LIBRARY OF THE UNIVERSITY OF CALIFORNIA. GIFT OF Class THE PACKARD COMMERCIAL ARITHMETIC. S. S. PACKARD, PRESIDENT OF PACKARD'S BUSINESS COLLEGE, NEW YORK, AUTHOR OF THE BRYANT AND STRATTON BOOK-KEEPING SERIES, AND OF PACKARD'S COMPLETE COURSE OF BUSINESS TRAINING, AND BYRON HORTON, A.M., PRINCIPAL OF THE MATHEMATICAL DEPARTMENT OF PACKARD'S BUSINESS COLLEGE. NINTH EDITION. NEW YORK: S. S. PACKARD, 805 BROADWAY. 1883. THE. PACKARD COMMERCIAL ARITHMETIC. COMPLETE EDITION, 328 PAGES, OCTAVO. SCHOOL EDITION, 276 PAGES, 12MO. KEY TO COMPLETE EDITION (FoR TEACHERS), $1.00. KEY TO SCHOOL EDITION IN PREPARATION. The complete edition is published both with and without answers. Unless otherwise ordered, books without answers will be sent. COPYRIGHT, 1882, BY S. S. PACKARD AND BYRON HORTON. Electrotyped by Printed by SMITH & McDouoAL. RUSSELL BROTHERS PREFACE. THE question as to whether a new Commercial Arithmetic was called for, is answered in the ready sale which has attended the publication of this volume. It does not necessarily argue that other arithmetics have failed to meet a large popular demand, or that those who use them are dissatisfied with them. It simply emphasizes the fact that what may suit one intelligent teacher will not, for that reason alone, suit another ; and nothing could make this point clearer than to state, what is really true, that all the Commercial Arithmetics that have appeared during the past ten years have been prepared by active teachers, who required cer- tain things in their own work not to be found in existing books. There are few, if any, text books that could not, in some respects, be changed to advantage by those who use them ; and the main reason why there are not fifty text books where there is but one is a reason of economy, rather than of inability of teachers to pre- pare their own books, or even of entire satisfaction with the books in use. It is worthy of notice that, in the line of commercial text books particularly, there is a growing tendency to authorship on the part of wide awake teachers ; so much so that there are to-day twenty treatises on book-keeping where there was one twenty years ago ; and in the line of commercial mathematics, commercial law and practical grammar, one can safely calculate on a new book every six months. Nobody has a right to complain of this tendency. It should, in fact, give great satisfaction to all who are interested in practical education ; for it not only speaks of the growing energy and intelligence of the teachers who have this education in charge, but especially of the appreciation of the public, through whose encouragement alone such worthy ambition can be gratified. The authors of this book do "not claim to have discovered, all at once, that nobody hitherto has had the ability to prepare an arithmetic, or that it was impossible longer to utilize the books 183983 iv PREFA OE. that have served the purposes of the past. They do not even claim that their book is better, or worse, than any or all of its pre- decessors ; they claim only that it is different from any of them, and in this difference lies their only excuse for its appearance. The book was written to supplv a known want in a single school, with the feeling, also, that other schools, having felt a similar want, might find it met, in some measure, through the efforts here put forth. In fact, a large number of teachers have already expressed such satisfaction in a practical way, and there are doubtless others, on the point of issuing their own books, who, upon a close exam- ination of this, will find it so well suited to their purpose that they will be induced to lay aside for a time their unfinished manu- script, and possibly to defer publication indefinitely. There is no desire on the part of the authors of this book to discourage the publication of new arithmetics ; but they are quite willing to do what lies in their power, in connection with their fellow-authors already in the field, to satisfy teachers so fully that they will find no good excuse for diverting their energies from the great work of oral instruction, but will seek rather to give to it new zest, with the consciousness that others are both willing and able to relieve them from the irksomeness and risk of book-making. It is not deemed necessary to point out with particularity the peculiar merits or demerits of the book. Both will be readily dis- cerned by those who use it, and those who do not use it will care very little about them. We will only say that it is not a re- hash of any book or books that have gone before it, and that in not a single instance have the authors relied for their statistics, their statements of local laws and customs, or any of their facts, upon other authors, either of the present or the past, but have uniformly obtained their information from the highest authentic sources. And, moreover, they propose to keep open these avenues of infor- mation, and to revise all future editions closely in reference to any changes that may occur. It is but justice to say that the main work of authorship has been done by the one whose name stands second on the title page, which renders it possible to add that it has been conscientiously and faichfully done. NEW YORK, October 2, 1882. CONTENTS. PACK PROPERTIES OF NUMBERS 1 Prime Factors . . 3 Common Divisors 4 Common Multiples 6 Cancellation 8 REVIEW EXAMPLES 11 FRACTIONS 14 Reduction 16 Addition 20 Subtraction 22 Multiplication ... 23 Division 27 REVIEW EXAMPLES 32 DECIMALS 36 Reduction 40 Addition 41 Subtraction . 43 Multiplication 44 Division 45 REVIEW EXAMPLES 46 DENOMINATE NUMBERS 49 Divisions of Time 49 Linear Measures 51 Square Measures 52 Cubic Measure 54 Liquid Measures 56 Dry Measure 66 Measures of Weight 57 Circular Measure 59 United States Money 60 English Money .... 63 Foreign Moneys of Account 64 Reduction of Denominate Integers 65 Reduction of Denominate Fractions 67 Addition 71 Subtraction 72 Multiplication 74 Division 75 Longitude and Time 75 THE METRIC SYSTEM 77 Linear Measure 78 Square Measure 79 Cubic Measure 80 Dry and Liquid Measure 81 Weight 82 Table of Equivalents 84 Approximate Rules 85 FOREIGN WEIGHTS AND MEASURES 88 Vi CONTENTS. PAGE REVIEW EXAMPLES 90 PERCENTAGE 95 DISCOUNTS 100 BILLS. 102 COMMISSION AND BROKERAGE 110 PROFIT AND Loss 114 INTEREST 117 Accurate Interest 127 PROBLEMS IN INTEREST 129 To find the Rate 129 To find the Time 130 To find the Principal, the Interest, Time, and Rate being given. . . 131 To find the Principal, the Amount, Time, and Rate being given. . . 132 PRESENT WORTH AND TRUE DISCOUNT 133 REVIEW EXAMPLES 134 ANNUAL INTEREST ] 37 COMPOUND INTEREST 139 COMMERCIAL PAPER 143 BANK DISCOUNT 149 PARTIAL PAYMENTS 153 United States Rule 153 Mercantile Rules 156 Connecticut Rule 159 New Hampshire Rule 161 Vermont Rule 162 RATIO AND PROPORTION 163 INSURANCE 166 Fire Insurance 168 Marine Insurance 169 EXCHANGE 174 Domestic Exchange 175 Foreign Exchange 178 EQUATION OF ACCOUNTS 187 When the items are all debits or all credits 187 When the account contains both debit and credit items 198 Equation of Accounts Sales 203 ACCOUNTS CURRENT 207 STOCKS AND BONDS 216 Government Bonds 218 New York Stock Exchange 221 TAXES 235 DUTIES 238 PARTNERSHIP 249 NATIONAL BANKS 264 SAVINGS BANKS 269 LIFE INSURANCE 273 GENERAL AVERAGE 280 CLEARING HOUSES 285 DETECTION OF ERRORS IN TRIAL BALANCES 290 REVIEW EXAMPLES 291 APPENDIX 296 Drill Exercises 296 Short Method of finding the Balance of an Account 298 Short Methods in Multiplication 299 Short Methods of Division 310 Explanatory Notes 312 V OF THE I UNIVERSITY ) COMMERCIAL ARITHMETIC. PROPERTIES OF NUMBERS. DEFINITIONS. 1. A Unit, or Unity, is one, or a single thing; as one, one foot, one dollar. 2. A Number is a unit, or a collection of units ; as one, four, three feet, five dollars. 3. All numbers are either integral or fractional, abstract or concrete. 4. An Integral Number, or Integer is a number which expresses whole things ; as two, four gallons, seven dollars. 5. A Fractional Number, or Fraction is a number which expresses one or more equal parts of a unit ; as one-half, three-fourths. 6. An Abstract Number is a number which does not refer to any particular object ; as one, six, ten. 7. A Concrete Number is a number applied to an object, or quantity ; as three apples, five pounds, ten dollars. 8. Integral numbers are either odd or even, prime or com- posite. 9. An Odd Number is a number whose unit figure is 1, 3, 5, 7, or 9 ; as 7, 21, 39. 2 PROPERTIES OF LUMBERS. 1C. An Even Number is a number whose unit figure is 0, 2, 4, 6, or 8 ; as 6, 40, 74. 11. A Prime Number is a number which can be exactly divided only by itself and unity ; as 1, 7, 13, 29. 12. Numbers are prime to each other when no integral number greater than 1 will divide each without a remainder. Numbers that are prime to each other are not necessarily prime numbers. Thus, 25 and 28 are prime to each other, but they are not prime numbers. 13. A Composite Number is a number which can be exactly divided by other integers besides itself and unity. Thus 28, the product of 4 and 7, is a composite number. It is exactly divisible by 4 and 7. DIVISIBILITY OF NUMBERS. 14. An Exact Divisor of a number is any number that will divide it without a remainder. Thus 2, 3, 4, 6, 8, and 12 are exact divisors of 24. 15. A number is said to be divisible by another when the latter will divide the former without a remainder. Any number is divisible 1. By 2, if it is an even number ; ae 6, 28, and 32. 2. By 3, if the sum of its digits is divisible by 3 ; as 849 (8 + 4+9 = 21, 21 is divisible by 3), 7323, and 47892. 3. By 4, if the two right-hand figures are ciphers, or express a number divisible by 4 ; as 1100, 216, and 7328. 4. By 5, if the right-hand figure is or 5 ; as 40 and 135. 5. By 6, if it is an even number and the sum of its digits is divisible by 3 ; as 216, 840, and 732. 6. By 8, if the three right-hand figures are ciphers, or express a number divisible by 8 ; as 3000 and 7168. 7. By 9, if the sum of its digits is divisible by 9 ; as 216, 783, and 12348. PRIME FACTORS. PRIME FACTORS. 16. The Factors of a number are those numbers which multiplied together will produce the number. Thus 4 and 7 ; 2 and 14 ; 2,2, and 7 are factors of 28. The number itself and unity are not regarded as factors. The factors of a number are also the exact divisors of it. 17. A Prime Factor is a prime number used as a factor. Thus, 2, 2, and 7 are the prime factors of 28. 4 is a factor of 28, but not & prime factor. 18. To find all the prime factors of a composite number. Ex. What are the prime factors of 6930. OPERATION. ANALYSIS. Any prime number that is an exact divi- 2 ) 6930 sor of the given number is a prime factor of it. Divide , qj/- the given number by 2 (15, 1), the least prime divisor of it, obtaining the quotient 3465. Next, divide this quo- 3 ) 1155 tient successively by 3 (15, 2), 3, 5 (15, 4), and 7. The 5 ) 385 last ( l uotient 11 is a P rime number and therefore a prime factor. The several divisors 2, 3, 3, 5, 7 and the last quo- ) ' tient 11 are the prime factors required. 11 2x3x3x5x7x11 = 6930. 19. RULE. Divide by the least prime ninriber which will divide the given number without a remainder. In like manner divide the resulting quotient, and continue the division until the quotient is a prime number. The several divisors and the last quotient are the prime factors. EXAMPLES. 2O. Resolve the following numbers into their prime factors : 1. 3465. 7. 6552. 13. 8192. 19. 6660. 2. 3003. 8. 7826. 14. 6561. 20. 2448. 8. 4158. 9. 6006. 15. 3125. 21. 8525. 4. 3150. 10. 5368. 16. 1800. 22. 9936. 5. 3675. 11. 3825. 17. 1935. 23. 9576. 6. 2310. 12. 5324. 18. 2475. 24. 5075. PROPERTIES OF NUMBERS. COMMON DIVISORS. 21. A Common Divisor, or Common Measure, of two or more numbers is any number that will divide each without a remainder ; hence it is a common factor of each of them. 22. The Greatest Common Divisor of two or more numbers is the greatest number that will divide each without a remainder ; hence it is their greatest common factor. Thus, 2, 3, 4, and 12 are common divisors of 36, 48, and 60 ; 12 is their greatest common divisor. 23. PRINCIPLE. TJie greatest common divisor of tivo or more numbers is the product of all their common prime factors. 24:. To find the greatest common divisor of two or more numbers. Ex. What is the greatest common divisor of 168, 252, and 420 ? FIRST OPERATION. * * * * 168 = 2x2x2x3x7 ANALYSIS. Resolve the numbers into * * * * their prime factors. The product, 84, of the common factors 2, 2, 3, and 7 is the greatest 420 = 2x5x3x5x7 common divisor. (Prin.) 2x2x3x7 = 84. SECOND OPERATION. ANALYSIS. Divide the given numbers by 4 ) 168, 252, 420 an y number that will divide them all without anc * Divide the quotients in the ) 4%, bo, 105 same manner until the last quotients have no 3)6, 9, 15 common divisor. Since 4 will divide all the I o I given numbers, and 3 and 7 will divide successively the resulting quotients, their 4x7x3 = 84. product, 84, is a common divisor of the given numbers. Since the last quotients have no common divisor or factor, 84 is the greatest common divisor. 25. RULE. Resolve the numbers into their prime fac- tors. The product of the factors common to all the numbers will be the greatest common divisor. Or, Divide the given numbers by any factor that will divide all of them without a remainder. In H7ce manner divide COMMON DIVISORS. 5 the resulting quotients, and continue the division until the quotients have no common factor, ^e product of the sev- eral divisors will be the greatest common divisor. EXAMPLES. 26. Find the greatest common divisor of the following numbers : 1. 24, 36, and 48. 9. 108, 144, and 360. 2. 35, 56, and 70. 10. 144, 336, and 240. 8. 42, 56, and 28. 11. 165, 550, and 220. 4. 30, 60, and 75. 18. 792, 144, and 216. 5. 64, 96, and 128. 13. 405, 243, and 324. 6. 66, 198, and 330. 14. 378, 126, and 252. 7. 90, 150, and 210. 15. 375, 625, and 250. 8. 84, 420, and 126. 16. 288, 720, and 864. 27. To find the greatest common divisor of two numbers when they are not readily factored. 28. PRINCIPLES. 1. If the smaller of tivo numbers is a divisor of the greater, it is their greatest common divisor. 2. A common divisor of two numbers is a divisor of their sum, and also of their difference. 3. A divisor of a number is a divisor of any multiple of that number. 29. RULE. Divide the greater number by the smaller, and divide the last divisor by the remainder; and so con- tinue until there is no remainder. The last divisor will be the greatest common divisor. ~3 ' NOTES. 1. When the greatest common divisor of more than two numbers is required, find the greatest common divisor of the smallest two first, and of this greatest common divisor and the next greater, and so on, until all tlie numbers are used. The last divisor will be the greatest common divisor of all the given numbers. 2. If, at any step in the process, a prime factor appear that is not common to all the numbers, it may be rejected. (See second operation of example.) 3. If the remainder at any time is a prime number, and it is not contained in the last divisor, there is no common divisor greater than 1 ; it will there- fore be useless to further jontinue the division. 6 PROPERTIES OF NUMBERS. Ex. Find the greatest common divisor of 391 and 437. OPERATIONS. DEMONSTRATION. Since 391 ) 437 (1 23 is a divisor of 46, it is a di- 391 Or, visor of 368 > a multiple of 46 ~7 \ QQ1 / Q 9 \ K (Prin - 3) ' ' ShlCe 23 1S a diviS01 ' of itself and 368, it is a divisor 368 23)391(17 of their sum, 391 (Prin. 2). 23 ) 46 ( 2 23 Since 23 is a divisor of 46 and . 391, it is a divisor of their sum, 437. 23 is therefore a common 161 divisor of 391 and 437, the rt given numbers. The greatest common di- visor of 391 and 437, whatever it may be, is a divisor of their difference, 46 (Prin. 2) ; also of 368, a multiple of 46 (Prin. 3) ; also of 23, 391 368 (Prin. 2). Since the divisor of a number cannot be greater than itself, the greatest common divisor of the given numbers cannot be greater than 23. 23 is therefore the greatest common divisor. 3O. Find the greatest common divisor of the following numbers : 1. 319 and 377. 6. 744, 984, and 522. & 259 and 629. 7. 391, 667, and 920. 3. 589 and 713. 8. 451, 481, and 737. 4. 903 and 989. 9. 504, 756, and 252. 6. 611, 799, and 987. 10. 425, 748, and 561. COMMON MULTIPLES. 31. A Multiple of a number is a number that is exactly divisible by it ; or, it is any product of which the given number is a factor. 32. A Common Multiple of two or more numbers is a number that is exactly divisible by each of them. 33. The Least Common Multiple of two or more num- bers is the least number that is exactly divisible by each of them. Thus, 12, 24, 36, and 48 are common multiples of 4 and 6; 12 is their least common multiple. COMMON MULTIPLES. 7 34. PRINCIPLES. 1. A multiple of a number contains all the prime factors of that number. 2. A common multiple of two or more numbers contains all the prime factors of each of those numbers. 3. The least common multiple of two or more numbers contains all the prime factors of each of the numbers, and no other factors. 35. To find the least common multiple of two or more numbers. Ex. What is the least common multiple of 12, 18, 20, and 40? FIRST OPERATION. ANALYSIS. Since 40, a multiple 12 = 2x2x3 of 20, contains all the prime factors of 18 = 2 X 3 X 3 20, the number 20 may be omitted in AQ 2x2x2x5 * ne o P era ^ on - Resolve the numbers into their prime factors. The least 2x2x2x3x3x5 = 360 common multiple must contain 2 as a factor 3 times in order to be divisible by 40 ; it must contain 3 as a factor twice in order to be divisible by 18 ; and it must contain 5 as a factor, in order to be divisible by 40. 360, the product of the factors 2, 2, 2, 3, 3, and 5, is the least common multiple of the given numbers, since it contains the different factors the greatest number of times that they occur in the given numbers, and no other factors (Prin. 3). SECOND OPERATION. ANALYSIS. The factors of the re- 2)12, 18, 40 quired multiple may be selected by the 2 \ Q Q OQ following process. Divide the given num- bers by any prime number that will divide 3)3, 9, two or more of them, writing the quo- -^ 3 10 tients and the undivided numbers be- neath. Treat the resulting numbers in 2x2x3x3x10 = 360 like manner, and continue the process until no two of the numbers have a com- mon factor or divisor. The product of the several divisors and the remaining quotients and undivided numbers will be the least common multiple. 36. EULE. Resolve the given numbers into their prime factors, ^e product of the different prune factors, taking each factor the greatest number of times it appears in any of the numbers, will be the least common multiple. Or, 8 PROPERTIES OF NUMBERS. Divide the given numbers T}y any prime number (see Note 2) that will exactly divide two or more of them, writing the quotients and undivided numbers beneath. Repeat the operation with the resulting numbers until there is no exact divisor of any two of them. The product of the several divisors and the last quotients and undivided numbers will be the least common multiple. NOTES. 1. In the operation, reject such of the smaller numbers as are divisors of the larger; also reject such of the quotients and undivided num- bers as are divisors of the others. 2. Divide by composite numbers when they are exact divisors of all the numbers. EXAMPLES, 37. Find the least common multiple of the following numbers : 1. 2, 3, 4, 5, and 6. 15. 18, 24, and 36. 2. 8, 10, 12, and 15. 16. 10, 24, and 32. 3. 12, 15, 18, and 24. 17. 16, 18, and 20. 4. 6, 10, 15, and 30. 18. 24, 36, and 40. 5. 16, 24, and 48. 19. 32, 48, and 72. 6. 30, 40, and 60. 20. 16, 22, and 24. 7. 2, 4, 8, and 16. 21. 18, 28, and 30. 8. 14, 21, and 28. 22. 12, 16, and 20. 9. 5, 8, 15, and 18. 28. 33, 44, and 55. 10. 6, 9, 21, and 24. 24. 27, 36, and 42. 11. 12, 20, and 30. 25. 36, 45, and 60. 12. 6, 10, 30, and 40. 26. 28, 35, and 42. IS. 32, 48, and 60. 27. 45, 55, and 60. 14. 24, 32, and 40. 28. 60, 72, and 84. CANCELLATION. 38. Cancellation is a method of shortening an operation by rejecting equal factors from both dividend and divisor. 39. PRINCIPLES. 1. Canceling or rejecting a factor from a number, divides the number by that factor. 2. Dividing both dividend and divisor by the same number does not affect the value of the quotient. CANCELLATION. 9 Ex. Divide 84 x 36 by 27 x 14. OPERATIONS. ANALYSIS. Indicate the oper- Or, ations to be performed as in the flU v * . . I . m . margin. It is seen by inspection w ,-,. r that 36 and 27 contain the com- 6 4 rnon factor 9 > tnerefor e cancel or reject it from both, retaining the 8 factors 4 and 3 respectively. 14 and 84 contain the common factor 14; therefore reject it, retaining the factor G in the dividend. [Since cancel- lation is a process of division, the rejecting of 14 does not destroy it, but divides it, leaving 1 as a quotient. It is unnecessary to write 1 as a quotient, except when there are no other factors in the dividend.] 3 is a common fac- tor of 6 and 3 ; therefore reject it from both, retaining the factor 2 in the dividend. The product of the remaining factors, 2 and 4, is the required quotient. 40. RULE. Indicate the operations to be performed, by writing the numbers denoting multiplication above a hori- zontal line, and the numbers denoting division below. The numbers above the line will form a dividend, and the num- bers below a divisor. Cancel or reject the factors common to both dividend and divisor. The product of the remain- ing factors of the dividend divided by the product of the remaining factors of the divisor will be the required quo- tient. EXAMPLES. 41. 1. Divide 27 x 48 x 60 by 54 x 36 x 1-0. What is the value of the following expressions : 40x36x42x18 24x30x54x35 9x35x30x8 ' 14x15x21x64* 360_x28_x272<6 17 x 36 x 25 x 144 * 25x42x18x12* ' 48x60x108x51' 1760x175x6 1760 x 6 x 145 4x9x100x10* 100x365 1500 x 144 x 5 144x625x37x12 ~ 365x100 288x375x185 10. Multiply 72 by 3 x 18, divide the product by 8 times 9, multiply the quotient by 7 x 20, divide the product by 360 ; mul- tiply the quotient by 6 times 8. 10 PROPERTIES OF NUMBERS. 11. If 42 tons of coal cost $147, what will 16 tons cost ? 12. A man gave 9 pounds of butter at 1 7 cents a pound for 3 gallons of molasses ; how much was the molasses worth a gallon ? 13. If 20 pounds of beef cost 250 cents, what cost 75 pounds ? 14. How many potatoes at 65 cents per bushel will pay for 13 weeks' board at $7.50 per week ? 15. A merchant bought 375 barrels of flour at $5.50 per barrel, and paid in cloth at $2.75 per yard ; how many yards did it require ? 16. How many pounds of coffee at 27 cents per pound should be given for 57 bushels of corn at 63 cents per bushel ? 17. Sold 28 bushels of apples for $21 ; what should I receive for 42 bushels ? 18. How many cows worth $35 each must be given in exchange for 84 tons of hay at $15 per ton ? 19. How many bushels of corn at 52 cents a bushel must be exchanged for 324 bushels of oats at 39 cents per bushel ? 20. If 430 bushels of wheat are obtained from sowing 7 bush- els, how much would be obtained from sowing 21 bushels ? 21. What should be paid for the transportation of 3600 pounds of cheese at the rate of 47 cents per 100 pounds ? 22. What must be paid for transporting 31600 pounds of iron at $5 per ton of 2000 pounds ? 23. What will 7840 pounds of coal cost, at $6 per ton of 2240 pounds ? 24. If 3 men eat 7 pounds of meat in one week, how much would 6 men eat in 4 weeks ? 25. How many canisters, each holding 40 ounces, can be filled from 3 chests of tea, each containing 55 pounds of 16 ounces ? 26. How many times can 16 bottles, each holding 3 pints, be filled from 6 demijohns, each containing 10 gallons of 8 pints each ? 27. A man exchanged 275 barrels of potatoes, each containing 3 bushels, at 54 cents per bushel, for a certain number of pieces of muslin each containing 45 yards, at 11 cents per yard. How many yards did he receive ? 28. If a person travel 24 hours each day at the rate of 45 miles an hour, how many days would it require to pass around the globe, a distance of 25000 miles ? REVIEW EXAMPLES. 11 REVIEW EXAMPLES. 4:2. 1. Write in figures each of the following numbers, add them, and express in words (or numerate) their sum : Forty-five thousand and forty-five ; sixteen thousand three hundred and sixty ; one hundred and sixty-seven thousand ; eight hundred and fifty thousand and ninety-two ; nine million and twenty-four. 2. Subtract eight hundred and fourteen thousand nine hun- dred and sixteen from four million and nineteen thousand. 3. Multiply five hundred and sixty thousand seven hundred and eight by eighteen hundred and sixty. 4. A quantity of merchandise was bought for $27618.75, and sold for $32418.25. What was the gain ? 5. What is the sum of 2817, 273, 30006, 97, 7285, 2700576, 7000781, 27 ? 6. If I sell goods for $23876, and gain $5389, what did the goods cost me ? 7. What is the sum of the prime numbers from 20 to 50 ? Add the following numbers as they stand, from left to right, and from right to left. [In making out bills, and in other com- mercial operations, a great deal of time can be saved by adding in this manner, without re-arranging the numbers. ] 8. 17, 27, 36, 14, 43, 42, 65, 73, 81, 35. 9. 137, 414, 528, 345, 678, 975, 864, 357, 121, 234. 10. 67.16, 5.12, 3.75, 475, 38.42, 59.27, 38.75, 175.25. 11. 2345, 16, 375, 4218, 376, 7, 8475, 247, 39. 12. 1234.27, 348.25, 775, 7.16, 89.76, 374.12, 5673.56, 397.23. Find the difference between the numbers in each of the fol- lowing groups. [In all of these cases the subtrahend is-placed above the minuend, the purpose being to give the student practice in subtracting downward rather than upward, as the general cus- tom is. It is often requisite in business to perform the work in this way, and the accountant should practice both methods.] (13.) V4.) (15-) (16.) (17.) 76534 19827 26347 72016 12345 81279 84362 71356 99385 54321 12 PROPERTIES OF NUMBERS. 18. One factor of a certain number is 217 and the other 5280 ; what is the number? 19. Find the prime factors of 108108. W. If the quotient is 375 and the divisor 246, what is the dividend ? 21. If the product of two factors is 450072, and one of the factors is 987, what is the other factor ? 22. What is the sum of the composite numbers from 60 to 90 inclusive ? 23. Divide 76432801 by 783. Prove that your solution is correct. 24.. A clerk receiving a salary of $1256, pays $468 a year for board, $180 for clothing, and $150 for other expenses. "What amount has he left ? 25. What is the least number that can be exactly divided by each of the following numbers : 24, 32, 80, 48, and 90 ? 26. If I take 24889 from the sum of 9872 and 24967, divide the remainder by 50, and multiply the quotient by 18, what is the product ? 27. If 160 acres of land cost $10720, how many acres can be bought for $8844? 28. What is the least common multiple of the nine digits ? 29. If 75 head of cattle cost $2550, what will 59 head cost ? SO. A merchant sold 426 barrels of flour for $2556, which was $639 more than he gave for it. What did it cost him a barrel ? 31. What is the greatest number that will exactly divide each of the following numbers : 246, 744, and 522 ? 32. What is the smallest sum of money with which horses can be bought at $96 each, cows at $30 each, or sheep at $5 each, using the same amount in each case ? 33. A merchant bought 387 yards of cloth at 79 cts. per yard ; he sold 298 yards at $1.16 per yard, and the remainder at 97 cts. per yard ; how much did he gain ? 34. Cash on hand at beginning of the day, $6492.75 ; cash received, $11456.75; cash paid out, $13285.26. Required the cash balance at the end of the day. 35. Mr. A has three farms, the first of which contains 158 acres, the second 32 acres less than the first, and the third as many as the other two. What is the value per acre, if all are worth $26128 ? REVIEW EXAMPLES. 13 36. There are five bidders to supply the government with 800 tons Lehigh, 500 tons Cumberland, and 700 tons Baltimore coal. A offers Lehigh at $6.29, Cumberland at $4.38, and Baltimore at $7.23. B offers Lehigh at $6.80, Cumberland at $4.12, and Balti- more at $7.24. C offers Lehigh at $6.40, Cumberland at $4.45, and Baltimore at $7.18. D offers Lehigh at $6.17, Cumberland at $4.19, Baltimore at $7.20. E offers Lehigh at $6.50, Cumberland at $4.33, and Baltimore at $7.25. Who is the lowest bidder for the whole amount, and how much does each bid amount to ? 37. A drover bought a number of cattle for $12204, and sold the same for $13560, by which he gained $4 per head. How many cattle were purchased ? 38. A farmer raised in one year 512 bushels of wheat, the next year twice as much as he raised the first year, and the third year four times as much as he did the second year. What was the value of the three crops at $1.65 per bushel ? 39. How many pounds of tea at 78 cts. per pound must be given for 375 bushels of wheat at $1.56 per bushel ? 40. Bought 75 tons of hay at $16 per ton ; gave in payment 56 sheep at $3.75 each, and the remainder I paid in butter at 33 cts. per pound. How many pounds of butter were required ? 41. Bought 225 acres of land for $12600, and sold 116 acres at $65 per acre, and the remainder at cost ; how much did I gain ? 42. The estimated number of bushels of corn produced in the United States in 1877 was 1,342,558,000, the total value of crop was $480,643,400, and the total area of crop was 50,369,113 acres. What was the average value per bushel, and average value of yield per acre ? 43. In 1878 there were 39258 postmasters in the United States, and their total salaries were $7,977,852 ; what was the average salary paid ? 44. July 1, 1866, the public debt of the United States was $2,773,236,173, and May 1, 1880, $1,968,314,753; what was the average monthly decrease ? 45. A sold to B 175 acres of land at $135 an acre, and by so doing gained $1925 ; B sold the land at a loss of $1750. What did A pay per acre, and what was B's selling-price per acre ? 46. A merchant sold 800 barrels of flour for $5867, 144 barrels of which he sold at $7 per barrel, and 225 barrels at 16.75. At how much per barrel did he sell the remainder ? FRACTIONS. DEFINITIONS. 43. A Fraction is one or more of the equal parts of a unit ; as one-half (J), two-thirds (f ), one-fourth (J), seven-eighths ($). If a unit be divided into four equal parts, each part is called a fourth. If one of these parts be taken, the expression will be one-fourth (; ; if three parts, three-fourths (f ), etc. 44. The greater the number of equal parts into which a unit is divided, the less will be each part ; the less the number of parts, the greater will be each part. One-half (-) is greater than one-third () ; one-fourth (|) is less than one- third (i). 45. A fraction is usually expressed by two numbers, one written above the other, with a line between. Fractions written in this form are usually called Common Fractions. 46. The number below the line is called the Denominator, because while indicating the number of equal parts into which the unit is divided, it denominates or names those parts. 47. The number above the line is called the Numerator, because it shows how many of the parts are taken to form the fraction. 48. The numerator and denominator, taken together, are called the Terms of the fraction. In the fraction three-fourths (f ), 3 and 4 are the terms ; 4 is the denomi- nator, and shows that the unit is divided into four equal parts, called fourths ; 3 is the numerator, and shows that three of these parts are taken to constitute the fraction. 49. A fraction is an expression of unperformed division. The numerator is the dividend, the denominator is the divisor, and the value of the fraction is the quotient. DEFINITIONS. 15 50. A Simple Fraction is a single fraction, both of whose terms are integers. 51. Simple fractions are proper or improper. 52. A Proper Fraction is one that is less than a unit ; the numerator being less than the denominator. Thus, , f, and -J are proper fractions. 53. An Improper Fraction is one that is equal to, or greater than a unit ; hence the numerator must be equal to, or greater than the denominator. Thus, f, , -J, and ty- are im- proper fractions. 54. A Mixed Number is an integer and a fraction united ; as 24, 4J, 18$. 55. A Compound Fraction is a fraction of a fraction ; as i of |, I of 74, | of |. 56. A Complex Fraction is one whose numerator is a } 105f 75J 3f 124 fraction or mixed number ; as ~, ^ , 9 -f-, ~-~- o 1/c lo o 15 Q3 The expression indicates division, and is not properly a fraction, D 2 A unit cannot be divided into 5| equal parts. 57. PRINCIPLES. 1. Multiplying the numerator or dividing the denominator by a number multiplies the fraction ly that number. 2. Dividing the numerator or multiplying the denominator by a number divides the fraction by that number. 3. Multiplying or dividing both numerator and denominator by the same number does not change the value of the fraction. EXERCISES. 58. 1. Read the following fractions, and copy separately : 1, the simple fractions ; 2, the proper fractions ; 3, the improper fractions ; 4, the mixed numbers ; 5, the compound fractions ; 6, the complex fractions : H; *i; ; A; 1; <>*; ; i; if; ?f; SJ; 46|; ^; ft; - ; f; | of f . 16 FRACTIONS. 2. Write the following fractions: three fourths ; seven eighths; nineteen sixteenths ; five, and one half ; one hundred and three thirty-seconds ; one hundred, and three thirty-seconds ; forty- eight, and five twelfths ; eleven tenths ; nine forty-fifths ; thirty- six twenty-eighths ; sixty-five forty-eighths. 3. Write the following fractions : eight ninths ; thirteen, and two-thirds ; sixteen twenty-fourths ; ten tenths ; fourteen, and forty-six hundredths ; nineteen one hundred nineteenths ; thirty- six four hundred thirty-seconds. REDUCTION. 59. Reduction of Fractions is the changing their form without changing their value. 60. A fraction is reduced to lower terms when the numerator and denominator are expressed in smaller numbers. 61. A fraction is in its lowest terms when its numerator and denominator have no common divisor. 62. A fraction is reduced to higher terms when the numerator and denominator are expressed in larger numbers. 63. To reduce a fraction to its lowest terms. Ex. Eeduce -ffo to its lowest terms. OPERATION. ANALYSIS. Dividing both terms of the fraction, f/j -J-f = f T Vir> by the common divisor, 6, the result is -|f ; dividing both terms of ^ by the common divisor, 7, the result is . Since 2 and 3 have no common divisor, the fraction is reduced to its lowest terms (61). The value of the fraction has not been changed, because both terms have been divided by the same number (57, 3). * The same result is often more readily obtained by dividing both terms by the greatest common divisor. 64. EULE. Divide the terms of the fraction by any number that will divide both without a remainder, and continue the operation -with the resulting fractions until they have no common divisor. Or, Divide the terms of the fraction by their greatest com- mon divisor. RED UCTION. EXAMPLES. 65. Reduce to their lowest terms, 1. H. 9. T %. 17. -ffff. 25. |ff. 2. -*0. f. is. m- 00- iff* if ^. i-Il ^. 6. -ffg. 13. iff}. ^. & TV. ^- Hi- ^. 15. #&. 23. 66. To reduce a fraction to higher terms. Ex. Reduce f- to a fraction whose denominator is 32. OPERATION. ANALYSIS. The fraction f is reduced to thirty - 32 -f- 4 8 seconds^ without changing its value, by multiplying jl 24. the terms by the number that will cause its denomina- tor 4 to become 32 (57, 3). By dividing the required denominator 32 by the given denominator 4, this number is found to be 8. Multiplying both terms of f by 8, the result is f $. 67. RULE. Divide the required denominator by the denominator of the given fraction, and multiply both terms of the given fraction by the quotient. EXAMPLES. 68. 1. Reduce |- to 48ths. 2. Change -fe to an equivalent fraction having 60 for its denominator. 3. Reduce f , |, & each to 48ths. 4. Reduce -f, , -f-J each to 105ths. 5. Reduce f|-, f, J- each to 56ths. 6. Reduce T \, -}J, -Jf each to 96ths. 7. Reduce -J, f, t 3 o each to 360ths. 8. Reduce }, f , fj- each to 72ds. P. Reduce |, ff, ^-f each to 108ths. ^. Reduce f, f, J each to 360ths. 18 FRACTIONS. 69. To reduce two or more fractions to equivalent fractions having their least common denominator. 70. A Common Denominator of two or more fractions is a denominator to which they can all be reduced, and is the com- mon multiple of their denominators. 71. The Least Common Denominator of two or more fractions is the least denominator to which they can be reduced, and is the least common multiple of their denominators. Ex. Reduce , f-, |, ^ to equivalent fractions having their least common denominator. OPERATION. ANALYSIS. The least common 2 _ AQ. 2 ) $ 4 6 10 multiple of the denominators is I _ T| ^ found to be 60 (3>)' which we take od as the least common denominator. By Art. 67, f is reduced to ft. We A = |f proceed in the same manner with each of the other fractions. The value of each fraction remains unchanged, since both terms have been multi- plied by the same number. In many cases, the least common denominator can be readily found by inspection. 72. RULE. Find the least common multiple of the given denominators for the least common denominator, and reduce the given fractions to this denominator. EXAMPLES. 73. Reduce the following fractions to equivalent fractions having their least common denominator : i- t TV T V * , ft 9. , -V 3 -, v- A tt> A, r. 4, , f ^- H, H> - 4 t -VS A- A , I, a ft , - 74. To reduce an integer or a mixed number to an improper fraction. Ex. In 18 units, how many fourths ? REDUCTION. 19 OPERATION. 18 ANALYSIS. In 1 there are 4 fourths (), and in 18, 4 eighteen times 4 fourths, or 72 fourths (^ 2 -). Hence, 18 = - 7 A 72 fourths. Ex. Eeduce 16 J to an improper fraction. OPERATION. 16-J Q ANALYSIS. In 1 there are 8 eighths (f), and in 16, sixteen times 8 eighths, or 128 eighths (if*). 128 128 eighths. eighths and 7 eighths are 135 eighths. Hence, _7 eighths. 1J = *&> 135 eighths. 75. EULE. Multiply the integer by the required denom- inator, and to the product add the numerator of the frac- tion, and under the result write the denominator. NOTE. When the numerator of the fraction is a small number, add it mentally to the product of the integer and the denominator. EXAMPLES. 76. 1. In 27, how many ninths ? 2. Eeduce 46 \ to halves. 3. How many eighths of a peck in 37 -J pecks ? Eeduce the following to improper fractions : 4. 37f; 19|; 208^. 9. 81f ; 196 ; 375|. 5. 56| ; 49|; 182f 10. 116ft; 456 T \ ; 87H- 6. 375| ; 94 T V ; 46f. 11. 24 t \ ; 179ft ; 1767 J. 7. 44|;37A;19ft. 12. 87| ; 490^ ; 168ft. 8. 12i;48&;45&. 18. 384| ; 161f; 175ff 77. To reduce an improper fraction to an integer or a mixed number. Ex. Eeduce - 2 ^- to a mixed number. ANALYSIS. 1 = ; hence in - 2 7 , there are as many units as 4 fourths are contained times in 27 fourths, or 6f . 78. EULE. Divide the numerator by the denominator. 20 FRACTIONS. EXAMPLES. 79. 1. Change -4- 1 to a mixed number. 2. Eeduce $ of a dollar to dollars. Reduce to integers or mixed numbers : J. 8. 4. 9. ADDITION. 80. Addition of Fractions is the process of finding the sum of two or more fractions. 81. PRINCIPLE. In order thai fractions may be added, they must have like denominators and le parts of like units. Ex. What is the sum of ^, -^ and T ^? OPERATION. ANALYSIS. As these frac- -fa -\- fy + iV ~~ T!" - % ~ -^i tions have a common denomina- tor, we add their numerators, and write their sum, 15, over the common denominator, 12. j-f = 1|, the re- quired result. Ex. Add f, f, and |. OPERATION. ANALYSTS. Reduce the given fractions to equivalent fractions having the least common denominator, 12 (72). Then proceed as in previous example. Ex. Find the sum of 29-fc 38}, 17|, and 42J. OPERATION. 3g|. is ANALYSIS. The sum of the fractions is 176. 14 If = lf> which added to the sum of the inte- gers, gives 127|, the required result. 2f ADDITION. 21 Ex. How many yards in 12 pieces of prints containing 46 1 , 48 2 , 51 2 , 49 3 , 44 1 , 48 2 , 47 1 , 49, 47 3 , 50 3 , 48 1 , 48 2 yards respec- tively. OPERATION. 451 471 ANALYSIS. The sum of the fourths is ^- 5 1 2 47 3 = 5|-, which added to the sum of the integers 49 s 50 3 gives 580, the total number of yards. 441 48 1 48 2 4S 2 580 1 . 82. RULE. Reduce the given fractions to equivalent fractions having the least common denominator. Write the sum of the numerators over the coimnon denominator, and reduce the resulting fraction to its simplest form. Wlien there are mixed numbers or integers, add the integers and fractions separately, and then add the results. EXAMPLES. 83. Add the following : 1- fb ii A, and if. 5. 127A, , l^i and f. 2. |, f, |, and -i. 6. 141^, 197$, and 43^. 3. 12J, 7|, 16A, and 38f. 7. 75f, |, 1028|, and . and 17 8. 119 240 and 9. 46 1 , 48 3 , 40 2 , 49, 47 3 , and 46 2 . 10. 40 3 , 41 1 , 48 2 , 44 1 , 49 3 , 48 2 , 49 3 , 49 1 , 47 3 , 48 3 , 48 3 , and 49 1 . 11. 18|, 27i, 42|, and 51|. 12. 146J-, If, 53^, and 68J. 18. 1172f, 19f, 440J, and 6|. 14. A, 106A-, 37f, and 7f ^5. 175, llfrft, 143J, and 27f JTfi. 20|, 164f, ff, and 43|. 77. 44i 16f, 29^, and 13|. J& 31 1 , 48 3 , 62 1 , 19 3 , 27 2 , 48 1 , and 37 3 . 19. 61 3 , 48 1 , 47 3 , 48, 48 2 , 49 1 , and 45 3 . 20. 19|, 444^, 737J, and 385|. 22 FRACTIONS. SUBTRACTION. 84. Subtraction of Fractions is the process of finding the difference between two fractions. 85. PRINCIPLE. /ft order that fractions may be subtracted, they must have like denominators and be parts of like units. Ex. From f take f. OPERATION. ANALYSIS. As these fractions have a common f- f f = J denominator, we take the difference of the numer- ators, and place it over the common denomina- tor, f = is the result required. Ex. What is the difference between J and f ? OPERATION. ANALYSIS. Reduce the given fractions 9 8 j to equivalent fractions having the least ^~ 12 ~ T2" common denominator (72). Then proceed as in the previous example. Ex. From 176| subtract 89}. OPERATION. 176|. s. ANALYSIS, f from we cannot take ; we therefore 8q 1 take 1 = f from 176, leaving 175. f + f = ^ V ~ 8 =f. 175-89 = 86. 86 + | = 86|. set 86. RULE. Reduce the given fractions to equivalent fractions having the least common denominator. Write the difference of the numerators over the common denomi- nator, and reduce the resulting fraction to its simplest form. When there are mixed numbers, subtract the integers and fractions separately, and add the results. EXAMPLES, 87. Find the difference between 1. j and |. 4. 2% and 1-&. 7. H and f. 2. | and -&. 5. ^ and T \. 8. f and T 4 T . 3. f and ft- 6. f and f . 9. 1 and |f MULTIPLICATION. 23 10. 17 and 9}. 17. 116| and 48f. 24- "^ and 375^. 11. 175J and 86J. 18. 381| and 17}. 86. 827J and 737f. 12. 138| and 17. 19. 157$ and 19}. 00. 919} and 447^ 6 . /& 149 and 18f 20. 118 3 and 48 s . 27. 376 1 and 287 3 . 14. 416} and 49}. ^. 387| and 116}. 0. 445* and 318 3 . 15. 512} and 53}. 22. 248^ and 129}. 29. 737 3 and 438 s . J0. 100 and 13}. 28. 764ft- and 375}. 50. 648 1 and 5263. MULTIPLICATION. 88. To multiply a fraction by an integer. 89. PKIKCIPLE. Multiplying the numerator or dividing the denominator by a number multiplies the value of the fraction by that number (57, 1). Ex. What will 4 pounds of tea cost @ $} a pound ? OPERATIONS. ANALYSIS. If 1 pound costs $|, 3. A. - Z_*_f _ 28 __ qi 4 pounds will cost 4 times $, or ~~$~~ 6 * $- 2 /-> equal to $3. Hence, 4 pounds of tea @$ will cost $3|. O r > To multiply f by 4, multiply the A 7 . _ QI numerator 7 by 4, or divide the de- ~ 8~^4 " * nominator 8 by 4 ; either operation will give 3|, the required product Or> (Prin.). % X f = I = 3 By cancellation (38), the opera- 2 tion is shortened, and the result is obtained in its lowest terms. Multiplying the numerator, as in the first operation, increases the num- ber of parts, their size remaining the same ; dividing the denominator multi- plies the fraction by increasing the size of the parts, their number remaining the same. Ex. Multiply 123} by 9. OPERATION. ANALYSIS. Multiply the fraction f and the integer 123 9 separately, and add the products. In practice, when possible, TT add the products mentally ; e.g., 9 times f are \ 7 -, equal to 6f. * Write the f. 9 times 3 are 27, and 6 are 33. Write the 3, and proceed as in simple numbers. 1113} 24 FRACTIONS. Ex. Multiply 227} by 175. OPERATIONS. ANALYSIS. As in preceding ex- 227} Or, 227} ample. 175 175 Or, by aliquot parts, when the A \ KOK or/i fractions are fourths, eighths, etc., / the fractions generally used in com- 1314- ^t mercial operations. 1135 1589 of 175 = 87J. 9O. RULE. Multiply the numerator or divide the de- nominator of the fraction by the integer. When the multiplicand is a mixed number, multiply the fraction and integer separately f and add the results. EXAMPLES. 91. 1. Find the cost of 20 yards of silk at f-J a yard. 2. How much grain in 12 bins, each containing 76 J bushels ? 3. If 1 man earns $J in 1 day, how much will 16 men earn in 26 days? 4. If a ton of hay cost 816}, how much will 22 tons cost? 5. Required the cost of 60 yards of muslin at 35$ cents a yard ? Multiply * A by 7. 77. 412f by 47. 0& 234J by 318. 7. by8. 18. 148? by 40. 05. 678f by 427. fttfty* JT0. 4124 by 89. 80. 625} by 516. 9. 110J. by ia 20. 775 by 65. 81. 71 8 J by 542. 10. 117} by 16. 21. 119A by 20. ,?0. 275| by 287. 11. 248 by 3. #& 772f by 17. 88. 813| by 319. 12. 146$ by 3. 3. 338| by 30. 54. 444J by 412. 13. 197^ by 7. 24. 550$ by 27. 85. 555 by 875. 14. 420^ by 8. 25. 643} by 121. 86. 817} by 416. 15. 384| by 12. 26. 875| by 234. 57. 913} by 375. 16. 375 by 48. 07. 91 6J- by 275. 88. 787} by 525. UNJVtK&l j T OF MULTIPLICATIO N. 25 92. To multiply an integer by a fraction, or to find a, fractional part of an integer. 93. PRINCIPLE. Multiplying by a fraction is taking such part of the multiplicand as the fraction is of a unit. Ex. If 1 ton of hay cost $18, what will j of a ton cost ? OPERATIONS. Or, Or, 18 4)18 3 13* ANALYSIS. If 1 ton cost $18, of a ton will cost of $18. of $18 is 3 times of $18. % of $18 is $4| (taking is the same as dividing by 4), and 3 times $4| is $13. Or, of $18 is of 3 times $18. 3 times $18 is $54. { of $54 is $13|. Ex. Find the product of 175 and 8f. ANALYSIS. Multiply by the frac- tion f and by the integer 8 separately, and add the products. OPERATIONS. 175 Or, _8J 4)525 175 H 43J 3 131J 1400 15314 131J 1400 1531J Ex. Multiply 275 by 47|, FIRST OPERATION. SECOND OPERATION. THIRD OPERATION. 275 J7| 8 ) 825 275 47| 275 _47| 68J 34* 1925 1100 34$ 3 103 1925 1100 103i 1925 1100 130284 13028J- 13028-J ANALYSIS. For the first and second operations, as in the pre- ceding examples. When the fractions are fourths, eighths, etc., multiply by means of aliquot parts. i of 275 = 68|. of 275, or of 68f = 34|. 26 FRACTIONS. 94. RULE. Multiply ~by the numerator of the fraction., and divide the product by the denominator. Or, Divide by the denominator of the fraction and multi- ply the quotient by the numerator. When the multiplier is a mixed number, multiply by the fraction and integer separately, and add the results. EXAMPLES. 95. 1. Find the cost of 8f yds. of ribbon at 25 cts. a yard. 2. What is the cost of 42^ pounds of butter at 26 cts. a pound. 8. Required the value of 48-J yards of flannel at 75 cts. a yard. Multiply 4. 84 by f . 10. 216 by 14f . 16. 780 by 64f 5. 126 by f 11. 375 by 24f 17. 512 by 37f 6. 49 by |. 12. 375 by 22f . 18. 611 by 87J. 7. 128 by 9J, 1& 146 by 28f. 19. 625 by 92|. 8. 156 by 8f 14. 184 by 16f 00. 937 by 75|. 9. 187 by lOf. 15. 110 by 41-}. 07. 575 by 81|. 96. To multiply a fraction by a fraction.* Ex. At If a pound, what will | of a pound of tea cost ? OPERATION . 3 v 7 __ si __ 7 ANALYSIS. If 1 pound cost $J, f of a pound will cost f of $. f of $ is 3 times \ of $, Or > } X i = -ft i of $| is $^ f and 3 times | is $| -J, or $ T V Ex. What is the value of 8 x 8$ x T \ x -^ ? 2 OPERATION ANALYSIS. Reduce the inte- ^. 5 ger 8 and the mixed number 8 f X ^ X ^ X ^ = ^ = 3-J- to improper fractions, and mul- ^ x tiply as in the preceding example. 97. RULE. Reduce integers and jnixed numbers to im- proper fractions. Cancel all factors common to the numerators and de- nominators. * The practical methods of multiplying one mixed number by another are given under Art. 1O8. DIVISION. 27 Multiply the remaining numerators together for the numerator, and the remaining denominators for the de- nominator. EXAMPLES. 98. Find the product of 1. | and -f. 5. | and ^. 9. , 13J, and f & f and f . . 6, 3J, and f. J0. 26}, f and |. 8. | and -&. 7. 5f, f, and fj. 11. f, j, and 16f 4. | and J^. A 124, lOf, and ^. 72. 13$, fc and -. Reduce the following compound fractions (55) to simple ones. The word " of" is equivalent to the sign x . 13. i of f of }. 17. | of | of 18. 21. | of JJ of |f. 14. | of 3| of f . #. | of llf of f #0. | of f of -I of |. 15. | of | of 7f ^P. Jf of f|. 23. } of 12J of 6|. 75. f of | of 5f 0. A of | of ^. 24. | of J| of 4}. Find the value of the following expressions : 25. | of 1728. 30. (\ + T %) x (f + T 5 i)- *0. I x 375. 31. (f - |) x + J). 07. -i times 864. 82. (& -f f ) x (-ft - *) ?. f of 75 x f of 16f . S3. 37J times f of ^ ^P. -i x f of ^ x f . 54. | of | by f of |. DIVISION. 99. To divide a fraction by an integer. 100. PRINCIPLE. Dividing the numerator or multiplying the denominator ~by a number divides the value of the fraction by that number (57, 2). 23 FRACTIONS. Ex. What cost 1 pound of tea, if 5 pounds cost $3J? OPERATIONS. ANALYSIS. If 5 pounds cost 10-1-5 2 $31, 1 pound will cost of $3J, -5-5= -3-* O p$|. To divide V- (3D *>y 5, divide n 10 * - 10 10 2 the numerator 10 by 5, or multiply JT > TT "* fi - 3~ x 5 ~ the denominator 3 by 5 ; either g operation will give f, the required Or > X i = f quotient (Prin.). Dividing the numerator, as in the first operation, decreases the number of parts, their size remaining the same ; multiplying the denominator divides the fraction by decreasing the size of the parts, their number remaining the same. Ex. Divide 867J by 4. OPERATION. ANALYSIS. Dividing as in simple 4 ) 867J 3f = numbers, 4 is contained in 867f, 216 ~21 fii& Xfi. _i- 4 14 times and a remainder of 3f . 3| equals ~ " \ 5 -, which divided by 4 is }. 101. RULE. Divide the numerator or multiply the denominator of the fraction ~by the integer. When the dividend is a mixed number, divide the integer and the fraction separately, and add the results. EXAMPLES. 102. Divide 1. | by 6. 11. 6371 by 9. 21. 5316| by 4. 2. | by 3. 12. 875.fr by 12. 00. 7144 by 5. 3. | by 6. IS. 1716| by 8. 23. 1729J by 3. 4. A b y 4 - ^ 1729 i b y 3 - % 1749 i b y 9 - 5. ^ by 4. 75. 2418| by 5. 25. 8763 by 6. 6. 16|by5. 16. 3516f by 5. ^. 7385| by 8. 7. 172J by 3. 17. 2428| by 3. 27. 4255 by 9. 8. 875fby6. 18. 6375| by 4. 28. 7134| by 7. 9. 935 J by 8. 19. 42871 by 2. M- 9727^ by 12. 10. 729Jby9. 20. 3281| by 8. 30. 6345| by 16. DIVISION. 29 103. To divide by a fraction. 104. The Reciprocal of a number is 1 divided by that number. Thus, the reciprocal of 4 is 1 divided by 4, or J. The Reciprocal of a Fraction is 1 divided by that fraction. 105. PRINCIPLE. 1 divided by a fraction is the fraction in- verted. Thus, 1 divided by f is f. This principle may be demonstrated as fol- lows : In 1 there are 4 fourths. 1 fourth is contained in 4 fourths 4 times. Since f is 3 times j, f is contained in 1 ^ as many times as . Hence, f is contained in 1 ^ of 4 times, or f times. The reciprocal of a fraction is the fraction inverted. Ex. At 8f a yard, how many yards of cloth can be bought for $5 ? OPERATIONS. ANALYSIS. Since 1 yard cost 5 _t_ 3 . 2_o. _i_ 3. . gs. $|, as many yards can be bought for $5 as $| is contained times in $5. Or, 5 -7- f = f X | = : - 2 / : - 6| 5 is equal to ^ and 3 fourths is con- tained in 20 fourths 6| times. Or, $| is contained in $1 f times (Prin.) t and in $5, 5 times | or ^-, equal to 6f times. Ex. At $| a yard, how many yards of cloth can be bought for $| ? OPERATIONS. ANALYSIS. Since 1 yard f -r- | = U -T- A = It cost $|, as many yards can be n _ 5 v 4 -- ^ 1 1 bought for $| as $| is con- tained times in $|. f is equal to T ^, and | is equal to If. Jr > f f ' = < f - - V" : A f T \ is contained in ^ 1 times. Or, $| is contained in $1 | times (Prin.), and in $|, f times f or f f, equal to 1 times. Ex. If 6| yards of cloth cost $5, what will 1 yard cost ? OPERATIONS. ANALYSIS. 6| yards are 5 -f- - 2 / : = (5 -*- 20) X 3 = f equal to -\- yards. Since y Or 5 o s v 3^ _ IB _ a y ards cost $ 5 i of a yard K * F ' will cost ^ of $5 or $1, and Or, 5 -v- - 2 / = f X A = } f or 1 yard will cost 3 times 4 $1- or $f. Or, the price per yard equals the cost, divided by the quantity as an ab- stract number. 5 divided by % n - equals 5 times 1 divided by - 2 /, or 5 times ^ (Prin.), equal to f . 30 FRACTIONS. Ex. Divide 2195J- by 175f. OPERATION. 175 1 ) 2195f ANALYSIS. Reduce both divisor and divi- 6 6 dend to improper fractions, and divide as in 1054 ) 13175 ( 12 1 preceding example. Or, multiplying both divisor and dividend by the same number does not affect the quo- 2635 tient. Multiply both divisor and dividend by QIAO 6, the least common denominator, and divide /41U5 . as m simple numbers. 527 2 1054 106. RULE. Reduce the divisor and dividend to equiv- alent fractions having a common denominator, and divide the numerator of the dividend by the numerator of the divisor. Or, Invert the terms of the divisor and proceed as in multi- plication. In dividing mixed numbers, multiply both divisor and dividend by the least common denominator, and divide as in simple numbers. EXAMPLES. 107. Divide 1. 1 by |. U. 73 by 8*. W. 920 by 73|. 2. 16 by f 15. 45 by 7f . 28. 720 by 43$. 3. 28 by f . 16. 8J by 3}. 29. 700 by 37$, 4. 49 by f 17. 6| by 3J. SO. 560 by 26}. 5. 88 by f. 18. 4f by 3f. SI. 682 $ by 45 J. 6. J by -f. 19. 7$ by 8$. 88. 847 by 89}. 7. f by f. W. 9J by 18$. S3. 984* by 75 3 . 8. ^ by j. 81. 875 by 33J. &. 862 s by 18 3 . 9. T \ by |. 88. 625 by 83$. S5. 731 1 by 56*. m f by J. 83. 516 by 34f. 55. 431 i by 18f. 11. 28 by 4$. 84. 917 by 43f. 57. 983$ by 29$. 18. 33 by 3|. 05. 864 by 86|. S8. 504| by 36|. IS. 64 by 5f. 05. 702 by 30f S9. 583$ by 43 J. DIVISION. 31 Find the value of the following complex fractions (56) and expressions of division : 5A. 4 I. 24f fof4 40.31 r' ~9~' 35' "36" * fo ' 5f-3 ?i. ?l. 40' 13' 5*. i. A H' V *' 175J 68|--MJ f 38f 186 J' 8f 1O8. To multiply mixed numbers together.* Ex. What cost 101 6 J pounds of cotton, at 12$- cents per pound ? Instead of reducing the mixed numbers to improper fractions, use the fol- lowing methods. The second method (by aliquot parts) is preferable, and is well adapted to commercial operations, in which the fractions are usually halves, fourths, eighths, etc. In business transactions, it is customary to omit the fraction in the result, if it is less than |, and to add 1 to the cents if it is more than -|. Unless other- wise stated, the exact answers will be given to examples. . FIRST OPERATION. 1016$ 8 ) 3049^ 12198 125.79 T 3 SECOND OPERATION. 1016J ANALYSIS. Multiply 1016 1 by the fraction | by multiplying by the numerator 3 and dividing by the de- nominator 8 (92) ; theij multiply 1016| by the integer 12 (88), and add the results. 12198 ANALYSIS, f = + . Multiply 101 6| by by di- viding by 4. Multiply 1016| by $ by taking of the 254, the product by . Multiply 1016'- by 12 (88), and add the results. * The multiplication of mixed numbers is purposely put in this connection, as it appro- priately comes here, a knowledge of division of fractions being a prerequisite to a fair understanding of the process. 32 FRACTIONS, EXAMPLES. 109. (1.) 837f 150794 15917J (2.) 16754 Or, 837} [prod, by 4] 418J[prod.byi(4of4)] 1734 11725 6700 5025 5826554 16754 347J 4 ) 50264 1256| 1734 11725 6700 5025 5826554 864} [4+i] 126} [4 + i] 432|- [prod, by 4] 108A [Pi'od. byi( 63 [126 xi] Or, 5184 10368 109498f4 Multiply in like manner, 4. 8754 by 84 ; 5. 737J by 104; 6. 512} by 74 ; 7. 449-f by 16} ; 8. 1612}. by 134 ; 9. 2437f by 164 5 by 12J by 274 by 36| by 42| by 12{ 5 by 26}. ; by 44|. by 64}. by 45}. by 185}. 126| 8 ) 4323| 944 4)378 5184 10368 109498J4 REVIEW EXAMPLES. 11O. 1. Eeduce fff to its lowest terms 2. Eeduce | to forty-eighths. 3. Eeduce 72 7| to an improper fraction. 4. Eeduce J- 3 % 51 to a mixed number. 5. Add 17-4, 37}, 18|, 49}, 13|, and REVIEW EXAMPLES. 33 6. From 1728 take 865. 7. Multiply i X 3| x A x T 3 TO> ~nn5> I"~n5> ^l^Toinr? i o o o o 13. 16-,%, 19-rffo, 345^, 14. 28rdHhr, 3W, Sf&rJWr 15. 170^^, IGOOOnflyU 38^, 16. 40 DECIMALS. REDUCTION. 126. To reduce a fraction to a decimal. Ex. Eeduce f to a decimal. OPERATION. 4. \ 3^00 ANALYSIS, equals of 3 units. 