IMAGE EVALUATION TEST TARGET (MT-3) k A {./ 1^ /. /, % 1.0 I.I 11.25 ^i^ IIIIIM 1^ |3^ 2.0 U III 1.6 Photographic Sdences Corporation S 23 WEST MAIN STREET WEBSTER, NY. M580 (716) 872-4503 fV <^ v a^ ^ r \% % -)y 26 X 30X 24X 28X J 22X ?np^f¥^. The copy filmed here has been reproduced thanks to the generosity of: IMational Library of Canada L'exemplaire film6 fut reproduit grdce d la g6n6rosit6 de: Bibliothdque nationale du Canada The images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. The last recorded frame on each microfiche shall contain the symbol — ♦- (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les images suivantes ont 6t6 reproduites avec le plus grand soin, compte tenu de la condition et de la nettet6 de l'exemplaire film6, et en conformity avec les conditions du contrat de filmage. Les exemplaires originaux dont la couverture en papier est imprimde sont fiimds en commengant par le premier plat et en terminant soit par la dernidre page qui comporte une empreinte d'impression ou d'illustration, soit par le second plat, selon le cas. Tous les autres exemplaires originaux sont filmds en commenpant par la premidre page qui comporte une empreinte d'impression ou d'illustration et en terminant par la dernidre page qui comporte une telle empreinte. Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, selon le cas: le symbols — ► signifie "A SUIVRE ", le symbole V signifie "FIN". Les cartes, planches, tableaux, ate, peuvent dtre filmds d des taux de reduction diff^rents. Lorsque le document est trop grand pour Stre reproduit en un seul clich6, il est film6 d partir de I'angle sup^rieur gauche, de gauche d droite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivants illustrent la m6thode. 1 2 3 22X 1 2 3 4 5 6 THIRD EDITION — REVISED AND ENLARGED CANADIAN Commercial Arithmetic COMPRISING OVER 3,000 PROBLEMS AND EXAMPLES WITH Clbar and Concisb Rules, Explanations and Solutions numbfiring over 300 : nearly 50 principal titles and OVER 700 Distinct Definitions, with more THAN 30 Valuable Tables and 30 Illustrations. also new chapter on THE METRIC SYSTEM OF MEASUREMENT Now legal In Canada, from MS. examined by SIK HENRI JOLY, MINISTER OF INLAND REVEN0E FOR CANADA AND A CHAPTER ON THE INSTITUTE OF CHARTERED ACCOUNTANTS RKVISKD BY HABRY VIOEON, ESQ., F.C.A., SEC'Y TO THE INSTITUTE. WITH THEIR Examination Questions m Mercantile Arithmetic making the most complete Text Book and Ready-Reference Manual for the Commer- cial Student, Merchant, Accountant, Lumberman, Contractor, Artisan and Farmer. compiled and EDITED BY CLARKE MOSES, | R. C. CHESWRIGHT, PUBLIC SCB. iNsr., Haldimand Co. Math. Master, sf.afurth H. 8^ TORONTO COMMERCIAL PUBLISHING COMPANY S> CliUKCH STREET 1897 V *,* The answers to the Problems in this Book are printed separately in pam- phlet form, and supplied in literal proportion without extra charge, for the use of Teachers in Business Colleges, Schools and Institutions- Entered according: to Act of the Parliament of Canada in the year one thousand eight hundred and ninety-seven, by C. A. Benoouoh, in the office of the Minister of Atrrlculture. ■ti PRINTINci AM) BINDIXli BY DAVIS * Hendbrbon, Printers and bindkhs M BAV STBr.RT TORONTO kleitkotvpinli and 8tebe0typimo by National Electbotvi'e and stekeotvpb Co 12 ADEI.AinF. ST Wkst TOROmO ^ PUBLISHER' S PREFACE. THIS Arithmoti,- has lH..en so well received by Business C.llepcw Schools TiiK Metkic System having been le- galized in Canada, a chapter has been added dealing with this imiwrtant subject. This chapter is the most complete and |)ractical to be found in any work. It has been compiled with special reference to commerchil usntre and avoids Physics on the one hand ,u..i Higher Mathematics on the other. The M.s was submitted for revision to .sni HiNi'i JoLV, Mit Uter of Inland Revenue fur Can- ada, who is the highest authority on the subject in the Dominion, having' nia6 365 365 .365 SKi 865 86.5 370 365 ,364 .3ti8 .368 .iG8 ,)69 .30-(J39 Solids— Definitions 6.1(MM,5; 048-l!.'>l .. —J^rism or Cylinder 640-617 ^_ —Pyramid or Cone 0.5,')-o.')8 „ ,. —Sphere 65»-664 Lublcal ICistprnsand Bln8..66.')-666 Contents / Casks, Gauging of . .667-OGU Measurement of Carpeting, Wall Paper, Saw Logs, Lumter, bhlngling,Fencinp,Painting, Paving, Latliing. Plastering, htone-work. Brick-work 670-711 Mercantile Arithmetic — In- stitute Char. Acc'nt Exam. „„>t"e8tion8 428-430 METRIC SYSIEM op MEA.S't 418-423 MiSCELLANKOns PROBLEMS. . . 78-83; M««„. f /> [143-152; 240-247; 348-385 MoNEi&CuRRKNov, with Tables 113-134 MULTii'LiCAnoN, Short Metliods in. 6-18 Painting and Kalsomining.Meas- urement of. 094 Papering (Wall) Mea.'iurom't of. .'674-078 Partial Payments, howKeck'd 198-204 Partnkrship 3a7.WH Definitions mi-I^ Division of Gain or Loss, equal time 529 Division of Gain or Loss',' 'un'- equal time 530 To find Net Gain or Loss.'....! .Wl ' each Partner's Inter't. 532-534 raving, Meas>urement of 694 Pbrckntacjk (with Table) 84-89 Perpetual Annuities.tofind Value m) Plastering, Measurement of 6.9.').6»8 P>>WKRs AND Roots 386-383 Definitions 586 .5H6 Sqn.nrc Root .'.'.'.'.'.'597-000 Cube .601-004 294 02-67 I ractical Mensuration 384 iU Profit AND Loss mm Proportion 'anirJS siinj.le Proiwrtion ....■.■.■.:;::' ' S? .a9n ^ Tax Tabl; at 3 mills .sis IRUE Discount, how Reckon'd..S.'i7-300 Wall Paper, Mensurenient of.. . .074-078 Weights and Measures 91-61 Money and Currency (with Tables) ll."-134 Alwthecaries'Weight and Mea.'.l.S.'i-iss Avoirdupois •• (witli Tab.) 139-142 Comparative Table of Wgts. ... 143 Grain Measure (Table) 144 pry,, •' " 145-1,'* f.'quld ' " 151.] 54 Linear " Includ. Survey- or's (Tables^ ir>riii,% Square Measure, Inclu. Survey- _ or's (Tables) ;'. 1511.104 Cubic Measure (Table) 16')-108 «'.™®.. J',. (Tables) io!i.]79 Miscell. Tables-Counting iso " " —Paper isi ,,,. , ^, " —Books 182 \v hole Life Insurance (Table of Rates) 584 i r -'«*j CHARACTERS AND ABBREVIATIONS USED IN BUSINESS. @ a/c % t V V V X £ 6/3. At. Account. Cents. Per cent. Number. One and one-quarter. One and one-half. One and three-quartera. Check mark. By, as 14x18 inches. Dollars. Pound sterling. English shillings and are frequently written in this manner the shillings on the left of the sloping line, and the pence on the right, the above meaning, 6 shillings and 3 pence. May 18/21 The day of maturity, as expressed in a note, and the last day of g3:ace are indicated by writing the first on the left and the second on the right of the sloping line. ® »16, and 6 doz. at »18 per doz. 1100 pounds gross weight, 156 lbs. tare 155 946 lbs.. ^LT;^^^*'*^* W\d-' — X "■•> 945 lbs., net weight. *^l The numbers in ^ps.ofif 138 yds. *"^ bracket are the ^« number of yards in ^^1 each piece respec- in -I tively. 5 @ 2 shUhngs per doz.: 6 No. 8 @ 3«. 6rf. per doz. W. W and similar characters and letters, are placed on pack- ages to designate a particular lot or shipment • hhd. Sugar. 1100 No. doz. ''{jj;^'^ 7 by 9 in. 7 in. wide, y may 9ia. ^ ^ First claM. V^j'^' Account. ■^'^.^ Adventure. f«^ Agent. f™,*- Amount. ■*^8 '^ Assorted. ^•? Bill-book. 5^ Balance. ^5 Barrel. gf^'s Bundles. Bg8 Bags. gj^ts Baskets. ^r Black. g'« Bales. Bot Bought. B.L. or B. of L.Bill of Lading. glf^'^y Bills payable! S"r ^^^"^ B'"8 receivabta. g"k Bank. Brot Brought. gque Barqua. Br .Brig. g«8 Bushels. BxB Boxes. C Cents. O or centum . . Hundred. ^i^ Cash-book. Ck Check. ^ftP Capital. J:^°- • •• Company. ci?f::::::::glS'"^«"'"'- Cr Creditor. ^"™, Commission. ^0"st Consignment. J:^^ Cases. X !" Hundredweight. C/o Care of. i, Pence. g?* Draft. S?^: Dividend. ^"0» Discount. vm CHARACTERS AND ABBUEVIATI0N8. Do. or Ditto. .The same. Doz Dozen. Dr Debtor. Ds Days. K& Each. K. E Errors expected. E. & (). E. . .Errors and oniisi iHsions excepted. Eng English. Ent'd I'Jntered. Ex. Without, as ex-divi- dend. Exch Exchange. Expa Expenses. Emb'd Embroidered, Fis'd Figured. Fir .Firkin. F. o. b Free on board. I'ol Folio. F' wd or for'wd. Forward. Fr From or French. Fc Franc. Fr't Freight. Ft Feet. Gal Gallon. Gro Gross. Guar Guarantee. Hdkf Handkerchief. Hhd Hogshead. Hand Hundred, !• B Invoice-book. In. or " Inches. Ins Insurance. Insol Insolvency. Inst. (Instant). This month. Int Interest. Inv Invoice. Invfy Inventory. !• 0. IT I owe you. Lbs Pounds. M Thousand. Mdse Merchandise. Mo Month. Mols Molasses. M.'t Empty. Net Without deduction. No Number. N. P Notary public. O- !• B Outward invoice-book Oz Ounces. Paym't Payment. P'd .Paid. Pkgs Packages. Pr. or Per By. Per cent By the hundred. Pp Pages. Pr Pair. Prem Premium. Prox. (Proximo) The next month Ps Pieces. Pts Pints. Qr Quarter. Qts Quarts. Qtls Quintals. Rec'd Received. Recpt Receipt. R. R Railroad. Rs. or Rls Reals. R- W Regular way. B Shilling, Shipt Shipment. Shs Shares. Sohr Schooner. S. S Steamship. Hq Square. Stor Storage. Stb't Steamb'.iat. Sunds Sundries. Super Supertino. Str Steamer. Tes Tierces TJlt. (Ultimo) The last month. Ves Vessels. Vs Against. Viz Namely, Wt Weight. W. I West Indies. Yds Yards. Yr Year. •^-*.l ADDITION. 1. Rapidity and accuracy in addition are of the first importance to the commercial student. These can be acquired only by a thorough familiarity with the Bimple combinations of numbers, and Hroper practice with these combinations. ^^ The following Tables exhibit all the combinations of numbers and the attention of the student is espedaUy Combinations ending with a 1 9 10 2 8 S 5 10 10 10 10 Combinations ending with i. 1 2 9 4 7 5 6 1 11 11 11 11 Combinations ending with 2. 3 9 12 4 8 12 5 7 12 6 6 la Combinations ending with 3. 2 1 8 4 9 o 8 6 7 18 13 18 8 ADDITION. Combinations ending with 4. 2 2 3 1 4 5 'J 6 8 4 4 4 14 14 Combinations ending with 5 7 7 14 3 2 4 1 5 6 9 5. 5 5 16 Combinations ending with 6. 7 8 15 3 4 .? 2 5 1 6 7 9 8 6 « 6 6 16 16 Combinations ending with 7. 4 5 6 7 8 2 10 8 9 7 7 7 7 17 Combinations ending with 8. 4 5 6 7 8 4 3 2 10 8 8 8 8 8 Combinations eroding with 9. 9 18 5 4 6 3 7 2 8 1 9 99999 After the student becomes familiar with the foregoinff oumbmations his attention is directed to the use of the endings. For example : 7 4 6 = 13, 6 & 7 = 18, 17 A 6 16 A 7 28, 27 A 6 = 88, 87 A 6 = 43, Ao. 28, 26A7-88, 86A7=»48,Ao. t.e., the sum of any two numbers, one of which ends with 6 and the other with 7, produces a number ending with 8 A thorough drill of this kind should be given with all the Combinations. ADDITION. 3 2. An effective drill may be given to the student by the use of the following diagram : 1 The teacher places any number within the circle and requires the pupils to add to it any number or succession of numbers to which he may point. Kapidity and accuracy in addition can be gained only by adding columns of figures. «. In adding ledger columns, accountants frequently use Che following devicea : ^ EXAMPLB 1.— «926.42 49.98 C7.84 87C.55 48«7.89 946 74 6487.45 #14222.87 4454 3 ^ Thejigure to be carried is placed under the column tn wkhk u belong, so that in case of interruption or mistake u'maybe used for reference. I ADDITION. 4« EXAUPLX 2.— 328808 98746 2386 91642 28735 82614 79186 26788 87264 19285 63127 68432 203846 82691 35417 63529 48763 21734 252184 784288 The column to he Med a divided into ,mmd ^r,. n„, „„ added and tHe .« „/ <,. .^^Z! X'. J^:T °''"° "' "»" """"- "' '"e «"»e toe. 86 89 76 47 247 Method aw Addition— a To find the sum of any series of numbers which nave a common difference. RCLB. ilfuZrtpZy . 997 .. .. 3 M2 .... 8 989024 (8ee~Note 1.) EXERCISE II. 6- 88 X 93. 7. 87 X 88. 8. 84 X 92. 9. 75 X 96. 10- 93 X 86. EzAupi^ 8 686 .. 815 4 682260 (see Note 2.) 97 X 96. 95 X 93. 94 X 96. 99 X 94. 98 X 92. 11. 12. 13. 14. 16. 993 X 995. 997 X 992. 995 X 993. 989 X 788. 991 X 886. •i". an X H6. Jf' ;° ""'"ply by means of factors. ■•a •>Z^:7:'22T - ''"' ■>-">- *se product Multiply 866 by 86. " 35 = 7 X 6 866 7 MRTHOD OMITTING MUWrPLIERS 866 6056 product by 7 6055 produced bv 7 5 •' 80275 J- 626 X 36. 2. 327 X 54. -i- 495 X 48. 4. 378 X 77. 5. 6. 7. 8. 30276 18. 14. 16. 16. i< 85 30687 X 105. 20956 X 121. 41378 X 164. 86254 X 235. " 35 (6 times 7) EXERCISE. 296X99. 9. 1351 X 42 343X72. 10. 4164 X 35.' 764x56. 11. 8127x126. factor of CXr °"' ^^^ "' *^^ '""^"Plier is a nr J . , RULE. 467 248 3736 product by 8. 11208 <• « OA /, f ^i (3 times the product by 8>. 115816 MULTIPLICATION. Example 2— Multiply 643 by 486. 643 486 2572 prodaot by 4. ^^3148 '• '. 36 (9 times the product by 4). 280348 Example 3— Multiply 3247 by 842. 3247 842 • 6494 product by 2. ^2988 " .. 4 (2 times the product by 2). 26976 " «' 8 (2 " " 4). la 2733974 EXERCISE 12. 1. 364 X 126. 2. 476 X 279. 8. 896 X 142. 4. 867 X S57. 6. 943 X .426. 6. 864 X 369. 7. 876 X C32. 8. 3164 X 427. 9. 4275 X 246. 10. 8137 X 189. 11. 2S56 X 284. 12. 4765 X 927. 18. 8259 X 936, 14. 4371 X 183. 15. 16. 17. 18. 19. 20. 21. 37281 X 4132.5 X 63587 X 49126 X 64273 X 47821 X 45314 X 832. 756. 618. 428. 535. 1682. 2468. 50. To multiply by a mixed number. Example 1— Multiply 363 by 6^. 868 6i 90f 2178 product by J = 363 J " " 6. r 4 = 90 22681 Example 2— Multiply 3426 by 5§. 3426 5? 1370if 17130 product by f = 3426 " 5. X 2 + fc 18500J '«( 14 o 1. 3. a. 4. 5. 8126 by 3^, 4371 by 15|.' 2137 by 41?, 4CJ,5 by 22i^, MULTIPLICATION. EXERCISE 13. 14?. 21*. 35g. 8*. 26i, 17§, 33f. 18«. 11*. lOJ. 3«A. 47A. 42f 52#. --^^-ia:2;i^.i:^.^^*;. Bhortc.- method to reduce the m!l1 """"^ ^* ^« °^*«° '^ fraction and to mm^y^l^n^^^^^^^^ exercise contains muItfplU of tht ^°,"" ^'^ ^^^^^^^^^ Multiply 689 by 83^. 689 X 83J «689xi5? 3 « 68900 „ • -g— = 229661 1. 2. 8. 4. 6. 6. 7. Multiply-- 3964 by IJ, 1375 by 14^, 4137 by 663, 3164 by 44^, 227 by 86f 383 by 266|, EXERCISE 14, 33*. 18^,22^, 28^ 36A. 71^, 65f, 45« 64 A. 288J, 77^, 63^! ^14f 88S. 72A.128f -^^^84...,; isj;.;^'^. Multiply 638 by 2^. The following list eon. . .. . ^^m^ «f *i, , may be used in this way/ . tr" r °^"^"P"«r« that preceding exercise ar« 628 <"'^i "^; in-tipliers used in the *^ MULTIi'LWATlOiS. If 1. 1| a 10 + 8. 12. 62J = -,00 + 8 2, IJ = 10 J. 6. 13. 58J = 700 -f 12 8. 2^ r-. 10 + 4. 14. 87i = 700 + 8 4. 6 « 10 4- 9. 15. lir,§ = 700 + 6 «. 8J a 100 4- 19. 16. 175 = 700 -f 4 6. l^ 3 .100 ; 8. 17. 112i = 900 T- 8 7. l»f .-1 100 -f 6. 18. 2-25 = 900 -r 4 fi 25 -= 100 4- 4. 19. 83J sr 1000 -f- 12 9. 87i = 800 -r 8. •20. 125 = 1000 -r 8. 10. 76 = 300 -i- 4. 21. 166J = 1000 4- 6. 11. 4]| s 500 + 12. 22. 833^ a 1000 ■;- 8. EXERCISE 15. Multiply— 1. 346 by li. 1§, 2J. 5, 8i. 2. 258 by 12J, 16|, 25, 87i, 76. 8. 512 by 41§, 62J,68J, 87i. 4. 545byn6§, 176, 112J, 6. 