOy when the trustee's certificate hereon is duly executed by Lowry F. Sater. as Tjrustee. 3n: SliltltBiI 9)l^irtof, the said The Ohio Gravel and Sand Company hat tamed these - pieaents to be signed by its President and its corporate seal to be annexed, attested by its Secretary, and tlie attached coupons to be aulhenbcated by the fac simile of the : of its Secretary engraved tWeoti. this 1st day of December. 1912. THE OHIO GRAVEL & SAND COMPANY, 198 STOCKS AND BONDS showing the amount of interest, when due, and where pay- able. There is one coupon for each interest payment, to be detached and negotiated like any other commercial paper. 330. A registered bond is a bond payable to the owner whose name is registered in the books of the issuing company. A registered bond can be transferred only by assignment. 331. The value of a bond depends on the security back of it, on the rate of interest it pays, and on the time it has to run. Values are affected by current money rates just as any other values are affected by them. The ^ usual par value, called denomination^ of a bond is $1000. No frac- tional part of a bond can be purchased. The following table, called a bond table, is used in determining the value of a bond, which has 20 yr. to run. 'J'he left-hand column gives the rate of income ; the top row gives the rate paid on the bond ; the figures in the body of the table show what can be paid for any given bond to net a certain per cent on the investment. Thus, a 5% bond, if bought for Ilia 68, will net 4% ; if bought at f 110.04, will net 4^%, etc. Likewise, a 3% bond, bought at 184.78 will net 4^%. Also, a man wishing to make an investment on a .5J % basis might buy a 4^ % bond at $87.96. 20 YEARS— Interest Payable Senrf-^nnaally. | Itetper IB- Bom. BONDS BBARINO INTEREST AT THE RATE OP | 7% 6% 6% 4i% 4% 3^% 3% 4 141.03 127.36 113.68 106.84 100.00 93.16 86.32 4.10 4.20 139-32 138.90 137-63 125.76 126.37 124.19 112.20 111.84 110.75 105.42 106.07 104.03 98.64 98.31 97-3J 91.86 91.64 90.59 85.09 84.78 8387 4X 136.80 123.42 110.04 lOS.M 96.65 89.96 83.27 4.30 4.40 '35-98 134,76 134.35 122.65 121.61 121. 14 109-33 108.27 107.93 102.66 101.66 101.32 96.00 95.04 94.72 88.11 82. 68 81.80 8..51 *>i 132.74 119.65 106.65 100.00 93.45 86.90 80.35 4.60 4.70 131-16 130.77 r29.6i 118. 18 117.82 116.74 105.19 104.86 103.86 98.70 98.38 97-43 92.21 91.90 90.99 85-72 85.42 84.55 79.22 78.94 78.1. 43< 128.84 116.02 103.20 96.80 90.39 83,98 77.67 4.80 490 128.08 126.95 126.58 115-32 114.27 113-92 102.55 101.69 101.27 96.17 96.24 94-94 89.79 88.90 88. 61 83.40 82,66 82.28 •77-02 76.22 75 '95 6 125.10 112.66 100.00 93.72 87.45 81.17 74.90 5.10 5.20 123-65 123.29 122.22 111.20 110.87 109.87 98.76 98.45 97-53 92-53 92.24 91-36 86. 31 86.03 85-19 80.09 79". 82 79-02 73.86 73.61 72.85 y/ 121.51 109.22 96.93 90.78 84.64 78.49 72.34 5.30 5.40 120.81 119.77 119.42 108.57 107.60 107.28 96.33 95.44 95-14 90.21 89.86 89.07 84.09 83.27 83.01 77-97 77.19 76.94 71-85 71.11 70.87 y/i 118.06 106.02 93.98 87.96 81.94 75.92 69.90 116.38 114.74 "3.13 104.47 102.95 101.46 92.55 91.16 89.78 86.59 85.26 83-95 80.64 79.36 78.11 74. 6S 73.46 72.27 68. 72 67.67 66.43 6 111.56 100.00 88.44 82.66 76.89 71.11 65.33 6'A 6^- 108.50 105.65 102.72 97-17 94.45 91-83 85.84 83.34 80.95 80.18 77.79 75-50 74-51 72.24 70.06 68.85 66.69 64.62 63-19 61.14 59-17 7 100.00 89.32 78.64 73.31 67.97 62.63 67.26 BONDS 199 EXERCISES Allow for no brokerage in the first seven problems. 1. Using the table, find the price at which 20-yr. bonds can be bought to yield as follows : 5% bond to yield 41%. 6% bond to yield 5.4%. 4i% bond to yield 5.3%. 2. Find the rate of income on 20-yr. bonds bought as follows : 6% bonds bought at 114.27. 3| % bonds bought at par. 5% bonds bought at 80.95. 3. A man invested in first-mortgage industrial bonds bear- ing 5 % at a price which yielded him 4.80 %. What was the quoted price ? (In this problem, and in those to follow, consider all bonds as maturing in 20 yr. ; interest coupons as due Jan. 1 and July 1.) 4. An issue of $15000 of 5% bonds is sold for f 14,449.50. What rate do they pay the purchaser ? 5. On June 12, I purchased five 1 1000 3J% bonds quoted at 82 and interest. How much do I pay for them ? Suggestion. Compute the accrued interest from the time of the last payment, and add to the quoted price. 6. If I buy a $1000 7% bond at 102.8 + 127.50 accrued interest, what is the rate of income on my investment ? 7. A Paris, France, municipal loan of 141,000,000 3% bonds was oversubscribed 70 times, that is, the subscription amounted to 12,870,000,000. If the bonds were allotted pro rata according to subscriptions, what amount was awarded to the man who subscribed for 1130,000 worth? 200 STOCKS AND BONDS 8. A man having 17000 to invest wishes to secure an income of 4| % on a 4^% bond. How many 81000 bonds can he buy, and how much will he have left of his $7000 ? Note. The broker's charge for the purchase or sale of a bond is the same as for stocks ; viz., ^ of 1 %, or $ 1.25 for each $ 1000 bond. Fill in the blank spaces in the following. Notice that under " quantity " the par value of the purchase is given in- stead of the number of bonds. Quantity Bond Priob Cost Com. Total Cost 9. $6000 C. & 0. 41'8 99J __ 10. 9000 Cin. Sewer 4's — S9225 11. — U. S. Reg. 2'8 1930 — — .$15 a 12195 12. 6000 Scioto Val. 5's — 41K)0 — — 13. — U. S. Mex. 4'8 — 8987 60 — 9000 14. A man deposits $25000 with his broker for the pur- chase of Northern Pacific 4's at 98|, brokerage | %. How many bonds will be purchased for him, and what cash balance will he have left with the broker ? 15. Cole & Co., brokers, sent this statement to R. T. Allen: " We have this day bought for your account and risk as per instructions and in accordance with the rules and customs of the New York Stock Exchange, through Wilson & Co. : Quantity Stock or Bond Prick Cost Com. Tax Total Cost $4000 $6600 A. E. & C. 5'8 Am. G. & E. 5's 101 1 10:} — — — ?i What is the amount of R. T. Allen's investment ? What commissions do Cole & Co. get ? What is the rate of income on the entire investment ? Note. The tax, called a transfer tax, is a charge, paid by the seller, on all stock sales. This charge is 2j^ per share of $100 par value; the tax on shares of $25 par value would be 50^ per 100 shares. EXCHANGE 332. Exchange is the term applied to the transfer of money from one place to another otherwise than by actually sending the money itself. 333. Exchange is domestic, if between two places in one country ; foreign, if between two places in different countries. 334. There are three important factors in exchange : 1. The amount to be transferred. 2. The charge for such transfer. 3. The value of ready money in one place as compared with that in another. 335. It is not surprising that money may have different values in different places. This value depends on the rate at which it can be borrowed from the banks. If the banks in one community have plenty of money on hand, and there is no great demand for it, money will be " cheap " ; i.e., the rate of interest on loans will be low. But if there is no great surplus of cash on hand, and much money is needed for carrying on business, money will be " dear " or " tight " ; i.e., the rate will be higher. 336. The value of money in one place as compared with its value in another is called the rate of exchange between these t'wo places. 337. Rates of exchange fluctuate, being governed by trade, or business conditions. Published rates of exchange usually include the cost of the transfer. 201 * 202 EXCHANGE 338. The principal money centers in the United States are New York, Chicago, and San Francisco, and rates of exchange are usually quoted as " New York exchange," etc. Foreign exchange would be quoted as " London exchange," " Paris exchange," etc. DOMESTIC EXCHANGE 339. Money may be transferred by : (a) Postal money order. The government, through its post offices, accepts money and issues an order therefor, pay- able at any office the purchaser may desire. Postal money orders are issued for any amount up to ilOO. The cost of transfer by postal money order, called a " fee," is determined by the following table : Table For orders for sums not exceeding ^2..')0 If over $2.50 and not exceeding $5.00 If over $5.00 and not exceeding $10.00 If over $10.00 and not exceeding $20.00 If over $20.00 and not exceeding $30.00 If over $30.00 and not exceeding $40.00 If over $40.00 and not exceeding $50.00 If over $50.00 and not exceeding $60.00 If over $60.00 and not exceeding $75.00 If over $75.00 and not exceeding $100.00 3 cents. 5 cents. 8 cents. 10 cents. 12 cents. 15 cents. 18 cents. 20 cents. 25 cents. 