3 units equal 300 hundredths. of 300 hundredths equal 75 hundredths. 75 127. RULE. Annex decimal ciphers to the numerator, and divide by the denominator, pointing off as many deci- mal places in the quotient as there are ciphers annexed. 128. A fraction in its lowest terms can be reduced to a pure decimal only when its denominator contains no prime factors but 2 and 5. If the denominator or divisor contain any prime factor other than 2 and 5, the division will not end. The decimals thus produced are called Interminate or Repeating Decimals, and the figures repeated, Bepetends. When a fraction is in its lowest terms, its numerator and denominator have no common factors (61). Annexing ciphers to the numerator intro- duces the factors 2 and 5 only ; hence, if the denominator is an exact divisor of the numerator with the ciphers annexed, it must contain these prime fac- tors and none others. EXAMPLES, 129. Reduce to equivalent decimals : 1. f 4. * 7. H- 10. A- IS. 16f 2. f. 5. -&. 8. f. 11. f 14. 27if. 3. f. 6. ||. 9. f .12. f 15. 36ff. 130. To reduce a decimal to a fraction. Ex. Reduce .075 to an equivalent fraction. ANALYSIS. A decimal is changed to a OPERATION. fraction by writing its denominator, and omit- .1)75 = Yoinr 4*V ting the decimal point and prefixed ciphers. ADDITION. 41 Ex. Change .83 J to a simple fraction. OPERATION. ANALYSIS. Reduce the -3 3 = H* = * fraction to a simple fraction by multi- plying both terms by the denominator 3. (57, 3.) 131. RULE. Omit the decimal point, supply the proper denominator, and reduce the fraction to its lowest terms. EXAMPLES. 132. Reduce to equivalent fractions : 1. .25. 8. .128. 15. .33. 88. .44f. 8. .75. 9. .00144. 70. .41|. 85. .142857-?-. S. .375. 70. .512. 17. .066|. 0J. .0833J. 4. .625. 11. .5625. 7S. .37. 25. 28.0375. 5. .875. 70. .1875. 19. .104f 00. 107.166-f. 6. .125. 75. .12f )80. .097f. 87. 175.096. 7. .016. 14. .16f. 07. .0053f 0*. 6.0175. ADDITION. 133. Since decimals, like integers, increase and decrease uni- formly according to a scale of ten, with the exception of placing the decimal point in the result (usually called pointing off), they may be added, subtracted, multiplied, and divided in the same manner as integers. Ex. What is the sum of 28.7, 175.28, .037, 25.0045, and 4.08 ? OPERATION. ANALYSIS. Write the numbers so that units of the 175.28 same order stand in the same column. % 03^ If the decimal points are in the same vertical line, 25 0045 tentns will necessarily be under tenths, hundredths under hundredths, etc. Add as in integers, and place the point _Z___ in the result directly under the points of the numbers. 233.1015 42 DECIMALS. Ex. Add .6, .37|, 16.048$, 8.1234f, and 24.125. OPERATION. ANALYSIS. Reduce the complex deci 6 .6 mals as far as the decimal places extend .37} = .3775 in tlie other numbers. Since the fractions 16 048 l = 1604834- now express parts of the same fractional ' 9 oL unit > the y ma y be add ed. In practice, the fractions may be re- 24.125 = 24.125 jected if the decimals are carried one 49.2742A 3 - place, at least, farther than accuracy is re- quired. 134. RULE. Write the numbers so that their decimal points are in the same vertical line. Add as in integers, and place the decimal point in the result directly under the points in the numbers added. EXAMPLES. 135. 1- Add ninety-seven hundredths ; three hundred and forty-seven thousandths ; sixteen, and seventy-five hundred-thou- sandths; four hundred and seventy-five, and two thousand and thirty-seven millionths. 2. Add four, and eighty-one thousandths ; thirty-seven, and two hundred and one ten-thousandths ; seven thousand and eight hundred-thousandths ; seven thousand, and eight hundred-thou- sandths ; nineteen hundredths ; three hundred and sixty-four, and nine tenths; and fifty-six, and fifty-four thousandths. 3. Add three hundred and seventy-five, and eight hundredths ; eighteen thousandths ; ninety-six, and eighty-four hundredths ; four, and four tenths ; and eight hundred and seven ten-millionths. 4. What is the sum of 18 hundredths ; 716 hundred- thou- sandths ; 6342 millionths ; 11567 ten-millionths ; 625 ten-thou- sandths ; 9 tenths ; 99 hundredths ; and 512 thousandths ? 5. Add 81.86; 12.593; 4.004; 18.00129; .443; 400.043; .12875; 175.00175; 17.3008; 9000.0016; and .9016. 6. Required, the sum of 99 ten-thousandths ; 157 thou- sandths ; 789} millionths ; 6 tenths ; 18} hundredths ; 1728 ten- millionths ; and 88 hundredths. 7. Add $1728.64; $0.37 ; $18.44; $10.18}; $6.25; and $0.16^. SUBTRACTION. 43 8. What is the sum of $12.37|; $144.18 J; $6.62; $175.06J ; $40.17$; and $398? 9. Add .1264|; 12.875; 187.25; 9.1414f ; .12; 5.7604^; and .0008f. 10. Add .26J; 4.18|; .0017f; .008644; .04f; 17.387^; and .0102075. SUBTRACTION. 136. Ex. From 12.75 subtract 8.125. OPERATION. ANALYSIS. Write the subtrahend under the minuend so 12.75 that units of the same order stand in the same column. Sub- 8.125 tract as in integers, and place the point in the result directly ~ under the points of the numbers. 4:.o/c> j^ ag j n thj s exam pi e) the minuend has not as many deci- mal places as the subtrahend, suppose decimal ciphers to be annexed until the right-hand figures are of the same order. (12O.) Reduce complex decimals as in addition (133). 137. EULE. Write the numbers so that their decimal points are in the same vertical line. Subtract as in inte- gers, and place the point in the remainder directly under the points in the minuend and subtrahend. EXAMPLES. 138. L From four, and sixty-five thousandths, subtract eight hundred and forty-seven ten-thousandths. 2. From twenty-seven hundredths take twenty-nine hundred- thousandths. 8. From nine thousand, and thirty-four ten-thousandths, sub- tract nine thousand and thirty-four ten-thousandths. Find the difference between 4. 8.3644 and 7.8996. 12. 17.864| and 16.94. 5. 17.4586 and .785. IS. 144. 43^ and 113.3875. 6. 1.010101 and .999999. 14. 54.3 7| and .98f. 7. $173.46 and $87.29. 15. 117.48J and 49.43f 8. 3 and .873845. 16. 448.987^ and 389.28f 9. 17.24 and 18.973J. 17. 5556.&J- and 44.48. 10. $510.60 and $389.45f 18. 968.44f and 37.386|. 11. $1728 and $.06f. 19. 49.45 and 48.9876f 44 DECIMALS. MULTIPLICATION. 139. Ex. Multiply .144 by .12. OPERATION. ANALYSIS. For convenience, write the right-hand figures 144 ^ *ke ^ ac ^ ors i n * ne same vertical line. 12 .144 x .12 = T Vir 4 (r x fifa = iWA- Multiply the numera- tors of the two factors for the numerator of the product, as .01728 in multiplication of fractions. In the above multiplication of fractions, it will be observed that the number of ciphers in the denominator of the product equals the sum of the ciphers in the de- nominators of the two factors. Since each cipher represents a decimal place, the product should have as many decimal places as both factors. If the number of figures in the product is less than the number of decimal places in the two factors, supply the deficiency by prefixing ciphers. 140. EULE. Multiply as in integers, and from the right point off as many decimal places in the product as there are decimal places in the two factors. NOTE. -To multiply a decimal by 10, 100, 1000, etc., remove the decimal point as many places to the right as there are ciphers in the multiplier, annexing ciphers to the multiplicand, if necessary. EXAMPLES. 141. 1. Multiply three hundred and forty-four ten-thou- sandths by twelve thousandths. 2. Multiply one hundred and ninety-two thousandths by four, and nineteen hundredths. 5. What is sixteen hundredths of six hundred and thirty-two millionths ? 4. What is five hundredths of $864.32 ? Of 3645.75 francs? 6. What is .058$ of 784.65 ? Of 943.25 ? 6. What is .99 x 1.106 x .25 ? 4.105 x .625 x .512 ? Multiply Multiply 7. 8.716 by .39 ; by .047. 12. 17.28 by .016| ; by 2.55$. 8. .00865 by .625 ; by 97.75. 18. 64.32$ by 1.44| ; by .06$. 9. .00128 by 8756.8 ; by 7.865. 14. 86.75 by 1.33$ ; by 5.76f 10. 387.25 by .0147$ ; by .087f 15. 5.78 by .0885 ; by .66f . 11. 58.625 by .488f ; by .375. 16. 237.5 by .345$ ; by 4.468^. DIVISION. 45 17. Of 1728, what is .75 ? .33 ? .25? .125? .20? .625? 18. Multiply (2.108 -f .0074) by (12.684 .465). 19. Multiply .01837 by 1000 ; .00145 by 100000 ; .6874 by 100 ; 5.375 by 10 ; 17.056 by 10000. What is the sum of the products ? 20. What is the square of .0364 ? Of 20.75 ? Of 45.25 ? 21. What is the cube of 8.045 ? Of .0875 ? Of 67.375 ? DIVISION. 142. Ex. Divide .01728 by 1.44. OPERATION. ANALYSIS. Dividing as in integers, witli- 1.44 ) .01728 ( .012 out reference to the decimal points and pre- 144 fixed ciphers, the quotient is 12. Since the OOQ dividend is the product of the divisor and quo- tient, it must contain as many decimal places as both of them. Hence the number of decimal places in the quotient must equal the number in the divi- dend less the number in the divisor. If, as in this example, the number of figures in the quotient is less than the number of decimal places to be pointed off, supply the deficiency by pre- fixing ciphers. 143. RULE. Divide as in integers, and point off from the right of the quotient as many decimal places as the number in the dividend exceed those in the divisor, NOTES. 1. If the divisor contains more decimal places than the dividend, before dividing make them equal by annexing ciphers to the dividend. If necessary to continue the division, more ciphers may be added. 2. If, after dividing all the figures of the dividend, there is a remainder, the division may be continued by annexing ciphers (12O). The ciphers thus annexed must be regarded as decimal places of the dividend. 3. To divide a decimal by 10, 100, 1000, etc., remove the decimal point as many places to the left as there are ciphers in the divisor, prefixing ciphers to the dividend, if necessary. EXAMPLES. 144. 1. Divide three thousand four hundred and fifty-six hundred-thousandths by seventy-two hundredths. 2. Divide six, and twenty-five hundredths by twenty-five thou- sandths. 46 DECIMALS. Divide 3. 35.88 by .345 ; by 4.16. 8. .0648 by .00425 ; by .0288. 4. .89958 by .47 ; by .319. 9. .31752 by .648 ; by .00384. 5. 12.6 by 14.4 ; by .125. 10. .1898 by .33$ ; by .0048f . 6. 96.3 by .20 ; by .25. 11. 85.2451 by 4.56| ; by 8.27f 7. 5.27 by 1.24; by .85. 12. 45.367 by .016f ; by l.OSOf 13. Divide 17.28 by .20 ; by .25 ; by .33| ; by .125 ; by .66|. 14. 321 is .178 of what number ? 15. 186 is five hundredths of what number ? 16. What must 37.375 be multiplied by to produce 448.5 ? 17. What must 631.25 be divided by to produce 250 ? 18. Divide 176.824 by 100 ; 876.35 by 1000 ; 17380.5 by 10000 ; 2886.57 by 10 ; 375 by 1000000. Find the sum of the quotients. 19. $12.52 is how many hundredths of $375.60 ? 20. $273.60 is how many thousandths of $1728 ? REVIEW EXAMPLES. 145. 1. Add 16 hundredths, 137 millionths, 48 ten-thou- sandths, and 2016 ten-millionths. 2. Add 16.07, 240.127f, 6.04}, 27.1234. 3. Reduce -ff to a decimal. 4. Reduce .083^ to a fraction. 5. From 175 take 16.083J. 6. From 375.16f take 1 98.888 -f. 7. Change .8375 to a fraction. 8. Multiply 117.084 by 7.37|. 9. Divide 43.75 by .0125. 10. Divide .06f by 1.66f. 11. 1.75 is I of what number? 12. What is of $175.75 ? 13. What is .33 of 187.5 ? 14- What is .33J times 1728 ? 15. $3.75 is how many hundredths of $75 ? 16. $86.40 is how many hundredths of $2592 ? 17. 16.56 is '.05 of what number? 18. What will 17280 bricks cost at $3.25 per M. ? 10. If 278 barrels of pork cost $4378.50, what is the cost of 100 barrels ? REVIEW EXAMPLES. 47 20. What cost 12456 feet of plank at $8.75 per M. ? 21. What is the value of 5 bbls. sugar, containing 312, 304, 301, 305, 304 pounds respectively, at 9-f cents per pound ? 22. A miller wishes to purchase an equal quantity of wheat, corn, and rye ; he pays for wheat $2.22-}- a bushel ; for corn, 98 \ cents a bushel; and for rye $1.16-| a bushel. How many bushels of each can he buy for $92776.50 ? 28. Bought 280 cords of hard wood, at $6.75, and 790 cords of soft wood, at $3.62 per cord. Also, 750 bushels of corn, at 62 J cents, and 925 bushels of oats, at 37 cents per bushel. What was paid for the whole, and what was the average price of wood per cord, and of grain per bushel ? 24. Bought on contract 350 reams of foolscap paper, at $3.83-}- per ream, 45|- reams of which were returned as unsuitable, and 275 reams of letter, at $2.67-}- per ream, 37-| reams of which were rejected. How much was paid for the remainder ? 25. A merchant paid for merchandise during the year $137618.75, and sold merchandise to the amount of $146347.87. What was the gain, if the net market value of the merchandise remaining unsold was $24378 ? 26. A quartermaster has $8345 on hand, and receives $4379.62 from each of six sales of property ; he turns over to quarter- master A $2875.28, and pays $120 for corn. Upon being relieved from duty, he turns over to quartermaster B one-third of the residue, and divides the remainder equally among three others, C, D, and E. What was paid over to each ? 27. Merchandise on hand, Jan.l, 1879, $46312.85; merchan- dise sold during the year, $317829.32 ; merchandise purchased in the same time, $301449.72 ; merchandise on hand, Dec. 31, 1879, $61378.12. What was the net gain or loss ? 28. A farmer sold land for $22.50 an acre, as follows : to A, 98f acres ; to B, | of the number sold to A ; and to C ? the number sold to A and B both. How much land was sold, how much did B and C each receive, and what was the amount realized ? 29. What are the prime factors of 2791 ? 30. At $28.75 per thousand, how many feet of lumber should be given for 2816 pounds of sugar at 7 T 3 g - cts. per pound ? 31. Mr. A offered to sell his horse for -^ more than it cost him, but afterward sold it for $504, which was T V less than his first asking price. How much did his horse cost him ? 48 DECIMALS. 32. In England, during the year 1875, there were 147,730,313 tons of bituminous coal produced, 535,845 persons employed, and 1244 lives lost. How many tons of coal were produced to each person employed, how many tons to each life lost, and how many persons were employed per life lost ? S3. In the anthracite coal mines of Pennsylvania, during the year 1875, there were 22,000,000 tons of coal produced, 69,589 persons employed, and 238 lives lost. How many tons of coal were produced to each employe, how many to each life lost, and how many persons were employed to each life lost ? 34. In the Lehigh district of Pennsylvania, in 1878, there were 3,956,588 tons of coal produced, and 51,492 kegs of powder used. How many tons of coal were produced per pound of powder used, each keg containing 25 pounds ? 35. A man bequeaths -J of his property to his wife, to his son, -J to his daughter, and the remainder, which is $36375, to charitable institutions. What is the amount bequeathed to each, and the total amount ? 36. If a person traveling 3-J miles per hour completes a jour- ney in 16J- hours, what time would it require if he traveled 4J miles per hour ? 37. If I purchase two building lots for $3750 each, and sell one for | more than it cost, and the other for . 33-J less, what is the gain or loss on the two lots ? 38. A speculator sells two farms for $6000 each ; how much does he gain or lose, if he sells one for .20 more than it cost, and the other for - less than it cost? 39. A gentleman after spending -J- of all his money, and { of the remainder, had $177.50 remaining ; how much had he at first ? 40. A merchant bought 100 yards of cloth at $3.62J per yard, and 87J yards at $4.12 per yard. At what average price per yard should he sell the whole, to realize a profit equal to ^ of the cost ? Jt.1. If 31J bushels of corn cost $17.50, how many bushels can be bought for $616 ? 1$. *In 1864 there were 33908 miles of railroad in operation in the United States, and in 1878, 81841 miles. What was the aver- age annual increase of mileage ? * This is exclusive of sidings. Mr. Poor, from whose Manual the above was taken, esti- mates that there are 19,500 miles of railroad in double, treble, and quadruple tracks, sidings, etc., making the total length of single track equal to 101,341 miles in 1878. DENOMINATE NUMBERS. DEFINITIONS. 146. A Denominate Number is a concrete number (7), and may be either simple or compound. 147. A Simple Denominate Number refers to units of the same name and value ; as 7 inches, 4 pounds. 148. A Compound Denominate Number refers to units of different names, but of the same nature ; as 3 feet C inches, 4 pounds 8 ounces. 149. Denominate numbers are used to express divisions of time, weights, measures, and moneys of different countries. 05 O. The scale of integers and decimals is uniform ; that of most denominate numbers is varying. The moneys of the United States, Canada, France, Italy, Spain, Germany, Norway and Sweden, Denmark, Brazil, Japan, and of some other countries, and the metric system of weights and measures, have a uniform decimal scale. DIVISIONS OF TIME. 151. The natural divisions of time are the year and the day, the other divisions being artificial. The year is the time in which the earth makes one revolution around the sun. The day is the time in which the earth makes one revolution on its axis. 152. The Solar Day is the interval between two consecutive returns of the sun to the meridian. On account of the varying motion of the earth around the sun, the solar days are of unequal length. For civil purposes in measuring time the average of all the days in the year is taken as the unit. 4 50 DENOMINATE NUMBERS. TABLE. 60 Seconds (sec.) 60 Minutes 24 Hours 7 Days 365 Days, \ 52 Weeks, 1 day, or > = 1 Common Year 12 Calendar Months ) 366 Days 100 Years 1 Minute min. 1 Hour hr. 1 Day da. 1 Week . wk. yr. 1 Leap Year yr. 1 Century C. NOTE. In many business transactions the year is regarded as 360 days, or 12 months of 30 days each. 153. The Calendar Months with the number of days they contain are as follows : Season. Days. C 1. January (Jan.) 31. WINTER. < 2. February (Feb.) 28. " in leap year 29. ( 3. March (Mar.) 31. SPRING. < 4. April (Apr.) 30. ( 5. May 31. Season. Days. C 6. June 30. SUMMER. < 7. July 31. ' 8. August (Aug.) 31. C 9. September (Sep.) 30. AUTUMN. < 10. October (Oct.) 31. ' 11. November (Nov.) 30. WINTER. 12. December (Dec.) 31. 154. The Solar Year is the time between two consecutive returns of the sun to the vernal equinox. Its exact length is 365 da. 5 hr. 48 min. 50 sec. in mean solar time. For civil pur- poses, the year consists of 365 or 366 days. In the calendar established by Julius Caesar, B.C. 46, and thence called the Julian calendar, three successive years were made to consist of 305 days each ; and the fourth, of 366 days. According to the Julian calendar, the average length of the year was 365^ days, thus making an error of 11 min. 10 sec. each year ; which in 400 years would amount to 73 hours, or about 3 days. In the sixteenth century, in consequence of the excess of the Julian year above the true solar year, the error in the calendar was 10 days. To correct the calen- dar, and to prevent any error in the future, Pope Gregory XIII. decreed that 10 days should be omitted in the month of October, 1582, and that all centen- nial years not divisible by 400 should be common years. Thus, the years 1700, 1800, and 1900, which according to the Julian calendar would be leap years, would according to the reformed calendar be common years. This LINEAR MEASURE. , 51 calendar is sometimes called the Gregorian calendar. It is now used in all civilized countries except Russia. The Julian and Gregorian calendars are also designated by the terms Old Style and New Style. In consequence of the years 1700 and 1800 being com- mon years by the Gregorian calendar, the difference between the two styles is now 12 days. Thus, when it is July 4 in Russia, it is July 16 in other countries. 155. KULE FOR LEAP YEARS. All years divisible, by 4> except centennial years, are leap years. All centennial years divisible by J00 are leap years. LINEAR MEASURE. 156. Linear or Long Measure is used in measuring dis- tances, also the length, breadth, and height of bodies, or their linear dimensions. In measuring length, the yard derived from the standard yard of England is the standard unit, the yards of the United States and England being iden- tical. Theoretically, the yard is equal to f fff of the length of a pendulum that vibrates seconds in a vacuum, at the level of the sea in the latitude of London ; that is, a pendulum that vibrates seconds under the above conditions is 39.1393 inches in length. The standard yard is, in fact, the distance be- tween two points on a brass bar, preserved at Washington, the distance to be taken when the bar is at a temperature of 62 Fahrenheit. This bar was obtained from England in 1827. TABLE. 12 Inches (in.) = 1 Foot . . ft. 3 Feet = 1 Yard . . yd. 5| Yards =1 Rod . . rd. 40 Rods = 1 Furlong fur. 8 Furlongs = 1 Mile . . mi. mi. fur. rd. yd. ft. in. 1 = 8 = 320 = 1760 = 5280 = 63360 1 = 40 = 220 = 660 = 7920 1 = 5= 16i= 198 I- 3 = 36 1 = 12 NOTES. 1. The inch is usually divided into halves, quarters, eighths, and sixteenths. 2. The foot and inch are divided by civil engineers and others into tenths, hundredths, thousandths, etc. 3. In measuring cloth, ribbon, and other goods sold by the yard, the yard is divided into halves, quarters, eighths, and sixteenths. 4. At the U. S. Custom Houses the yard is divided into tenths and hun- dredths. 5. The mile (5280 ft.) of the above table is the legal mile of the United States and England, and hence it is sometimes called the statute mile. 52 DENOMINATE NUMBERS. 157. Other Denominations. The following denomina- tions are also used : pendulam makers . Point = A Inch. 1 Line = T V Inch. 1 Size = | Inch. Used by shoemakers. 1 Hand = 4 Inches. Used in measuring the height of horses. 1 Fathom = 6 Feet. Used in measuring depths at sea. 1 Cable-length = 120 Fathoms, or 240 yards. 1 Geographic Mile = 1.15+ Statute Miles. Used in measuring distances at sea. 1 Knot = 1 Geo. Mile. Used in determining the speed of vessels. 60 Geo. Miles, or ) _ ^ -^ \ of latitude on a meridian,, or of longitude 69.16 Stat. Miles \ * } on the equator. 360 Degrees = the Circumference of the Earth. SURVEYORS' LINEAR MEASURE. 158. Surveyors' Linear Measure is used in measuring land, roads, etc. The unit of this measure is a chain, 4 rods or 66 feet in length, called Gunter's Chain. It is divided into 100 parts called links, each link being 7.92 inches in length. lOOLinks(^) = 1 Chain 80 Chains 1 Mile . TABLE. ch. mi. ni. ch. ft. I. in. 1 = 80 = 5280 = 8000 = 63360 1 = 66 = 100 = 792 .66 = 1 = 7.92 NOTES. 1. Links are written decimally as hundredths of a chain. 2. 1 rod = 25 links. 3. Engineers for railroad and other purposes use a chain or tape 100 feet long, the feet being divided into tenths. SQUARE MEASURE. 159. Square Measure is used in measuring surfaces. The unit of square measure is a square bounded by lines of some known length. Thus, a square inch is a square whose sides are one inch long ; a square foot, a square whose sides are one foot long ; etc. SURVEYORS' SQUARE MEASURE. 53 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. NOTE. 1 Rood = 40 sq. rds. % A. The rood has practically gone out of use. 16O. The Area of a surface is an expression for that surface in terms of square units. 4 feet. In the diagram each small square represents a square foot. Since there are 3 rows, and 4 square feet in each row, there are 3 times 4 square feet, or 12 square feet in the rectangle. Hence, the area of any rectangle may be found by multiplying together the numbers denot- ing its length and breadth, in the same denomination ; or, more briefly, To find the area of a rectangle, multiply its length by its breadth. SURVEYORS' SQUARE MEASURE. 161. Surveyors' Square Measure is used in measuring land. TABLE. 10000 Square Links (sq. 1) = 1 Square Chain . . . sq. cli. 10 Square Chains = 1 Acre ....... A. 640 Acres = 1 Square Mile . . . sq. mi. NOTES. 1. 1 Pole or Perch = 1 sq. rd. = T V sq. ch. = 2. The acre is the common unit of land measure. 3. In the vicinity of St. Louis, and in ether parts of the Mississippi valley that were settled by the French, the old French arpent is still used as the unit of land measure. It contains about of an English acre. 162. U. S. Public Lands are divided by north and south lines run according to the true meridian, and by others crossing 54 DENOMINATE NUMBERS. them at right angles, so as to form townships of six miles square. Townships are subdivided into sections, containing, as nearly as may be, 640 acres each, or 1 square mile. Sections are subdivided into half -sections, quarter-sections, half -quarter-sections, and quarter-quarter-sections. 1 Township 1 Section 1 Half-Section 1 Quarter-Section 1 Half-Quarter-Section 1 Quarter-Quarter-Section = TABLE. = 6 mi. x 6 mi.= 36 sq. mi.= 23040 A. = 1 " x 1 " = 1 " = 640 " = 1 " x i " = i " == 320 " = i 516. 12| grams, or 192.9 grains. 6J grams, or 96.45 grains. Standard dollar, Half dollar, or ) 50 cent piece, ( Quarter Dollar, or 25 cent piece, Dime, or 10 cent piece, COPPER AND NICKEL. 5 cent piece, 5 grams, or 77.16 grains. 3 cent piece, 30 grains. 1 cent piece, 48 grains. The Mill is not coined. ^ 183. The Trade Dollar contains 420 grains of standard silver (.900 fine). It is not now coined, and is not a legal lender. It was originally coined for the purposes of trade in China and Japan. ^ 183. The gold and silver coins of the United States contain 9 parts by weight of pure metal and 1 part alloy. The alloy of silver coins is copper; and the alloy of gold coins, copper, or copper and silver. (The silver in no case exceeds -fa of the whole alloy.) 184. Gold Coins are a "legal tender in all payments at their nominal value when not below the standard weight and limit of tolerance"* provided bylaw; and, "when reduced in * " Any gold coin of the United States, if reduced in weight by natural abrasion not more than one-half of one per centum below the standard weight prescribed by law, after a C2 DENOMINATE NUMBERS. weight, below said standard and tolerance, are a legal tender at \ valuation in proportion to their actual weight." ^ 185. Standard Silver Dollars are " a legal tender at their nominal value for all debts and dues, public and private, except where otherwise expressly stipulated in the contract." "The Secretary of the Treasury is authorized and directed to purchase * * * silver bullion * * * not less than $2,000,000 worth per month, nor more than $4,000,000 worth per month, and cause the same to be coined monthly, as fast as so purchased, into \ such dollars." (Act of Feb. 28, 1878, Sec. 1.) ^ 186. Silver Certificates. Any holder of standard silver dollars ' ' may deposit the same with the Treasurer, or any Assist- ant Treasurer of the United States, in sums not less than $10, and receive therefor certificates of not less than $10, each corres- ponding with the denominations of United States notes " (189). These certificates are "receivable for customs, taxes, and all public dues, and when so received may be reissued." (Act of Feb. 28, 1878, Sec. 4.) 187. Subsidiary Coins. "The present (1880) silver coins of the United States of smaller denominations than $1" are "a legal tender in all sums not exceeding $10, in full payment of all dues, public and private." (Acts of 1st session, 46th Congress, Chap. XII, Sec. 3.) " The holder of any of the silver coins of the United States of smaller denominations than $1 may, on presentation of the same in sums of $20, or any multiple thereof, at the office of the Treasurer or any Assistant Treasurer of the United States, receive therefor lawful money of the United States." (Acts of 1st session, 46th Congress, Chap. XII, Sec. 1.) 188. Minor Coins. The 5 and 3 cent pieces contain J copper and J nickel. The 1 cent piece contains 95 per cent, copper and 5 per cent, tin and zinc. These coins are " a legal tender, at their nominal value, for any amount not exceeding twenty-five cents in any one payment." 189. United States Notes ("Greenbacks") are "a legal tender for all debts, public and private, except duties on imports circulation of twenty years, as shown by its date of coinage, and at a ratable proportion for any period less than twenty years, is received at its nominal value by the United States treasury and its offices." The "Coinage Act of 1873" allows a deviation from the standard weight of I of a grain, or less, in the manufacture of the dollar piece. ENGLISH MONEY. 63 and interest on the public debt." Since Jan. 1, 1879, they have been redeemable " in coin * * * on their presentation for redemption at the office of the Assistant Treasurer of the United States in the City of New York, in sums of not less than $50." They represent the values of $1, $2, $5, $10, $20, $50, $100, $500, $1000, $5000, and $10,000. The Act of May 31, 1878, fixed their value at $346,681,016, and forbade their further contraction. 190. National Bank Notes are not a legal tender ; but, since they are " secured by bonds of the United States deposited with the U. S. Treasurer at Washington," and are redeemed in lawful money by the national banks and the Treasurer of the United States, they are usually accepted in the payment of debts in any part of the United States. They are "receivable in all parts of the United States in payment of all taxes and excises and all other dues to the United States except duties on imports, and also for salaries and other debts and demands owing by the United States to individuals, corporations, and associations within the United States except interest on the public debt." They represent the values of $1, $2, $5, $10, $20, $50, $100, $500, and $1000. Since Jan. 1, 1879, no notes of the denomina- tion of $1 and $2 have been issued to national banks (R. S. 5175). Since the act of Jan. 14, 1875, the volume of national bank notes has been unlimited. Nov. 1, 1879, their total circulation, includ- ing gold banks, was $337,181,418. ENGLISH MONEY. 191. English or Sterling Money is the legal currency of Great Britain. TABLE. Value in TJ. S. money. 4 Farthings 1 Penny . . . d. . . . $ .02 + 12 Pence = 1 Shilling . .''-.* ..... 243 + 20 Shillings = > . . . 4.8665 (1 Sovereign > *" NOTES. 1. 1 Crown = 5 shillings, or } of a pound ($1.216 + ). ^ 2. 1 Guinea = 21 shillings ($5.11). It is not now coined. 3. The gold coins of Great Britain are 22 carats (|i), or .916| fine. (The old carat system (170, note) is generally abandoned except for jewelry. 1 carat = .041f.) 4. The silver coins of Great Britain are .925 (f) fine. DENOMINATE NUMBERS. 192. FOKEIGN MONEYS or ACCOUNT AND THEIR VALUES IN- UNITED STATES MONEY. Country. Monetary Unit. Standard. Value in U. S. Money. Florin of 100 kreutzers . Silver. .40 7 Franc of 100 centimes . Gold and silver .19 3 Bolivia b Boliviano, 100 centavos Silver .82 3 Brazil Milreisof 1000 reis Gold . . .54 6 British America. . . Dollar of 100 cents Gold $1.00 Chili . . . Peso of 100 centavos . . Gold and silver 91 2 Cuba Peso of 100 centavos. . . Gold and silver .93 2 c Crown of 100 ore Gold .26 8 Ecuador b Peso of 100 centavos . . Silver . .82 3 Egypt. , Piaster of 40 paras Gold . . . 049 France a Franc of 100 centimes Gold and silver 19 3 Great Britain Pound sterling 1 . Gold 4 86 64 Greece Drachma of 100 lepta . Gold and silver. .. .19,3 German Empire Mark of 100 pfennige Gold 23 8 India Rupee of 16 annas d . Silver .89 Italy "Lira of 100 centesimi Gold and silver. . .19 3 Japan . . . Yen of 100 sen Silver 88 8 Liberia . . . Dollar of 100 cents . . . Gold 1 00 Mexico Dollar of 100 centavos Silver 89 4 Netherlands Florin of 100 cents Gold and silver. . . .40,2 Norway c Crown of 100 ore Gold .26 8 Peru b Sol of 100 centavos Silver 82 3 Portugal Milreis of 1000 reis . . Gold 1.08 Russia Rouble of 100 copecks. Silver .65 8 Sandwich Islands Dollar of 100 cents . . . Gold 1.00 Peseta of 100 centimes. Gold and silver 19 3 Sweden Crown of 100 ore Gold 26 8 Switzerland Tripoli Franc of 100 centimes. Mahbub of 20 piasters Gold and silver... Silver .19,3 74 3 Turkey Piaster of 40 paras Gold 04 4 U S. of Colombia . b Peso of 100 centavos . . Silver .82 3 Venezuela Bolivar Gold and silver. . .19 3 The above rates, proclaimed by the Secretary of the Treasury, Jan. 1, 1881, are used in estimating, for Custom-House purposes, the values of all foreign merchandise made out in any of said currencies. () The franc of France, Belgium, and Switzerland, the peseta of Spain, the drachma of Greece, the lira of Italy, and the bolivar of Venezuela have the same value. ( b ) The peso of Ecuador, and United States of Colombia, the boliviano of Bolivia, and the sol of Peru have the same value. ( c ) The crowns of Norway, Sweden, and Denmark have the same value. ( d ) The anna contains 12 pies. REDUCTION. 65 REDUCTION. 193* Reduction of Denominate Numbers is the chang- ing their denomination without changing their value. 194. To reduce denominate numbers from higher to lower denominations. Ex. How many pence in 8 16s. Id. ? OPERATION. s. d. 8 16 7 OQ ANALYSIS. Since there are twenty shillings in 1 pound, in 8 pounds there are 8 times 20 shillings, or 160 shillings. 160s. (F or convenience multiply by 20 as an abstract number.) 16s. 160 shillings plus 16 shillings equal 176 shillings. Since i r/c there are 12 pence in 1 shilling, in 176 shillings there are 1 176 times 12 pence, or 2112 pence. 2112 pence plus 7 pence equal 2119 pence. When possible, add mentally the num- ber of the lower denomination to the product. 195. KTJLE. Multiply the number of the highest denom- ination given by the number of the next lower denomina- tion required to make 1 of this higher, and to the product add the given number, if any, of such lower denomination. Treat this result, and the successive results obtained., in lilce manner until the number is reduced to the required denomination. EXAMPLES. 196. Eeduce: 1. 9 13s. lOrf. to pence. 11. 5 mi. 36 rd. lift, to feet. 2. 6 gal. 3 qt. 1 pt. to gills. 12. 456 miles to feet. 8. 112 18s. 5d. to farthings. 13. 16-J- hands to inches. 4. 6 T. 12 cwt. 65 Ib. to pounds. 14. 3 mi. 46 ch. 75 I to links. 5. The year 1896 to hours. 15. 7 mi. 55 ch. to rods. 6. The year 1881 to minutes. 16. 29 sq. rd. to square feet. 7. 245 15s. 3 far. to farthings. 17. 97 sq.rd. to square yards. 8. 48 bu. 3 pk. 6 qt. to quarts. 18. 5 sq. mi. to acres. 9. The year 1900 to hours. 19. 5 miles square to acres. 10. 18 Ib. 8 oz. to pennyweights. W. 16 cords 112 cu.ft. to cu.ft. 5 66 DENOMINATE NUMBERS. 21. How many cubic feet in a vessel whose measurement is 2135 tons ? 22. How many pounds in 16 T. 3 qr. 18 lb. (Long Ton Table) ? 23. How many quarts in 3 libl. 24 gal. cider ? 24. How many pounds in 2375 bushels corn ? 25. At 1 cent each, what is the value of 20 great gross pens ? 26. How many days from Jan. 1, 1888, to Jan. 1, 1906 ? 27. How many days in 8 m. 26 da. ? 197. To reduce denominate numbers from lower to higher denominations. Ex. Eeduce 2119 pence to higher denominations. OPERATION. ANALYSIS. Since there are 12 pence in 1 12 ) 2119^7. shilling, in 2119 pence there are as many shillings 20 ) 176s 4- Id as -^ P ence are contained times in 2119 pence, or 176 shillings, and 7 pence remaining. Since there are 20 shillings in 1 pound, in 176 shillings 2119c. .8 16s. 7d. there are as many pounds as 20 shillings are con- tained times in 176 shillings, or 8 pounds, and 16 shillings remaining. Therefore, 2119tf. = 8 16s. Id. 198. RULE. Divide the given number by the number of that denomination required to make 1 of the next higher, reserving the remainder, if any, as part of the answer. Treat the quotient, and the successive quotients obtained, in like manner until the number is reduced to the inquired denomination. The last quotient and the several remain- ders will form the answer. EXAM PLES. 199. Reduce 1. 8475^. to pounds. 11. 13387^. to pounds. 2. 9683 cu.ft. to cords. 12. 10224 ft. to fathoms. 3. 7534 pte. to bushels. 18. 60427 J. to chains. 4> 9817 pts. to barrels. 14. 16338/tf. to chains. 5. 5280 ft. to miles. * 15. 5384 rods to chains. 6. 7633 sq.yds. to sq. rds. 16. 6375 I to rods. 7. 8437 days to com. yrs. 17. 5316 sq. rds. to acres. 8. 6375 hrs. to weeks. 18. 49380 sq. I. to acres. 9. 9537 sec. to hours. 19. 38425 sq. ch. to sq. mi. 10. 6239 in. to rods. 20. 7685 poles to acres. REDUCTION OF DENOMINATE FRACTIONS. 67 21. What is the cost of 465 yards of cloth at 9J pence per yard? 22. What is the value of 49375 pounds of corn at $0.64 per bushel ? 23. What is the value of 27425 pounds of corn at $0.95 per cental ? 24. Required the value of 18643 pounds of oats at 75 cts. per bushel. 25. Find the cost of 17387 pounds of oats at $1.88 per cental. 26. The report of a cannon is heard 4|- seconds after the flash is seen ; what is the distance of the cannon, if sound moves 1090 feet per second ? 27. What cost 21370 pounds of straw at $8 per ton ? 28. Required the cost of 875 pounds of feed at $1.15 per cwt. 29. In 327 days, how many months of 30 days each ? SO. What is the freight of 39445 pounds of merchandise at 64s. per ton of 2240 pounds ? REDUCTION OF DENOMINATE FRACTIONS. 200. A Denominate Fraction is a fraction whose integral unit is a denominate number. The principles, analyses, and rules of denominate fractions are essentially the same as those of denominate integers ; therefore, no special rules are necessary for their reduction. A sufficient number of illustrative examples are given to fully explain the different cases that may arise. 201. To reduce denominate fractions from higher to lower denominations. Ex. Reduce T \ of a to pence. ANALYSIS. Since there are 20 shillings in 1, in T V (.4375) of a there are T V i x A _3 5 5< (.4375) of 20 shillings, or -^ (8.75) shillings. V Since there are 12 pence in 1 shilling, in % 5 35_ >< A 1056/. (8.75) shillings there are \ 5 - (8.75) times 12 pence, or 105 pence. Or, multiply the 5 3 given fraction by the numbers of the scale O r > A x ^ X ^T 105(?. required to reduce its denomination to the required denomination. 68 DENOMINATE NUMBERS. Ex. Eeduce .4375 of a to pence. OPERATIONS. .4375 x 20 = 8.755. 8.75 x 12 = 105d. ANALYSIS. As in previous example. Or, .4375 20 8.75005. 12 105.0000<1 Ex. Eeduce T \ of a to integers of lower denominations, i.e. to shillings and pence. OPERATION. x = 9rf. = 85. 96?. ANALYSIS. Multiplying by 20, T 7 g = 8| shillings. Reserve the integral part of the result, and reduce the fractional part to pence. Multiplying by 12, f shilling 9 pence. Hence, &fa Ss. 9cf. Ex. Eeduce .4375 of a to integers of lower denominations. OPERATIONS. .4375 x 20 = 8.755. .75 X 12 = Or, .4375 20 5.8|.7500 12 d. 9|.0000 ANALYSIS. Multiplying by 20, .4375 = 8.75 shillings. Reserve the integral part of the result, and reduce the decimal part to pence. Multiplying by 12, .75 shilling = 9 pence. Hence, .4375 = Ss, 9d. EXAMPLES. 2O2. 1. Eeduce .625 of a to pence. 2. Eeduce .875 of a to shillings and pence. 3. Eeduce -^ of a to pence. 4. Eeduce -^ of a to integers of lower denominations. 5. Change 2.333^ yrs. to lower denominations. 6. Change 16.467 to lower denominations. 7. If 1 pound sterling can be bought for $4.87, how many pounds can be bought for $10000 ? 8. Eeduce 2.417 yr. to lower denominations. REDUCTION OF DENOMINATE FRACTIONS. 69 9. A cistern is 16.25/2. long, 9. 6 ft. wide, and 6.25 ft. deep; what is its capacity in cu. yd. etc. ? 10. A certain sum at a certain rate will in 1 ?/r. produce $60 interest ; in what time will the same sum at the same rate produce $15.50 interest ? 2O3. To reduce denominate numbers to fractions (or decimals) of higher denominations. Ex. Reduce f of a penny to the fraction of a . OPERATIONS. ANALYSIS. Divide the given fraction 3 i 9 _ t_ e by the numbers of the scale required to re- "F ~ -** o * / j i_ on i n duce pence to pounds. If the answer is required in the form of ^ r ? -f X i^f X T^O" -f-^-Q a decimal, reduce the resulting fraction to a 4 decimal by Art. 127. ^ = .0025. Ex. Reduce .6 of a penny to the decimal of a . OPERATION. i 9 \ g ,7 ANALYSIS. As in previous example. If the answer is required in the form of a fraction, reduce the resulting decimal to a fraction by Art. 131. .0025 .0025 = T ^. Ex. Change 9 pence to the fraction of a . OPERATIONS. ANALYSIS. For first operation, as in pre- t v i_ v l- JL vious exam P le - T 4 * ' Or, since there are 240 pence in 1, 1 Or 9 3_ penny equals ^ of a , and 9 pence equal ^ or ^ of a > Ex. Reduce 9 pence to the decimal of a . OPERATIONS. 12 )9. d. 20 ) .75 s. ANALYSIS. As in previous example. .0375 . Ex. Reduce 12s. 9d. to the fraction of a . OPERATION. 125. 9d. = 153^. ANALYSIS. 12 shillings 9 pence = 153 pence. 1 _ 240^. Since 1 = 240 pence, 1 penny equals ^ of a . and 153 pence equal f f , or f of a . irrb" ? * 70 DENOMINATE NUMBERS. Ex. Reduce 18 12s. 9d. to the decimal of a . OPERATION. ANALYSIS. Write the denominations given in a verti- 12 ) 9. d. cal column, the lowest denomination at the top. Since 20 ) 12 75 S tnere are 12 pence in 1 shilling, 9 pence are equal to .75 shilling ; to which annexing the 12 shillings given, we 18.6375 h^ 13> 75 shillings. Since there 20 shillings in 1, 12.75 shillings are equal to .6375, to which annexing the 18, ive have 18.6375. Hence 18 12*. 9d. = 18.6375. EXAMPLES. * 2O4. 1. Reduce | of a penny to the fraction of a pound. ^ 2. Reduce .875 of a shilling to pounds. 3. Change 12 cwt. to the decimal of a ton. 4. Reduce 420 grains to the fraction of an ounce Troy. ^ 5. Reduce J of a penny to the decimal of a pound. ^ 6. What part of a mile is .165 of a foot ? 7. What decimal of a are 18s. 6tl ? NOTE. The following method for reducing shillings, pence, arid farthings to the decimal of a pound is sufficiently accurate for most business purposes : Write one-half of the greatest even number of shillings as tenths, and if there be an odd shilling write 5 hundredths ; reduce the pence and farthings to far- things, and write their number as thousandths. If the number of farthings is between 12 and 36, add 1 to the thousandths ; if between 36 and 48, add 2 to the thousandths. Thus, 8 17s. Sd. = 8 + .85 + .033 = 8.883. 8. Reduce 116 cu.ft. to the decimal of a cord. 9. Reduce 247 14s. Qd. to pounds. ^ 10. What decimal of an acre are 16 sq. rds. ? 11. Reduce 75 feet to the fraction of a mile. 12. Reduce 27 105. 6d. to pounds. 13. What is the cost of 22480 pounds of coal at $4.25 per ton (2240 pounds) ? 14. What is the cost of 16 tons 12 cwt. of "Nut" coal at &6.80 per ton, and 8 tons 16 cwt. of " Chestnut" coal at $6.10 per ton ? 15. What is the cost of 8364 pounds of oats at $1.65 per cental ? 16. What is the cost of 8375 pounds of oats at $0.56 per bushel ? 17. If 1 pound is equivalent to $4.8 7f , what is the value of 1234 165. 9rf. in U. S. money ? 18. Reduce 25 12s. Qd. to the decimal of a , and multiply the result by .05. ADDITION. 71 ADDITION. 205. Denominate numbers are added, subtracted, multiplied) and divided by the same general" methods as are employed for like operations in abstract numbers. The only difference arises from the use of a varying scale instead of the uniform scale of 10. Ex. Add 5 11s. 4=d., 7 14s. 9d., 6 16s. Sd., and 7 5s. 9 OPERATION. ANALYSIS. Write the numbers so that like denomina- s. d. tions stand in the same column, and begin to add at the right. 5 11 4 The sum of the pence is 3Qd. = 2s. Qd. Write the Qd. under 7 14 9 the column of pence, and add the 2s. to the column of shil- 6 16 8 h n s > obtaining for the sum 48*. = 2 8s. Write the 8$. -, Q under the column of shillings, and add the 2 to the column of pounds, obtaining for the sum 27 ; which write under 27 86 the column of pounds, producing the entire sum, 27 8*. Qd. EXAMPLES. 206. 1. Add 16 5s. 4&, 12 8s. 9d, 13 14s. Sd., 42 Os. 7&, and 18s. 6d. 2. Add 3T. IScivt. 2qr. 16 lb., 4T 7 . I3cwt. 3qr. 14/5., 1ST. 13 cwtf. 24 lb., and 42 T 7 . 8 c? St. Louis and Calcutta. 2. Boston and Paris, 5. Philadelphia and Berlin. 3. Chicago and San Francisco. 6. San Francisco and Calcutta. Find the difference in time between 7. New York and Greenwich. 10. Eome and London. 8. Chicago and New York. 11. Paris and Albany. 9. Kichmond and Calcutta. 12. Calcutta and Jefferson City. THE METRIC SYSTEM. 77 13. The difference in time between New York and Greenwich is 4 lir. 56 min. % sec. ; what is the difference in longitude ? When it is 12 o'clock noon at New York, what is the time at Greenwich ? 14. A navigator finds that when it is noon at his place of observation, it is 16 min. 34 sec. past 10 P.M. by his chronometer, Greenwich time ; what is his longitude ? 15. When it is 6 o'clock P.M. at Richmond, Va., what is the time at St, Louis, Mo. ? 16. If the difference of time between two places is 1 7tr. IS min. 4 sec., what is the difference of longitude? 17. When it is 20 min. past 2 P.M. at Boston, Mass., what o'clock is it at San Francisco ? 18. When it is 9 o'clock P.M. in San Francisco, it is 3 min. 3^ sec. past 11 A.M. in Calcutta; what is the longitude of San Francisco, if the longitude of Calcutta is 88 19' 2" E.? 19. When it is noon in Chicago, it is 5 min. 29^ sec. of 1 P.M. in New York ; what is the longitude of Chicago, the longitude of New York being 74 3" W. ? THE METRIC SYSTEM. 221. In the Metric System, the Meter is the basis of all the weights and measures which it employs. 222. The Meter is the unit of length, and is equal to one ten-millionth part of the distance measured on a meridian of the earth from the equator to the pole, and equals about 39.37 inches. The standard meter is a bar of platinum carefully preserved at Paris. Exact copies of the meter and the other units have been procured by the * The use of the metric system is (1878) obligatory in Belgium, France, Germany, Greece, Netherlands, Italy, Portugal, Roumania, Spain, and Switzerland ; in the Argentine Republic, Brazil, Peru, San Domingo, United States of Colombia, and Uruguay countries aggregating a population of 181,000,000 while its use is partial or legalized in Austria, Azores, Madeira and Cape de Verde Islands, Central American States, Denmark, Japan, Sweden, Norway, Turkey, Spanish Possessions, Great Britain and the British Possessions, and our own country, aggregating a population of 375,000,000 more. For the year ending June 30, 1877, the value of our imports from countries where the metric system is obligatory amounted to $177,807,4(59; partially in use, $17,378,785; legalized, $265,211,585; not legalized or in use, only $23,804,140. Of the amount received from countries where its use is legalized, Great Britain and British Possessions furnish $185,667,400. With th/se countries our present system is partly in harmony, but unfortunately the bulk of our trade with them is made up of articles measured by the bushel and gallon, neither of which standards corresponds to any bushel or gallon of this country. It should be borne in nVlnd that the only legalized system of weights and measures in this country to-day is the metric system, and that this system is the only one we possess in harmony with that of any other country. 78 DENOMINATE NUMBERS. several nations, including the United States, that have legalized the system. Comparisons with the standard units are made under certain conditions of temperature and atmospheric pressure. 223. The names of the higher denominations, or multiples, of the unit are formed by prefixing to the several units the Greek numerals, deka (10), hecto (100), kilo (1000), and myria (10000) ; as dekameter, 10 meters, hectometer, 100 meters, etc. To assist the memory, observe that the initial letters of the multiples are in alphabetical order ; thus, D, If, K, and M. 224. The names of the lower denominations, or divisions, of the unit are formed by prefixing to the several units the Latin numerals, deci ( T V), centi (TOO)> m ^ (roW) 5 as decimeter, ^ meter, centimeter, -^ meter, etc. To assist the memory observe that the following words are derived from the same roots: dime, decimal, decimate, decennial, etc.; cent, cental, century, centennial, etc.; mill, millennium, etc. LINEAR MEASURE. 225. TABLE. 10 mm. = 10 cm. = 1 Millimeter. 1 Centimeter. 1 Decimeter '(woir f a meter) (T&U f a me t er ) (.jig. of a meter) = . 03937 in. .3937m. 3.937 in. 10 dm. = 1 METER . . . .(1 meter) _ 39.37 in. 10 w. = 10 Dm. = 10 Hm. = 1 Dekameter. 1 Hektometer 1 Kilometer. . (10 meters) . . . .(100 meters) ....(1000 meters) = 32.8/J. 328. 09 /*. .62137 wit. NOTES. 1. The meter, like the yard, is used in measuring cloths, ribbons, laces, short distances, etc. 2. The kilometer is used in measuring long distances, and is about f of a mile. 3. The centimeter and millimeter are used by artisans and others in measuring minute lengtiis. The other denominations are rarely used. EXAMPLES. 226. 1. Eeduce 875275 meters to kilometers. ANALYSTS. Since 1 kilometer equals 1000 meters, in 875275 meters there are as many kilometers as 1000 is contained times in 875275, or 875.275. To divide by 1000 place the point three places to the left (143, 3). 2. Reduce 675.318 kilometers to meters. ANALYSIS. Since 1 kilometer equals 1000 meters, in 675.318 kilometers THE METRIC SYSTEM. 79 there are 675.318 times 1000, or 675318 meters. To multiply by 1000, place the point three places to the right (14O, note). 3. Keduce 383.64 meters to centimeters ; to kilometers. 4. Keduce 175.16 centimeters to kilometers ; to meters. 5. Reduce to meters and find the sum of 876.2 decimeters, 30347 centimeters, 176.48 meters, 8.175 kilometers. 6. A ship sails 5712 kilometers in 48 days ; how many kilo- meters does she sail per day? 7. What is the value of 56.4 meters of silk at $1.75 per meter ? 8. 16 pieces of cloth contain 38.5 meters each ; 18 pieces con- tain 39 meters each; and 24 pieces contain 41.2 meters each; how many meters in all ? 9. How many meters of ribbon at 27 cents per meter can be purchased for $245.70 ? SQUARE MEASURE. 227. The unit of square measure is the square meter. TABLE. 100 Square Centimeters, sq. cm. = 1 Square Decimeter = 15.5+ sq. in. tOO Square Decimeters, sq. dm. = 1 SQUARE METER, Sq. M. = 1.196+ sq.yd. NOTES. 1. The square meter is used in measuring flooring, ceilings, etc.; the square decimeter and the square centimeter are used for minute surfaces. 2. Since units of square measure form a scale of hundreds, each denomi- nation must have two places of figures. 228. The unit of Land Measure is the are, and is equal to a square dekameter (100 square meters), or 119.6 square yards. TABLE. 1 Centare. ..(1 square meter) = 1550 sq. in. 100 Centares, ca. = 1 Are (100 square meters) = 119.6 sq. yd. 100 Ares, A. = 1 Hectare. ..(10000 square meters) = 2.471 acres. NOTE. The hectare is the ordinary unit for land. EXAMPLES. 229. 1. Write 16 sq. m., 8 sq. dm., 24 sq. cm., having the square meter as the unit. Ans. 16.0824. 2. Write 83 sq. m., 9 sq. dm., having the sq. m. as the unit. 80 DENOMINATE NUMBERS. 3. In 47 ares how many square meters ? 4- In 60.25 hectares how many centares? 5. How many square meters in a building lot 8 m. by 32 m.? 6. How many building lots, each containing 225 sg. m., can be formed from a field containing 9 hectares ? 7. How many hectares in a farm 1.024 Km. in width and 1.625/iw?. in length? 8. AVhat is the cost of a mirror 2.25m. by 1.44?^., at $3.84 per s^. m. ? 9. How many lots 25 m. wide by 60 m. deep, or haying an equivalent area, can be laid out from 6 hectares ? 10. A man bought a piece of land for $6950.50, and sold it for 87603.30, by which transaction he made $6.80 a hectare; how many hectares were there ? 11. If the forward wheels of a carriage are 3.5 meters in cir- cumference, and the hind weels 4.8 meters, how many more times will the forward wheels revolve than the hind wheels, in running a distance of 8.4 kilometers? CUBIC MEASURE. 230. The unit for measuring ordinary solids is the cubic meter. TABLE. 1000 Cu. Millimeters, cu. mm. = 1 Cu. Centimeter = .061 eu. in. 1000 Cu. Centimeters, cu. cm. = 1 Cu. Decimeter = 61. 027 cu.in. 1000 Cu. Decimeters, cu. dm. = 1 Cu. METER = J 35 - 317 cu -f L ll. 808 CM. yd. NOTES. 1. The cubic meter is used in measuring embankments, excava- tions, etc.; cubic centimeters and cubic millimeters for minute bodies. 2. Since units' of cubic measure form a scale of thousands, each denomi- nation must have three places of figures. 231. The unit of "Wood Measure is the ster, and is equal to a cubic meter, or 35.317 cubic feet. TABLE. 10 Decisters, da. = 1 Ster. . . .(1 Cubic Meter) = \ ' 3759 cord ' ( 35. 317 eu. ft. 10 Sters, ,9. = 1 Dekaster, Ds. .(10 Cubic Meters) = 2.759 cords. APPROXIMATE RULES. 85 8. In 5000 U. S. bushels, how many hectoliters ? How many dekaliters ? 9. In 875 cu. yd. how many cu. m. ? 10. In 1000 cu. m. how many cu. yd. ? 11. Reduce 1728 gal. wine to liters ; to dekaliters, 12. In 244 sq. m. how many sq. yd. ? How many sq. ft. ? 13. Reduce 220 oz. Av. to grams ; to kilograms. 24O. APPROXIMATE VALUES. When no great accuracy is required, we may, for all practical purposes, consider 1 decimeter = 4 inches. 1 cu. met. or ster = l cu. yd., or \ cord. 1 meter 39 inches. 1 liter = 1 quart. 5 meters = 1 rod. 1 hectoliter = 2| bushels. 1 kilometer = f- mile. 1 gram = 15 grains. 1 square meter = lOf square feet. 1 kilogram = 2i pounds. 1 hectare = 2| acres. 1 ton ~ 2200 pounds. APPROXIMATE RULES. 241. To reduce avoirdupois ounces to grams : Multiply by SO, and then deduct one-twentieth (5 per cent.). NOTE. Answer too great by about 5g. for every 1000 #. of the result. 242. To reduce avoirdupois pounds to kilograms : Divide ~by 2, and then deduct one-tenth. NOTE. Answer too small by about 8 kilos for every 1000 kilos of the result. If -/y, instead of y 1 ^, be deducted, the answer will be too great by 2 kilos for every 1000 kilos of the result. 243. To reduce avoirdupois pounds to half-kilograms, or German pounds : Deduct one-tenth. NOTE. The answer by this rule will be too small by about 8 German pounds for every 1000 German pounds of the result. If -^ be deducted, the answer will be too great by 2 German pounds for every 1000 German pounds of the result. 244. To reduce tons (2000 Ibs.) to metric tons : Deduct one-tenth. NOTE. The same relative error as in Art. 242. 86 DENOMINATE NUMBERS. 245. To reduce yards to meters : Deduct one-twelfth. NOTE. Answer too great by 2J m. for every 1000m. of the result. 246. To reduce square yards to square meters : Deduct one-sixth. NOTE. Answer too small by about 3 sq. m. for every 1000 sq. m. of the result. 247. To reduce cubic yards to cubic meters : Divide by 1.3. NOTE. Answer too great by about 6 CM. m. for every 1000 CM. m. ot the result. 248. To reduce U. S. gallons to liters : Multiply by 4) and then subtract one-twentieth (5 per cent.). NOTE. Answer too great by about 4Z. for every 1000?. of the result. 249. To reduce U. S. bushels to hectoliters : Divide by 3, and then add one-twentieth (5 per cent.). NOTE. Answer too small by about Ihl. for every 1000 hi. of the result. 250. To reduce grams to avoirdupois ounces : Divide by 30, and then add one-twentieth (5 per cent.). NOTE. Answer too small by about 8 ounces for every 1000 ounces of tLa result. 251. To reduce kilograms to avoirdupois pounds: Multiply by 2, and then add one-tenth. NOTE. Answer too small by about 2 ll\ av. for every 1000 Ib. av. of the result. 252. To reduce German pounds, or half-kilograms, to avoirdupois pounds : Add one-tenth. NOTE. Same error as in Art. 251. 253. To reduce metric tons to U. S. tons (2000 Ibs.) : Add one-tenth. NOTE. Answer too small by about 2 TJ. S. tons for every 1000 tons of the result. APPROXIMATE RULES. 87 254. To reduce meters to yards : Add one-twelfth, and 1% of the original number. NOTE. Answer will be too small by only \ yd. for every 1000#d of the result. This method is used at the New York Custom House and is sufficiently accurate for practical purposes. If -^ be added, the answer will be too small by about 2^ yd. for every 1000 yd of the result. If ^ be added, the answer will be too great by about 6 yd. for every IQWyd. of the result. Ex. According to above rule, how many yards in 324 meters ? (Exact result is 354. 33 yd. Error only . 09 yd. ) OPERATION. 324 255. To reduce square meters to square yards : Add one-fifth. NOTE. Answer too great by about 3 sq. yd. for every 1000 sq. yd. of the result. 256. To reduce cubic meters to cubic yards : Multiply by 1.3. NOTE. Answer too small by about 6 cu. yd. for every 1000 cu. yd. of the result. 257. To reduce liters to U. S. gallons : Multiply by 2.11, and then divide by 8. NOTE. Answer too small by about 1.7 gal. for every 1000 gal. of the result. Ex. In 144 liters, how many U. S. gallons ? OPERATION. 144 144 288 (Exact result should be 38.04. Error only .06 gal. 8 ) 303.84 37.98 258. To reduce hectoliters to U. S. bushels. Multiply by 3, and then subtract one-twentieth (o per cent.). NOTE. Answer too great by about 46w. for every 1000 Zw. of the result. 88 DENOMINATE NUMBERS. 