357 by 83A. 125. 166*. 226. aaai. 23. To multiply by 75. Multiply by 100 and subtract one quarter of the produck. iJxASiPiai— Multiply 863427 by 75. 75 - 100 - 25 (one-fourth of 100) Operation— 86349700 - product by 100. 21585675 - one-fourth of the produoA. 64757026 24. To multiply by 125. 126 = 100 + 25 (one-fourth of 100) Multiply by 100 and add one-fourth of the product. ExAMPLB— Multiply 1234769 by 126. Opkbation— 124376900 - product by 100. one-fourth of the product by 100. 31094225 166471125 1. 2. 8. 4. 367258 43729 27364 376298 EXERCISE 16. X 66§. X 95. X 976. X 950. 6. 36254 X 105. 6. 27936 X 133J. 7. 478266 x 160. 8. 236471 X 1026. m i^^yii^ioa. C^'VISION. I>TVmBIUTY OF mJMBERS. a«- Aneyenn«n,k • "^ "'"">'"» remainder, liviso. '" ■""-"^^ « » -mberof wWoi 2 ia » e»„t ar. An odd number ia o 3xact divisor. " * ""^''^'^ of which 2 is not m as. Any number is divisible- 3- % 4, if the two risht haadfl " """' ''^ »• -press a /ulbtrd^r b"V""""' °' 7828. uiVisibJe by 4, as 1500, 4. By 5, if the right hand figure is nr « . ^' By 6, if it ia an even number Id . i." ''' ''* BJ 8, ,f the three right hand figures ar« • i or express a number div\STl I ''P^'''«' 9248. divisible by 8, as 4000, i^ DIVISION. 17 7. By 9, if the sum of its digits is divisible bv 9 as 45387. ' 8. By 11, if the difference of the sum of the digits in the even places, and the sum of the digits in the odd places is 0, or is divisible by 11 as 48263, 459173. ' 9. By 26, if the two right hand figures are ciphers or expi-eas a number divisible by 25. as 4700 367))'. TO. By 75, the same as for 25, providing also that the sum of the digits is divisible by 3. as 8900 41476. 89. To divide one number by another leaving out tiae products. ^ BULK. 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. Divide 42343014 by 973. ordinary method. 978 ) 42343014 ( 43518 ikavino out the products. 3^92 42343014 j 978 8423 2919 5040 4865 3428 5040 1751 7784 0000 43518 1751 973 ^< T784 0000 METHOD. whI' *"* ^"°;7*/g°" " 4. by which we multiply. 4 times 3 are 12. which subtracted from 14 (the next number greater ending with 4) eavcB 2 write z in the remainder and carry 1. 4 times 7 are fls'and 1 earned makes 29. which, subtracted from 38 (the next numbTr ^ter 18 DIVISION. ending with 3). leaves 4. Write.- » ^'«- is .„„p,:.,7' "^'"" '" »>« *«»^. s:'^,::ra i^rx EXERCISE 17. 1- 743297 -f 527. 2. 14839 -;. 869.' 3. 87064 -f 743_ »^«ea6..7M.,6..,«e,sm;S 4. 36287^667. 6- 64925 J. 784 6- 34681^ 42a." 3»- To d.v.de by a mixed number. i>ivide 736 by 5|. fij ) 736 ( 17 ) 2208 ( 12915 17 60 84 168 153 15 Divide— EXERCISE ]& A 3624 by 131 4a oi o,f ^' ^»- 35 ) ,024395 ,' 2 2 I 70)1248790 '^17839 1 *» DIVISION. 19 ExAMPM 2— Divide 13476 bv loa. 16§ ) 13476 ( 6 6 808^ ,.^°™'7J' *''« .^''f '■/'"binder ia required it may be obtained by dividmg the remainder found by the number by which we multiply the 1. 4826 ^ 6. 2. 3827 -5- 25. 8. 9109 -f 75. 4. 4863 -f 175, 6. 3798 -f 225. 6< 8306 -f 46. EXERCISE 19. 7. 32068 -i- 12J. 8. 68934 -f 8J. 9. 32165 J. 1^. 10. 8327i i 83J. 11. 4932S ^ 33^. 12. 9306 + 62J, »3. To divide by any number that a convenient divisor by increasing or an aliquot part of itself. 13. 21396 -f 41§. 14. 9201 J. 36^. 15. 7345 -i- 57f 16. 6287 H- 125. 17. 312(34 -i- 87J. 18. 31907 -f- 142f. can be changed to diminishing it by BULB. After dividing by the divisor so increased tyr diminished increase or diminish the quotient in the same proportion. Divide 1920 by 24. Operation. •iff ) 192p • 4 ) 64 16 80 the quotient. Explanation. J of 24 = 6 24 + 6-80 - ■ 1920 -f 30 = 64 i of 64 = 16 80 the quotient, EXERCISE 20. 1. a. 8. 4. 1845 -f- 45. 8640 -f 86. 2822 -f 64. 16216 4- 48. 5. 7704 4- 24. 6. 8343 4- 27. ] 7. 41472+ 8li ] 8. 141120 + 180. ] 9. 24300 + 18}. 10. 21500 + 87^. 11. 887500 + 75. 12. 42r)100 + 125. 20 DIVISION. 88. To dW Je by means of factor of the divisor. Example l.-Diviue 25380 by 108. 108 = 9 X 4 X 3 or 6 X 8 V a «. o - 108 ) 25380 ( 236 216 378 324 540 540 8)[25380 4 ) 8460 9 ) 2115 235 *) 25380 6 )6460 6)l4i0 235 9 ) 25380 6)J820 2 ) 470 286 BxuttLB 2.— Divide 6306 by 75. 75 » a X 6 X 6, • U326 «)_2108 ..21 3 1 Xt + 8 8 *W21..8| 8xfl-Q -'>-To«fl ~8i 11 ,^°' 8x3 + 2- 26 «*•• 1(1X 6 X 8«,16 ■•■''-26 26 troe remainder. ^.r5".ir^:5°^ ^^rr.t'ri i^- «"«^ -.<«■ 1. 25380 + 86. 2. 1/8584 + 48. 8. 23741 i 42. 4. 43165 + 64. EXERCISE 21. 6. 31279 + 78. 8. 43827 + 84. 7. 19875 + 126. 8. 41643 + 186. 9. 48718 + 168. 10. 29878 + 81. 11. 41668 + 46. IS. 28726 -f 96. 34. To divide by cancellation DIVimON. Divide 18 x 16 x 28 by 12 x 7 x 14 3 ^ ;?_x_16_x ?8_ » X 16 ^;2 X 7 X ;^ - if— = ^ ot BULB. ai 2| 8 7 n 16 ??? 48 Cancel the factors common to the divisor and dividend, and divide the product of those remaining in the dividend by the product of those remaining in the divisor. Divide — 1. 2. 8. 4. 6. 6. 7 EXERCISE 22. 6x9x 7xllby7x5x 80 X 56 X 18 by 2 X 3 X 70 X 39 X 13 by 26 x 21 x 28 X 49 X 75 by 7 X 15 X 8x6x 8x72by2x3x 74 X 12 X 14 X 16 by 28 x 72 x 112 X 27 X 178 by 54 x 63 x 72 by 44 X 32 X by 27 X 18 X 154. by 72 n in X )). 8. 128 X 16 X 9. 185 X 12 X 29 la 45 X 63 X 144 3 X 4 X 7. 84. 4 X 24. 89. 18. 11. 6. 18. II FACTORING. 87. A Factor, a Measure, or an Ev=.-.* n- • g.ven number is a. integral number fharwi^T; l" given number without a remainder. ™^' ""* «fe*- ite!^L* rar3,",'l3, T" "'^' ""' "o '-"»" faf^: ^ ''^■"* '''''" « " P«- --ber used as a fa^; tsiZrsSTaVrsiTo^" '^- -- o'-e- cowTumw!' "' '™"" ""'■"'■''« «" factors of a **• ^° '*'""™ » ""■""er into its prime factors. . BUIJt. Divide the number hu thp ;^^»* t^nt. CmUnue thi, process ZJL J ''"""'"^ ««<'■ number i. re.cke,. nlrr^rill'f T " ^'^ are the prime factors. «»^»»or« and the last quotient Find the prime factors of 420. 1 2. 3. 4. 5. 2)420 2 ) 210 3 ) ] 05 5 ) 36 7 EXERCISE 23. Find the prime factors of— *20 = 2 X 2 X 3 X 5 X 7 2,3,.5and7aretheprimefaotor8. 1050, 2C25. 1820. 1485. 1155. 6. 7. 8. 9. 10. 6986. 4620. 4802. 5432. 7000. 11. 12. 13. 14. 16. 8140. 8712. 1320. 17C8. 1848. 16. 17. 18. 19. 20 1906. 1858. 1478. 2956. 2406. 21. 22. 23. 24. 2526. 2978. 2992. 3936. 25. 8430. liL_ HIGHEST COMMON FACTOR. 28 HIGHEST COMMON FACTOR. 48. A Common Factor of two or more numbers is a number that will exactly divide each of them ; thus 2, 4 6 or 12 is a common factor of 24 and 86. ' * ' 44. The Highest Common Factor, also called the Greatest Common Divisor or Greatest Common Mea- sure, of two or more numbers, is the greatest number that will exactly divide each of them, thus 12 is the H G F nf 24 and 36. • v^. x . oi 45. To find the H. C. F. of two or more numbers : BULK. Divide the greater number by the less, and the less number by the remainder, if any, and so continue to divide the last dtvisor by the last remainder until there is no remainder. Ihe last divisor will be the H. 0. F. If more than tivo numbers are given, find the H G F of two of them, then of this factor and the third number 'and so on. Find the H. 0. F. of 1386 and 2268. FIRST METHOD. „„„„ SECOND MKTUOD. 1386 ) 2268 1386 882 ) 1386 ( 1 882 604 ) 882 ( 1 504 H. C. F. 378 ) 504 ( 1 378 1886 QUOTIENTS 1 882 1 604 1 378 1 126 8 2268 1386 882 504 378 378 H. C. F. 126 ) 378 ( 8 378 NoTE.-Obserye that the second method is the same as the first the Zttrnr'^' """''* '° '^"^^^^^^^^ *^^ -^""^ Of the SviloJ The column for quotients may be omitted. 24 HIGHEST COMMON FACTOR. subtract 1386 downwards. 1512 H. 0. F. 136 TBIBD METHOD. MtJLxn'LrKKs j 2268 2 2772 subtract UouiuvanJa 8 604 * 604 • FOURTH METHOD. By means of prime factors PRIME FACTORS FOUND. *»tlUrS. PRIME FACTORS ABRANOBD 1386 =2 X 3 X 3 2268 = 2x2x3x3x3x3x% ' Common prime factors multiplied. -* X 3 X 3 X 7 a 126 = H. C. F. _ KtTUI. ^solve the given number* into their vrime fn., product of all the vrimM fa^t^.. ^ factorg ; the J line prime factor* common to them is the If F 2 8 3 1 1386 _693 231 11 FIFTH MKTHOD. 693~ 1134 231 878 77 11 126 2x8x8x7 = 126 H.O.P. BVU. Divide the given number* by the nrim^ fr. * ^. , , EXERCISE 24. ' Find the H. C. P. of 1. 328, 425. 8. 2. 228, 399. 9. 8. 616, 735. 10. 4. 819. 945. 11. 6. 949, 871. 12. 6. 825, 960. 13. 7. <589, 1575. 14. 961, 1178. 5366, 6545. 4166, 24720. 7668, 3784. 3876, 1983. 7966, 7668. 9864. 9628. 15. 16. 17. 18. 19. 20. 46, 67, 63, 99, 72, 84, 306,408, 610 420, 462, 84. 546,462. gao 81. 90. 96. 21. 900,936,2520. LEAST COMMON MULTIPLE. 25 LEAST COMMON MULTIPLE. give a pro- 2268, which h a aamber X 7 X 11 X 7 altiplied. ?r«; the U.O.F. mon to a F. 81. 90. 96. 10. H. 32. 0. 46. A Multiple of a number is one that is exactly divisible by that number, thus 86 is a multiple of 6. 47. A Common Multiple of two or more numbers is a number which is exactly divisible by each of them, thus 18, 86, 72, are common multiples of 2, 8, 6 and 9. 48. The Least Common Multiple of two or more numbers is the least number which is exactly divisible by each of them, thus 18 is the least common multiple of 2, 8, 6, and 9. Find the L. C. M. of 18, 28, 42. FIRST METHOD. By means of prime factors. 18 = 2 X 3 X 8 28 = 2x2x7 L.C. M. -2x2x8x9x7 = 252 42 = 2 X 8 X 7 EULE. Resolve the given numbers into their prime factors ; the product of the different prime factors taking each the greatest number of times it appears in any of the numbers will be the L. C. M. BEOOND METHOD. Find the L. C. M. of 9, 15, 18, 16, 12, 80, 45. ^, ;?, 18, 16. 12, 30, 45 9, 8, 6, ;^, 45 4, ?, 45 2 X 2 X 4 X 45 = 720 L. C. M. or a, 2, 3 I y. 15. 18 , 16^12, .SO. 45 a X 2 X 8 X 4 X 45 = 720 L. 0. M. 26 ^^SI COMMON MULTIPLE. BULB. Write the numbers in a kori~n„f^j ;• tlu'. smaller numbers as arefXst^^^^^^^ ^'"^^^"^'^^ '-^ of any prime factor or prime iZ f ^'''*^''*' ^"^ ^''i^^' h or. ore o/tke ^i^^Z^T^W^L 7e Zf' '''''' '^^ uxd^vided numbers, if an,, in a U.^LZT '"' ^'^ Continue this process until the results nr. ■ other. ^*""« <^^^ prime to each The product of all the divisors and fh. „ ; • line will be the L. C. M. '^"'' "* *^'' ^"»' Find the L. C. M. of EXERCISE 26. 1. 2. 3. 4. 5. 6. 7. & 9. 6, 6, 16. 7, 14, 21, 28. 4. 8, 12, 16. 5, 7, 15, 21. 3. 14, 21, 28. 9. 2, 6, 18, 24. 8, 7, 12, 21, 24. ^« 2, 15, 7, 35, 8. 6, 9, 54. ^ 7, 9, 12, 14, 36. 11. 12. 13. 14. 15. 10. 17. 18. 19. 27, 63. 12. 35, 9, 60, 24, 27, 51, 63, 12, 16, 64, 81, 19. 27, 22, 27, 15. 84'. 68. 72. 14, 24, 63, 86, 64, 20. 9646. 6364. 148ig. 210. 26. 14. 68. loa FM ACTIONS. 27 FRACTIONS. 49. A Fraction is one or more of the equal parts of a unit, or anything regarded as a whole ; thus, one-half, two-thirds, three- fourths, are fractions. 50. The unit of the fraction is the unit which is divided. One of the equal parts is the fractiona unit. 51. Fractions obtained by the division of the unit into tenths, hundredths, thousandths, etc., are called Decimal Fractions. All other fractions are called Common Fractions, 52*. A Common Fraction is expressed by two numbers called the Numerator and the Denominator, the former written over the latter, with a line between them, thus : One-third is written J Three-fourths " £ Three-eighths " | Five-sixths is written f Seven-thirteenths " JL Eleven-twentieths " ji 58. The numerator and the denominator are called the terms of a fraction. ^ 54. The Denominator of a fraction, written below the line, shows the number of equal parts into which the unit is divided and also names the unit : thus in |, 8 is the denominator and shows that the unit is divided into eight equal parts, named eighths. 55. The Numerator of a fraction, written above the line, shows the number of equal parts taken to form the fraction ; thus in f , 7 is the numerator, and shows that seven of the eight equal parts are taken or expressed by the fraction, 56. Since the denominator of a fraction shows how many fractional units in the numerator are equal to one integral unit, it follows n FRACTIONS. ana ,He ^^ of <*.>t;- 1" ■ 1 tZr' " "' *"""'• »r. aENEnAL PBItlclPLES OF FRACTIONS. I. MtiUipli/ing the numerator or divUin„ ih. j '^^n.m.r ..t>,Ue. tUe ..J^^^Z^ZZ II. Dividing the numerator or multivlmnn th. ^ hy nun^er ahUe. .*./™., Jt^Til^j™"""'"'"' ^^i- Multiplying or dividing both numerator «„^ ^ If we divide both numerator fnd^ ^"^^ ™l»e «e J. *he result is J, whiohSa": stetrrr "' ' '" '' int^gVaatw' ''"'"■''" '" ""' """"^ '"-» - •»«■ *i."*-. \^'°^^ Fraction is one whose numerator i. i«.. ^an .ts denominator : hence its value is lesTtCi. a! |! FIliCTIONS. 29 EXERCISE 26. 1. Read the following fractions, and tell what each numerator and each denominator shows : A. A. }f il ^, ^^, ip. jjjgjj, ^0,^^ 2. Express the following in figures* ';^'*^ird; fom ninths; ll^l^^nueths: seyenteen uoenty.thirds . thirty one.hmdred,and.eightks; three Joe-tkousandths • ' twelve hundred ninety-thouaandtha ; three aeventha of nineteen /or tyrji/tht, 8. Write: three and a half ; fourteen and a quarter; sixty-five and twenty-threeforty-eightha : eighteen and eleven eighty-fourtha! REDUCTION. 68. Reduction of Fractions is the changing of their form Without changing their value. fra*c«oi° '^"^"'^ '"^^^^'^ °' "''*^'* ""™^^'^ ^° improper ExAMPUB 1.— In 18 units how many flfthp ? SOWJTION. In 1 unit there are 6 fifths •• 18 unit? '. 18 times 5 fifths Qi 90 fifths (s^) Henoe 18 s ^ ExAOTiB 2.-B«daoe ^^ to an improper fraction. ,g, ' ExPIiANATION. ^ (Example 1) is = 90 fifths J- g= 8 fifths i»# = 98 fifths (itf) iV/uiiip/y «;»« M,feoZe numfter by the denominator nf the frc^<^^^on,to tke product add the numerator, and aet their aum over the denominator. 80 FRACTIONS. EXERCISE 27. Reduce to improper fractions- IV. 27A. V. 6|. 19^. 07- *-l^>t*- a mfnel" ul"e" "" '""'™''" '"'«<»- '» an integer or f"""'-««"'"¥«oa„i.«d„„„ber. OOIiUTION. 5 ) 48 jj Expiration, the division we Obtain 9# for nni-!:/""'^ the division we obtain 9f for quoWet" EXERCISE 28. Beduoe to mixed numbers— II. r. Ha III. «5. To reduce a fraction to higher terms, ExAMPLK.-Reduce i to sixteenths. Solution. a.- ... .^'^^^natiom, IV. - = l2Li - ? ^ 4 12 4 4x4 4'^4 = r6 Since it is required to change} to six ^eenth.. (U) a fraction whose dfnom^ at »8 10, we must multinlv th.^ a • 4 by 4; thenbyAr 57 Hi t ""°'^'' change the value of the fraction '' "°* *° multiply the numerator 3 by;.' " """^ RDIiB. Torefeffi ttfinrtion to higher term, rli„u. „ denominator hy the denominator oTTC tT ^ """'""' Reduce — 1. 2. 3. 4. 6. 6. 7. 8. 9. 10. FRACTIONS. EXERCISE 29. 81 hi, 1. i. hi, 5. h 3 to twelfths. to eighteenths, to eighths, to twenty.fourtha. to seventy-seoonda. to sixteenths, to fifty.fourths. to forty-fifths, to forty-eightha. to thirty-sixths. 