30 cents. (h) Express money order. This is similar to a postal order except that it is issued by an express company instead of by the government. The fee for an express money order is the same as for a postal money order. (c) Telegraphic money order. Telegraph companies will accept money at au}^ office and pay it out at an}^ other office after an exchange of telegraphic messages. DOMESTIC EXCHANGE 203 The cost of such transfer is greater than that of other forms of exchange. The sender must pay for the sending of two ten-word messages, and 1 % of the amount transferred. There is no charge less than 25)^ plus twice the ten-word rate, but on amounts over #1000, only | % is charged for the excess. ((^) Bank check. (See § 253.) In local transactions involving bank checks there is no charge for collecting. Collection is usually charged on bank checks sent to any place outside the city in which they are issued or outside the banking zone where they are received. The charges vary according to the amount of the check, the bank's ar- rangement with the customer, the distance between the two towns, etc. (e) A certified check is a check across the face of which some officer of the bank, usually the cashier or paying teller, has stamped and signed a statement certifying that the check is good. CO M a A^iKRid^ Trust & Savings Bankl^ '■- Dollars ^^^rL^ /t^h^^^^yL^,^*^ TKptLi^ A Certified Check (/) Certificates of deposit (see § 252) are issued without charge, but are subject to the usual rates of exchange if cashed at a point other than that at which they are issued. (^) A bank draft is a check drawn by one bank on another. It is the most common form of exchange be- cause it is safe. 204 EXCHANGE "TUEFjI^TjpTlqjV/JL^/fJVK ^^ Yvncennes. Ind °l SEC 261912 153 502187 To THE NATIONAL PARK BANK. NE-W YORK 1-54 NOT OVER T£M DOLLAHS SiOi 'AC A Baitk Draft Under some circumstances the cashier of the bank will issue a cashier's check, instead of a draft. This is merely the bank's check drawn on itself ; its function is essentially that of a bank draft. (A) Travelers' checks are issued by some express com- panies as a convenience to travelers. They are issued in denominations of #10, #20, $50, $100, and $200. They differ from the money orders issued b}^ these companies in that they are payable at any office of the company instead of at some designated office. The holder is identified by his signature. Travelers' checks are also issued by many banks belonging to the American Bankers' Association; they are ca-lled A. B. A. checks. ?/^ A Trayelehs' Check DOMESTIC EXCHANGE 205 Travelers' checks are issued at a cost of | % of the amount with a minimum charge of 50 j^. (^) A commercial draft is a form of commercial paper used commonly in collecting accounts. It is an order, signed by the creditor or drawer, directing the debtor, or drawee, to pay a stipulated amount to a designated third party, usually a bank. For example : A and B live in different cities, and A owes B flOO. B may "draw" on A for the amount, using a commercial draft for the purpose. B deposits this draft with his bank, which forwards it to a bank in the town where A does business. This bank presents the draft to A, and if it is honored (paid) by A, deducts its charge for col- lecting and remits the proceeds to B's bank. B's bank thereupon pays, or credits, the amount to B less its charge, if any, and the transaction is closed. tsi^ E\^t i>ri0t0 ^ign (^Inmpnn^ g At BW jiag tfl tiff ©rlJpr 0f_.„-?^ ^:<^ '^^^^^^ ^ S^*>^^ __ Q :^5r?^< _ A^ /Zf v.jrr-r Sollara, ^»5";z 4 ^'-^ Z Valnr xmitith. anb (ipirgr to tift arronnt nf ©n .-.-.-^?r^^*?rr^:.--^t!:^^ ff milt Srurto Bign (fiomtiana ____ oC:t^ yp^. a^. S «» Q^XA^.^^^ A Commercial, Draft The charge for collecting commercial drafts is not fixed by any rule, but is slightly larger than that on other kinds of exchange owing to the trouble of presenting and col- lecting. Commercial drafts usually read " with exchange " or "without exchange.'-' "With exchange" means tliat the collection charge is to be added to the face of the draft 206 EXCHANGE when presented, and paid by the person drawn on ; " with- out exchange" demands payment of only the face of the draft, and the charge is deducted after collection and the proceeds paid or credited to the maker of the draft. 340. When a draft is presented for payment, the person on whom it is drawn may, if he wishes, " accept " it, that is, write across the face of the draft the word " accepted," with the date, and sign his name. This acceptance acknowledges the indebtedness and the correctness of the amount, and vir- tually constitutes a promise to pay. The accepted draft is held until due, and then presented for payment. 341. A protest is a written or printed declaration by a notary public that a negotiable paper has been dishonored ; i.e.^ payment has been refused. 342. A sight draft is a commercial draft calling for pay- ment " at sight " or at presentation. 343. A time draft is a commercial draft calling for pay- ment at some future time, say in 3 da., 10 da., 30 da., etc. 344. The person drawn on may honor a commercial draft in two ways : by immediate payment, or by acceptance. (See § 340.) 345. Charges for exchange ought never to exceed the cost of shipping the actual money. In general they may be divided into two classes : 1. Those paid by the sender by the purchase of an order, payable at par at the point to which the money is sent. These include bank drafts, money orders, etc. 2. Thosie paid by the recipient of the money on the re- ceipt of an order payable at the point from which the money is sent. These include bank checks, commercial drafts without exchange, etc. ^ DOMESTIC EXCHANGE 207 346. New York, Chicago, and San Francisco being the principal money centers of the United States, most ex- change is drawn against banks in those cities. Any large city, however, is a money center for the territory surround- ing it, and banks in small towns issue drafts on banks in these various centers. 347. The rate of exchange (§ 336) is usually quoted in cents per $1000 premium or discount. Thus: At Detroit New York exchange at par. At Louisville New York exchange at 20 f^ premium. At St. Paul . . . . . . . New York exchange at 45^ premium. At Denver New York exchange at 80^ premium. At Chicago New York exchange at 15 ^ discount. EXERCISES 1. What is the cost of a postal or express money order for 11.12? for $23.70? for|75? for 15.95? for 117.25? 2. The ten-word telegraphic rate from Cincinnati to Dallas being 60 j^, how much will it cost to send ilOO by telegraphic money order ? 3. A, in Boston, sends to B, in Denver, his personal check for 12.50. The charge for collection is Jg %. How much does B receive on the check ? 4. What is the cost of sending $328.50 by express money order? $125? $157.50? $418.33? Suggestion. Distinguish between the cost of the order which includes the amount sent and the cost of sending. 5. A, in Cincinnati, wishes to send B, in Minneapolis, $2456.87. If the collection charge is ^^ %, for how much must A draw his check to cover the amount plus the charge? 6. If New York exchange is quoted at 70 ^ premium, how much will the following New York drafts cost : $850, $ 2378.60, $1200, $10000, $375 ? 208 EXCHANGE 7. A bank charges 5^ for each draft on Chicago of i25 or less, 10 ^ on 125 to i50, and 15 i on 150 to *100. How much will each of the following drafts cost: $7.55, $23.61, i87.19, $66.90, 140? What check will cover the cost of all the drafts ? 8. An Indianapolis merchant owes a New York importer $890.25. There is an agreement between them that payment is to be made in New York exchange, but that the importer is to pay the charge. If New York exchange is quoted at | % premium in Indianapolis, for what amount must the draft be made ? 9. A certificate of deposit for # 500, issued by the City National Bank of Columbus, Ohio, Jan. 15, 1914, draws 3 % interest. It is cashed in Milwaukee on Nov. 15, 1914, the collection charge being -^^ %. How much is paid for it by the Milwaukee bank ? 10. How much will a person pay for 10 travelers' checks of $20 each ? for 10 of $ 100 each ? 11. If San Francisco exchange is quoted at -^-^ % discount, what will be the cost of drafts on a San Francisco bank for $1800, $5000, and $1250? 12. On July 16, A drew on B for $450 at 30 da. sight, without exchange, and placed the draft with his bank for collection. Allowing four days' time in the mails, on what date may A expect returns from the draft, and what will be the proceeds, if the collection charge is J %? 13. A Cleveland manufacturer sells goods to a dealer in Decatur, 111., on Nov. 1, amounting to $2750.60, net 30 da. By agreement the manufacturer draws on the dealer on Dec. 1 at sight, with exchange. For what amount must the dealer draw his check to meet the draft, if the exchange (charge) FOREIGN EXCHANGE 209 14. Smith & Co., of St. Louis, sell Jones & Co., of Grand Rapids, Mich., goods amounting to 11976.50, f. o. b. cars St. Louis. Smith & Co. draw on Jones & Co. at sight, less 2 % for cash. The bank's charge for handling the draft is ^ %, to be paid by Jones & Co. How much will Jones & Co. liave to pay in order to get the goods from the railroad com- pany, the freight charges being $ 72.41 ? 348. The clearing house is an organization of banks in a large city for the purpose of exchanging local checks. 1. Determine the balance for or against each bank in the following clearing house statement. Check your work. Bank No. Ck. Dr. ('R. Dk. 1 1 123678 04 $ 125919 21 2 87664 13 82479 20 3 108362 87 101475 78 4 52117 69 63540 03 5 72604 10 71012 61 FOREIGN EXCHANGE 349. When money is sent from one country to another, the sending agent (post office, express company, or bank) converts the amount to be sent into terms of the money of the country to which it goes. 350. Money is thus transferred by : (a) postal money orders, (6) express money orders, (c) telegraphic or cable money orders, (c?) travelers' checks, (e) letters of credit, (/) bills of exchange. 