259. FOREIGN WEIGHTS AND MEASURES. ARGENTINE CONFEDERATION. Metric system used in the assess- ment of duties. Old Spanish weights and measures (see Spain) in common use. AUSTRIA, (AS GERMANY.) BELGIUM, (METRIC SYSTEM.) BOLIVIA. The metric system is the legal sys- tem, but the law has not been rigidly enforced. Old Spanish weights and measures (see Spain) still in use. For coin weight the metric gram is used. BRAZIL, (METRIC SYSTEM.) Diamonds are permitted to be sold according to the old Portuguese outava (55.34 grains). Ships' freights, are, for the most part, settled according to the English ton (2240 .). CANADA, (AS GREAT BRITAIN.) CAPE OF GOOD HOPE, (AS GREAT BRITAIN.) CEYLON, (AS GREAT BRITAIN.) CHILI, (AS BOLIVIA.) For custom purposes, the metric system is enforced. CHINA. ITael 1 Catty 1 Picul 1 Chih = \\oz. av. = lft. a v. = 133'- ft- av. = 14.1 inches. 1 Chang = 11.75 feet. COLUMBIA, (METRIC SYSTEM.) DENMARK. 1 Pound (I kilogram) = 1.102 ft. av. 1 Centner (100ft.) 1 Tonde of grain 1 Tonde of coal 1 Fod (Foot) 1 Viertal 1 Alen (Ell) = 110.23ft. av. = 3.948 U.S.&M. = 4.825 U.S.&M. = 1.03 U.S. ft. = 2.04 U.S. gal. = .6864yd Coinage laws are metric. The in- troduction of complete metric system is in prospect. ECUADOR, (METRIC SYSTEM.) ENGLAND, (SEE GREAT BRITAIN.) EGYPT, (METRIC SYSTEM.) FRANCE, (METRIC SYSTEM.) The old French aune = 45 inches is still used to some extent in the silk industries of France and the U. S. GERMANY. Metric system with a few changes in subdivisions in general use. 1 Pound (i kilogram) = 1.1023ft. av. 1 Centner (100 pounds) = 110.23ft. av. 1 Wispel (metric ton) = 2204.6 ft. av. GREAT BRITAIN. Imp. Gallon = 1.2 U.S. gal " Bushel =1.03U.S.Zw. " Quarter = 8.25 U.S. bu. Ale or Beer Gallon = 1.22 U.S. gal. Cental = 100 ft. Quarter of Wheat ) AQn 77 at London f ~ ' lb ' 1 Quarter of Wheat at Hull ) _ Kn4 and Newcastle. f ~ 1 Quarter of Wheat at Dnn- ) _ AQR dee and other places. f ~ Metric system permitted by law of 1864. FOREIGN WEIGHTS AND MEASURES. 89 GREECE. Metric system with the common Grecian names in general usa. In the Ionian Islands the English weights and measures have been legalized since 1829. HONG KONG, (AS CHINA.) INDIA. 1 Seer = 16 chattacks. 1 Bombay Maund of 40 seers 28 Ib.&v. 1 " 42 " =29.4 " 1 Surat " 40 " =31 " 1 " "42 " =391 1 " "44 " =41 T y< 1 Bengal Factory Maund =74| " 1 " Bazaar " =82$ " 1 Madras Maund =25 " !Bom'yCandyof20niaunds=560 " 1 Surat " " " =746|" 1 Madras " " M =500 " 1 Travancore" " " =660 " 1 Tola =180$r. 1 Guz of Bengal = 1 Eng. yard. 1 Corge =20 units. 1 Corge Pound =20 Ib. Metric system permissive. ITALY. 1 Palm = .555 cu. ft. Metric system in general use. JAPAN. 1 Picul = 133 i Ib. av. For coinage, in part, the metric unit of weight is used. JAVA. 1 Amsterdam Pond = 1.09 #>. av. 1 Picul = 133^ " 1 Catty = li " 1 Chang = 4 yards. LIBERIA. British weights and measures gen- erally used. MEXICO. Weights and measures are legally the metric, but the metric system is not generally in force, the old Spanish weights and measures (see Spain) being still employed. NETHERLANDS. Metric system with a change in names in general use. 1 Last (30 hectoliters) = 85.134 bu. NORWAY AND SWEDEN. 1 Swedish Skalpond = 0.93^ Ib. av. 1 Swedish Centner = 93 1 Norwegian Fund = 1.1 1 Swedish Fot = 11.7 inches. 1 Norwegian Fod = 12.02 " In Norway the metric system is used to some extent. In Sweden, the coin weight and the medicinal and apothecary weight are metric. The complete metric system is now permissive, and will be obliga- tory after 1882. PERU, (AS BOLIVIA.) PORTUGAL. Metric system compulsory since Oct. 1, The chief old measures are 1 Libra = 1.012 Ib. av. 1 Almunde of Lisbon = 4.42 U. S. gal. 1 Alquiere = .3928 U. S. bu. RUSSIA. 1 Pound = 0.9 Ib. av. 1 Pood (63 to a ton) = 36 " 1 Berkowitz = 360 " 1 Chetvert -= 5.956 U.S.&w. 1 Vedro = 3.25 U. S. gal. 1 Arsheen = 28 inches. 1 Ship Last = 2 tons. Metric system partially in use. SIAM. 1 Tael = li oz. av. Picul, Catty, and Chang, same as Java. 90 DENOMINATE NUMBERS. SPAIN, (METRIC SYSTEM.) In many of the South American States and in Cuba, the old Spanish weights and measures, principally Castilian, are used. They are as fol- lows : 1 Libra = 1.014 Ib. av. 1 Arroba (25 Libras) - 25.36 " 1 Quintal (100 Libras) = 101.44 " 1 Vara - .914 yd. SWITZERLAND. Metric system used with some changes of names and subdivisions. Pure metric system optional. TURKEY, (METRIC SYSTEM.) URUGUAY, (AS ARGENTINE CONFED- ERATION.) VENEZUELA, (METRIC SYSTEM.) REVIEW EXAMPLES. 26O. 1. How many days from Mar. 1C to Oct. 4 ? From June 30 to Dec. 25 ? 2. Find the time by compound subtraction from Aug. 23, 1882, to Jan. 15, 1884. 3. How many leap years from 1881 to 1897 ? From 1795 to 1845 ? From 1889 to 1909 ? 4. Reduce 2.375 years to years, months, and days. 5. Suppose a person's income to be $1000 per day, how much is that per minute ? 6. How many chains in one mile ? 7. In 4376 feet how many chains ? How many inches ? 8. In 396 rods, how many chains ? How many feet ? 9. In 37.56 chains, how many feet ? How many rods ? 10. Children's size 1 of shoemakers' measure is 4 inches long ; what is the length of boys' size 8, youths' size 1, and men's size 10 ? (Size 1 of the second series is one size longer than size 13 of the first series. See Art. 157.) 11. How many square feet in a rectangular lot, whose breadth is 25f feet and whose length is 116 \ feet ? 12. How many square feet in a lot 25 feet front and 100 feet deep? IS. How many acres in a rectangular field, 28.50 chains by 46.38 chains ? 14* How many acres in a rectangular piece of land, 224 links by 448 links ? 15. How many acres in a square lot whose side is 31 6 links ? 208. 71 feet? 16. How many square yards in a floor, 16ft. 6 in. by 12ft. REVIEW EXAMPLES. 91 17. How much will it cost to carpet a floor 16ft. by 18/i!f., with carpeting f yd. wide, at $1. 60 per yard ? 18. What is the value of a field 320 rd. long and 160 rd. wide at $22.50 an acre? 19. A rectangular lot contains 24 acres ; what is its width, its length being 1056 feet ? 20. How much will it cost to dig a cellar 36 ft. long, 30 ft. wide, and 6 ft. deep, at 30 cents per cubic yard ? 21. If a pile of bark is 40 ft. long and 4 ft. wide, how high must it be to contain 10 cords ? 22. How many feet, board measure, in 16 boards each IS ft. long, 10 in. wide, and 1 in. thick ? 23. How many feet, board measure, in 12 planks, each 10 ft. long, 12 in. wide, and 2 in. thick ? . How many board feet in 225 cubic feet ? 25. What is a pile of wood, 19/2. long, ll//. 5 iw. high, and 8/tf. 7m. broad, worth, at $5.62 per cord? 26. Paid $222.75 for boards at $13.50 per M.; how many feet were purchased ? 27. What is the value of 27315 ft. of lumber at $12 per M. ? 28. How many pills, each containing 5 grains, can be made from 1 Ib. av. of quinine ? 29. In 70 oz. Tr., how many oz. av.? 30. In 70 II. Tr., how many Ib. av. ? 5^. What is the cost of 11 T. 12 cwt. of "Nut" coal at $6.95 per ton, and 9 T. 16 cwt. of "Chestnut" coal at $6.25 per ton? 32. What is the freight of 16 T. 17 cwt. 25 Ib. at $5 per ton (2240 Ib.) ? 33. What is the cost of 15669 pounds meal at $1.10 per cwt.? 34. What cost 16450 pounds of hay at $15.50 per ton? 35. In 27318 pounds of corn, how many bushels ? What is the value of the same at 48|- cents per bushel ? 36. What is the value of 27318 pounds of corn, at 87.1 cents per cental ? NOTE. Examples 35 and 36 illustrate the present and the cental systems of buying and selling produce, and show the calculations saved by using the latter. 37. In 7346 pounds of oats, how many bushels ? 38. What is the cost of 273-Jj- bu. oats, at 58 c. per bushel ? 39. What is the value of 281 Ib. peas at $1.05 per bushel ? 92 DENOMINATE NUMBERS. 40. What is the value of 291 Ib. of peas at $1.75 per cental ? 41. What is the value of 186 Ib. of beans at $2.25 per bushel ? 42. Wk'.t is the cost of 192 Ib. of beans at $3.75 per cental ? 43. At what price per bushel is rye at $1.227 per cental? Oats at $1.66 per cental? Barley at $2.126 per cental ? Malt at $2.75 percental ? 44- How many bushels in 27316 pounds of wheat? In 24375 pounds of corn ? In 16218 pounds of oats ? In 21412 pounds of barley? In 17387 pounds of malt? 45. How many bushels in 54 centals of wheat ? In 87 centals of corn ? In 46 centals of oats ? In 53 centals of barley ? In 67 centals of malt ? 46. How much per cental, is wheat at $1.85J per bushel? Corn at 76J- cents per bushel ? Oats at 48} cents per bushel ? Bar- ley at 87 cents per bushel ? 47. How much per bushel is wheat at $1.27 per cental ? Corn at $1.323 percental? 48. How much per cental is timothy seed at $1.75 per bushel ? Clover seed at $8. 55 per bushel ? 49. What is the cost of 561 23 bushels oats at 43 cents per bushel ? Of 41 1 14 bushels corn at 46 cents per bushel ? 50. A quartermaster purchased 75000 pounds of corn, at 31} cents per bushel ; 32113 pounds of oats, at 32^ cents per bushel ; and 79500 pounds of hay, at $22.37 per ton (2000 pounds). What was the total cost of the purchase ? 51. A farmer sold 18360 pounds of corn, art 64 cents per cen- tal ; 22450 pounds of oats, at 94 cents per cental ; and 36650 pounds of hay, at $1.31 per cental. How much was realized from the sale ? 52. How many sheets of paper in 5 reams ? 53. When 1 gold dollar was worth $2.85 in currency, what was the value of the legal tender dollar in gold ? 54. How many grains of gold and alloy respectively are re- quired for the coinage of 6983 gold dollars ? 55. How many Troy ounces of pure silver would be required in the coinage of 2,000,000 standard silver dollars ? How much copper ? 56. What is the avoirdupois weight of 100000 double-eagles, 25000 eagles, 1000 half-eagles, 4000 quarter-eagles, and 1983 gold dollars ? REVIEW EXAMPLES. 93 57. What is the value of an oz. Tr. of standard gold, making no allowance for the alloy and coinage ? Of an oz. av. ? 58. What is the value of an oz. Tr. of pure gold, making no allowance for the alloy and coinage ? Of an oz. av. ? 59. Feb. 26, 1879, the Nevada Bank of San Francisco sold 100,000 ounces of pure silver to the United States, at $1.08 per ounce. At this rate, what is the intrinsic gold value of the stand- ard silver dollar ? 60. The coinage at the mints of the United States during the fiscal year ending June 30, 1879, was as follows : GOLD Double-eagles, $57,234,340; eagles, $1,03.1,440; half- eagles, $1,442,130; three - dollars, $109,182; quarter-eagles, $1,166,800; dollars, $3,020 ; total gold, $ . SILVER Dollars, $27,227,050; Half-dollars, $225; quarter- dollars, $112.50 ; dimes, $45; total silver, $ . MINOR COINAGE 5-cents, $1,175; 3-cents, $984; cents, $95,639 ; total minor coinage, $ . How many pieces were coined and what was the total value of the coinage ? 61. Add 27 16s. 10c?., 6 10s. 8d., 47 15s. lid., 25 7s. U., 3 14s. 8^., and 23 16s. 3d. 62. In 47 guineas, how many shillings and pounds ? 68. What is the value of 45000 tons of steel rails at 97s. 6d. per ton ? What is the value per ton in U. S. money ? Of total in U. S. money ? 64. How many yards of cloth at 3s. 6d. per yard can be bought for 7 ? 65. Beduce 19 16s. 3d. to the decimal of a pound. 66. If 1 sterling is worth $4.87, what is the value of 225 18s. Qd. ? 67. From 16 12s. 9d. deduct .05 of itself. 68. What is the value of 20 yd. silk at 10s. Qd. per yard ? 69. If 1 franc is worth $.193, what is the value of $1 in francs ? 70. What is the value in U. S. money of 875 Napoleons? (1 Napoleon = 20 francs.) 71. What is the cost of 50 meters silk at 8.25 francs (8 francs 25 centimes) per meter ? 72. What is the value in U. S. money of 24000 marks? 73. What is the value in U. S. money of 5,528,364 Brazilian reis ? Of 7387 Portuguese mi^-eis ? 94 DENOMINATE NUMBERS. 74. In 8375 pies (money of India), how many annas and rupees ? 75. What is the value in dollars of 500 Eussian poods of rye at 75 copecks per pood ? 76. The gold yen of Japan contains 1 grams of fine gold and weighs If grams. What is its fineness, and what is its intrinsic value compared with the U. S. gold dollar ? How many yens can be coined from 10 grams of Japanese standard gold ? 77. The difference in the local time of two places is 3hr. 43 min. 12 sec. ; what is the difference in longitude ? 78. When it is 4 hr. 40 min. A.M. at Chicago, what is the time at Calcutta? 79. How many bushels will a box 10 ft. long, 5 ft. wide, and 4 ft. high contain ? NOTE. Since a bushel is about l cubic feet, the following approximate rules may be used for all practical purposes : To reduce cubic feet to bushels : Deduct one-fifth. The result will be too small by about 4 bushels for every 1000 bushels of the result. To reduce bushels to cubic feet : Add one-fourth. The result will be too great by about 4 cubic feet for every 1000 cubic feet of the result. Solve the above example, both exactly and approximately, and compare the results. 80. How many hectoliters of grain will a box 4 meters long, 3.2 meters wide, and 2.5 meters high contain ? 81. How many gallons of water will a cistern hold which is Sft. long, 7 ft. wide, and 10 ft. deep? 82. What is the capacity in liters of a cistern 25 meters long, 2.2 meters wide, and 3 meters deep ? 88. In 52 meters cassimere, how many yards ? 84. The specific duty on Brussels carpet is 44 cents per square yard ; what is the duty per square meter ? 85. In a pane of glass 24 in. by 30 in., how many square deci- meters ? 86. The duty on pig-iron is $7 per ton (2240 Ib.) ; what is the duty per metric ton or millier ? 87. The U. S. custom duty on alcohol is $2 per gallon ; what is the duty per liter ? 88. The duty on tallow candles is 2 cents per pound; what is the duty per kilogram ? PERCENTAGE. 261. Percentage is a term applied to all operations in which 100 is used as the basis of computation. It is also the name given to any number of hundred ths of a number. 262. Per Cent. (%} is an abbreviation of the Latin per centum, meaning on or by the hundred. Thus, 5% means 5 of every hundred, or 5 hundredths ( T f P , or .05). 263. Any per cent, may be expressed in the form of a decimal or fraction. Thus 5 per cent. = 5% = 5 hundredths = .05 T f ^ = ^. The first two forms are used in the statements of questions ; the others in the operations. 264. In percentage, three elements are considered, viz : the Base, the Rate, and the Percentage. Any two being given, the other can be found. 265. The Percentage is the result obtained by taking a certain number of hundredths of a number. 266. The Base is the number of which a certain number of hundredths are taken. 267. The Rate is the number of hundredths, or the num- ber per cent. Thus, in the statement, Q% of 300 is 18, the Percentage is 18, the Base 300, and 6 per cent. (.06) is the Rate. 268. Applications of Percentage. The principles of per- centage are applied to many of the most common business trans- actions. Among the most important of these are Trade Discounts, Commission, Insurance, Profit and Loss, Duties, Interest, and Exchange. 96 PERCENTAGE. 269. Ex. What is 5 per cent, of 300 ? OPERATION. ANALYSIS. 5% is equivalent to 5 hundred ths (^, or 300 Base. .05). 5 hundredths of a number may be found by mul- .05 Rate. ti plying it by 5 hundredths. For convenience, the raul- " tiplication is performed by expressing the 5 hundredths in the form of a decimal. .05 x 300 = 15, the percentage required. Therefore, the Percentage is the product of two factors, the Base and the Rate. Or, \% of 300 is 3, and 5^ is 5 times 3, or 15. Ex. 15 is 5 per cent, of what number ? OPERATION. ANALYSIS. In this example there is given the Per- Rate. Percentage. cen t a ge and Rate, to find the Base. Since the Percentage^ .05 ) 15.00 tbe Base x tlie Rate? tlie Bage _ t i ie Percentage -r- the Base. 300. Rate. Or, if 15 is 5% of a certain number, 1 % is \ of 15, or 3 ; and the number, or 100% , is 100 times 3, or 300. Ex. 15 is what per cent, of 300 ? OPERATION. ANALYSIS. The Base and Percentage are given, Base. Percentage. Rate. to find the Rate gince the p erc entage = the Base 300 ) 15.00 ( .05 x t ] ie Rate, the Rate = the Percentage -=- the Base 15 -5- 300 = .05 (5fo\ the required per cent. Or, 15 is aVv or ^ of 300. ^ = T f ^ or 5# . Ex. What is 4^ of 247 13s. Qd. ? ANALYSIS. Multiply the number of each denom- ination by .04, as in the margin, and then reduce the /c47 lo decimal parts to integers of lower denominations .04 (201). 91 88 52 24 ^ r ' re( ^ uce shillings and pence to the decimal of a pound (see note, Ex. 7, Art. 204), take the re- quired per cent., and reduce the decimal result to S. 18J.12 lower denominations. Thus, 12 247 13*. Qd. = 247.675 d T~68 247.675 x .04 = 9.907 = 9 18s. 1.68& 270. These principles may be expressed by the following formulae : P = B x R\ B = P -r- R; R = P -f- B. 271. EULES. 1. To find the percentage, multiply the base by the rate expressed decimally. PERCENTAGE. 97 2. To find the base, divide the percentage by the rate expressed decimally. 3. To fi1^d the rate, divide the percentage by the base. NOTE. In finding the rate, to produce a quotient of hundredths, make the decimal places of the dividend exceed those of the divisor by 2. 272. When the rate is an aliquot part of 100, it is generally more convenient to use the equivalent fraction. Thus, 50% = .50 = f 16|% = ,16f = f 6J% = .06J = T V 33#= .33^ = i 12i% = .121 = i- ^ = .05 = fr. 25% = .25 = \. 10% = .10 = ^ 3% = .034 = A- 20% - -20 = f 8J% EXAM PLES. 273. What is Find 7. J of 1728 ? 6. 16% of $375. 2. -fa of 2456 ? 7. 8% of $24.25. 5. .25 of 5280 ? & 2% (i of 10 %) of 876. 4. 25% of 8424? 9. 7 \% (10% J of 10%) of $1678. 5. \% of 1000 ? 10. l%(\%- ^%) of $21275. 11. What is the difference between 2J% of $16000 and 5% of $8475 ? ./#. A merchant bought goods amounting to $375.60, and sold them so as to gain 30% of the cost ; how much did he gain ? 13. A lawyer collected $2875, and charged 5% for his services ; how much did he retain for his services, and how much did he pay over ? lit. What is the duty on twelve watches valued at $75 each, at 25% of the value? 15. Jan. 10, a merchant buys a bill of goods amounting to $876.40 on the following terms : 4 months, or less 5% if paid in 10 days. How much would settle the bill Jan. 18 ? 16. The product of two factors is 75 ; if one of the factors is .03, what is the other factor ? 17. The percentage is 60, and the rate 2J% ; what is the base ? 18. $18.08 are 5% of what ? 22. 165/2. are 33% of what? 19. $324 are 3% of what? 23. 240 are 3% of what ? 20. $37.56 are 2J-% of what ? 24. $12.25 are 6% of what ? 21. $17.28 are 24% of what ? 25. 96 francs are % of what? 7 98 PERCENTAGE. 26. An agent sells a house and lot for $16450, and receives 5$ for his services ; what does he pay to the owner of the property ? ; 27. Mr. A invests 42$ of his capital in real estate, and has $53070 left ; what is his capital? 28. If a man fails to pay his tax until he is charged 8$ addi- tional, how much will he lose if his tax is $36.75? 29. If the rate is 20$ and the percentage 440, what is the base? 80. A has 35$ of his property invested in stocks, 10$ in horses and cattle, 18$ in grain, and the remainder, which is $24235, in real estate. What is the total value of his property ? 31. A merchant, failing in business, pays 43$ of his indebted- ness ; he owes A $3750, and B $6280 ; how much does he pay each? 82. The product of two numbers is 375 ; if one of the numbers is 30000, what is the other number ? Express answer in hun- dredths. 83. The assets of a bankrupt are $27387, and his liabilities $82161 ; what % of his indebtedness can he pay? What per cent, of 84. 375 is 75 ? 38. $1000 is $12.50 ? 35. $1728 is $144? 39. $3720 is $232.50 ? 86. $3456 is $72 ? 40. $2416 is $60.40? 87. 5280 ft. is 165 ft. ? 41. $1484 is $21.20 ? i 42. A merchant paid for goods $345 and sold them for $258.75 ; the loss is what % of the cost ? 48. If a paymaster receives $150000 from the treasury, and fails to account for $225 thereof, what is the percentage of loss to the government ? 44- Total imports and exports carried in foreign vessels during the fiscal year 1858, were valued at $160,666,267 ; in American vessels for the same time, $447,191,304. What per cent, were carried in American vessels ? In foreign vessels ? J 4-5- $640 being increased by a certain % of itself equals $720 ; required the rate %. 46. A commission merchant sold 450 barrels of flour at $5.30 per barrel ; how much should he send to the miller, if he charges 2 per cent, for making the sale ? PERCENTAGE. 99 47. A horse was sold for $658, which was 16f$ more than it cost ; what was the cost ? NOTE. The cost of the horse was f$, or 100% of itself ; since the gain was \\% of the cost, the selling price (the cost plus the gain) was 116f $ of the cost. $658 is 116f ^ of what number? What number increased by "What number decreased by 48. 25% of itself is 500 ? 51. 5% of itself is $307.80 ? 49. 8% of itself is $1004.40 ? 62. 40$ of itself is 3726 ? 60. 125% of itself is 999 ? 68. 25% of itself is $342.60 ? 54- When the premium on gold was 17f$, what amount of gold was it necessary to sell to pay a note of $3000 in currency ? 55. What is 116$ of 1200 ? 56. 144 is 120$ of what number ? 51. 375 is what $ of 300? 68. Find 95$ of $1260. 69. Of what number is 275, 100$ ? 60. $187.50 are 2J$ of what ? 61. Total imports and exports carried in foreign vessels for the fiscal year, 1879, were valued at $911,269,232; in American ves- sels for the same time, $272,015,697. What per cent, were carried in American vessels ? 62. The total tonnage entered at ports of the United States during the year ended June 30, 1879, was 13,768,137 tons. What per cent, was entered at the port of New York ? (See Ex. 64.) 63. The tonnage entered at the four ports of New York, Baltimore, Philadelphia, and Boston, for the year ended June 30, 1879, was 10,489,660 tons. This amount constituted what per cent, of the total tonnage entered at ports of the United States ? (See Ex. 62.) 64. The total tonnage entered at New York during the year ended June 30, 1878, was 5,545,026 tons ; during the year ended June 30, 1879, 6,661,825 tons. What was the increase per cent. ? 65. The earnings of the Chesapeake and Ohio B.R. Co. for the month of July, 1878, were $14,026,189 ; for the month of July, 1879, $17,338,273. What was the per cent, of increase ? 66. Find 5% of 375. 69. Find 10$ of 37 8s. 9tZ. 67. Find 2$ of 64 16s. 70. 16s. is 2$ of what ? 68. Find 4^ of 75 12s. Qd. 71. 1 8s. 4rf. is 4$ of what ? 100 PERCENTAGE. DISCOUNTS. 274. It is customary in many branches of business for manu- facturers and dealers to have fixed price-lists of certain kinds of merchandise ; and when the value changes, instead of changing a long price-list, the rate of discount is changed. The fixed price is called the List-Price, and the discount allowed the Trade Discount. Books are usually sold by publishers and jobbers at certain discounts from the retail prices. 275. Many kinds of merchandise are sold at "time" prices, subject to certain rates of discount if paid at an earlier period. 1. Thus, the following or similar announcements are usually found upon the bill-heads of wholesale dealers : u Terms, 4 months, or 30 days, less 5$" ; or, " Terms 60 days, or 1$ discount in 30 days, or 2$ discount in 10 days." 2. In the same business house, certain goods are sold on long credit, and others on short credit. 3. When no rate of discount has been offered, merchants are generally willing, when bills are paid before maturity, to deduct the interest on the amount of the bill for the remainder of the time at the legal rate per annum. Ex. The list-price of a scale is $80 ; what is the net price if a discount of 25% and 10% is allowed? OPERATION. $80 List-price. ANALYSIS. The first rate of discount is reckoned 20 25$ , or 4. upon, and deducted from the list-price, and the others are deducted from the successive remainders. The result is not affected by the order in which the _6 10$, or ^ discounts are taken. A discount of 25$ and 10$ is the 54 Net-price same as a discount of 10$ and 25$. EXAMPLES. 276. 1. The gross amount of a bill of shoes is $82.68. What is the net amount, the rate of discount being 5% ? 2. A stove is sold for $45 less 30% ; required the net price ? NOTE. If the discount is not required, multiply by .70 (100$ 30$); the product will be the net price. 3. What is the value of 466 Ib. 0. W. casing @ 45 cts. per pound, less 1-J per cent. ? DISCOUNTS. 101 4. The gross amount of a bill of mdse. is $106.36; what is the net amount, the rates of discount being 20 % and 10 $ ? 5. The gross amount of a bill of notions is $49.75 ; what is the net amount, the rates of discount being 10 $ and 10 $ ? 6. What is the value of 12 pair shoes @ $1.60 per pair, less 5 $ ? 7. What direct discount is equivalent to a discount of 15 % and 10$ ? 45$ and 10$ ? 20$ and 12$ ? 60$ and 10$ ? 75$ and 12^$ ? 8. What is the net value of one case prints containing 2273 yd., @- 4 s cts., less 5$, cooperage 25 cts. ? 9. A bill of merchandise amounting to $442.38 was bought Aug. 18, 1879, on the following time : " 4 months or 5$ off 30 days." How much would settle the bill Sept. 16, 1879 ? 10. What is the net value of a bill of iron amounting to $1103.75, at a discount of 45, 10, and 2 per cent.? 11. What is the net value of 1 case prints containing 3039 2 ?/(7. @ 5 cts. per yd., less a discount of 3$ ; cooperage $.25 ? 12. The net amount of a bill of files was $36. 75 ; what was the gross amount, the rate of discount being 10$ ? 18. Mr. A. is offered dress goods at 26 cts. per yd., " 4 months, or less 6$ cash "; how many yards can he purchase for $49.82 ? 14. The net amount of a bill of hardware is $175.26 ; what is the gross amount, the rate of discount being 45$ and 10$ ? 15. What is the difference on a bill of $875 between a discount of 40$ and a discount of 30$ and 10$ ? 16. A bill of tinware is sold at the following discounts : $74.20 at 20$ and 10$; $43.75 at 40$ and 5$ ; $69 at %?>\% and 10$ ; and $49.17 net. What is the total net amount of the bill ? 17. A bill of dry goods amounting to $914.37 is sold, Aug. 19, on the following terms : " 60 days, or less 1$ if paid in 30 days, or less 2$ if paid in 10 days." How much would settle the bill Sept. 18 ? How much Aug. 27 ? 18. Of a bill of hardware, $61.51 are sold at a discount of 60 and 5$; $18.75 at a discount of 10$; $16.86 at a discount of 124$; $44.25 at a discount of 40 and 5$ ; $29.60 at a discount of 40, 12J, and 10$ ; $28.04 at a discount of 55^ ; $16 at a dis- count of 65, 10, and 10$ ; $18.70 at a discount of 50$ ; $19.75 at a discount of 20$; $18.50 at a discount of 15$ ; $307.55 at a discount of 75 and 12|$; $36.61 at a discount of 60 and 10$ ; and $218.25 net. What is the total net amount of the bill ? 102 PERC ENTA GE. BILLS.* A Bill is a detailed statement of merchandise sold, or of services rendered. Bills of merchandise state the place and date of the sale, the names of the buyer and seller, the terms of the sale, the quantity, price, and distinguishing marks and num- bers of the merchandise, and other details. The terms Bill and Invoice are used by many interchangeably. The term Invoice is applied more particularly to statements rendered by consignees to commission merchants, showing marks, numbers, values, and accrued charges of goods shipped; to bills rendered to jobbers ; and to bills received from for- eign countries. EXAMPLES. 278. Copy and extend the following bills : (1. Canned Goods.) Folio 316. WILMINGTON, DEL., Nov. 16, 1876. Messrs. WM. DOLTON & Co., Bought of JAMES MORROW & SON. Cases. Doz. 3 Ib. Peaches - - - - - 2 " Saco Corn - - - - 2 1 " Salmon - - 3 " Tomatoes, B. & L. - - 2| " Col. Pears - - - - 2 1 " Apricots Ctge. 225. 185 385 1*0 4aa 4 Q.O 00 50 (2. Flour.) BUFFALO, N. Y., Dec. 6, 1880. Messrs. DANIEL GROUSE & SONS, Bought of SCHOELLKOPP & MATTHEWS. Interest charged on all accounts after 30 days. We allow no Expressage or Exchange. 20 25 Bbls. Flour " Sunlight " Sacks - $7.05 Bbls. - 7.25 *** *** ** ** 25 " " Victor " Sacks - - 6.05 *** ** 25 Bbls. - - 625 *** ** 15 " " Dakota " Sacks - - 5.30 #* 5s"S 5 " "Superlative" Sacks 8.55 #* X-Jfr 20 bags 70 " 9177 Ih ^ Mpal 120 ** *** ** *** ** 264 9 2- bu Oats .56 * For explanation of marks, numbers, abbreviations, etc., used in the bills of this chapter, see page 312. BILLS. 103 BARK ENTERPRISE, Terms Cash. (3. Storage, etc.) BROOKLYN, N. Y., Jan. 30, 1879. To J. P. & G. C. ROBINSON, Dr. Storage 16319 23 bu. @ %? 122 39 Elevating - - - - 163 19 23 @ w ** ** Delivering - - - - 16319 23 @ yj' *# X-* Weighing - - - - Carting - - - - - 16319 23 16319 23 @ %? @ i? ** **# ** Loading ship - - - Separating damage - 16301 34 16301 34 per M. $7^ @ y^ *** ^ Blowing on delivery - 16301 34 @ #f ** ** Weighing on " 16301 34 @ y^ ** ** *** ** (4. Provisions.) CLEVELAND, 0., Oct. 9, 1876. Messrs. L. C. MAGAW & SON, Bought of J. P. HOBISON & Co. Terms Cash. No goods sold on 30 days. 10 "Rhlsi S M Pork 17 #** " MPS<^ Bppf 10 75 ** " Hams 90 a 1376 b ^98 c **** d 14? " Shoulders 58 744 -57 *** 9? " Dr. Beef 33 241 -22 *** 14? Tc. Lard 406 -60 *** 11? *** ** ** *** a Number of pieces. b Gross weight. c Tare, or weight of barrel or tierce. d Net weight. (5. Fish.) GLOUCESTER, MASS., Sept. 28, 1876. Messrs. DANIEL WEIDMAN & Co., Bought of CLARK & SOMES. Subject to sight draft without notice after thirty days. Of! NPW GPO Cod ^ 7*1 ** ** 1 Bbl Ex 8 1 Mackerel 20 00 ** ** 10 10 2 10 5 3 Kits 15 Ibs. Ex. *1 Mackerel - - - 1.80 " 201bs. Bay 81 " - - - 1.80 Bbls. jf 2 Shore " Ig. - - 12.00 Kits 20 Ibs. 82 Shore " " - - 1.50 Halfs New Labrador Herring - - - 3.82 " Round Shore " - - - 2.95 Box >38 , ctg. in Boston - 90 ** ** ** ** ** * # ** *# ** ** ** ** ** $*** *# 104 PER CENT A GE. (6. Groceries.) Order Book, 410-22. Day Book, 115-797. Messrs. EDWARDS & Co., Terms Cash 30 days. Shipped per National Line. NEW YORK, Feb. 1, 1880. of H. K. & F. B. THURBER & Co. When you desire to order goods, same as had before, give date of purchase, and the Order and Day Book pages. M C P #4385 1 3 3 4 1 2 25 10 1 1 Cask Old Prunes 1544 - 134 = **** Ibs. - 4f 165 glO 15 .39 .65 .16 l"o .25 .25 ** * * * * * * 4Ht * -X- 1 #** #-x ** *# ** ** ** 15 " " Layer Cream Tartar, \ foil - Yeast-Cakes, 3 doz. ea., Ibs. Whole Pepper .... - 20 Ibs. - - 6 doz. Box 0. K. Mustard, }'s - - i's - - Cartage Bag - - 12 Ibs. - - 12 " - on all - - (7. Groceries.) Messrs. HORTON, CRARY & Co., NEW YORK, Aug. 13, 1876. Bought of AUSTIN, NICHOLS & Co. W. B. 1 Bag -20 Rio Coffee 132 23 30 56 A Jf99 1 " * 80 " ...... 131 2l ** ** 1 Bbl/25 R oa . Java Coffee *|} - 100 25| ** ** 2 " -50 .. Rio 112-22221* & 04' Ml ** H. R. P. 1 10920 42 " Case Cone. Lye ($. - - 5 50 Union. 2 Boxes Yeast Cakes, ea. 3 - - V 65 * A. N. & Co. 25 5 1 Ibs. Spice, Bag 20^ - - jk * - 15. V Mats Cassia vL*HL" . 21| 26' Keo- Gr Mustard - 50 35 * * #* ** ** 10 lbs White Glue .... .,-,;- - - 40 # 257-20 *;J* A. N. & Co. 5 Bbls. X. C. Sugar - - StS -^ SI-io v 4? n| ** ** $134 1 " W. D. Syrup ... . 4 ^ *** 60 ** ** $114 1 " C. D. " .... 4 ^ *** 50 ** ** Ctg. 2 - - - 1 50 Syrup, 60 days - - **.** $*** ** Balance, 30 " - - ***** SMMHI BILL Si 105 (8. Dry Goods.) NEW YORK, March 20, 1879. Messrs. FIELD, LETTER & Co., Bought of H. B. CLAFLIN & Co. Terms Cash in 30 days less 5, or 4 months' note delivered within 30 days, and payable at Bank in New York exchange. 2875 8039 3369 1290 1590 2179 2507 6515 2985 1650 Bale Boott M. Brown " Continental C. do. " Pequot A. 36 in. " Great Falls E. ----- - " Atlantic H. - - - 1038 - .07 3 Less 4$ - " Boott F. F. " Pepperell 600 Drill - - - Case Blackstone A. A. .... " Dwight Anchor " Great Falls Q. .... " Pearl River Ticking - - - Cooperage 800 800 967 1111 $** 800 622 1649 1139 1492 708 07 1 07 3 07 1 09 08 15 2 54 VV7T 75 Messrs. DAVIDGE, LANDFIELD & Co., (9. Dry G-oods.) NEW YORK, March 23, 1878. Bought of TEFFT, GRISWOLD & Co. 2 Naumkeag Bl. Jean - Jy - - - 95 09 8 55 4 Roll Cambric - - - (SvS ' " ###* 05 2 * ** ,47 s 3 Pprmprpll T)rill ' 3ft 3 **** 08 * ** 1 T nwAll 1 / "RTnvvn 38 14 2 * ** . 1 p 1 40 *** 07' 2 * on men a ^ V I 5 i45 s /45 New Market N. - - - /45JW 1 *#* 06' ** 2 Champion Cheviot - - ( ^i - - MH 09 * ... 2 Otis B. B. Dk Stripe - - { g - - - MM 10 ** ** 1 Hamilton 30 in. Tick 48 3 II 3 * ** 2 Thnrni^ilrp C 1 ###* 08- ** ** 2 Wamsutta C. Blea. - - gfl - - - **#* 12 M ** 8 AndrosL. - - - /g. g. g gl - #** 07 3 ** ** 1 T-J flrtl 1 1 / 36 3 22 * ** Pir /4 *** ** Cooperage - 1 25 #** ** 106 PER CENT A GE. (10. Dry Goods.) Book 174, Page 148. NEW YORK, March 30, 1878. Mr. JAMES MORGAN, Milwaukee, Wis. Bought of H. B. CLAFLIN & Co. Terms : Net 6O Days, or \% discount in 30 days, or 2# ) discount in 10 days, N. Y. Funds. No Exchange allowed, f $4641 53 PC'S Gordon Prints (Job) 21 2 48 2 38 40 1 48 2 48 3 37 2 48 48 44 49 2 44 3 48 2 49* 49 3 49 2 42 56 48 2 49 1 28 2 49 1 49 48 3 49 1 28 48 s 37 33 2 49 2 52 33 3 40 48 49 1 49 1 24 48 2 48 2 52 48 3 49 47 2 48 1 48 2 49 l 49 2 48 3 48 2 48 2 43 2 49 1 49 2 - ***** *2601 54 PC'S Do. 433 48 49 42 22 1 49 1 49 48 2 53 2 48 2 47 3 48 3 48 2 49 44 49 49 2 48 2 49 2 49 49 48* 47 3 47 48 2 49 1 56 50 2 49 1 41 1 48 1 50 27 1 49 48 2 48 3 21 3 29 1 51 3 46 3 48 2 48 2 28 2 48 2 49 1 49 2 45 2 47 48 2 40 2 50 1 39 2 48 2 46 1 ***** 4765 61 PC'S Do. 30 2 49 2 42 49 2 32 48 46 48 2 46 2 42 3 47' 22 1 33 46 48 49 2 48 2 48 42 42 48 28 48 1 49 2 48 2 49 49 49 2 48 2 28 2 49 2 43 49 1 48 2 49 2 48 38 2 29 25 26 3 49 1 49 3 49 1 49 48 2 34 3 48 3 45 49 49 1 49 a 48 1 36 48 29 2 49 3 48 2 31 1 48 2 49 48 1 - - ***** ***** .04 2 *** ** Cooperage - 1 00 *** ** Messrs. JORDAN, MARSH & Co. (11. Dry Goods.) NEW YORK, March 20, 1878. Bought of A. T. STEWART & Co. Job. 8 Cases Gordon Fancy J. U. $4561 2810 S. B. R. 4157 2902 1 H. Z. 3473 2787* S. J. L. 4224 2880* G.Q. 2777 2821 l J. B. 3504 2842 2 J. Z. 3970 2883 1 J. H. 4198 2863 1 - - ****** .05 **** ** Less 5fe - ** ** **** ** BILLS. 10? (12. Hosiery.) NEW YORK, June 28, 1886. Messrs. JOHN FORD, SONS & Co., Claims for Damages or Errors must be made on receipt of Goods. Net SO Days. Note to your own order Payable at a Bank in New York City. Bought of JAMES TALCOTT. 1789 35 Doz. 3458 Mixed % Hose - - .80 28 25 " 2032 Fancy " " - - - .80 ## 12 853 Col'd " - - - 1.00 ** 12 " 1691 Fancy " - - - 1.00 ** 18 " 1759 " . . . .75 ** ## 20 1713 " ... 1.00 ## 16 " 1716 " - . . 1.10 *# ** 6 " 3438 Fchmx^ " - - - .90 & ** 22 " Job Misses " - - - .75 Ml ** $*** *# Shipped per P.R.R.&C.B. & Q.R.R. Mr. JOHN BERWOLD, Terms Cash. (13. Books.) CHICAGO, ILL., May 7, 1878. Bought of HADLEY BROS. 12 18 24 36 18 12 6 6 6 Randall's Arithmetics, Part 1 - .60 " 2 - .50 Smith's Primers (paper) - - - .06 Spellers .22 " 2d Readers .45 3d " .70 " 4th " 1.15 " 5th " .... 1.35 Doz. Brown's Copy Books - 1.80 7 20 #* *-K- * Less 33%^ #* ** ** ** 6 6 6 6 Jones' Geographies ft 1 - - - - .35 " . 2- - - - .63 3 - - - - 1.10 4 - - - - 2.00 2 * * fc* 10 3 3 Less 25 % Boxes Chalk Crayons - - - - .18 Doz. Blank Copy Books - - - .50 * *-x- ** t ** $** ** 108 PER C ENTA G E. Messrs. N. RUTTEE, SON, & Co., Terms 60 days. (14. Hardware.) PHILADELPHIA, PA., Aug. 13, 1880. Bought of BIDDLE HARDWARE Co. 24 Sets W'd Wh'l Bed Casters * 1 2 in. - .18 * ** 60$ - - * # 1 Doz. Russell's S.B. Knives 14 in. S1540 - 11 2.40 2.55 3.15 3.20 200 Carriage Bolts % x 1 2^ 5% 5% Ml ** 4.50 4.70 4.90 5.30 100 " Vie x 534 5% 63^ 734 ** sf* 5.95 6.25 6.50 6.85 100 " H x 5M 5 63^ 6% ** ## 7.15 7.45 100 " " M x 734 7% .... ** ** 7.90 8.05 100 " " % x 8> 8% - - ** ## 6.50 8 00 10.40 100 " Vie x 2^ 4V 7^ - - ** ** 10.80 i.1.20 100 " VieX 8 8^ - - - - ** ** 7.25 7.75 9.25 100 ^ x 2 gjf 4 . . - #- ** 11.25 11.75 13.25 100 " K x 6 6^ 8 - - - #* *# **# ## X C. Machine Bolts % x 8 8.70 * ** ** ** 15.10 16.60 % " % x 6 7 - - - Mt ** 99 Ibs. " "M x 11 .10^ ** ** ** ** 5 Cases Packing and Cartage - 1 ** *# (15. "Watches and Jewelry.) NEW YORK, Mar. 7, 1877. Mr. CHARLES BABCOCK, Bought of WHEELER, PARSONS & HAYES. Terms : Net Cash 4 months, or lesp 5$ 30 days, with Exchange on New York. H658 20422 18 k. Ancre 17 L. full Engrd & Enid S. W. 14 k. Russell 17 L. flat C. B. 18 k. Plain Ring 3% dwts. @ !" - Premium 14 k. Guards with slides ^, ~ @ Pr. Solid Roman SI. Buttons 908 - 90 46 #** 10 Gold BILLS. 109 (16. Tinware.) ROCHESTEB, N. Y., Oct. 16, 1880. Messrs. MCCARTHY & REDFIELD, Bought of JOHN H. HILL. Terms 60 days. If paid in 10 days 2 per cent, discount. 2 Doz. 821 Pieced Dish Pans - - 8.25 ** ** K " 9 in. Wash Boilers - - 36.00 ** 3 " Pieced Bread Pans 3x9x3- 2.00 * 3 "5x9x2- 2.00 * 1 " 85 Pieced Covered Pails - 2 50 3 " 813 Cups - .90 * ** 1 " 815 " Dippers - 1 25 2 " 825 " " ... . . 1.75 * #* 6 Nests 8021 Flaring P'ls & Dippers 1.14 * #* ** ** 20&12^^ - ** ** ** ** 1 Doz. Champion Nutmeg Graters 1 75 1 Case .15 1 " Nests 8 4 Fancy Cov'd Pails 6 00 15 1 " .17 1 " 84 Burnished Tea Pots - r 6 75 17 *# ** 25 & 12%% - * ** * ** 1 " 89 Pudding Pans - - - - 3 50 2 "810 " "-;.'.': 4.25 * ** i^ " 8 200 Pressed Kettles - - 5.50 * ** 1 " 8220 " 7 ** ** 37*^ - * ** ** ** 6 2 qt. En'ld Bel. Sauce Pans - - .63 * ** 3 " " " " " .73 * ** * ** 40% - * ** * ** 6 .75 .90 Enameled Kettles Ea. 45 qt. - * ** 1.10 1.30 12 6 8qt, - ** ** 80* - 11 *-;;- ** 1 Crate 7 8 W. H. Tea Kettles ... .95 45^ - * *# it ** 4 Boxes 2.06, Carting .38 - # * #* ## N.Y.C.&H.R.R.9751bs. Qlty 110 PERCENTAGE. COMMISSION AND BROKERAGE. 279. Commission or Brokerage is an allowance made to an agent for transacting business for another; as, the sale or purchase of property, the collection or investment of money, etc. An additional percentage is usually charged by commission merchants for guaranteeing the payment of sales made on credit. 280. The party who transacts the business is called a Com- mission Merchant, or Broker; and the one for whom he acts is called a Principal. NOTES. 1. Commission Merchants usually have possession of the subject- matter of the negotiation, and make sales and purchases in their own name. 2. Brokers do not have possession of the merchandise bought or sold, and generally make contracts in the names of those who employ them and not in their own. They simply effect bargains and contracts. The name broker is often erroneously applied to dealers in stocks, bonds, etc., who buy and sell on their own account only. 281. A Consignment is a quantity of merchandise sent by one party to another. The party who seijdp it is called the Con- signor ; and the party to whom it is sent, "the Consignee. 282. The Net Proceeds of a consignment is the balance due the consignor after all charges or expenses have been deducted. The whole amount realized from a sale is called the gross proceeds. The commission is usually a certain per csnt. of this amount. 283. An Account Sales is a detailed statement rendered by the Commission Merchant to the Consignor, showing the sales of certain goods, the charges or expenses attending the same, and the difference or net proceeds. The charges embrace freight, cartage, inspection, advertising, storage, insurance, commission and guarantee, etc. 284. An Account Purchase is a detailed statement rendered by the Commission Merchant to his Principal, showing the cost of certain goods, and the charges or expenses attending the pur- chase. 285. Commission or brokerage is usually computed at a cer- tain per cent, of the amount realized or invested, or of the amount COMMISSION AND BROKERAGE. Ill involved in the transaction. In such cases the general principles of percentage are applied. NOTES. 1. In buying and selling stocks, bonds, etc., the par value, and not the actual value, is taken as the base. 2. The commission for buying:*and selling some kinds of merchandise is usually computed at a certain price per unit of weight or measurement ; as, grain per bushel, cotton per bale, etc. **\^ EXAMPLES. 286. 1. A commission merchant sold goods to the amount of $8G4 ; what was his commission at 2J- (J of 10) % ? J 2. A salesman sells goods at a commission of 2^% ; what must be his sales, that he may have a yearly income of $5000 ? / 3. What is the brokerage for selling 850 fcajies of^otton at the rate of $25 per 100 bales ? * ^ i J 4. A lawyer collected a note of $2375; how' much did he pay to the owner of the note, his commission being 5% ? 5. My agent in Chicago purchases for me 600 barrels of flour at $3.75 per barrel ; how much do I owe him, his commission for purchasing being 2% ? 4 <.\ f- 6. An officer collected $17850, and deposited $17493 in the Treasury, retaining the remainder as his commission. What was the rate per cent, of the commission ? 7. Sent to a commission merchant in Toledo $2080.80 to in- vest in flour, his commission being 2% on the amount expended; how many barrels of flour would be purchased at $4.25 per barrel ? 8. A commission merchant sells merchandise amounting to $3325 ; how much is paid \to the consignor of the merchandise, the charges being, for transportation $117.50, for advertising $10, for storage $15, for commission 2-|% ? 9. My agent in Chicago buys for me 1187.76 centals wheat at $2.123 per cental. What is his commission at J per cent.? 10. A commission merchant purchased for me 9-^ bushels of clover seed at $8.55 per bushel. How much should I send to him in settlement, if his commission for purchasing is 1 per cent. ? 11. A broker buys 8375 pounds of leather at 26 cents per pound. What is his brokerage at |% and what is the net amount received by the seller, the brokerage being paid by him ? 12. A freight broker procures transportation for 375 tons of merchandise at $3.50 per ton ; what is his brokerage at 112 PERCENTAGE. IS. A collector deposits $28117, retaining 3% on tlie whole amount collected. What amount did he collect and what v/as his commission ? 14. A lawyer, collecting a note at a commission of 6% thereon, received $6. 25 ; what was the face of the note ? 15. An agent sold 6 mowing-machines at $120 each, and 12 at $140 each. He paid for transportation $72, and, after deducting his commission, remitted $2208 to the manufacturer. What was the % of his commission ? 16. A merchant instructs his agent in Cincinnati to buy pork to the amount of $5000. The charges on the pork being $16, and the agent's commission 1|% how much must be remitted to settle the bill? 17. What are the net proceeds of the sale of 12372 pounds of leather at 22 cents per pound, the charges being $31, and a com- mission of 2-J% being paid for selling and 2% for guaranteeing payment ? 18. A real estate agent, who charged 2J% for making the sale, paid to the owner of a house and lot $42412.50 ; what was the value of the property ? 19. A commission merchant sells 240 bbl of potatoes at $3.75 per bbl., and 260 bbl. at $3.60 per bbl. How much is due the con- signor, the commission being 12 \ cents per barrel ? 20. John Smith is a disbursing agent of the United States. Jan. 1, 1880, there is in his hands $11870.63. Feb. 1, he pays out $3220.34, on which he is entitled to a commission of \\%. Mar. 1, he receives $3750.87. May 1, he pays out $3795.01, on which he is entitled to a commission of 2%. Make a statement of his account, showing balance due the United States. . 21. What are the proceeds in currency of $2611.06 gold, at 1.06-|, commission for selling -fa% ? 22. A, having a claim against the government of $10970, agreed to pay an agent 8 per cent, of the amount collected. But the amount collected was 22 per cent, less than the amount of the claim. How much was received by A ? 23. B sends $2240.70 to his agent in Cleveland requesting him to invest in provisions after deducting his commission for pur- chasing of 3% ; what was the sum invested ? 24. A broker received $62.50 for selling some bonds, charging \% brokerage. What was the par value of the bonds ? COMMISSION AND BROKERAGE. 113 25. A commission merchant sold 300 bales of cotton, averaging 462 Ib. to the bale, at 15.70, his commission being 250 per bale, and the charges $161. He purchased for the consignor dry goods amounting to $2576.37, charging a commission of 1|% How much was still due the consignor ? 26. A of Chicago, sends to B of New Orleans, 8000 bu. of wheat and 500 Ibis, of flour with instructions to sell it and invest the proceeds in sugar. B pays freight and cartage 83420 ; sells the wheat at $1.60 per bushel and the flour at $5.25 per barrel; charges 2% commission on the flour and 10 per bushel on the wheat : how many pounds of sugar are purchased at 8J cents per pound, the commission for purchasing being 3% ? Copy the following accounts, and make the necessary exten^ sion, etc. (27. Account Sales.) NEW YORK, Oct. 19, 1880. Sold for account of A. W. RANDOLPH & Co., By DAVID Dows & Co. 1880. Sept. M Oct. 12 18 30 14 18 100 Bbls. " Sunshine "- - - - 5.75 125 " "Pride of the West" - 6.25 IfiO " "Sunshine"- - - - 6. 75 " " Pride of the West " - 6.50 50 " " - 6.60 #::--* *# ### **# ** ** ## ***-::- ** Sspt. Oct. 10 10 19 19 Charges. Transportation 500 Bbls. @27f- - - Cartage 400 " @ 5^ - - - Storage 400 " @ 3^ - - - *** ** ** ** 19 Commission and Guarantee 5% - - - ##* ** **# ** Net proceeds - - - - - **#* ** (28. Account Purchase.) TOLEDO, O., Mar. 6, 1S77. Purchased by A. L. BACKUS & SONS. For account and risk of L. A. & W. B. SHAW. 9 227 928 Bags " Montauk " .21 Bu. Mammoth Clover Seed - - 9-- " Clover Seed - 8 55 # * 931 " Timothy Seed I 75 * *** ** Charges. OK * ** * Jfrvf Charffe vour ^ *** ** 114 PERCENTAGE. PROFIT AND LOSS. 287. Profit and Loss treats of the gains (profits) and losses which arise in business transactions. ' The profit or loss is always estimated on the cost price, or the amount invested. " Discounts are reckoned on the market or asking price. (See Art. 274.) 288. The difference between the cost of goods and the price at which they are sold is a profit or a loss, profit if the selling price is the greater, loss if the cost is the greater. EXAMPLES. 289. 1. A man purchased a horse for $250, and sold it at a gain of 16$, What was the gain ? (Gain = .1C x cost.) 2. A merchant sold goods that cost $325 at an advance of 12$; what was the selling price ? (Grain = .12 x cost, and selling price = cost + gain ; or, selling price = 1.12 x cost.) 3. Bought a farm for $3600, and sold it at an advance of 25$; what was the gain ? NOTE. If, as in the above example, the rate per cent, is an aliquot part of 100, it is more convenient to use the equivalent fraction (2712). Thus, 25% = .25 = \ ; gain \ of cost. 4. Cloth is bought at $6 per yard, and sold at a loss of 20$. What is the selling price ? (Selling price = f of cost.) 5. Bought a house for $3475 ; at what price must it be sold to gain 36$ ? 6. Purchased flour at $6.25 per barrel ; at what price must it be sold to gain 20$? 7. If I buy hats at $27 per dozen, at what price must they be sold apiece to gain 33-J-$ ? 8. A factory which cost $8775 was sold at a gain of 16%. What was received for it ? 9. If silk costs $1.68 per yard, and is sold at an advance of 12J-$, what is the profit per yard ? 10. A merchant purchased goods to the amount of $8735, and sold them at a loss of 12$ ; what was his loss ? 11. Bought 125 barrels of flour for $600. If sold at an advance of 15$, what was the profit per barrel ? PROFIT AND LOSS. 115 12. A lot of dry goods was sold at an advance of 18$. If the gain was $436.50, what was the cost ? (Gain = .18 x cost; hence, gain -r- .18 cost.) 18. A farm was bought for $7200, and sold at a gain of $900 ; what was the gain per cent. ? (Gain = gain % x cost ; hence, gain % = gain -r- cost.) 14.. A man paid for merchandise 1875, and sold it for $1015 ; what per cent, did he gain ? 15. A man paid for merchandise $1015, and sold it for $875 ; what per cent, did he lose ? 16. Find the rate % of profit on goods bought for $324 and sold for $364.50. 17. A painting was sold for $2343, at a gain of 32% ; what was the cost? [Selling price = 1.32 (100% + 32%) x cost ; hence, cost = selling price ~- 1.32.] 18. Find the cost of goods sold at an advance of 12$, being a profit of $76. 19. How much was paid for a farm sold for $9878, at 12$ below cost ? 20. What is the profit on iron sold for $4520, at an advance of 13% on cost ? 21. What is the selling price of tea which cost 32 cents per pound and is sold at a profit of 37-J-% ? Maine RO/ n Virginia RCL Rcf. Maryland 6% 6% Washington (Ter ) . . . 10% Any Massachusetts 6% Any "West Virginia, 0<& 8 Michigan 7^, \{\'ff. Wisconsin 7& 10<#i Minnesota ' 7 7% 10^ Wyoming (Ter. N ' / 12% Any (*) Not organized. (b) "Pawnbrokers are allowed to charge 5% per month." (c) "On judgments recovered in the courts 7%, but must not be com- pounded in any manner." ( d ) "Most banks pay 6% on time deposits and charge from 1 to 2% per month on loans." ( e ) "Advances payable on demand (call loans), of not less than $5000, on negotiable collaterals, are not subject to the interest laws, but may be made for any compensation agreed upon in writing." INTEREST. 119 299. Interest for Parts of a Year. Although many of the States have rigid laws in regard to the rate per cent, to be charged per annum, few of them specify on what basis interest should be reckoned for a period of time less than a year. The following methods are in common use : 1. Finding the time in months and days (Compound Subtrac- tion, Art. 21O, 1), and regarding the months as twelfths of a year, and the days as thirtieths of a month or 360ths of a year. This method, although implied by the general interest laws * of the State of New York, is not uniform, since it allows the same interest for February with its 2S days as for March with its 31 days. Its results are sometimes greater and sometimes less than those of accurate interest. 2. Finding the exact time in days (21O, 2) and regarding the days as 3 60th s of a year. Since a day is -g-J-g- of a year, this method produces too great a result. It is however used by mer- chants, brokers, and bankers generally, and by many banks f in discounting notes. 5% by this method is equivalent to 6^% accu- rate interest. 3. Accurate Interest. Finding the exact time in days (21O, 2) and regarding the days as 365ths of a year. This method is used by the United States government, and by some merchants and banks ; but, on account of its inconvenience when interest tables are not used, it is not generally adopted. NOTES. 1. By the first method, the time from July 10 to Sept. 10, would be 2 months, and the interest would be T 2 ^ or | of the interest for one year. On $10000 at 6$ for 2 months, the interest would be $100 (-J- of .06 of $10000). 2. By the second method, the interval between the same dates would be 62 days, and the interest would be 5 2 ff of the interest for one year. On $10000 at b% for 3 6 6 3 ff of a year, the interest would be $103.33 (jfo of .06 of $10000). * " For the purpose of calculating interest, a month shall be considered the twelfth part of a year, and as consisting of thirty days ; and interest for any number of days less than a month shall he estimated by the proportion which such number of days shall bear to thirty." (R. 8., page 1165.) t According to the banking laws of the State of New York, banks are authorized in discounting notes to charge interest, in advance for the exact number of days which the note has to run (Ch. XVIII, Title 2, 300). This law appears to conflict with the law quoted above which implies that the time shall be found in months and days. It does not state whether tbe days shall be regarded as 360ths or 365ths of a year. 120 INTEREST. 3. By the third method, the interval between the same dates would be 62 days as in the second method, and the interest would be ^ of the interest for one year. On $10000 at Q% for -/fa of a year, the interest would be $101.92 (gVir of .06 of $10000). 4. The difference between ordinary interest and accurate interest for the same number of days is ^ of the former, or ^ of the latter (317). Thus in the above example, the difference between the results, $1.41 ($103. 33-101.92), is ^ of $103.33, or ^ of $101.92. 5. Unless the words " Accurate Interest " are used, all computations in this book are made on the basis of 360 days to the year. 300. Interest is an application of percentage, the element of time being introduced. Therefore the four elements or parts in interest are the Principal (the Base), the Rate, the Interest (the Percentage), and the Time ; any three of which being given, the other may be found. 301. To find the interest for any number of years and months. Ex. What is the interest and amount of $324, for 2 yr. 3 mo., at S%? OPERATIONS. $324 Principal. Or 8324 .18 IntereBtforlyr. 2592 324 58.32 324. Interest for 2* yr. $382. 32 Principal. Amount for 2 yr. ANALYSIS. At 8%, the interest of $324 for 1 year is .08 of $324 (the Principal), or $25.92. If the interest of $324 for 1 year at 8% is $25.92, for 2 yr. 3 mo. (2 yr.\ it is 2 times $25.92, or $58.32. The amount is $324 plus $58.32, or $382.32. 3O2. RULE. To find the, interest, multiply the principal by the rate per cent, expressed decimally, and that product ~by the number of years, and the months as a fraction of a year. To find the amount, add the principal to the interest. INTEREST. 121 NOTES. 1. When the rate per month is given, apply the same rule, i.e., multiply the principal by the rate per month expressed decimally, and that product by the number of months. 2. Instead of multiplying by the rate and time separately, the process may be shortened by multiplying the principal by the product of the rate and time. In the above example, multiply $324 by .18 (2 x .08). EXAMPLES. 303. Find the interest of 1. $875 for 2 yr. at 1%. 6. $816.40 for 5 yr. 3 mo., at 5$. 2. $642.50 for 3 yr. at %. 7. $1275 for 7 yr. at Gf c > 3. $1010.10 for 6 yr. 6 mo., at 8$. 8. $2789.40 for 3 yr. 2 mo., a 4. $3010.75 for 3 yr. 4 mo., at 1% 9. $456.75 for 4 yr. 8 mo., at 5. $3745. 80 for 4 yr. 1 mo., at 6$. .#?. $10180 for 3 yr. 4 wo. , at NOTE. In the folio wing examples find the time by Compound Subtraction. 11. What is the interest of $6488 from May 3, 1879, to Sept. 3, 1881, at 7^? 12. What is the amount of $396.60 from Aug. 16, 1880, to Dec. 16, 1882, at S%? 13. Find the interest of $864.30 from Jan. 1, 1881, to June 1, 1883, at 4$. 14. Compute the interest of $250.75 from Nov. 20, 1882, to July 20, 1884, at ty%. 15. Loaned on interest, New York, Dec. 16, 1880, $1739.75 (no rate specified); what amount should I receive, June 16, 1881 ? 16. In settling with a merchant Oct. 3, 1882, I gave my note for $254.60, at 7^; what must be paid Aug. 3, 1883 ? 304. To find the ordinary interest (360 days to the year) for any rate and time. 305. 60-day Method at 6%. 6% for 12 months or 1 year, is equivalent to \% for 2 months (60 days), or -J- of one year. \% of any amount is readily ascertained by placing the point two places to the left. Hence the interest of any sum at 6% per annum for 2 months, or 60 days, may be found by placing the point two places to the left. NOTE. It will be found advantageous to use a perpendicular line as a separatrix in solving examples by this method. All necessity for pointing off will then be dispensed with, and confusion prevented. 122 INTEREST. Ex. What is the interest of $1236 for 80 da., at 6% ? OPERATION. $12 $16 36 int. for 60 da. 12 = 48 = " 20 da. " 80 da. ANALYSIS. The interest of $1236 at % for 60 da. is found to be $12.36, by the process already explained. If the interest for 60 da. is $12.36, for 20 da. (\ of 60), it will be i of $12.36, or $412. Hence for 80 da., it will be $12.36 plus $4.12, or $16.48. Ex. What is the interest of $864 for 1 yr. 10 mo. 15 da., $8 "95" Q $97 OPERATION. 64 = int. for 60 da. n 04 = int. for 22 mo. 16 = " " 15 da. 20 = required int. ANALYSIS. The interest of $864 at Q% for 2 mo. is $8.64. For 1 yr. 10 mo. (22 mo.), it will be 11 times $8.64, or $95.04. If the interest for 60 da. is $8.64, for 15 da. ( of 60), it will be of $8.64/ or $2.16. Hence the interest for the given time will be $95.04 plus $2.16, or $97.20. at Ex. What is the interest of $1732.80 for 2 yr. 9 mo. 23 da. OPERATION. $17 32.80 = int. for 2 mo. or 60 da. 8 6640 103 9680 173 280 5 776 866 6)292 554 48 759 $341 313 int. for 20 da. (( (( Q (( " " given time at %. " " " 1%. ANALYSIS. The interest for 2 mo., forming the basis, is $17.328. Mul- tiply this by 16!, to fin(i tlie interest for 33 mo. (2 yr. 9 mo.}. As 23 is not an aliquot part of 60, take 20, which is of 60, and 3, which is ^ of 60. Divide the basis, which is the interest for 60 da., by 3, to find the interest for 20 da. ($5.776) ; and the same sum by 20, to find the interest for 3 da. ($0.866). By adding these various sums, we have the interest for the given time at Qfo ($292.554). To this result add of itself, which is the interest for the given time at 1 % , and the required interest is obtained ($341.31). INTEREST. 123 306. Aliquot Parts of 60. 1 = ^ ; %=>', 3 = ^ ; 4 = A; 5 = A; 6 = ^; 10 = i; 12 = i ; 15 = }; 20 = i; 30 = f NOTES. 1. To divide by 10, place the figures of the basis one place to the right. 2. To divide by 20, 30, or 60, divide by the first figure and write the quotient figures one place to the right. 