66. To reduce a fraction to its lowest terms. SoiiDTrON. -c, 12 .1. 4 a i-XPLANATION. • ^ *» By Art. 57. Ill,, we may divide both numerator and denominator by 4 without , , ^^ a changing the value of the fraction. 4 S- I. A. h A. i ^< 3- A. f, §, 1 i' i- A. if. A 12 16 16 -r 4 or I— 16 3 4 Bni.B. Divide both terms of the fraction successively by all the pnrne factors cornjon to the two, or by the continued product Ih C fT""' ' ^'"^ '^''^ ^''^''' <^ommon factor. NoxB.-A fraction is in its lowest terms when th. numerator ..A denommator have no common factor. numerator and EXERCISE 30. Reduce to lowest terms — I. « H A H II. /A III. H H A*r m IV. ■BTff m V. rsirt iff* mi ToiTBT least common denominator navmg a 32 JPBACTIONS. Llf •!.' *^"' <^«'^°^^"torB" ''°°"''^''*°'^°'*'^e fractions must oommon'J^omi^aton^^ *' *' * *° ^"^^»l«>t fractions having a least Solution. The least common denominator = li. C. M. of 2, 3 ,8 = 24 i = H * = A (Art. 65) ExPtANATIOK. .We&stfindtheL.C.M.onhe given denominators which is 24 Thas n.nst be the least common denominator to which the given fractions can be reduced (Note Art C7-) »«ia«inge*oh fraction to the denommator 24 (Art. 66). w« obtain ♦*. Yf, Tft, as aesults. 7 ET- BOLE. '-; lli''.ii^/ '*' -" ^-*»'- for «. Keduce to their le.,Uom„,ondeaomi„.t„,. 8. 4. 6. 6. 7. A-. i. *, i. «, ». A. 3. i, f of *, A. A- »■ if, 42. 8. 9. 10. 11. 12. *. A. 2*. A. if*. W- A. i. A. iof J, ADDITION. ««. BxAMPLH l._pind the sum of I i j. SOLUTIOV. *' *• A- 13. m., mi im. ^* *• H' A. A. A 7. A- *of f A. «. BwtANATIOlf. In order that fractions may be added they must have like denomilorswl be parts of like units. f « 18 tweniy.fourths. i = 21 twenty-fourths. jSi^iOtwenty^rths. il;tweuty-tourlhiTjj,g^^,^ iaving a least 2i 131 4A FRACTIONS. Example 2. — Find the aam of 2|, 13Z, 4JL. Solution. 1^- Explanation! 18 The Bum of the integers, 2, 13 ». *. h H. A- t. H. H. M. *f • 8- 3*. 4^, 2A. »• 1*. 2§, 3|, 4*, 5f, 6f. 10. 7E.10I. 4^, 7^. 11- 4,V,8A,2A. 12. H, 2J, 1^, 2A, 5tV. 18. 24|. 18i, 4f , 70. 14. 21, 15|,fi^, 4^^, *• *. i' ♦. f. I, I, A. 14. 21, 15|,fi^, 4^.y, 6|. SUBTRACTION. 6». Example l.-Find the difference between ^ and f. Explanation. In order that fractious may be subtracted, they must have like denominators and be. parts of the same unit. A = 14 twenty-fourths (Art. 66.) 1=9 twen tyj-fourths. A - 8 = 6 twenty-fourths = ^ Ana. Example 2.-Find the difference between 83^ and 45|. ' A i Solution. ■ 24ths. "14 9 A Ans. 83A 45 1 riOLUTION. 24th8. 88^r Ana. 14 9 Explanation. The difference between the integers a The difference between the f raotioaa = The result = 38^"a^. A Si FRACTIONS. Solution. I ISths 36* pi J9| I 15 IftAAna. A tiliMPU 3.-rind the difference between 36J and 19». " Explanation. Yon can't take +4 from .*- tj„ from qA n j • "' •°°'^ro^ Unity ^om 36. Keduce it to eighteenths, and then add result to A which makes «. H from f§ leaves j!^. " 19 from 35 leaves 16. Result, IBj^, R0LS I. To subtract fractions.-r*m necessary, reduce th, fi-acon. to their least comrnon denominator g^Z, It numerator of the suitrahend from O^ nuuZlorofTrnt' W, and place ike difference o.er tke co,n,non dl^n^Z'. RtTLE II. >..cessar^, to a common denominator, and if the tmMi • .^. suUraUendi. smaller than that i^ the ^LtnTlZZ one jracttcm from the other, and the smaller Ihl 7 rrom the large" whole number But iTT , . """'*'" s^tral^en, i. U.rg. than that in ^JJ^^CZ llZ the ..koU. j^n^oer. After changing it to the laZdenlmZ tor as tke fraction, add it to the fraction ,« Ta '^^nomma- Then subtract as before. ^ "" '^' ^*'^^^^^- EXERCISE 33. Find the difference between— 1. f and f. 2' { and \. 8. \ and fj. 4. W and f . 5- #* and ^. 6. A and ^. 7. H and «. 8. t/^ and ^. 9. A and ^^. 10. A and VSr. 11. 16f and 7J 12. 8f and If 18. 2J andlxV. 14- 6^ SQdSfl. 16. 8f and 6|. 16. 3A and If 17. 64| and 31^f. 18. 19 and ^. 19. H8| and 76* 20. 21. 38JJ and 23j^. 18f and 6J. MULTIPLICATION. 70» BxAKPLK 1— Multiply f by f . Solution. Explanation 8 2 8x2 £ 1 The nameratora are maltipHed 12-8 '*' » new numerator and the d«. nominators for a new denominator. X 7 at —. ■„ 8 4x8 FRACTIONS. EXAMPM 2.— Multiply i by ij by g by f Solution. 85 '^ ^ f ^ ^ ^ ? ^ 9 ~ 9 ExPi;ANATION. dee Art. 36. HULE. Reduce integers and mixed numbers to improper fractions Multiply the numerators together for a new numerator, and th^ denominators for a new denominator. Reduce the result to its simplest form. NoTB—Cancellation often shortens the operation. EXERCISE 34. Find the product of— 1. J 3.* 5.^ X * X t X X X X X fi- A X il X 7. a X H X I. I i- I A- h 8. § X 9- # X 10. I X 11. 2J X 12. 3^ X 13. 8i X 14. f X 12 15 18 A X 1? X A X I I s 16 18 20 f ♦ of 20. ? X 21. * X 27. -1,\ X I A X 3f X 22. 77 H 4J X ♦ X 1- Ax 91. DIVISION. 71. To divide a fraction by an integer. ExuiPLE 1.— Divide ^ by 3. 21 26 + 8 Solution. 21 -^ 3 25 7_ 26 Example 2.— Divide f by 2. Solution. 8 8 8 4 ■*■ 2 ' 4~x~2 = 8 Example 3.— Divide 34f by 11. Solution. ExPLANAXIOa; Art. 67. S. EXPLANATIOM. Art. 67, 2. 84 -f 11 1?_ 6 g + IJ 8, rem. 1 5_ 83 Explanation. Divide the integer by 11, quotient 8, rem. 1. This rem. prefixed to the fraction makes If. or f, yet to be divided. Divide this improper frac- t'on and combine the rosoiis. lU I 86 fS ACTIONS. 34| ^ 11 104 3 = IT ^ 11 = Divide — 1- H by 4. 6. I by 6. 7. A by 8. 8. i by 7. 9. T^r by 3. lo. Explanation. E«Juce th. ni„d number l„ .„ EXERCISE 35. 2. 8. 4. 5. H by 11. **by ilby 16f by 42^ by 6. 5. 7. 3. 11. 12." 13. 14. 16. Example.— Divide f by f EXPLANATIOS. 67i by 6. 19* by 8. 16* by 7. IItV by 11. 24f by 6. SoLtmoN, 3 fifths ^ 2 thirds - 9 fifteenths. 10 fifteenths Art. 6S = — = 339 10 5 X 2 = 5 X 2 = - Ana. • multiplied by^, (the divisor inverted). RULE. (t.e) 1. 2. 8. 4. 5. 6. • • 8. 9. 10. 11. 12. 18. Divide — * by |. ? bj' ^. iVby A. /? by |. A by |. * by |. t of /j. bv -f'j. 2* X 7i by 3^ 11 by I ; 16 by |. 49 by ^. 73 by ^, 6* by |. EXERCISE 36. A. 5* X 14. 16. 16. 17. 18. 19. 20. 21.* 2J by IJ. 18? by 4ff. m by AVr. 24 1| 73 of ^ 7- 22. /, X A 23. § of 13i», 24. 4^ 26. A of I 26. ISf by *. by If by ^. by 1^ X j of * of 12A. f of A. A. by bv by by A. A. 27. iao'« Kt.- "'" by 4}f . FRACTIONS. 37 GREATEST COMMON MEASURE. •78. A Measure of a fraction is any number that is contained m the fraction an exact integral number of times • thus ^ IS a measure of ^ being contained in it 3 times! Hence, 74. A fraction is a measure of a given fraction when its numerator is a measure of the given numerator, and its denommator is a multiple of the given denominator. 75. A Common Measure of two or more fractions is any number that is contained in each an exact integral number of times ; thus, ^ is a common measure of J and i, being contained in J 8 times, and in ^ 6 times. Hence, 7©. A fraction is a common measure of two or more given fractions when its numerator is a common measure of the given numerators, and its denominator is a common multiple of the given denominators. 77. The Greatest Common Measure of two or more given fractions is the greatest number that is contained in each an exact integral number of times; thus, ^ is the greatest common measure of ^ and ^. Hence, 78. A fraction is the greatest common measure of two .or more given fractions when its numerator is the greatest common measure of the given numerators and Its denominator is the least common multiple of the oriven denominators. Example— Find the greatest common measure of f , fy, and H- Solution. The G. C. M. of 5, 5 and 15 = 5 The L. C. M. of 6, 12 and 1(5 =: 48 Therefore the G. 0. M.of the given fractions is ^j Ans. Proof. * -^ A = 8 A -J- A = 4 H -^ A « 9 The quotients 8, 4 and 9 are prime to each other. 88 ■M FRACTIONS. folXttl": """'^'^ "'" '"-^'ion^ „e derive the P,-n^ +u EXERCISE 37. ^ind the greatest common measure of-. 1. 2. 8. 4. 6. 6. 7. I. 2A. 8. 8, f ^o A n^^^^"^ COMMON MULTIPLE ^'^^^^:^::i^ -. number't^at con- i is a multiple of ^ 8^0! T 2? """^^''"^ *^°^««' ^^us, Hence. '^' ''"'^ * ^^^tarns ^ 3 times. ^^^fZZ:^^ ^'.^ ^-- ^-tionwhen its denominator a rat're%ntX;^r"^^^^^ . «>• A Common Multiple off wo or moreT^'r IS any number that contains ««!k ^'""''^ ^'^°*^o°8 numberoftimes;thu8,na ' t^ *^^^^«* integral .ivl\t:r:rj:r^^^^^^^ ^^ *- or more of the given numerators, ZT^ZZlT ""^^'^^^ measiirAof*},^ f,; 1 """^^^atoris acnm»r'-- ^i ,L,o givcu aenommators. " FRACTIONS. 89 88. The Least Common Multiple of two or more given fractions is the least number that contains each an exact integral number of times ; thus, ^ is the least common multiple of -^ and \. Hence, 84. A fraction is the least common multiple of two or more given fractions when its numerator is the least com- mon multiple of the given numerators and its deuomina- tor the greatest common measure of the given denomina- tors. ExAMPLB. — Find the least common multiple of |, JW, and M. Solution. L. 0. M. of 3, 5 and 15 = 16 G. G. M. of 4, 12 and 16 = 4 Therefore the L. C. M. of the given fractions b W Proof. ¥ - * = 6 ¥ -^ A = 9 ¥ ^ H = 4 The quotients 5, 9 and 4 are prime to each other. Prom these principles and illustrations we derive the following rule : I. Reduce whole and mixed numbers to improper fractions and all fractions to their lowest terms. II. Find the least common multiple of the given numerators for a new numerator, and the greatest common measure of the given denominators for a neio denominator. This fraction will be the least common multiple sought. EXERCISE 38. Find the least common multiple of — 1- «. A. **. A. 2. 8. 4. 5. 6. T. TO' 3*1 1 as 80 57- 4*, 5J. A. A. i^ 40 DECIMALS. i(i DECIMALS. - one LosTTe^l^^^^^^^ \'ZT'. f '^^ ^-•-'• ciphers : '' ^ ^^"o^ved by one or more sr. The Decimal Si-rn /T ! denominators. I'y ite position, the den^m n»i°or „f,'r*J'"""' '''="^™taes. number composed of anTt '° i^° °'''"'' "'"'' » » where the decimal part be^i,!:*"' ' ''^°™'^' « -'■■^w^ ^oUoXtZZl"' °°"'°" "'" -^ "-' -P'-ed by the nftn, •■ .003,' .. ,. ^ ''""•'^I'hs. The nmwalor ahue h „;i„ V"""-'""!"- «*« rf«<,W,wtor oA the fra-lim T " "" "'''"■'■' '" «« beJiUed Willi cipher, "'"'"" '"'''"'■ '/ ""V, is *"»^'rBL™l™he"olb:- 1;::,',^';'^8"» ^ each other TABLE. Naixbs. i ^ O " O (H c q oj O 3 DO .4 3 S OQ OS 2 ,« 2 a 9 CO O B CJ a a 9 DECIMALS. 41 From this it appears th^ t 2222.222 = 2000 + 200 + 20 + 2 + ^ + t»tt + tAtt- 90. The method of representing decimal fractions is merely an extension of the method by which integers are represented, since the local value of each digit increases tenfold as we advance from right to left, and also decreases in the same proportion as we advance from left to right. From the foregoing we derive the following principles : PHINCIPLKS. 91. 1. Decimals are governed by the same law of local value that governs the notation of integers. 2. The different orders of decimal units decreaae from left to right and increase from right to left in a tenfold ratio. 3. The value of any decimal figure depends upon the place it occupies at the right of the decimal point. 4. Each removal of a decimal order one place to the left increases its value tenfold. 5. Each removal of a decimal order one place to the right decreases its value tenfold. 6. Prefixing a cipher to a decimal diminishes its value ten- fold, since it removes every decimal figure one place to the right. 7. Annexing a cipher to a decimal does not alter its value, since it does not change the place of any figure in the decimal. EXERCISE 39. Express in decimal form and read — L II. III. IV. iV im T^ A\fe A Tzfinr ttjW iWo l i Ml T*f(r T^V Vt^ rU ^ m T^i'^ Express in the form of a fraction and read — VI. VII. VIII. IX. X. •9 -27 8.7 .0005 .0304 •06 .006 4.05 .81600 .00001 •28 .450 .005 .0404 .16000 V. TTTou Vff »1 8 ? 1060 Ill ! 42 DECIMALS, m Express &b decimals — XI. Five-tenthg, . ^ XTT rru- . *'®''°" ten-thoxuandtlu,. ' All. Thirty, and «ere«.<,'/( by 1.20;j. 9- 03 X 05 X .016 X .64. 10. .304 X .2 X .03 X .26. ^At-re ar. t^mma^ places in both factors: '^ DECIMALS. 45 CONTRACTIONS IN MULTIPLICATION. 161. Multiply 62.87416 by 2.34169 so as to retain only 4 places of decimals. Obdinabt Method. 62 . 37416 2 ■ 34169 56 136744 374 24496 623 7416 24949 664 187122 48 1247483 2 146.0609 467304 Contracted Methob. 62.37410 96143.2 1247483 = 62374 X 2 + 1 187122 = 62374 X 3 24950 = 6237 X 4 + 2 624 = 623 X 1 + 1 374 62 X 6 + 2 56 6x9 + 2 146.0609 103. It frequently happens in multiplication that a greater number of decimal figures is obtained in the pro- duct than is necessary for practical accuracy. This may be avoided by contracting each partial product to the required number of decimal places. 103. From this principle and illustrations similar to the foregoing example we derive the following : RULE. Write the multiplier with tlj' order of the figures reversed, and with the units place under that figure of the multiplicand which is the lowest decimal to he retained in the product. Find the product of each figure of the midtipUer by the figures above and to the left of it in the mtdtiplicand, increasing each partial product by as many units as ivould have been carried from the rejected part of the multiplicand, and one more when the highest figure in the rejected part of any product is 5 or greater than 6 ; and write these partial pro- ducts with the lowest figure of each in the same column. Add the partial products, and from the right hand point off the required number of decimal figures. Note 1.— In obtaininf^ the number to be carried it is generally neoesaary to multiply (mentally) only one figure at the right of the figure above the 46 DECIMALS, multiplying figare; but when the figures are Ur,r« t>,. i.- ,- should oomn,enoe at least two places tfthe rTht ' -'^*'P'-'^*-n las't pl'r '' ^'^^'^ ' "^'"^*^ *° ^'^ ^"- °* °- - two nnits in the ciphers. Proauoi, supply the deficiency by annexing EXERCISE 44. 4.3678 retaining 2 decimal places. 467.32 .08245 .73168 .12739 .02736 .693847 36.275 41..3076 17.0036 .43261 .003647 6. 700.375 7. .374825 X X X X X X X 3 4 3 4 3 6 DIVISION. PRINCIPLE. 104. Multiplying both divisor and dividend by the name number aoes not alter the quotient. 105. Multiplying a decimal expression by 10, moves the decimal point one place to the right; by 100. two places to be right; by 1000, three places to the righi, et^ Thr fore, moving the decimal point in divisor and dividend' the same number of places to the right, multiplies each of them toy the same number. «"om Example 1.— Divide 16.678 by 5.4. ' ■ ^ Explanation. Multiply the divisor and dividend by 10 and we obtain 64 as divisor and 166.78. Now 54 will divide into 165, 3 times, and therefore 8 is the integral part of the quotient. 