351. On money orders and travelers' checks, and on letters of cre4it, the cost of exchange is determined by pub- BUS. ARITH, — 14 210 EXCHANGE lished rates. On bills of exchange it varies according to the money market, as determined by conditions of trade. I % is usually charged for issuing travelers' checks. The charge for cable transfer is the cable rate of exchange, plus \ % commission, plus the telegraph and cable charges. 352. Letters of credit are issued by bankers. They call for the payment of a specified amount at any one of a num- ber of banking institutions in various parts of the world. The usual charge for issuing a letter of credit is 1 %. 353. Bills of exchange include bank and commercial 'drafts, checks, etc., used in the transfer of funds from one country to another. They include : (a) Those issued by banks. These are used in foreign exchange just as bank drafts are used in domestic exchange. They are sometimes issued in duplicate or triplicate, the various copies being sent by different mails to avoid mis- takes and loss. (5) Those issued by individuals. These include all forms of commercial drafts. They may be divided into two general classes : (1) Documentary bilU^ with shipping receipts, bills of lading, insurance policies, etc., attached as evidence that the drawer of the draft has performed his part of the trans- action ; (2) Clean hills^ having no documents attached. 354. As in domestic exchange the cost of foreign exchange should never exceed the cost of shipping the actual money. The banks, through which most of the exclianges are made either directly or indirectly, maintain the rates by actual shipments of money, usually gold. 355. The par of exchange between any two countries is based on the value of the pure metal (gold or silver) con- tained in the unit coin of any country, expressed in terms of the coin of another country. For example : The United FOREIGN EXCHANGE 211 States dollar (as a unit of money) contains 23.22 grains of fine gold ; English pound sterling contains 113.0016 grains. The par of exchange between the United States and Eng- land is, therefore, 113.0016 ^23.22, or X 1 = 84.8665. For the values of foreign money see page 241. The most im- portant exchange rates are quoted as follows : England £ =$4.8665 France $1 = F. 5.18^ Germany M. 4 = | .95 Holland 1 guilder = $ .40 356. Indirect exchange (called arbitrage) is used when the quotations are such that it becomes cheaper to send money to London via Paris than to send it direct. Suppose the quotations are as follows : London exchange in New York ......£ 1 = $4.88J London exchange in Paris £ 1 = F. 25.10 Paris exchange in New York |1 = F. 5.23 EXERCISES 1. I wish to send $ 50 by money order to each of the fol- lowing countries : Germany, England, France, and Holland. For how much will each order read, in terms of the money of the country to which it is to be sent ? 2. Exchange being at par, what will be the cost of a draft on London for £ 62 98. Id. ? 3. What will be the cost of a draft on Paris for F. 1000, exchange being quoted at t^q % premium ? 4. What will be the cost of a letter of credit for $ 5000 ? Of travelers' checks for $ 800 ? 5. What will it cost to cable $ 400 to London, the cable rate being S3 ? If London exchange is quoted at par, what amount in English money will be transferred ? 212 EXCHANGE 6. How large a draft can be bought on Denmark for $2000? (See table in appendix.) On the Pliilippine Islands for 1 125 ? On Sweden for 11285.67 ? 7. A firm owes £283 5«. 6d. in London, F. 16,723 in Paris, and M. 4933 in Germany. Quotations at the time of sending are as follows : Sterling $4.8595 Francs 5.20 Marks 94^ What will be the amount of the firm's check to purchase the exchange ? 8. What will be the cost of a draft on the City of Mexico for 2550 pesos ? 9. Will it be cheaper to send £ 1000 to London direct or to convert the money into Paris exchange and have it con- verted into pounds and sent to London ? If so, how much cheaper? (Use quotations in § 356.) 10. What is the value of a bill of exchange on Paris for F. 7160, at 5.18^ 11. If exchange on Berlin is at par, what will be the cost of a bill of exchange for M. 3750 ? 12. How much English money should a traveler receive for a travelers' check for 1 20 ? How much French money ? 13. I hold a London acceptance for <£ 112 8*. lOd., due in 45 da. If money is worth 4%, and the collecting charge is J %, how much can I get for the acceptance at my banker's ? 14. How much German money would a traveler receive for a letter of credit for X 200 ? 15. What will be the cost of a letter of credit for £ 100 PARTNERSHIP 357. A partnership is an association of two or more persons for business purposes. 358. The profits or losses are shared according to agree- ment. 359. The capital of a firm is its total investment. 360. The resources of a firm are its total investment plus all debts or obligations owing to the firm. 361. The liabilities of a firm are the total debts or obliga- tions to others. 362. The excess of the resources of a firm over its lia- bilities is its present worth ; the excess of its liabilities over its resources is its insolvency. 363. The net gain is the excess of gains over losses. 364. Tlie net loss is the excess of losses over gains. 365. To find what part of the profit each partner receives. The capital employed in a business partnership is f 10,000, of which A furnishes 16000, and B furnishes 14000. What part of any profit should each receive ? A has invested y\ (_6_o_o_o_.^ ^f the capital; hence he re- ceives -^Q, or -| of the profits. B has invested | of the capital ; hence he receives | of the profits. If the profits should be f 2000, A would receive | of $2000, or 11200 ; B would receive f of 12000, or #800. 213 214 PARTNERSHIP EXERCISES 1. A, B, and C form a partnership, agreeing to share gains and losses according to the amount of their investments. A invests 14000, B 85000, and C $6000. Their gain the first year is ilOOO. Find the present worth of each. 2. A and B have a joint capital of $15000. At the end of 3 yr. their present worth is $21000. What is each partner's gain if they share equally ? 3. D invested $4000 and E $5000 in a business. At the end of one year their resources amount to $18000, their lia- bilities to $3000. Find each partner's present worth. 4. Three men invest $3000, $4000, and $ 5000, respec- tively, in a business. They agree to share gains and losses according to investment. At the end of one year their present worth is $ 8000. What was each man's loss ? 5. Jones, Smith, and Deliver engage in business and agree to share gains and losses according to investment. Jones invests $10,000, Smith $12,000, and Doliver $13,000. At the end of the first year their ledger accounts were as follows: Merchandise, gain $ 10,000 ; patents, gain $ 1000 ; expense, loss $2500; real estate, gain $1858.75; equipment, loss $875 ; interest, loss $ 200.50. What is each partner's pres- ent worth, and what per cent did he make on his investment ? 6. On Jan. 1, 1911, A invests $5000 in business. April 1, 1911, B puts $4000 in the same business. Jan. 1, 1912, their ledger shows a gain of $2000. How much does each partner gain, if they share according to the amount of the investment and length of time it was invested ? [A invests $ 5000 for 12 mo., which is the same as $ 60,000 ($ 5000 x 12) for 1 mo. B invests $4000 for 9 mo., which is the same as $36000 ($4000 X 9) for 1 mo. Then A's share is f of the profits.] RAILROAD RATES 366. Railroad rates are of two kinds, class and commod- ity. Class rates are applied to all kinds of shipments, whether in carload lots or less, and the rates are fixed at a certain price per 100 lb. All articles of commerce are classified in each " freight territory " by a commission, which publishes the result of its work in the form of a freight classification. A joint rate commission, made up of representatives of all railroads in the territory, meets and fixes the rates to apply for each class, subject to the sanction of the Interstate Com- merce Commission. These rates are published in what is known ^^ 'd freight tariff. 367. Commodity rates are applied to certain kinds of heavy freight, usually in carload lots. Among the articles which get special commodity rates are : coal, coke, ice, rough stone, lumber, grain and grain products, iron ore, and arti- cles of iron and steel manufacture. In the case of some of these the rate is based on 100 lb. as the unit, on others the rate is so much per barrel, while on most of them the ton is the basis for the rate. Among the commodities rated by the short ton (2000 lb.) are : rough stone, sand, ice, coal, coke, and paving brick. Iron ore and articles of iron and steel manufacture are rated by the long ton (2240 lb.). 368. Carload shipments must be loaded by the shipper and unloaded by the consignee, but the railroad company switches the car to whatever siding is most convenient. Less-than-carload shipments are handled by the employees of the railroads. Carload rates are always lower for the 215 216 RAILROAD RATES same article than the less-than- carload rates, but are always based on a certain specified minimum weight; for instance, if a shipper has 25000 lb. of canned goods and the minimum weight is 30,000 lb., he will have to pay freight on 30,000 lb. in order to get the benefit of the carload rate. If he has over 30,000 lb., he pays freight on the actual weight. EXERCISES 1. A shipment of sixth -class freight moved from Parkers- burg, W. Va., to Syracuse, N. Y. The rate was 12J ^ per 100 lb. and the consignment weighed 240,000 lb. What were the freight charges ? 