307. If the number of days given is other than any of the above, which are aliquot parts of 60, it will need to be so separated that the component parts will be aliquot parts of 60. Numbers not aliquot parts of 60, with best divisions : 7=6 + 1 ; 8 = 6 + 2; 9 = 6 + 3; 11 = 6 + 5, or 10 + 1; 13 = 10 + 3; 14=12 + 2; 16=10 + 6; 17 = 12 + 5, or 15 + 2 ; 18 = 12 + 6. (The interest for 18 days may be found by multiplying the basis by 3, and placing the figures of the product one place to the right); 19 = 15 + 4, or 10 + 6 + 3; 21 = 15 + 6; 22 = 20 + 2 (2 = T V of 20); 23 = 20 + 3 ; 24 = 12 + 12 (Or multiply by 4 and place the figures of the product one place to the right) ; 25 = 20 + 5 (5 = \ of 20) ; 26 = 20 + 6 ; 27 = 12 + 15 ; 28 = 12 + 12 + 4 (4 = i of 12), or 20 + 6 + 2 ; 29 = 12 + 12 + 5, or 20 + 6 + 3. 308. RULE. Draw a perpendicular line two places to the left of the decimal point; the result will be the interest at 6% for 2 months, or 60 days, the dollars being on the left, and the cents on the right of this line. Multiply this result by one-half the total number of months. To this product, add that proportion of the interest for 60 days, which the given number of days is of 60. 309. The interest for any other rate may be found from the interest at Q% as follows : At \%, divide by 6 ; at \\%, divide by 4 ; at 2%, divide by 3 ; at. 3%, divide by 2 ; at 4%, subtract J ; at 4-1% subtract J ; at 5#, subtract | ; at 7$, add ; at 8#, add J ; at 9$, add ; at 10$, divide by 6, and multiply by 10 by placing the point to the right one place ; at 12$, multiply by 2. At any per cent., divide by 6 and multiply by the rate. 310. 6% Method. At 6^, the interest for one year is .06 of the principal. For one month, ^ of a year, it will be -fa of .06, or .OOJ (.005). For one day, ^ of a month, it will be ^ of .005, or.000. 124 INTEREST. Ex. What is the interest of $864, at $%, for 2 yr. 7 mo. 20 da. ? OPERATION. 2 x .06 = .12 7 x .OOJ = .035 20 X .OOOJ- = .003 ANALYSIS. If the interest for 1 yr. is .06 of the principal, for 2 yr. it will be twice .06, or .12. If the interest for 1 mo. is .00^ of the principal, for 7 mo. it will be 7 times .00 J, or .035. If the -j Koj, interest for 1 day is .000| of the principal, for 20 da. it will be 20 times .000, or .003 J. Hence 288 the interest for the given time will be .158 of the 6912 principal ($864), or $136.80. 4320 _864_ $136.800 311. RULE. Multiply the given principal by the decimal obtained by taking for every year six hundredths, one-half as many hundredths as there are months, and one- sixth as many thousandths as there are days. The product will be the interest at 6%. NOTES. 1. In using this method, to multiply by f , write twice ; to mul- tiply by f , take and i. 2. The interest at any other per cent, may be found as in Art. 3O9. 3. The decimal obtained by the above rule, if regarded as cents and mills, expresses the interest of $1 for the given time at 6%. The interest of $1 at 6% for 1 year is $.06 ; for 1 month, $.00^, or $.005 ; for 1 day, $.000^. 312. 6% Method for Days. This is a modification of the preceding method, and may be applied to any example if the time is reduced to days. Ex. What is the interest of $1735 for 173 days at % ? OPERATION. $1735 173 ANALYSIS. The interest of $1735 for 173 days is equiv- alent to the interest of 173 times $1735, or $300155 for 1 day. Since the interest of $1 for 1 day is $ of a mill, or 12145 .000 of the principal, the interest of $300155 for 1 day is as 1735 many mills as 6 is contained times in 300155, or 50025 mills, 6 ) 300155 or $50.025 + OF THE UNIVERSITY OF INTEREST. 125 313. EULE. Multiply the principal by the number of dctfijs, divide the product by 6, and place the point 3 places to the left. TJie result will be the interest at 6%. NOTES. 1. The interest at any other per cent, may be found as in Art. 3O9. To find the interest at 3 % , divide by 12 instead of 6 ; at 4 % , by 9 ; at 9/ , by 4. 2. If the principal is a multiple of the divisor (6 in the above example), time can be saved by performing the division first. Thus, to find the interest of $1200 for 113 days, divide 1200 by 6, and multiply the quotient 200 by 113, producing 22600. By pointing off three places, the required interest is $22.60, EXAMPLES. 314. What is the interest of -1. $375.60 for 8 mo. 20 da., at 6% ? 2. $1727 for 7 mo. 15 da., at Q% ? 8. $449.38 for 1 yr. 4 mo. 12 da., at 6% ? At 4. $285 for 1 yr. 5 mo. 10 da., at % ? At 6% ? o. $432.65 for 2 yr. 2 mo. 6 da., at % ? At 8% ? 6. $1235 for 2 yr. 5 mo. 5 da. 9 at 6% ? At 4% ? 7. $445.25 for 5 mo. 4 da., at 6% ? At $1000 for 93 days, at $% ? At 1 ? $2416.60 for 72 days, at 6^ ? At $3210 for 62 days, at Q% ? At 8% ? $735 for 75 days, at 6% ? At 5% ? $812.45 for 121 days, at 6% ? At 4% ? tf& $2440.50 for 97 days, at 6% ? At 7^ ? 14. $3125 for 38 days, at 6^ ? At 7^ ? / 15. $247.50 for 69 days, at 6% ? At % ? 10. $512.45 for 5 mo. 11 da., at 6^ ? At 1% ? 17. $1478 for 1 yr. 2 wo. 13 da., at 6^ ? At 1. $2810.60 for 9 mo. 24" for 100 days ? 9. $3110.45, at 5J#, for 90 days ? m $373.70, at 1%, from June 4 to Dec. 28 ? 11. $500, at 6#, from July 24, to Sept. 16 ? 7. $365, at 6%, from June 30 to Dec. 21 ? 18. $1080, at 5#, from May 9, 1878, to Jan. 30, 1879 ? 14. $1728, at 1%, from Jan. 6, 1878, to Jan. 21, 1880 ? 15. Required the exact interest on three U. S. bonds of $5000 each, at 3J$, from July 1 to Aug. 11. 16. What is the interest on three U. S. bonds of $1000 each, at 4J#, from Sept. 1 to Nov. 15 ? 17. What is the interest on a $5000 U. S. bond, at 4$, from Oct. 1 to Dec. 16 ? 18. What is the interest on a U. S. bond of $1000, bearing 3J$ interest, from May 1 to July 19 ? 19. What is the interest on a $500 IT. S. bond, at 4$, from Apr. 1 to May 10 ? W. What is the interest on a $5000 U. S. bond from Nov. 1, 1881, to Jan. 3, 1882, at 3J^? 21. What is the difference between ordinary and accurate interest of $10000 for 219 days at 6%? PROBLEMS. 129 PROBLEMS IN INTEREST. 319. To find the rate, the principal, interest or amount, and time, being given. Ex. At what rate will $720 in 1 yr. 4 mo. 10 da., produce $44.10 interest? OPERATION. ANALYSIS. The interest on a $7 57 20 given principal for a given time is in o proportion to the rate per cent. At one per cent., $720 will in 1 yr. 4 mo. 10 da., produce $9.80 interest. To produce 20 $44.10 interest, the required rate must ^ be as many times 1 % , as $9.80 are con- tained times in $44.10, or 4| times. 80 ) $44.10 ( 4|- Ans. Hence the answer is 41 6)58 ' $9 32O. EULE. Divide the given interest ~by the interest of the given principal, for the given time, at 1%. NOTE. When the amount is given, find the interest by subtracting the principal from the amount. EXAM PLES. 321. At what rate will 1. $864 in 8 mo. 10 da. produce $42 interest ? 2. $1000 in 9 mo. 9 da. produce $54.25 interest ? 3. $852 in 1 yr. 7 mo. 16 da. amount to $935.21 ? 4. $1926 in 2 yr. 8 mo. 24 da. produce $263.22 interest ? 5. $375.60 in 1 yr. 10 mo. 22 da. amount to $425.41 ? 6. $1872 in 7 mo. 17 da. produce $41.31 interest ? 7. $435.60 in 1 yr. 2 mo. 18 da. amount to $478 ? 8. $1338.72 in 6 mo. 27 da. produce $34.64 interest? 9. $1728 in 8 mo. 21 da. amount to $1778.11 ? 10. $3456 in 5 mo. 8 da. produce $91.01 interest ? 11. $5280 in 11 mo. 11 da. amount to $5720.12 ? 12. $1234 in 8 mo. 22 tfa. produce $80.83 interest ? ^. $6975 in 3 mo. 28 da. amount to $7215.06 ? 14. $525 in 1 yr. 11 mo. 18 f/or. produce $309.75 interest? 15. $500 in 3 yr. 11 mo. 12 da. amount to $658 ? 16. $4680 in 2 yr. 6 mo. 11 rfa. produce $710.58 interest ? 17. $614.45 in 162 days amount to $633.805? 130 INTEREST. 322. To find the time, the principal, interest or amount, and rate, being given. Ex. In what time will $426, at 6$, produce $59.427 interest ? OPERATIONS. $426 Or $426 .06 .06 $25. 56) $59. 427 (yr. 2.325 $25.56 ) $59.427 ( 2 yr. 51 12 _J.2 51 12 8307 mo. 3.900 8.307 7 668 30 12 6390 da. 27.000 $25.56 ) 99.684 ( 3 mo. 5112 76.68 12780 23.004 12780 30 $25. 56) 690. 120 ( 27 da. ANALYSIS. The interest on a given principal at a given rate %, is in proportion to the time. In one year, $426, at 6%, will produce $25.56 interest. To produce $59.427 interest, it will require as many years as $25.56 is contained times in $59.427, or 2.325 yr. 2.325 yr. equal 2 yr. 3 mo. 27 da. (201). 323. RULE. Divide the given interest by the interest of the given principal, at the given rate, for 1 year. The integral part of the quotient will be years. Reduce the decimal, if any, to months and days (2O1). EXAM PLES. 324:. In what time will 1. $3000, at 7$, produce $108.50 interest? 2. $1728, at 6%, amount to $1872 ? 8. $3932, at 1%, produce $597.88 interest? 4. $735, at 5%, amount to $742.66 ? 5. $1222.25, at 6$, produce $39.52 interest? 6. $375.60, at 7#, amount to $425.41 ? 7. $1461.75, at 6#, produce $420.25 interest? 8. $1200, at 3}%, amount to $1413 ? 9. $4500, at 5%, produce $181.25 interest ? 10. $276.50, at 10$, amount to $303.46 ? PROBLEMS. 131 11. $1020, at 6%, produce $89.25 interest? 12. $6495, at 1%, amount to $7161.81 ? 13. $100, at Q%, produce $100 interest ? 14. $125, at 1%, amount to $375 ? To find the principal, the interest, time, and rate, being given. Ex. What principal will produce $152.64 interest, in 1 yr. 5 mo. 20 da., at 6^? OPERATION. $.088J) $152.64(1728. > * ANALYSIS. The interest on any principal 5 i s as m any times greater than the interest of 1929 $1, as that principal is greater than $1. One 1855 dollar, in 1 yr. 5 mo. 20 da., at Q% (31O), will produce $.088^ interest. To produce $152.64, the principal must be as many times $1 as $.088- is 530 contained times in $152.64, or $1728. 2120 2120 326. RULE. Divide the given interest by the interest of for the given time, at the given rate. EXAMPLES. 327. What principal will produce 1. $1235 interest, in 1 yr. 8 mo. 12 da., at 6% ? 2. $49.81, in 9 mo. 24 da., at 1% ? 8. $186.75, in 1 yr. 4 mo. 20 da., at 4. $244.44, in 7 mo. 18 da., at 5%? 5. $375.60, in 2 yr. 4 wo. 6 ) a ^ 6% W *H amoun t to $1.088. To amount to $1880.64, the prin- cipal must be as many times $1 as $1.0883 6530 are contained times in $1880.64, or $1728. 26120 26120 329. EULE. Divide the given amount ~by the amount of $1 for the given time, at the given rate. EXAMPLES. 330. What principal will amount to 1. $1272.254, in 6 mo. 6 da., at 6$? 2. $5538.72, in 8 mo. 12 da., at 1% ? 3. $3695.04, in 1 yr. 4 mo. 18 da., at 4. $442.71, in 2 yr. 2 mo. 24 da., at 5. $14794.31, in 3 yr. 3 mo. 3 da., at 6% ? 6. $1793.38, in 7 mo. 17 da., at % ? 7. $1010.65, in 5 yr. 8 mo. 6 da., at 7% ? 5. $977.75, in 1 yr. 10 mo. 10 da., at 6$? 9. $1716.75 in 3 yr. 4 mo. 21 ^., at % ? 70. $2808.08, in 2 yr. 8 mo. 12 da., at 8% ? ./I. $4312.22, in 1 yr. 2 mo. 11 flf., at 12. $6528.49, in 4 yr. 7 mo. 6 rfa., at 73. $1763.02, in 1 yr. 2 mo. 21 . To calculate interest on English money, reduce the shillings aud pence to the decimal of a pound (see Art. 2O4, Ex. 7, Note), apply any of the methods under Art. 316, and reduce the resulting decimal to shillings and pence. Find the accurate interest of 25. 425, from Aug. 4 to Dec. 28, at 5%. 26. 625 125., from Jan. 12 to Apr. 1, at 4%. 27. 717 16s. 10d., from Mar. 3 to June 1C, at 28. 429 10s. 8rf., from Sept. 16 to Nov. 30, at 29. 516 18s. 3d., from Aug. 1 to Oct. 18, at 80. 612 6s. lid., from July 1 to Nov. 3, at 6%. 81. 225 15s. &d., from Feb. 11 to Sept. 8, at 2|-%. 82. A commission merchant sold 24160 pounds of leather at 26f cents a pound, paid transportation $60.40, cartage $20, his commission being 2J%, and his charge for inspection $20. What were the net proceeds ? 83. What per cent, profit does a merchant make who buys at a discount of 20, 10, and 12%, and sells at the list price ? 34. At what per cent, above cost must goods be marked, so that when sold at a discount of 5%, there would be a profit of 25% ? 85. A buys a bill of goods amounting to $2776.40, on the fol- lowing terms : "4 months, or less 5% cash." He accepts the latter, and borrows the money at 6% to pay the bill. How much does he gain ? 86. I purchase books at $2 each less 33 J% and b% for cash. What was the net cost, and what per cent, discount may be given on the list price to produce a net profit of 10% ? 37. C of New York sells for D of Atlanta, a quantity of cotton, amounting to $7317.83, and charges a commission of 2%. By instructions, he invests the proceeds in dry goods, after deducting a commission of \\% of the amount expended. What was the total commission? 88. A lawyer collected 75% of an account of $3416, charging 5% commission. What amount should he pay over ? * When the time is less than 1 year, and the rate is ) vA rxO ' COMPOUND INTEREST. 5 141 342. Table showing the sum to which $1, prdd at the beginning of each year will increase at compound interest, in any number of years not exceeding 50. Yrs. 8jt. Stf. 4*. 5*. 6*. 7* 8*. 10*. Yrs. 1 1.0300 1.0350 1.0400 1.0500 1.0600 1.0700 10800 1.1000 1 2 2.0909 2.1062 2.1216 2.1525 2.1835 2.2149 22464 2.3100 2 3 3.1836 3.2149 3.2485 3.3101 3,3746 3.4399 3.5061 3.6410 3 4 4.3091 4.362) 4.4163 4.5256 4.6371 4.7507 4.8666 51051 4 5 6.4634 5.5502 5.6330 5.8019 5.9753 6.1533 6.3359 6.7156 5 G 6.6625 6.7791 6.8933 7.1420 7.S938 7.6540 7.9228 8.4872 6 7 7.8923 8.0517 8.2142 8.5491 8.8975 9.2598 9.6366 10.4359 7 8 9.1591 9.3685 9.5828 1C.0286 10.4913 10.9780 11.4876 12.5795 8 9 10.4633 10 7314 11.0061 11.5779 12.1803 12.8164 13.4866 14.9374 9 10 11.8078 12.1420 12.4334 13.2083 13.9716 14.7836 15.6455 17.5312 10 11 131920 13.6020 140258 14.9171 15.8699 16.8885 17.9771 23.3843 11 12 14.6178 15 1130 15.6288 16.7130 17.8321 19.1406 20.4952 23.5227 12 13 16.0863 16.6770 17.2919 18.5983 20.0151 21.55J5 23.2149 26.9750 13 14 17.5989 18.2957 19.0135 20.5786 22.2780 24.1290 26.1521 80.7725 14 15 19.1569 19. 9 no 20.8.245 22.6575 JJ6.88S1 29.3243 34.9497 15 16 20.7816 21.7050 22.6975 24.8434 27 21-39 ^29.8402 32.7502 39,5447 16 17 22.4144 23.4997 24.6454 27.1324 29^9057 32.9390 36.4502 44.5992 17 18 24.1169 25.3573 266712 29.5390 32.7600 36.3790 40.4463 50.1591 18 19 25.8704 27.2797 28.7781 32.0630 35.7856 39.9955 44.7620 56.2750 19 20 27.6765 29.2695 30.9692 34 7193 38.9927 43.8652 49.4229 63.0025 20 21 29.5368 31.3290 33.2480 37.5352 42.3923 48.0058 54.4568 70.4027 21 21 31.4529 33.4634 35.6179 40.43)5 45.9J58 52.4561 59.8968 785430 22 SB 33.4-265 35 6365 38.0826 43.5023 43.8156 57.1767 65.7648 87.4973 23 34 35.4393 37.9499 40.6459 46.7271 53.8645 62.249 ) 72.1059 97.3471 24 25 37.5530 40.3131 43.3117 50.1135 58.1564 67.6765 18.9544 108-1818 25 26 39.7096 42.7591 46.0342 53.6931 62.7058 73.4838 86.3508 120.0999 26 27 41.9309 45.2908 48.9576 57.40 }6 67.5281 79.6977 94.33h8 133.2099 27 28 44.2138 47.9103 51.9603 61.3227 72.6393 86.3465 102.9659 147.6309 29 46.575* 50.6227 55.0349 65.4338 78.0592 93.4608 112.2a32 163.4940 29 30 49.0027 53-4295 53.3283 69.7638 83.8017 101.0730 122.3459 180.9434 30 31 51.5028 56.3345 61.7015 74.2933 898898 109.2182 1&3.2135 200.1378 31 32 54.0778 59.341 1 65 2035 79.0838 96.3432 117.9334 144.9506 221.2515 32 33 56.7302 62.4532 68.8579 84.0670 03.1838 127.2583 157.6267 244.4767 33 34 59.4621 65.6743 72.6522 89.3203 10.4348 137.2369 171.3168 270.0244 34 35 62.2719 69.0076 76.59*3 94.8383 118.1209 147.9135 186.1021 298.1268 35 36 65.1742 72.4579 80 7022 100.6231 126.2681 159.3374 202.0703 329.0395 36 37 68.1594 76.0239 84.9703 106.7095 134.9042 '171.5610 219.3159 868.0484 37 38 71.2342 79.7.249 89.4091 113.0950 144.0535 184.6403 237.9412 400.4478 33 39 74.4013 83.5503 94.0255 119.7998 153.7620 198.6351 258.0565 441.5926 39 40 77.6633 87.509J 98.8235 126.8393 164.0477 213.6096 279.7810 486.8518 40 41 81. Or 2 91.6074 103.8196 134.2318 174.9506 229.6322 303.2435 536.6370 41 42 84.4839 95.8486 109.0124 141.9933 136.5076 246.7765 328.5830 591.4007 42 43 88.0484 100.2383 114.4129 150.1430 |198.75.Sf) 265.1208 355.9496 651.6408 43 44 91.7199 104.7817 120.0294 ,158.7002 211 7435 284.7493 385.5056 717.9048 44 45 95.5015 109 4340 1258706 167.6852 225.5081 305.7518 417.4261 790.7953 45 46 99.3965 114.3510 131.9454 1771194 240.0986 328,2244 451.9002 870.9749 46 47 103.4084 119.3383 138.2632 137.0254 255.5645 352.2701 489.1322 959. 1723 47 48 107.5406 124.6018 144.8337 197.4267 271.9584 377.9930 529.3427 1056- 1P96 48 49 111 7963 129.9979 151.6671 i208.3480 289.3359 1405.5389 572.7702 1162.9085 49 50 116.1307 135.5328 158.7738 219.8154 307.7561 434.9859 619.6718 1280.2993 53 To find the sum to which a given amount, per annum, will increase at compound inter- est, at any of the rates per cent, and number of years expressed in the above Table : Multiply the given amount, per annum, by the sum to which one dollar per annum will increase at the rate and for the number of years required, marking off as many decimals from the product as there are decimals in the multiplier and multiplicand. NOTE. If the amount be payable semi-annually, and compound interest is to be allowed semi-annually, take the amount for double the number of years at one-half the rate per cent. Thus, for a semi-annual payment of $1 for 10 years at 10 per cent., take the amount of $1 for 20 years at 5 per cent. = $34.7193. For a quarterly payment, take the amount for four times the number of years at one -fourth the rate per cent. 142 INTEREST. EXAM PLES. 343. 1. What will $450 amount to at compound interest, in 4 years, compounded annually at 4% ? At 3% ? 2. Find the compound interest of $360, for 2 years, interest compounded semi-annually at %. At 5%. & What is the compound interest of $800 for 1 yr. 3 mo. at 8$, interest compounded quarterly ? 4. At compound interest, what is the amount of $1728 for 3 yr, 4 mo. 16 $B., interest compounded annually at 3% ? At 6% ? NOTE. First find the amount for 3 years, and uss this amount as the principal for the remaining time. 5. B holds a mortgage against A's property dated Apr. 1, 1881, for $20000, interest payable annually at 6%. The interest due Apr. 1, 1882, is not paid until May 26, 1882. How much is then due, A having consented to pay interest upon interest ? (See Note 2, Art. 339). NOTE. In solving the following examples, uso the tables in Art. 34 1 - 342. 6. A gentleman deposits in a savings bank $100 when his child is one year old. How much will this amount to when he is 21 years old, interest being compounded semi-annually at 4%? At 5#? 7. If at the age of 25 years, a person places $2000 on interest, compounded annually at 6$, what will be the amount due him when he is 50 years old ? 8. What will $625 amount to at compound interest, in 36 years, compounded annually at 3% ? At 4% ? 9. At the age of 20, and every year thereafter, a young man places $200 at compound interest at Q%. How much will he have at the age of 30 ? At the age of 40 ? (See Art. 343.) 10. How much will a gentleman have at the end of three years, if he places at compound interest at 5%, $300 at the beginning of each year ? 11. Mr. B., whose life is insured for $4000, pays an annual premium of $114. How much would this amount to at 6^ com- pound interest in 20 years ? 12. A lady deposits $50 in a savings bank Jan. 1 and July 1, of each year; how much will be placed to her credit in 15 years, money being worth 6%, compound interest ? COMMERCIAL PAPER. 143 13. What sum must be placed at compound interest, at 6^, to amount to $1000 in 5 years? NOTE. In compound interest, as in simple interest, the amounts are proportional to the principals; hence the amount of any principal is as many times greater than the amount of $1, as that principal is greater than $1. To find the principal, divide the given amount by the amount of $1 for the given time and rate. In simple interest, the interest on a given principal for a given time is in proportion to the rate per cent., and at a given rate, in proportion to the time ; but, in compound interest, such is not the case. If the rate or time be doubled, the interest is more than doubled. 14- How much should a gentleman invest at compound inter- est, 6^, for his son who is now G years old, so that, when he becomes 21 years of age, he may have $10000 ? 15., In the above example, how much should be invested at the beginning of each year to produce the same sum? 16. A gentleman at his death left $7350 for the benefit of his only son, 12 years old, the money to be paid to him when he should be 21 years of age. How much did he receive, interest at 6%, compounded send-annually ? 17. How much must a person at the age of 25 years, place at compound interest at 6$, so that the amount due him, when he is 50 years old, will be $20000 ? 18. In the above example, how much should he invest annually to produce the same sum? COMMERCIAL PAPER. 344. Commercial Paper embraces notes, drafts, bills of exchange, etc. 345. A Note (also called a Promissory Note) is a written promise to pay a certain sum of money on demand or at a specified time. 346. The Maker of a note is the person who signs it, and thus becomes responsible for its payment. The Payee is the person to whom, or to whose order, it is made payable. The Face of a note is the sum promised. In Note 1, Art. 352, Peter Cooper is the maker ; George Peabody is the payee ; the face of the note is $100U. r 144 INTEREST. 347. A Negotiable Note is a note which is made payable to bearer or to the order of some person (See Notes, Art. 352). 1. A note is non-negotiable when it is payable only to the party named in the note. 2. A negotiable note made in New Jersey must contain the words " with- out defalcation or discount ; " in Missouri, the words " negotiable and payable without defalcation or discount." 3. Negotiable notes payable to order may be sold or transferred by the payee writing his name upon the back of the note. He then becomes an indorser. 348. The Indorser of a note or draft is the person who writes his name on the back of it, and by so doing guarantees its payment. If Mr. Erastus Corning desires to sell or,|ransfer Note 3, Art. 352, it will be necessary for him to indorse it. If he writes his name only, it is called an indorsement in blank, and the note is then payable without further indorse- ment to any person lawfully holding the same. He may indorse it in full by making it payable to a particular person, thus " Pay to the order of Henry R. Pierson, Erastus Corning." Before it can be again transferred, it will require the indorsement of Henry R. Pierson. For greater security, checks, notes, drafts, etc., are indorsed in full when sent by mail. If an indorser does not wish to guarantee the payment of a note, draft, etc., he writes " Without recourse " over his name at the time of the indorse- ment. Sometimes notes and drafts are drawn to the order of the maker or the drawer (to the order of myself or ourselves) to facilitate their transfer without the indorsement of the holder. 349. A Draft, or Bill of Exchange is an order or request addressed by one person to another directing the payment of a specified sum of money to a third person or to his order. 350. The Drawer of the draft is the person who signs it. The Drawee is the person on whom it is drawn. The Payee is the person to whom, or to whose order, it is made payable. In Draft 5, Art. 352, C. P. Huntington is the drawer ; Drexel, Morgan & Co. are the drawees ; J. & W. Seligman & Co. are the payees. 1. The person in whose favor the bill is drawn is sometimes called the buyer, and becomes the " remitter." After the bill is presented and accepted, the drawee is called the acceptor, and the draft, an acceptance. The draft then has the same legal significance as a promissory note. 2. A person accepts or promises to pay a draft by writing the word " Accepted" and the date over his name across its face. COMMERCIAL PAPER. 145 3. Drafts are sometimes accepted in the following form : "Accepted August 20, 1881, and payable at the National Park Bank, New York, G. B. Horton & Co. " 4. In the State of New York, both by law and custom, the drawee of a draft may demand 24 hours consideration from the time the draft is presented for acceptance. When accepted, it must bear the date when first seen by him. 5. To " honor " a draft is to accept it or pay it on being presented. 351. A Protest is a formal statement made by a Notary Public, declaring that a draft or note has been presented for payment or acceptance, and was refused. 352. FORMS OF NOTES AND DRAFTS. 1. DEMAND NOTE. $1000. NEW YORK, August 19, 1881. On demand, I promise to pay GEOKGE PEABODY, or bearer, One Thousand Dollars. Value received. PETER COOPER. The above note is payable on demand, that is, whenever presented ; is negotiable (payable to bearer) ; and bears interest from date at the legal rate of the State in which it is made. If the words " or bearer " were omitted the note would not be negotiable. 2. TIME NOTE INTEREST-BEARING. $875^. CINCINNATI, OHIO, July 16, 1882. Six months after date, I promise to pay GEO. C. MILLER, or order, Eight Hundred Seventy-five and -fa Dollars, with interest at eight per cent. Value received. ALEX. MCDONALD. The above note is payable 6 mo. 3 da. after its date, or Jan. 19, 1883 ; is negotiable (payable to order) ; and draws interest from its date at 8% per annum. If the rate of interest was omitted, it would bear interest at the legal rate of the State for such cases, 6^. (See Art. 298.) 3. TIME NOTE WITHOUT INTEREST - PAYABLE AT A BANK. $6000. ALBANY, N. Y., December 4, 1881. Sixty days after date, I promise to pay to the order of ERASTUS CORNING, Six Thousand Dollars, at the Second National Bank. Value received. E. C. KOONZ. 146 INTEREST. The preceding note is payable 63 days from Dec. 4, 1881, or Feb. 5, 1882. It is payable at the Second National Ban 1 !!. No interest will be due at maturity (Feb. 5). If the note is not paid at maturity, it will bear interest from that date. 4. JOINT AND SEVERAL NOTE. $^16^- WORCESTER, MASS, May 27, 1882. Four months after date, we jointly and severally promise to pay JOHN S. BALLARD & Co., or order, Four Hundred Sixteen T 3 ^j- dollars, with interest from date, value received. T. K. EARLE. CHAS. W. SMITH. If the above note were written "we jointly promise, etc.," it would be called a joint note- The makers of a joint note must be sued jointly, each being responsible for one-half of the amount of the note. The makers of a joint and several note may be sued separately, either being responsible for the full amount of the note. 5. SIGHT DRAFT. $8000. SAN FRANCISCO, CAL., May 1, 1882. At sight, pay to ttie order of J. & W. SELIGMAN & Co., Eight Thousand Dollars, value received. C. P. HUNTINGTON. To DREXEL, MORGAN & Co., New York. 6. TIME DRAFT. $5000. BURLINGTON, IOWA, June 18, 1881. At sixty days' sight, pay to the order of ADDISON BALLARD, Five Thousand Dollars, value received, and charge to account of A. G. ADAMS. To BARTON & JONES, Chicago, 111. Drafts are sometimes drawn a certain number of " days after date." For Foreign Bills of Exchange, see Art. 418. NOTES. 1. A note should contain the words " Value received," as a con- tract without a consideration is not legally binding. 2. Negotiable securities are good in the hands of ono who purchases in good faith and before maturity, although the seller may have found or stolen them. 3. Where no place of payment is specified, a promissory note is payable at the maker's place of business, or if none is known, at the residence of the maker. COMMERCIAL PAPER. 147 4. A note or draft must be presented at the place where it is made pay- able. If at a bank, during banking hours ; if at a place of business, during business hours ; if at a residence, during family hours ; and if the maker, or some one for him, is not ready with legal tender currency to pay it, the holder need not call again. A check, even if certified, is not a legal tender, and may be lawfully refused. 353. Days of Grace and Maturity. The day of ma- turity is the day on which a note becomes legally due. According to the laws of most of the States, a note is not legally due until three days after the expiration of the time specified in the note, except the note contain the words "without grace." These days are called days of grace, but they are of no advantage to the payer, since interest is charged for them as for any others. 1. California has abolished days of grace altogether. In Georgia, Ala- bama, and Kentucky, grace is allowed on promisscry notes only in case they are made payable, or are discounted or left for collection at a bank or private banker's. (March, 1879.) 2. By statute in the State of New York and most of the States, all bills and notes due on Sunday are payable on Saturday, and all due on a legal holiday are made payable on the business or secular day next preceding. Thus, if a holiday falls on Thursday, all notes, etc., must be paid on Wednes- day ; if a holiday falls on Monday, all notes due Sunday or Monday would be payable on Saturday ; if a holiday falls on Saturday, notes due Saturday or Sunday would bo payable on Friday. 3. The legal holidays in the State of New York are New Year's Day (Jan. 1), Washington's Birthday (Feb. 22), Decoration Day (May 30), Inde- pendence Day (July 4), Election Day (the first Tuesday after the first Monday in November), Thanksgiving Day (the day appointed by the President of the United States and Governor of the State, usually the last Thursday of November), and Christmas (Dec. 25). 4. When a legal holiday falls on Sunday, Monday is, by the statute of New York, made a legal holiday, and notes, etc., maturing on Sunday or Monday, must be paid on the preceding Saturday. 5. A note made due at a fixed date in the future, carries 3 days' grace (unless the words " without grace " are used in the contract). Thus, a note stating that " on May 1, 1882, 1 promise, etc.," would carry 3 days' grace, and would be payable May 4, 1882. 6. When the time of a note is expressed in months, calendar months are used to determine the day of maturity ; when in days, the exact number of days is used. Thus, a note dated July 16, and payable two months from date, would nominally mature Sept. 16, and, including the three days of grace, would legally mature Sept. 19. A note having the same date, and payable 148 INTEREST. sixty days from date, would nominally mature Sept. 14, and, including the three days of grace, would legally mature Sept. 17. 7. A note due in one or more months from date, matures on the corres- ponding day of the month up to which it is reckoned, if there are so many days in that month ; but if not so many, it then matures on the last day of said month, to which the usual grace must be added. Thus, notes dated Jan. 28, 29, 30, or 31, and payable one month from date, would become due Mar. 3 (Feb. 28 with 3 days' grace added). 8. When drafts are payable a certain time after sight, the date of accept- ance and the time of the draft determine the day of maturity. Thus, if a draft is dated May 16, accepted May 20, and payable sixty days after sight, it would mature or be due 63 (including 3 days of grace) days after May 20, or July 22. If payable 60 days after date, it would mature 63 days after May 16/or July 18. It is not necessary to present for acceptance drafts drawn a certain time after date, but as a courtesy to the drawee, it is usually done. 9. Days of grace are allowed on drafts according to the custom of the place where they are payable. The statute of New York forbids grace on all sight drafts, no matter on whom drawn, and on all time drafts which appear on their face to be drawn " upon any bank, or upon any banking association or individual banker, carrying on the banking business under the act to authorize the business of banking." EXAMPLES. 354. 1. How much would be due on Note 1, Art. 352, Jan. 1, 1882, finding the time by compound subtraction ? 2. How much would be due on Note 2, Art. 352, at its matu- rity? How much March 1, 1883 ? Supposing the rate of interest was omitted in the note, how much would be due May 4, 1883 ? 8. Ninety days after June 21 is what date ? OPEKATIONS. ANALYSIS. Subtract from the given 90 Or 9 June. number of days, the number of days re- 9 June. 31 July. maining in June, and from this remainder, ~ 3-^ Aug. subtract successively the number of days in the following months until the remain- 31 July. 18 Jan 10 4 mo $6000 Jan 10 41% 19 Mar 3 6 mo. $8775 Apr. 30 4|% 20. What were the proceeds of Note 3, Art. 352, if discounted Dec. 16, 1881, at the legal rate ? 152 INTEREST. 21. Find the date of maturity and proceeds of a note of $5000, payable 60 days from date, dated and discounted at a Philadelphia bank, Aug. 3. (See Art. 358.) 22. Find the date of maturity and proceeds of a note of $3750, payable 60 days from date, dated and discounted at a Maryland bank, Jan. 31, 1882. ^ 23. A broker discounts a note payable in 4 months at 4f%, and charges \% brokerage. This is equivalent to what rate of interest per annum, making no allowance for the days of grace ? 2Jf. A merchant can discount a note at his bank at 6%, 365 days to the year, or through n broker at 4f %, 360 days to the year, broker's commission %%. How much better is the latter method on a note of $10000, payable in 4 months, dated and discounted May 21 ? Find the date of maturity and proceeds of the following interest-bearing notes : (25.) $3000. ALBANY, N. Y., September 16, 1881. Four months after date, I promise to pay W. J. KLINE or order, Three Thousand Dollars, with interest at 5$, value received. J. M. THOMAS. Discounted Nov. 3, 1881, at 6$. NOTE. Compute the discount at 6% for 77 days (Nov. 3 to Jan. 19) on the amount due at maturity ($3000 plus the interest of $3000 for 4 months and 3 days at 26. A note dated May 27, 1879, payable in 3 months, for $3750, with interest at 7% ; discounted May 27, 1879, at 8$. 27. A note dated Jan. 16, 1879, payable in 4 months, for $1632, with interest at Q% ; discounted Mar. 5, 1879, at 1%. 28. A note dated Oct. 12, 1878, payable in 6 months, for $875, with interest at 1%; discounted Jan. 10, 1879, at 10$. 29. For what amount must a note be given for 60 days to afford $1000 proceeds, if discounted at 6$ ? ANALYSIS. The proceeds of any note is as many times greater than the proceeds of $1, as the face of the note is greater than $1. If a note of $1 is discounted for 63 days, at 6%, it will afford $.9895 proceeds ; to afford $1000 proceeds, the face of the note must be as many times $1, as $.9895 is con- tained times in $1000, or $1010.61. PARTIAL PAYMENTS. 153 The following approximate method is generally used by business men : To the given proceeds, add the interest for the given time. The interest of $1000 for 63 days is $10.50. $1000 + $10.50 - $1010.50. Since the interest is reckoned on the proceeds instead of the face of the note, the error, 11 cents, is equivalent to the interest of the interest ($10.50) for the given time. Where greater accuracy is required, the necessary correction may be made. The interest of $10.50 for 63 days is 11 cents. $1010.50 + $.11 = $1010.61. 30. A owes B $1500 ; how large a 90-day note must A give B that when discounted at a bank at %, the proceeds will be suffi- cient to pay the debt ? 81. I hold a note of $3000 against Mr. C., which he pays by giving a new note at 90 days for $1500, and the balance, includ- ing the discount on the new note, in cash. Required the amount of cash paid. ^ 82. A merchant having $8000 to pay, gets a note for $500Q> that will mature in 40 days, discounted at a bank at 6%. How large a note must he draw, payable in 90 days, for discount at the same rate, that the proceeds of the two notes may enable him to meet his payment ? PARTIAL PAYMENTS. 361. Partial Payments are payments in part of a note, mortgage, or other debt, made at different times. 362. Indorsements are the acknowledgments of the pay- ments, written on the back of the note, mortgage, etc., and stating the amount and date of the payment. Special receipts are sometimes given for such payments. UNITED STATES RULE. 363. Ex. How much would be due Sept. 1, 1882, on a note of $600, dated March 1, 1882, with interest at 6^? Suppose a payment of $100 be made Sept. 1, 1882, to pay the interest and part of the principal, how much would then be due ? Ans. $518. Ex. How much would be required to settle the above note Jan. 1, 1883, the balance of $518 remaining on interest at the same rate from Sept. 1, 1882? Ans. $528.36. 154 INTEREST. Ex. Find the amount due on the following note, Jan. 19, 1885: $1000. BOSTON, MASS., Aug. 1, 1881. One year after date, I promise to pay JOKDAN, MARSH & Co., or order, One Thousand Dollars, for value received, with interest from date, at 6 per cent. ALEXANDER H. RICE. On this note are the following indorsements : Received Apr. 21, 1882, $200. Received Aug. 1, 1883, $100. Received Dec. 1, 1882, $25. Received July 7, 1884, $400. NOTE. The method given in the following operation, is that adopted by the Supreme Court of the United States, and has been made the legal method of nearly all the States. By the United States Rule, as this is generally called, settlements are made whenever the payments are equal to or exceed the interest due ; if the payment exceeds the interest, it is applied first to discharge the interest, and the surplus is applied towards paying the princi- pal ; if the payment is less than the interest, it is not applied until the payments, taken together, are sufficient to pay all interest due ; since no unpaid interest is added to the principal to draw interest, a new principal can never be greater than the preceding principal. OPERATION. Face of note, or principal, from Aug. 1, 1881 .... $1000 Interest from Aug. 1, 1881, to Apr. 21, 1882 (8 mo. 20 da.), added 43.33 Amount, Apr. 21, 1882, 1043.33 First payment, Apr. 21, 1882, 200.00 New principal from Apr. 21, 1882 843.33 Interest of $843.33 from Apr. 21, 1882, to Dec. 1, 1882, (Vmo.lQda.) $30.92 (Interest exceeds the payment, and a new principal is not formed.) Interest of $843.33 from Dec. 1, 1882, to Aug. 1, 1883, (8 mo.) 33.73 _6465* [Payments $125 ($25 + $100), now greater than the interest due ($64.65)]. Amount, Aug. 1, 1883, 907.98 Second and third payments, $25 + $100 125 New principal from Aug. 1, 1883 782.98 * In many cases it can be determined mentally in advance whether the payment is greater or less than the interest. In this case the interest could he taken at once from Apr. 21, 1882, to Aug. 1, 1833 (1 yr. 3 mo. 10 da.), since it is evident that the payment ($25) is less than the interest of $843.33 for 7 mo. 10 da. (The interest of $800 for 7 mo. is 3J- x $8, or $28, and it would be more on $843.33 for 7 mo. 10 da.) If it is doubtful whether the payment is greater or less than the interest, perform all the work. PARTIAL PAYMENTS. 155 New principal from Aug. 1, 1883 $782.98 Interest of $782. 98 from Aug. 1 , 1883, to July 7, 1884 (1 1 mo. 6 da. ) 43.85 Amount, July 7, 1884, 826.83 Fourth payment, July 7, 1884, 400 New principal from July 7, 1884 426.83 Interest of $426.83 from July 7, 1884, to Jan. 19, 1885 (6 mo. 12 da.) 13.66 Amount due Jan. 19, 1885, the final day of settlement, . Ana. $440.49 364. UNITED STATES RULE. Find the amount of the given principal to the time when the payment or the sum of the payments exceeds the interest due; subtract from this amount the payment or the sum of the payments. Treat the remainder as a new principal, and proceed as before, to the time of settlement. EXAMPLES. 365. NOTES. 1. In the following examples, find the time by compound subtraction. 2. In the first five examples, all the payments exceed the interest. 91680. TBENTOJ*, N. J., Oct. 9, 1880. 1. On demand, I promise to pay COOPER, HEWITT & Co., or order, Sixteen Hundred Eighty Dollars. Value received. A. On this note were indorsed the following payments : Dec. 21, 1881, received $289.12. June 9, 1883, received $991.50. How much was due Jan. 30, 1884 ? 2. On a note dated May 11, 1877, for $2000, are the following indorsements : Aug. 6, 1879, $361; Feb. 11, 1880, $901.60; Nov. 2, 1882, $1000. What remained due Feb. 2, 1883, at 6$? A 4- Kf/ V ja.i dye . 3. On a note dated July 11, 1878, for $2400, are the following \ indorsements : Sept. 17, 1879, $200 ; Jan. 29, 1880, $400 ; Nov. 29, 1881, $1150. What is the amount due Jan. 11, 1882, the interest being at 6% ? At 1% ? 4. On a mortgage for $1700, dated May 28, 1880, there was paid Nov. 12, 1880, $80; Sept. 20, 1881, '$314; Jan. 2, 1882, $50 ; Apr. 17, 1882, $160. What was due Dec. 12, 1882, at 6$? At 8^? 156 INTEREST. 5. On a note dated May 30, 1879, for $1666, are the following indorsements : Apr. 9, 1880, $314; Nov. 4, 1880, $180; Aug. 25, 1881, $575. What was due June 30, 1882, at Q% ? At S%? 6. What was the amount due Oct. 17, 1881, upon a note for $1000, dated New York, Mar. 2, 1880, and on which the following payments were indorsed : June 2, 1880, $80; Dec. 15, 1880, $20 ; May 2, 1881, $32; June 2, 1881, $60? 7. A note for $3600, dated May 12, 1880, bore the following indorsements : Jan. 2, 1881, $255 ; Mar. 15, 1881, $225; June 3, 1881, $120 ; Aug. 6, 1881, $300 ; Feb. 3, 1882, $30. What was due June 2, 1882, at 6% ? At 10^ ? 8. A note for $4000, dated Mar. 9, 1874, was indorsed as fol- lows : Jan. 18, 1876, $300 ; June 4, 1876, $400; Dec. 9, 1876, $1800 ; Sept. 1, 1879, $2000. How much had to be paid Jan. 1, 1880, to take up the note, at % ? At 1% ? 9. A mortgage of $6000 is dated May 9, 1877, on which there were the following payments: July 15, 1878, $500; Nov. 27, 1878, $1000; June 1, 1879, $100; May 9, 1880, $275; Sept. 27, 1880, $2000. What was due Nov. 9, 1880, the interest being at Q%? At 12^? 10. What remained due June 3, 1882, on a note dated June 21, 1880, for $3300 with interest at the legal rate in Illinois, the following payments having been made ? Oct. 9, 1880, $90 ; Jan. 15, 188.1, $60 ; Mar. 27, 1881, $100 ; Aug. 6, 1881, $60 ; Dec. 15, 1881, $500. W T hat remained due at the legal rate in Nevada ? MERCANTILE RULES. 366. The following methods are frequently used by merchants in finding the balance due on a note where partial payments have been made. They are similar to the methods in general use for finding the balance due on an open account (451). 367. When the note runs for one year only, or less. 368. RULE. Compute the interest on the principal from the time it commenced to draw interest, and on each pay- ment from the time it was made until the time of settle- ment, and deduct the amount of 'all the payments, includ- ing interest, from the amount of the principal and interest. PARTIAL PAYMENTS. 157 NOTES. 1. This rule is used by some merchants when the note runs more than one year, although it is greatly to the disadvantage of the creditor, or holder of the note. 2. In solving examples by this rule, the different methods for finding time and interest, given in Art. 299, are used. The results of the following examples will be given for the first method (Compound Subtraction and 360 days to the year). EXAMPLES. 369. 1. According to the mercantile rule, find the balance due May 12, 1882, on a note for $2400, dated July 12, 1881, on which the following payments have been made : Dec. 16, 1881, $40; Jan. 2, 1882, $100; Mar. 15, 1882, $150. OPERATION. Face of note, or principal, July 12, 1881, $24QO.OO Interest on the same to May 12, 1882 (10 mo,} .... 120.00 Amount, May 12, 1882 2520.00 First payment, Dec. 16, 1881, $40.00 Interest on the same to May 12, 1882 (4 7720. 26 da.) . .97 Second payment, Jan. 2, 1882, 100.00 Interest on the same to May 12, 1882 (4 mo. 10 da.} . 2.17 Third payment, Mar. 15, 1882, 150.00 Interest on the same to May 12, 1882 (1 mo. 27 da.) . 1.42 294.56 Balance due May 12, 1882 $2225.44 2. On a note dated Jan. 13, 1882, for $1234, are the following indorsements: May 17, 1882, $234; June 16, 1882, $345; July 27, 1882, $123 ; Sept. 19, 1882, $135. What remained due Nov. 13, 1882, at 6% ? At 1% ? 3. A note for $1567, dated Jan. 14, 1881, bore the following indorsements : Mar. 11, 1881, $50 ; May 13, 1881, $245 ; June 19, 1881, $374; Aug. 30, 1881, $412 ; Sept. 28, 1881, $316.40. What was due Jan. 1, 1882, at 6%? At 5%? 4. On a note dated Aug. 17, 1881, for $3300, were the follow- ing indorsements : Dec. 18, 1881, $320 ; Feb. 5, 1882, $425 ; Apr. 13, 1882, $550; June 29, 1882, $630 ; July 16, 1882, $375 ; Aug. 1, 1882, $500. What amount was due Aug. 17, 1882, at 6% ? At 10$ ? 5. On a note dated Mar. 16, 1883, for $2468, are the following indorsements : July 11, 1883, $750 ; Aug. 4, 1883, $428 ; Sept. 21, 1883, $150; Nov. 12, 1883, $170 ; Dec. 18, 1883, $128 ; Jan. 16, 1884, $224 ; Feb. 13, 1884, $600. What is the amount due Mar. 6, 1884, at 6^ ? At 158 INTEREST. 370. When the note runs for more than one year. 371. Since it is the custom of merchants and bankers to balance their accounts annually, the following method is used by them in computing the balance due on a note when it runs more than one year. It is equivalent to finding the balance due yearly by the previous rule, and treating the balance as a new principal. The periodical settlements are made annually, semi-annually, or quarterly, depending upon the custom of the merchant or banker in balancing his accounts. Some merchants make the end of the business year, Jan. 1 or July 1, the periodical rest, or date of settlement for notes and accounts. When payments are made yearly greater than the interest due, this rule is the same as the New Hampshire rule for notes " with interest annually." 372. RULE. Find the amount of the principal for one year ; also of each payment made during the year from the time the payment ivas made to the end of the year ( 1 yr. from the date of the note). From the amount of the prin- cipal, subtract the sum of the payments, including interest. With the remainder as a new principal, proceed thus for each entire year that follows, and for the interval between the end of the last year and the final date of settlement. EXAM PLES. 373. 1. By the above rule, find the balance due Jan. 19, 1885, at 6%, on a note for $2400 dated Aug. 1, 1881, on which the fol- lowing payments have been made : Apr. 21, 1882, $200; Dec. 1-, 1882, $25; Aug. 1, 1883, $100; July 7, 1884, $400. (Time by Compound Subtraction.) OPERATION. Face of note, or principal, Aug. 1, 1881, $2400.00 Interest on the same for 1 year, 144.00 Amount, Aug. 1, 1882, 2544.00 First payment, Apr. 21, 1882, $200.00 Interest on the same to Aug. 1, 1882 (3 mo. 10 da.} . 3.33 203.33 Balance and new principal, Aug. 1, 1882, .... 2340.67 Interest on the same for 1 year, 140.44 Amount, Aug. 1, 1883, 2481.11 PARTIAL PAYMENTS. 159 Amount, Aug. 1, 1883, 2481.11 Second payment, Dec. 1, 1882, $25.00 Interest on the same to Aug. 1, 1883 (8 mo) . . . 1.00 Third payment, Aug. 1, 1883, 100.00 126.00 Balance and new principal, Aug. 1, 1888, 2355.11 Interest on the same for 1 year, 141.31 Amount, Aug. 1, 1884, 2490.42 Fourth payment, July 7, 1884, $400.00 Interest on the same to Aug. 1, 1884 (24 da.) . . 1.60 401.60 Balance and new principal, Aug. 1, 1884, 2094.82 Interest on the same to date of settlement, Jan. 1 9, 1885 (5 mo. 18 da.) 58.65 Balance due Jan. 19, 1885, $2153.47 i 2-10. Solve Examples 2-10, Art. 365, according to the mercantile rule. CONNECTICUT RULE. 374. The following rule for computing interest on obliga- tions, where one or more payments have been made, was estab- lished by the Superior Court of Connecticut, March, 1784. (Kirby's Eeports, page 49.) 375. EULE. /. Compute the interest to the time of the first payment ; if that be one year, or more, from the time the interest coimnenced, add it to the principal, and deduct the payment from the sum total. If there be after-pay- ments made, compute the interest on the balance due to the next payment, and then deduct the payment as above ; and in lilce manner from one payment to another, till all the payments are absorbed ; provided the time between one pay- ment and another be one year or more. II. But if any payment ~be made before one year's interest hath accrued, then compute the interest on the principal sum due on the obligation for one year, add it to the principal, and compute the interest on the sum paid, from the time it was paid, up to the end of the year ; add it to the sum paid, and deduct that sum from the principal and interest added as above. III. If any payment be made of a less sum than the interest arisen at the time of such payment, no interest 160 INTEREST. is to be computed, but only on the principal sum for any period. NOTES. 1. Should the final date of settlement be less than one year from the last date of settlement, compute the interest on the principal and the payments, if any, to the final date of settlement. 2. When the time between the payments is one year or more, and the payments exceed the interest due, the Connecticut Rule is the same as the U. S. Rule (364). When the time between the payments is less than one year, and the payment exceeds the interest due at its date, the settlement ia made by the first Mercantile Rule (368). EXAMPLES. 376. 1. According to the law of Connecticut, how much is due June 1, 1885, on a note dated Aug. 1, 1881, for $1000, the following payments having been made? Apr. 21, 1882, $100; Dec. 1, 1883, $300; July 1, 1884, $20; Sept. 1, 1884, $200; Mar. 1, 1885, $300. OPERATION. Face of note, or principal, Interest on the same for 1 year, .... Amount, Aug. 1, 1882, First payment, Apr. 21, 1882, Interest on the same to Aug. 1, 1882 (3 mo. 10 da.} Balance and new principal, Aug. 1, 1882, Interest to date of next payment, Dec. 1, 1883 (1 yr. 4 mo.} Amount, Dec. 1, 1883 Second payment, Dec. 1, 1823, Balance and new principal, Dec. 1, 1883, .... Interest on the same for 1 year, Amount, Dec. 1, 1884, Third payment, July 1, 1884 (less than interest due) Fourth payment, Sept. 1, 1884, Interest on the same to Dec. 1, 1884 (3 mo.} Balance and new principal, Dec. 1, 1884, .... Interest to final date of settlement, June 1, 1885 (6 mo.} Amount June 1, 1885, Fifth payment, Mar. 1, 1885, Interest on same to June 1, 1885 (3 mo.} . Balance due at date of settlement, June 1, 1885, $100.00 1.67 $20.00 200.00 3.00 $300.00 4.50 $1000.00 JSO^OO 1060.00 101.67 958.33 _ 76 i 67 1035.00 300.00 735.00 J14.10 779.10 223.00 556.10 16.68 572.78 304.50 268.28 2-10. Solve Examples 2-10, Art. 365, according to the Con- necticut Eule, at the legal rate (298). PARTIAL PAYMENTS. 161 NEW HAMPSHIRE RULE.* 377. According to the laws of New Hampshire, when pay- ments are made upon a note, or other contract, by virtue of which interest is payable annually (336), they should be applied in the following order to the payment of 1. Any simple interest that may have accrued upon the annual interest. 2. The annual interest. 3. The principal. 378. EULE. Find the interest due upon the principal and the annual interest at the annual rest (the time when the annual interest becomes due from year to year) next after the first payment. To the payment or payments made before this rest, add interest from the dates when they were inade to the date of the rest, unless there is no interest due upon the principal, excepting that which is accruing during the year in whicli the payment or pay- ments were made, and the payments together are less than the interest thus accruing, in which last case no interest is to be added to the payments. Deduct the payment or payments, with or ivithout interest, as aforesaid, from the amount of principal, annual interest, and simple interest upon the annual interest due at the time of said rest, if such payment or payments equal or exceed the annual and simple interest then due ; if less than such annual and simple interest, but greater than the simple interest due upon the annual interest, deduct the same from the sum of the annual and simple interest, and upon the balance of such annual interest find simple interest to the time ivhen the next payment or payments are applied ; if less than the simple interest due upon the annual interest, deduct the same from such simple interest and add the balance ivithout interest to the other interest due at the time luhen the next payment or payments are applied. Proceed in like manner to the time of the first annual rest following the next payment, and to the end of the time required. * From Report of State Superintendent of Public Instruction (1877). 11 162 INTERE ST. EXAMPLES. 379. 1. According to the law of New Hampshire, how much is due Jan. 1, 1886, on a note dated Jan. 1, 1880, for $2000, with interest annually at 6%, the following payments having been made : July 1, 1882, $500 ; Oct. 1, 1883, $50. OPERATION. First annual interest due Jan. 1, 1881, $120 + 2 yr. simple interest thereon, $14.40 Second annual interest due Jan. 1, 1882, $120 + 1 yr. simple interest thereon, $7.20 Third annual interest due Jan. 1, 1883, Principal $134.40 127.20 120.00 2000.00 $2381.60 $500 15 First payment, July 1, 1882, .... Interest thereon from July 1, 1882, to Jan. 1, 1883, Balance of principal due Jan. 1, 1883, Fourth annual interest of $1866.60, due Jan. 1, 1884, Second payment, Oct. 1, 1883 (being less than the interest accruing during the year, it does not draw interest) .... Balance of fourth annual interest unpaid Fifth annual interest of $1866.60, due Jan. 1, 1885, Sixth annual interest of $1866.60, due Jan. 1, 1886, Simple interest on unpaid balance of fourth annual int. for 2 yr. . Simple interest on fifth annual interest for 1 year .... Balance of principal Amount due Jan. 1, 515.00 1866.60 112.00 50.00 62.00 112 112 7.44 6.72 1&J8.60 2166.76 2-10. Solve Examples 2-10, Art. 365, according to the New Hampshire Rule, at the legal rate (298), supposing each note to contain the words " with interest annually." VERMONT RULE. 38O, The Vermont Rule for notes with interest is essentially the same as the United States Rule (364) ; and for notes " with interest annually," it is the same as the New Hampshire Rule, except that when payments -are made on account of interest accru- ing but not yet due, they draw interest from the date they were made to the annual rest, whether they are greater or not than the interest accruing during the year. Thus, by the Vermont Rule, the payment of $50, in the above example, would draw interest from Oct. 1, 1883 to Jan. 1, 1884, or 3 months. The unpaid balance of fourth annual interest would be $61.25 ($112 $50.75). RATIO AND PROPORTION. D EFINITION S. 381. Ratio is the relation of two numbers as expressed by the quotient of the first divided by the second. Thus the ratio of 6 to 3 is 6-r-S, or 2. 1. There is no ratio between quantities of different kinds ; as 6 bu. and 3/. But a ratio exists between quantities of the same kind though of differ- ent denominations ; as 6 ft. and 8 in. To express the ratio in such cases, the quantities must first be reduced to the same denomination. Thus, the ratio of 6 ft to 8 in. is 72 in.-r-S in., or 9. 2. The ratio between two numbers is denoted by placing a colon (the sign of division without the horizontal line) between them. Thus, the ratio of G to 3 is expressed 6 : 3. 382. The numbers whose ratio is expressed are the terms of the ratio. The two terms of a ratio form a couplet, the first of which is the antecedent, and the second, the consequent. 383. Proportion is an equality of ratios. The ratio of 6 yd. to 3 yd. is 2, and the ratio of $24 to $12 is 2 ; hence from the two equal ratios the following proportion can be formed 6 yd. : 3 yd. $24 : $12. This expression is read, " The ratio of 6 yd. to 3 yd. equals the ratio of $24 to $12." In place of the sign of equality (=), four dots (: :) are generally used ; thus, 6 yd. : 3 yd. : : $24 : $12. The expression is also read, "6yd. is to 3 yd. as $24 is to $12." 384. The first and fourth terms of a proportion are called the extremes ; and the second and third, the means. 385. PRINCIPLES. 1. Tlie product of the means is equal to the product of the extremes. 2. A missing mean may be found by dividing the product of tlie extremes by the given mean. 164 RATIO AND PROPORTION. 3. A missing extreme may be found by dividing the product of the means by the given extreme. 386. To solve examples by proportion. Ex. If 24 hats cost $27, what will 32 hats cost ? ANALYSIS. For convenience, make the fourth term the missing term, or the required answer. Since the third and fourth terms must be of the same denomination and the denomination of the answer will be dollars, take $27 as the third term. From the nature of the example, the answer will be more than $27, the third term, therefore make 32 hats the second term, and 24 hats the first term. The proportion will then be stated as follows : 24 hats : 32 hats : : $27 : x (Let x represent the unknown term). Multiplying 32 by 27, and dividing the product by 24, the fourth or missing term will be $36. 