64 ) 165.78 ( 3.07 1«2 878 878 Example 2.— Divide .736644 by 234 6 234.6 ) .736644 { 234G ) 7.36644 ( .00314 7038 8284 2346 !>384 9384 Here in dividing we ase aa the first partial dividend 7.366 or 7366 thousandths, and hence our first quotient figure 3 thousandths which expressed as b decimal is .003. DECIMALS. 47 BULB. 106. Move the decimal point to the right of the divisor, and the same number of places to the right in the dividend. Divide as in simple division, placing the decimal point in the quotient as soon as the tenths figure is used or brought down. NoTB.— If the dividend does not contain as many decimal places as the divisor, annex eiphers to the right of the decimal before removing the points. EXERCISE 45. 1. 48.591 - •r .96. 6. .0774 ^ 480. 9. 10.66 ^ 1.3 2. 2.56 - •r .0032. 6. 21.3 ^ 37.5. 10. 15.77 -s- .19 3. 31 - .025. 7. 202 4 .01. 11. 134.25 .f 7.5 4. .0012 - - 1.6. 8. 40 8 + .018. 12. .73326 .^33 13. Divide 1.21 > 11. 1.1, .11, .011, .0011, .00011. 14. Di vide .03'' i> h)0, 180, 18, .18, .018. CONTRACTED DIVISION. I07. Divide 763.14163 by 21.3642, correct to four places o.' decimals. Obdinaky Method. Oontbaothd Mbthoo. 318642 ) 76314163 ( 85.7306 640926 122215 106821 318642 ) 7631416.3 ( 35.7206 640926 122215 106821 15394 14954 439 427 12 10 1 6 68 94 690 2J4 40600 6 8210 72390 15394 14956 489 427 13 n 1 Buza. 108. Compare the highest or left hand figure of the divieor with the unite of like order in the dividend, and determine how many figures will be required in the quotient. For the first contracted divisor take as many significant figures from the left of the given divisor, as there are pUicee 48 ^JiiC'IJlALS ''"i''''''d in the quotient, and nf. u . Divide— -• 27.3782 2. 487.24 8- ?^47326 *' .8487564 by S- 478.326 by 6. 8972.436 7. 1 EXFRCISE 46. 4.3267 8. by by 1.003076 by 76.43 .075637 1.43 J by 756.3452 by 1.007633 •»53728by 44.73664 °°«ect to 3 decimal places. 2 5 •• „ " 3 .. 3 '• „ 4 .. 6 .. 3 .. a „u,nerator, and for a ienoninaLZ , ., there are fignr.s i,. ,/„. p.„, „ /„■,,, rf„„ „„, ,f^^,„^ '* EXERCISE 47. Express as circulating decimiils— 2- M, A, H. H. iS. /„ .J, I^. ""^• Express as fractions in theii- lowest terms— 3- -7, .57, .306, .46, .369. .162, .2635 4. 27. .47. .31, .235, .246, .34734. .71271. ». .030. .00247, .0356, .261(i, .0357. .71*03 WEIQHTS AND MEASUIiES. 51 WEIGHTS AND MEASURES. CANADIAN CURRENCY. 113. Money is the measure of value. 114. Currency is the money employed in trade. 115. Coins or Specie are species of metal of known purity and weight, stamped at the Mint, and authorized by the Government to be used as money at fixed value. 116. Bullion is uncoined gold or silver, and includes bars, goid-dust, etc. 117. Paper Money is a substitute for metallic currency It consists of Dominion Notes issued by the Government and iJank Notes issued by Chartered Banks. 118. Canada money is the legal currency of the Do- minion of Canada. It is founded on the Decimal Notation and Its denominations are, Dollars, Cents and Mills. 11». The Silver coins are the fifty-cent piece, the twentv- five-cent piece, the twenty-cent piece, the ten-cent piece and the five-cent piece. The Copper coin is the cent. There are no Canadian gold coins ; those of England and the United States are a legal tender. TABLE. 130. 10 Mills = 1 Cent 100 Cents s 1 Dollar ct. or fi. dot. or i. 62 WEIGHTS AND MEASURES. ct. d. dot. or $ E. UNITED STATES MONEY. oitl^}:nefk^::irol' ^7^^ -— 3^ «' t^. united States, and is Dimes. Cents and Mills "^^ '^-^^-'^tions are Eagles. Dollars. eartte'd:iirp,rar '''''■ ^^'^ ^^«-«le. ^oarter- di^*' ""'^ '"^" "^''^^ -^"^^ *h« ^°"-. b-^lf-dollar. quarter-dollar, and The Nickel coins are the one-cent and three-cent pieces. The Bronze coin is the one-cent piece. -»•»- TABLE. 1-24. 10 Mills . -in* in n i • =1 Cent 10 Cents . _ 1 T^- in T\- ' ■'■ Dime Dimes or 100 Cents = ; Dollar 10 Dollars . . , ^ jjagle ENGLISH MONEy. bS ^"*""' "''^'""« ""-y" 'he currency ,f Great J' Koia sovereign, is equal m value to $4.8665: 4 Farthings (gr. or/ar.) = i Pen„y . 12 Pence _ , auu- "• 20 Shillings . ■ : J p*''"'"^ . 21 Shillings . * ■" , ^^""'Jo'^ Sovereign £. t*%si ' '^ ^ Guinea. I-SS. The gold coins are the sovereign and th« », u 1 29. The silver rnin* half-sovereign. (2*. 6d.). the shilling, and tie LXXr^' '''•^- *'^ '-^'-o- carats tfttrn^VrrX^^^^^^ ^^Z'' ^"^* ^^*^^" ^« ^^ U pure silver and A alloy. "^ "°^- ^^** °^ *1^« «lver coins is ^ TROY WEIGHT. The measuring unit is the pound. WEIGHTS AND MEASURES. 68 i-eagle, qnarter- .a..i«aa. TABM. 188. 24 Grains (gr.) = 1 Pennyweight diet. 20 Pennyweights = 1 Ounce - oz. 12 Ounces . . = l Pound - lb. 134. The value of diamonds and other jewels is esti- mated by carats. A carat is the weight of four grains. APOTHECARIES WEIGHF. 135. Apothecaries Weight is used by druggists and physicians in compounding medicines, but drugs and medi- cmes are bought and sold by avoirdupois weight. The measuring unit is the pound. The pound, ounce, and grain are the same as in troy weight. "^ TABLE. 20 Grains = 1 Scruple 3 !*oruple8 = 1 Dram 8 Drams = 1 Ounce 12 Ounces = 1 Pound 136. sc. or 3 dr. or 3 oz. or 5 lb. APOTHECARIES' FLUID MEASURE. 137. Apothecaries' Fluid Measure is used in mixing liquid medicines. * 138. TABLE. 60 Minims, or Drops {m.) = 1 Fluid Drachm /3 8 Fluid Drachms . . = l Fluid Ounce - f f 20 Fluid Ounces . . = l Pint . . q ® ^^°*' • • . . = 1 Gallon . . Cong. AVOIRDUPOIS WEIGHT. 139. Avoirdupois Weight is used for all the ordinary purposes of weighing. ^ The measuring unit is the pound. 140. TABLE. 16 Ounces (oz.) . . = l Pound . 2000 p'^'i' • • • = 1 Hundredweight 2000 Pounds, or 20 cwt. = 1 Ton lb. cat. T. I ^ 54 141. 143. 144. WEIGHTS AND MEASURES. LOXO TON TAflLK. 16 Ounces (oz.) = l Pound . . n,, 112 Pounds . =1 1 Hun:lrodweight cwt. 2240 Pounds . = 1 Ton ... y. SPECIAL AVOIRDUPOIS WEIGHTS. 14S* 100 Ihs. 100 lbs. 196 lbs. 200 lbs. Nails Dry Fish Flour . = 1 Keg. = 1 Quin'.al. = 1 Harrel. Beef or Pork = 1 Bairel. COMPARATIVE TABLE OF WEIOHTS. TROY. AVOIRDUPOia. APOTHECARIES. 1 Pound = 5760 Grains = 7000 Grains — 5760 Grains. 1 Ounce = 480 = 437i " = 480 175 Pounds = 144 Pounds = 175 Pounds GRAIN MEASURE. 14 lbs. 34 lbs. 36 lbs. 40 lbs. 44 lbs. 48 lbs. 48 lbs. 48 lbs. 50 lbs. 56 lbs. 56 lbs. 60 lbs. 60 lbs. 60 lbs. 60 los. 60 lbs. 60 lbs, 60 lbs. 60 lbs. 60 Z6s. 70 lbs. TABLE. Blue Grass Seed Oats Malt Castor Beans Hemp Seed - Barley - Buckwheat Timothy Seed Flax Seed Indian Corn Rye Wheat - Beans Red Clover Seed Potatoes Turnips 'Jarrots Parsnips Beets Onions - Bituminous Coal = 1 Bushel. •t It 111 •4 •( H << It »• ire usually gauged, and have their capacities in gallons marked on them. 154. A Measure is a standard unit established by law or custom, by which extent, dimension, capacity, amount, or value is estimated. 06 WEIGHTS AND MEASUHES. MEASURES OF EXTENSION. 155. Measures ot Ext. ..sion are those used to ascertain how long a hue is, or in calculating the sizo ^.xtent) of a surface or solid. A line has only one dimension— length. LINEAR OR LINE MEASURE. In measuring length, linear or line measure is used. TABLB. 156. 12 Inches {in.) . = i Foot - ft. 8 Feet . . = l Yard 6 J Yards, or KJJ/t. = i Rod 820 Rods . . = 1 Milo yd. rd. mi. 1 Mile KQUIVALENTS. 820 Rods = 1760 Yards = 5280 Feet = 633C0 Inches. SURVEYORS' MEASURE ^^7: Pf"*'"'' ^^^^°' ""^^^ ^y ^^"•^ surveyors, is 4 rods, or 66 feet long, and consists of 100 links, each 7.92 inches long. TABLE 15^. 7.92 Inches . . = i Link 25 Links . . = 1 Rod 4 Rods, or 66 Feet = 1 Chain 80 Chains . . = i Mile SQUARE MEASURE. Ik. rd. eh. mi. 159. Square Measure is used in measuring surfaces • as of laud, boards, painting, plastering, etc. 160. Area or Surface has length and breadth only, and 18 the space or surface inclu.led within any given lines. 161. A square inch, square foot or square yard is a square, each side of which is respectively, I'inch, 1 foot, or 1 yard in length. WEIGHTS AND MEASUHKS. 57 TABLE. 16Sl« 144 Square Inohe3 (sq. in.) 9 Square Feet 80J Square Yards . . 160 Square Rods . 640 Acres . = 1 Square Foot = 1 SqiiAre Yard ■ 1 Square Rod ss 1 Acre - 1 Square Mile tq.ft. «?• yd. sq. rd. A. tq. mi. Artificers estimate their work as follows -. By the square foot : glazing and ston -cuttij^:. By the square yard : painting, plaster n,r pavit^:, ceiling and paper-hanging. By the square of 100 square feet : floor;, ;, partitioning, roofing, slating, and tiling. Bricklaying is estimated by the thousand bricks, by the square yard, and by the square of 100 square feet. Notes l.-In estimating the painting of moldinf-s. cornices, etc., the ^measuring-hne is carried into all the moldings and cornices. hf'innrf ^*'"^^""^"^''^'°^^y''**'"'^**^°^°^^« y^'^ «r the square Jf 100 feet, the work is understood to be 12 inches or IJ bricks thick. 8. A thousand shingles are estimated to cover 1 square, being laid unches to the weather. th SURVEYORS' SQUARE MEASURE. 18. This measure is used by surveyors in computinff irea of land. ® TADLB. t» 626 Square Links = 1 Pole ... p 16 Poles . . = 1 Square Chain - sq. ch. 10 Square Chains = 1 Acre - . . ^ 640 Acres . . = l Square ittile . sq. mi. V «53C!ubi CUBIC MEASURE. volifm^"^'' ^^'^''''' '' '"'"'^ '"^ measuring solids or 166* \soUd is that whi.-h haq •'»!"-*«- • <■• thicknesi — " «»« -ns.u, uicaatn, ana 68 WEIGHTS AND MEASUBES. 107. A Cube is a regular solid bounded by six equal squares called faces. Hence length, breadth, and thick- ness are equal to each other. Cubic Foot Cubic Yard 1 Ton - cu.ft. cu.yd. T. TABIiB. 168. 1728 Cubic Inrhes (eu. in.) . , = 1 27 Cubic Feet - i 40 Cubic Feet of Round Timber, or) _ 50 Cubic Feet of Hewn " J~ 16 Cubic Feet =1 Cord Foot - cd.ft. 8 Cord Feet, or 128 Cubic Feet = 1 Cord of Wood Cd. 24| Cubic Feet ^ 1 Perch of Stone )„. or Masonry / ^''"■^ Notes.— 1. A cubic yard of eiirth is called a load. 2. Railroad and transportation companies estimate light freight by the ■ apace it occupies in cubic feet, and heavy f rei;^h^ by weight. 3. A pile of wood 8 feet long, 4 feet wide, and 4 feet high, contains 1 / cord ; and a cord foot is 1 foot in length of such a pile. / 4. A perch of stone or of masonry is 16i feet long, IJ feet wide, and / foot high. / 5. Joiners, bricklayers, and masons, make an allowance for windov^ doors, etc., of one half the openings or vacant spaces. Bricklayers a»l masons, in estimating their work by cubic measure, make no allowajf-e for the corners of the walls of houses, cellars, etc., but estimate their -^k by the girt, that is, the entire length of the wall on the outside. i MEASURE OF TIME. 169. Time is the measure of duration, unit is the day. , ITO. Time is naturally divided into days and years. T^ormer are measured by the revolution of the earth on its axis ; the latl by its revolution around the sun. The meaafing TABLE!. (sec 171. 60 Seconds 60 Minutes 24 Hours 7 Days 365 Days 366 Days 12 Calendar Months 100 Years ) • = 1 Minute .hin. . = 1 Hour - . / hr. , = 1 Day - - da. = 1 Veek wk. =« 1 Common Yt c. yr. = 1 Leap Year • I. yr. onths = . Jivil Yeaif- yr. . = 1 Century a. WEIGHTS AND MEASURES. 59 172. The Civil Year includes both common and leap years, and is divided into 12 Calendar Months, viz. : January (Jan.) ... 31 Days. February (Feby) ... 28 "' In Leap Year 29 " March (Slar.) . . . 31 » April (Apr.) . , . . 30 '*' May (May) . . . , ai " June [Jum) .... .SO " July (July) . . August (Aup.) September (Sept.) October {Oct.) November (A'ov.) December (Dec.) 31 D 31 30 31 30 31 ITS* The numbers of days in each month may be ■ easily remembered from the following lines : " Thirty days hath September, April, June and November ; February, twenty-eight alone, All the rest have thirty-one, But in leap year, then is the time When February has twenty-niue." i LEAP YEAR. 1^4. The period of time required by the sun to pass from one vernal equirkx to another, called the vernal or tropical year, is exactly 365 da. bhr. «mt«. 49.7 sec. IT*. If 365 days be reckoned as one year, the time lost in the calen- dar wilBje, In 1 Year . - 5 /tr. 48 mm. 49.7 sec. In 4 " - . 2-Ahr. 15 mm. 18.8 sec. The tiiA thus lost in 4 years will lack only 44 min. 41.2 sec. of 1 entire day. Henk - If every Airth year be reckoned as leap year, the time gained in the calendar wil\be, 4 Years ... Umin. 41.2sec. 100 " (= 25 X 4) 18 /jr. 37 mm. 10 sec. The time thA gained in 100 years will lack only 5 hr. 22 min. 50 sec. of 1 day. Hence, ^ If every four^year be reckoned as leap year, the centennial years excepted, the timUost in the calendar will be. In lA Years - - 5 Ar. 22 mm. 50 ««. In 400^ .. . . 21ftr. 31mm. 20 see. The time thus loatv, 400 years lacks only 2 hr. 28 min. 40 sec. of 1 day Hence, ^ f' j 60 WEIGHTS AND MEASURES. It every fourth year be reckoned aa lean vear a of •«««, a * • , . years excepted, the time gained in theZeS J,l be!^ ' "°*^°""' In 400 Years . . 2 hr. 29 min. iO sec. In 4000 .. . . 2ihr.46min.i0,eo. Jl^\^^' /'^y'"'^ '"^' ^""^ ^^"P ^'^' ^"i therefore 4000 years """* '' "^''" ' '^^ ^°^ ' ^^^^' of RULE. I. Bv^rpyear that is exactly dMnhU by i U a Imp year I ^'ece«Un„,al years excepted , ths other years are LLonI II. Bv^ centennial year that i, exactly iioMUe by 4oi i m ■ I ■ ^ LONGITUDE AND TIME. LONGITUDE AND TIME. STANDARD TIME. Ca».da and the n„,ted Slates adopted what is luown as the Standard T,me System." This system divides Canada and the United States into four sections or tim - belts, each covering 16 degrees of longitude, Ti" of which are east and TJ" are west of the governing or standard meridian and the time throughont each hel? :, the same of tha?ber°™°" " '""' ""' "' '"' «"'""'"« ""«'*"» ,„«u' 8"veming meridians are the 76th. the 90th, the 05th, and the 120th, west of the Greenwich Observatory London England, and as these meridians are jnst l^ |.art. there .s a difference in time of exactly one hour between any one of them and the one next on Ihe east, ^i beltT ° '7""' "■" ""■"""rd meridian next on the east being one hour faster, and the one next on the west one hour slower. Hence, the 60- of longitude is fou hours, the 75- five hours, the 90' six hours, the lOS' seven hours, and the 120" eight hours slower than GreenS Z;,r7jZ''^:""'' ""'''''<" «f '""« betw eHhe Atlantic and the PaciBc Oceans, viz. : Intercolonial, Eastern Central, Mountain, and Pacific. ' n»J.'