2. What is the fifth-class rate from Chicago to Richmond, Va., when a shipment weighing 4400 lb. costs f 118.80 for transportation ? 3. The all-rail rate from Columbus, Ohio, to Provi- dence, R. I., is 43|y per 100 lb. for third-class ; the rail-aiid- water rate between these points for the same class is 41 ^ per 100 lb. How much will a man save by forwarding a third- class shipment weighing 12500 lb. by rail-and-water route ? SuGGKSTiON. Is it necessary to find full charges by separate routes? 4. In the official classification, automobiles by carloads are rated at 110% of first-class rate, minimum weight 10,000 lb. The first-class rate between Vincennes, Ind., and Utica, N. Y., is 70^ per 100 lb. What will it cost to forward a shipment of automobiles weighing 11,250 lb. between these two points ? 5. A druggist in Bluefield, W. Va., received a consign- ment of toilet soap from Cincinnati, Ohio, rated at 35 ^ per 100 lb. He notified the freight agent that tliere was an error in the freight rate, which should have been 27^^ per 100 lb. The agent refunded -$1.80. What did the soap weigh? RAILROAD RATES 217 6. The rate on canned vegetables in less-than-carload lots, from Wheeling, W. Va., to Baltimore, Md., is 22 j^ per 100 lb. The carload rate is fifth-class, or 15^ per 100 lb., but the shipment is charged on a basis of 30,000 lb. mini- mum weight. A firm in Wheeling has a shipment of canned vegetables weighing 22,000 lb. Should it be billed as a carload lot, or less-than-carload shipment? How much cheaper is this way? 7. A shipment of first-class freight weighing 8000 lb. moved from Cleveland, Ohio, to Richmond, Va., via C. A. & C. and N. & W. Rys. The C. A. & C. received 20 % of the rate and earned $8.72 for hauling the shipment from Cleveland to Columbus, Ohio. What is the first-class rate from Cleveland, Ohio, to Richmond, Va.? 8. A consigned 40,000 lb. of baled hay to B at f 18 per ton, allowing B to deduct the amount of the freight charges from the invoice. A got 8330 from B. What was the freight rate? 9. The fourth-class rate from Columbus, Ohio, to New York is 27 j^ per 100 lb., and the third-class rate is 38J^ per 100 lb. By mistake the rate clerk applied the third- class rate to a shipment which should have been rated at fourth-class. The delivering road corrected the error and refunded the consignee 116.10. How much did the ship- ment weigh ? 10. The first four class rates from Buffalo, N. Y., to Seattle, Wash., are 13.60, $3.10, $2.60, $2.20 per 100 lb., respectively, governed by the western classification. This classification makes shoes first-class, leather in bags second- class, and last blocks fourth-class. What are the freight charges on the following shipment between these two points : 1 bx. shoes, 80 lb. ; 1 bag leather, 120 lb.; 1 bbl. last blocks, 150 lb.? 218 RAILROAD RATES 11. The carlx)ad rate on flour from Minneapolis, Minn., to Tacoma, Wash., is 90^ per 100 lb., minimum weight 56000 lb. The less-than-carload rate is S1.83 per 100 lb. Washburn, Crosby & Co. have a consignment of 150 bbl. of Gold Medal flour to ship to Tacoma. Should they bill it as a carload or less-than-carload shipment? How much cheaper is this way? 12. A farmer in Cheyenne, Wyo., ordered a wagon, a hay rake, and a corn planter from a firm in Milwaukee, Wis. When these are taken apart and tied in bundles, the western classification makes wagons first-class, rakes second- class, and corn planters third-class. The wagon weighed 800 lb., the rake 350 lb., and the corn planter 500 lb. The rates for the first three classes, Milwaukee to Cheyenne, are i3.05, #2.60, .f 2.20 per 100 lb. How much did he have to pay for his shipment? 13. The rate on flour carloads from Indianapolis, Ind., to Wilmington, N. C, is made 10|^^ per 100 lb. to Kenova, W. Va., and 46 ^ per bbl., Kenova to Wilmington. A car- load of flour moved from Indianapolis to Wilmington. What were the transportation charges? 14. A farmer wants to move from Logansport, Ind., to Columbia, S. C, and Jias some live stock to ship with his household goods. The rate is made 35 ^ per 100 lb. from Logansport, Ind., to Cincinnati, official classification, minimum weight 12000 lb.; and 53^ per 100 lb. from Cincinnati to Columbia, S. C, southern classification, minimum weight 24000 lb. The shipment weighed 18000 lb. What are his freight charges for moving? PARCEL POST 369. The Parcel Post Act of Congress, which went into effect on Jan. 1, 1913, provides for the transportation in the mails of merchandise at low rates. The accompanying table gives the rates provided by law : Table op Rates First Zone Second Zone, 50 TO 150 Mi, Third Zone, 150 TO 300 Mi. Fourth Zone, 30(» TO 600 Mi. Fifth Zone, 600 '10 1000 Mi. Sixth Zone, 1000 to 1400 Mi. Sev- enth Zone, 1400 TO 1800 xMi. KwillTH ZorE, Weight Local rate Zone rate, 50 mi. ALL OVER 1800 Mi. lib. 10.05 10.05 10.05 $0.06 $0.07 $0.08 $0.09 $0.11 $0.12 2 1b. .06 .06 .06 .08 .11 .14 .17 .21 .24 3 1b. .06 .07 .07 .10 .15 .20 .25 .31 .36 4 1b. .07 .08 .08 .12 .19 .26 .33 .41 .48 6 1b. .07 .09 .09 .14 .23 .32 .41 .51 .60 6 1b. .08 .10 .10 .16 .27 .38 .49 .61 .72 7 1b. .08 .11 .11 .18 .31 .44 .57 .71 .84 8 1b. .09 .12 .12 .20 .35 .50 .66 .81 .96 9 1b. .09 .13 .13 .22 .39 .56 .73 .91 1.08 10 1b. .10 .14 .14 .24 .43 .62 .81 1.01 1.20 111b. .10 .15 .15 .26 .47 .68 .89 1.11 1.32 20 1b. .15 .24 .24 .44 .83 1.22 1.61 2.01 2.40 50 1b. .30 .54 .54 The local rate is applicable to parcels intended for delivery at the office of mailing or on a rural route starting therefrom. 370. Under the parcel post act the country is divided into units. Each unit is a quarter of a quadrangle formed by meridians of longitude and parallels of latitude. 219 220 PARCEL POST 371. The average length of the quadrangles north and south is 69 mi., their average width east and west is 54 mi. The unit, therefore, is about 34| mi. long (north and south) and 27 mi. wide (east and west), with an area of a little over 930 sq. mi. 372. Each of the 6000 (approximately) units thus estab- lished is the center of a system of eight zones. The first zone, called the 50-mi. zone, consists of the unit itself and its eight contiguous units. 373. The limit of weight for packages for local delivery and for delivery at other post offices within the first and second zones is 50 lb. The limit of weight for delivery in other than the first and second zones is 20 lb. EXERCISES 1. What will it cost to send a 7-lb. package to a point in the 300-mi. zone ? One weighing 9 lb. ? 2. How far (into what zone) can a package weighing 3 lb. be sent for 25 ^ ? for 15 ^ ? for 36 i ? 3. A mail-order house sent out in one day 820 2-lb. parcels. 556 of these went into the 50-mi. zone, 234 into the 150-mi. zone, and 30 into the 300-mi. zone. What post- age was paid on all of them ? 4. How much will it cost to send a 20-lb. package 95 mi.? 5. Find the cost of sending 5 11-lb. packages into the fifth zone. MISCELLANEOUS PROBLEMS Group 1 Find the tax on the following : 1. 18765 at .0091. 2. 12300 at 4 mills on the dollar. 3. 11400 at .0126. 4. $6800 at 11.75 per -f 100. 5. 13750 at 1.871%. 6. The assessed valuation of a town is $3,250,000, and a property owner pays $44.85 on property assessed at $3900. What is the total amount raised by taxation ? 7. A's property, assessed at $16000, is taxed 11 mills on the dollar. By paying his taxes promptly he secured a discount of 1 % from the amount. How much does he pay ? 8. What is the duty on 2200 T. of hay at $4 per ton? on 5000 lb. of writing paper at 3j^ per pound? on a yard of silk ribbon worth 40 j^ at 50%? on a pair of shoes costing $3 at 15%? 9. What is the duty in United States money on French goods valued at F. 11630 at 30 % ? 10. What is the premium on a life insurance policy for $2500, if the premium on $10,000 is $267.10? Group 2 1. A building insured for $11,000 is valued at $16,500. Under the coinsurance clause, what will the insurance com- pany pay in the event of a loss of $1376.28 ? 221 222 MISCELLANEOUS PROBLEMS 2. A man has two houses wortli, respectively, $4500 and 'f 3200. Taxes are 1| %, insurance is i 15.50 on the first, and $11.20 on the second. The first rents for $40 per month; the second, for $30. Which is the better investment ? 3. An insurance company collects premiums amounting to $14,692,308.32 ; it pays out losses amounting to $5,342,200.20. What is the loss ratio (percentage of losses to premiums) ? 4. The owner of a 1913 model 20-horse-power automo- bile costing $2500 insures the machine (1) against injury to persons, at $1.20 per horse power; (2) against damage by collision, at 2% of the value of the car; (3) against damage to property, at 30^ per horse power; (4) against fire and theft, at 2| % of the value of the car. What is the total amount paid by the owner for such protection ? 5. A coal mining company whose yearly pay roll is $30,000 is insured against claims for damage due to injury to its employees at $1 per $100 of the pay roll. What premium does the company pay ? 