387. RULE. For convenience,, take for the third term the number that may form a ratio with, or is of the same denomination as, the answer. If from the nature of the example, the answer is to be greater than the third term, make the greater of the two remaining terms (which must be of the same denomination) the second term ; when not, make the smaller the second term. Then multiply the means (the second and third) together, and divide their product by the given extreme (the first term). NOTE. After the example is stated, any factor of the given extreme may be cancelled with an equal factor of either of the means. EXAMPLES. 388. Find the missing term (represented by x) in each of the following proportions (See Principles, Art. 385) : 1. 16 : x :: 24 : 18. 5. $48 : $75 : : $32 : x. 2. x : 27 : : 18 : 54. 6. $375 : $144 : : 625 Ib. : x. 3. 32 : 27 : : x : 135. 7. $1728 : $288 : : $666 : x. 4. 24 bu. : 32 bu. : : $27 : x. 8. 144 yd. : 175 yd. : : $18 : x. 9. If 19 yd. of silk cost $28.50, what will 37 yd. cost? 10. If 64 yd. of carpet 36 in. wide will cover a floor, how many yards 27 in. wide will be required to cover the same floor ? 11. A cane 3ft. 3 in. high casts a shadow tyft. long; how long a shadow is cast by the steeple of a church which is 234 feet high? RATIO AND PROPORTION. 165 12. If the freight of a long ton (172, 3) is 70 shillings, what is the freight of 16375 pounds? 13. The net assets of a bankrupt are $27675, and the liabilities $138375. How much must be paid to Mr. A, whom he owes $4800? 14. A building is insured in several companies for $28000. During a fire the building is damaged to the amount of $13500. What is the loss of company A, whose risk is $5000 ? 15. A invests in business $8450, and B $7200, and the gain or loss is divided according to the investments. What is each part- ner's share of gain, the total gain being $3474.30? 16. The U. S. gold dollar (181, 183) contains 23.22 (25.8 A) grains of pure gold, and the standard silver dollar 371.25 (412.5 iV ) grains of pure silver. What is the relative value of pure gold to pure silver ? 17. The assessed value of the property of a certain town is $325000, and the total tax is $10238. How much is the tax of Mr. A, whose property is valued at $5700 ? 18. A bankrupt whose assets were $43225, pays 44 cents on a dollar ; what did his debts amount to ? 19. A cask holds 45 English (167) gallons ; how many Amer- ican gallons will it hold ? 20. A company with a capital of $250000 divides $8750 among its stockholders. How much will be received by a stockholder who owns 36 100-dollar shares? 21. If a long ton of coal is worth $4.25, what is the value of a short ton ? 22. If a farm valued at $4500 is taxed $26.24, what should be the tax on property valued at $23500 ? 23. If a man can walk a mile in 10 minutes, in what time can he walk a kilometer ? 24. A piece of land 40 rods long and 4 rods wide contains an acre ; what is the breadth of a piece 32 rods long, that is equiva- lent to an acre ? 25. A merchant gains $625 by selling $12000 worth of goods ; what amount must he sell to gain $8000 ? 26. Find the value of 6 T. (2240 lb.) 7 cwt. 2 qr. 20 Ib. of iron at 85s. per ton. 27. How many feet of boards will be required for a fence 764 feet long, if 888 feet of boards are required for 288 feet ? INSURANCE. DEFINITIONS. 389. Insurance is a contract by which one party (The Insurer or Underwriter) engages for a stipulated consideration (The Premium) to make up a loss which another may sustain. Insurance is effected on property against loss or damage by fire and water, and on lives of persons. (For Life Insurance, see Art. 524:.) Insurance is also effected against accidents to persons, the breakage of plate-glass, the loss of live stock, and the dishonesty of employees. 390. An Insurance Company is a company or corporation which insures against loss or damage. Insurance companies usually make a specialty of a certain kind of insur- ance, as Fire, Marine, Life, Accident, etc. Certain companies combine Fire and Marine Insurance, while some of the large English companies have Fire, Marine, and Life departments. 391. Insurance companies may be classified according to prin- ciples of organization as follows: 1, Stock; 2, Mutual; 3, Mixed, or Stock and Mutual. Of the 188 Fire (126), Fire-Marine (49), and Marine (13) insurance com- panies doing business in the State of New York in 1879, 165 were Stock, 11 Mixed (Stock and Mutual), and 12 purely Mutual. Their net assets, Dec. 81, 1879, were $150,600,689 ; amount of risks in force, $6,997,419,444. The above does not include many town and county co-operative insurance companies. 392. A Stock Insurance Company is one in which the capital is owned by individuals, called stockholders. They alone share the profits and are liable for the losses. INSURANCE. 167 The business of a stock company and also of a mixed company, is managed by directors chosen by the stockholders. No policyholder, unless a stock- holder, has any voice in any way in the election of the officers, or in the management of its business. 393. A Mutual Insurance Company is one in which there are no stockholders, and the profits and losses are shared among those who are insured (the policyholders). Non-participating policies, the holders of which do not share in the profits or losses, are issued by certain mutual and mixed companies. 394. A Mixed Insurance Company is one which is con- ducted upon a combination of the stock and mutual plan. Usually in a mixed company, all profits above a limited dividend to the stockholders are divided among the participating policyholders. 395. The Policy is the written contract between the Insur- ance Company (the Insurer or Underwriter) and the Insured. It contains a description of the property insured, the amount of the insurance, and the conditions under which the policy is issued, etc. 396. The Premium is the amount paid for the insurance. 1. Premium rates are expressed by giving the cost in cents of $100 insur- ance. The rate is sometimes expressed as a certain per cent, of the amount of the risk. Thus, a rate of 75 cents per $100 is equivalent to \%. 2. The premium rates depend upon the nature of the risk, and the length of time for which the policy is issued. 8. A fee of $1, or $1.25, is sometimes charged for the policy in addition to the premium. 397. An Insurance Agent is a person who represents an insurance company or several companies, and acts for them in soliciting business, collecting premiums, adjusting losses, etc. 398. An Insurance Broker is a person who effects insur- ance, for negotiating which he receives a commission or brokerage from the company taking the risk. Brokers are regarded as agents of the insured, and not of the insurance company. 399. The Surplus of an insurance company is the excess of the assets over the liabilities (including capital and unearned premium). 168 INSURANCE. FIRE INSURANCE. 400. Fire Insurance refers to insurance against loss or damage by fire. Fire policies are usually issued for periods of from 1 to 5 years. Certain companies issue policies for longer periods. Of the outstanding risks of the largest insurance company of New York, Dec. 31, 1879, about 50 % were for 1 year or less, 2% for 2 years, 2S% for 3 years, 4^ for 4 years, and 16$ for 5 years. 401. Adjustment of Losses. In an ordinary fire insur- ance policy, a person who insures will be paid the extent of his loss up to the amount of his insurance ; but in policies contain- ing the "average clause," the payment is such proportion of the loss as the amount of the insurance bears to the total value of the property. 1. The following is the usual form of the "average clause" above referred to : " It is a condition of this insurance, that if the whole value of the above described property, contained in any or all of the above mentioned buildings and premises, shall exceed the whole amount of insurance thereon, then, in case of loss or damage by fire, this policy shall contribute to the payment of said loss or damage in the proportion only that the whole amount of insurance on said property shall bear to the whole value of said property, in all of said buildings, at the time said loss or damage may occur." 2. Under a policy containing the " average clause," a person who insures $5000 on property worth $10000, would receive only $2500 in case of an actual loss of $5000 ; $1500 in a loss of $3000 ; $4000 in a loss of 3. Insurance companies usually reserve the privilege of replacing or repairing the damaged premises. 402. A Floating Policy is one which covers property stored in several buildings or places. The name is applied more particu- larly to policies which cover goods whose location may be changed in process of manufacture or in the ordinary course of business. The "average clause" is a usual condition of policies of this class. 403. Short Rates are rates for a term less than a year. If an insurance policy is terminated at the request of the policy holder, the company retains the customary " short rates " for the time the policy has been in force ; if terminated at the option of the company, a ratable propor- tion of the premium is refunded for the unexpired term of the policy. MARINE INSURANCE. 169 MARINE INSURANCE. 404. Marine Insurance refers to insurance of vessels and their cargoes against the dangers of navigation. 1. Inland and Transit Insurance refer to insurance of merchandise while being transported from place to place either by rail or water routes, or both. 2. Policies on cargoes are issued for a certain voyage, or from port to port, and on vessels for a specified time or for a certain voyage. 3. The particular average clause is the clause which exempts the insur- ance company from the payment of any partial loss or particular average, unless it exceeds a certain per cent, of the value of the property. The particular average clause is sometimes applied to the value of each parcel or series of parcels, according to invoice numbers. 4. Insurance Certificates, showing that certain property has been insured, and stating the amount of the insurance and the name of the party abroad who is authorized to make the settlement, are issued by marine companies. They are negotiable, and are usually sent to the consignee of the merchandise to make the loss payable at the port of destination, and to otherwise facilitate the adjustment of the insurance in case of loss. 405. Adjustment of Losses. In marine insurance, in case of loss or damage, the insurance company contributes such proportion of the loss as the amount of the insurance bears to the total value of the property. 1. The adjustment of marine policies in case of loss is on the same principle as the adjustment of fire policies containing the "average clause " (401, 1). 2. In the adjustment of marine losses, the pound sterling is usually estimated at $4.95. 406. An Open Policy is one upon which additional insur- ances may be entered at different times. It covers merchandise which may be shipped on "Vessel or Vessels" from "Ports and * Places" to "Ports and Places/' for amounts "as endorsed "and at rates "as agreed." 1. The date of the shipment, name of vessel, ports of shipment and destination, the amount of the insurance, rate, premium, and a description of the property are entered on the policy or in a pass-book, which is regarded as part of the policy. (See Ex. 29, Art. 4O7.) 2. Open policies with pass-books attached and insuring merchandise against loss or dainags by fire, are issued by fire insurance companies. 170 INSURANCE. 3. Open policies, which cover all risks whether accepted and endorsed on the policy or not, are issued to merchants who are receiving merchandise from foreign countries, and who do not always have a definite knowledge of the time and mode of shipment. Such policies usually contain the following clause : " The company are to be entitled to premiums at their usual rates on all shipments reported or not. It is warranted by the assured to report every shipment on the day of receiving advice thereof, or as soon thereafter as practicable, when the rate of premium shall be fixed by the President or Vice- President of the Company. " The above policies cover the invoice cost and 10% additional until the amount of the risk is endorsed on the policy or pass-book. 4. Open policies are sometimes issued which cover only such risks as may be accepted and endorsed on the policy by the company. EXAMPLES. 4O7. I. A building was insured for $2500 in one company at and for $5000 in another company at 125 cents. What was the total premium paid? 2. A cargo of goods was insured for $9000 at \%. What was the cost of the insurance, $1.25 being charged for the policy ? 3. What is the total premium of the following insurances : $5000 at \\% for 2 years, $7000 at 450 for 5 years, $1500 at \% for 4 years, $2000 at 5% for 7 years, $3500 at 450 for 1 year, $2000 at 700 for 4 years, $4000 at \\% for 5 years, $2000 at 600 for 4 years, $4500 at 250 for 2 years, $3600 at 1250 for 1 year, and $3000 at 240^ for 4 years ? 4. $20 were paid for an insurance of $2500 ; what was the premium rate ? 5. $25.20 were paid for an insurance at the rate of 700 per $100. What was the amount of the risk ? 6. A factory was insured for $7500 for 1 year at 2-j% stock for $2500 at 2%, and raw material for $2500 at l%%. What was the total premium ? 7. What is the cost of insuring a house for $5000 at the rate of 45^ per $100 ? 8. A cargo of merchandise was insured for $6500 at \%, includ- ing the risk of fire while on wharf awaiting shipment. What was the premium? 9. A building was insured Jan. 1, 1880, for $2000, for 7 years, at 5% ; what was the value of the unearned premium, Jan. 1, 1882? EXAMPLES. 171 10. A shipment of goods was insured in the Pacific Mutual Insurance Co. for $9600 at 750 less 20% in lieu of scrip and inter- est. What was the net cost of the insurance ? 11. A house was insured for $5000 for 4 years at 600 per annum. The house was destroyed by fire. What was the actual loss of the company, making no allowance for interest ? 12. Suppose the above house was worth $8000. What was the actual loss of the owners ? 13. A cargo of hides from Montevideo to New York having increased in value since the insurance was effected, the anticipated profits were insured for $3000 at If % less 20%. What was the premium ? 14. A factory (worth $3000) and its contents are insured for $10000 as follows : $2000 on building, $3000 on machinery (worth $5000), and $5000 on stock (worth $8000). The building is damaged by fire to the amount of $1000, the machinery $4000, and stock is a total loss. How much is the claim against the insurance company ? 15. A cargo of goods valued at $20000 was insured for $12000. If the goods were damaged to the amount of $15000, how much of the loss would be paid by the insurance company ? (Art. 4O5.) 16. A building is insured in several companies for $60000, and is damaged by fire to the extent of $24000. What per cent, of its risk is paid by each company ? 17. A stock of goods was insured, May 1, for 1 year, for $6000, at 90^. The policy was cancelled Nov. 1, at the request of the insured. How much was the return premium, the short rate for 6 months being 630 ? How much would have been returned by the company, if the policy had been cancelled at its request ? 18. A quantity of merchandise valued at $6000 is insured for $5000. It is damaged by fire to the amount of $1728. How much of the loss is paid by the insurance company, the policy containing the "average clause" (4O1)? 19. What was paid for insuring a cargo of merchandise for $8750 at \% less 20% ? 20. A marine rate of %% for a voyage of 10 days is equivalent to what rate per annum ? 21. What were the average net assets for every $100 insured of the F. F.-M., and M. Ins. Cos., doing business in the State of New York in 1879 ? (See Art. 391, Note.) 172 INSURANCE. 22. A factory and its contents are insured for $5000 in com- pany M, $5000 in N, $5000 in 0, $4000 in P, and $2500 in each of the following companies : Q, K, S, T, II, V, W, X, Y, and Z. What was the total premium, the rate being 2^ less 10$ ? 23. The above insurance covered the following property : $4000 on building marked A on plan, $4000 on B, $5000 on C, $500 on D, $500 on E, $3500 on stock and materials in building marked A on plan, $8000 on machinery, etc., in A, $11500 on stock and materials in B and C, $4000 on machinery, etc., in B and C, $2500 on horses in D, $500 on harness, hay, feed, etc., in D. Suppose building A and its contents were totally destroyed by fire, what would be the loss of company M ? Of P ? Of T ? NOTE. The above insurance was divided pro rata among the several companies, each policy designating the exact amount on each building, etc. 24. In the above example, what is the amount of the risk of company M on the building marked A on plan ? On C ? 25. The net invoice value of a quantity of goods is $6325, and the insured value $6500. The insured value is what per cent, greater than the invoice value? 26. A quantity of merchandise valued at $9035, is insured for $9000. What is the insurance on part of the same, the estimated value being $2638 ? 27. If 500 packages of merchandise are insured for $2627.78, what is the insurance on 60 packages ? 28. The estimated sound value of a quantity of merchandise, damaged at sea, was $328.55, and the proceeds when sold at auc- tion, $299.35. How much of the loss was shared by the Insurance Co., the insurance having been $315.33 ? 29. Make the extensions of the following "open policy" and find the total amount. Date. Name of vessel. From. To. On. 1^ Rate. ~Ha f\5 |oS 1881. Sept. 2 Othello. N. Y. via Hull. Stockholm. 50Ba.Mdse. 5100 H ** 4 *# " 7 Algeria. New York. Liverpool. 68 " 6675 * s-^** ." 16 Germanic. New York. Liverpool. 92 " 13500 i *# > ** " 17 Rialto. N. Y. via Hull. Christiania. 6 " 600 i H-^ " 23 Otranto. N.Y. via Hull. Orebro. 30 " 2700 T,PSS < H >,n# #* ** $*## *# #* #* EXAMPLES. 173 30. Claim of Shultz, South wick & Co., for partial loss on mer- chandise, per "Lessing," from New York to Hamburg, Feb. 24, 1882. Insured value of cargo . . ' . $10000 Net invoice value 9696 Advance . *** = ****%. Marks and Num- bers. No. of pkgs shipped. Invoice weight Invoice value. No. of damaged. Propor- tional invoice weight. Propor- tional invoice value. Advance at *.**"% Insured value of damaged. Sound wt., Germ. Ibs.t H R 251 550 9497 28^ 233 4023 1146.55 3621 2 150 3357 28 46 1029 293.26 927 3 275 4702 27| 118 2018 554.95 1817 # * # * # # # * 2001 1071 $5137.03 &***_** $****.** 16792 Sound weight 16792 Ibs. -223 Iba. (Tare) =***** tts. @ 1.35 Rm.=Rm. Less discount 1 % . . . . Sound value, . . . Rm? Gross proceeds at auction . Loss ...... Rm. ******* ***** ******* 14729.81 **** Loss = **.**% of sound value. Insured value of damaged $****. ** Charges, . . . Rm. 201.32 Inspection .... 185.44 Agents' fees, . . . 22_3__ Rm. ***** @ 24* = Total claim . $***. 31. The total paid-up capital of the joint-stock fire and fire- marine companies doing business in the State of New York (excepting foreign companies), Dec. 31, 1879, was $50,992,220, and the surplus $34,998,146. The total surplus was what per cent, of the total capital ? 82. The above companies, with the exception of the New York Mutuals (6), during the year 1879, received $69,657,129 in gross premiums for insuring $7,991,450,000. What was the average premium for every $100 insured ? 33. Dec. 31, 1879, the capital stock of the Insurance Co. of N. A., Philadelphia, Pa., was 12,000,000; surplus, $2,338' 378 ; dividend paid during 1879, $400,000. The surplus is what per cent, of the capital stock ? The dividend is what per cent, of the capital, and of the capital and surplus ? t Sae Art. 243. EXCHANGE. DEFINITIONS. 408. Exchange is the system by which merchants in distant places discharge their debts to each other without the transmission of money. Suppose, for example, A of New York owes B of Chicago $1000 for grain, and C of Chicago owes D of New York $1000 for dry goods. The two debts may be discharged by means of one draft or bill of exchange without the transmission of money. Thus, B of Chicago draws on A of New York for $1000, and sells the draft to C of Chicago who remits it to D of New York. D of New York presents the draft to A of New York for acceptance or pay- ment, and thus both debts are cancelled. There is in effect a sstting-off or exchange of one debt for the other. The business of exchange is usually conducted through the medium of banks and bankers, who buy commercial bills and transmit them for credit to the places on which they are drawn. They also sell their own drafts on their correspondents in any amounts demanded. 409. A Bill of Exchange, or Draft, is an order or request addressed by one person (the Drawer) to another (the Drawee), directing the payment of a specified sum of money to a third person (the Payee) or to his order. It is issued at one place and payable at another. (See Art. 352, 5-6.) For brevity, bills of exchange are frequently called " exchange." According to the laws cf most States, drafts drawn in one State and pay- able in another, are termed foreign bills of exchange. For the purposes of this book, the term " domestic exchange " will be applied to bills drawn and payable in the United States. 410. Bills of exchange are of two kinds, Inland or Domestic, and Foreign. 411. A Domestic or Inland Bill of Exchange is one which is payable in the same, country in which it is drawn. DOMESTIC EXCHANGE. 175 412. A Foreign Bill of Exchange is one which is payable in a different country from the one in which it is drawn ; as a draft drawn in the United States and payable in England. 413. When drafts sell for more than their face value, exchange is above par or at a premium ; when for less than their face, below par or at a discount. When Chicago owes New York the same amount that New York owes Chicago, exchange will be at par ; that is, drafts will sell at their face value. When Chicago owes New York more than New York owes Chicago, drafts on New York will sell at a premium ; there will be more buyers of exchange than sellers, and drafts will sell for more than their face value. When Chicago owes New York less than New York owes Chicago, the demand in Chicago for drafts on New York will be less than the supply, and drafts will sell for less than their face value, or at a discount. DOMESTIC EXCHANGE. 414. Domestic or Inland Exchange relates to drafts drawn at one place on another in the same country. 415. The domestic exchanges on New York at the places named were quoted as follows, May 7, 1881 : Savannah, -J- @ -f premium; Charleston, -J @ premium; New Orleans, $1.50 @ $2.50 premium; St. Louis, 25 cents premium ; Chicago, 50 @ 75 cents premium ; and Boston, 25 cents discount. 1. At Savannah and Charleston the rates per cent, of the premium or discount are given. Thus, when exchange is quoted at premium, a draft of $100 may be purchased for $100^ ($100.25). 2. At New Orleans, St. Louis, Chicago, and Boston, the premium or dis- count per $1000 is given. Thus, a draft of $1000 at $2.50 premium may be purchased for $1002.50. $2.50 per $1000 premium is equivalent to \% premium. 3. The selling rates are about \% ($1.25) higher than the buying rates, and bankers' exchange is usually higher than commercial. 4. The rate of domestic exchange is limited by the cost of shipping gold or currency by express, and the premium or discount will not exceed this cost. Thus, if a merchant in Chicago is charged a premium of $10 for a draft of $10000, and he can send the currency by express for $7.50, it will be to his advantage to remit by the latter method. The following appeared in a New York financial paper, May 8, 1881, the date of the above quotations: "The domestic exchanges at the West are sufficiently high to permit of a movement of funds Eastward, but at the East, 176 EXCHANGE. New York funds are still at a discount and some shipments of gold and currency continue to be made to the Eastern cities." 5. The preceding quotations refer to sight exchange. Time drafts are dis- counted in the same manner as promissory notes. In certain cases bankers in discounting notes and drafts payable in distant places, charge interest for the time required for the return of the money when the note or draft is paid ; and in the case of drafts drawn a certain number of days after sight, bankers sometimes charge interest for the time required for the acceptance of the drafts. Thus, if a draft was drawn in New York on St. Louis and payable CO days after sight, it would require, in the ordinary course of the mails, 3 days for the acceptance of the draft. The draft would be paid in 63 days (including the days of grace), and 3 days would elapse before the money would be returned to New York. The banker would be justified in charging interest for 69 days, the interval between the day he advanced the money in New York, and the day it was returned to him again. If the draft was drawn on San Francisco, fully 19 days (8 days for the acceptance, 3 days of grace, and 8 days for the return of the money) would be added to the time of the draft. Between New York and San Francisco and other distant places, money is frequently transferred by telegraph. EXAMPLES. 416. 1. What is the value in Savannah of a draft on New York for $8750 at \% premium ? 2. Find the cost in New Orleans of a draft on New York for $8375 at $2.50 premium. Find the value of the following drafts : Face. Exchange. Face. Exchange. S. $5000, \% premium. .$4287.75, 15? discount. 4. $4375, \% discount. 9. $3416.33, 25^ premium. 5. $8417, $$ premium. 10. $2825.49, $1.25 discount. 6. $9873, |% premium. 11. $9873.62, $2.50 premium. 7. $5284, % discount. ^.$8412.75, 75^ discount. 13. A of Chicago buys cattle for B of New York to the amount of $9858.07. How large a draft should be drawn on B, so that when sold at a discount of 50^ (-fa%) 9 the proceeds would be sufficient to pay the bill ? NOTE. To find the face of a draft, instead of dividing the value of the draft by the rate of exchange (in the above example, .99|g- or .9995), business men and bankers calculate the premium or discount on the value of the draft, and subtract or add it to the value as the case requires. Thus, in the above example, the discount would be * of T V% of $9858.07, or $4.93, which added to the given proceeds would produce the face $9863. This method produces too small a result in all cases, the error being equivalent to the percentage of the premium or discount. In this example the error is less than cent. DOMESTIC EXCHAN G E. 177 For ordinary examples in business, the foregoing method is sufficiently accurate. At \ % , or $5.00 (a very high rate for domestic exchange) on a draft whose value is $10000, the error would be only 25 cents. If greater accuracy is required, the necessary correction can be made by adding the percentage of the premium or discount. Thus, if the value of the draft is $10000, and exchange is \% discount, the face would be $10000 + $50 (\% of $10000) f $0.25 (\% of $50) $10050.25. If at \% premium, the face would be $10000 - $50 + $0.25 = $9950.25. By the above method, find the face of the following drafts : Value. Exchange. Value. Exchange. 34. $1876.16, \% premium. 19. $7375, 250 premium. . 15. $2437.75, ^discount. 0. $9218, 500 discount. 16. $3342.38, \% discount. 21. $6438, $1.00 premium. 17. $2238.42, -J^ premium. 22. $9243, $1.25 premium. 18. $8175.50, \% premium. 28. $5280. 750 discount. 24. A of New Orleans being indebted to B of New York $9316.75, forwards to him a check on a New Orleans bank for that amount, to cash which B is obliged to allow a discount of %%. How much does A still owe B, and for what amount should the check have been drawn to net B the amount due ? 25. What is the value of a draft on New York for $3000, payable in 60 days (63 days) after date (353, 8), exchange being J% premium, and interest 6$? NOTE. From the face of the draft, subtract the interest, and to the result add the exchange. 26. Find the proceeds of a draft drawn at Chicago on New York for $12000, and payable 90 days after sight, exchange 500 discount, interest 5%, and allowing 3 days additional for the acceptance of the draft. 27. A banker in New York discounts a draft for $8000, pay- able in San Francisco 60 days after sight ; what would be the proceeds, exchange being \% discount, interest 6$, and allowing 8 days for the acceptance and 8 days for the return of the money ? 28. A merchant paid $6920.64 in Charleston for a sight draft of $6912 ; what was the rate of exchange ? 29. A commission merchant sold 13475 pounds of leather at 26f cents a pound. If his commission is 5%, and exchange \% premium, how large a draft can he buy to remit to the consignor ? SO. How large a 60-days' draft must I draw, so that when sold it will produce. $10000, exchange \% discount, interest 12 178 EXCHANGE. FOREIGN EXCHANGE. 417. Foreign Exchange relates to drafts or bills of exchange drawn in one country and payable in another. Foreign bills of exchange are usually drawn in the moneys of account of the countries in which they are payable. Thus, drafts on England are usually drawn in pounds, shillings, and pence ; on France, Belgium and Switzerland, in francs ; on Germany, in marks ; on the Netherlands (Holland), in guilders. Foreign bills of exchange are usually drawn at sight (3 days) or at sixty (63 days) days' sight. Sight drafts are frequently called "short" exchange, and 60 day drafts, " long" exchange. "Long" exchange is sold at a rate below that for " short " exchange, sufficient to equalize the difference in interest between the dates of maturity of the two classes of bills. 418. To secure safety and speed in the transmission of foreign bills of exchange, they are drawn in sets of two or three of the same tenor and date. The separate bills are sent by different steamers, and when any one of them is paid, the others become void. Some merchants send only the first and second, and pre- serve the third. SET OF EXCHANGE. EXCHANGE FOR 1000. NEW YORK, May 16, 1882. Sixty days after sight of this FIRST of Exchange (Second and Third unpaid), pay to the order of A. T. STEWART & Co., One Thousand Pounds Sterling, value received, and charge the same to account of No. 1738. BROWN BROTHERS & Co. To BROWN, SHIPLEY & Co., London, England. (2.) EXCHANGE FOR 1000. NEW YORK, May 16, 1882. Sixty days after sight of this SECOND of Exchange (First and Third unpaid), pay to the order of A. T. STEWART & Co., One Thousand Pounds Sterling, value received, and charge the same to account of No. 1738. BROWN BROTHERS & Co. To BROWN, SHIPLEY & Co., ) London, England. J FOREIGN EXCHANGE. 179 (3.) EXCHANGE FOB 1000. NEW YORK, May 16, 1882. Sixty days after sight of this THIED of Exchange (First and Second unpaid), pay to the order of A. T. STEWART & Co., One Thousand Pounds Sterling, value received, and charge the same to account of No. 1738. BROW^ BROTHERS & Co. To BROW^, SHIPLEY & Co., j London, England. j 419. A Letter of Credit is an instrument issued by a banker and addressed to bankers generally, by which the holder may draw funds at different places and in amounts to suit his con- venience, the total amount drawn not exceeding the limit of the letter of credit. A bill of exchange is payable at a certain place, at a certain fixed time, and for a certain amount, while a letter of credit is payable at different places, at different times, and in different amounts. A person, who intends to travel in foreign countries, may procure a letter of credit by depositing either cash or securities with a foreign exchange banker for the amount of the letter. When the American banker is notified of the payment of the traveler's drafts in London, he debits the account of the holder of the letter of credit with the amount drawn and the charges, at the current rate of exchange. A small rate of interest is allowed on the account, and a settlement is made on the return of the traveler. If a person has business connections, he may avoid making a deposit by having some commercial firm sign a bond as security. By this method, when the New York banker is notified of the payment of the traveler's draft in London, he immediately draws a sight draft (42O) for the amount and the charges (42O) on the traveler's representative, and no account is kept with the traveler on the books of the banker. In this case, a settlement is made with the commercial house on the return of the traveler. The holder of a letter of credit desiring funds, presents it to a banker at the place he may be visiting. The banker will prepare a sight draft, which the holder of the letter will sign, on the London banker mentioned in the letter of credit. If the signature on the draft and on the letter of credit correspond, the draft will be cashed by the banker at the current rate of exchange. The bankers who cash the drafts of the holder of the letter, write the date of pay- ment, their names, and the amounts drawn (in words and figures), on the back of the letter of credit. When the London banker pays the drafts, he immediately notifies the American banker (the issuer of the letter of credit). The foreign bankers mentioned as correspondents in a Letter of Credit are bound to honor the drafts of the holder ; but other banks and agencies where the parties are known, are also free to respond. 180 EXCHANGE. BROWN BROTHERS & Co/s CIRCULAR LETTER OF CREDIT. T No. B 1450G. NEW YoRK) June ^ I881f GENTLEMEN : We request that you will have the goodness to furnish ME. EUGENE HORTON, the bearer, whose signature is at foot, with any funds he may require to the extent of 1000 (say One Thousand Pounds Sterling), against his drafts upon MESSRS. BROWN, SHIPLEY & Co., London ; each draft must bear the num- T> ler (No. 5 14506) of this letter, and we engage that the same shall meet due honor. Whatever sums MR. HORTON may take up, you will please endorse on the back of this Circular letter, which is to continue in force till June 2, 188*2, from the present date, June 2, 1881. We are respectfully, gentlemen, Your obedient humble servants, BROWN BROTHERS & Co. The Signature of EUGENE HORTON. To MESSRS. THE BANKERS, Mentioned on the third page of this Letter of Credit. 42O. The following draft, drawn by the issuer of the letter of credit on the traveler's American representatives, shows the expense connected therewith : No. 51931. . s. d. Draft dated Lucerne, July 20. 25 Commission @ 1^, .... 5 T> fv 14-^ofi Interest for 33 days @ 5^, . 2 3 25 7 3 NEW YORK, Aug. 11, 1881. EXCHANGE FOR 25 7s. 3d. , at $4^- per = $122^, On demand, pay this FIRST of Exchange (Second unpaid), to our order, the sum of Twenty-five Pounds 7 / 3 Sterling, for value received by MR. EUGENE HORTON. BPOWF BROTHERS & Co. To MESSRS. G. B. HORTON & Co.. | New York. j FOREIGN EXCHANGE. 181 NOTES. 1. The commission is charged only on amounts drawn and not on the face of the letter of credit. 2. The interest charged is calculated to cover the time between the pay- ment of the original draft in London and the maturity of a shortsight remit- tance from New York in reimbursement. 3. Exchange is charged at the current rate of sight exchange on London. 421. The Intrinsic Par of Exchange is the value of the monetary unit of one country expressed in that of another, and is based on the comparative fineness and weight of the coins, as determined by assay. The intrinsic par of exchange between different countries and the United States, is given in Art. 192. 4:22. The Commercial Par of Exchange is the market value in one country of the coins of another. 423. The Commercial Rate of Exchange is the market or buying and selling value in one country of the draffs on another. 1. In giving quotations of foreign exchange, no reference is made to the par value, the quotations being given by means of equivalents. 2. Premium or discount for exchange can not long exceed the transporta- tion charges and insurance of shipping coin ; for, if a merchant can ship gold cheaper than he can buy a bill of exchange, he will choose the former method of paying his indebtedness. When sight exchange is 4.84, gold can be im- ported at a small profit ; and when sight exchange is 4.89|, gold can be exported at a profit. 424. The quotations of foreign exchange, Apr. 20, 1881, were as follows : Where payable. 60 days. Sight. London : Prime bankers' . ... 4 81| 4 84 Good bankers' and prime commercial 4 81 4 83i Documentary commercial 4 78 J 4 8H Cable transfers 4 84 > Paris (francs) 5.27-|- 5.24f 5.27| 5.24- Swiss (francs) 5. 26 J 5.23^ Amsterdam (guilders) . .39| 39J Hambur' (reichsmarks) . . . 93| .941 Frankfort (reichsmarks) . ... 93 .94| Bremen (reichsmarks) .93| 94| Berlin (reichsmarks) .93| 94J 182 EXCHANGE. In the preceding quotations, exchange is below par. (See intrinsic par values below, or in Art. 192.) When exchange is above par, we are exporters of gold ; when below par, we are importers of gold. 425. Exchange on England (Sterling exchange) is quoted by giving the value of 1 in dollars and cents. Thus, when exchange is 4.84, a draft of 1 will cost $4.84 ; of 100, $484. The intrinsic par value of 1 is $4.8665 (192). 426. Exchange on France, Belgium, and Switzerland is quoted by giving the value of $1 in francs and centimes (hun- dredths of a franc). Thus, when exchange is 5.27^, $1 will buy a bill of 5 francs and 27 centimes; a draft of 1000 francs will cost $189.57 (1000 -J- 5.27-|). The intrinsic par value of 1 franc is 19^ cents (192) ; of the equivalent exchange, 5.18| (1.00 -5- .193). In French, Belgian, and Swiss exchange, the higher the apparent rate, the less the value of the draft. Thus, when exchange is 5.13, a draft of 1000 francs is worth $194.93, and each franc is worth 19 T W cents. When exchange is 5.26|, the same draft would be worth $189.98, and each franc 19 cents. 427. Exchange on Amsterdam (Netherlands) is quoted by giving the value of one guilder (gulden) or florin in U. S. cents. The intrinsic par value of 1 guilder is 40 T 2 .45__ ) 8.3160 ( 92 days after July 6, or .0908 Oct. 6, 1882. ANALYSIS. If the account is settled July 6, the assumed date of settle- ment, Mr. R. would be entitled to a discount on the debit side of $16.396, and Mr. S. on the credit side of $8.08; or, Mr. R. would be entitled to a net dis- count of $8.316. If, by paying the balance of the account, July 6, Mr. R. is entitled to a discount of $8.316, it is evident that he should be allowed to defer payment until the balance would produce an equivalent interest, or 92 days. Hence, the true date of settlement is 92 days after July 6, 1882, or Oct. 6, 1882. When the balance of the account and the balance of interest are both due the same party, the equated time is previous to the assumed date of settle- ment ; and, when the balance of the account and the balance of interest are due different parties, the equated time is after the assumed date. 444. In the following operation, the latest due date is assumed as the date of settlement for all the items : Due July 6, Aug. 19, Oct. 5, " 26, 60)5.45 .0908)1.8590 ( 20 days before Oct. 26, or .0908 Oct. 6, 1882. ANALYSIS. If the account is settled Oct. 26, the assumed date of settle- ment, the payer will be obliged to pay $1.859 interest in addition to the balance of the account. Hence, the date when the balance only may be paid without loss to either party must be 20 days before Oct. 26, 1882, or Oct. 6, 1882. Days. OPERATION. Interest. Due Days. Interest $456 112 $8. 512 July 26, $400 92 $6. 133 384 68 4. 352 Aug. 10, 375 77 4. 812 216 21 . 756 Oct. 9, 288 17 . 816 552 . 00 1063 11. 761 1608 13. 620 1063 11. 761 * See Art. 436. EQUATION OF ACCOUNTS, 445. OPERATION. APPROXIMATE INTEREST METHOD.* 201 Dr. Cr. Mo. Days. Credit. Interest. Mo. Days. Credit. Interest. June 6, 1456 30 da. j $2.28 .456 1 July 26, $400 $2.00 1.333 / 3.84 40 " 20, 38460 da. -j 1 28 \ TtV/ 3 75 1 July 5, 216 3 mo. \ ( -L /WO 4.32 .18 11.04 2 Aug. 10, 2 " 10, 375 j 288 60 da. j t/ 4 fJ .625 5.76 .48 1 " 26, 552 3 mo. < 1.84 1063 14.348 ( .552 1608 25.788 1063 14.348 o \ 5.45 2.725) 11.440 (4 mo. 6 da. after May 31 , or 2.725 10.900 Oct. 6. .540 30 2.725)16.200(6 days. EXAM PLES. 446. 1. At what date may the balance of the following account be paid without loss to either party ? Dr. ISAIAH B. PRICE. Or. 1832. 1883. May 16 To Mdse. 437 00 May 23 By Cash. 400 00 " 31 324 00 I June 16 300 00 2. Find the average date of maturity for the balance of the following account : Dr. WILLIAM C. DOUGLAS. Cr. 1881. 1881. Jan. 4 Mdse. 30 da. 516 00 Feb. 1 Cash. . . 500 00 " 28 " 60 da. 325 00 " 1 Note 60 da. 300 00 Feb. 4 " 4 mo. 437 00 * Ses second interest method, Art. 437, and second method, Ex. 14, page 194. 202 EQUATION OF ACCOUNTS. 3. Average the following account : Dr. JOSEPH H. WEIGHT. Or 1882. 1882. Mar. 27 Mdse, 4 mo. 716 48 Apr. 16 Cash. . . 300 Apr. 16 " 60 da. 325 75 May 2 u 400 May 1 " 4 mo. 413 40 July 8 u 500 June 4 " 4 mo. 716 87 4- What is the equated time for the payment of the balance of the following account ? Dr. A in account with B. Or. 1882. Mar. 16 Mdse. 4 mo. 444 57 1882. July 1 Cash. . . 400 " 30 " 60 da. 376 82 " 20 a 375 Apr. 20 " 30 da. 712 19 Aug. 16 tt 700 May 17 4 mo. 628 75 " 30 a 600 " 28 4 mo. 419 31 5. Average the following account. What will be the amount due Jan. 1, 1882 ? Dr. C in account with D. Or. 1881. 1881. June 16 Mdse. 30 da. 517 25 June 16 Note 60 (63) da. 1000 " 28 " 60 da. 487 50 July 30 Cash. . . 375 July 5 " 4 mo. 816 75 Aug. 13 Mdse. 4 mo. 900 " 21 " 6 mo. 924 30 Oct. 5 Cash. . . 500 Aug. 12 " 4 mo. 317 65 6. When will the balance of the following account commence drawing interest ? How much would be due Mar. 1, 1883. Dr. ANDREW CARNEGIE, Pittsburg, Pa. Or. 1882. Sept. 4 Cash 100 1882. Aug. 16 Mdse. 4 mo. 647 13 4 Note 4 mo. 900 " 29 " 4 mo. 322 85 Oct. 31 Cash 250 Sept. 4 " 4 mo. 412 90 Dec. 28 it 600 " 17 " 4 mo. 588 33 " 17 30 da. 246 12 Nov. 4 " 4 mo. 683 45 EQUATION OF ACCOUNTS SALES. 203 7. Find the equated time for the payment of the balance of the following account. Dr. JAMES B. FARWELL, Chicago, 111. Cr. 1881. 1881. Jan. 4 Mdse. 4 mo. 637 20 Mar. 16 Cash. 300 00 " 14 4 mo. 412 87 Apr. 20 u 400 00 " 14 60 da. 214 35 May 3 n 200 00 Mar. 16 " 4 mo. 298 60 3 Note 4 mo. 800 00 " 28 " 30 da. 973 25 8. Average the following account : Dr. ARNOLD, CONSTABLE, & Co. Or. 1882. Apr. 4 Mdse. 4 mo. 426 32 1882. Apr. 25 Cash. 375 " 20 Cash. 387 40 June 30 (4 600 May 13 60 da. 622 39 July 31 Note 60 da. 600 " 27 " 30 da. 584 75 Aug. 15 Cash. 500 July 5 " 4 mo. 224 50 Oct. 31 it 400 " 16 11 4 mo. 838 95 447. To find the equated time for the payment of the net proceeds (282) of an account sales (283). 448. 1. The sales form the credit side of the account, and fhe charges and advances the debit side. 2. The charges for transportation, cartage, and other items paid by the commission merchant are considered due at the time of the payment of the same. 3. The commission and other after-charges of the commission merchant are considered due by some at the average due date of the sales; and by others, at the average date of the sales. Since the commission is so small compared with the gross sales, in many examples, it makes no difference which date the commission is considered due. Certain merchants enter the commission at the date the account sales is rendered, and, by so doing, produce a result sufficiently accurate. 4. Many commission merchants, when the consignments are not separated and numbered, enter the sales and commission only on the account sales (See Ex. 4, Art, 45O), and enter the advances 204 EQUATION OF ACCOUNTS. and the general charges in the account current (See Ex. 6, Art. 458). Accounts ^Vs, when the shipments are continuous, are rendered montnl^tu uhe manufacturers or consignors, and "sketches " weekjty'ur whenever a sale is made. 5. With the exception of finding the date for the commission and other after-charges, the process of averaging an account sales is exactly the same as that of averaging an account both debit and credit items. 449. Ex. What is the equated time for the payment of the net proceeds of the following account sales ? NEW YORK, Dec. 1, 1881. Account sales of Seed For account of WILLIAM STEPHENS & Co. By FRANKLIN EDSON & Co. 1881. Nov. 4 45^- bu. Timothy Seed . 30 da. IHJL 79 53 a 18 50 " Mammoth Cl. Seed 60 da. 9ILO. 450 t( 28 49AA Clover Seed . . Cash. gl-fi. 418 32 947 85 CHARGES. Oct. 31 Transportation 60 00 Dec. 1 Commission 5% as Dec. 22, 1881. ( _47 39 107 39 Net proceeds due Dec. 26, 1881. . . 840 47j ANALYSIS. The average due date of the sales is Dec. 22, 1881, which is taken as the due date for the commission. The account sales to be averaged will now be as follows : Dr. Due Oct. 31, 1881, " Dec. 22, " Or. $60.00 Due Dec. 4, 1881, $79.53 47.39 " Jan. 17, 1882, 450.00 " Nov. 28, 1881, 418.32 By averaging the above, we find the net proceeds, $840.46, are due Dec. 26, 1881. If the commission is considered due Nov. 21, 1881, the average date of the sales, the net proceeds will be due Dec. 28, 1881. NOTE. If the same assumed date, or focal date, be taken in finding the average due date of the sales as in finding the average due date of the net proceeds, the operation of the former will form the credit side of the latter operation. EQUATION OF ACCOUNTS SALES. 205 EXAMPLES. 45O. Find the net proceeds and equated time of the ioilowing accounts sales. (Unless otherwise stated, the commission is con- sidered due at the average due date of the sales.) 1. Sales of 400 bbls. flour received per N. Y. C. & H. R. R. R., for account of A. W. ARCHIBALD, Ottumwa, Iowa. 1881. rwi j_ May 11 125bbls. " Kirkwood " cash, . . 615- #** a 7f ^* tt 12 150 " "Iowa" 4 mo., . gin tt* " 18 125 " "Kirkwood "4 mo., . 7JUL 816' #*# V**i tf CHARGES. May 3 Transportation and Cartage, . . . 425 tt 4 Inspection, iL . 15 tt 18 Storage, 45 . Commission and Guaranty 5%, . . 3S1 II **'* *# E. & 0. E. E. R. LlYERMORE. NEW YORK, May 20, 1881. What would be the equated time for the payment of the above proceeds, if the commission and guaranty were considered due at the average due date of the sales ? At the average date of the sales ? If considered due May 18, the date of the last sale ? 2. Account sales of 900 sides hemlock sole leather by MAS- SET & JAIS^EY, for account of GRANT & HORTON, Ridgway, 1881. Aug. ft Aug. tt E Pi 14 18 21 2 & aiL. Sides. Description. Terms. Weight. Price. ##** 'Mi ##** it it ** #*#* *** ** ** 400 300 200 Tran Inspe Comi Proct 0. E. iDELI "Ridgway" #7 #7 88 CHA sportation $70, ction, 4 mo. 4 mo. 30 da. RGES. Cartag 9407 6875 4712 e$9, . 27 27J #* 9 #*# r & J nission and Guaranty 5$, . . ;eds due , 1881, .... MASSE3 HIA, PA., Aug. 22, 1881. ##** AtfNEY. ftt 206 EQUATION OF ACCOUNTS 3. Find the equated time for the payment of the net proceeds of Ex. 27, Art. 286, supposing that the merchandise was sold for cash, and that the commission was due at the date given. 4. Sales by JAMES TALCOTT, New York, for account of Phenix Mills, Cohoes, N. Y. March 31, Date. Cases. No. Description. Time. Yards. Price. Amount. Mar. 1 2 7619 Fancy Cassimere. 30^0. 966 s 1.35 ****** " 10 4 3475 <( (( 10 da. 1994 1.70 ****** " 13 3 4157 <( (t 30 da. 1506 1 2.30 **** ** " 17 4 6283 ** Less Commission 5%, Proceeds due , 1882, ***** ** *** ** ***** ** 6. Account Sales of merchandise by JOHN F. COOK, for account of Excelsior Packing Co., Cincinnati, Ohio. 1881. Oct. 1C 50 Bbls. Mess Beef, . . Cash. HJJL *** ** (t 24 100 " N. M. Pork, . . 17JLJL **** (f 31 25 " Hams 6376 Ibs., . 10 da. 13^ *** ** Nov. 9 25 " Shoulders 5717 Ibs., 60 da. 9^ *** ** " 18 75 " C. M. Pork, . . 4 mo. 13^ **** ** **** ** CHARGES. Oct. 13 Transportation, 325 k< 15 Cartage, 37 50 15 Cooperage, 15 (( 15 Inspection, 13 75 Nov 18 Storage, 48 75 Commission 5$, *** ** *** ** ~N~ot irpopppfl s fJno Iftftl . **** ** E. & 0. E. JOHN- F. COOK. NEW YORK, N. Y., Nov. 20, 1881. * If the commission is considered due at the average due date of the sales, and since there are no other changes, the net proceeds will be due at the same date. ACCOUNTS CURRENT. DEFINITIONS. 451. An Account Current is an itemized account of the business transactions between two houses, showing the balance or amount due at the current date. The amount due is sometimes called the cash balance. 1. An account current is a transcript of the ledger account with the addition of certain details taken from the books of original entry, and is arranged in a different form. 2. Interest is charged, or not, according to the custom of the business, or the agreement between the parties. This chapter treats only of accounts in which interest is charged. When inter- est is not charged, the balance due is the difference between the two sides of the account as originally entered in the ledger. The interest may be reckoned according to any of the methods of Art. 299. In the illustrative example the exact time in days is found, and the days are regarded as 360ths of a year. In the examples for practice, unless otherwise stated, the interest is reckoned on the same basis. 3. Accounts current are rendered by merchants, bankers, and brokers annually (Ex. 2), semi-annually (Ex. 1), quarterly (Ex.3), or monthly (Ex. 6). Since the interest draws interest after the account is balanced, the oftener the account is balanced, or the interest is added to the account, the greater the amount due. Some merchants render partial accounts current monthly, but do not carry the interest to the main column until the end of the year (Ex. 11). The twelve partial accounts current make, when combined, the complete account current for the whole year. 4> There are three methods in common use for finding the amount due on an account, including interest, at a certain date, all of which are presented in the following illustrative example : 1. By interest ; 2. By products ; 3. By daily balances. 208 ACCOUNTS CURRENT. 4:52. Ex. Find the amount due, including interest at 6$, on the following account Jan. 1, 1882. Dr. GEO. W. CHILDS in account with A. A. Low. Or. 1881. 1881. Oct. 1 Balance. 1800 Oct. 31 Cash. 1000 " 16 Mdse. 30 da. 360 Nov. 16 NoteSOtfa. 600 Nov. 27 30 da. 432 Dec. 4 Cash. 240 Dec. 18 BillofH.O.&Co. 420 " 26 u 300 453. OPERATION. INTEBEST METHOD. Dr. Cr. Due. Amount. Days. Interest. Due. Amount. Days. Interest. Oct. 1, $1800 92 $27. 60 Oct. 31, $1000 62 $10. 33 Nov. 15, 360 47 2. 82 Dec. 19, 600 13 1. 30 Dec. 27, 432 5 . 36 it 4, 240 28 1. 12 K 18, 420 14 . 98 tt 26, 300 6 , 30 $3012 $31. 76 $2140 $13.05 2140 13. 05 872 18.71 = 890.71. ANALYSIS. First find the due date of each item of the account. Each item will draw interest from its due date until the day of settlement, or Jan. 1, 1882. The total interest on the debit side of the account is $31.76, and on the credit side, $13.05. The balance of interest, $18.71, is therefore in favor of the debit side, or is due Mr. Low. Since both the balance of the account ($872) and the balance of interest ($18.71) are due the same party, the net amount due Jan. 1, 1882, is f 872 plus $18.71, or $890.71. If the balance of interest had been on the credit side of the account, the net amount due would have been $872 minus $18.71, or $853.29. NOTES. 1. It will sometimes happen that certain items will fall due after the day of settlement. The interest on such items should be transferred to the opposite side of the account. (See Ex. 8.) 2. If the account has been averaged, the amount due at a given date may be found by calculating the interest on the balance of the account from the time it is due to the date of settlement. If the date of settlement is earlier than the average date, subtract the interest from the balance of the account ; if later than the average date, add the interest. (See Art. 438, Ex. 7, Note.) 3. The interest method is generally used in business. Since it gives the interest on each item and is readily understood, it is more satisfactory to those to whom accounts current are sent than the product method. When interest tables are used, it is shorter than any other method. ACCOUNTS CURRENT. 209 454. The following is a common form of an account current including interest : Dr. GEO. W. CHILDS in % current with A. A. Low. Or. 1881. Days. Interest. Amounts. 1881. Days. Interest. Amounts. Oct. 1 Balance. 92 27.60 1800.00 Oct. 31 Cash. 62 10.33 1000.00 " 16 Mdse. as Nov. 15. 47 2.82 360.00 Nov. 16 Note as Dec. 19. 13 1.30 600.00 Nov. 27 " Dec. 27. 5 .36 432.00 Dec. 4 Cash. 28 1.12 240.00 Dec. 18 BillofH.C. &Co. 14 .98 420.00 " 26 " 6 .30 300.00 1882. 1882. Jan. 1 Bal. of Interest. 18.71 Jan. 1 Bal. of Interest. 18.71 " 1 " " Account. 890.71 1882. 31.76 3030.71 31.76 3030.71 Jan. 1 Balance. 890.71 455. EULE FOR THE INTEREST METHOD. First find the due date of each item of the account. TJien find the inter- est on each item from the date it becomes due to the day of settlement. The difference between the sums of the debit and the credit interest will be the balance of interest. To find the net amount due, ivhen the balance of interest and the balance of items are on the same side, take their sum ; ^vhe^^ on opposite sides, talce their difference. 456. OPERATION:. PRODUCT METHOD. Dr. Or. Due. Am't. Days. Products. Due. Am't. Days Products. Oct. 1, $1800 X 92 = 165600 Oct. 31, $1000 X 62 = 62000 Nov. 15, 360 X 47 = 16920 Dec. 19, 600 X 13 = 7800 Dec. 27, 432 X 5 = 2160 a 4, 240 X 28 = 6720 a 18, 420 X 14 = 5880 a 26, 300 X 6 = 1800 $3012 190560 $2140 78320 2140 78320 $872 + $18.71 = $890.71. 872 6 ) 112240 $18.706 ANALYSIS. By multiplying the number of dollars by the number of days, and taking the sum of the products on each side of the account, we find that the total debit interest is equivalent to the interest of $190560 for 1 day, and the total credit interest to the interest of $78320 for 1 day. The balance of interest is therefore equivalent to the interest of $112340 for 1 day. The interest of $1 for 1 day is $ of a mill (311, 3), and of $112240, 18706 ( of 112240) mills, or $18.71. Since the balance of items ($872) and the balance of interest ($18.71) are both due the same party, the net amount due is their sum, or $890.71. 210 ACCOUNTS CURRENT. 457. OPERATION. BY DAILY BALANCES. Date. Dr. Cr. Dr. Balances. Days. Dr. Products. Oct. 1 1800 1800 30 54000 " 31 1000 800 15 12000 Nov. 15 360 1160 19 22J040 Dec. 4 240 920 14 12880 " 18 420 1340 1 1340 " 19 600 740 7 5180 " 26 300 440 1 440 27 432 872 5 4360 3012 2140 92 6 ) 112240 2140 872 + 18.71 = 890.71. 18.706 ANALYSIS. Arrange the debit and the credit items in the order of their dates as in the operation. Find the balance of the items at each of the dates. There is a debit balance of $1800 for 30 days ; the interest of which is equiv- alent to the interest of $54000 for 1 day. The interest of the next balance, $800, for 15 days is equivalent to the interest of $12000 for 1 day, etc. The total balance of interest is equivalent to the interest of $112240 for 1 day, or $18.71. The net amount due is $872 plus $18.71, or $890.71. (See Art. 311, Note 3.) NOTE. If, at any time in the above operation, there had been a credit balance, it would have been necessary to have had additional columns for "Cr. Balances 5 ' and "Or. Products." EXAM PLES. 458. 1. Find the balance due on the following account, Jan. 1, 1883, interest being reckoned at 6%. Dr. HOWAKD THORNTON. Cr. 1882. July 1 Aug. 24 Oct. 18 Balance. Mdse. Draft C.&C. 1830 448 387 45 00 40 1882. Sept. 13 Oct. 31 Nov. 5 Net Proceeds. a (( Cash. 876 912 1000 40 36 00 Dec. 12 Draft H. & Co. 516 88 ACCOUNTS CURRENT. 211 2. What is the net amount due on the following account, July 1, 1882, at % ? Dr. C. H. MILLS in % current with G. F. SWOETFIGUER. Cr. 1881. 1881. July 1 Balance. 1275 46 Nov. 14 Mdse. 4 mo. 587 19 Sept. 13 Draft #1012. 871 52 1882. 1882. Mar. 13 " 30 da. 612 35 Jan. 4 " #1017. 913 27 Apr. 27 " 60 da. 846 93 May 17 " #1024. 345 63 June 3 Cash. 500 00 8. What is the balance of the following account, Apr. 1, 1882, at Dr. W. J. HILLIS in account with LANGRAVE SHULTS. Cr. 1882. 1882. Jan. 16 Dft. M. & C. 937 64 Jan. 1 Balance. 3456 75 " 31 " B. & D. 856 75 u 27 Sales as Mar. 15 1225 19 Mar. 3 W. & Y. 1749 30 Feb. 4 Mdse as Mar. 6 673 75 " 24 V. &0. 912 38 " 28 Sales as Mar. 19 2428 35 4. Find the amount due Aug. 1, at 6%, on the account repre- sented in Ex. 7, Art. 438. (See Note, Ex. 7, Art. 438.) 5. Find the amount due Oct. 1, 1882, at 6%, on the account represented in Ex. 4, Art. 446. 6. Find the balance due Apr. 1, 1882, at 6$, on the following account current. PHENIX MILLS in % current with JAMES TALCOTT, New York, Apr. 1, 1882. Date. Dr. Amounts. Date. Cr. Amounts. 1882. 1882. Mar. 1 Balance. 45108 34 Mar. 31 Net Proceeds 16 Draft #676. 1000 of Account " 18 " #675. 2000 Sales due Apr. " 24 " #678. 5000 26, 1882. 12505 70 " 28 Cotton Bill. 3176 42 (See Ex. 4, " 30 Transportation. 875 10 Art. 45O.) 212 ACCOUNTS CURRENT. 7. Find the gain or loss on the following consignment account, taking as the day of settlement Jan. 29, 1881, the day the draft for the balance of the account was drawn and sold, and reckoning interest at 6% (365 days to the year). Cons. F. L. BRUCKMANN, #14. I860. Apr. <( 25 25 Dr. Mdse. Net Cash. ) Clearance. 