!tif'r/ """ °'''°''' """^ "^ '*'™'<"' in'" 360 equal t".rts called degrees, and since the time in which the earth makes one revolution on ite axis may be divided intrt LONGITUDE AND TIME. aa Do equal parts called hours, it follows that the earth on revolv- ing on Its axis passes through ^ of 860° or 15^ of longitude m one hour ; through V of longitude in VW of an hour, or 4 minutes, and through 1' of longitude i? A of 4 minutes or 4 seconds. 185. TABLE. 360° of Longitude = 24 Houra or 1 Day of time 1^° " = I Hour of time - . *^ •• =r 4 Minutes of time * *• = 4 Seconds of time da. - hr. - min. sec. Solution. 7° 18' 4_ 20 min. 12 sec. 186. To find the difference in time between two known °'" ""^"^^^"^ "^^^^ *^^ difference of longitude is ExAirPLE — If the difference in longitude of two places be 7° 18' what must be their difference in time ? Explanation. Since each minute of distance equals 4 aeconds of time, 18 minutes of distance will equal 72 seconds, or 1 minute 12 seconds of time. Since each degree of distance equal 4 minutes of time, 7 degrees will equal 28 mmutes, plus 1 minute, gives 29 minutes. BtHiE. Multiply the distance between the two places expressed in degrees and minutes by 4, and the result is the dijference in time expressed in minutes and seconds. Notes.-! If one place be in east and the other in west longitude the difference of longitude is found by adding their longitud... Id i he sum be greater than 180 degrees, it must be subtracted from 3W I9^n' ,^'"°'f ' '''° ^PP^^'-^ *° ™^^« from east to west, when it is exactly belOre 12 at all places west Hence, if the difference of time between two places be Subtracted from the time at the easterirplace Z result will be the time at the westerly place; and if the dkl^t Easterly ^ll' "'""''' ""' ''' """'*"'" "^ *'>«*™-t«- 64 LONGITUDE AND TIME. V k- n 187. To find the difference of longitude between two places or meridians, when the difference of time is known. EXAMBLS— If the difference of time between two places b^ 28 minutes, 20 seconds, find the difference in longitude. ExPLANAnOH. Since 4 minutes of timo aqnal 1 degree uf longitude, 9S minutes ot time equal T of longi-tuJe. Since 4 seou. -Is of time equal 1 ir inute of longitude, 20 seooruia U time oyaal 6' of longitude. BULE. Dhide the difference in time between the places expressed m minutes and seconds by 4 and the quotient is the difference tn bngitude expressed in degrees and minutes. Solution. 4 ) 28 viin. 20 a ge. 7* 5' TABLE OF L0NG8TUDES. • Toronto, 79° 21' 15" W. Kingston, . 76" 28' 26" W. Ottawa, 7-'° 40' 35" W. Winnipeg, . 97° oC 42" W. Ohioago, . 87° 37 45" W. Calcutta, . 88° 19' 2" E. Montreal, . 76° 28' 16" W. London (Can.) 81' 16' 6" W. New York, . 74° 0' 3" W. Paris, . . 2° 20' 22" E. Belleville, . 77° 26' 2* W. Quebec, . . 71' 31' „a" -^^ Berlin, . . is" 23' 46" E. Philadelphia, 76° 10' W. Victoria, . 123° 12' 15" W. Hamilton, . 79'' 52' 30" W.- London (Eng.) 0° 5' 38" W. Regina, . . 105° 2' 26" VV. Brantford, , 80° 28' 38" W. Halifax, . 63° 36' 42" W. EXERCISE 48. Find the difference in longitude between— and London (Eng.) 1. 2. 8. 4. 6. 6. Toronto Quebec and Calcutta. Ottawa and Victoria. Hamilton and Berlin. Brantford and Winnipeg. Einsston and Paris. LOHQITVDE AND TIME. Find the difference in solar time between— &5 7. 8. Toronto Kingston 9. Ottawa 10. Montreal and Greenwich, and Winnipeg, and Victoria. and Regina. 11. London (Can.) and London (Eng.) 12. Philadelphia and Calcutta. Find the difference in standard time between- 18. Quebec and Ottawa. 14. Montreal and Victoria. 15. Toronto and Winnipeg. 16. Kingston and Eejiina. 17. Montreal and Winnipeg. 18. Halifax and Victoria. Find the difference between the standard time and th. soJar time m the following cities : 19. Toronto, 20. Montreal, 21. Winnipeg, Ottawa. Victoria. Halifax. 66 LONGITUDE AND TIMJi, i % i REDUCTION. 189. Reduction is the process of changing the denom- nation of a quantity without changing its value. It is of two kinds, Descending and Ascending. 1»0. Reduction Descending is changing a number of one^denommation to another denomination of less unit 191. Reduction Ascending is changing a number of one denommation to another denomination of greater unit ~Aiue« 1»9. To reduce Higher denominations to Lower. ExAMPxai._Reduoe 26 bbl. 8 gal. 8 qt. to quarts. Solution. 2666?. a gal. 8qt.. 4 8311 qu. Ana. Explanation. Smoe 81i gal. make 1 bbl., there are . 81i times as many gallons as barrels, ana 819 + 8 = 827 gallons. Like' wise, there are 4 times as many quarts as gallons, and (827 x 4) + 3 a 3311 quarts. BULB. Multiply the highest denomination by the number requi ed of the next lower to make a unit of the higher, and to the product add the lower denomination. Proceed in this manner with the successive denominations ttll the one required is reached. ' LONGITUDE AND TIME. EXERCISE 49. f 67 1. ^lldys. IBhrs. 27mm., how many second, ? 2. :Redr,oel2mi.8r,LHyd.2/t. to inches. 8. Bednoe2i3lb. 3 oz. 6 dwt. to grains. 4. In 83 c. yd«. how many cubic inches ? 6. •^ISS 6«. 8rf., how many farthings? 6. How many pence are there in ^164 8.. 0^ f 7. In 481 sovereigns how many pence? 8. In4wi. 120rd. 2ud ^ ft fl v , i inches? ^ ^"•' '^"^^ '"'^"y '°d«? y^'^dB? feet ? 9. Bednoe 16 T. 8 cwt. 86 Zi. to pounds. 10. Reduce 184. 22 sa rd qij.^ „j 4. ,, _ '»'=»?. ra. i^sq.yd. to square feet. H. How many grains in 16 lb. Avoirdupois ? 12. 2 2 -•- in Sir,,., in * mi., how many rods ? yards ? feet ? inches ? 13. In 47 gumeas how many pounds and shillings ? 15 ? '/ 't' ''''''' '°" "^°^ '^^^'°«- Apothecaries? 10. ijind the cost of 2 hi !?;.,.», i a t3.874 a ream "' ' ""' ' ^^ '^ ^^««*« °^ P^per, at 1»3. To reduce Lower denominations to Higher. ExA»u.Mi.-Reduce 167540 minutes to weeks. Explanation. K ^J^f"^ *''' ^^^° °"™''^^ °* ™i°ute3 by 60, because there are ^ as many hoars as mmutes, we obtain 2625 hours pins a remainder of 40 minutes. 60 ) UmoZn J^^ "':? ^'"'^^ *^« 2626 honrs by 24, * aa. + J fir. 109 days plus a remainder of 9 hours Lastly, we divide the 109 days by 7 because there are f as many weeh as day^, and we find that 109 days = 15 wc€! ^ plus a remainder ot « days The -- - .wiotient and the several remainders arranged in the order of the succeeding denominations form the answer. 15 wk. + 4 da. lbwk.4da.9hr.^min. Ans 68 LONOITUDE ANlj TljjJU. I ! EXERCISE 50. Beduce — 1. 1913551 ounces 2. 8. 4. 5. 6. 7. 8. 9. 97!)20 43709 27150 3270 to tons, grains to Iba. inclies to miles, pounds to long tons. P'°*« *o gallons, to days, to cubic yard! io £ '60 cords, to reams, to half-crowns, to lbs. to dollara, to miles, to bushela, to miles, to S. lbs. Avoirdupois to lbs. Troy, oz. Troy to oz. Avoirdupois. 184760 seconds 278t>48 cubic inches 32459 farthings 4789(50 cubic feet 10. 283546 sheets of pape 11. 2468 pence 12. 23750 grains, Troy, 13. 15G30 mills 14. 1800356 links 16. 4562 pints 16. 20436 rods 17. 1020300 " 18. 70 19. 350 20. 21 F-../T ^™'"^'^P°*^- to lbs. Avoirdupois. 2. Fmd the pnce of 462 tush. 23 lbs. of wheat at 95c. a bushel 23. How many bushels are there in 5160/6.. of timet: .eed?" 24. What is the freight on 528 bushels of corn at 32c. a c^t ? 25. What is the freight on 16 T. 17 cwt. 20 lb of coal at ftl an . of 2240 lbs. 7 ^^ ** *^-20 per ton Find the amount of the following bill of grain- 1360 lbs. of oats @ 45c. a bushel. 1216 lbs. of barley (S). 68o. •• 51Q0 lbs. of beans (g $i.oo 21.'i0 lbs. of rye @ 56c. 2468 lbs. of v.-iieat @ gso. 26, It £>ENUMINA2'E NUMUKHS. m DENOMINATE NUMBERS. numbers have an irregular sonl. of nL t an 1 7'""*' while simple numbe. have a uniforn, loeilncai:"'""' ADDITION. Findth. ,r^oi-^lK 1 oz. IQdwt, 12 ,r • 17// - Solution. 3 17 12 oz. 7 5 li (hot. 10 18 !> 84 i6. Ow. 18(Z„,^ 12 4 16 7 f/r. Explanation. Write the numbers of the same unit vue,n the same column. Beginning tl^elowestdeuomination.addasii! «>nple numbers, and reduce to higher ^i-nom.nations according to the scale ■;l I Add— (1) ^ush. pk. qt. pt. 91 3 7 1 14 3 17 2 68 8 9 1 EXERCISE 51 5 3 1 <5 1 I I (2) £ X. 145 160 17 175 14 160 ID 1199 6 d. 9i 8 8| 10 (8) hhd. ffal- qt. pt 79 62 3 1 3 59 2 (ii 13 2 i 169 4 1 1 66 27 i 70 * I I DENOMINATE NUMBEE8. Add— (4) (») ■ (f) 'lal. qt. pt. 49 2 1 71 3 6 1 1 16 3 1 68 3 1 gi. 8 2 mi. A. sq.p. 60 75 30 791 11 ir, sq.yd 15 11 T. 56 14 tet. 16 11 lb. 17 5 1 87 345 31 16 63 19 fli 8 2 76 473 29 15 29 18 30 20 919 89 6 1 20 4 7. Add 236Jft. ioz. I5dm., 83lb. lUz. 21gr., 46Z6, Iddm., lOSlb. 8. Add jr. Ucwt. 25lb., UT. 9cwt. 16lb. 8oz., 36eu>t. 17». UT 12 ewt., and 6 cwt. 10 lb. 14 oz. 9. Find the sum of 12 wk. 3 da. 5 hr. 20min. i2seo.. 4da.l2hr BOmin Sir*. Ida. 10 ^r. 40mm., and 16 *r. 36mt„. 30«;. ' 10. Addeoc. 5ci./r. Bed. 6cdft. 9cu.ft., Ud.ft. Ucu.ft.,^i6cd. 11. Off of one field of wheat were raised 37 bush Ivk <} «/ • «# - =-- j field 41.... ,,.. sq.; of a third. 36 'L JJ .' ';. T fourth, 43 6««A.3pA.lgt. How much was the whole? ''■ ^ iTIT iT^r'^.r '°'T' °' ' ''"'• °' ^"^" ' *''« fl"* weighed llT .1 ,o' *^«T°'*'12«"'^ 15^6.; the third, 9 cwt. 16 ft ; the fourth 12 c,.t; the fifth. 11 c«,.. 24». ; thesixth, 9 ,,.«. 24»! the seventh. 13 cwt. TTow much did the seven hogsheads oontai^^ 18. A person has 5 pieces of ground; the first contains 16^. 8rd • the second. 17^ Uq.p. 45sq.ft.; thethird. 11 ^. Usq.p. S's'q n the fourth 2^. 120.,,.A: and the-flfth. 41 ^. Isq.p. What is theamountof the whole? wnaL is 14. A person owes several sums of money ; to one 17s. 6i. ; to another £3 5s. Sd.; to another. £25 11,. loj^. ; to another. £ 2 8^ o another, l^s^ 3|rf. ; to another. £126 4.; to another i^, it lOid. ; to another. £50 4,. 4ii. What is the whole a nouat ? 15 16. 9/^ the second day; 31 mi. 15 rd. lift., the third day; 26 mf 12/^. the fourth day; and 33 mi. Urd. lift., the fif h dr^' How far does he go during the five days ? ^' 10Z6 60. 20^r.; on another. 6 oz. 3 dwt. 1«,..; on another V, I V^ ^''- ' ""^ ^''°*^"'^' ^^ '*• * «• 15 du>f . 16 or. Hoi much does he receive in all ? DENOMINATE NUMBERS. 7) SUBTRACTION. EXAMPLB.— Subtract 12 tt Qn, 11 ; « ir Explanation. Write the numbers as for simple rabtraotion; take each subtrahend term from its corresponding minuend term. In case any subtrahend term be greater than the minuend term borrow 1 as in simple subtraction.' and reduce it to the denomination required, eto. lb. 27 12 Ulh. 8o». SOLtTTION. OZ. dwt. 5 16 9 n 12 21 pr. (1) £ ». d. 186 4 OJ 98 11 2| (4) ^- sq.p. sq.yd. 75 14 11 78 10 16 EXERCISE 52. (2) lb. OZ. dwt. ffr. 114 3 16 12 91 4 12 19 (^») lb. 5 3 3 ffr fi8 1 7 2 12 15 7 2 15 cwt. 58 27 (8) lb. OB. 16 2 20 1 dr. 6 6 rrf. 1(1 14 (C) yd. ft. in. 5 1 11 5 2 9 ao« he .till owe" • '°'"'" ^^ ■«•■ "■■ ''»"»«1. MX n y . «■»"". vvnat wastheremamder? iU. ttow long 18 It from June 2lBt isflfi t«r» ,. , "' ^^"°' «> December 14th, 1888? 11. ■'■"elatitndoof Hamilton is 4.1* 19' >ft» «*/-> , 72 DENOMINATE NUMBEUS. MULTIPLICATION. Solution. „ ,, ■ll'Xl'I/ANAXinN, '"• OZ. dwt. ar Tir -i. ji 17 6 13 ffi ^^"*«**ie multiplier under the low. ij est denomination of the multiplicand, '''VoL: '""''■ = '^'"- ^^^^- ^-^t clown 16 under... Carry I'idwu X 7 + (idm. carried) = 95^,.^ = 40. 15*,, p„, . 16 under dwt. Cafry 4 to o^. ■*oz.ii,dwt. Put down 5oz. X 7 + (4 03. carried) = adoz - ^ih 9 3 under OZ. Carry 3 to /6. ~ " ^''"- ^^^ ^own 17/6. X 7 H- (3^i. earned) =,22^6. Put down I'i 122 under lb. EXERCISE 53. 1. Multiply 38^6. doz. ndwt. by I7. 2. Multiply 19 2-. iscwt. 18 lb. by 19 3. Multiply 3». 45 23 13l7 7r. by IL 4. Multiply Uy^i ij-f 11 .^^ j^y2i. o. Multiply 17 ,„/. 2 ,-^ 15. If you can buy 15 square rods of land for £1, for how many pounds can you buy one acre ? ^ f"""U8 16. Divide a square milo into 15 equal parts. ^^ ^ rrdlyT""^ ^^^"^ ""' "^'■'' '° ^^ '^'^' ' ''°^ ^''' '^'^ »^« *r*vel IS Acartman earned 117 c.f ilOo..,^. in 100 loads ; how much did he average a load ? I'l "i m ^^ DENOMINATE FRACTIONS. DENOMINATE FRACTIONS. ^AXV^V.. 105.. £.«75x 20X12 = 105d. = 8«. 9d. ]05d. = 8< or £.4375 20 «. 8.7600 12 rf. 9 0000 .-. £.4375 s: 8«. 105d. . 9d. 9d. •'• i^A = 8s. 9d. or 7 JO 16 ) HO f 8». 128 12 16 ) Ml f r^d. ri»2/<^- X f X V = A in Ann ♦nor . Opbrauon. Opkiution. Opbiution. DENOMINATE FRACTIONS frA?-*' ^^ ^^*"^^ °"® denominate number to the fraction or to the decimal of another. the d J"aUfVg7lfon'"" ' '" '' ''' "^ ^'^ *'^ ''^°*^°° «' « ^"^ (2), to Solution. q ..» . dolution. 10 A COMMON FBAOTION. Q „, , . _ TO A DECIMAIi. 3qt Ipt. = Tpt. 2) 1.0 pt. I gal. = 8pt. . \S-r * "JPt- - i 01^ gal. , —875 ^aL Ans. ihede.fluTa'r''^'""''*- ^^ «/- ^ «-t^e fraction o. a . (2). to c Solution. bOLDTION. _„ , TO A DECIMAL. TO A COMMON FBAOTION. A \ o f .•."7/„. : ^r*r - ^°^3ia-.. „ ^^'^ = .778125 of a £. o££l-17rrr'"~'''''""^' '"• ^-(^-^^-^^^ 'action (2).tothedeciinal Solution. £1 3«. 4d. = 380d. £1 17a. 4rf. = 448d. .*. £1 3«. 4d. = ||o of £1 i7^_ 4^^ = f of = .625 of «' EXERCrSE 55. 1. B«5aoe rAi of » mUe to the fraction of a yard 2. What is the value of .8525 of a £ ? 8. Redace f of a pennyweight to the faction of a pound, Troy 4. What part of 3 weeks is 4 da. 16 hr. 30 nin ? ^' 5. What part of IJ bushels is .45 of a peck ? 6. Reduce .425 of a foot to the fraction of a mile 7. Reduce £617 la. U. to the decimal of a £. 8. What is the value of | of a mile ? 9. What part of an inch is ^ of a yard ? 10. What part of a Ih. Troy is .76 of a grain ? 11. Reduce 8 6u*A. Iph. 3 qt. to the decimal of a bushel. 12. Reduce 2.333J years to integers of lower deno„.i„ationt 18. Reduce £14 16s. 9d. to the decimal of . £ ffi" 5!^°°" ! °! * ^""dredweight to the fraction of an ouaoe 15. Reduce ^ of a mile to the frantinn nf a <.f „ „,,. ■°*- IG. Rorfnoe£2 10». - - . -. a ro. OJrf. to the decimal of £2 17«. 2d. i 76 ALiquOT FAliTS. ALIQUOT PARTS. '•r- '■ I»9. An aliquot part of a number or auanflfv ,-. „ exact divisor of that number or quantity "\ Z aliquot part of 20; 38i of 100. ^ Many buainess calculations may be shorfnn^^ k bining the values of convenient aliquot tT'' ' ""* £x.«„... l._what will 576 yards of cloth cost at $1.87* a yard ? Solution. At *1.00 per yard ti, rj .. ', tlie price would be ?5.76 p, „ " .. 510.80. Ans. Example 2.—What will 7 &i(s/j ^nk Rnt r.t v, x bushel ? ^*' *' 3'- °' ^heat cost at »1.60 a SoLfTION. 7 bushels ^ ^1 go = 2 pecks = J bushel a, 1 peck = J bushel ~ 4 quarts = J peek ^ _2 9. i3 bush. 2pk. Iqt. of corn at 58c. a bushel ? 11. 270 yds. Bilk at £1 5s. 6d. per yd? 12. 326 bbls. flour at $7.87J per bb/. ? 13. 164. 3 r. 20 rd. land at »60 per acre ? 14. 12r. 17c«;«. freight at «4 per ton? 15. 7cwt. 3gr. 12 lb. at »61.50 per long ton , 16. 27 yds. of cloth at 3s. 9|d. per yd. ? 17. Sicu.yds. iicu.ft. at »2..50 per a, ud. f lA. 13 nal. Iqt. Ipt. wine at «3 per j,.,/ > 19. 