6. What is the cost of 20 shares of stock at 55 J, broker- age \ % ? 7. C buys 50 shares of stock at 106. In 18 mo. time he receives 4 dividends of 6% each. If money is worth 5%? how much does he gain over and above this rate ? 8. A sent 70,000 lb. of wheat to be sold and the proceeds invested in. Southern Pacific stock. The agent sold the wheat for 90^ per bushel and charged a 2% commission. Southern Pacific cost 110, brokerage ^ % . How many shares did A receive, and what surplus had he left over ? 9. What is the rate of investment on Atlantic and Pacific Railroad 4's bought at 83, brokerage | % ? 10. I receive $375 every 6 mo. as interest on Erie 5's. If I bought them at 98|, plus |% brokerage, how much did I invest ? MISCELLANEOUS PROBLEMS 223 Group 3 1. The following is the form in which a broker keeps his records of a transaction made for a customer. In this ac- count, the customer bought 100 shares of New York Central on Nov. 5, at 115. He deposited 11000 on the transaction, the broker lending him at 6% the amount necessary to make the purchase. When the stock is sold, the customer is credited with the amount of the sale, interest is charged, and the balance is credited to the customer. Dr. Ck. Nov. 5 100 N.Y. Cent. 115 Com. buying $11500 12 50 Nov. 5 Cash $1000 Nov. 20 Com. selling Tax selling 12 2 50 Nov. 20 100 N.Y. Cent. 117 Int. on $1000 Nov. 11700 Int. on §11,512.50 5 to Nov. 20 2 50 Nov. 5 to Nov. 20 28 78 • Balance 1146 72 $ 12702 50 $12702 50 The profit in the transaction is the customer's balance ($1146.72) minus his cash deposit (11000), or 1 146.72. Note. Interest is charged on the full amount of the purchase, and credited on cash deposit. For tax (|2) see note, page 200. Using the above as a model, make and fill in forms for the following transactions. Compute interest at 5%. Tax, 2j^ per share on sales. Date Bought Stock Price Amount Cash Uep. Date Sold Price Amount 2. Aug. 3 20 P. Coal 23^ 1100 Oct. 18 251 3. May 10 100 U. S. Steel 75i 800 Sept. 20 78 4. Jan. 14 50 Gen. Elec. 180 1200 Feb. 19 192 5. Mar. 2 75 Amer. Loco. 4U 375 Mar. 22 41i 6. Dec. 10 200 So. Pac. 1091 5000 Dec. 20 111 224 MISCELLANEOUS PROBLEMS 7. A bank bid #831.58 above par for an entire issue of il5000 5% school bonds. What return does the invest- ment make the bank ? 8. A corporation has outstanding 86,000,000 of 6% pre- ferred, and 'f 12,000,000 common stock. Its net earnings for the year are 11,131,885. What per cent dividends will the common stock earn ? 9. A man having 83000 to invest buys 12 shares of stock at 400, borrowing enough additional on the stock as collateral to make the purchase. If he pays 5% on his loan, and the stock pays 25 % dividends, what per cent is he mak- ing on his investment ? (Par value, 8100.) 10. Which is the better investment, 100 shares of 6% pre- ferred stock at 107|, or 50 shares of 12% common at 214|? (Brokerage, ^%.) Group 4 1. A salesman sells in one year 1128,466.73 worth of goods on a 5% commission. His expenses for the year are $3246.80, and he pays 8117.43. taxes and 8245.48 insurance. He buys 10 shares of bank stock direct from the owner at 8165 per share, and sete aside 8263.63 for a cliecking account at the bank. If he deposits the rest of his year's income in a bank at 3J%, what interest will it bring him annually ? 2. I discount a 10-day acceptance for 82500 at 5| % and use the proceeds in buying a telegraph money order. If the 10-word rate is 60 ^ what amount is available to the person receiving the order ? 3. A draws on B at sight for 8162.57 with exchange. To meet the draft B borrows the money at his bank at 6% for 60 da. What is the amount of B's note when due ? (Exchange, 20^.) 4. A corporation issues 875000 6% bonds, which it is forced to sell at 87. In paying the interest on its bonded MISCELLANEOUS PROBLEMS 225 indebtedness what rate does it pay on the money actually received for the bonds ? 5. A buys 100 shares of stock at 27 1 and sells them at 30. Allowing brokerage of ^% on each transaction, how much does he gain ? 6. The firm X, Y, Z makes a gross profit in one year of 8 25,004. They charge oif $■ 1484 to depreciation on machin- ery, 8675 to depreciation on trade mark, and pay $6160 for general expenses and wages. If the three members of the firm are equally interested in the business, how much will each receive as his share of the net profits ? 7. A borrows 815000 on his note at 7 %. To secure the note he takes out a life insurance policy for 8 18000 at 8 14.62 per thousand, annual premium. The 815000 is invested in a third interest in a business which shows a profit at the end of the year of 33|^ %. What is the net rate of income on the investment ? 8. Find the proceeds on the following sight drafts: Face of Draft Collection and Exchange $28.63 10^ 162.45 • i% 4216.53 • ■ 5V7o 6.20 6^ 683.10 io/o 1370.64 J^o/o 9. Find the cost of a bill of exchange for : -£ 362 lis. M if 1 £ = $4.8725 F.3624 if F. 5.161 = 11 M. 11360 if M. 4 = $.95| 10. A bond issue of 8 1,000,000 was oversubscribed 3|^ times ; that is, the subscriptions amounted to 83,500,000. If each subscriber receives bonds in proportion to his subscription, what did the subscriber receive who asked for 8 14000 worth ? BUS. ARITH. 15 226 MISCELLANEOUS PROBLEMS Group 5 1. How much will I receive for a 90-day acceptance for $ 350, discounted at 6 %, exchange {%? 2. How much' will it cost to telegraph $125 from Cleve- land, Ohio, to Nashville, Tenn., the telegraph rate being 60 ^? 3. An importer buys £ 163 8«. Sd. worth of goods on which he pays a duty of 20 %. For how much U. S. money must he sell to realize a profit of 20 % of the cost ? 4. A and B own a business, A holding a | interest, and B a I interest. If they sell a third interest for $6200, what must A and B each receive in order that A, B, and C may thereafter be equally interested in the business ? 5. A has 15000 invested in a store, B has '13000, and C has 12000. They decide to add $4000 to the capital em- ployed. What part of this amount must each partner furnish in order that their relative interests may remain unchanged ? 6. What is the value of a 90-day acceptance for X 112 Is. 46?., London exchange being quoted at $4.84|, discounted at 6%? 7. An inventor holds 100 shares of 6% preferred stock, 200 shares of 5% common, and $22000 6% bonds of the same company. What is his income ? 8. A bank capitalized at $300,000 has a surplus of $317,578. What per cent dividends might be declared by appropriating 60 % of the surplus to such a purpose ? 9. A company purchased M. 18000 worth of German goods on which it paid $450 duty and $106.85 freight. The goods were sold for $6320, less 2%. What was the profit? 10. A, holding B's note for $270 with interest for 4 mo. at 7 %, draws on B through the First National Bank of Burt, Iowa, at sight for the full amount. B's place of business is Denver, Col. Write the draft. REVIEW PROBLEMS ORAL EXERCISES 1. 34 X 11 2. 45 X 200 3. 93 X 97 4. 472 X 300 5. 67 X 11 6. 4532x11 7. 6469 X 150 8. 9540 X 125 9. 61 X 10. 51 X 5J 11. 450 X 450 12. 6ix6i 13. 9ix9J 14. 425 X 625 15. 625 X 4.25 16. 8ix8J 17. 7fx7f 18. 425 X 8250 19. 91x91 Find the following: 58. 10 % of 280 59. 20 % of 60 60. 48 % of 175 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 61. 62. 63. 325 X 925 750 X 750 290 X 150 756 X 175 35 X 35 .95 X .65 8.5 X 750 121 X 1.25 75x25 10| X lOi 6|x6f 5J X 5^ 2f x2| 925 X 725 81 X 8.31 4x1375 5|^6 foff 16| % of 660 1081% of 240 92% of 150 227 39. 424-25 40. 7650-50 41. 60 -^f 42. 725^1.331 43. 125-^1 44. 452 -.161 45. 7840-125 46. 475 -^f 47. 5896-^.161 48. .12i = ? 49. .081=? 50. .331=? 51. .871 = ? 52. .58^ = ? 53. 1.331 = ? 54. .55| = ? 55. .561 = ? 56. 57. 06J ,621 = 9 64. .2% of 640 65. .3% of 5 66. 150% of 500 228 REVIEW PROBLEMS 67. .l%of.l 69. .08|ofl2 71. a3i%of3| 68. .01% of 740 70. 16|%of45 72. I % of 36 73. 56 J % of 48 74. 12 is 4 % of what number ? 75. 24 is 41| % of what number ? 76. .25 is 80% of what number? 77. .83^ is 20 % of what number? 78. 4 is I % of what number? 79. 35 is 6| % of what number? 80. .621 is 83J% of what number? 81. Reduce | to 24ths. 83. Reduce |J to lowest terms. 82. Reduce f to 21sts. 84. From | take |. 85. From /j take -^. Find the interest at 6 % : Pkinoipal Tihb 86. i400 Syr. 87. 250 120 da. 88. 325 80 da. 89. 720 1 mo. 10 da. 90. 600 40 da. 91. A man had ^2000 and spent 20% of it. How much money had he left ? 92. Owning a farm of 420 A., I sold 16|% for 84900. What price per acre did I receive ? 93. Owning 60% of the stock of a manufacturing com- pany, T sold 20% of my share for $2400. What was tlie value of the entire stock ? of my share ? 94. I sold a horse for $ 200, which was at a loss of 20 % of the cost. Find the cost. 95. How many times can 36 be subtracted from 300 ? 96. A baseball team wins 14 games and loses 10. What is its per cent of games won ? REVIEW PROBLEMS 229 97. A catalogue lists an article at 145, but allows 25% and 20 % off. Find the net selling price. 98. Brown gained |500 the first year and after adding his gain to his investment, lost \ of the amount the second year. He then had $1800. How much had he at first ? 99. A invests 1600 and B $800. Their gain is 8300. What should each receive ? 