3 Days. Interest. Amounts. 279 300 17 (6544 72 20 May 10 Insurance. *## * ir-A- 40 1881. Jan. 29 Balance of Interest to debit. ##* w* 1880. May Nov. 29 7 20 Gain. Or. Draft 18000 Reiclismarks " 2000 **# ** ### *** ## ** #### ** *** * *:; ** 4258 468 42 75 1881. Jan. 29 " 9998 2368 28 29 Balance of Interest to debit. **# -::* *## ** **** #-x- 8. What was the amount due on the following account Feb. 13, 1881, the estimated due date of a sight draft drawn Jan. 29, 1881, for the balance, reckoning interest at 5% (365 days to the year) ? F. L. BRUCKMANN on account of Consignment #14. 1880. Dr. Days. Interest. Amounts. Oct. 25 Account Sales due Jan. 9, 1881 35 44 80 9344 82 Dec. 31 " Mar. 7, 1881 22417 54 1881. Feb. 13 Balance of Interest to credit. *** ** **# ** ***** ** 1880. Cr. June 30 Freight due May 14, 1880 *** #* ** 1176 32 May 6 Draft 60 days' sight " July 18, 1880 I *** *** ** j 8000 6 lk GO " " " " 18, 1880 ) e 10080 Nov. 19 " 60 " " " Feb. 1,1881 *# * ** 2000 1881. Feb. 13 Interest Km. 22417.54 " Mar. 7, 1881 ** ** ** " 13 Balance of Interest to credit. *#* ** Jan. 29 Draft at sight to balance due Feb. 13, 1881 **** ## *** ** ***** ** ACCOUNTS CURRENT. 213 NOTES. 1. The interest on all items falling due after the day of settle- ment should be entered in the interest column on the opposite side of the account. Some accountants enter these items of interest on the same side of the account in red ink so that they will not be added to the other items, and transfer the " red interest " in one amount to the opposite side. 2. The foregoing represents an account in German marks (reichsmarks) kept in an auxiliary book by a consignor of merchandise to a commission merchant at Hamburg, Germany. The due dates of drafts, accounts sales, and other items are obtained from the letters from the commission merchant and from accounts sales and memoranda rendered by him. The corresponding consignment account as entered in the books of the consignor is represented in Ex. 7. 9. What was the balance due Jan. 1, 1882, at 6$, on the account represented in Ex. 5, Art. 446. 10. Find the amount due Mar. 1, 1883, at 6$, on the account represented in Ex. 6, Art. 446. 11. Calculate the interest Jan. 1, 1883, in the following partial account current, and find the total amounts. (Interest 6$, 365 days to the year. ) (See Art. 451, 3. ) G. D. SLOCUM in account with W. B. 1882. Dr. Days. Interest. Amounts. May 1 Totals from statement of May 1. 1882. 1387 63 28765 72 tt 6 Draft H. B. Claflin & Co. 240 50 71 1285 43 K 9 " Austin, Nichols & Co. *** #* ** 674 89 * 13 " W. H. Schieffelin & Co. *** ** #* 346 27 a 25 " Early & Lane. ##* ** *# 418 43 28 " Mitchell, Vance & Co. #** ** ** 576 80 **** *# ***** ** 1882. Or. May 1 Totals from statement of May 1, 1882. 973 42 22413 71 < 5 Sales as June 28, 1882. #* #** vr-iv 7316 84 ti 12 " " Aug. 1, 1882. *** #* ** 2110 92 " 18 " " July 13, 1882. *** *## ** 13446 85 " 25 Cash. **# #* ** 2000 **** ** ***** ** 214 ACCOUNTS CURRENT. 12. Find the balance due on the following account Feb. 13, 1881. (5$, 365 days to the year.) Dr. A. WEIN GREEN & Co., on account of Cons. #25. Cr. Date. Days. Interest Amounts. Date. Days. Interest. Amoun 1881 1880. Dec. 3! Ace. Sales Aug. 5 Freight. *** Ml ** 653 due Feb. Nov. 19 Draft due Feb. 1,1881. M M *# 18rt. When one has sold stock which he does not own, hoping to realize a profit by buying in at lower prices, he is said to be " short." 12. Syndicate. A combination of bankers who together undertake the placing of a loan. 13. Watering a Stock. The act of increasing the quantity of a stock without a corresponding increase in the value of the property which it repre- sents. This is usually done in the reorganization of a railroad, or in the consolidation of two or more railroads. EXAM PLES. 481. 1. A bank with a capital (459) of $250,000, declares a semi-annual dividend of 3J$. What is the amount of the divi- dend, and how much will a stockholder receive who owns 16 shares of $100 each (459, 1) ? 2. An insurance company divides among its stockholders $18000. What is the rate of the dividend, the capital stock being $225000 ? How much is paid to Mr. A., who has a certificate (459, 2) for 25 shares ? 3. A gas company declares a dividend of 5%, and divides among its stockholders $125000. What is its capital stock ? 4. The board of directors of a mining company declared a divi- dend of $100,000, being five cents per share (par value $10) on the capital stock of the company. What was the capital stock, and in how many shares was it divided ? The dividend was what per cent, of the capital stock ? 5. An installment of 10$ was assessed and called on the capital stock of a new railroad company. How much was paid by Mr. B. who had subscribed for 50 shares (par value $100) ? 6. A railway company, whose capital stock is $1,750,000, declares a dividend of 3 per cent. What was the amount of the dividend ? STOCKS AND BONDS. 227 7. The Union Pacific Railway paid to its stockholders, in 1879? $2,204,700. What was the par value of its stock, the rate of the dividend being 6% ? 8. A quarterly dividend of 3|% was declared by a manufactur- ing company. What was the capital stock, the amount of the dividend being $2100 ? 9. If stock is quoted at 116-f, what is the market value of 200 shares ? 10. How many shares of W. U. Tel. can be bought for $43725 at 79-f, brokerage \%? 11. What is the total par value (459, 3) and the total market value of 100 shares Lake Shore at 118-f (474), 300 sh. N. J. Central at 89f, 500 sh. W. U. Telegraph at 78$, 200 sh. U. S. Express at 73}, and 500 sh. N. Y., L. E. & W. com. at 40$, and 800 sh. K Y., L. E. & W. pref. (46O) at 90$ ? 12. What is the cost of 250 shares Tex. & Pac. at 50-f and 100 shares Ohio & Miss. pref. at 104, brokerage \% (475) ? 13. What are the proceeds of 600 shares Morris and Essex (half stock, 459, 1) sold through a broker at 121J ? 14- What are the proceeds of the following stocks sold through a broker? 200 shares Union Pacific at 117$, 2000 shares K Y., 0. & W. at 27}, 800 shares A. & T. H. pref. at 88, and 600 shares Chi. & Alton at 131}. 15. Find the cost of 10 shares Manhattan Bank at 135, $5000 Erie 7's (461, 5) cons, gold bonds (461) at 128, $1000 Toledo and Wabash 2d, s. 3 (461, 5 480, 10) at 108$, $5000 C. R. I. & P. 6's, 1907, coupon (461, 2) at 129, and $5000 Ohio Southern Income (461, 5) at 45, usual brokerage. 16. Find the proceeds of $15000 U. S. 4's, registered, 1907 (467), b. 3, at 117, and $10000 U. S. 4fs coupon (466) at 114|-, usual brokerage. 17. How much must be invested in U. S. 4's, 1891, to produce a quarterly income of $675, bonds selling at 114$ ? 18. When Ohio 6's, 1886, are sold at 109J, what is received for six $500 bonds, brokerage }% ? 19. When Pittsburg, Fort Wayne and Chicago 2d 7's, 1912, are worth 135, what will $12000 in bonds cost ? 20. How many $500 bonds shall I receive for $4735 invested in U. S. 4's at 118$ ? 28 STOCKS AND BONDS. <\ k 21. How much must be sent to a broker that he may purchase $8000 U. S. continued fives (465) at 102f , commission \% ? 22. An executor sold Central of New Jersey stock at 52-f, and purchased with the proceeds $42000 in U. S. 4's, 1907, at 100 }. What was the par value of the stock sold, usual brokerage ? 23. A broker bought on his own account 200 sh. Nor. Pac. pf. at 69-}, and sold the same the same day at 73|. What was his gain? 24. How many shares of 111. Cen. bought at 129-f and sold at 132f, usual brokerage, will produce a gain of $1375 ? 25. What income will be produced by investing $235250 in 4% bonds at 117| ? 26. The common stock of a railroad company is $46,000,000, and the preferred stock (46O) $8,000,000. The company declares a dividend of 3%% on the preferred stock, and %% on the common stock. What is the surplus, if the net earnings are $1,317,645? 27. Bought June 4, 800 sh. Ohio & Miss. pref. at 35J, s. 30. The stock was delivered June 24. What was the amount paid including interest (48O, 10) ? 28. Bought May 16, 200 sh. Lake Shore at 116}, b. 60, and called for the stock July 5. What was the cost including interest (48O, 3) ? 29. Jan. 10, sold 100 sh. Phil. & Eead. at 65J-, s. 3. Jan. 13, the stock was quoted at 68-J. How much was the difference (48O, 7) paid by the seller in settlement ? 30. What was the cost, including commission (475, 2) at the N. Y. Mining Stock Exchange of 500 sh. (par value $10) mining stocks at 7.50 ? What would have been the total cost, if bought at the N. Y. Stock Exchange (475, 1) ? 31. The transactions of the United States in refunding the Public Debt from Mar. 1, 1877 to Oct. 1, 1879 were as follows : Loan of 1858, 5's, $260,000; ten-forties of 1864, 5's, $193,890,250 ; five-twenties of 1865, 6's, $100,436,050; consols of 1865, 6's, $202,663,100 ; consols of 1867, 6's, $310,622,750 ; consols of 1868 6's, $37,473,800. In place of the above bonds there were issued the following : Funded loan of 1891, 4|'s, $135,000,000; funded loan of 1907, including certificates, 4's, $710, 345,950. What was the total amount refunded, and what was the annual saving in interest ? STOCKS AND BONDS. 229 32. Sept. 1, 1865, the interest-bearing debt of the United States was as follows : 4 per cents., $618,127.98 ; 5 per cents., $269,175,727.65; 6 per cents., $1,281,736,439.33; 7^ per cents., $830,000.00. What was the total annual interest charge ? * 33. The interest-bearing debt of the United States was as fol- lows, Jan. 1, 1881: 6's, $202,266,550; 5's, $469,651,050; 4J's, $250,000,000; 4's, $739,347,800; 3's, $14,000,000. What was the decrease during the year 1881 in the annual interest charge ? (See statement of Jan. 1, 1882, Art. 463.) What was the inter- est of the debt for one day (-^J T yr.) Jan. 1, 1882 ? 34. The population of the United States and Territories Jan. 1, 1881, was 50,152,554, and the public debt was $1,899,181,735. What was the debt per capita ? What was the average monthly decrease of the debt during the year 1881 ? (See statement, Art. 462.) 35. The interest-bearing debt of the United States was as fol- lows, Dec. 1, 1881 : Continued 6's (3|'s) (464), $159,452,500, last interest paid July 1 ; continued 5's (3J's) (465), $401,504,900, last interest paid Nov.l ; 4J's (466), $250.000,000, last interest paid Sept. 1 ; 4's (467), $739,347,800, last interest paid Oct. 1 ; navy pension fund (3's), $14,000,000, last interest paid July 1. What was the aggregate of the interest-bearing debt, and the accrued interest, Dec. 1, 1881 ? 36. The gross earnings (including the Omaha bridge) of the Union Pacific Eailway Co. for 1879, were $13,201,077.66 ; the operating expenses (including taxes) were $5,475,503.44. What were the surplus earnings, and what per cent, of the gross earnings were the operating expenses ? 37. A synopsis of the report of the N. Y. C. & H. E. R. E. for its fiscal year ended Sept. 30, 1881, is as follows : Gross earnings from passengers, $6,958,038 ; from freight, $20,736,749 ; from miscellaneous, $4,653,608; expenses, $19,464,786; interest, rentals, and taxes, $4,990,783. What was the surplus for the year after the declaration of a dividend of 8% on a capital stock of $89,229,300 ? The expenses were what per cent, of the total earnings ? 38. The L. S. & M. S. Railway reported as follows for the year ended Dec. 31, 1880 : Gross earnings, $18,749,461 ; operating expenses and taxes, $10,418,105 ; interest, rentals, dividend on guaranteed stock, and $250,000 for the sinking fund, $3,000,374, 230 STOCKS AND BONDS. After paying a dividend of 8$, there was a surplus for the year of 81,373,662. What was the amount of the dividend, and the capi- tal stock ? 89. The gross earnings of the M. C. E. R. for the year ended Dec. 31, 1880, were $9,085,749 ; operating expenses and taxes, $5,738,751; interest and rentals, $1,586,410. After declaring a dividend, there was a surplus of $261,532. What was the rate of the dividend, if the amount of the stock was $18.738,200 ? For the year 1881, a dividend of 2$ was paid on the same stock; what was the amount of the dividend ? * 40. The capital stock of a railroad company was "watered" (48O, 13) by declaring a stock dividend of 10$. If the market value of the old stock was 110, what should be the value of the new stock ? >/ 41. Jan. 1, 1882, the A. & B. E. R., having a capital stock of $20,000,000, was consolidated with the B. & C. E. E., having a capital stock of $32,000,000. The new company was organized under the name of the A., B., & C. E. E. For every share of the A. & B. E. E. there was issued 1 1 shares of the new stock, and for every share of the B. & C. E. E. there was issued 1 shares of the new stock. What was the capital stock of the new company, and how much was the stock " watered " ? J4#. Before the consolidation, the stock of the A. & B. E. E. was worth 1.20 in the market, and the stock of the B. & C. E. E., 90. What should be the quotation of the new stock ? 43. During the year 1881, the A. & B. E. E. divided among its stockholders $1,600,000, and the B. & C. E. E., $1,920,000. During the year 1882, the new company divided an amount equal to the total dividends of the two companies in the preceding year. What were the rates of the dividends of the two companies in 1881, and the rate of the dividend of the consolidated company in 1882 ? 44. 'Mr. A. had 10 shares of the A. & B. E. E., and 16 shares of the B. & C. E, E. What was the total amount of his dividend in 1881 ? How many shares of the new stock did he receive, and what was the amount of his dividend in 1882? 45. A gentleman bought bank stock, paying regular annual dividends of 6$, at 120. What was the rate, per cent, of his in- come, or what per cent, did he receive on the money invested? STOCKS AND BONDS. 231 ANALYSIS. Since dividends are reckoned on the par value of the stock, the dividend on 1 share of $100 would be $6. Since each share costs $120, and pays $6 income, the per cent, will be $6-r-$120, or / . NOTE. The above analysis will not apply to bonds that mature at a cer- tain fixed time, unless the investor expects to sell the bonds before maturity at the cost price. If 6% bonds that mature in 1891 are purchased in 1881 at 120, and are sold at the same rate before maturity, they will pay % on the investment, or cost. If the bonds are held until maturity (1891), or for 10 years, the owner would receive from the government the par value only, or $100 for a bond of that amount, and the bonds would yield less than 5%. If 6% bonds, maturing in 10 years, are purchased at 1.07 j^ and held until maturity, they will pay 5% on the investment (See Ex. 64). If Q% bonds, that mature in 2 years, are purchased at more than 112, there would be a loss of interest to the purchaser instead of a gain. 46. Which is the better investment, stock paying a regular annual dividend of 5$ and bought at 80, or stock paying 8$ dividends and bought at 120 ? 47. If insurance stock paying regular dividends of 10$ annually is bought at 137, brokerage J$, what per cent, of income will it produce ? 48. Which investment will produce, the greater annual income and how much, $20,000 invested in Chemical Bank stock at 2000 which pays dividends of 15$ every 2 months, or the same amount invested in Chatham Bank stock at 125 which pays regular semi- annual dividends of 3$ ? 49. What rate can you afford to pay for stock paying regular annual dividends of 10$, in order to realize 6$ on the invest- ment ? 50. At what price must 8$ stocks be purchased to afford 5$ on the investment ? To afford 6$ ? 51. Stocks bought at 80 pay regular dividends of 5$. What is the rate per cent, on the investment ? At what rate should they be purchased to afford 4$ on the investment? To afford 8$? 52. I sell 200 sh. H. & St. J. pf. at lllf, and $10000 K Y. Elevated 1st mortgage bonds at 119. What will be the net pro- ceeds of the sale, allowing usual brokerage ? 53. Purchased 400 shares Lake Shore at 118-J-, and 200 shares Chesapeake and Ohio 2d pref., at 24|. Sold the Lake Shore at 113f, and the Chesapeake and Ohio at 22J. What was the loss, usual brokerage, no interest ? STOCKS AND BOXDS. 54- July 26, a broker received from a customer a remittance of $1000 as a margin (478) and purchased for him 100 shares of St. Paul Common at 59. On Aug. 2, the broker sold the stock at What was the customer's profit ? OPERATION. Dr. July 26. To 100 shares St. Paul Com. 59. Commission \% . $5900 12.50 5912 50 Aug. 2. Interest $5912.50, 7 days. * ** *#** ** Cr. July 26. Aug. 2. By margin deposited " 100 shares St. Paul Com. 64|. Commission \ % . $6450 12.50 1000 6437 50 Aug. 2. Interest $1000, 7 days . . * #* **** *# Balance. *fc## ~*# The profit is equal to the balance less $1000, the original deposit. 55. Aug. 30, a broker purchased for the account of a customer 300 shares Northwestern Railroad stock at 78. He deposited as a margin $3000. On Sept. 22, the stock was sold at 74}. What was the loss ? (Interest 6%, usual commission.) 56. May 10, a speculator deposited with his broker $5000 as a margin, and directed him to purchase for his account 500 shares K". Y., L. E., & W., pref. at 90|. May 20, the stock was sold at 94rJ-. What was the gain, interest 6$, usual brokerage ? 57. Sept. 10, I deposited with my broker $5000 as a margin, and he purchased for me 200 sh. Cen. Pac. at 90-J-, 200 sh. Morris & Essex (half stock) at 122J, 200 sh. Tex. & Pac. at 49}. The stocks on Sept. 30 were quoted as follows: Cen. Pac. 80}, Morris & Essex 120-J, Tex. & Pac. 41f. How much should I have deposited with my broker to make my margin of 10% good, and to cover commission for buying and selling, and interest ? If I had been unable to have made an additional deposit, and the broker had "sold me out," what would have been my loss ? 58. An operator, supposing Erie would decline in value, ordered his broker to sell short 100 shares at 50, and at the same time deposited with him as a margin $1000. The broker on receiving the order sold for his account 100 shares at 50, and borrowed the stock for delivery. When the market price declined STOCKS AND BONDS. 233 to 45, he ordered the broker to " coyer his short sale " (buy the stock for delivery), and return the stock to the party from whom it was borrowed. What was the gain, usual brokerage ? OPERATION. Cr. By margin deposited $****** " 100 shares Erie borrowed and sold at 50. . . ****** $****.** Dr. To 100 shares Erie bought and returned at 45. . $****.** " commission for selling the stock \%. . . . ** % *# " buying and returning the stock \%. ^** .** ****** " amount to credit. . ' ##** t * The net profit equals the balance less the margin deposited. NOTE. There is no interest charged on short sales, but it sometimes happens that a small bonus has to be paid for the use of the borrowed stock. 59. A broker sold "short" for me 400 sh. 0. B. & Q., at 135}, and 100 sh. C. R. I. & P., at 132. My "short" sale on C. B. & Q. was " covered" at 131, and C, R. I. & P. at 133}. What was my net profit, usual brokerage ? (No interest. ) 60. Sold Aug. 11, 500 shares Chicago & Alton, s. 3, at 94 J, and covered my short sale Aug. 14, at 91. What was my profit, allowing the usual brokerage ? 61. June 16, bought a Call (479, 1) on 300 shares Michigan Central at 86, for 30 days, for which I paid $300. Called the stock July 6, and sold it in the market the same day at 91^. What was my gain, commission on call -fa% 9 for selling stock \%> interest Q%? NOTE. Calls bear interest at 6^ from the date of the contract till the contract is closed, but Puts do not. 62. If, in the preceding example, the stock had not advanced to 86 at any time within 30 days, what would have been the loss ? What would have been the result if the stock had been sold July 16 at 87 & and called for delivery? If sold July 1 at 86 ? 63. Sept. 18, bought a Put (479, 2) on 400 shares C. C. & I. C. at 20, for 30 days, for $400. I purchased the stock at 16 and made my delivery on the Put. What was my gain, commission on Put T V%, on stock \% ? What would have been my loss, if the stock had not fallen below 20? What would have been the result, if the stock were purchased for delivery at 18| ? At 19J- ? 234 STOCKS AND BONDS. 64. At what price may Q% bonds, maturing in 10 years, be purchased, so that the investment will pay b% ? NOTE. Tables have been constructed on various plans, and different methods are used by bankers and financiers, for the solution of problems relating to bond investments; two of which are given below. ANALYSIS. 1. In the following method, it is presumed that the accruing interest is not reinvested, but that a sufficient part of it is set aside as a sinking fund to make up the amount which was originally paid out as premium. A $1000 bond in 10 years at 6^ would amount to $1600 ($1000 + 10 x $60). $1 in 10 years at 5^ would amount to $1.50. To amount to $1600, the prin- cipal, or the amount paid for the bond, must be as many times $1 as $1.50 are contained times in $1600, or $1066.66f (106jj-$). If a $1000 bond is purchased at 108|, it will be necessary to set aside as a sinking fund each year $6.66f (f%) to make up the premium in 10 years. The annual interest, $60, less $6|, the annual sinking fund, is $53y, which is 5fo of $1066|, the cost of the bond or the amount invested. If the amount set aside as a sinking fund is placed at interest, either simple or compound, % bonds, maturing in 10 years and purchased at 106|, would pay a little more than 5 % . 2. The following method anticipates compound interest throughout ; i. e., the interest is immediately reinvested at compound interest. The holder of a $1000 bond would receive $60 interest annually, and $1000, the face of the bond, in 10 years. If money is worth 5%, the several interests in the 10 years at compound interest would amount to $754.674 ($1 placed at compound interest at the beginning of each year would amount in 9 years to $11.5779 (342). $11.5779 plus $1 of the last inter- est = $12.5779. $60 would amount to 60 times $12.5779, or $754.674). $1000, the principal, plus $754.674, the compound amount of the interest, equals $1754.674, the total value of the bond at maturity, money being worth 5$. The present worth of $1754.64, due in 10 years, at 5% compound inter- est, is $1754.64 -f- $1.6289 (341), or $1077.19. Hence the bonds must be purchased at 1.07 T 7 ^ to pay 5% on the investment. See Ex. 45, Note. 65. What must I pay for 6^ bonds, maturing in 15 years, that my investment may yield ty% ? (Both methods.) 66. 6f bonds, maturing in 10 years and bought at 106f , pay what per cent, on the investment ? (See 1st analysis, Ex. 64.) ANALYSIS. A $1000 bond would amount in 10 years at 6% to $1600. If $1066.66| is paid for the bond, the net interest for 10 years is $1600- $1066 66|, or $533.33| ; and for one year $533.33J-;-10, or $53.331. An income of $53.33| on an investment of $1066.66| is equivalent to 5# ($53.33|-r-$1066.66f). 67. What rate of interest do I receive on my investment, if I buy 7% bonds maturing in 20 years at 133J? TAXES. DEFINITIONS. 482. A Tax is a sum of money assessed on persons and property to defray the expenses of a state, county, town, corpo- ration, or district. 1. In certain states all citizens above 21 years of age are required by law to pay a certain tax on the person. This tax is called a Capitation or Poll Tax. 2. The expenses of states, counties, towns, etc., are paid by a direct tax upon the property or polls of the same. The methods of assessing taxes differ in the several states. In some states, a certain percentage of the whole tax is assessed upon the polls, while in others the poll tax is a fixed amount for each citizen. In certain states, the whole tax is paid by the owners of the property of the same. 3. The expenses of the United States government are paid by duties on imports ; the internal revenue (the tax upon distilled spirits, fermented liquors, tobacco, snuff, and cigars, proprietary medicines, perfumery and cosmetics, playing cards, matches, etc.) ; sales of public lands ; tax on circulation, deposits, and capital of national banks ; customs fees, fines, penalties, and forfeitures; fees, consular, letters patent, and land ; profits on coinage, etc. The receipts of the United States for the fiscal year ended June 30, 1881, were as follows: Customs (including tonnage dues), $198,159,676; internal revenue, $135,264,385; public lands, $2,201,863; miscellaneous, $25,156,366. 483. Real Estate is fixed property ; as land, houses, etc. 484. Personal Property is movable property, as money, stocks, bonds, mortgages, furniture, merchandise, etc. 485. An Assessor is a person appointed or elected to esti- mate the valuation of all property liable to taxation. 486. A Collector or Receiver of taxes is a person appointed or elected to collect or receive the taxes of a city, town, village, or district. Collectors receive a commission on the amount collected or a fixed salary. 236 TAXES. EXAM PLES. 487. 1. For the fiscal year 1879, the N". Y. State tax levy was at the rate %-&$ mills. How much would this rate produce, the valuation of the taxable property being $2,686,140,000 ? 2. The rate of taxation of a certain county was 3J mills, and the amount of the tax $40,653.48. What was the valuation of the property ? 3. The following were the rate& of taxation of New York for state purposes, 1880 : schools, 1.085 mills ; general purposes, 1.475 mills ; new capitol, .6 mills ; canals, .34 mills. What was the total rate of taxation, and how much was raised by a county whose valuation was fixed by the state board of equalization at $11,047,534? How much was raised for school purposes? 4. The state tax of a certain county was $38,666.37, and the valuation of the county, $11,354,880. How much of this tax was paid by a town whose valuation was fixed by the board of super- visors at $3,938,663.17? 5. The total county expenses of the same county were $25,063.35. How much should be apportioned to the above town ? 6. Taxes were levied in a certain town for the following pur- poses : support of poor, $2,000 ; roads and bridges, $500 ; accounts audited by town auditors, $2,876.10 ; accounts audited by super- visors, $19.48 ; county expenses, $9,774. 72 less a surplus of $6,055.90 in the county treasury ; state and school tax, $15,079.88 ; surplus tax, $868.98. What was the rate of taxation, the total valuation of the property, as made by the town assessors, being $4,321,252 ? What was the tax of Mr. A., whose valuation was $7,300 ? 7. Find from the following table the tax on $16750. OPERATION. ANALYSIS. By looking in the table oppo- Tax on $16000 is $92.80 site 1 and under G, we find that the tax on <( 750 435 $16 is $.0928, and by removing the point 3 IBT q^T^ places to tlie right> we find tlie tax on y '- lc $16000 to be $92.80. In the same manner, the tax on $750 is found to be $4.35. The tax on $16750 is $92.80 plus $4.35, or $97.15. 8. How much was paid by Mr. B. on an assessment of $6400, the collector charging a commission of \% additional ? (Use table.) TAXES. 237 NOTE. To save labor in the calculation of taxes, a table similar to the following is usually prepared by the accountant. TAX TABLE. Kate, 5.8 mills on $1. l 2 3 4 5 6 7 8 9 1 .0580 .0638 .0696 .0754 .0812 .0870 .0928 .0986 .1044 .1102 2 .1160 .1218 .1276 .1334 .1392 .1450 .1508 .1566 .1624 .1682 3 .1740 .1798 .1856 .1914 .1972 .2030 .2088 .2146 .2204 .2262 4 .2.320 .2378 .2436 .2494 .2552 .2610 .2668 .2726 .2784 .2842 5 .2900 .2958 .3016 .3074 .3132 .3190 .3248 .3306 .3364 .3422 6 .3480 .3538 .3596 .3654 .3712 .3770 .3828 .3886 .3944 .4002 7 .4060 .4118 .4176 .4234 .4292 .4350 .4408 .4466 .4524 .4582 8 .4640 .4698 .4756 .4814 .4872 .4930 .4988 .5046 .5104 .5162 9 .5220 .5278 .5336 .5394 .5452 .5510 .5568 .5626 .5684 .5742 9. Mr. D. being delinquent was charged 5% additional. How much was he obliged to pay on a valuation of $9500 ? 10. What was the total tax. including commission of 1% of Mr. C., whose real estate was assessed at $24000, and personal property at $15500 ? 11. In the City of Brooklyn, N. Y., the following is the law regarding the payment of taxes : On all taxes and assessments which shall be paid to the collector, before tbe expiration of one month after the warrant for the collection of the same shall have been delivered to him, an allowance shall be made at the rate of 7yV% per annum for the unexpired portion thereof. On all taxes or assess- ments paid after the expiration of one month from the time the same shall have become due and payable, there shall be added to such tax or assessment interest at the rate of 9 % per annum. According to the above law, how much tax was paid Jan. 16, by Mr. A., the valuation of whose property was $7500, the rate of tax being $2.376 per $100, and the warrant having been delivered to the collector, Jan. 4 ? How much was paid by Mr. B., on a valuation of $12500, Mar. 26 ? (365 days to the year.) 12. What is the total tax on 8375 pounds tobacco at 16& 4360 gallons distilled spirits at 70^, 2165 barrels beer at $1 ? 13. How much is the semi-annual tax of a national bank whose average circulation is $225,000 at \%, average deposits $1,416,387 at %, average capital stock $400,000 at % ? DUTIES. DEFINITIONS. 488. Duties or Customs are taxes assessed by the Govern- ment upon imported merchandise for the purpose of revenue for the support of the government and for the protection of home industry. 1. The total ordinary revenues of the United States for the fiscal year ended June 30, 1881, were $360,782,292, of which $198,159,676 were received from customs. Of the latter amount, $138,908,562 were collected at the port of New York, leaving $59,251,114 as the amount collected at all other ports of the country. 2. The waters and shores of the United States are divided into collec- tion districts ; in each of which there is a port of entry and one or more ports of delivery. Thus, the district of Boston and Charlestown comprises all the waters and shores within the counties of Middlesex, Suffolk, and Norfolk. Boston (including Chelsea) is the port of entry, and Medford, Cohasset, Hingham, Weymouth, Cambridge, Roxbury, and Dorchester, the ports of delivery. All ports of entry are also ports of delivery. 3. All cargoes chargeable with duties shall be entered and the duties paid, or secured to be paid, at the port of entry, before permission shall be given to discharge the same at the port of delivery. 4. The principal officer of every district is the collector, who is assisted by deputy-collectors, surveyors, appraisers, weighers, gaugers, inspectors, etc. The duties of the above vary in the several collection districts and ports. There is also in the leading ports of entry, a " naval officer," whose depart- ment is a check upon that of the collector. He receives copies of all invoices and entries, estimates duties, countersigns permits, clearances, certificates, debentures, and other documents, granted by the collector. 5. The surveyor usually superintends and directs the inspectors, weigh- ers, and gaugers, within his port. 6. An importer desiring a permit to land merchandise, presents his invoice, with the consular certificate, bill of lading, and the formal entry attached (See Ex. 25, Art. 499), to the entry clerk at the custom-house, and makes the necessary oath before the collector or his deputy. The duties, if DEFINITIONS. 239 any, are estimated in the departments of the collector and the naval officer. The amount of the estimated duties having been paid, or secured by a bond, the collector, together with the naval officer, where there is one, grants a per- mit to land the merchandise. It is the custom of custom-house brokers and many merchants to calculate the duties and enter the same on the entry. The permit is presented to the inspector in charge of the vessel, who allows the merchandise to be landed. The collector indicates on the permit by numbers what packages shall be sent to the public store for exam- ination. When the merchandise is examined by the appraiser (495), he enters on the invoice (494) or manifest the rate of duty to be collected. The invoice and the accompanying papers are then sent to liquidators in both the collec- tor's and naval officer's departments for adjustment. The liquidators check the calculations on the entry, or again calculate the duty it' the appraiser has changed the rate or the dutiable value, or if the returns of the weigher or gauger differ from the weight or measurement in the invoice. The amount of duty to be refunded or collected is marked on the entry, if the difference between the duty as estimated and as liquidated is less than $1, it is disre- garded, and the liquidator approves the original estimate. 489. A Custom-House Broker is a person who makes entries, secures permits, and transacts other business at custom-houses for merchants. He is familiar with the tariff laws and the details and regulations of custom-house business, and usually acts under a power of attorney. 1. The necessary blanks for making entries are provided by the broker, or they may be obtained at any stationer's. 2. The greater part of the business at the New York custom house is done through brokers. 490. The following are the principal entries made at custom- houses : 1. Import entry of merchandise for immediate consumption. 2. Import entry of merchandise for storage in a bonded warehouse, called a " Warehouse entry." (See Art. 49(5.) 3. Import entry of merchandise for immediate transportation in bond (in sealed cars) to another port of entry ; as goods landed at New York to be transported in bond to Chicago. In this case the goods are appraised, and the duties assessed and collected at Chicago. * 4. Entry of merchandise for immediate transportation in bond to Canada or Mexico, or other foreign country. In this case no duties are collected. 5. Withdrawal entry from bonded warehouse for consumption at the place of importation. (See Art. 496.) 240 DUTIES. 6. Withdrawal entry from bonded warehouse for immediate transporta- tion in bond to another port of entry. 7. Withdrawal entry from bonded warehouse for immediate transporta- tion in bond to Canada, Mexico, or other foreign country. 8. Export entry of merchandise manufactured in the United States, for the benefit of drawback (497). 491. Duties are of two kinds, ad valorem and specific. 492. An Ad valorem Duty is a tax assessed at a certain per cent on the dutiable value of the merchandise ; as silks at ?, watches at 2-5$, linens 30, 35 and 40%, china 45 and 50%. 1. The dutiable value ot merchandise is its market value at the port cj! export, but not less than its invoiced cost, commission added, whether paid or not. It is usually the original cost plus all charges, excepting the consul's fee, to the vessel on which the shipment is made. The charges include the transportation to the place of export, the value of the sack, box, etc., in which the merchandise is contained, commission at the usual rates, but in no case less than %\% t brokerage and all other charges, except the consul's fee. There is no duty on the freight or transportation from the port of export. The appraised value is sometimes greater than the invoice value (494). 2. In reducing foreign money to U. S. money for the purpose of calcu- lating duties, if the cents of the result are less than 50, they are rejected ; if more than 50, $1 is added to the dollars. 493. A Specific Duty is a tax assessed at a certain sum per ton, pound, foot, yard, gallon, or other weight or measure, with- out reference to the value ; as leaf tobacco at 35^ per pound, ale and beer (not bottled) 20^ per gallon, clay $5 per ton, plate glass per square foot, playing cards 25 and 35 cts. per pack, brandy $2 per proof gallon, lumber per M feet board measure, salt (in bulk) 8 cts. per 100 Ibs., flaxseed 20 cts. per bushel (56 Ibs.), cotton goods per square yard. 1. Before specific duties are calculated, allowances are made for tare (the weight of the box, barrel, or cask), leakage (of liquids in barrels), and breakage (of liquids in bottles, usually 5 %\ 2. The U. S. Custom House ton contains 2240 Ibs. (172, 3), the hundred- weight 112 Ibs., and the quarter 28 Ibs. 3. On certain goods, there is both a specific and an ad valorem duty (sometimes called a combined duty) ; as iron wire $20 3| cts. per pound and 15%, tobacco pipes (excepting common clay) $1.50 per gross and 75 %, statuary marble $1 per cubic foot and 25 % , woollen goods 50 cts. per pound and 35^. DEFINITIONS. 241 494. An Invoice (277) is a statement made by the seller or shipper of merchandise giving a description of the same, and show- ing marks, numbers, quantity, value, charges, and other details. (See Ex. 26, Art. 499.) 1. All invoices shall be made out in the weights and measures of the country from which the importation is made. 2. All invoices of merchandise subject to a duty ad valorem, shall be made out in the currency of the country or place from whence the importa- tion is made. 8. When the value of the foreign currency is fixed by law (see Art. 192), the value is to be taken in estimating the duties ; when the value is not fixed by law, the invoice must be accompanied by a consular certificate showing its value. 4. All invoices of importations must, before the shipment of the mer- chandise, be produced to and authenticated by the U. S. consular officer, where there is such an officer. In countries without a U. S. consular officer, the authentication is made by a consul of a country in amity with the United States ; or, if there be no such consul, then by two respectable resident merchants. All invoices must be made in triplicate ; the three copies to be regarded as one invoice, and subject to only one charge for consular certificate. One of the triplicate invoices is returned to the person producing them ; another is carefully preserved in the office of the consul ; and the third is transmitted to the collector of the port of destination of the merchandise. 5. When the value of merchandise imported into the United States shall not exceed $100, the collector is authorized to admit the same to entry, with- out the triplicate invoice required in other cases. 495. Aii Appraiser is an officer of the customs who ex- amines imported merchandise and determines the dutiable value and the rate of duty of the same. 1. The place where the examinations are usually made is called the "Public Store." 2. One package of every invoice, and one package at least out of every ten similar packages, shall be sent to the public store for examination. Certain bulky and heavy articles are examined at the wharf where unloaded. Weighable and gaugable goods on which the duties are specific, are not sent to the public store for examination. 3. W r hen the appraised value of any merchandise subject to an ad valorem duty is 10% more than the invoice value as entered by the importer, then in addition to the duty imposed by law on the same, there shall be col- lected 20 % of the duty imposed on the same. 496. A Bonded "Warehouse is a place for the storage of merchandise on which the duties or taxes have not been paid. 242 DUTIES. 1. If an importer does not desire to place his goods at once in the mar- ket, or anticipates exporting the same, by giving a bond for the payment of the duties and making the entry in the proper form, he may have the mer- chandise stored at his own risk in a bonded warehouse, and thus defer the payment of the duties. 2. The importer may select any U. S. bonded warehouse in which to deposit his merchandise. 3. Merchandise may be withdrawn from a bonded warehouse for expor- tation to Canada or other foreign country, without the payment of the duty on the same. 4. Merchandise is frequently sold "in bond" at prices which do not in- clude the duty. 5. Merchandise that may be in warehouse under bond for more than one year, will be liable when withdrawn for 10 ^ additional duty. 6. Any goods remaining in public store or bonded warehouse beyond three years shall be regarded as abandoned to the government, and sold under certain regulations and the proceeds paid into the Treasury. 497. Drawback. When distilled spirits, fermented liquors, medicines, and perfumery, upon which an internal revenue tax has been paid, and foreign merchandise upon which an import duty has heen paid, are exported, the tax or duty upon the same is refunded. Such return of the tax or duty is called a Drawback. 498. The Free List is a list of articles which are exempt from duty. In making entries of free goods, the value as given in foreign money must be reduced to U. S. money (See Ex. 28, Art. 499), permits must be obtained to land the goods, and certain packages are sent to the public store for examination. EXAMPLES. 499. 1. A merchant imported from Lyons an invoice of silk, the dutiable value (492, 1) of which was 4-8765 francs. What was the dutiable value of the same in U. S. money, and what was the duty at 60% (4:92) ? NOTES. 1. For foreign moneys of account and their values in United States money, see Art. 192. 2. 48765 francs at 19.3^ = $****. (See Art. 486, 2.) 60^ of $**** = $****.** 2. Find the duty on 1617 pounds of almonds, at 6 cts. per pound. DUTIES. 243 3. What were the average daily receipts of the New York custom-house for the fiscal year ended June 30, 1881, making allowance for 62 Sundays and 7 holidays. (See Art. 488, 1.) 4. An invoice of woollen cloth weighing 516 pounds, and valued afc 327 16s, was imported from England. What was the duty at 50 cts. per pound and 35$ ? 5. An importer on making his entry at the custom-house, paid the duty on 38716 pounds (Invoice weight) of tobacco, at 35 cts. per pound. According to the return of the custom-house weigher, the net weight was 38472 pounds. How much of the duty was refunded when the entry was liquidated ? 6. The duty on 28432 pounds of sugar was paid at the rate of 2} cts. per pound. According to the weigher's return, the net weight was 28218 pounds. How much additional duty was collected, the appraiser having fixed the duty at 3J cts. per pound ? 7. Find the duty on an invoice of linens from Ireland, dutia- ble value 424 15s. 6d., at 35% ? 8. What is the duty on an invoice of porcelain vases from Paris at 50%, dutiable value 9843 francs ? 9. Find the duty on 475 cu. ft. of statuary marble imported from Italy, dutiable value 16425 lire, at $1 per cubic foot, and 25%. 10. What is the duty on 37420 pounds of pig iron at $7 per ton (493, 2) ? 11. Find the duty on an invoice of leather goods from Vienna, dutiable value 6429 florins, at 35%. 12. What is the duty on an importation of toys from Germany, dutiable value 8437 marks, at 50% ? 13. What is the duty at 28 cents per sq. yd. and 35%, on 1248 yards of Brussels carpet, 27 in. wide, invoiced at 3s. 6d. per yard, shipping charges (less consul's fee) 2 16s. 9d. 9 14. Find the duty on an importation from Canada of 5284 bushels of potatoes, invoiced at 45 cts. per bushel, and 37475 pounds of hay, invoiced at $1250 per ton (2000 Ibs.), the duty on potatoes being 15 cts. per bushel, and on hay 20%. 24:4: DUTIES. 15. On a certain invoice of 34216 pounds of pepper, there are discounts for damage as follows: 12$ on 6190 pounds, 8$ on 6438 pounds, and 5% on 9642 pounds. After deducting the dis- count, what would he the duty on the remainder at 5 cents per pound ? 16. The duty on burlaps is 30$ ad valorem. What is the amount chargeable on a bale containing 50 webs, each being 54 yds. and 16 in. long, and 27 in. wide, and valued at 30 cents per sq. yd.? 17. What is the amount of duty chargeable on 2465 pounds of wool, valued at 171 8s., when the rate of duty is 10 cts. per pound and 11$ ad valorem? 18. The duty on certain glass plates being 35 cents per sq.ft., find the duty on 316 boxes, each containing 20 plates, and each plate being 24 in. by 30 in. 19. Find the duty at 25$, on one engraving, cost in London 34 5s., case and shipping charges 15s., commission 2J$. 20. What is the duty at $1 per cu. ft. and 25$, on a block of marble 2x3x7/2., imported from Italy, dutiable value 3450 lire? 21. Find the duty on 4175 Ibs. cloves at 50. per lb., 476 Ibs. cinnamon at 20^, and 5437 Ibs. rice at 2 Make the extensions, find the dutiable value, and calculate the duty on the following invoices and accompanying entries: 22. Entry of merchandise, imported by TEFFT, WELLER & Co., from Berlin in the Str. "Silesia." Arrived Jan. 14, 1882. New York, Jan. 16, 1882. Marks. Nos. Packages and Contents. 605?. ^ 351 One case half silk goods, . . . Commission 2J$, . . . Em. ****.** 23.8^ = 60$ of **** = $***. Rm. 2399.80 ##*# ** 1***^** D UTIES. 245 NOTE. The following is an entry of free goods. Free goods are entered and the foreign monetary units reduced to U. S. money for statistical purposes in the same manner as dutiable goods. 23. Entry for consumption of merchandise, imported by W. H. SCHIEFFELIX & Co., in the Str. "Ailsa" from Savanilla, on the 10th day of January, 1882. New York, Jan. 12, 1882. Free. 33 bales Medicinal Bark, 2310. Packing, 12. Commission 2^, ** ** (Pesos of U. S. of Columbia), . . **** ** '$****. 24. Invoice of one package merchandise, purchased by GLAD- HILL & Co. for account of D. BUCKLEY & Co., New York, and forwarded for shipment to D. & C. MAC!VER, Liverpool. . s. a. D. B. 4 Pieces Drab Cotton Pantaloon 32 in. wide, . 207 #1729 79^, 30 80, 31 77$, 32 79, 315$ (less ^) 307 @ 2s. 2d., . ** * * \\% discount, Verification and Commissioner's fee, . 14 10 2$% Commission, 16 5 ** * Less Consul's Certificate (not dutiable), 14 10 33 11 7 Entry of merchandise, imported by D. BUCKLEY & Co. in the Str. "Catalonia" from Liverpool. New York, Jan. 12, 1882. D. B. One case cotton, 33-11-7 207 @ 4.8665 ***** Duty 35^ of $*** = $**.** 246 D UTIES. 25. Invoice of 700 bales leaf cobacco shipped by F. B. DEL Rio & Co., per Sir. "Niagara" for New York, and consigned to FREDERICK DE BABY & Co. F. B. 700 bales 83077 Ibs. (See Art. 259, Spain) CHARGES. 3328 / 4027 Baling, ....... $525. Export duties, ..... 3407.39 Consul fee, ...... 2.75 Small charges, ..... '49 Commission Spanish gold HAVANA, Dec. 27, 1881. $35000 **** I***** ** ** Custom House, New York, Collector's Office, Jan. 4, 1882. Bond No. 9817. Entry of merchandise, imported on the third day of January, 1882, by FREDERICK DE BARY & Co., in the Str. "Niagara" from Havana. Marks. Nos. Packages and Contents. 35c. F B 3338 700 bales Leaf Tobacco 84240 Ibs. $39958.74 027 @ .93,2= Duty 84240 Ibs. @ 350 = $*****. f Weighers return 83675 Ibs. at 350 = *****.** !##**, Eefund, .... $*** .** t Added by the liquidator. 26. What is the duty on an invoice of crockery invoiced at 1275 16s. 6d. /. o. 1). (free on board), at 40% ? 27. What is the duty on 28916 pounds of steel rails at 1J# per pound, and 11438 pounds of tin plates at 1 T V^ per pound? 28. The duty on spool thread of cotton, containing 100 yds. to the spool, is 6^ per dozen spools and in addition thereto 30% ad valorem. What is the duty on 11160 spools valued at 3^ a spool? D UTIE S. 247 29. SHEFFIELD, ENGLAND, Dec. 14, 1881. Mr. A. R. WHITNEY. Bought of THOS. WIDDOWSON & Co. -/r c. gr. Ibs. I . d . <^W\J1 1 Cask Corset Steel 3| x%6, . . 12 21 NX JP 1 " " " " 12 22 83 i a C* . 13 20 #4 1 (i f(' i( t( 12 2 7 ** T ** 25/_ ** ** ** 4 Casks 6 /- each, * Carriage to Liverpool 1 6 / 8 P er ton j . * * * Shipping Expenses 8 / 6 " " . * * Consul's Fee, .... 10 4 Commissioner's Fee, . 4 6 W Entry of Merchandise, imported by A. R. WHITNEY in the Str. Gallia" from Liverpool. New York, Dec. 30, 1881. t Four Casks Steel, Less C. C., Charges, . ****lbs. @%y= *i 67 15s. 6d. 14 10 50 C. 3 qr. 14 Ib. @ 4.8665 = 1***^** 67 8 1 13 6 68 14 2 $*** NOTE. On all merchandise the growth or produce of the countries east of the Cape of Good Hope (except wool, raw cotton, and raw silk, as reeled from the cocoon, or not further advanced than tram, thrown, or organzine), when imported from countries west of the Cape of Good Hope, there is levied a discriminating duty of 10 % ad valorem in addition to the duties imposed on any such articles when imported directly from the place of their growth or pro- duction (R. S. 2501). If the following goods, which are on the " Free List " (41)8), had been imported directly from the place of their production, there would have been no duty on the same. 248 D UTIE S. SO. Invoice of fifty-six (56) packages merchandise (purchased in London), shipped by THOMAS ROBINSON per Str. " City of Lincoln," for account and risk of and consigned to McKESSON & ROBBIES, New York. A H & C GUM A.NIMI . s. 4f 20 / /25 C. qr. Ib. 6 cases 8 2 23 net @ 11 10s., . . Discount 2J$, *** * * ** Expense, #* ** 1 M. &R. COIR FIBER. ** ** IVi't (?. ?r. 0. 50 bales 89 9 net @ 31s. 6d. . . *** * Brokerage, #** 1 ** 4 CHARGES. *** * . . rf. Shipping charges, cartage, etc., 3 18 7 Consul's certificate, . . . . 14 10 * ** LONDON, Dec. 21, 1881. *** ** PORT OF NEW YORK, Jan. 6, 1882. Entry for Consumption of Merchandise, imported by MoKES- & BOBBINS in the Str. " City of Lincoln," from London on the fourth day of January, 1 882. Marks. Numbers, Packages and Contertts. We. A. H. & C. M.&R. Six cases Gum Animi (Gum Copal). C. qr, Ib. wff. 8 2 23 975 Ib. Cost, . l /50 Fifty bales Coir Fiber. C. or. Ib. wg. 8U 9 9977^6. Cost, Charges (less C. C.), *** *s. *d. @ 4.86G5 = $***. Discriminating duty, 10^ of $**** = ***. ** 97.13.8 141.10 3.18.7 PARTNERSHIP. DEFINITIONS. 500. Partnership is the association of two or more persons who join their capital and services for the purpose of conducting business, the gains or losses being shared in such. proportion as may be stipulated in the agreement. The business association is called a Firm, House, or Company ; and each individual of the association is called a Partner. 501. A Special Partner is one who takes no active part in the business, and whose liability is limited to the amount of his investment. In order to thus limit his liability, the amount of his investment must be duly advertised, and he must take no active part in the business. The partners who conduct the business are called General Partners. Their private property is liable for the debts of the partnership. 502. The Capital or Capital Stock is the money or other property which is invested in a business. The partners' accounts are used to show the amounts invested. In most firms, the investments are entered in the partners' " stock ac- counts," and the amounts withdrawn by the partners during the year and their salaries are entered in their " private accounts." 503. A Resource or Asset is any kind of property belong- ing to the concern having a financial value. 504. A Liability is a debt owing by the concern. 505. The Net Worth of a concern is the excess of its resources over its outside liabilities. 250 PARTNERSHIP. 506. The Net Insolvency of a concern is the excess of its outside liabilities over its resources. The concern being unable to pay its debts in full, it is said to be insolvent. 507. G-ains or Losses, how shared. In most partner- ships, the gains or the losses are divided according to certain fractions or percentages ; the inequalities of the investments are adjusted by allowing interest upon the same; and the part- ners receive salaries for their services rendered. (See Ex. 34, Art. 51O.) Sometimes the net gain or net loss is shared in proportion to the investments (Ex. 15, Art. 51O), or the average investments. (Ex. 21, Art. 51O.) In joint stock companies the gains (dividends) and the losses (assessments) are shared in proportion to the investment or the amount of stock held. 508. G-ains or Losses, how found. When the books have been kept by "Single entry," and when no books have been kept, the gain is found by subtracting the net worth (5O5) at commencing, or the investment, from the net worth at closing ; and the loss, vice versa. When the books have been kept by " Double entry," the gain may be found as above, or by subtracting the sum of the separate losses from the sum of the separate gains. The results by the two methods should be the same and should prove each other. EXERCISES. 5O9. In the following exercises find the gain or the loss : 1. Capital at commencing, $5000 ; capital at closing, $3000. 2. Capital at commencing, $5000 ; capital at closing, $8000. 8. Capital at commencing, $5000 ; insolvency at closing, $1000. 4- Capital at commencing, $5000 ; insolvency at closing, $7000. 5. Insolvency at commencing, $5000 ; capital at closing, $2000. 6. Insolvency at commencing, $5000 ; capital at closing, $6000. PARTNERSHIP. 251 7. Insolvency at commencing, $5000 ; insolvency at clos- ing, $4000. 8. Insolvency at commencing, $5000 ; insolvency at clos- ing, $9000. Find the capital or the insolvency at closing : 9. Capital at commencing, $5000 ; gain during the year, 00. 10. Capital at commencing, $5000 ; gain during the year, 00. 11. Capital at commencing, $5000 ; loss during the year, 00. 12. Capital at commencing, $5000 ; loss during the year, (00. 13. Insolvency at commencing, $5000 ; gain during the year, 00. 14. Insolvency at commencing, $5000 ; gain during the year, '00. 15. Insolvency at commencing, $5000 ; loss during the year, '00. 16. Insolvency at commencing, $5000 ; loss during the year, 00. Find the capital or the insolvency at commencing: 17. Capital at closing, $5000 ; gain during the year, $3000. 18. Capital at closing, $5000 ; gain during the year, $6000. 19. Capital at closing, $5000 ; loss during the year, $4000. 20. Capital at closing, $5000 ; loss during the year, $9000. 21. Insolvency at closing, $5000 ; gain during the year, $1000. 22. Insolvency at closing, $5000 ; gain during the year, $8000. 28. Insolvency at closing, $5000 ; loss during the year, $2000. 24. Insolvency at closing, $5000 ; loss during the year, $7000. $3000 10 $6000. 11. $2000. 12 $8000 13 $1000 u $7000 15 $4000 16 $9000 EXAMPLES. 51O. 1. A and B are partners, A sharing f of the gain or loss and B . A invests $5000, and B $2350. At the end of the year their resources and liabilities are as follows : merchandise on hand, per inventory, $2000 ; real estate, $7000 ; cash, on hand and 252 PARTNERSHIP. in bank, $1532 ; due on personal accounts, 81640.25 ; notes on hand, $1000; notes outstanding, $800; owing by the concern to sundry persons, $4471.69. What is the amount of net resources belonging to each partner ? FIRST OPERATION. RESOURCES. Merchandise on hand, . . $2000 Real estate, .... 7000 Cash on hand, . . . 1532 Personal accounts, . . 1640.25 Bills receivable, . ... 1000 $13172.25 LIABILITIES. Bills payable, . . . $800 Personal accounts, . . 4471.69 5271.69 Present worth, $7900.56 Investments (subtracted), .... 7350. Total net gain, . , . $550.56 f of $550.56 = $367.04, A's share of the gain, i of $550.56 = 183.52, B's share of the gain. A's investment, . . . $5000 Plus his gain, . . . 367.04 Equals his present worth, .... $5367.04 B's investment, . . . $2350. Plus his gain, . . . 183.52 Equals his present worth, .... $2533.52 Total present worth, as above, . . . $7900.56 SECOND OPERATION. ANALYSIS. Theoretically, all the resources of a business belong to the creditors and the partners (proprietors), the partners' investments being regarded as liabilities ; hence, the resources and liabilities including the partners' accounts should be equal. If in a statement of the condition of a business, the resources and liabilities thus considered should not be equal, it is evident that the partners' accounts do not show their true interests, and the inference is that a gain or loss has occurred which has not been entered to their accounts. The excess of resources over liabilities would in such case show the gain, as would the excess of liabilities over resources show the loss. In order to restore the equilibrium, the gain should be credited or the loss debited to the partners' accounts. PARTNERSHIP 253 1. STATEMENT BEFORE ADJUSTING PARTNERS' ACCOUNTS. RESOURCES. LIABILITIES. Merchandise, Real estate, Cash, . Personal accounts, Bills receivable, . 2000 Bills payable, . 7000 Personal accounts, 1532 A's investment, 1640.25 B's do. 1000 13172.25 12621.69 800 4471.69 5000 2350 12621.69 Excess of resources (net gain), 550.56. A's f , $367.04 ; B's |, $183.52. 2. STATEMENT AFTER ADJUSTING PARTNERS' ACCOUNTS. RESOURCES. Merchandise, Real estate, Cash, . . . Personal accounts, Bills receivable, . 2000 7000 1532 1640.25 1000 13172.25 LIABILITIES. Bills payable, . Personal accounts, . A's investment and gain, . B's do. 800 4471.69 5367.04 253352 13172.25 2. A and B are partners, A sharing f of the gain or loss and B . A invested $5000, and B $2350. During the year the con- cern gained on merchandise, $955.56 ; on real estate, $315. The expense account showed a loss of $675 ; the interest account, $45. What was the net gain, and balance of each partner's account. NOTE. The above example is the complement of Ex. 1. The books having been kept by double entry, the separate gains and losses are given, and the net gain thus found. The loss and gain account and the partners' accounts are shown in the following operation in " skeleton ledger " form. OPERATION. B. Balance, 5367 04 Investment, 2000 Gain, . . 