17 cwt. 2qr. at «7.50 per toD ? 20, I do,, elbows at §2.75 per ,i)«. ? 78 MISCELLANEOUS PROBLEMS. MISCELLANEOUS PROBLEMS. EXERCISE 57. 4. How many pounds of wire will it reanirn fn f remaining in the bank ? ""i^'ier, iji4J. How much had he 6 A man invests in trade at one time «r>sn u* a third time, «1,680. and on a fourth orsr«42o"R" ''"'' *'''' "* add to the sum of these that the amouTtZ ^f^^" 00^7 ""' """^'^ .arLs^orrurr;:!^:^^^^^^ I'^b^? ^-^^'^ - - How much money did he receive? ^' '''''''"*'" ^° '"°'^«.V. 9. A man bought 45 acres of land at 1P38 an acre and 7fi „ an acre, and sold the whole at 845 an acre 1);/^ °' ""^ ^^^ much? ^»*oanaore. Did he gam or lose, and how 10. The cost of the Atlantic TeXMra^y, r<„Ki « foUowB : 2.500 miles at »485 per S IQ ^'t T "="""" "'^'^^' "''^ per mile, and 26 miles shore enTi 8, oTn '^.'''' ^^ ^'''^'''^'^ iotai cost? ** ^^'^^^ P«' °"le. What was its ^liliCELLANEOVS PROliLEMA. 7y 11. pouna. VVhat IS the price of the sugar a pound? gain ? "^^ °®°*^> '^o^^ many centa will she 7. What is the smallest sum of monflv w!fi, i • i. . either sheep at «3.50 a head, calves atToVolt^ °- P"f^-- horses at $105 ? ff^-J'-JW, cows at »35, oxen at $70, or a A coal dealer sold 5 tons of coal for $67 50 whinh ^ . as he received for all he had left at $7.(J63 per ton H * '' ""''^ he sell? *' "Of per ton. How many tons did 9. How many times is the Q. 0. M of 4a fti ^a in the L. C. M. of tlie same numbers? " ^' *' *' *°"^ ^'^ contained 10. If 3,^ tons of coal will last as lon^ as 4ia onr^o f tons of coal will last as Ion, as 13^ cords of^ood? ^""^^ '°" "^^"^ III. 3i cd., at another, 2| cd. What was the rem ^" '^'" '°^'* "^ °°« ^""^ fi TT^^ *'^^ '^^^^■'nder worth at «41 ft oorH 9 5. How many acres of land can be bought for <25 000 if coats 25o. ? ^ ' ™' •iJO.OOO, if « sqnaro foot revdnl'tTd't'^L' of es^milt"" ""' "^'^^ ^^^ -«>y 7. If 5} lbs. of coffee cost $1^, what will 27Ji6.. cost? S. Uow manvtip\es nan a «»-.<.=..! — .l..- . . . i of a barrel conf aining .s"l j gallons y '"""""'^^ * "^ "* ^^"o'^ be filled from ■ li !" 80 MISCELLANEOUS PROBLEMS !>• A o' a certain number exceeds * of is the nnmber? the same number by 156. Wliat IV. K r,,v^e the sum of .076 and .0075 by the difference of 7.6 and .75 -. F,nd the least common multiple of ^, ^, ^| ,„<> 8" being ,2 6. Bought 12 T. 3. .,, ■ , many tons of ice may be taken frnn. J, .L° ''^ ^^.'"''^^^ ^^'<^^- How ice to weigh 56 poon*^ ? "" ^'^'""' =-i'P°°i"8 * cubic foot of H2 MISCELLANEOUS PROBLEMS. nft t* n V^^ 'T''"' ^'"■^ "" * ''^''^'^y '« '^ ««"*« •* "^ile. bnt i is allowed off full fare when return tickets are bought, find the distance^ Z„ two places if a return ticket costs »1.80. wiween 5 450 leaves of a certain kind of paper make an inch of thickness ye^V^V °' '^ book 6 inches by 4 incheMn which 10 B^uare yards of the paper are uaed. »4ua,re 6. It costs »23.10 to fence a square field at 3J cents per yard How many acres in the field ? 2 = y^i yara. a.ovf 7. From 10 acres take 8^. 159 pr 30yd. %ft. 108 m i^L2T^::^::iTm''' ''' '- '--^'^^ 'y •^^- *^^ quotient by .025, 9. Express 3.74976 minutes as the decimal of a week. 10. What is the least number from which 1,224 and 1,656 may each bp taken an exact number of times ? ^ ^ VIII. 1. If water in freezing expands ^, find the weight of a cubic foot of .ce, a cubic foot of water weighing 1,000 ounces. 2. Find the difference between 9.^. 159/,.. .Oyd. a,V. ,Uin. and 10^ ? a. Divide $760 among A. B. and O so flinf u than A., but 550 less than C. ''••■'' '^^'^ *^'« ™°'-« 4. How far may a person ride in a carriage gov. ^ at the rat« of s miles per hour, so that if he walked back at the'rate of 3 mUes Per W he may be gone 5J hours ? P*^' ^^""^ 5 What will it cost to dig a ditch on each aide of « r«o^ a 1 o. chains long at 40 cents a rod ? ^"^ ^ ""''^^ »« 6. Walking 4J miles an hour, I start after a friend whos« «*«. • a mUes an hour ; how long shall I be in overtaking h'm? ^"" '' ' 7. How many square rods are there in 100 square chains ? 8. A man owns .187,5 of a mine- he soliu 1-7 „* i • ^ fractional part has he left ? ' ''^ °^ '"' ''^"«- ^hat 9. Reduce § of an hour to the decimal of | of 48 minutes . 10. What will it cost to fence a s .uaro 10 acre field at 80 cents a rod ? IX. io^>^'^zz.T^:r ""' " "" " "°" ' -'- »' ""' ''■' "^. 2. A ship with its cargo is worth «840,000, S of the VAte« nf *i,^ «» worth 3 the value of the ship. Find the vai;! of each f *'' "^'^ '^ K v\ MISCELLANEOUS PhOBLEMS. 3. Divide 6 dy. 17 hr. 11 ,«/„. by Z^. copy? ^^ newspaper for a year, allowing a sheet for „„e every It^^l ^to Z '"^"', ' "'^ '''''' '"' "^ *"- P--« '- y H seconds. Ho . many mil., an hour is the train travelling ■> in J r ' ™'"^ P""""^' °"^"* *h« ^'^""le 'o hold ■> 7. Divide $82.00 anion^ 27 men and S7 hov« a„ *i, * have three times as much as each boy ' ' *''"* ''°^ '"'^'^ ^^^^ 8. By selling my cloth at ftl.26 a vard r t„v;„ 1 1 lose by selling it at »1.03 a y ird WhT^' \aT .°°°*' ™°'*" *'^''" ^ at «1.40 a yard ? ^* '""'''^ ^ «'*^° ^^ ««"'°g 800 yards 10 Var7^ "*? '' ""'' ''"• '■" ' ''' ^'^•"^ ''^ ^^- «' *^« estate, goinasecondf^'*^""'"^^'^ ""^^ - W. how many yards will it t^.!?.:. rjn'r "'" *'^ ^^^^'^^'^ "^-"'^ °^ ^ -^^^^ «° ^r^nd in as the oih^! '''' '^^"^^'^ *^° P^"-^- - *^^* one shall have J as much • ^'^ ''!^'°^°* marching 3^ miles an hour makes 110 «t«,r,= • minute. What is the length of the step ? ^*^P' '" ** 4. I bought 20 pounds of opium by Avoirdupois weight at HH n. . an ounce and sold by Troy weight at 00 cents an ounce Did r! lose, and how much ? ounce. jJid I gam or 5. The G. 0. M. of two numbers is 12 ; their L. 0. M is 72 • on« ♦ the numbers is 24 ; find the other ? ' °°® °' ftA ^"u^^'i?^ *^^^ ^™°"^ "^^ ®- ^"-^ C., so that B. will receive 85 for a - »4, while C. receives $6 for A.'s $5. *^ ^""^ ^- » 7. Which is the greater .0025 of a mile or -79 of a rod ? 8. How long will it take a train 20 rods lono a.nA ^ • 15 miles an hour, to cross a bridge 15 rods Z^, ' ' ** ^' '''' "' a pounT?" " °™ °* '*'^' " "°'*^ »^^'^^- -^-* - »he value of .04 of 10. A coal dealer bought a quantity of coal at «fi » • 41|%, 68*%, 66?%, 831%. 12. 135%. l|o^, 90%, 43^^^ a04. To change a decimal or a common fraction to an equivalent per cent 205. Since any per cent, is changed to an equivalent decimal or common fraction by expressing it as so many hundredths, that is by dividing it by 100, it follows that any decimal or common fraction can be changed to an equivalent per cent, by multiplying such decimal or frac- tion by 100. Example 1.— What per cent, is equivalent to .06 ? Solution. .06 = (.06 X 100) % = 6%. Example 2._What per cent, is equivalent to the fraction | ? Solution. EXERCISE 58. What per cents, are equivalent to the following fractions ? 1. 2. 3. 4. 6. 6 7. 8. 9. 10. i. h h h A. iV. A. 4 J. §. h h A. A. A. A. H. f, h h ♦. A. A. TbIS' Toll I JSffFi 4. S. &, h A. T*Tr. 1 -. 7 1557' DTu' TSBTT' I A, A- tV. A. 4?. h h h A. A. A. 41. 30- H. ■iamwiiiiUMttii ■I ■i F/ i 86 PERCENTAGE. What per cents, are equivalent to the following decimals '> 11. .8. .7, .6, .03, .07, .06, .003, .007, .005. .1&. .056 006 12. .035. .064, .09, .01, .001, .3875, .0625, .03125, .0025 13. .03J, .028f. .OOi, .OOi, .06§. .OOOJ. .33i, .OllJ. 306. To find the value of any per cent, of a number or quantity. Example — Find 8% of 626. Solution 1. Opeeaxion. Explanation. 1% {xhs) of 626. = 8% " •« Explanation. 8% of 625 = .08 of (or times) 626 « 60.00. 6.26 8 60.00 SoiiOTioK 2. Operation. 625 .08 60.00 Solution 8. Operation. I^xplanation. T*,, X 625 = 60 8% of 625 = ,^ of 626 = 60 Find— EXERCISE 59. 1. -20% of 6, 26, 46, 76, 126, 96. 2. 25% of 4, 36, 76, 96, 128, 240 3. 4% of 25, 75, 126, 250, 300, 1000. 4. 12Jo^ of 64, 96, 160, 320, 480, 500. 5. m% of 6, 36, 72, 84, 132, 324. 6. 8i% of 12, 72, 60, 240, 252, 372 7. 37 J % of 80, 32, 48, 75, 90, 724 8. 66§% of 9, 27, 75, 335, 47, 520. 9. 6J% of 32, (54, 25G, 90, 750. 10. 31 J % of 48, 80, 144, 75, 380. 11. 87^% of 16, 72, 108, 35(5, 968. 12. 22^% of 27, 45, (!8, 567, 6.56. 13. 2&^% of 21, 36, 50, 987, 770. 14. 7^% of 20, 39, 78, 117, 273. 16. 75% of 24, 32, 28, 204, 760. 16. 90% of 70, 110, 40, 350, 660. 17. 31% of 86, 475, 373, 2.'i4. 18. 44% of 374, 228, 937, 8321. 19- 60% of i, J, ^, ^^, ^. 20. 126% of »7.50, »376, 436 bushels, 328 tons 21. 8% of 37i, 62^, 87i, 6^ 4J, 33i. 32. 6% of 850yds., 450 men, 375 lbs., 5k0oz. PEROENTAQE. 87 20T. Given the value of any per cent, of a number, to find the number. EZAMPLB.' Solution 1. Opeeation. .08 ) 24 ( 300. Solution 2. Operation. V X 100 = 800. SotUTION 3. -24 is 8% of what number ? Explanation. The question is 08 x what number ae 24. If 24 is the product of two factors, one of which is .08, the other factor may be foand by dividing 24 by .08. Explanation. If 8% of the number = 24 then 1% " " =|of24 = 8 " 100% " " = 100 X 3 = 300 Explanation. The question is ^^ of what number »B 24. If 24 is composed of two fac- tors, one of which is x^u. the other factor may be found by dividing 24 by EXERCISE 60. Opehation. 24 X ^s>■ = 300. Find the numbers of wbich- 1. 60 2. 96 8. 640 4. 32 5. 320 6: 252 7. 105 8. 84 9. 350 10. 220 11. 48 4%. 20%, 8 125%, 8 8J%, l«a%. 30%, is 12*%, 418%, 15%, 77^%, s 24%. 3%, 25%, 160%, 9iV%, 36%, 40%, 37i%, 68J%, 35%, 34%. 16%. 2%, 50%, 226%, 7A%, 44*%, 60%, 62i%, 6fiJ%, 45%. 9f%, 12%, 6%, 76%, 160%, 7|%, 14f%, 00%, 87i%, 42f%, 55%, 23J%, 10%, 6%. 90%. 80%, ^%, 12J%. 70%. Hi%. 154%- 65%. 83J%. 24%, 85%. 36%. 20«. To find what per cent, one number is of another. Example.— What per cent, of 60 is 15 ? Expl.\nation. As 15 is ^ of 00, and as the frac- tion ^ expressed as % is m x 100)% = 25% Art. 205, it follows that 15 is 25 % of 60. Solution 1. H = (« X 100)% = 25%. t f vic'^ ~ SlOO Ist Disrmiiit = _ ^0 = 20 % of $100 80 2nd Disvuunt ^ H = 10% of $80 Net prico = j)i7-.>. Total discount on $100 = 5100 -- *72 = f28 .'. discount = 28 %. 235. From similar examples we derive the following rule to find a single discount equal to two successive dis- counts. RULE. From the sum of the discounts subtract y^^ of their product. 236. Then in the above example the discount = 20 + 10 - ?«^» = 28%. When a third discount is given, combine it with the result obtained from the other two. Thus, if discounts of 20, 10 and 5 % off are given. From the preceding illustration, 20% and 10% are equal to a single discount of 28 %, combining 28 % and 5 % we get a discount of 28 + 5 - '-^ = 31^%, the single discount equal to the discounts of 20, 10 and 6 % off. 96 TRADE DISCOUNT. S'^A},J. may still have a profit of 26 ? Solution. Selling price = »4.00 + 25 o^ of H 00 - Sfi nn and 20 o^ less than the marked pnce Z ffy' . . •• 80 0^ of marked price = 5.5o ~ ^^"'"^ Pnce »5.00. marked price = ^^ ^ g.Qo = jq 35^ EXERCiSE 64. Find cash price of — LIST PRICE. TKADB DISCOUNT. 1. 8360, 5 and 20 % off. 30 and 5 % off. 20 and 10 % off. 10 and 8 % off, 40 and 20 % off. 25 and 10 % off. 30 and J % off. 40 and I % off. 2. $475, 3. «800, 4. »750, 5. $1G00, 6. 81750, 7. $1840, 8. 83200, TBADB DISCOUNT. 10, 5, and H % off. 6, 2J, a»d i- % off. 20, 5, and 2^ % off. 10, 8J, and J % off. 40, 10, and 6 % off, -'jO, 30, and 1 % off. 20, 10, and 3J % off LIST PHIOE. 9- $3(i0.60, 10. 82142.45, 11. *402,18, 12. $675.36, 13. 817425, 14. S.'iDGfiO, 15. $4302.50, What direct discounts are equal ,„ discounts- -ou:x^td^'^~;3o^-^ profit 0' 20 %. What must be the lied" """^ " 24. If the hst price of certain coods is *io ^vhat will I gain „r lose by bu,-i„rof Mr A 7 ^T counts are tiSV and ino/ • , J' . *- *'"'"» ^i^- c »re ^o^, and 10%, instead of from Mr R „,i discounts are 20, 10 and 6 % off ? ' ^"'^ TRADE DISCOUNT 07 25 For what must I mark goods which cost $S fin yet receive thetetj prL w ^'^ '^'^^^^^ ^^°^^«^ price. ^ P''"'- ^^^* '^"st l^e the marked MISCELLAIVEOUS EXERCISE 65. at 600. per boahe., tos "c v 'foL^ f^" h'"' '.^^' how n>„ch did he pay f„, .he whole qua^tTt; f " '"' '"''-■ vation. whieh p^fd for « ;,? 1'™ ^^"' "'""-f" ""Hi- --..■a...o.e.a„h':s^T-x;st;^: many mmates are there now ? '^^' ^'''' additiiZXrit^o;^^^^^^ ^^-^O. and paid an age. freight, etc. Vhat Lt^he eirihem7l" ''' "^'■ on the whole cost ? ^^'^ ^^"^ *° S^in 40°^ 5. In a mixture of alcohol and water ft^o/ • , , How many giUa of alcohol in 3 gallons of fh ^ . ^^'°^°^- how many gills of water ? ^ °^ *^' "^^^'"^«' and 6. 560 bushels of wheat, bought at %l m , , w«re »„,d at a p^fitof 10,. Whft'dM tttwh/JJirr; 98 TlUDi: JJISCOUM'. 7. Jiought a bill of goods amounting to $875.60, from which wae deductod 5%. What was the percentage allowGd, and the amount paid ? 8. Having $IDJ20. I invested '15% of it in land, and 12^ % of the remainder in fencing it. Wliat remained ? 9. Two men engaged in trade, each with |B,540. One of them gained 83^ of his capital, and the other gained (50 %. How much more did the one gain than the other ? 10. A little boy who has 8 apples gives 25 % of them to his brother, vn% to his sister, and 50% to his mother. What per cent, and how many has he left ? 11. Charles sold his sled, which had cost him $1.75, at 20% below cost. How much did he get for it ? 12. A lot of daniageJ calicoes are to be sold at 75% below the marked pr. e. What prices must be asked for those that are marked 8c., 10c. , 12^c., 16o., 20c., 30o. ? 13. A grain dealer bought wheat for $9,38i, and sold it at a gain of ^ %. What did he receive for it ? 14. If a man owes $2,500, and agrees to pay it in 4 instal- ments, the first to be 50 % of tiie wliok;. tlu; second 25 %, the third 15 %, the fourth 10 %. What will each instalment be ? ■ t Mill II. 1. A merchant owes $6,500, and his property is worth only $6,425. What per cent, of his debt can he pay ? 2. A man shipped 3,800 barrels of flour to England, and- during a storm 19 barrels were thrown overboard. What per cent, was lost ? 3. If I have $374.50 in currency, how much gold can i buy when it Bells at a premium of 7 a' ? r /---/"-•r THADE DISCOUNT. increase per year ? ""^^ ^^'' ^^'^^8^' ^'^^e of sold ptroTiS: ^40 rrr ^^ ^^°^^' ^* -^^^ - --'- -^^ of the land cUd he til ? ^'^ ""^ ^^'^^ ^^^' I-'" -"*• 7 Bought sugar for $160 and sold it for $167.50 per cent, was the gain ? •p'-ji-ov. 8. A merchant owes $8,250, his assets arp «!•■{ •> .n per cent, of his debts can bo pay? ^ ' ^• 9. Sold i acres of land for what the whole cost was the per cent, gain ? ' 10. What per cent, of 366 days are 30 days ? 11. Bought a number of eggs, and solH 1 1 f«. *u paid for 18. What per oent'^sX "l, "' """"'" 12. A regiment went into battle wJf h unn out »ith 820. What per cent "ere ll't? '""'• ■""■ °'""« ce.