100. What will it cost to send a 7-pound parcel into the 150- mile zone by parcel post ? WRITTEN EXERCISES 1. Add and check : 2. Add and check 2875648 9572674 1792559 8468739 1624076 7254927 9217845 6248725 7384957 9764523 6294738 78654 7549629 837642 6872597 9872937 827358 1640735 75646 8295439 198478 764375 7354629 4874062 6473746 567432 1897645 28739 735490 543721 6487 17687 954398 649586 2872594 7468929 7658 8295437 64352 7804 230 REVIEW PROBLEMS 3. Add and subtract alterDately 8972549 2762597 2437538 7642973 297364 4. Add: 687.25 -384.20 72.85 16.92 140.62 45.07 83.98 8549321 5432976 849278 5. Add by the balancing account method and check : Balance Check Deposits Balance A B C D E F 985.72 487.68 95.98 168.75 72.59 354.86 342.89 159.20 20.07 68.92 14.09 215.96 58.72 268.73 75.00 934.58 54.72 134.17 Total 6. Find the balance : Dr. Or. 12874.58 11975.62 1784.63 8573.74 8873.19 175.14 982.73 1354.05 3214.95 938.15 REVIEW PROBLEMS 231 7. Multiply and check 78549872 927 8. Multiply : 147268 9154 9. Find the G. C. D. of 24, 132, 144. 10. Find the L. C. M. of 81, 120, 117. 11. Add: 765.641 421 678. 6 J^ 4572. 68^ 62.141 759f 12. Multiply 534| by 8.24J. 13. Divide 7825963^1 by .16f. 14.- Multiply 18 bu. 3 pk. 2 qt. by 12. 15. Extend and foot the following : NuMBKR OF Pounds Article Price Value 84000 12578 6250 5348 28364 Hay Corn Oats Bran Chop $ 10 per ton 80 f per bushel 40 ^ per bushel $18 per ton $30 per ton Total . . 16. The hypotenuse of a right triangle is 400 ft., the base 200 ft., what is its area? 17. Find the area of a circle whose diameter is 10 ft. 18. What will it cost to carpet a room 16' x 18' x 15', if the carpet is | of a yard wide, at •'^1.50 per yard? 232 REVIEW PROBLEMS 19. At '$5 per thousand what will it cost to shingle a flat roof 150' X 60', allowing 850 shingles to a square ? 20. How many cords of wood in a pile 20' x 4' x 8' ? 21. A commission merchant sold a carload of lumber, and sent the owner ^3564.25, after paying f 70 freight charges, and retaining 2| % commission for selling. What was his commission? 22. A pay roll made from time slips and rates per hour as shown below will amount to how much? • Time Uatb AuorNT A B C D E 24 hr. 40 hr. 48 hr. 50 hr. 40 hr. .12^ per hour .14 per hour .20 per hour .17| per hour .22^ per hour Total . . . 1! 23. What sum must a man invest in 5% bonds bought at 120 to give his son an annual income of ^1200 ? 24. A man having money to invest in bonds has a list from which he wishes to select the investment most profitable to him. The list includes : 1. 5 % bonds, market price f 110 2. 6 % bonds, market price 120 3. 4 % bonds, market price 100 4. 4J% bonds, market price 60 5. 3 % bonds, market price 90 Which bonds should he purchase ? 25. A commission merchant sold for his principal 400 bu. of potatoes at 90^ per bushel, and after deducting $3.80 for freight, and his commission of 3 %, remitted a check for the proceeds. What was the amount of the check ? REVIEW PROBLEMS 233 26. I sold two houses for 18000 each. On one I gained 20 % of the cost, and on the other I lost 20 % of the cost. Did I gain or lose on the whole transaction, and how much ? 27. A real estate dealer sold a house for iTOOO ; after pay- ing expenses of §440, he finds that his gain is 16|% of the cost. How much did the house cost him ? 28. Which is better for the buyer, a discount series of 20, 20, and 10, or 25, 15, and 10, and how much ? 29. An article at §4.50 was discounted 20% and 1.80. What was the second rate of discount ? 30. How shall goods that cost 145 be marked so that a discount of 10% may be made from the marked price and then sell at a profit of 10 % of the cost ? 31. A lent B $900 for 2 mo. At the same rate, what amount shall B lend A for 3 mo. in return for tlie accommo- dation ? 32. On April 3, a carriage manufacturer in Ohio sells a shipment to a Texas dealer, amounting to f 850. He attaches the bill of lading to a 60-day sight draft which he discounts at his bank at 6%. Allowing 12 da. before the consignee can receive and inspect the shipment, and 3 da. for return to the Ohio bank after payment in Texas, what are the proceeds of the draft, collection charges being -^^ % ? 33. A shoe manufacturer discounts at his bank the follow- ing notes from out-of-town customers : Face Time Rate % .$123.45 240.00 93.25 107.70 90 da. • 30 da. 30 da. 60 da. 7 % from date 5i % from date 6 % from date 6 % from date 234 REVIEW PROBLEMS What are the proceeds of these notes, if the bank discounts them at 5 % ? (Add 4 days' time in discounting to allow for time in transit.) 34. A farmer ships a car containing 38762 lb. of pota- toes to a broker, who sells them for 82^ per hundredweight. Freight charges are 173.20, and the broker charges a com- mission of 2 %. What amount is returned to the farmer? 35. The Detroit Times shows the following circulation for one month : MON. Tubs. Wed. Tilt-. Fr.. Sat. Total 36555 36302 36310 36258 36338 36303 36233 36500 36173 36147 36668 38710 40871 43005 43609 43458 43351 35835 35967 35881 36733 76940 36514 36359 36998 36198 36329 (a) Find the total circulation for each week. (K) Find the total circulation for each day in the week. (c) Find the total circulation for the month. (c?) What is the average circulation per day? (e) What day is nearest the average? 36. Which of two salesmen, A and B, whose yearly sales are given below, returns more profit to his firm ? A sells $225,000 worth, showing an average profit to the firm of 11|^% of his sales; cost of collections \^\%^ selling expenses, $6450. B sells $260,000 worth at an average profit of 10|% of his sales; cost of collection, |%, selling expenses, $7200. 37. A company issues $100,000 7% preferred stock, and $ 100,000 of common stock. It earns in one year $28,762.20. What amount can be added to the surplus if it pays 11% dividends on the common stock, and charges $3333.33 to depreciation of plant and equipment ? REVIEW PROBLEMS 235 38. If the advertising expense incident to the sale of an article is i 10,000, and this expense is divided among manu- facturer, jobber, and retailer according to the profits of each, what part will be paid by each, if the profits are, respectively, 22%, 13%, and 15%? 39. A merchant buys $15000 worth of goods at 2% -10, net 60. How much will he save by borrowing the money for 30 da. at 6 % in order to discount the bill ? 40. If a retailer sells an article for fl2.50, showing 20% profit on the selling price, at what can he afford to sell it if he is willing to take only 10 % profit on the cost ? 41. Find the difference between simple interest and com- pound interest on 19375 for 10 yr. at 6 %. 42. An agent sold for his principal goods to the amount of 110,000, charging 3 % commission. He invested the pro- ceeds in wheat after deducting a commission of 2 % for buy- ing. If he paid 90 % per bushel for the wheat, how many bushels did he buy ? 43. The average circulation of the Bosto7i Daily Post for August was 418,562, a gain of 59,056 copies per day over August in the previous year. What per cent of increase is shown ? 44. In 1912 the population of the United States was ap- proximately 95,000,000. The family expenditures were as follows : Article Amount Food $8000000000 Clothing 3000000000 Intoxicants 2000000000 Tobacco 1000000000 Fuel 800000000 Life Insurance 600000000 Furniture 600000000 236 REVIEW PROBLEMS (a) What per cent of the total expenditure was spent for tobacco and intoxicants combined ? (b) What is the total expenditure on these items for each person in the United States ? 45. A dealer sold a buggy for i98, an advance of 16|% over the cost. If he extends to the purchaser credit for 6 mo. without interest, what was his real per cent of gain, money being worth 6 % ? 46. An agent sells 80,000 lb. of wheat at 90^ per bushel. He accepts a 60-day note, which, wlien discounted at 5 %, pays the bill. What is the face of the note ? 47. A owes four bills which he pays by New York drafts, the amounts being as follows: $49.50, i8?286.75, $158.76, and $61.10. If exchange is J%, what exchange does he pay? 48. A buys goods to the amount of $4586.90, less 3 % for cash. He holds B's 30-day acceptance for $1200, and C's 60-day note for $2256.30 at 5%. If A discounts the ac- ceptance and the note at 5%, and remits the full amount of his purchase by bank draft, exchange being ^V%' what does he save by paying cash ? 49. A man has $25,050 to invest. Which will yield the more in one year, Norfolk and Western R. R. at 167, no brokerage, paying 5% dividends, or a deposit in a savings bank at 3 % interest yearly ? 