367 5367 04 5367 Balance, . 5367 Balance, 2533 52 Investment, 2350 Gain, . . 183 53 2533 52 2533 52 Balance, . 2533 53 Loss AND GAIN. Expense, . . 675 Mdse., . . 955 56 Interest, . . 45 Real Estate, 315 A's Gain |, . 367 04 &* J, . 183 52 1270 56 1270 56 254 PARTNERSHIP. 3. A and B started in business July 1, 1881. Each put into the concern $2200. The resources on Jan. 1, 1882, were as fol- lows: goods, $4000; bills receivable, $1500. The liabilities were $580. A has drawn out cash, $3000 ; and B, $2000. How much is due each partner, the gain or loss being divided equally ? NOTE. It must be "borne in mind that the amounts drawn out by the part- ners are as fully resources of the business as if charged to an outside party. 4. On Jan. 1, my brother and I started a business in which I invested $900, and he $400. We now propose to separate, and the business stands as follows : stock in store, $1800 ; cash on hand and in bank, $1200; outstanding accounts, considered good, $1200. According to the agreement, I am entitled to -f of the net gain, and my brother ^. During the time of the copartner- ship, I have drawn $4000 and he, $2800. Of the assets given above, how much are we each entitled to ? 5. C, D, and E are partners, each investing $10000, and each to share J of the gain or loss. The resources and liabilities at the close of business are found to be as follows, viz. : Merchandise on hand, per inventory, $8159.50; cash on hand, $5012.88 ; per- sonal accounts due the firm, $4235 ; notes and accepted drafts (bills receivable) on hand, $5000 ; real estate, $8000 ; bonds and stocks, $12000 ; owing by the firm to sundry persons, $5505 ; firm's notes outstanding (bills payable), $3000. C lias withdrawn during the year $1247.87 ; D, $1400 ; and E, $1489. What is each partner's interest in the concern at closing ? 6. C, D, and E are partners, sharing the gains and losses equally. C's net investment was $8752.13 ; D's, $8600 ; and E's $8511. During the year the firm's gains were as follows: Mer- chandise, $8529 ; stocks and bonds, $650 ; interest, $985.25. The cost of conducting the business was $2125. What was each part- ner's interest at closing ? 7. M and N are partners, M sharing J of the gain or loss and N . M invested $15000 and N $5000. At the close of the busi- ness year, the resources and liabilities of the concern are as fol- lows : cash on hand, $2128 ; bills payable, $4000 ; bills receivable, $3000 ; the firm owes sundry persons, $8375 ; due the firm from sundry persons, $16427 ; rent paid in advance, $375 ; mortgage held by the concern on the property of A. G. Pope, $5000 ; accrued PARTNERSHIP. 255 interest on the same, $150 ; store fixtures valued at $835 ; mer- chandise on hand, $9416 ; accrued interest on firm's notes out- standing, $112 ; accrued interest on notes held by the firm, $75. M has withdrawn $2465 ; and N, $2275. According to the agree- ment, each partner is to receive a salary of $2500. What are the separate interests at the close of the business ? 8. R, S, T, and U enter into copartnership with equal capital, upon the following conditions : R to receive as a salary $2000 ; S, $1500; T, $1200; and U, $1000; the gain or loss to be divided equally. At the close of the year, the net gain, exclusive of salaries, proves to be $5400. To how much of this amount is each entitled ? 9. X, Y, and Z commence business without capital. Accord- ing to the partnership contract, X is to receive a salary of $3000 ; Y, $2500 ; and Z, $2000 ; the gain or loss to be divided equally. During the year, X withdraws $3000 ; Y, $2800 ; and Z, $1800. What is the balance clue each partner at the end of the year, if the gain, without taking into account the partners' salaries, is $9000 ? 10. A and B are partners, A investing f of the capital, and B ^ ; the gains or losses to be shared in the same proportion. The following is an exhibit of the business, excepting the part- ners' accounts, at the close of a certain period : Resources, cash, $3775 ; Stone & Co., $150 ; A. R. Mead, $1200 ; bills receivable, $5500 ; interest on the same, $125 ; merchandise, $5140. Liabil- ities, L. Blair, $500; W. H. Rice, $723; Martens & Bultman, $517.64 ; bills payable, $3300 ; interest on the same, $169. The net gain during the year was $3174. What was each partner's original investment ? 11. Upon a close valuation of the personal accounts due the firm in the preceding example, the partners are convinced that Stone & Co.'s is worth no more than 50^ of its face ; and A. R. Mead's, 25% of its face. Upon this valuation what would be the gain, and what the condition of the partners' accounts at closing ? 12. P and Q are partners, each to receive interest on his net investment at the rate of G% per annum, and the net gain or loss to be divided equally. P invests, Jan. 1, $5000 ; Mar. 1, $4000 ; June 16, $1500 ; and draws out Apr. 16, $2500. Q invests, Jan. 1, 256 PARTNERSHIP. $8000 ; Sept. 16, $2000; and draws out June 1, $1500 ; Nov. 11, $500. At the close of the year, the net gain is found to be $4475.25, without taking into account the interest on the part- ners' accounts. What is the amount due each partner after the gain is adjusted ? (Time by Compound Subtraction.) 13. A and B have been doing business as partners, A sharing | and B f of the gains and losses. A invested $4500, average date Mar. 25, 1882 ; and drew out $2700, average date Sept. 12, 1882. B invested $7200, average date June 17, 1882 ; and drew out $3750, average date Oct. 25, 1882. At the time of their dissolu- tion, Jan. 1, 1883, the debts of the firm were all paid and they had on hand belonging to the firm $8750 in cash. How shall the money be divided, each being allowed interest at 6^ on his investment and charged with interest at the same rate on the amounts drawn ? (Time by exact days. Interest 360 days to the year. ) 14. A and B are partners, A having -| and B f interest. A advanced in business $12000, average date Jan. 12, 1883 ; and drew out $1265, average date Oct. 20, 1883. B advanced $7500, average date Apr. 5, 1883; and drew out $2560, average date Nov. 25, 1883. Jan. 1, 1884, A purchases B's interest in the business, and at that date the assets are as follows : Cash, $5800 ; merchandise, $6250 ; notes on hand, $7300; accrued interest on the same, $387.14; personal accounts, $5700. The liabilities are as follows : Notes outstanding, $4200 ; accrued interest on the same, $227.65 ; personal accounts, $2500. How much is B entitled to, 5% of the personal accounts being considered uncol- lectible, and interest being reckoned on the partners' accounts at 6$ per annum (365 days to the year) ? 15. A and B are partners in business, the gain or loss to be divided in proportion to investment. A invested $8750 ; B in- vested $4000. The net gain is $2726.15. What is each partner's share ? FIRST OPERATION. FRACTIONAL METHOD. ANALYSIS. Since A's investment, $8750, is T VWV of tlie total investment, he is entitled to ^Wo of *^ e g a > and for a similar reason, B is entitled to .|s of 12720.15 = $1870.89, A's ffain. H of $2726.15 = $855.26, B's gain. PARTNERSHIP. 257 SECOND OPERATION. BY PROPORTION. ANALYSIS. The total investment is to each partner's investment as the total gain is to each partner's gain. $12750 : $8750 :: $2726.15 : $1870.89, A's gain. $12750 : $4000 :: $2726.15 : $855.26, B's gain. NOTE. Cancel any factor common to the given extreme and either of the means. THIRD OPERATION. BY PERCENTAGE. ANALYSIS. $2726.15, the gain, is 21.3818$. of $12750, the total invest- ment. The partners' gains are therefore 21.3816% of their respective investments. 21.3816^ of $8750 = $1870.89, A's gain. 21.3816$ of $4000 = $855.26, B's gain. NOTE. In order to produce exact results by this method, it is necessary to extend the number expressing the rate per cent, of the gain or loss to several decimal places. 16. E, F, G, and H enter into a joint speculation. E advances $5000, F $7000, G $8000, and H $10000, the gain or loss to be divided according to investment. They gain $14285. What is .the share of each ? 17. Four merchants ship goods on joint account. A puts in $6000, B $5500, $4200, and D $4800. What will be each man's share, if the gain is $9200 ? 18. A lot, whose front is 240 feet and whose depth is 100 feet, is bought by A, B, and 0, who pay respectively $3000, $4000, and $5000. How many feet front is each entitled to, if it is divided in proportion to their investments ? 19. Five persons having claims against the government, placed their claims in the hands of an agent for collection ; A's claim amounted to $500, B's to $425, C's to $300, D's to $250, and E's to $175; but, after the agent had deducted his fees, there re- mained only $1237.50. How much did each claimant receive ? %0. A and B are partners^. They have cash and notes on hand to the amount of $6475.28. A has drawn from the concern $2478.30, and B has drawn $1016.48. A invested $4287.46, and B, $1037.75. The firm owe sundry persons $5016.82. What is each partner's present interest in the concern, if they share equally in gains and losses ? 258 PAR TNE RSHIP. 21. A and B are partners, gain or loss to be divided in pro- portion to average investment. A invests, Jan. 1, $4000 ; Mar. 1, $2000 ; Oct. 1, $3000 ; and withdraws July 1, $1500 ; Dec. 1, $1000. B invests, Jan. 1, $6000 ; Sept. 1, $3000. They close their books Jan. 1 of the following year and find they have gained $3456. What is each partner's share ? NOTE. An Average Investment is an investment for a certain period of time equivalent to several investments for different periods of time. OPERATION. A invested Jan. 1, $4000 x 12 : Mar. 1, 2000 x 10 Oct. 1, 3000 x 3 : A withdrew July 1, 1500 x 6 Dec. 1, 1000 x 1 : A's average investment for 1 month, OR, A invested Jan. 1, Mar. 1, 2 = $4000 2000 6000 x 4 = withdrew July 1 1500 4500 x' 8 = invested Oct. 1, 3000 7500 x 2 = withdrew Dec. 1, 1000 6500 x 1 = A's average investment for 1 month, $48000 20000 JMMM) 77000 9000 _i_qoo 10000 67000 $8000 24000 13500 15000 6500 $67000 ANALYSIS. By the first operation, we suppose each investment to be made for the remainder of the time. To find the average investment, multi- ply each investment and withdrawal by the interval between its date and >time of settlement. Subtract the products obtained from the withdrawals from the products obtained from the investments. The remainder will be the average investment for 1 month, if the time is found in months. A's invest- ment of Jan. 1 is in the business 12 months (Jan. 1 to Jan. 1); the use of $4000 for 12 months is equivalent to the use of $"48000 for 1 month. Treating the other investments in like manner, we find A's total investments are equivalent to $77000 for 1 month. A's withdrawals are equivalent to $10000 for 1 month. A's net average investment is therefore equivalent to $67000 for 1 month. By tho second operation, we find the actual amount in the business for each month of the year. Jan. 1, A invested $4000, which was in the business until Mar. 1, or for 2 months. Mar. 1, he added $2000, making his total invest- PARTNERSHIP. 259 ment $6000, which was in the business until July 1, or for 4 months. July 1, he withdrew $1500, leaving in the business $4500 until Oct. 1, or 8 months, etc. The several net investments as found in this manner are equivalent to $67000 for 1 month. B's average investment, as found by either of the above methods, is $84000 for 1 month. A's average investment for the year is $5583.33* ; and B's, $7000. To avoid fractions, divide the gain in proportion to the average investments for 1 month. After the average investments are found for a common time, the gain may be divided according to either of the methods under Ex. 15. By the fractional method, A would be entitled to T 6 g 7 T of the. gain, and B to T 8 g\. 22. and D are partners, gain or loss to be divided in propor- tion to average investment. C puts in $6000 for one year, and $7000 for one and a half years ; D puts in $6000 for two and a half years. The net loss is $1565.40. What is each one's share ? 23. A, B, and C are partners. A puts into the concern $3000, but withdraws half of it at the end of 6 months ; B puts in $2000, and adds $500 to it at the end of 4 months ; C puts in $2500 for the whole year. The gain during the year is $1700. What is each one's share ? 24. Three contractors agree to build a road for $10000. A has 25 men at work for 16 days and 30 men for 34 days. B has 40 men for 10 days and 45 men for 40 days. C has 48 men for 50 days. C receives $200 extra for superintending the work. How much is each contractor entitled to ? 25. J, K, and L are partners, gain or loss to be divided accord- ing to average investment. J invests as follows : Jan. 1, $6000 ; Apr. 1, $4000 ; K invests, Jan. 1, $8000 ; L invests, Jan. 1, $7000; Apr. 16, $2500 ; and draws out June 16, $3500. At the end of the year the net gain is found to be $4135.60. What is each partner's share ? (Time by Compound Subtraction.) 26. A, B, C, and D were partners for two years. When the firm commenced business, A's investment was $6000, B's $3500, C's $2800, and D's 1700. At the end of 8 months, A withdrew $3000. At the end of 10 months, D added $1300 to his former investment. At the end of one year, B withdrew $800. At the close of the two years, they had gained $4727. What was each partner's share of the gain ? 27. A and B are partners for one year, the gain or loss being divided in proportion to their average investments. A invested, Jan. 1, $8000 ; June 16, $1500 ; Aug. 1, $2500 ; and drew out 260 PARTNERSHIP. May 1, $1500. B invested, Jan. 1, $10000; Apr. 1, $500; and withdrew Aug. 16, $2500. How much should A invest Sept. 1 to entitle him to one-half the gain ? 28. A, B, and C form a copartnership under the following con- ditions : A is to manage the business, and to receive therefor $2400 per annum, which amount is to be credited as July 1. He is to receive interest on his salary and to pay interest on sums with- drawn at the rate of Q% per annum. B and are to furnish the capital, and to receive interest therefor at the rate of 6% per annum. The net gain or loss to be divided equally. B invests, Jan. 1, $10000 ; Apr. 1, $5000. C invests, Jan. 1, $10000 ; July 1, $5000 ; and draws out Sept. 16, $500. A draws out, Feb. 1, $200 ; Mar. 1, $400; July 11, $500; Oct. 1, $200; Nov. 21, $100. At the end of the year, the gain without taking into account either the salary to be paid to A or the interest on the partners' accounts is $8437.16. What will be the balance of each partner's account, when all the items have been properly entered ? 29. C and D are partners. According to agreement C is to share f of the gain or loss, and D J. At the end of the year, D desires to increase his investment so that he will be entitled to a J- interest. How much must D invest, the partners' accounts after the books are closed being as follows : C's debit, $6712.38 ; C's credit, $27000 ; D's credit, $9000 ? 30. A and B buy a ship for $80000, A having | interest and B f. Subsequently pays $40000 for -J interest, and A and B agree to have each interest. How is the $40000, which C pays in, divided between A and B ? 31. A, B, and C are partners, A investing $25000 capital, B $5000, and C nothing. The proportionate interests are : A 60%, B 25%, C 15%. At the expiration of the term of copartnership, and after the gains and losses have been adjusted, A's credit of capital stands intact, B has a credit of only $1000, while C has overdrawn his account $8534. C being insolvent, how r much must B pay into the concern to adjust his share of the loss ? 32. M, the owner of a mill, employs S, a miller, under the fol- lowing conditions: M is to furnish the requisite capital, and S to receive, in lieu of salary, -J of the profits. M has a store connected with the mill, on the books of which are entered all time sales of mill products. The grain, etc. for the mill is furnished by M. At the beginning of the year the value of the grain, flour, feed, PARTNERSHIP. 261 etc. is $1727. During the year M's purchases for the mill amount to $19275. S has received for cash sales $16337, of which he has paid over to M $15550. The sales on account, as shown on M's books, amount to $8375 ; and the value of the products on hand is $2828. During the year S has purchased goods at M's store to the amount of $837.65. How much is owing to S at the expiration of the year? 83. A and B form a copartnership Jan, 1, 1878, A having J interest and B J. For the purpose of a valuation to be covered by insurance, the inventory of merchandise is increased at the end of the first year $1550. Jan. 1, 1879, the terms of copartnership are changed, A having \ interest and B -|. At the end of this year, the inventory is increased fictitiously $700 more, or $2250 in all. The same basis of copartnership continues for the year 1880, at the close of which year the inventory is additionally increased $1293.75. Jan. 1, 1881, the terms of copartnership are readjusted, A having T %, and B T %- interest. At the close of this year the inventory was increased additionally $432.50. Jan. 1, 1882, the copartnership was made equal, each partner holding a half interest. The proposition is now made to so adjust this fictitious valuation that each of the partners shall be properly credited in accordance with the new terms of copartnership. 1. What entry should be made to accomplish this purpose ? 2. What entry should be made to cancel the fictitious valuation of merchandise, and place the partners' accounts in the proper condition ? SJf. A, B, and C are partners, A sharing f of the gain or loss, B f, and . Interest is to be reckoned at the rate of 6% per annum (365 days to the year) on the partners' accounts, and each partner is to receive a salary of $1800, to be credited as July 1. A invested, Jan. 1, $16000 ; and withdrew during the year $4875, average date, Aug. 21. B invested, Jan. 1, $20000 ; and with- drew $6224, average date, June 18. C invested, Jan. 1, $5000 ; and withdrew $2625, average date, July 31. Jan. 1, of the following year, the merchandise account shows a gain of $18437.16; the interest account (not including the interest on the partners' accounts) a gain of $586.38 ; sundry consignment accounts show a net gain of $1287.14. The expense account (not including the partners' salaries) shows a loss of $3424.75. What is each partner's interest in the business at closing? How will A be affected if each partner's salary is increased to $2500 ? 262 PARTNERSHIP. 35. A and B unite in conducting a summer hotel, on the follow- ing basis : 1. Each is to receive interest at the rate of 6% per annum on his investment ; 2. A is to receive a salary of $1000 and B of $800, for the season ; 3. The profit or loss of the general busi- ness is to be divided in the proportion of A |, B -J ; the profit or loss of the livery business attached thereto in the proportion of A ^, B f ; the profit or loss of the bathing business in the propor- tion of A -J-, B J. A invests an average of $10150 for four months, and B an average of $6750 for the same time. At the close of the business the accounts showing loss and gain stand as follows: Outgo. HOTEL. Income. Outgo. LIVERY. Income. 15150.75 | 25175.19 1592.75 | 3279.50 Outgo. BATHING. Income. 759.12 I 1275.30 There is besides an item of service amounting to $375, which at the time could not be easily apportioned in the charges, and which, of course, does not appear in the above outgoes. It is agreed that this item, as also the sums severally due the partners for interest and salaries, shall be charged to the several depart- ments of the business in proportion to the net gains. There is, also, an inventory in the livery business amounting to $429.33. How much clear gain from all sources will each partner get out of the business. 36. A, B, and are equal partners in a mill, each to receive 6% per annum interest on his average investment. C is to super- intend the business and receive therefor a yearly salary of $3000 ; B keeps a store at which the operatives trade, and is to pay to A and C 5% on sales to operatives. A negotiates the products of the mill, for which he is allowed 10$ on the net profits as existing before his percentage is taken. A's average investment for the year is $9750; B's $5750 ; C's $5000. Leaving out the interest, salary and percentages, the net gain for the year is $15000. B's sales to operatives amount to $1575. What share of the $15000 is each partner entitled to ? 87. A owns a business, the good will of which is estimated at $10000, and the stock on hand at $15000. B and C agree to. unite with him on the following conditions : B to invest $25000 PARTNERSHIP. 263 cash, and C to devote his entire time to the business, for which he is to receive, in addition to his interest, an annual salary of $1000. The capital is to be kept intact, and no interest to be allowed therefor. The gain or loss to be divided equally between the three partners. At the end of the year the resources, includ- ing good will, book accounts, notes, inventories, etc., but not in- cluding amounts drawn by the partners, amount to $67000, and the liabilities to outside parties, to $10500. C has drawn out during the year $2500 ; B, $1575 ; A, $2000. Of the resources above named there are bad debts not to be counted, amounting to $575. What is the condition of each partner's account? tfS. A, B, and C are partners in business, investing as follows : A, $4000; B, $6000; C, $8000. The partners are to share the profits and losses in proportion to their investments. Each is entitled to compensation for services at the rate of $150 per month, payable at the end of each month and not to bear interest. In case that either partner shall draw a greater amount than shall at the time be due him for services, he shall be charged interest upon such overdraft at the rate of \% per month for the length of time such overdraft continues. At the end of the year B and C purchase the interest of A, and in the payment therefor, it is desired that the remaining members shall so invest that their interests shall be equal. It is mutually agreed that the "good will" of the business shall be valued at $3000 in the final settlement. It is also agreed that a discount of b% shall be allowed upon all un- collected accounts as a fund to meet bad debts and costs for col- lecting. A statement of the business previous to closing shows the following results : merchandise, horses, wagon, office fixtures, and cash on hand, $12410 ; sundry debtors, $17030 ; sundry creditors, $4050 ; expense account (not including partners' salaries), $2400 ; profit on merchandise sold, $15290. A withdrew on account of salary Apr. 1, $450 ; July 1, $300 ; Oct. 1, 400. B withdrew Mar. 1, $400 ; Apr. 1, $150 ; June 1, 400 ; Oct. 1, $800; Dec. 1, $500. C withdrew Apr. 1, $600; July 1, $700; Oct. 1, $600 ; Nov. 1, $200. How much must B and C each in- vest or pay A, and how should the books of the new firm be opened ? (Condensed from "The Book-Keeper.") NOTE. B and C, not desiring to have the new books encumbered with the contingent accounts of "good will" and "reserve fund/' closed these accounts after a settlement was made with A. NATIONAL BANKS. DEFINITIONS. 511. A National Bank is a bank organized under the laws of, and chartered by, the United States. 1. Associations for the purpose of carrying on the business of banking may be formed by any number of persons, not less in any case than five (R. S. 5133). 2. No association shall be organized with a less capital than $100,000 ; except that banks with a capital of not less than $50,000 may, with the approval of the Secretary of the Treasury, be organized in any place the population of which does not exceed 6,000 inhabitants. No association shall be organized in a city the population of which exceeds 50,000 persons with a less capital than $200000 (R. S. 5138). The capital stock shall be divided into shares of $100 each. 3. Every national bank, before it shall be authorized to commence busi- ness, shall transfer and deliver to the Treasurer of the United States, any U. S, registered bonds, bearing interest, to an amount not less than one-third of the capital stock paid in ; except that national banks having a capital of $150,000 or less, shall not be required to deposit U. S. bonds in excess of one- fourth of their capital stock, as security for their circulating notes. (Act of July 12, 1882.) 4. National banks are authorized to discount and negotiate notes, drafts, etc. ; to receive deposits ; to buy and sell exchange, coin and bullion ; to loan money on personal security ; and to issue circulating notes (R. S. 5136). 5. National banks are prohibited from making loans on real estate (R. S. 5137), or on security of their own shares of capital except to secure debts previously contracted (R. S. 5201). Real estate purchased or mortgaged to secure a pre-existing debt shall not be held for a longer period than five years (R. S. 5137). They are also prohibited from making loans to one person or association, excepting on business paper representing actually existing value as security, in excess of one-tenth of the capital of the bank (R. S. 5200). 6. The stockholders of a national bank are individually liable (equally and ratably, and not one for another) for an amount equal to the par value of the capital stock held by them. DEFINITIONS. 265 Circulation. Upon a deposit of registered bonds, the association making the same shall be entitled to receive from the Comptroller of the Currency circulating notes of different denomi- nations (19O), in blank, equal in amount to ninety per centum of the current market .value not exceeding par, of the United States bonds so transferred and delivered, and at no time shall the total amount of such notes issued to any such association exceed ninety per centum of the amount at such time actually paid in of its capital stock. 1. Any national bank desiring to decrease its circulation, in whole or in part, may deposit lawful money (specie or legal tenders) with the Treasurer of the United States in sums of not less than $9,000, and withdraw a propor- tionate amount of bonds held as security for such notes. No national bank which makes any deposit of lawful money in order to withdraw its circulating notes, shall be entitled to receive any increase of its circulation for the period of six months from the time it made such deposit. Not more than $3,000,000 shall be deposited during any calendar month for this purpose. (Act of July 12, 1882.) 2. The State bank circulation wholly ceased after Congress had imposed a penalty of 10^ in the form of a tax every time it should be issued. This act took effect Aug. 1, 1866. 513. Redemption. The circulating notes of national banks are redeemed in lawful money by the banks which issued them and by the Treasurer of the United States at Washington, D. C. 1. Section 3 of the act of June 20, 1874, provides that every national bank shall, at all times, keep and have on deposit in the Treasury of the United States in lawful money of the United States, a sum equal to 5% of its circulation, to be held and used for the redemption of such circulation. 2. " Section 5222 of the Revised Statutes requires that all national banks which go into voluntary liquidation shall, within six months thereafter, deposit in the Treasury an amount of lawful money equal to the amount of their circulating notes outstanding. The law also requires that full provi- sion shall be made for the redemption of the circulating notes of any insol- vent bank before a dividend is made to its creditors. Thus it will be seen that no association can close up its business without first providing for the payment of all its circulating notes, and that the amount deposited for their redemption must remain in the Treasury until the last outstanding note shall have been presented. It is therefore plain that the government, and not the bank, receives all the benefit arising from lost or unredeemed circulating notes." #66 NATIONAL BANKS. 514. Official Eeport of a National Bank. T3EPORT OF THE CONDITION OP "THE MERCHANTS' NA- .Lt TIONAL BANK," at New York, in the State of New York, at tlie close of business on the llth day of March, 1881 : RESOURCES. Loans and discounts $6,443,761 75 Overdrafts 2,417 71 U. S. bonds to secure circulation (par value) 400,000 00 U. S. bonds on hand (par value) , 95,000 00 Other stocks, bonds, etc 9,000 00 Due from other National banks 265,104 90 Due from State and private banks and bankers 158,515 75 Banking house $181,000 00 Other real estate , 25,000 00 206,000 00 Current expenses and taxes paid 15,748 72 Premiums paid 14, 187 50 Checks and other cash items 87,440 57 Exchanges for Clearing House (546) 3,987,982 71 Bills of other banks 45,418 00 Fractional paper currency, nickels, and cents 970 00 Specie, viz. : Gold coin $280,578 39 Gold Clearing House Certificates (547, 15). ... 730,000 00 Silver coin 4,217 60 1,014,795 99 Legal tender notes (1 89) 796,192 00 Redemption fund with U. S. Treasurer (5% of circulation) (513, 1) 18,000 00 Total $13,560,535 60 LIABILITIES. Capital stock paid in $2,000,000 00 Surplus fund 389,850 91 Undivided profits 346,361 55 National bank notes outstanding 360,000 00 State bank circulation outstanding 2,689 00 Dividends unpaid 3,320 25 Individual deposits subject to check $5,417,189 10 Demand certificates of deposit 6,124 36 Certified checks 1,567,905 28 Cashier's checks outstanding 280,699 59 7,271,918 33 Due to other National banks 2,543,987 11 Due to State and private banks and bankers 642,408 45 Totai. . $13,560,535 60 NATIONAL BANKS. 267 515. Reserve. The national banks in the reserve cities* are required by law to hold a lawful money reserve of 25% of their deposits ; all other national banks 15%. The excess above legal requirements is called "surplus reserve." The reserve is made up of specie, legal-tender notes (189), U. S. certifi- cates of deposit, balances due from reserve agents, and the 5% redemption fund, with the U. S. Treasurer (513, 1). 516. Surplus Fund. The law provides that a surplus fund shall be accumulated, by setting aside, before the usual semi-annual dividend is declared, one-tenth part of the net profits of the bank for the preceding half-year, until the surplus fund shall amount to 20% of its capital stock. 517. Taxation. The national banks pay to the United States a tax of 1% annually upon the average amount of their notes in circulation, \% annually upon the average amount of their deposits, and \% annually upon the average amount of cap- ital not invested in U. S. bonds. The banks, other than national, pay taxes to the United States on account of their circulation, deposits, and capital, at the same rates as are paid by the national banks. EXAMPLES. 518. 1. Oct. 2, 1879, the number of notes held by the national banks was 808,269, and the total amount $875,013,107. What was the average amount of each note discounted ? 2. The impairment of the capital stock ($300000) of an insol- vent national bank was $216000. What was the rate per cent, of the assessment made upon the stockholders for the purpose of making good the deficiency (511, 6) ? How much was Mr. A. obliged to pay, who owned 80 shares ? 8. What amount of bank notes is issued to a national bank that deposits $780000 in U. S. bonds to secure circulation (512) ? How much is its redemption fund (513, 1) ? 4- A national bank, desiring to reduce its circulation, deposits with the Treasurer of the United States $27000 in legal-tenders, * The reserve cities are New York, Boston, Philadelphia, Baltimore, Albany, Pitts- burgh, Washington, New Orleans, Louisville, Cincinnati, Cleveland, Chicago, Detroit, Mil- waukee, Saint Louis, and San Francisco. 268 NATIONAL BANKS. and sells the bonds withdrawn (512, 2) in the market at 118|. What were the proceeds ? 5. The circulation of a national bank having a capital of $150000 is $57600; what is the remaining amount of circulation which it may call for by depositing the necessary amount of bonds (512)? What is the par value of the bonds now on deposit? What additional amount of bonds will the bank be required to deposit if the circulation is increased to the maximum ? 6. How much is the redemption fund of a bank whose circulation is $427500? What is the amount of bonds on deposit to secure its circulation ? 7. The New York associated banks, according to the state- ment of Saturday, Mar. 25, 1882, held $58,602,100 in specie and $16,150,900 in legal-tenders. Their deposits on the same date were $285,659,600. What was the excess of reserve (515) above legal requirements ? 8. Oct. 1, 1881, the national banks of Boston had $8.286,182 in specie, $3,457,379 in legal-tenders, $75,000 in U. S. certifi- cates of deposit, $11,735,499 due from reserve agents, and a redemption fund with U. S. Treasurer of $1,603,628. What was the ratio of the reserve to the deposits, which were $95,776,386? What amount of 'reserve was required? What was the surplus reserve ? 9. What amount of reserve was required by the national banks of the State of Maine, their deposits being $9,558,878 ? 10. The net earnings of a bank, whose surplus (516) is less than 20% of its capital ($300000), are $10475.38. What amount must be carried to the surplus account, and what are the undivided profits after declaring a dividend of 3% ? 11. What is the semi-annual tax (517) upon a banker whose capital is $5358, and whose average deposits are $18368 ? 12. What is the semi-annual tax upon a national bank whose average circulation is $462,730, average deposits $1,185,952, capital $1,500,000 ? 13. A bank having a capital of $250,000, and a surplus of $50,000, for a period of six months, earned $58693, and declared a dividend of $30000. What was the rate of the divi- dend ? The dividend is what % of the capital and surplus ? The net earnings are what % of the capital and surplus ? SAVINGS BANKS. DEFINITIONS. 519. Savings Banks are institutions for the deposit and safe keeping of small sums of money. They are designed to encourage thrift and economy among the working classes. 520. Interest is usually declared Jan. 1st and July 1st of each year, and when declared is carried at once to the credit of each depositor on the books of the bank, where it stands as a deposit, and is entitled to interest the same as any other deposit. Savings banks, therefore, pay compound interest. No interest is allowed on the fractional parts of a dollar, nor is any interest allowed on any sum withdrawn previous to the first day of January or July, for the period which may have elapsed since the last dividend. 521. Deposits are practically payable on demand, though the right to require a notice of 60 or 90 days is reserved. In some savings banks, deposits commence to draw interest Jan. 1st, April 1st, July 1st, and Oct. 1st ; in others, deposits made on or before the first of any month draw interest from the first days of those months respectively. 522. According to the laws of the State of New York, No person shall have a deposit larger than the sum of three thousand dollars, exclusive of accrued interest, unless such deposit was made prior to the passage of the act (May 17, 1875), or pursuant to the order of a court of record, or of a surrogate. Savings banks are restricted to 5% per annum regular interest or divi- dend. They must, however, declare an extra dividend at least once in three years, when their surplus earnings amount to 15$ of their deposits. Saving's banks are allowed to pay interest on all sums deposited during the first ten days of January and July, and the first three days of April and October from the first of those months respectively. 70 SAVINGS BANKS. EXAMPLES. 523. Perform the following examples according to both methods mentioned in Art. 521. Where no rate is mentioned, 4% is understood. 1. Mr. A. deposited in a savings bank, Jan. 1, 1882, $145. How much interest should be credited to him July 1, 1882 ? OPERATION. 145 ANALYSIS. In any savings bank, lie would be credited for 02 the interest of $145 from Jan. 1 to July 1, or 6 mo. at 4% per an- num. k.% per annum is equivalent to 2% for 6 mo. 2. Mr. B. deposited in a savings bank Mar. 29, 1880, How much interest, at 5$, should be credited to him July 1, 1880 ? Ans. $2.75. OPEBATION. ANALYSIS. He is entitled to the interest of $220 *% from Apr. 1 to July 1, or 3 mo., at 5^ per annum. 5 f / 55 %. per annum is equivalent to \\% for 3 mo. ^\% is found o A as in the operation. S. A person deposited Dec. 30, 1881, $150; Feb. 20, 1882, $40 ; April 1, 1882, $120 ; May 30, 1882, $60. What amount was due July 1, 1882, nothing having been withdrawn ? ANALYSIS. If interest begin on the first of each quarter, the first deposit, $150, will draw interest from Jan. 1, or for 6 mo. ; the second and third deposits, $160, will draw interest from April 1, or for 3 mo. ; the last deposit, made May 30, will draw no interest July 1. If interest begin on the first of each month, the first deposit, $150, will draw interest from Jan. 1, or for 6 mo. ; the second deposit, $40, made Feb. 20, will draw interest from March 1, or for 4 mo. ; the third deposit, $120, made April 1, will draw interest from April 1, or 3 mo.; the fourth deposit, $100, made May 30, will draw interest from June 1, or for 1 mo. 4- The following deposits were made in a savings bank : July 1, 1881, $100 ; July 16, $40 ; Aug. 1, $75 ; Aug. 29, $45 ; Sept. 30, $75 ; Oct. 28, $200 ; Nov. 25, $30 ; Dec. 31, $100. What was due Jan. 1, 1882 ? 5. How much interest was due on the following account July 1, 1883 ? Deposits, Oct. 1, 1881, $200 ; Dec. 31, 1881, $160 ; Mar. 24, 1883, $100. SAVINGS BANKS. 271 6. Mr. A. made the following deposits in a savings bank: Jan. 1, 1879, $100 ; May 1, 1879, $140 ; June 30, 1879, $40 ; Oct. 1, 1879, $60 ; Feb. 28, 1880, $120 ; June 30, 1880, $45 ; Aug. 29, 1881, $200. What was the balance due Jan. 1, 1882 ? 7. What is the balance of the following account July 1, 1879, interest being reckoned at Q% until July 1, 1877, and at 5% there- after : Deposits, Oct. 14, 1876, $200; Mar. 30, 1878, $135; April 1, 1879, $90. 8. How much is due on the following account July 1, 1879, interest being reckoned at 6% until Jan. 1, 1877, and at 5% there- after : Deposits, Jan. 31, 1876, $100 ; Apr. 1, 1876, $100 ; Oct. 28, 1878, $30 ; Nov. 30, 1878, $30 ; Feb. 1, 1879, $25 ; Mar. 1, 1879, $25. 9. What is the balance of the following account July 1, 1882 ? Balance due Jan. 1, 1882, $103. Deposits, Jan. 28, $40 ; Mar. 30, $125 ; May 26, $80. Drafts, Feb. 20, $20 ; April 18, $15 ; May 3, $25 ; June 16, $100. ANALYSIS. In order to more readily determine the amounts that are entitled to interest, arrange the account in the following form, and find the balance after each draft or after two or more drafts made without any inter- mediate deposit. Date. Deposits. Drafts. Balances. Jan. 1, 103 28, 40 Feb. 20, 20 123 Mar. 30, 125 Apr. 18, 15 May 3, 25 208 26, 80 June 16, 100 188 The smallest balance found is $123, the amount remaining on deposit after the draft of Feb. 20 ; of this balance, $103 was on deposit Jan. 1, and the remaining $20 was deposited Jan. 28. (It is the custom to deduct the drafts from the last deposits made). Since the balance June 16, $188, is less than the balance, May 8, $208, it is evident that the excess, $20, has been with- drawn, and therefore is not entitled to interest. Of the $188, interest has already been allowed on $123, and the remaining $65, it is seen by inspection, was deposited Mar. 30. If interest commence the first of each quarter, the several amounts will SA VINGS BANKS. draw interest as follows : $103 from Jan. 1, or 6 months ; $30, deposited Jan. 28, and $65 deposited Mar. 30, making $85 from April 1, or 3 months. If interest commence the first of each month, the several amounts will draw interest as follows : $103 from Jan. 1, or 6 months ; $20, deposited Jan. 28, from Feb. 1, or 5 months ; $65, deposited Mar. 30, from April 1, or 3 months. 10. What is the balance of the following account July 1 ? Balance due Jan. 1, $30; deposits, Feb. 16, $50; Apr. 1, $185. Drafts, Mar. 12, $60 ; May 10, $50 ; June 20, $60. 11. Find the balance of the following account, Jan. 1, 1883. Deposits, July 1, 1882, $175 ; Aug. 1, $40 ; Sept. 16, $280. Drafts, Oct. 18, $90 ; Nov. 27, $125. 12. Balance the following account, Jan. 1, 1882. Deposits, July 28, 1881, $100; Aug. 16, 1881, $75; Oct. 17, 1881, $50; Oct. 30, 1881, $20. Drafts, Sept. 30, 1881, $25 ; Nov. 30, 1881, $100. 13. Balance the following Jan. 1, 1881. Balance due July 1, 1880, $300. Deposits received, Aug. 1, $150 ; Sept. 27, $60 ; Oct. 12, $325. Drafts paid, July 16, $150 ; Sept. 1, $150 ; Nov. 17, $70 ; Dec. 18, $140. 14. What is the balance of the following account July 1, 1882 ? Balance due Jan. 1, 1882, $364.48. Deposits, Jan. 24, 1882, $50 ; Feb. 16, 1882, $80 ; Apr. 30, 1882, $40 ; June 28, 1882, $100. Drafts, Mar. 30, 1882, $75 ; May 19, 1882, 810. 15. How much is due on the following account Jan. 1, 1882 ? Deposits, Dec. 16, 1880, $300; Feb. 25, 1881, $100; Mar. 16, 1881, $40 ; July 1, 1881, $25 ; Sept. 24, 1881, $50 ; Dec. 30, 1881, $100. Drafts, June 18, 1881, $75 ; Nov. 13, 1881, $30. 16. What is the balance of the following account July 1, 1882 ? Deposits, Jan. 3 (as Jan. 1), 1881, $500; Mar. 30, 1881, $90; Oct. 1, 1881, $160 ; Feb. 20, 1882, $80 ; Mar. 28, 1882, $40. Drafts, July 20, 1881, $100 ; Jan. 2 (as Jan. 1), 1882, $40 ; June 1, 1882, $60. 17. How much was due July 1, 1882, on the following pass-book? Dr. FRANKLIN SAVINGS BANK in account "with F. G. SNOOK. Or. 1881. 1881. Jan. 1 Four Hundred Dollars. 400 Aug. 1 Two Hundred Dollars. 200 Mar. 15 Ninety Dollars. 90 1882. 1881. Interest to July. * *# Jan. 16 One Hundred and Sept. 16 Two Hundred Dollars. 200 Sixty Dollars. 160 1882. Interest to January. * *# Junel Eighty Dollars. 80 Feb. 27 Two Hundred and Sixty Dollars. 230 Mar. 8 One Hundred Dollars. 100 LIFE INSURANCE. DEFINITIONS. 524. Life Insurance is a contract by which a company (the insurer), in consideration of certain payments, agrees to pay to the heirs of a person, when he dies, or to himself, if living at a specified age, a certain sum of money. Life Insurance Companies may be classified according to principles of organization the same as Fire Insurance Companies (31)1). Of the 31 Life Insurance Companies doing business in the State of New York in 1879, 2 were Stock (392), 17 Mixed (394) (Stock and Mutual), and 12 purely Mutual (393). Their assets Dec. 31, 1879, were $401,515,793 ; sur- plus as regards policy holders, $65,277,722 ; number of policies in force, 595,486, insuring $1,439,961,163. Of the companies chartered by the State of New York and doing business in 1879, 10 were Mixed (Stock and Mutual), and 2 were purely Mutual. 525. The principal kinds of policies issued by Life Insurance Companies are the following: Ordinary Life, Limited Pay- ment Life, Endowment, and Annuity. Tontine Investment, Reserve Endowment, Convertible Life, Accelerative Endowment, Yearly Renewable, and other special policies are issued by some companies. 526. Ordinary Life Policies. On this kind of policy, a certain premium is to be paid every year until the death of the insured, when the policy becomes payable to the persons named in the policy as the beneficiaries. A policy of this kind gives more insurance, for the same sum of money paid annually, than any other, though it is necessary to continue the payments longer ; as according to its terms the payment of the premiums annually con- tinues during the life-time of the insured. 374 LIFE INSURANCE. 527. Limited Payment Life Policies. On a policy of this kind, premiums are paid annually for a certain number of years fixed upon at the time of insuring or, until the death of the insured, should that occur prior to the end of the selected period. The policy is payable on the death of the insured, whenever that may occur. The payments on this class of policies may all be made wliile the insured is still young, or in active business ; then if he Jives to old age the policy is not a continual expense, bat, on the contrary, the dividends afford a yearly income in cash ; or they may be used to increase the amount assured. These policies are issued with single payments, or with 5, 10, 15, 20, or 25 annual payments. 528. A Term Life Policy is an agreement to pay to the representatives of the insured a certain sum on his death, provided that event happens within a certain fixed term. 529. Endowment Policies. An Endowment Policy pro- vides '(1) insurance during a stipulated period, payable, like that of any other policy, at the death of the insured should he die within the period; and (2) an endowment, of the same amount as the policy, payable at the end of the period if the insured survive until that time. The Endowment Policy gives the insured the advantage of a limited term as to payments ; provides insurance during the period in which his death would cause most embarrassment to his family ; and, if he lives to the stipu- lated age, the amount of the policy is paid to him at a time when he may need it. An Endowment policy is a combination of a Term Life Policy and a Pure endowment. These policies are issued for endowment periods of 10, 15, 20, 25, 30, or 35 years, and may be paid up by a single payment, by annual premiums during the endowment period, or by 5 or 10 annual payments. 530. Annuity Policies. An Annuity Policy secures to the holder the payment of a certain sum of money every year during his life-time. It is secured by a single cash payment. 531. A Joint-Life Policy is an agreement to pay a certain sum on the death of one of two or more persons named. 532. The Reserve of life insurance policies is the present value of the amount to be paid at death less the present value of all the net premiums to be paid in the future. DEFINITIONS. 275 533. The Reserve Fund of a Life Insurance Company is that sum in hand which, invested at a given rate of interest to- gether with future premiums on existing policies, should be suf- ficient to meet all obligations as they become due. It is the sum of the separate reserves of the several policies outstanding. The legal rate for tlie reserve fund according to the laws of the State of New York, is \% ; of Massachusetts 4%. 534. A Non-Forfeiting Policy is one which does not become void on account of non-payment of premiums. 1. According to the laws of the State of New York, after three full annual premiums have been paid, the legal reserve of the policy, calculated at the date of the failure to make the payments, shall, on surrender of the policy within six months after such lapse, be applied as a single payment at the published rates of the company in either of two ways, at the option of the assured. (1) To the continuance of the full amount of the insurance so long as such single premium will purchase term insurance for that amount, or (2) to the purchase of a non -participating paid-up policy. 2. According to the Massachusetts limited forfeiture law of 1880, after two full annual premiums have been paid, and without any action on the part of the assured, the net value (Massachusetts standard) of the policy less a sur- render charge of 8 % of the present value of the future premiums which the policy is exposed to pay in case of its continuance, shall be applied as a single payment to the purchase of paid-up insurance. 3 Certain companies voluntarily apply all credited dividends to the continu- ance of the insurance ; others voluntarily apply the legal reserve to the pur- chase of term insurance at the regular rates. 4. In some companies, all limited payment life policies and alt endowment policies, after premiums for three (or two) years have been paid and the original policy is surrendered within a certain time, provide for paid-up assur- ance for as many parts (tenths, fifteenths, twentieths, etc., as the case may be), of the original amount assured, as there shall have been complete annual premiums received in cash by the Company. 535. The Surrender Value of a policy is the amount of cash which the company will pay the holder on the surrender of the policy. It is the legal reserve less a certain per cent, for expenses. The Tontine Investment, Reserve Endowment, and other special policies guarantee to the policy-holder a definite surrender value at the termination of certain periods. 536. The Expectation of Life is the number of years which one may probably live. This average number of years has been determined from the experience of Insurance Companies. 276 LIFE INSURANCE. TABLE OF RATES. 537. Annual premium for an Insurance of $1,000, with profits. LIFE POLICIES. Payable at Death, only. ENDOWMENT POLICIES. Payable as Indicated, or ut Death, if Prior. AGE. ANNUAL PAYMENTS. AGE. In 10 Years. In 15 Years. In 20 Years. AGE. For Life. 10 Years. 15 Years. 20 Years. 25 $19 89 $42 56 $32 34 $27 39 25 $103 91 $66 02 $47 68 25 26 20 40 43 37 32 97 27 93 26 104 03 66 15 47 82 26 27 20 93 44 22 33 62 28 50 27 104 16 66 29 47 98 27 28 21 48 45 10 34 31 29 09 28 104 29 66 44 48 15 28 29 22 07 48 02 35 02 29 71 29 104 43 66 60 48 33 29 30 22 70 46 97 35 76 30 36 30 104 58 66 77 48 53 30 31 23 33 47 98 36 54 31 03 31 104 75 66 96 48 74 31 32 24 03 49 02 37 35 31 74 32 104 92 67 16 48 97 32 33 24 78 50 10 38 20 32 48 33 105.. U 67 36 49 22 33 34 25 56 51 22 39 09 33 26 34 105 31 67 60 49 49 34 5 26 38 52 40 40 01 34 08 35 105 53 67 85 49 79 86 30 27 25 53 63 40 98 34 93 36 105 75 68 12 50 11 36 87 28 17 54 91 42 00 35 83 87 106 00 68 41 50 47 87 38 29 15 56 24 43 06 36 78 38 106 28 08 73 50 86 38 39 30 19 57 63 44 17 37 78 39 106 58 69 09 51 30 C9 40 31 30 59 09 45 33 38 83 40 106 90 69 49 51 78 40 41 32 47 60 60 46 56 39 93 41 107 26 69 92 52 31 41 42 33 72 62 19 47 84 41 10 ,42 107 65 70 40 52 89 42 43 35 05 63 84 40 19 42 34 43 108 08 70 92 53 54 43 44 36 43 65 57 50 61 43 64 44 108 55 71 50 54 25 44 45 37 97 67 37 52 11 45 03 45 109 07 72 14 55 04 45 48 89 58 69 26 53 68 46 50 46 109 65 72 86 55 91 46 47 41 30 71 25 55 35 48 07 47 110 30 73 66 56 89 47 48 43 13 73 32 57 10 49 73 48 111 01 74 54 57 96 48 49 45 09 75 49 58 95 51 50 49 111 81 75 51 59 15 49 50 47 18 77 77 60 91 53 38 50 112 68 76 59 60 45 50 1. The above table represents the maximum rates of the leading New York companies. Surplus premiums or dividends are returned annually com- mencing at the payment of the second premium. 2. Policies which do not share in the dividends of the company, are issued at fixed rates 15 to 20 % less than the above. 3. The above rates are for annual payments only. To obtain semi-annual payments, add 4# and divide by 2. To obtain quarterly payments, add Qfi and divide by 4. LIFE INSURANCE. 277 538. ANNUAL REPORT OF A LIFE INSURANCE Co., Jan. 1, 1882. Amount of assets, Jan. 1, 1881 $36,889,011.66 REVENUE ACCOUNT. Premiums $6,003,036.16 Interest and rents 2,033,650.00 8,036,686.16 44,925,697.82 DISBURSEMENT ACCOUNT. Losses by death, including Reversionary additions to same 1,569,854.22 Endowments matured and discounted 1,015,256.22 Annuities, dividends, and returned premiums on cancelled policies 2,236,379.97 Taxes and re-insurances 173,608.64 Commissions, brokerages, agency expenses and physicians' fees 626,253.30 Office and law expenses, salaries, advertising, printing, etc 307,392.81 5,928,745.16 88,006,059.66 ASSETS. Cash in bank and on hand 1,961,701.48 Invested in j&nited States, New York City, and othe^locks 14,556,192.94 Real estate\|rU 4,974,573.68 Bonds and ^mortgages, first lien on real estate.. . 15,313,278.95 Temporary loans (secured by stocks, market value $1,300,000) 850,000.00 Loans on existing policies 621,403.02 Quarterly and semi-annual premiums on existing policies, due subsequent to Jan. 1, 1882. . 367,989.02 Premiums on existing policies in course of trans- mission and collection 211,625.23 Agents' balances 22,199.23 Accrued interest on investments Jan. 1, 1882. . . 317,989.11 38,996,952.66 LIABILITIES. Adjusted losses, due subsequent to Jan. 1, 1882. 225,662.64 Reported losses, awaiting proof, etc 213,271.31 Matured endowments, due and unpaid 32,780.98 Premiums paid in advance 16,543.25 Reserve for re-insurance on existing policies at 4i per cent 30,682,025.00 31,170,283.18 Surplus at 4| per cent 7,826,669.48 38,996,952.66 278 LIFE INSURANCE. EXAMPLES. 539. 1. Find the amount of premium for an ordinary life policy (526, 537) of $5000, issued to a person 35 years of age. 2. What is the first annual premium of a life policy of $6000, issued to a person 30 years old, $1.00 being charged for the policy ? NOTE. The policy fee is added to the first premium only. 3. Find the annual premium for a 20-payment life policy (527, 537) of $4000, issued to a person 28 years old. 4. What annual premium must be paid for a 20-year endow- ment policy (529) of $8000, age of the insured at nearest birth- day, 40 years ? If the insured dies during the tenth year, how much more would have been paid than if he had been insured on the ordinary life plan ? 5. What is the average daily cost of a life policy for $1000, no allowance being made for probable dividends, insurance commenc- ing at age 25 ? At 35? At 45? 6. How much must a person, aged 35, lay aside weekly to secure a life policy of $1000, payable in 20 annual payments ? 7. When 40 years old, a person took out a 20-year endowment policy of $10000. He survived the endowment period. How much less did he receive than he paid as premiums, not reckon- ing interest ? 8. Mr. A. when 26 years old took out an ordinary life policy of $20000. He died aged 41 years 2 months. How much more did his heirs receive than had been paid as premiums, no allow- ance being made for interest ? 9. In the above example, supposing money to be worth 6% (simple interest), what was the net gain of the above insurance ? 10. The annual premium, without profits, on a life policy of $10000 at age 35 is $222. How much would it be necessary to invest at 6% interest to secure the payment of the annual pre- mium ? How much would the insured leave his family at his death ? 11. A gentleman, age 30, insures his life for $20000, ordinary life plan. How much must he place in trust so that the interest at 5% will be sufficient to pay the premiums on the policy ? At his death, how much does he leave his family ? LIFE IXSURANCE. 279 12. Mr. C. when 25 years of age secured a 20-year endowment policy of $6000 ; when he was 30 years of age, he obtained an ordinary life policy of $4000 ; when 35 years of age, he toot out a 20-payment life policy of $10000. What was the total annual premium after taking the last policy ? 13. Suppose Mr. C. had died at the age of 40-J- years, how much more would his heirs receive than had been paid as premiums ? 14- A single premium for an assurance of $1000, without profits, for a person 32 years of age, is $300. What would be the excess of the assurance over the amount produced by placing the money at compound interest (341) at 4%, supposing the insured to live 20 years? 30 years ? What would be the excess of the amount pro- duced by the money at interest at 5% over the assurance in 30 years ? 15. Mr. B., age 40, has $10000 at interest at 6$, which he in- tends to leave his family. What will this amount to at compound interest (341) in 25 years at 6% ? How much will he leave his family if he takes out a life policy and pays the premium with the interest on his investment of $10000 ? 16. Mr. A., aged 30, secures an ordinary life policy, annual premium $100. How much more would his heirs receive from the insurance company than from the money at compound interest (34:2) at 5#, should he die at the age of 32? Of 40 ? Of 50? At about what age would the amount received from the money at interest exceed the assurance ? 17. What is the semi-annual premium (537, 3) on a 20-year endowment policy for $6000, age 32 ? The quarterly premium ? 18. Mr. A., who will be 35 years of age July 1, takes out Apr. 1 a 20-payment life policy for $10000, premium payable semi-annu- ally. Mr. B., of the same age, takes out Apr. 1 the same kind of policy for $5000, and Oct. 1, another policy of the same kind for $5000, premium payable annually. How much less does Mr. B. pay as premium each year than Mr. A. ? (537, 3.) 19. An ordinary life policy issued at age 35 for $10000 has, at age 45, a 4% reserve of $1262.60. How much non-participating paid-up insurance will this amount purchase, the single premium rate per $1000 at age 45 being $475.44 ? 20. In the statement, Art, 538, the surplus is what per cent, of the reserve required by the State of New York ? The net assets (the total assets less the first four items of the liabilities) are what per cent, of the reserve ? GENERAL AVERAGE. DEFINITIONS. 