\%-'/;:ir"''''''^'^ '»""«-- What per ano.her.i.e. ^''^^ ^^ S^l XI ::,ZZZf; "' What What What III. 1. A merchant owes $15 i<2n a^A u- What per cent, of hie deM^'oan'he"^'';""" "" *'''«^»- 2. If $62.60 is paid for th« nqn ^.^ *^.« , the rate per cent if S5fi 7n ;J -j r **"""' ^ y«»r, what is P cent. ,t $56.70 is paid for the use of $1,260 ? 100 TRADE DISCOUNT. Hi ', ' 3. A man shipped 2,600 bushels of grain from Chicago, and 455 bushels were thrown overboard during a gale! What was the rate per cent, of his loss ? 4. One number is 6% of another. What per cent, is the latter number of the former ? 5. My furniture is worth $7,200. which is 90% of the value of my lot ; and the value of the lot is 33^ % of that of ray house. How much are lot, house, and furniture together worth ? 6. A gentleman who had a yearly income of $2,000 for four years, spent $1,800 the first year, $1,500 the second $1,200 the third, and $2,260 the fourth. What per cent! of his income did he save during the four years ? 7. A person expended 16 % of all he was worth in buying 20% of the stock of a mining company. If the entire stock of the company sold for $100,000, how much was the person worth ? 8. A merchant, embarking in two speculations, in the first made £37 9s. 3^., which was 4 % of his investment- in the second he lost f 27 16«. 8d., which was 6% of his invest- ment. How much had he invested in both enterprises? 9. A.'s yearly income, which is 7% of $27,000, is 150% of B.'s income. If B. receives an income of 10 % annually from his property, how much is he worth ? 10. A leap year is what per cent, of a common year ? 11. C. from an income of $5,340, spends $4,966.20; D from an income of $2,790.40, spends $2,650.88 ; E. on an- incorae of $1,559.60. saves as much per cent, as the rate per cent, that C. saves, exceeds the rate per cent, that D. saves. How much does E. save? 12. What is the cost of a house which sells at a loss of 7^%, the selling price being $11,500? TRADE DISCOUNT. 101 13 A merchant owes $12,575. and his assets are $7,500 What per cent, can he pay ? ▼ > • 14 Soldtwocitylots at $1,500 each; on onel made 15% on the other I lost 15 o^. ^hat did I gain or lose ? IV. loJqqf ' wkV "'f^'" """'^'' ^^°^ °^ ^*««lf' we have 109.835. What would we get, if we subtracted from the same number 11 % of itself ? 2. In a certain nursery, 15 % of the trees are pear trees, 1% cherry trees 4 o^ plum trees, and the rest, numbering 480, are apple trees. How many trees in all. and how many pear, cherry, and plum trees does the nursery con- 3. P having lost 20°^ of his capital, was worth exactly as much as Q., who had just gained 12°^ on his capital. Q. 8 capital was originally $15,000. How much was P.'s ? 4 A railway company sold 12°^ of its land, and then mortgaged o o/ of what was left. It then had 250.800 acres unencumbered. How many acres had it originally ? 6. What number, increased by 2^°^ of itself, equals 12i- diminished by 33| % of itself ? ^ T 6. What fraction, increased by 21 % of itself, equals \^ ? 7. 240 is 33 J % more than what number ? a biiltf'^77f ' wf'^' ^ °^ commission, pays $634.75 for a bill of $775. What amount of the bill does he collect ? 9. What is !■% of $1,728? 10. What is 9^ % of 275 miles ? 11. What is the differencfl bfl*:wpan Ri"/ -f tanrt ;» - t . of $1,050 ? '"' "^'* "^^^^^' ^''^ ^^^^ 102 TRADE DISCOUM. 12. 26 % Of 800 bushels is 2^ % of how many bushels ? 13. Sold 105 barrels of potatoes, which was 35 % of all I raised. How many did I raise ? 14. A farmer sold 7.6 acres of land, which was 16°^ of all he owned. How many acres did he own ? V. 1. What per cent, of a number is 25 % of f of it ? 2. i% of 1,268 is ^ % of what number ? 3. What per cent, of a number is 20 % of f of it ? 4. A man spends $825.60, which is 83^°^ of his salary Jlow much 18 his salary ? of $243.72. How much had he in bank ? 6. If a man, owning 40 °^ of an iron foundry, sells 25 »/ of his shai-e for $1,246.60, what is the value of the whole foundry ? 7. A farmer sold 3.160 bushels of grain and had 30 »/ of his entire crop left. What was his entire crop ? 8. If a man owning 45 °^ of a steamboat sells 16§ % of his share for $5,860, what is the value of the whole boat ? 9. The assets of a business man are $136,700 which sum IS 43 % of his debts. What is his indebtedness'? 10. A fruit dealer sold a lot of oranges for $337.50, which allowed him a profit of 12^ o^. What did he pay for thou. ? 11. A city lot was sold for $25,500. the ,,ain on the cost' being 325%. What was the cost ? 12. A grocer sold 300 bunhels of potatoes for $285 which was 16§o^ less than he had paid for them. How much did they cost him per bushel ? U TRADE DISCOUNT. 10!) t $29 V* nf ^""^l ^ll ^"'" "^ ^^°^- 2'« profit was f 29.70. How much did he sell them for ? veltn/thT^ a lot of goods for $880. 1 gain 3 times the per cent, that would be gained by selling them for $840 SesCrf- " '""' ^" ^'^ ^^**^^ --^ ^«- - «-0 = 15 In the schools of a village yesterday there were 1.235 pupils present, which was 95 o^ of the whole number belong- ing. How many belonged to the schools ? VI. v.ln/°WK ''"*'' ["' ^^*^' ''^''^' ''''' 15"^ '««« *han his value. What was his value ? ^' ^ ""f^^^-^^'^g increased his bank deposit 40°/ it amounted to $840. How much had he at first ? 3 My income this year is $2,232. which is 7% less than It was last year. How much was it last year ? 4. A man sold 160 acres from his farm, which was 12*0/ less than the number of acres he retained. How many acres m his farm ? ^ 5 The price of a single ticket from Princeton to Wood- stock is 30c.. but 20 coupon tickets can be bought for $6 What per cent, is saved by buying coupon tickets? What per cent, is lost by buying single tickets ? 6. 10 o^ of a flock of sheep were killed by dogs ; 64°/ of the rest were lost; 33Jo^ of the remaining number were numbe?' "^ """'"'• '''''' ^'^ ^^« °"g-a! 7. At harvest time a farmer sold 60 bushels of wheat ' hesttT'' '.f °' *': ^""^*'*-^ ^^ ^^«* *° -"!• -d what he sent to mill was 40°^ of what he kept over till the n.xt spring. How many bushels had he at first ? 104 TRADE DISCOUNT. 8. When a merchant sold hia goods for $261. he gained twjce as much as Ije would have lost had he sold them fr *^07. What was his gain per cent 9 ,vr 10S3 is the difference between%261 and »207^) ^^°" ""^"^ '"^'^ *^« 9^ A grocer sold butter at 12 % profit. Had he sold it tor 2c. more per pound, he would have gained 20 "/ What did 50 pounds cost him? "«^"/o. What 10 A boy buys an old pair of skates for 50c. and sells for 50c. What per cent, did he lose on the first pair what per cent, did he gain on the second ? ^ ' 11. If a dealer buys a hat for $3, and sells it for $4 what tor $3, what per cent, does he lose ? 12. One hundred pounds of beef were sold for $6, having been bought at 4c. a lb. What per cent, profit ? ^ boott'for'lt'n t'^'' M°'*' ""'^ '^''' «°^^ SO pairs of boots for $300 they cost him $6 a pair. What rate per cent, did he gain ? ^^^ 14 A merchant bought goods for $500. What per cent T.^n\ T'l""' «ellingthem for $530? For $525 ? For IL$1,500T''''' ^"^'"'^ For $575? For $600? VII. for^9.r" wi; ^"'' ^ P'"''"^^" ^'' ^^°- ^°^ «^"« it to James for 25c. What per cent, does William gain, and what per cent does James lose ? e . • wuac pei # 8i i of the daily session, how many hours in the session ? 8. If a boolt is marked to be sold at 26% above cost bnf .t IS sold at 20% below the marked price, what wis thei' or loss per cent. ? ^ " Jr i ir TRADE DISCOUNT, 106 i I 4. If 80 pounds of coffee are exchanged for 120 pounds of sugar, what per cent, is the coffee worth per pound more than the sugar ? 5. What per cent, do I gain by selling an article for $3 for which I paid $2.25 ? What per cent, do I lose by buy- ing an article for $3 and selling it for $2.25 ? 6. A drover sold a horse for $226, and thus gained 25 %. What did he pay for him ? 7. Bought 800 long tons coal at $3.75 a ton and sold it at $4 60 a short ton. What is the per cent, profit ? 8. Bought a barrel of syrup for $20. What must I charge a gallon in order to gain 20% on the whole ? 9. Sold 25 tons of coal at $5.64 per ton, and made $62 What did the coal cost, and what per cent, was the profit ? 10. A quarter section of land was sold for $4,563, which was 8 % less than cost. What was the cost per acre ? 11. If 15 % of what is received for goods is gain, what is the gain per cent. ? 12. Sold goods for $29,900 and made 15 % after deducting 5% for cash. What was the cost and the marked price ? 13. A dealer sold 1,600 bbls. beef for $24,000, which was a loss of 25 %. What did the whole cost, and what did he set a barrel ? ° 14. A builder sold a house for $8,250, which was 12% more than it cost him. What was the cost ? 1 VIII. 1. A merchant sold cloth at $S per yard, and thereby gamed 20%. What per cent, would he hav- gained if he had sold the cloth at $3.75 mr yard ? 106 TRADE niSCUUNT. » iti ;, 2. A person at two auction sales bought 1,170 books buying at the second 30% of the number purchased at the nrst. How many did he buy at the second ? 3. What number, diminished by 25% of half of itself equals 12,000 ? ' J. Mr. A. paid three times as much for his horse as for his gig. If he bad paid 15 % more for his gig. and 8^ % less tor his horse, they would together have cost $468. How much did he give for each ? , '; ti?''^'"* '"^ 'V^ "^^^^ ^ °^ °° ^^« «^PitaJ' and in 1873, 3i % on his capital thus increased. Capital and profit then equaled $2-2^351. What was his original capital ? What was his profat in 1873 ? 6. A offered B. $6,046 for a farm; which B. declined, as iT-^t f ? ^^^"^ '^ '°'* ^^^- ^- afterward sold it for ^b.35o. Did he gain or lose on the farm, and what per cent ? ^ 7. A statue was sold for $753.75, which was i of 1% more than it cost. Had it been sold for $700, what per cent, would have been gained or lost ? 8. Sold goods for $4,026.76, at a loss of 8^%. What would they have had to sell for to yield a profit of 3^% ? 9 B. bought a horse for $200, and sold it at 20 % advance to C.. who sold it to D. at a loss of 10%. and D. sold it to h. for 6 /o more than it cost him. If E. had paid $21.60 less for the horse, would D. have lost or gained, and what per cent. ? 10 K sold X. some goods for $394, at a loss of 1*°/ X. sold them to Y., at a profit of li%. Did they cost Y more or less than K., and how much ? sol^' lf\ ^^^?f'i ^ ^^' '*■ ^PP^^' ^^"^ ^31-^9i clearing 4%. What would they have had to sell for per bushel to yield a profit of 9%'? per ousdel, to TRADE niaCOUNT. 107 hogs. On the hogs he lost 7%, on the sheep he made 15"/ and on the cows he losf l o/ jf -. . ^ , ™a^® -^"^ /°» 1151 Kq« J u , : "^^^ ^^ "^ received for the whole than h., „„g.„al offer. How mach did his bo^ZZuZ 14. The population of a certain citv in lft7i ,-»«. j iH71 m 1873 It increased 6% on that of 1872 and amounted to 1.389.024. What was its population in 1870 ? 15. If a certain number be increased by 16f% of itself and the sum is diminished by 50"^ of itself 10°/ nf ft remainder is 14. Eecjuired. the number ^° *'' *^ 1 IX. .iLVTI'^^'"' "'"' ''"■'" 8'""'' ™ 8 months' credit is flowed a deduction of 6 »/ for payi„g Us bill within 80 day What can he save on a bill of $560 ? How mnoh on $8 650 ^ , Jt; ," T,"" "f '■' '" P»y ■>'« ™'« «■" until he is ehareed l.%for^ delay, how mnoh will he lose if his water rate is 8 If 1% per month, counting from the .ime of payment .s allowed on all taws paid before July l.t and iT. month charged on all taxes remaining n„,l"L',^ff;; tanreach bl; lieZ '" '""^ '"'''"''- '^'' '"^'^ 4. What is the net amount of a bill of irood« +J,n i,- 4- pn. of which is $436, sold ,% off for cash. Sdit':: t(# TRADE DlSCOVilT. I i .i z it. , „, 5. Sold bfvM)k8 on 8 mo. amounting to $854.75 at a rlis eoun of 12J% f.„„ .otai, price, a,.d fo-, off for Lsh W . IS the net value of the bill ? 6. The gross amount of a bill is $236.37 ; the rates of discount are 15 % and 8 %. What is the net amounr? and 8^!''^ ^ ^^^'^ '*'''''""* '**"*^ *° * ^'''°""* «^ 12^% l/% p^^'* ^^'^''' ^^'^'^^^^ i« «5"al to a discount of 26 "^ and cou';t?f sVci" '?'''' ^^^^* ^« ^^« ^^ff— between a dis- count of 30% and a diacount of 25 % and 6 °^ ? 10. Bought books at a discount of 20% on the ret.il 11. What per cent, would I gain at a discount of 33J % ? 12. With a trade discount of 8% and 5% for cash, goods were sold for $825 at a profit of 15%. Wbat was thecost ? 13 A bookseller wishes to mark up the price of a book which he now sells for $2. so that he can deduct 15% and yet^rece.ve the present price. What must be the marked 14. A merchant sells cloths for $268 by which he gains /■ ^^T ™"^* ^^ "^^rk them so that he may deduct 4^- and make the same profit ? j y ■* r>ri!.!\??^Jf '^'*r'"^' ^* •^^^^- ^°^ ^"«t I »^ark the price that after abatmg 5 % the profit may be 25 % ? A f'Ti^^'J ''■ ^' ^^'^ P™' "^ ^° article from which you deduct 20% ;.,n. ' u .. 20 oents ? wmcn you MARKING GOODS. jqq MARKING GOODS. aas. It is customary in mercantile houses to use a private mark, which is phiced on the goods to denote their cost and se ing price. A word or phrase containing ten diiferent etters 18 taken, the letters of which are used to indicate the ten digits. For example, the word '< Sutherland " is selected ; then the letters represent the figures as folio ^vs : Sutherland 1 2 3 4 r. G 7 8 9 If it is required to mark $1.76. it is done thus. Sle: 47 hi ; 90 nd. ' aso. The following are among the words and phrases that may be used : Haliburton. Chelmsford. Cumberland Blacksmith. iNow be smart. Strike hard. Cash profit, Black horse, etc. aao. It sometimes happens that the selling pnce con- . tains three figures, while the cost price contains but two lo prevent this diflference from being noticed, the letter denoting the cipher is prefixed to the cost price. For instance, the cost price was 86 cents, it would be marked dae; and the selling price, sue; thus each price would be indicated by three letters. 281. An extra letter, called a " Repeater," is used to prevent the repetition of a figure. Instead of writing see for 1.65, which would show that the two right hand figures were alike, and thus aid in giving a clue to the key-word some additional letter is selected for a repeater,— y, for instance— and then the price would be written sey;*337 would be written tyl. aaa. Arbitrary characters are frequently used instead of letters, thus : 1284567890 110 MARKING GOODS. n 2»a. Fractions may be designated by additional letters or cliaracters ; thus g may represent ^; f, J, etc. EXERCISE 66. 