50. A business property is valued at $200,000. If the owner pays 1J% taxes, and allows 10% of the earnings for depreciation of the building, for how much must he rent it to clear 7 % on his investment ? APPENDIX THE METRIC SYSTEM The metric system is a decimal system of weights and measures. The United States Government requires the use of the metric system of measures in all medical work of the navy and war departments, and in the public health and marine hospital service. Linear Measure The unit of linear measure is the meter. Table 10 milliineters (mm.) = 1 centimeter (cm.) 10 centimeters = 1 decimeter (dm.) 10 decimeters = 1 meter (m.) 10 meters = 1 decameter (Dm.) 10 decameters = 1 hectometer (Hm.) 10 hectometers = 1 kilometer (Km.) 10 kilometers = 1 myriameter (Mm.) Square Measure The unit of square measure is the square meter for small areas, and the are of 100 sq. m. for land areas. Table 100 square millimeters (sq. mm.) = 1 square centimeter (sq. cm.) 100 square centimeters = 1 square decimeter (sq. dm.) 100 square decimeters = 1 square meter (sq. m.) 100 square meters = 1 square decameter (sq. Dm.) 100 square decameters = 1 square hectometer (sq. Hm.) 100 square hectometers = 1 square kilometer (sq. Km.) 237 238 APPENDIX Land Measure The unit of land measure is the are. Table 100 centares (ca.) = 1 are (a.) = 100 square meters 100 ares = 1 hectare (Ha.) = 10000 square meters Cubic Measure The unit of volume is the cubic meter. Table 1000 cubic millimeters (cu. mm.) = 1 cubic centimeter (cu. cm.) 1000 cubic centimeters = 1 cubic decimeter (cu. dm.) 1000 cubic decimeters = 1 cubic meter (cu. m.) Wood Measure The unit of wood measure is the stere. Table 10 decisteres (ds.) = 1 stere (s.) = 1 cubic meter 10 steres = 1 decastere (Ds.) = 10 cubic meters Measure of Capacity The unit of capacity for either solids or liquids is the liter., which is equal in volume to 1 cu. dm. Table 10 milliliters (ml.) = 1 centiliter (cl.) 10 centiliters = 1 deciliter (dl.) 10 deciliters = 1 liter (1.) 10 liters = 1 decaliter (Dl.) 10 decaliters = 1 hectoliter (HI.) 10 hectoliters = 1 kiloliter (Kl.) TABLES OF EQUIVALENTS 239 Measure of Weight The unit of weight is the gram^ which is the weight of 1 cu. cm. of distilled water in a vacuum, at its greatest density (39.2° F.). It weighs 15.4324 gr. Table 10 milligrams (mg.) = 1 centigram (eg.) 10 centigrams = 1 decigram (dg.) 10 decigrams = 1 gram (g.) 10 grams = 1 decagram (Dg.) 10 decagrams = 1 hectogram (Hg.) 10 hectograms = 1 kilogram (Kg.) 10 kilograms = 1 myriagram(Mg.) 10 myriagrams = 1 quintal (Q.) 10 quintals = 1 tonneau (T.) TABLES OF EQUIVALENTS Linear Measure 1 inch = 2.54 centimeters 1 centimeter — .3937 of an inch 1 foot = .3048 of a meter 1 decimeter = .328 of a foot 1 yard = .9144 of a meter 1 meter = 1.0936 yards 1 rod = 5.029 meters 1 decameter = 1.9884 rods 1 mile = 1.6093 kilometers 1 kilometer = .62137 of a mile Surface Measure 1 square inch = 6.452 square centimeters 1 square foot = .0929 square meter 1 square yard = .8361 square meter 1 square rod = 25.293 square meters 1 acre = 40.47 ares 1 square mile = 259 hectares 1 square centimeter = .155 square inch 1 square decimeter = .1076 square foot 1 square meter = 1.196 square yards 1 are = 3.954 square rods 1 hectare = 2.471 acres 1 square kilometer = .3861 square mile 240 APPENDIX Cubic Measure 1 cubic inch = 1G.387 cubic centimeters 1 cubic foot = 28.817 cubic decimeters 1 cubic yard = .7(546 cubic meter 1 cord = 3.624 steres 1 cubic centimeter = .061 cubic inch 1 cubic decimeter = .0353 cubic foot 1 cubic meter = 1.308 cubic yards 1 stere = .2759 cord Measures of Capacity 1 dry quart = 1.101 liters 1 liter = .908 dry quart 1 liquid quart = .9163 liter 1 liter = 1.0567 liquid quarts 1 liquid gallon = .3785 decaliter 1 decaliter = 2.6417 liquid gallons 1 peck = .881 decaliter 1 decaliter = 1.135 pecks 1 bushel = .3524 hectoliter 1 hectoliter = 2.8377 bushels Measures of Weight 1 grain Troy = .0648 gram 1 ounce Troy = 31.104 grams 1 ounce avoirdupois = 28.35 grams 1 pound Troy = .3732 kilogram 1 pound avoirdupois = .4536 kilogram 1 ton (short) = .9072 ton 1 gram = 15.432 grains Troy 1 gram = .03215 ounce Troy 1 gram = .03527 ounce avoirdupois 1 kilogram = 2.679 pounds Troy 1 kilogram = 2.2046 pounds avoirdupois 1 ton = 1.1023 short tons Convenient Equivalent Values 1 cubic centimeter of water = 1 milliliter of water, and weighs 1 gram = 15.432 grains 1 cubic decimeter of water = 1 liter of water, and weighs 1 kilogram — 2.2046 pounds 1 cubic meter of water = 1 kiloliter of water, and weighs 1 ton = 2204.6 pounds VALUES OF FOREIGN COINS 241 VALUES OF FOREIGN COINS Value in Country Le(}al Standard Monetary Unit Terms of U. S. Money Argentine Republic . . Gold Peso 10.9647 Austria-Hungary . . . Gold Crown .2080 Belgium Gold and silver Franc .1930 Brazil Gold Milreis .5460 Canada Gold Dollar 1.0000 Central American States: Costa Rica Gold Colon .4650 British Honduras . . Gold Dollar 1.0000 Nicaragua Gold Cordova 1.0000 Guatemala . . . . | Honduras . . . . [ Silver Peso .4340 Salvador .... Chile Gold Peso .3650 China Silver Tael .649 to .723 Denmark Gold Crown .2680 Egypt Gold Pound (100 piasters) 4.9430 Finland Gold Mark .1930 France Gold and silver Franc .1930 German Empire .... Gold Mark .2380 Great Britain .... Gold Pound sterling 4.8065 Greece Gold and silver Drachma .1930 Italy Gold and silver Lira .1930 Japan Gold Yen .4980 Mexico Gold ' Peso .4980 Netherlands Gold Florin .4020 Norway Gold Crown .2680 Panama Gold Balboa 1.0000 Philippine Islands . . . Gold Peso .5000 Portugal Gold Escudo 1.0800 Russia Gold Ruble .5150 Spain Gold and silver Peseta .1930 Sweden Gold Crown .2680 Switzerland Gold Franc .1930 Venezuela Gold Bolivar .1930 BUS. ARITH. 16 242 APPENDIX SQUARE ROOT The square root of a number is one of the two equal fac- tors of that number. Find the square root of 16796.16. ' 1'67'96.16' |129.6 Point off the number into periods of 2 two places each, beginning at the decimal point. Find, by inspection, the perfect square in 1, the first period, and place it in the root. Square 1, the figure al- ready found, and place the result under 1, the first period. Subtract this square from the first period, and bring down the next period, 67. Double 1, the root already found, and place the result at the left of 67 as a trial divisor. 2 will be contained in 6, the trial dividend of 67, 3 times. If we place this 3 in the trial divisor and in the root and multiply, the result, 69, cannot be subtracted from 67, so we must use 2 as the second figure in the root. Place 2 in the root and in the trial divisor, and multiply as shown. Write the result, 44, under the 67, subtract, and to the remainder (23) bring down the next period of the number (96). 2396 will be the new dividend. Double the root already found, divide 24 into 239, put 9 in the root and in the divisor, and multiply. Subtract 2241 from 2396. To the re- mainder bring down the next period. Double 129, divide 258 into 1551, put 6 in the root and in the divisor, and multiply. The decimal point is placed after the 9 in the root because the integers have all been used when 9 is obtained as a figure of the root. Note. The square root of a fraction is obtained by extracting the square root of both numerator and denominator; e.g.y V^^ = f. Or, change the fraction to a decimal and extract as above. 22 ~ 67 i4 249 2396 2241 2586 15516 15516 ABBREVIATIONS USED IN BUSINESS A. . . acre; acres dr. . . debit ace. or % account dr. . . debtor alt. or h. altitude ea. . . each amt. . amount e.g. . . for example @ • . at etc. . . and so forth av. . . average ex. . . example bal. . balance exch. . exchange bbl. or brl. barrel; barrels f. . . franc bdl. . . bundle ; bundles far. . . farthing bg. . . , bag; bags f.o. b. . free on board bl. . . bale ; bales frt. . . freight B/L . bill of lading ft. or ' . foot; feet bot. . . , bought gal.. . gallon; gallons br't for'd brought forward gi. . . gill; gills bu. . , . bushel; bushels gr. . . gross bx. . , , box; boxes h . . hypotenuse cd. . , . cord; cords hhd. . hogshead chg. . charge hr. . . hour; hours ck. . , . check i.e. . . that is c/o . . care of in. or " inch ; inches CO. . . company ins. . . insurance c. 0. d. . collect on delivery inst. . present month coll. , . collection int. . . interest com. . commission Kork area cr. . . credit ; creditor £ . . pound sterling cs. . , case; cases lb. . . pound; pounds ct. or ^ cent; cents L. C. D. least common denominator ctg. . . , cartage L.C.M. least common multiple cu. . , , cubic ltd. . . limited cwt. , hundredweight M. . . mark d. . . , pence m. . . mill ; miUs da. . . day; days mdse. . merchandise dft. . . draft mi. . . mile ; miles disc. . discount min. or ' minute; minutes doz. . . dozen mo. . . month; months 243 244 ABBREVIATIONS USED IN BUSINESS mortg. mortgage ■ rec't . receipt no. or # number ren'd . rendered o.k. . all correct rm. ream oz. . . ounce ; ounces ry. . . railway p. . . page s. . . shilling; shillings pay't . payment sec. or " second; seconds pc. . . piece sec. section; sections pd. . . paid sq. . . sfjuare % . . per cent St. ht. slant height pfd. . preferred T. . . ton; tons pkg. . package twp. . township pp. . . pages ult. . last month pr. . . pair; pairs via . by way of prox. . next month viz. namely pt. . . pint; pints vol. volume pwt. . pennyweight wk. . week; weeks qr. . . quire; quires wt. . . weight qt. . . quart; quarts yd.. . yard; yards rd. . . rod; rods yr. . . year; years rec'd . received INDEX (The figures refer to pages.) A. B. A. checks, 204 Abbreviations, 243 Above par, 192 Acceptance, 206 Account, checking, 158 purchase 134 sales, 134, 136 savings, 159 Acre, 68 Addition, 7 checking, 12 denominate numbers, 73 fractions, 51 horizontal, 14 Ad valorem duty, 183 Agate, 72 Aliquot parts, 47 Altitude, 93, 97 Amount, 117, 144 Angle, 92 Annuity, 155 Anticipation, 125 Apothecaries' fluid measure, 70 weight, 66 Apportionment, 181 Approximate measures, 107 Approximations, 107 Arbitrage, 211 Area, 93 of circle, 95 of parallelogram, 94 of triangle, 94 Assessment, stock, 192 tax, 180 Assessors, 180 Avoirdupois weight, 64 