540. If, in time of danger or distress, any loss or expense is voluntarily incurred for common safety of vessel, freight, and cargo, such loss or expense is made good by a " General Aver- ags ; " the amount or value of such loss or expense being assessed upon the value of all interests involved and benefited. All other losses and expenses are of a "Particular Average" nature, and are to be borne by the specific interests to which they apply. 541. The losses and expenses constituting general average are as follows : 1. Jettison, or throwing overboard of cargo to lighten the ship ; damage to cargo by water going down the hatches during jettison ; damage by chafing or breaking after jettison ; freight on cargo jettisoned. 2. Sacrificing ship's materials, as the cutting away of masts, spars, etc. One-third of the cost of repairs of ship's materials is a special charge on the ship, as the new work is considered better than the old. No deduction is made for anchors. 3. Expense of floating a stranded ship. 4. Expense of entering a port of refuge, either to repair damage which renders it dangerous to remain at sea, whether such damage were caused by accident or sacrifice ; or otherwise to avert a common danger. 5. Expense of discharging cargo for the purpose of making repairs, warehouse rent, reloading cargo, outward expenses, etc. 6. Wages and provisions of crew from the date of bearing up until ready for sea. GENERAL AVERAGE. 281 542. Contributory Interests and Values. The ship contributes on its full value at the time which is made the basis of contribution. The cargo contributes on its net market value at the port of destination, less freight and charges saved. The freight contributes on the full amount, less -J- for the wages, etc., of crew. In the States of New York, Virginia, Cali- fornia, and some others, is deducted. The underwriters (Insurance companies) contribute to the general average such a part of the expense as the insured value is of the market value of the goods (4O5). If, for example, a cargo is insured for $10000 and is worth in the market $12000, the underwriters are liable to pay of the general average expense. 543. To give rise to general average, it must be shown that there was an imminent common danger, that the sacrifice was voluntary and necessary, and that the act was prudent and successful. 544. An Average Adjuster is a person who is familiar with the general average laws of the leading commercial nations, and who adjusts and apportions the losses and expenses of a general average. The principal difficulty of an adjuster is to decide whether the loss should he made good by a general average or should be made a special charge (par- ticular average) upon some particular interest. After the general average charges are determined, the apportionment of the loss among the several con- tributory interests is a simple arithmetical problem. EXAMPLES. 545. 1. The bark Liberty sailed from New York for Galves- ton with the following cargo : Shipped by A, $5600 ; by B, $8700; by C, $16308 ; by D, $8360. After two days out the bark en- countered heavy gales and was damaged to the amount of $630.14. On the fifth day the vessel began to take water, and for the safety of the vessel and the cargo the bark bore away for New York for repairs. The disbursements of the agent at New York were as fol- lows : Custom-house fees, pilotage, protest, towage, unloading and reloading cargo, wharfage, inspection, consul fees, $1369.43; bill of H. Robin & Co., shipwrights, etc., $436 ; bill of Joseph Patti, ceiling ship $194.14, Agent's commission for advancing funds 282 GENERAL AVERAGE. and paying above bills, % ; on value of cargo landed^ $17388, Wages and provisions of seamen from point of deviation, $630.47. The gross freight was $8096, and seamen's wages, etc., of gross freight. How is the settlement to be made, the value of the ship being $10000 and the adjuster's fee $100 ? NOTE. In a general average, extracts from the log of the ship, the testi- mony of its officers, a complete statement of all expenses incurred, with the vouchers for the same, and all papers having any bearing upon the case are presented to the adjuster. The total amount of each item is entered in a column at the left of his statement of charges, and the amount is also entered in its proper column at the right. In addition to the general average column, there are usually columns at the right for the special charges upon the ship, owners, or cargo. STATEMENT OF CHAKGES. General Ship and Total. Average. Owners. 1369 43 Expense of entering harbor, landing cargo, etc. 1369 43 436 Bill of H. Robin & Co., shipwrights, etc. 436 194 14 " " Joseph Patti, ceiling ship. 194 14 Agent's commission for advancing funds and 99 98 paying above bills, 5 % . ** *# ** #:> Agent's commission on value of cargo landed, #** ## $17388, \\%. *## *# 630 47 Wages, etc., of seamen. 630 47 100 Adjuster's fee. 100 General average. **## #-:f 3047 :>? Ship and owners. **# -:; CONTRIBUTORY INTERESTS AND APPORTIONMENTS IN GENERAL AVERAGE. Ship, value 10000 @ .*** pays ## Freight, 8096 Less^ 4048 4048 @ .*** " #*-::- *:.' Cargo, A, 5600 @ .*** " *** B, 8700 @ .*** " TT*^ ** 0, 16308 .*** " **# ** D, 8360 @ .*** f< *## ** 38968 @ .*** " ##*# *-* ***** .*** " __. ###?:- ** GENERAL AVERAGE. SETTLEMENT. 283 BALANCES. DB CB To pay. To receive. Vessel and Owners. Pay ship's proportion of Gen. Aver. **# " freight's " " *** ## " owner's column. *** ** Receive seamen's wages. ### vr* 663 34 Cargo. Pay proportion of Gen. Average. **** ** 1753 56 Agents of Vessel. Receive their disbursements. **** #* " 4< commission. #*# ** 2316 90 Adjusters. Receive their fee. *** 100 3047 37 3047 37 2416 90 2416 90 2. The general average charges were $4375.86, and the con- tributory interests $64325. What was the per cent, of loss ? What was the loss of Mr. B., whose goods were valued at $7250 ? S. Suppose A's goods in Ex. 1 were insured for $5000, how much of the loss would be shared by the insurance company ? 4. The ship Amazon, from Aspinwall to New York, being in distress, threw overboard part of the cargo, cut away the masts, and finally bore away to a port of refuge to repair in order to com- plete the voyage. The cost of. replacing masts and rigging cut away was $6000 (less -J- new for old); the cargo jettisoned was worth compared with sound cargo delivered at destination $2000 ; freight on cargo jettisoned, $200 ; expenses of entering port of refuge, discharging, storing and reloading cargo, $1000; wages of master and crew from time of bearing away until ready for sea, $600 ; provisions of master and crew for same time, $500 ; adjuster's fee, $100. The vessel was valued at destination a,t $20000 (deduct gross repairs and add amount made good) ; cargo, value on arrival, $40000 (add amount made good) ; freight collected, $4000 (add amount made good and deduct ). What was the per cent, of loss, and how was the settlement made ? 5. The cargo of the ship Amazon was insured for $36000. How much was the claim against the insurance company ? 284: GENERAL AVERAGE. 6. The ship Union, in her passage from Liverpool to Boston, during a storm threw overboard cargo to the amount of $1580, and cut away masts and rigging. She then entered the port of Halifax for repairs. The cost of replacing the masts and rigging which were voluntarily sacrificed, was $4578 (less new for old) ; cost of repairing accidental damage, $568 ; freight on cargo jetti- soned, $314.75 ; expense of entering port of refuge, discharging cargo, etc., $716.87 ; wages and provisions of crew, $608 ; adjuster's fee, $150. The value of vessel on arrival at Boston was $30000 (deduct gross repairs and add amount made good) ; value of cargo delivered, less freight and duty, $48475 (add amount jettisoned) ; total expected earning of freight, $16320 (less -J in Boston. See Art. 54:2.). The cargo was shipped by the following persons : A $8519, B $20376, C $6875, and D $14285. The cargo jettisoned was a part of A's shipment. How ought the settlement to be made? 7. The ship Ocean Queen, from Pernambuco to New York, sprang a leak off Cape St. Roque, and for the safety of the vessel and cargo, threw overboard part of the cargo and put into Maran- ham for repairs. The disbursements at Maranham by the master of the vessel, including commissions, were as follows : Expenses of entering harbor, discharging, storing, and reloading cargo, $648.75 ; caulking and painting ship, carpenter work, etc., $843. Value of cargo delivered at New York, $34310.24 ; of cargo jettisoned, $1580.76 ; freight on cargo jettisoned, $364 ; wages and provisions of crew, $304 ; adjuster's fee, $150 ; agent's commission for col- lecting amount in general average, %\%. How shall the settle- ment be made, if the net value of the ship was $3157 (value on arrival $4000, less repairs $843), and the total expected earning of freight was $2516 (less ) ? 8. A vessel which put into a port of refuge for repairs was without funds. It being very difficult to obtain a loan on bot- tomry, or to negotiate a draft on the owners of the vessel, the mas- ter was obliged to sell part of the cargo to raise funds. Value of cargo sold compared with cargo delivered at destination, $4566.06 ; produced at sale, $2985.30 ; freight on cargo sold compared with freight on cargo delivered, $363.93. What was the cost of funds, and how much should be apportioned to each interest, the general average charges being $773.52, the special charges on ship $956.10, and on the owners $1181.06 ? CLEARING HOUSES. DEFINITIONS. 546. A Clearing House is a place where the daily exchanges are effected between banks, and where the payments of the bal- ances resulting from such exchanges are made. The New York Clearing House was the first of the kind established in America, and began its operations Oct. 11, 1853. Since that time Clearing Houses have been established in all the principal cities of the country, there now being twenty-two in the United States. Before the Clearing House at New York was established it was necessary for each bank every morning to make up its accounts with every other bank, and to send a messenger to the debtor banks to present accounts and receive balances, which were adjusted in gold. This finally became so laborious, dangerous, and complicated, that balances were arranged weekly every Friday. The Clearing House obviated this. Its settlements are made so rapidly that the transactions adjusted through it have amounted in a single day to over $250,000,000 all settled within an hour. The establishment of the Clearing House closed 2500 bank ledger accounts, with numerous daily entries in each, and enabled the banks to settle with each other every day without loss or delay, and with comparatively little trouble. 547. The New York Clearing House Association is composed of 45 national and 12 State banks, and the assistant treasurer of the United States at New York. The remaining banks (4 national and 9 State) make their exchanges through the others. During the year ended October 1, 1881, the total exchanges were more than $48,000,000,000, while the balances paid in money were less than $1,800,000,000. The average daily balances paid were nearly $6,000,000, or about \% of the amount of the settlements. The balances paid in money during the year consisted of $1,394,966,000 in clearing house certificates of the Bank of America (548, 15), legal-tenders (189) amounting to $8,633,161, and $372,419,000 in gold coin, weighing 686 tons. The largest transactions for any one day were on the 28th of November, 1880, and amounted to $295,821,422.37. 286 CLEARING HOUSES. 548. The Daily Routine at the New York Clearing House is as follows : 1. The checks, drafts, etc., which make up the exchange of each bank are those which were received the previous day on deposit, in payment of notes and drafts, and by mail from the correspondents of the bank. The checks which are received by the early morning mail are added to the above on the morning of the exchange. Each bank enters on slips of paper (See Form 1), a list of the checks, drafts, etc., upon each of the other banks. The slips together with the checks are enclosed in sealed envelopes or packets, upon the back of which is printed the name of the bank owning the checks and the name of the bank upon whom the checks are drawn. The total amount is written upon the outside of the envelopes. These amounts are entered upon the " Settling Clerk's Statement " (Form 4) under the head of " Banks Dr." opposite the names of the respective banks, and the aggregate is found. These amounts are also entered upon small tickets the use of which will be explained hereafter. The messenger's "Receipt List" (548,7) is also prepared at the bank. 2. Each bank sends to the Clearing House a messenger and a Settling Clerk, the former to deliver the packets of checks, drafts, etc., of which his exchange is composed, and the latter to receive the checks, etc., against his bank from the messengers of the other banks. 8. Each settling clerk, as he enters the Clearing House, leaves at the desk of the assistant manager a "credit ticket" (Form 3), showing the total amount of the exchanges which he brings to the Clearing House against the other banks. For example, the clerk from the Bank of America leaves the following : (Form 1.) J\'o. 6. fy-ril 5, Neto fork Clearing onsc. Credit BANK OF AMERICA, $3,416,728.37. G. H. WATSON, JR., Settling- Clerk. 4. The amounts on these tickets are entered on the "Clearing House Proof" (See Form 7), under the head of " Banks Cr." and added together, making in tlje example $25,416,328.96. This is the total sum sent in by all the banks, and is called the Credit Exchange. Since each packet is taken away by some bank, the total of the amounts entered under the head of " Banks Dr. ," after the exchange is made, should agree with the total under the head of " Banks Cr." CLEARING HOUSES. 287 5. Promptly at 10 o'clock, the assistant manager strikes a bell and says " Take your places " " Order " " Ready, go." A fine is imposed upon those who are not in their places at the first ringing of the bell. 6. Each Settling Clerk is now at his desk and has before him the " Settling Clerk's Statement " (See Form 4), the debit side of which shows the amount of checks, etc., his bank has against each of the other banks. The credit side, on which is entered the amounts received from the other banks, is now blank. 7. The messengers stand opposite their respective desks, and have the packets arranged in an open box in the order of their delivery. Thus, the messenger of No. 6 has his packets in the following order : 5, 4, 3, 2, 1, 76, 75, 74, 72, etc. He also has a " Receipt List," which is a copy of the " Banks Dr." of the " Settling Clerk's Statement " with a blank column for the signatures of the clerks of the receiving banks. 8. At the second ringing of the bell, each messenger advances one step for- ward and is brought opposite the first desk at which his delivery is to be made. He delivers the packet of checks designed for it, and also the " Receipt List." The Settling Clerk compares the amount on the packet with the amount on the list, and, if correct, signs his initials opposite the amount, and returns the list to the messenger. He also enters the amount received on his statement opposite the name of the bank under the head of " Banks Cr.," before receiving another packet. The messenger goes through the delivery at each desk in like manner. The whole line of messengers advance at the same time, and each messenger performs a similar operation. In 10 or 15 minutes the circuit of the 58 desks is made, bringing each messenger to the starting point opposite his own desk. His "Receipt List," signed by every Settling Clerk, is the voucher to his bank that he has deliv- ered all the checks intrusted to his care. 9. Each Settling Clerk has now on his desk the packets of checks which constitute his Debit Exchange. He has already entered the amounts in his Statement under the head of " Banks Cr." As soon as the exchange is made each messenger returns to his bank with the packets of checks, and with a memorandum of the total debit exchange which has been furnished to him by the Settling Clerk, and the balance in favor of or against the bank. The Settling Clerks are obliged to remain until the assistant manager announces an exact proof. The messengers call back the amounts on the packets as they place them in their satchels preparatory to returning to their respective banks. 10. The Settling Clerks carefully revise the addition of the column " Banks Cr.," and send to the desk of the assistant manager a "Balance Ticket," which shows the amount brought, the amount received, and the balance for or against the bank. (See Form 2.) The amounts received are entered on the Clearing House Proof under the head of "Banks Dr.," and the balances in the proper columns. The sum of the amounts under the head of "Banks Dr." should equal the sum under " Banks Cr." (See 548, 4.) 288 CLEARING HOUSES. (Form 2.) JVb. 6. jlpril 5, IS $2. Neto JDork (Clearing Ijouss. (Debit BANK OF AMERICA, Amount reo'd, $8,581,309.78. Credit " " brought, $3.416,728.37. $164, 5 &1--43-, debit balance due Clearing House. Cr. bal. due BANK OF AMERICA, $ ___ (7. JZ". TF^TSO.V, JR., Settling- Clerk. 11. When the exchange was made, each messenger distributed a set of tickets (Form 3) on which were amounts corresponding with the amounts on the packets of checks. These tickets are compared with the amounts on the Settling Clerk's Statements under the head of "Banks Cr.," and ought to correct all errors of transcription although the checks have been taken away. (Form 3.) No. 8. NATIONAL CITY BANK. From No. 6, BANK OF AMERICA. $876,439.43. 12. The assistant manager announces the error in the proof at 10:45 or earlier. The Settling Clerks have in the meantime been revising their work. When errors are discovered new balance tickets are sent to the assistant manager's desk with the amount of the error entered therein. To correct errors in addition, the Settling Clerk's Statements are all passed to the right and added by another clerk. If the error is not then discovered, clerk of Bank No. 1 passes down the line with his statement and calls back the amount he has received from each bank. The second clerk immediately follows the first, and the third the second and so on. At the other end of the line the same operation takes place, No. 76 passes down the line, followed by No. 75, etc. This is the final method of revision, and, if the additions are correct, should correct all errors. 13. There is a scale of fines for all errors discovered after 10:45. For all errors remaining undiscovered after 11:15, the fine is doubled ; after 12, the fine is quadrupled. 14. All balances due the Clearing House are paid before \\ o'clock, p. M., and the creditor banks send for the amounts due them between 1^ and 2 o'clock. CLEARING HOUSES. 289 15. To save the risk and inconvenience of handling gold, settlements are made by gold Clearing House Certificates of the Bank of America, the com- mon coin depository of the Associated Banks. These certificates are valid only in the Clearing House settlements, or directly between the bunks. Balances less than $1000 are paid in gold or legal-tenders (188). 16. Errors in exchanges, and claims arising from the return of checks, or from any other cause, are adjusted directly between the banks who are parties to them, and not through the Clearing House. (Form 4.)* No. 6. BANK OF AMERICA. SETTLING CLERK'S STATEMENT, April 5, 1882. No. Banks. Banks Dr. Banks Cr. No. 1 B'k of N. Y. Nat'l Bk'g Ass'n, 362 189 76 426 134 42 1 2 Manhattan Company, 228 065 43 280 772 87 2 3 Merchants' National Bank, 756 784 80 652 668 16 3 4 Mechanics' National Bank, 275 238 92 438 591 34 4 5 Union National Bank, 537 564 27 377 418 72 5 7 Phenix National Bank, 142 728 11 344 836 19 r< i 8 National City Bank, 876 439 42 615 971 24 8 10 Tradesmen's National Bank, 169 235 08 313 185 50 10 11 Fulton National Bank, 68 482 58 131 731 34 11 Exchanges, 3416 728 37 3581 309 78 Balance, 164 581 41 . (Form 5.) NEW YORK CLEARING HOUSE PROOF, April 5, 1882. -J Banks. Du Clearing House. Banks. Dr. Banks. Cr. Due Banks. No. 1 B'k of N. Y. Nat'l Bk'g Ass'n, 153 161 54 2 417 853 21 2 734 415 38 316 562 17 1 2 Manhattan Company, 3 670 729 36 3 517 567 82 2 8 Merchants' National Bank, 4 189 437 29 4 484 123 49 294 686 20 3 4 Mechanics' National Bank, 2 234 163 46 2 425 876 50 191 713 04 4 5 Union National Bank, 301 190 94 2874 109 28 2 572 918 34 5 6 Bank of America, 164 581 41 3581 309 78 3 416 728 37 6 7 Phenix National Bank, 245 R85 43 2537 41 S 4-2 2 291 532 99 7 8 National City Bank, 176 895 20 704 333 50 1 5871438 30 8 10 Tradesmen's National Bank, 1 437 528 49 1 573 419 22 135 890 73 10 11 Fulton National Bank, 709 446 17 312308 55 102 862 38 11 1041 714 52 25 416 328 96 25 416 328 96 1041 714 52 * For economy of space, Forms 4 and 5 are given with only 10 banks. DETECTION OF ERRORS TRIAL BALANCES. 549. The following hints apply to the detection of errors in trial balances, or in any operation in which errors are made in addition or subtraction, or in transferring numbers from one place to another. 1. Ascertain the exact amount of the error. Much time is sometimes wasted in looking for errors which do not actually exist. 2. Revise carefully the additions of the trial balance before looking for the error in the ledger or other books. 3. If the error is in one figure only (as 2000, 100, 50, etc.), it is probably an error in addition or subtraction. 4. If an amount is entered on the wrong side of an account, or is added when it should be subtracted or vice versa, the error will be twice the amount. 5. If the digits of any number are written to the right or left one, two, or three places, and the error be divided by 9, 99, or 999 respectively, the quotient will be the number. Thus, if $427 be written $4.27, the error will be $422.73 ; which divided by 90 (by 9 and 11), the quotient will be $4.27. The number of 9's by which the number can be exactly divided is equal to the number of places which the number has been transferred to the right or the left. 6. If two consecutive digits of any number are transposed, the error will be a multiple of nine ; and the quotient obtained by dividing the error by 9 will express the difference between the digits transposed. Thus, if 437, be written 473, the error will be 36 ; which divided by 9 produces 4, the difference between 3 and 7. The same error, 36, will arise if the figures transposed are and 4, 1 and 5, 2 and 6, 4 and 8, or 5 and 9. 7. If the error contains a number of figures, it is probable that some account or item has been omitted. 8. Look for the error systematically, and not in certain por- tions of the work selected at random. MISCELLANEOUS EXAMPLES.* 55O. 1. Add 17, 28}, 36J, 44, 89 T %, and 76 ; multiply the sum by 87 ; subtract 1022JJ from the product ; and divide the remainder by 234f. 2. Divide eighty-three, and seventy-five hundredths by one hun- dred and twenty-five ten-thousandths ; add to the quotient sixty- eight, and six hundred and twenty-five thousandths ; and multiply the sum by three, and two-tenths. 3. How many minutes in the month of February, 1900 ? 4. Find the cost of 7312 pounds of meal at $2.25 per cwt. 5. The difference in the local time of two places is 1 lir. 7 min. 13 sec. ; what is the difference in longitude ? 6. Find the number of square yards of paving in a street, 3000 ft. long and 50ft. wide. 7. What is the charge for packing, marking, and shipping 251 bales merchandise at 5s. 6d. per bale ? 8. If 46 T. 12 cwt. of coal are worth $174.75, what is the value of 37 T. 8 cwt. ? 9. How many square yards of linoleum would cover a floor 22 ft. 6 in. by 15//. 4 in. ? Find its value at 63^ per sq. yd. 10. What is the freight of 5 T. 9 cwt. 2 qr. 8 ?., at 70 shillings per ton (2240 Ibs.) ? 11. Find the cost of 4 T. 7 cwt. 3 qr. 20 Ib. of iron, at 15 4s. Qd. per ton (2240 Ibs.). 12. What is the weight in grams of the U. S. gold dollar ? 13. What is the value of a Lac (100,000) of rupees in U. S. money ? (See Art. 192, India.) 14. A bank collected a draft of $9375.16. What were the proceeds, the charge for collection being \% ? 15. What is the cost of insuring $18000 at 750 per $100 ? 16. What is the cost of 250 ft, 3-ply hose, at 60 cts. per foot, less 30 and 10$, and 5 sets couplings at $1.50 each ? 17. What is ty% of 159 13s. lOd. 18. A's property is assessed at $7500, and the rate of taxation is $2.165 on $100. What is his tax, including a commission of \% ? * Answers omitted. 292 MISCELLANEOUS EXAMPLES. 19. What is the duty at 60% on an invoice of silk amounting to 36475 francs ? 20. A merchant buys a bill of dry goods, Apr. 16, amounting to $6,377.84, on the following terms: 4 months, or less 5% 30 days. How much would settle the account May 16 ? The above discount is equivalent to what rate per cent per annum ? 21. Mr. B. purchased 36150 pounds of hay at $16.50 per ton, and 16438 pounds of oats at 70 cents per bushel. He sold the hay at a gain of 16%, and the oats at a loss of 8%. What were the proceeds ? 22. A merchant buys goods at a discount of 40 and 20% from the list price, and sells at a discount of 30 and 10%. What is the gain per cent ? 28. Mar. 16, a merchant buys a bill of goods amounting to $2475 on the following terms : 4 months, or less 5% if paid in 30 days. Apr. 15 he makes a payment of $1000, with the under- standing that he is to have the benefit of the discount of 5%. With what amount should he be credited on the books of the seller? How much would be due July 16, the expiration of the 4 months ? 24. May 10, A buys a bill of goods amounting to $5000 on the following terms : 60 days, or 1% discount in 30 days, or 2% discount in 10 days. May 20 he makes a payment of $2000, and June 9, of $2500. How much would be due July 9, the end of the 60 days' credit ? 25. Oct. 16, B bought a bill' of merchandise amounting to $2000 on the following terms : 4 months, or 5% discount in 30 days, or 6% discount in 10 days. Oct. 26 he made a payment of $1000. How much would settle the bill Nov. 15 ? 26. B bought a bill of merchandise May 16 amounting to $3416.72 on the following terms : 4 w?ox., or less 5% 30 days. He paid on account June 21 (6 days after the expiration of the 30 days) $3000, with the understanding that he should have the benefit of the discount by paying interest for the time elapsed, at 6% per annum. How much was due Sept. 16, no compound interest being reckoned ? 27. Paid for transportation $664.95 on an invoice of goods amounting to $8866. What per cent, was the value of the goods thereby increased ? What per cent, must be added to the invoice cost to make a profit of 20^ on the full cost ? MISCELLANEOUS EXAMPLES. 293 28. Find the total freight on 68 ft. mdse. at 35 shillings per ton (40 cu. ft.), and 123 ft. at 40 shillings per ton, plus 10% primage on each item. 29. A merchant buys a bill of goods amounting to $1000 on a credit of four months, or 6% off for cash. He pays $500 cash. For what amount should his account be credited ? 30. Bought coal by the long ton at $3.64, and sold by the short ton at $4.25. What was the gain per cent ? 31. A bought a bill of merchandise July 24, 1879, amounting to $6287.45 on the following terms : 6 months, or less 4% 30 days. He paid on account Aug. 23, 1879, $5000, with the understand- ing that the payment would cancel an equitable amount of the bill. How much was due Jan. 24, 1880 ? 82. A commission merchant in Chicago sells for me 12 bales brown sheeting, each bale containing 800 yards, at 7 cts. per yard ; pays transportation and other charges amounting to $72 ; and invests the proceeds in flour at $4.80 per barrel. If he charges %%% for selling and \\% for purchasing, how many barrels of flour does he send me ? 33. Find the date of maturity and the net proceeds of a note for $5000, dated May 16, payable 4 months after date, and dis- counted July 21 at 6%. 34. When the above note became due, its maker had discount- ed at 6% a new note, payable 90 days after date, whose proceeds were sufficient to pay the first note. What was the face of the new note ? 35. Apr. 1, a merchant buys a quantity of coffee on 90 days' credit, with privilege of discounting within 30 days from date of purchase at the rate of Q% per annum for the unexpired time. Apr. 16 he makes a payment of $28000 on account, no actual invoice having been rendered. May 1 he receives the invoice, amounting to $29215, and on the same date full settlement is made. What amount was required to cancel the bill ? (Exact days, 360 days to the year.) 36. Divide $2000 in such a manner between two brothers, aged 16 and 19 years respectively, so that when they arrive at 21 years of age they will have equal amounts, money being worth 6% simple interest. 87. What would be the share of each if money is worth 6% compound interest ? 294 MISCELLANEOUS EXAMPLES. 38. Find the amount due on the following note Jan. 1, 1883, by the United States and the Mercantile Rules : $50QO T (fe- DAVENPORT, IOWA, May 1, 1878. On demand, I promise to pay EDWIN D. MORGAN, or order, Five thousand dollars, with interest at ten per cent., for value received. E. H. CONGER. On this note the following payments were indorsed : Received Jan. 16, 1879, $400. Received Dec. 12, 1880, $150. Received Sept. 7, 1879, $100. Received Aug. 18, 1881, $850. Received May 1, 1880, $500. Received Apr. 23, 1882, $100. 39. How much would have been due on the above note if no rate of interest had been mentioned in the note ? 40. What is the value of a draft on Hamburg of 17468 marks at 95| ? 41. C. of London owes me for goods sold on my account, 129 18s. 7d. How much do I receive in payment, if I draw a bill of exchange for the amount and sell it at 4.85-f? 42. My agent in Paris buys an invoice of merchandise amount- ing to 12488 francs, at a commission of %\%. What is the cost of the draft which I remit in payment, the rate of exchange being 5.17|? 43. An exporter sold the following bills oi exchange through a broker: 10000 francs on Paris at 5.16|, 375 16s. 8d. on Lon- don at 4.83, 16480 marks on Hamburg at 94-|, 5287 guilders on Amsterdam at 41-J. What were the proceeds, brokerage \% ? 44- A commission merchant at New York sells goods for A. of Havre to the amount of $3435.27, and charges a commission of *ty% for selling. What is the face of the draft which he purchases and remits in settlement, exchange being 5.27 ? 45. My agent in London has purchased for me, at a commis- sion of 2$, 375 dozen kid gloves at 496?. per dozen, and 636 yards silk at 9s. 6d. per yard. When exchange is $4.86J, what will be the cost of the draft which I remit to him in settlement ? 46. Purchased in England, merchandise amounting to 324 10s. 7^., and paid freight and duties $487.34. How much per must I sell these goods to gain 12% on the full cost, and what must I charge for an article invoiced at 6s. 8^., exchange 4.88 ? 47. Bought stock at 1.16| and sold at 1.12-J. Loss, $1295. What was the par value of the stock ? 21ISCELLANEOUS EXAMPLES. 295 48. Average the following account : Mar. 16, 1882, $874.32 on 30 days credit. " 31, " May 5, " " 21, " June 18, July 3, " " 24, " Aug. 19, " Sept. 13, " 49. Average the following account. What will be the amount due Jan. 1, 1883 ? 518.65 " 60 " 373.78 4 months 429.31 60 days 657.70 " 30 " 242.28 60 " 983.75 " 4 months 716.30 4 536.60 " 60 days Dr. DANIEL S. LAMOKT, Albany, N. Y. Or. 1882. 1882. July 16 Mdse., 4 mo. $876 14 Sept.10 Cash, . . . $900 00 Aug. 4 " 60 da. 415 65 " 21 tt 700 00 Sept.10 " 30 da. 797 38 Oct. 13 a 500 00 " 21 11 30 da. 686 96 " 31 Mdse., 30 da. 322 16 Oct. 13 " 4 mo. 524 27 Nov. 2 Cash, . . . 400 00 " 31 " 30 da. 859 75 " 28 Note, 4 mo. 800 00 Nov. 28 " 60 da. 263 31 Dec. 27 Cash, . . . 500 00 Dec. 1 " 60 da. 172 64 " 30 " 30 da. 938 52 50. Prepare an account current, including interest at 6% to Jan. 1, 1883, from the above ledger account, according to the form and method of Art. 454. 51. Sold five $1000 bonds at 1.16-f, and invested the proceeds in railroad stock at 92-J, which I sold at 98 J. "What was the gain on the stock, allowing usual brokerage ? 53. Sold Aug. 11, 1879, 500 shares Chicago & Alton, s. 10, at 94, and covered my short sale Aug. 16, 1879, at 91. What was my profit, allowing the usual brokerage ? 53. What annual income will be obtained by investing $9923.75 in bonds, bearing 5% interest, and purchased at 1.16}? 54. What is the duty on a block of marble 2 x 3 x 7 ft., im- ported from Italy, dutiable value 3450 lire, and duty $1 per cubic foot and APPENDIX. DRILL EXERCISES, SHORT METHODS, ETC. 551. Useful Hints in Addition. 1, Write the numbers in vertical lines. Irregularity in the placing of figures is the cause of many errors. 2. Think of results and not of the numbers, themselves. Thus, in Ex. 1, Art. 555, do not say 3 and 4 are 7 and 9 are 16, etc., but 7, 16, 26, etc. 3. Make combinations of 10 or other numbers as often as pos- sible, and add them as single numbers. When a figure is repeated several times, multiply it instead of adding. Add 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5, 4, 3 and 3, etc., as 10 ; 7 and 2, 6, 2 and 1, 4 and 5, etc., as 9 ; 2 and 3, 4 and 1, 2, 2 and 1, as 5 ; etc., etc. 4. To avoid repeating the work, in case of interruption, write the figures to be carried in pencil underneath, as in Ex. 4. 5. In adding long columns, prove the work by adding each column separately in the opposite direction, before adding the next column. If, by adding both upwards and downwards, the two results agree, the work is probably correct. 552. Drill Exercise in Addition. Take any number less than 1000 ; repeat the number ; add the two numbers ; add the three numbers ; add the last three numbers, and so continue until there are twelve numbers. The numbers expressed by the three right hand figures of the fourth and twelfth numbers will be the same, if the original number is even, and will differ by 500 if the original number is odd. Add all the numbers. The sum will equal 1104 times the original number. (See Ex. 3, Art. 555.) 553. Drill Exercise in Subtraction. Take any number less than 1COO ; subtract it from 1000; subtract the remainder DRILL EXERCISES. 297 from the last number, omitting the fourth figure and borrowing from the fourth place when necessary ; so continue until sixteen subtractions have been made. The seventh and sixteenth remain- ders will be the same. Add the numbers. The three right-hand figures of the sum will be the same as the three right-hand figures of the product obtained by multiplying the original number by 391. (See Ex. 4, Art. 555.) 554. Drill Exercise in Multiplication and Division. Take any number ; find the continued product of it and any set of numbers. Use the last product as a dividend, and divide it by the same numbers in the same order, using each quotient as a dividend for the next division. The last quotient will be the original number. (See Ex. 5, Art. 555.) NOTE. In the drill exercises in addition, multiplication, and division, if the original number is a multiple of 9, each number and result will be a multiple of 9, and therefore the sum of the digits of each number will be a multiple of 9. This property of 9 may be used in the detection of errors. 555, EXAM PLES. Add 3456 9716 2356 7327 2468 7535 2845 9610 2581 1473 7812 1593 4826 7374 8259 4374 3213 W (A) WO (*) Add Add 1000 87 x 2 $37.16 347 517 174 x 3 875.25 347 483 522 x 4 412.75 694 034 2088 x 5 734. 1388* 449 10440 x 6 147.03 2429 585 62640 x 7 948.26 4511 864 438480 x 8 272.72 8328 721* 3507840 x 9 371.59 15268 143 2 ) 31570560 87.20 28107 578 3 ) 15785280 3.16 51703 565 4 ) 5261760 27.84 95078 013 5 ) 1315440 375.13 174888* 552 6 ) 263088 617.37 383088 461 7 ) 43848 583.14 24657 091 8 ) 6264 27.48 370 9~)783 344.22 721* 87 5.76 8147 V 298 A P P E NDIX. 556. Short method of finding the balance of an account. Ex. Find the balance of the following ledger account: Dr. C. E. & W. F. PECK. Or. 1882. Mar. 16 Merchandise. 1192 97 1882. Apr. 22 Cash. 800 M 80 Sundries. 567 40 " 22 Bills receivable. 1000 " 31 Merchandise. 384 30 May 1 Merchandise. 317 28 Apr. 22 Interest. 16 48 " 17 Cash. 424 79 ii 24 Merchandise. 846 51 July 1 Balance. 852 8i May 17 ' 387 25 3394 91 3394 91 July 1 Balance. 852 84~ ANALYSIS. It can readily be seen that the debit side is greater; therefore add that side first and write the sum as the total or footing of each side. Then pass to the other side of the account. The sum of the first column is 17, which subtracted from the next higher number, 21, ending with 1, the corresponding figure of the total, leaves 4, which write as the first figure of the balance, carrying the 2 to the next column. (If the right-hand figure of the sum of any column is the same as the corresponding figure of the total, subtract it from itself, and not from the next higher number ending with the same figure ; or write in the balance and carry the left-hand figure of the sum.) The sum of the figures in second column plus 2 carried is 11, which subtracted from 19 leaves 8, the second figure of the balance. Proceed in like manner until all the figures of the balance are obtained. Prove by adding all the numbers, including the balance. EXAMPLES. 557. Find the balances of the following accounts : (1.) (*.) (3.) Dr. Or. Dr. Dr. 817.20 812.20 237.25 112.27 1075. 375.60 222.22 214.13 900. 218.36 2318.42 218.24 427.30 375. 800. 717.49 812.10 717.37 810.75 412. 718.24 648. 938.40 244.45 416.30 717. 218.75 118.75 4312. 946.33 225. 538.98 222.48 719.46 203.13 108.75 SHORT METHODS. 299 SHORT METHODS IN MULTIPLICATION. 558. To multiply any number of two figures by n. 559. RULE. Place the sum of its digits between them when the sum is less than 10. When the sum is 10 or more than 10, write its right-hand figure in the second place and carry one to the left-hand figure of the multi- plicand. EXAMPLES. 560. 1. Multiply 34 by 11. ANALYSIS. 3 + 4 = 7, which placed between 3 and 4 produces the product 374. 2. Multiply 68 by 11. ANALYSIS. 6 + 8 = 14. Write 4 in the second place and carry 1 to the 6, the left-hand figure of the multiplicand producing the product 748. 3. Multiply the following numbers by 11 : 24, 16, 18, 32, 43, 33, 72, 81, 37, 44, 92, 87, 93, 64, 35, 36, 47, 17, and 19. 561. To multiply any number by n. 562. KULE. Write the 1st 7*ight-hand figure, add the 1st and 2nd, the 2nd and 3rd, and so on ; finally write the left-hand figure, carrying as usual. EXAMPLES. 563. 1. Multiply 783742 by 11. Ans. 8621162. ANALYSIS. Write the right-hand figure 2 ; for the remaining figures of the product, add 2 to 4, 4 to 7, 7 to 3, 3 to 8, 8 to 7, and write the left-hand figure, carrying when necessary. 2. Multiply the following numbers by 11 : 245, 346, 325, 416, 784, 517, 875, 918, 4218, 7324, 7218, 1728, 4375, and 8376. 564. To multiply by any number of two figures ending with i. 565. EULE.- Multiply by the tens of the multiplier, writing the product under the multiplicand one place to the left, and add. Or, 300 APPENDIX. Write as the first figure of the product the unit figure of the multiplicand ; multiply each figure of the multipli- cand by the tens of the multiplier, and at the same time, add mentally to each product the figure to the left of the one multiplied, carrying as usual. EXAM PLES. 566. 1. Multiply 456 by 61. 1ST OPERATION. 2ND OPEKATION. ANALYSIS, 2ND METHOD. -Write 6 in the 456 X 61 product. 6x6 + 5 = 41. Write 1 and carry 2736 61 4. 6x5 + 4 (carried) +4 = 38. Write 8 and 27816 27816 carry 3. 6 x 4 + 3 (carried) = 27. Multiply Multiply 2. 864 by 61 ; by 41. 5. 2345 by 121 ; by 111. 8. 717 by 31 ; by 71. 6. 7416 by 51 ; by 81. 4. 447 by 21 ; by 81. 7. 8324 by 41 ; by 21. NOTE. When the multiplier is any digit, any number of ciphers, and 1, the above principle may also be applied. Multiply Multiply 8. 375 by 301 ; by 401. 11. 48 by 701 ; by 801. 9. 425 by 201 ; by 101. 12. 376 by 201 ; by 901. 10. 46 by 601 ; by 501. 18. 87 by 3001 ; by 4001. 567. To multiply by any number between 12 and 20. 568. RULE. Multiply by the units of the multiplier, writing the product under the multiplicand one place to the right, and add. Or, Multiply the units of the multiplicand by the units of the multiplier, write the units of the product, and carry the tens, if any, to the next product ; multiply the remain- ing figures of the multiplicand by the units of the multi- plier, and at the same time add mentally to each product the figure to the right of the one multiplied, carrying as usual ; finally, to the left-hand figure of the multiplicand, add the number to be carried, if any, and write the result. SHORT METHODS. 301 EXAMPLES. 569. 1. Multiply 456 by 18. 1ST OPERATION. 2NI> OPERATION. ANALYSIS, 2ND METHOD. - 8 X 6 = 48. Write 8 and carry 4.' 8x5 + 4 (carried) + 6 = 3648 18 50. Write and carry 5. 8 x 4 + 5 (carried) 8208 8208 +5 = 42. Write 2, and carry 4. 4 + 4 = 8. Multiply Multiply 2. 785 by 13 ; by 17. 6. 1234 by 14 ; by 16. S. 378 by 14 ; by 16. 7. 2345 by 16 ; by 18. 4. 522 by 15 ; by 19. 8. 3456 by 19 ; by 13. 5. 376 by 18 ; by 16. 9. 7891 by 17 ; by 15. NOTE. The above principle may also be applied when the multiplier consists of 1, one or more ciphers, and a digit. Multiply Multiply 10. 875 by 101 ; by 108. 14. 147 by 1008 ; by 1001. 11. 936 by 102 ; by 103. 15. 385 by 1004 ; by 1007. 12. 877 by 104 ; by 106. 16. 783 by 1005 ; by 1003. 18. '736 by 105 ; by 109. 17. 546 by 1007 ; by 1006. 570. To multiply by any number ending with 9. 571. RULE. Multiply by 1 more than the given multi- plier, and from the result subtract the multiplicand. EXAMPLES. 572. 1. Multiply 387 by 49. OPERATION. 387 product by 1 19350 " " 50 (See Art. 43, Ex. 13.) 18963 49 (Subtracted downwards.) Multiply Multiply 2. 76 by 49 ; by 39. 5. 312 by 19 ; by 89. 3. 87 by 29 ; by 99. 6. 427 by 39 ; by 79. 4. 45 by 59 ; by 69. 7. 825 by 29 ; by 69. 362 APPENDIX. 573. To multiply by any multiple of 9 less than 90. 574. RULE. Multiply by the multiple of ten next higher than the given multiplier, and from the result subtract one- tenth of itself. EXAMPLES. 575. 1. Multiply 785 by 63. OPERATION. 785 70 54950 product by 70 J5495 " " _7 49455 63 Multiply & 67 by 18 ; by 27. 8. 34 by 36 ; by 45. 4. 77 by 54; by 63. 5. 84 by 72; by 81. 576. To multiply by 25. ANALYSIS. 63=70-7. 785 x 70 = 54950. Divide 54950 by 10 by placing its digits one place to the right. 54950-5495 = 48455. Multiply 6. 345 by 36 ; by 45. 7. 567 by 18 ; by 72. 8. 518 by 27 ; by 63. 9. 724 by 54 ; by 81. 577. RULE. Add two ciphers and divide the result by 4- Or, Divide the number by 4 / if there is no remainder add two ciphers; if there is a remainder of 1, add 25 ; of 2, add 50; of 3, add 75. EXAM PLES. 578. 1. Multiply 446 by 25. OPERATION. ANALYSIS. Since 25 is equal to 100 divided by 4, multi- plying by 100 and dividing the result by 4, is the same as 11150 multiplying by 25. 2. Multiply the following numbers by 25 : 24, 36, 37, 49, 62, 387, 448, 512, 746, 424, 817, 937, 544, 717, 318, 324, 256, 556, 9224, 8378, 5280, 1728, 5648. SHORT METHODS. 303 579. To multiply by 125, 580. KULE. Add three ciphers, and divide by eight. EXAMPLES. 581. 1. Multiply 637 by 125. OPERATION. ANALYSIS. Since 125 is one-eighth of 1000, multiplying 8 ) 637Q( by 1000 and dividing the result by 8, is the same as multiply- 79625 in S by 125. 2. Multiply the following numbers by 125 : 32, 48, 76, 87, 92, 88, 112, 147, 317, 324, 325, 378, 419, 516, 875, 819, 725, 717, 998, 444, 1234, 5287, 7326, 8317, 1728. 582. To multiply by any number one part of which is a factor of another part. EXAM PLES. 583. 1. Multiply 576 by 287. OPERATION. 576 287 4032 product by 7. 16128 " " 28 = 4 times product by 7. 165312 " " 287. OPERATION. 567 2. Multiply 567 by 936. 567 936 5103 product by 9. _20412 " " 36 4 times product by 9. 530712 " " 936. Multiply Multiply 3. 227 by 369 ; by 427. 8. 932 by 183 ; by 927. 4. 516 by 246 ; by 568. 9. 718 by 284 ; by 832. 5. 344 by 126 ; by 124. 10. 529 by 546 ; by 756. 6. 728 by 426 , by 189. 11. 638 by 217 ; by 618. 7. 325 by 147 ; by 273. 12. 435 by 248 ; by 428. 304 APPENDIX. 584. To multiply by any number near and less than 100, 1000, etc. 585. The Complement of a number is the difference between the number and the unit of the next higher order. 586. RUEE. Add to the multiplicand as many ciphers as there are ciphers in the unit next higher than the mul- tiplier, and from the result subtract the product obtained by multiplying the multiplicand by the complement of the multiplier. EXAM PLES. 587. 1. Multiply 456 by 98. OPERATION. 45600 product by 100. 912 " " _2. 44688 " " 98. Multiply Multiply & 77 by 99 ; by 93. 6. 387 by 93 ; by 999. 3. 84 by 98 ; by 95. 6. 416 by 95 ; by 994. 4. 72 by 94 ; by 96. 7. 528 by 93 ; by 992. 588. To multiply together two numbers, whose mean number may be squared mentally. 589. EULE. From the square of the mean number, subtract the square of the difference between the mean number and one of the given numbers. NOTE. This rule depends upon the algebraic formula, (a + b)x(a 6) = a*-b*. EXAM PLES. 590. 1. Multiply 37 by 43. Ans. 1591. ANALYSIS. The mean number is 40. Its square is 1600. The square of 8, the difference between the mean number and one of the numbers, is 9. 1600-9 = 1591. Multiply mentally 2. 87 by 73. 5. 93 by 87. 8. 112 by 108. 8. 63 by 57. 6. 42 by 38. 9. 116 by 124. 4. 22 by 18. 7. 48 by 52. 10. 115 by 105. SHORT METHODS. 305 CKOSS MULTIPLICATION-. 591. Cross Multiplication depends upon the following principles : Units multiplied by units produce units. Tens " units L tens. Units " tens J Hundreds " " units I Tens " tens L " hundreds. Units " hundreds 1 Thousands " " units Hundreds Tens " " tens " hundreds L " thousands. Units " thousands Ten-thousands " ' ' units i Thousands " " tens Hundreds " hundreds _ \- " ten-thousands. Tens " thousands Units " ten-thousands j Etc., etc. Ex. Multiply 68 by 74. Ans. 5032. OPERATION. 68 74 ANALYSIS. 4x6 + 3 (carried) 4x8 = 3 7x8 = 8 5032 7x6 + 8 (carried) = 50 Ex. Multiply 579 by 42. Ans. 24318. OPERATION. 579 42 24318 2x9 = 1 2x7 + 1 (carried) +4x9 = 5 2x5 + 5 (carried) +4x7 = 4 Ex. Multiply 567 by 348. 4x5 + 4 (carried) = 24 Ans. 197316, OPERATION. 567 348 8x5 = 40 8x6 = 48 8x7 = 56 4x5 = 20 4x6 = 24 4x7 = 28 197316 3x5 = 15 3x6 = 18 3x7 = 21 19 7 3 306 APPENDIX. 592. To multiply together numbers of two figures each whose units are alike. Ex. Multiply 76 by 46. Ans. 3496. OPERATION. ANALYSIS. 76 6 x 6 = 3 46 6x7 6x4 6x11 + 3 (carried) = 6 9 4x 7 + 6 (carried) = 3 4 Ex. Multiply 135 by 65. Ans. 8775. OPERATION. ANALYSIS. 135 5x5=2 \ *~x + 2 (carried) = 9 8775 * 6x13 + 9 (carried) = 87 593. RULE. Multiply units by units for the first figure of the product, the sum of the tens by units for the second figure, and tens by tens for the third figure, carrying when necessary. EXAMPLES. 594. Multiply 1. 56 by 56 ; 72 by 32 ; 94 by 44. 2. 65 by 75 ; 87 by 37 ; 46 by 36. 3. 99 by 49 ; 85 by 75 ; 34 by 24. 4. 47 by 37 ; 67 by 57 ; 85 by 45. 5. 125 by 65; 126 by 36 ; 154 by 84. 6. 76 by 76 ; 36 by 36 ; 114 by 114. 595. To multiply together numbers of two figures each, whose tens are alike. Ex. Multiply 87 by 85. Ans. 7395. OPERATION. ANALYSIS. 87 5x7 = 3 _85 8x5 7395 8x7 8x 8+9=73 SHORT METHODS. 307 Ex. Multiply 127 by 122. Am. 15494. OPERATION. ANALYSIS. 127 2 x 7 = 1 122 12 x 2 > > 12 x 9 + 1 = 10 15494 12 x 7 5 12 x 12 + 10 = 15 4 596. KULE. Multiply units by units for the first figure of the product, the sum of the units by tens for the second figure, and tens by tens for the remaining figures, carrying when necessary. EXAMPLES. 597. Multiply 1. 87 by 82 ; 81 by 87 ; 65 by 63. & 47 by 44 ; 56 by 52 ; 58 by 57. 8. 73 by 76 ; 79 by 75 ; 68 by 63. 4. 44 by 43 ; 52 by 55 ; 67 by 63. 6. 116 by 117 ; 107 by 105; 125 by 122. 598. To multiply together two numbers whose tens are alike, and the sum of whose units is ten. 599. RULE. Multiply the units together for the two right-hand figures of the product, one of the tens by 1 more than itself for the remaining figures. EXAMPLES. GOO. 1. Multiply 76 by 74. Ans. 5624. ANALYSIS. 6 x 4 = 24, the two right-hand figures of the product. 6 x 7 (6 + 1) = 42, the remaining figures. Multiply mentally 2. 24 by 26 ; 85 by 85 ; 128 by 122. 3. 17 by 13 ; 94 by 96 ; 112 by 118. 4. 34 by 36 ; 37 by 33 ; 104 by 106. 5. 25 by 25 ; 43 by 47 ; 143 by 147. 6. 35 by 35 ; 56 by 54 ; 152 by 158. 308 APPENDIX. 6O1. To multiply by means of complements (585). Ex. Multiply 991 by 996. OPERATION. ALGEBRAIC MULTIPLICATION. 991.. 9 991 = 1000 9 Q N " > sum = 2000 996. .4 996 = 1000 ' ' w L3 987036 1000 x 1000 9 x 1000 ' 4 x 1000 + 36 (1000 13) x 1000 + 33 ANALYSIS. From the above algebraic multiplication, it is observed : 1st, that as many of the right-hand figures as there are ciphers in the unit of comparison may be obtained by multiplying the complements together; 2nd, that the second part of the result is equivalent to the sum of the numbers less the unit of comparison multiplied by that unit. The sum of the numbers less the unit of comparison may be obtained by adding the numbers and omitting the 1 at the left-hand, or by subtracting either complement from the opposite number. Thus, 991 4 = 987. 602. RULE. From either nujnber subtract the comple- ment of the other, and to the right of the remainder write the product of the complements. NOTES. 1. When there are less figures in the product of the comple- ments than ciphers in the unit of comparison, write ciphers in the result to supply the deficiency. 2. When there are more figures in the product of the complements than ciphers in the unit of comparison, add the excess on the left-hand to the second part of the result. 3. After practice, the complements may be omitted in the operation. EXAMPLES. 603. 1. Multiply 88 by 95 ; 975 by 993 ; 9999 by 9999. (a.) (b.) (c.) 88.. 12 775.. 225 9999... 1 95... 5 993 7 9999... 1 8360 769575 99980001 Multiply Multiply 2. 97 by 99 ; by 94. 8. 993 by 992 ; by 994. 8. 88 by 91 ; by 95. 9. 990 by 991 ; by 988. 4. 89 by 93 ; by 96. 10. 982 by 994 ; by 995. 5. 75 by 97 ; by 98. 11. 925 by 996 ; by 994. 6. 92 by 98 ; by 93. 12. 875 by 992 ; by 993. 7. 86 by 94 ; by 95. 13. 847 by 990 ; by 988. I sum = 200 + 19 SHORT METHODS. 309 604. To multiply together two numbers of the same number of figures over and near 100, 1000, etc. Ex. Multiply 116 by 103. OPERATION. ALGEBRAIC MULTIPLICATION. H6 116 = 100 + 16 103 103 = 100 + 3 11948 100 x^OO -h 16 x 100 + 3 x 100 + 48 . (100 + 19) x 100 . + 48 605. KULE. From the sum of the numbers subtract the unit of comparison, and to the right of the result write the product of the excesses. NOTE. See notes to preceding rule. ' EXAMPLES. 606. 1. Multiply 124 by 104 ; 128 by 106 ; 1015 by 1006. () (*) (c.) 124 128 1015 104 106 1006 12896 13568 1021090 2. 112 by 106 ; by 111. 7. 145 by 107 ; by 112. 5. 102 by 103 ; by 104. 8. 176 by 111 ; by 108. 4. 122 by 108 ; by 105. 9. 1004 by 1006 ; by 1007. 6. 116 by 107 ; by 112. 10. 1125 by 1008 ; by 1012. 6. 118 by 101 ; by 109. 11. 1116 by 1015 ; by 1008.' 6O7. To multiply together two numbers, one of which is more and the other less than 100, 1000, etc. Ex. Multiply 109 by 97. OPERATION. ALGEBRAIC MULTIPLICATION. 109 9 excess. 109 = 100 97 3 complement. 97 10600 100 x 100 + 9 x 100 27 Product of excess | - 3 x 100 27 and complement. ) (100 + 6) x 100~ 27 :;r,h+ 310 APPENDIX. 6O8. RULE. Multiply the sum of the numbers less the unit of comparison by that unit, and from the product subtract the product of the excess and complement. EXAMPLES. 6O9. Multiply Multiply 1. 107 by 97 ; by 95. 6. . 1005 by 91 ; by 93. 2. 112 by 96 ; by 92. 7. 1007 by 95 ; by 97. 3. 116 by 94 ; by 98. 8. 1012 by 99 ; by 92. 4. 108 by 91 ; by 99. 9. 1018 by 94 ; by 96. 5. 115 by 99 ; by 88. 10. 1024 by 98 ; by 89. SHORT METHODS OF DIVISION. 610. Leaving out the Products. In long division the process may be shortened by the following : 611. RULE. Subtract the several products from the next number greater ending with the corresponding figure in the dividend, and carry each time the left-hand figure of the minuend to the next product. NOTE. If the right-hand figure of any product is the same as the corres- ponding figure of the dividend, subtract it from itself, and not from the next higher number ending with the same figure ; or, write in the remainder, carrying the left-hand figure of the product. Ex. Diftde 42343014 by 973. 42343014 3423 973 ANALYSIS. The first quotient figure is 4, by which we multiply. 4 times 3 are 12, which subtracted from 4oolo 14 (the next number greater ending with 4) leaves 2. Write 2 in the remainder and carry 1. 4 times 7 are ag, 1 carried makes 29, which subtracted from 33 (the 7784 next number greater ending with 3) leaves 4. Write 000 4 in the remainder and carry 3. 4 times 9 are 36, 3 carried makes 39, which subtracted from 42 leaves 3. Write 3 in the remainder and carry 4. 4 subtracted from 4 leaves 0. Bring down 3, the next figure of the divisor. So proceed until the division is finished. SHORT METHOD S. 311 612. To divide by 25. 613. RULE. Multiply the dividend by If, and divide the product by 100 by cutting off two figures from the right. Ex. Divide 11175 by 25. OPERATION. ANALYSIS. Since 25 is one-fourth of 100, multiplying by 4 4 and dividing by 100, is the same as dividing by 25. 447.00 EXAMPLES. 614. 1. Divide the following numbers by 25 : 1175, 1650, 1700, 2875, 3825, 4950, 3800, 1725, 1775, 1825, 1975, 2000, 1650. 615. To divide by 125. 616. RULE. Multiply by 8 and divide the product by 1000 by cutting off three figures from the right. Ex. Divide 21875 by 125. OPERATION. ANALYSIS. Since 125 equals 1000 divided by 8, multiplying 8 by 8 and dividing by 1000, is the same as dividing by 125. 175.000 EXAMPLES. 617. 1. Divide the following numbers by 125 : 13500, 17250, 16375, 23500, 19875, 17625, 20000, 14125, 19375, 16250. 618. To divide by 619. RULE. Multiply by 8 and divide by 100. 620. To divide by i6|. 621. RULE. Multiply by 6 and divide by 100. 622. To divide by 33f 623. RULE. Multiply by 3 and divide by 100. 312 APPENDIX. EXPLANATORY NOTES. 624. The marks, numbers, abbreviations, etc., of the bills in Art. 278 are explained in the following notes : 1. Bill 2, 7th item 2177 Ibs. Sifted Meal at $1.20 per cwt.\ 8th item 264^ (9 Ibs.) bushels Oats at 56 eta. per bushel. 2. Bill 3, 1st item 16319 bu. 23 Ibs. (f $) wheat. Since the rate per bushel is very small, the number of pounds may be omitted in the calculations. 6th item M., 1000 bushels. 3. Bill 5, 3rd item 10 Kits (15 Ibs. each) Extra Number 1 Mackerel at $1.80 per kit. 4. In Bills 6, 7, 8, 10, 11, and 12, the letters and numbers on the margin of the bills correspond with the distinguishing marks and numbers on the casks, barrels, kegs, boxes, cases, bales, and bags of merchandise. 5. Bill 6, 1st item ^ I&4385 " is mark and number upon the cask ; 1544, gross wt. ; 134, tare or weight of cask. 5th item J foil, put up in \ Ib. packages and wrapped in tin foil. 6. Bill 7. The small figures at the right of the words "bag" and " bbl" are the prices of the same. 3rd item 121 Ibs., gross wt., 21 Ibs., tare, 100 Ibs., net wt. 4th item 112 and 109, gross weights ; 22 and 20, tare ; 221, total gross weight; 42, total tare. 11th item 1st column, gross weight; 2nd column, tare. 12th item |, | gallon allowance for leakage. 7. In bills 8, 9, 10, and 11, the small figures represent fourths (quarters). 8. Bill 8, 1st column, number of yards in each bale or case. 2nd column, price per yard. 9. Bill 9, 1st item 2 pieces Naumkeag Bleached Jean containing 48 and 47 yards respectively ; total, 95 yards at 9 cents per yard. 10. In bill 10, the numbers represent the number of yards in the several pieces. 11. Bill 11,1st column, distinguishing aumberof each case. 2nd column, number of yards in the several cases. 12. Bill 12. Number on margin (1789), number of case. Numbers 3458, 2032, etc., manufacturer's distinguishing numbers (stock numbers). 13. Bill 14, 3rd item 200 carriage bolts of each of the following sizes : % in. thick x 1 in. long, in. thick x 2 long, in. thick x 5^ Jong, | in. thick x 5| in. long. The numbers 2.40, 2.55, 3.15, and 3.20 represent the prices per hundred of the several sizes. In the following items, the 1st fraction repre- sents the thickness of the bolts, and the other numbers on the same line the lengths of the different sizes. The numbers above the lengths represent the prices per hundred. 14. Bill 15. The letters and numbers on the margin refer to the num- bers of the watches. 4th item numbers 222 and 208 refer to the style num- bers (stock numbers) of the guards (chains), and the numbers above (37| and 56) express the weights in pennyweights ; $1.15 per pennyweight. OF THE UNIVERSITY UNIVERSITY OF CALIFORNIA LIBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW JUL1H917 JUL 16 1919 307n-l,'15 2 2440 183983