Balance, 158 Balancing account, 20 Bale, 72 Bank, 157 check, 157, 161, 203 discount, 164 draft, 203 Federal reserve, 158 National, 157 note, 64, 157 private, 158 savings, 158 state, 158 Barrel, 66, 70 Base, line, 68, 117 in mensuration, 93 in percentage, 117 Below par, 192 Beneficiary, 189 Bill, clean, 210 documentary, 210 of exchange, 210 Board foot, 104 Bond, 196 coupon, 196 registered, 198 table, 198 Bricks, 105 Broker commission, 133 Brokerage, 133, 193 Building and Loan Associations, 164 Bundle, 72 Bushel, 70 Cable transfer, 209 Canadian money, 64 Cancellation, 42 interest method, 146 Capital, 213 loans, 163 Carat, 66 Carload lots, 215 Carpeting, 100 Cash discount, 124 Cashier's check, 204 Cask, 66 Casting out 9's, 12, 24, 29 Cent, 63 Cental, 66 Centime, 64 Century, 71 Certificate, coupon, 196 of deposit, 160 stock, 193 Certified check, 203 Chain, 68 Check, A.B.A., 204 accuracy, 12, 18, 24, 29 bank, 161, 203 , cashier's, 204 certified, 203 travelers', 204 Checking account, 158 245 246 INDEX Circle, 71, 93 Circular measure, 71 Circumference, 93 Class rates, 215 Clean bills, 210 Clearing house, 209 Closed policy, 185 Coins, Canada, 64 United States, 63 Coinsurance, 187 Collateral, 162 notes, 162 Collection charge, 203 Collector, 133 Combinations in addition, 7 Commercial, discount, 123 draft, 204 fractions, 55 time table, 71 weight, 64 Commission, 133, 193 merchant, 133 Commodity rates, 215 Common, divisor, 40 fraction, 43 interest, 144 multiple, 41 stock, 193 Complement, 18 Compound interest, 153 subtraction, 106 time, 106 Cone, 97 Consignee, 134 Consignment, 134 Consignor, 134 Cord, 69 Corporation, 192 tax, 180 Cost, first or prime, 130 gross, 120 net, 120 Counting table, 72 Coupon, bond, 196 certificate, 196 Credit, 157 Cube, 39, 96 Cubic measure, 69 Customs, 183 Cylinder, 97 Date of maturity, 164 Day, 71 of grace, 164 Decimal, 43 point, 60 Decime, 64 Degree, 71 Denominate numbers, 63 Denomination, 198 Denominator, 43 least common, 46 Deposit, 158 certificate of, 203 slip, 158 Depositor's ledger, 20 Diagonal, 93 Diameter, 93 Diamond weight, 66 Difference, in time, 106 in percentage, 117 Discount, bank, 162, 164 commercial, 123 series, 127 time, 164 true, 168 Divisibility tests, 38 Division, 28 Divisor, greatest common, 40 in fractions, 58 Documentary bills, 210 Dollar, 63 Dozen, 72 Draft, acceptance, 206 bank, 203 commercial, 205 sight, 206 time, 206 Dram, 65, 67 Drawee, 205 Drawer, 205 Dry measure, 70 Duty, 183 '• Eagle, 63 Endowment policy, 189 English money, 64 Equalizing investment, 214 Equation, 88 Even number, 38 Exact interest, 151 time table, 166 Exchange, 201 bUl of, 210 cost of, 209 domestic, 201 foreign, 201, 209 indirect, 210 par of, 210, 211 rate of, 201, 211, 212 Exponent, 39 Express money order, 202 Factor, 38 method, 44 Factoring, 38 Farthing, 64 Fathom, 67 Federal reserve bank, 158 Fee, 202 INDEX 247 Fire insurance, 185 Firkin, 66 Flooring, 103 Foot, 67 board, 104 Footing, 14 Formulas, 94, 98, 118, 121 Fractions, 43 Franc, 64 Free list, 183 Freight, rates, 215 tariff, 215 French money, 64 Fund, 157 sinking, 155 Furlong, 67 Gain and Loss, 120 Gallon, 70 G. C. D. method, 44 Geographical mile, 67 German money, 64 GUI, 70 Gold, certificates, 64 coins U. S., 63 fineness of, 66 Government, land measure, 68 money, 63 Grain measure, 66, 67 Graph, 79 Greatest common divisor, 40 Great gross, 72 Gross, 72 cost, 120, 134 proceeds, 134 weight, 66 Guaranty, 134 Gunter's chain, 68 Hand, 67 Heaped bushel, 70 Horizontal addition, 14 Hour, 71 Hundredweight, 65 Hypotenuse, 92 Import duties, 183 Improper fraction, 45 Inch, 67 Income tax, 180 Incorporated companies, 192 Indemnify, 185 Indirect exchange, 210 Indirect tax, 180, 183 Indorsement, 161 Industrial loans, 163 Inheritance tax, 180 Insolvency, 213 Insurance, 185 fire, 185 life, 189 table of, 190 Interchange of fractions, 43 Interest, 144 bearing debts, 144 cancellation method, 145 common, 144 compound, 153 exact, 151 formulas, 144 laws, 144 6 per cent method, 148 60-day method, 147 special methods, 151 Investment loans, 163 Invoice, date of, 124 Joint rate commission, 215 Judgment notes, 162 Karat, 66 Keg, 66 Knot, 67 Land measure, 68 League, 67 Leakage, 183 Least common denominator, 46 Least common multiple, 41 Legal rate of interest, 144 Letter of credit, 210 Liabilities, 122, 213 License fee, 180 Line, 92 Linear measure, 67 Link, 68 Liquid measure, 70 Load, 69 Loans, 162 London exchange, 202 Long measure, 67 Long-time loans, 163 Long ton, 65 Loss, 213 Lumber 104 Making change, 18 Manual training, 107 Mark, 64 Market value, 192 Marking goods, 128 Maturity, 144 Measures, of capacity, 64 of value, 63 of weight, 64 Mensuration, 92 Merchants' rule, 171 Meridian, principal, 68 Metric system, 237 Mile, 67, 68 248 INDEX Mill, 63 Minimum weight, 216 Minute, circular measure, 71 time measure, 71 Miscellaneous, measures, 72 problems, 30, 83, 109, 137, 221 Mixed number, 45 Money, centers, 202 tables, 63 Month, 71 Mortgage loans, 163 Multiplication, 23 of commercial fractions, 55 of fractions, 53 rapid method of, 25 National Bank, 157 Negotiable paper, 162 Net cost, 120 gain, 213 loss, 213 price, 124 proceeds, 134 selling price, 121 weight, 66 wholesale price, 124 New York exchange, 202 Nonnegotiable paper, 162 Note, collateral, 162 judgment, 162 Numerator, 43 Open policy, 185 Ounce, apothecaries', 67 commercial, 65 Troy, 66 Painting, 100 Papering, 100 Par, 192 of exchange, 210 value, 192 Parallel lines, 92 Parallelogram, 93 Parcel post, 219 Parenthesis, 18 Partial payments, 169 Partnership, 213 Pass book, 158 Peck, 70 Pence, 64 Pennyweight, 66 Percentage, 117 Perch, 69 Perimeter, 93 Perpendicular, 92 Pfennig, 64 Pica, 72 Pint, 70 172, Plastering, 100 Point, 72 Policy, 185 endowment, 189 open, 185 term, 189 valued, 185 whole life, 189 Poll tax, 182 Polygon, 92 Postal, money order, 202 savings bank, 162 savings certificate, 162 Pound, commercial, 65 Troy, 66 sterling, 64 Power, 39 Practical measurements, 100 Preferred, risk, 187 stock, 193 F*remium, insurance, 185 stock, 192 Present worth, 168, 213 Price, list, 124 net, 124 Prime cost, 134 factor, 38 number, 38 Principal, 134, 144 meridian, 68 Printers' measure, 72 Prism, 96 Private bank, 158 Proceeds, bank, 164 gross, 134 net, 134 Profit, 130, 213 Proper fraction, 45 Properties of numbers, 38 Property tax, 180 Protest, 206 Pyramid, 97 Quadrilateral, 92 Quart, 70 Quintal, 66 Quire, 72 Radical sign, 40 Radius, 93 Railroad, 215 Range, 68 Rate, carload, 215 class, 215 commodity, 215 exchange, 201 legal interest, 144 per cent, 117, 144 railroad, 215 Ream, 72 INDEX 249 Reciprocal, 58 Rectangle, 93 Reduction, of denominate numbers, 73 of fractions, 44 Registered bond, 198 Resources, 122, 213 Retail merchants' table, 131 Review problems, 227 Right angle, 92 triangle, 92 Road taxes, 180 Rod, 67, 68 Roofing, 103 Root, square, 242 Savings bank, 158, 162 Score, 72 Scruple, 67 Second, circular measure, 71 time measure, 71 Section of land, 69 Security, 162 Share, 192 Sheet, 72 Shilling, 64 Shipment, 134 Short rate, 187 Short-time loans, 163 Sight draft, 206 Simple interest, 144 table, 149 Sinking fund, 155 Six per cent method, 148 Sixty-day method, 147 Size, 67 Slant height, 97 Solar year, 71 Solids, 96 Sovereign, 64 Special interest methods, 151 Specific duty, 183 Square, 68, 93 measure, 68 roofing, 103 root, 40, 242 Standard time, 71 State bank, 158 Statute mile, 67 Stocks, 192 assessment, 192 broker, 193 certificate, 192 common, 193 companies, 192 preferred, 193 Stone, 105 Stub of check, 161 Subsidiary coins, 64 Substitution, 89 Subtraction, 17 checking, 18 compound, 106 fractions, 52 Surface measure, 68 Surveyors' long measure, 68 Tables, aliquot parts, 47 bond, 198 commercial, 65 compound interest, 154 counting, 72 denominate numbers, 63 domestic exchange, 202 foreign coins, 241 foreign exchange, 211, 212 import duties, 183 insurance, 190 metric system, 237 miscellaneous measures, 72 money, 63 multiplication, 23 paper, 72 parcel post, 219 percentage, 47 printers', 72 retail merchants', 131 simple interest, 149 sinking fund, 155 time, 166 Tare, 66, 183 Tariff, 180 freight, 215 Tax, 180 apportionment, 181 assessment, 180 direct, 180 formulas, 180 indirect, 180, 183 transfer, 200 Telegraphic money order, 202 Teller, 158 Term, fraction, 43 of credit, 124 policy, 189 Tests of divisibility, 38 Time, 144 discount, 164 draft, 206 measure, 71 standard, 72 table, 166 Ton, 65 Township, 69 Trade discount, 123 Transfer, of money, 201 tax, 200 Travelers' checks, 204 Trial balance, 35 Triangle, 92 Troy weight, 66 250 INDEX True discount, 168, 192, 194 Trust companies, 158 Two-figure combinations, 7 United States, customs, 183 money, 63 rule, 170 Usury, 144 Value, of foreign coins, 241 insurable, 186 market, 192 par, 192 Valued policy, 185 Vinculum, 18 Volume, 97 Week, 71 Weight, apothecaries', 66 commercial, 64 Troy, 66 Whole-life policy, 189 Wholesale and retail profits, Winchester bushel, 70 Withdrawals, 160 With exchange, 205 Without exchange, 205 Wood, 105 Yard, 67 Year, 71 Zone, 220 130 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO 50 CENTS ON THE FOURTH DAY AND TO $1.00 ON THE SEVENTH DAY OVERDUE. SEP 251 9* 1 l5Dec'521K DEC 18 1952 i; MAR 5 19423 iSDec'KOLt •WTTjseo AUG 11 1944 >^ >. 05 NriVl4B6B 13Jec'£0Lf LD 21-100m-7,'40 (69368) VB 1 7221' y 30S986 UNIVERSITY OF CAUFORNIA UBRARY