1. What is the profit and what is the selling price of the following Cost ?i 10, " l.f-O, " 4.50, " 1.7"), " 2.;50, Freight 10%, " 10%. 10 '?,' Gain 20%. ■■■" /O- " 25 %. ' 20%. Selling price. of the above, using the word Mark the selling pnco " Chelmsford." •2. Knowing a merchant's profit on cloth to be 25 % and his key-word Haliburton, what letters would be used in indi- cating the cost price per yard, the selling price being hrb ? 3. What letters would be used in marking the selling price of single articles which were bought at $3.50 per dozen, and sold at a profit of 20%, using the word "Cumberland." 4. A publisher marks each copy of a work skd. What mark should he put on each so as to be able to allow the trade 80% discount ? (Key- word "Strike hard.") 5. What would be the selling price of imported articles bought at $4.60, on which the charges were 50% of the purchase price, if they were sold at 40% profit on total cost ? How would the selling price be marked if the phrase " Cash profit " be used, with y as a repeater ? 6. A merchant using as his key- word "Chelmsford," indicates the cost per yard of a piece of silk, thus cod. What mark will indicate the selling price so that he may sell it at 10 % less than the marked selling price and stUl make 20 % profit ? 7. A man wishing to sell a web of silk asks 40 % per yard more than it cost him, but he finally sold it at 10% less than his asking price, and made a profit of 52 cents a yard. Using the phrase " Now t j smart " indicat.<3 the cost price, thtj asking price and the selling price. II 'aOMMlSaiON AND BUUKEIUQE. Ill COMMISSION AND BROKERAGE. ■il^^, Commission is an allowance made to agents or comraission mercbauts for transacting business. It is usually calculated at so much per cent, on the amount of njoney received for sales or expended in purchase. 235. A Commission Merchant or Agent is a person engaged m the buying and selling of goods for another, as the purchase or sale of merchandise or real estate, collect- mg or investing money, etc. 3»6. An Agent's Commission for sale is computed cost ^'""^^ Proceeds, and for purchase on the prime 237. A Broker is one who effects purchases or sales in the mterest of buyer or seller. A broker do^s not generally take possession of the article bought or 80' He usually contracts in the name of the party from whom he receives his compensation. 238. Brokerage is the compensation paid to a Broker. 23». The Principal is the person for whom the business ■J5 transacted. 240. A Consignment is property received to be sold on commis'^ioii. 241. The Consignor or Shipper is the person who ships the goods to be sold. 242. The Consignee is the person to whom the goods are sent to be sold. 213. A Guarantee is the charge made lor assuming the risk of loss from non-payment by the purchaser. ' I i '. < I ^' i ; '< m Mi .%\ t. 112 COMMISSION AND BEOKERAGE. 344. Tlie Gross Proceeds of a sale or collection is the total amount received by the agent before deducting com- mission or other charges. 345. The Net Proceeds is what remains after all charges have been deducted. 346. An Account Sales is a statement in detail rendered by the Consignee to the Consignor, showing tue sales of the consignment, all charges or expenses attending the same, and the net proceeds. ^/T* i"" ^*^^°""* Purchase is a detailed statement made by the purchasing agent to his principal, showing the quantity, grade and price of goods bought on his account, a 1 expenses incident to the purchase, and the gross amount of the purchase. 34S. To find the Commission on a sale of goods, the gross proceeds, an«! per cent, of commission being given. ExAm.LE.-How much commission will be due an agent who sold a house and lot for 86,000, and charged 3 % for his services ? Solution. »6,000 X .03 = »180. Ana. ^IV^' u° fl""* *^^ Commission on the purchase of goods when the prime cost and the per cent, of commis- sion are given. which coTip'n""^^ T"* '" ^°"'^°° '^°""^'* ^"^ ""' 3^0 y^'^^ of «ilk. h's com^Lt ^ ''''' '' " '''^"^"^^^^^°" ^' ^^^- ^-^ *^« — of SoLCTIOlf. «2.50 X 350 = ms.lO = Cost Of silk. «87o.OO X .02 = fl7.50, Ana. 350. To find the amount of a Sale when the amount of^commission and the per cent, of commission are f C02miSSI0N AND BROKERAGE. ^^g Solution. 5% of amount received = 8245 1% 82i5 100% .. „ _ 8246 X 100 be invested and thtS'sZ^Ss^r '"^ ^■"'"'■" '» Solution. The amount to be invested is inno/ „* -, ,, ., sion is 3 o// of amount invested ^° ''^^' *^^' ^""^°^^«- io;i ' of anicuit to be invested = 1% 100% $5,160 f5450 103 f£450^x 100 /.The amount to be invested = $5 00^^' Commission, %5,m - «5,000 = »S Example 2. — Havino o,.i;i Bion, I am instructed to inZ:;:Z::2'^ "'/""^^ °" ^^° — -" commission of 2 % on the price paid fori '° "''^ ^""P^^-^^' ''-"^vin, a --n is ,.00. Pi., theLouSr.^- ; ^1 ^^^"^^ ^^^ Solution 1, «ien ^ of the amount of sales = /f«i .,„.„... . iVir 114 COMMISSION AND BliOKKliAQK. ( n every $102 of amount left after deducting Ist Com., the agent receives $2 for his second commipsion. .■. The agent's commission = -^ of the amount to be invested. Hence -jV of t^ = -yf ftr o* sales = second commission. •'• (t%i! + tUci) of sales = Agent's total commission, j^j of sales = S'iOO. Sales = $4,080. Ana. SoiiDTION 2. 3% + 2% = 3%. If the 5% commission had been charged on the whole amount of sales, the commission would have been 2 % of $200 = $4 more, i.e., the entire commission would have been $200 + $4 = $204 = 5% of sales. .-. 5 % of sales = $204, Sales = 14,080. Ana. Again: If the 5% commission had been taken on the amount of purchase money, the entire commission would have been 3% of $200 = $6 leas than it was, i.e., the entire commission would have been $200 - $6 = $194 = 5 % of purchase money. .•. 5 % of purchase money = $194. Purchase money = $3,880. HI Solution 3. It will be found that on every $102 from sale there is $5 entire commission. Suppose we allow for commission for spiling, $2 of the ;t»l02, leaving $100. For commission for purchasing, $3 of the $100, leaving $97. The entire commission would be $5. in the former case we have charged 2 % of $3 = 6 cents too much. But in the latter case we have charged 3 % of $2 » 6 cents too little, i.e., the excess equalp the deficit, and we have still $5 entire commission. Thnn, tSt of sales = $200. Sales = #4,080 GOMMISSIOX .u\D BliOKERAGE. 135 SOLUXION 4, Let 100% = Sale. rl of q?"/ Si l"""'^ = ^"^^ Commission. 9 o/ I /° " ^*^ ^ °^ "^'^ = Second 3%ofsalo + Ifjo^ofsale = Total . ^M % of sale = $200. 100% of sale = $4,080. From the foregoing solutions we obtain the follomn, f commission ou .ale is i% and on purohaseT* the entire commission = ±±±_ ,• 7 » ^ , *^ ** /°' '^® 4 + 3 . 7 , ^^'^ + 3' •^•' 103 0^ sale money, and fo6~ri« *•«•» 96 of purchase money. And generally if we have „ per cent, on sales, and n per oenl. on purchase, the entire commission . Jlii „, . ! money, and iii of pu^h^^ money. "" " " EXERCISE 67. Find the commission — 1. On the sale of merchandise for $8 160 at 9io/ 2. On the sale of a mill for nTn% ^°' 8. On he sale of 375 bbl. of flour, at $6.25 a bbl at 8W . On he purchase of a farm for $12,870. at 2^% ^°' 5. On the sale of 256 balpH nf on*+^^ i ^ . «20 lb., at UJcents a lb atli; ' '"* ™'«''"« Find the rate of commission— 8. When $189 is paid for selling a farm for jVseo.' Pmd th( amount of sales— to' ^'" f """"misBion of $860 is charged, at 2ir 10. When he brokerage charged is $48. at i% n. When the agent charges $69.60 commissi™ at m 1A mu lu f'^""""" are ipaa.70. commission S+y 14. When the net proceeds are $2,444.56. brokerage |^: 116 COMMISSION AND BROKER AQE. , i Find the amount to be invested and commission — 15. If $4,455 is remitted, deducting \^% commission. 16. If $9,909.40 is remitted, deducting 3^ % commission. 17. If $6,500 is received, and 1:^ % brokerage deducted. 18. If $2,846.25 is remitted, deducting 3i% commission. 19. What weight of wool, at 52 cents a lb., can be bought for $1,109.60, after deducting a commission of 4%. 20. Sent to my agent in Hamilton $1,508.80, to invest in flour at $5.75 a bbl., after deducting his commission at 2^ %. How many bbls. can he buy ? 21. An agent sold a house and lot for $8,500, and charged 3 % for his services. How much was his commis- sion ? 22. If an agent's charges are 2 %, how much commission will he earn by selling property valued at $10,500 ? 23. A real estate agent sold a farm of 75 acres at $85 an acre, on a commission of 2 % ; and the stock and imple- ments on the farm for $3,250, on a commission of 3%. Find the total amount of his commission. 24. An agent received $612.50 for gelling grain, on a commission of l\%. What was the amount of his sales ? 25. A collector's charges for collecting a note amounted to $14.10, at a commission of 5%. What sum was col- lected ? 26. An agent receives $12,504.20 to invest in wheat, on a commission of 3 %. Find the amount of money invested in wheat. 27. How many lbs. of wool at 27c. a lb., can be bought* for $8,424, if the agent is allowed 4 % for purchasing ? 28. Paid an agent a commission of $183.12^, at 2| %, to purchase wheat at $1.87;^ a bushel. How many bushels did he buy, and what was the amount of his bill ? a OOMMISSIOK AND BlmKEUAaB. jjj WoL™;, ''* '^ ' ^'""■'- ™^' ™» ""> -"^ Of "is 80. An agent in Montreal remitted %^ tq*? rr ^ of 540 barrels of ilour, at $7.25 1^^.!ei wLtUs^: ! rate of commiBsion ? ^'^^ ^"^ SmSfi ,-r'^'f *' ^'''''' '^^''^'^ ^182.34 for investiuo $12,166 zn a factory. What was his rate of brokerage ? 32^ I sell through my broker 7 tons of Brazil nuts at 17.60 per cwt. How much do I receive if H.1 i , charges lo^ for selling? ^^ '^ "'' ^'''^^' pril ari.^'''^^"T°*^" ^°^^°*«*° ^^' "--ted in prints at 12, cents a yard, after taking out his commission of H %. How many yards can he purchase ? 34. My attorney collected 80% of a note for -ftl 9nn a charged 5^ % commisainn w/ . •'Pl,200, and ^^ h 2 /o commission. What amount should he pay 35 An agent sells a consignment of flour for $7 539 8(. and then Durchasps l Hzin u i 1 , il>/.£>dZ.HU busb..l hi ^"'''"^T ^'^40 bushels of wheat, at §1.40 a Dusiui, his commission bpincr 9io/ wtv, j. "«•*"« rfiinif f^ fu • ^ ^^ ^°- W^8,t sum must he remit to the consignor ? "^^ou ue pay for a ccopt^iit ::c" :::& r; sr'^r" '° What did the house sell for ? * " "'''•""''• «/nnr,^. """""""'O" merchant received a remittance of . poundlolfd he '„;;"""• °""°« '^"- ^ '"•■ "°" --y rec'etef*^","? 'r:» 5;°"- "f «, for which the o.ner fi-t dea„;te.rfo; th: :!e";x::;;; !t r"^ ''^''"^' ^^"> 118 COMMISSION AND BliOKERAQE. k '< I. i« ^^-ir ^H; 39. How many barrels of flour, at $5.60, can be bought for $2,545.20, a commission of 1% for purchasing having also to be paid out of this sum ? 40. A commission merchant sold 500 lbs, of butter at 18c. per lb., and invested the proceeds in oats at 42c. a bushel. He charged 4^ % for selling and 1|% for buying. "What was his total commission, and how many bushels of oats did he buy ? 41. A fruit broker sold $680 worth of apples, and after deducting 6% commission and 20% for freight and other charges, invested the balance in oranges. How much did he invest in oranges if he charged 2 % for buying ? 42. My agent in Brantford sells for me a quantity of dry goods on commission at 6 %. How much must be sold that my agent can buy flour with the proceeds to the value of $5,400, after retaining his commission, for buying, of 2J ? 43. Sold goorta at 2|- % commission, which I invested in sugars, and sold them at a profit of 15%, realizing a gain of $240. How much commission did I receive, and how much did the goods sell for ? 44. A merchant purchased an invoice of grain, which, including a commission of 1^%, cost $5,050.65. The freight charges were $15.35. He sold the grain at a profit of 15 % on the entire cost, and invested the proceeds in sugar, which he sold at a profit of 5%. What was the amount paid for commission? What the entire cost of the grain, and how much were his profits ? 46. A commission merchant bought goods for which he received 5 % commission for buying and $63.25 for charges. The total cost of goods, commission, and charges was $3,250. What was paid for the goods ? ; i lL._ COMMISSION AND UUOKEIIAQE. j^o 46. An agent bought coffee at |% brokerage, and received *a50. He afterwards sold the coffee at a profit to his principal of $5,160. after deducting IJo^ commission on the amount for which it was sold. How much was his commission ? 47. I received from Day & Son, of Chicago, a ship load corn, which I sold for 60c. per bushel, on a commission ot 4/o ; and, by the shipper's instructions, invested the net proceeds in barley, at 75c. per bushel, charging 5 % for J)uying; my total commission was $1,350. How many bushe s of corn did Day & Son ship, and how many bushels of barley should they receive ? 48. A Buffalo brewer remitted $21,600 to a Toronto commission merchant, with instructions to invest 40 % of It m barley, and the remainder, less all charges, in hops. The agent paid 60c. per bushel for barley, and 20c. per pound for hops, charging 2 °^ for buying the barley, 3 "Z for buying the hops, and 5 % for guaranteeing the quality of each purchase. If his incidental charges were $187.60 what quantity of each product did he buy, and what was the amount of his commission ? 49 A Toronto factor received from Cincinatti a consign- ment of corn, which he sold at .75c. per bushel, on a com- mission of 5%; and by instructions of the consignor invested the net proceeds in wool, at 20c. per pound charging 2 % for buying, and 8 % additional for guaranty ot quality. If the total amount of the agent's commission receitT?" ' "" *''''"' '°" "^"^ *^"^^^^^ '' ^^ -" of fsofii^T^^:! '^'°* ''"^' ^^ ^° ^^^'^"^t Purchase of 360 bales of cotton, averaging 480 lbs. each, bought at than fnv '''' ^ «^"^"^'««^on of ^ %. His charges, other than for commission, were : freight advanced, $lW 120 COMMISiJION AND BROKERAQE. What sum should cartage, $53.25, and insurancb, $18.75. I remit to pay the account ? 51. An agent sells a consignment of goods for $2,100. He pays $33.50 for freight, and, re.sorving his commission remits $2,02 1.77. Find the rate of his commission. 52. An agent sells 1,100 harrels of flour, at $4.50 a barrel, and charges 2^ % commission. He invests the pro- ceeds m steel, at l^c. a Ih., charging ^^% commis.sion. What 18 his entire commission, and how many tons of steel (2,240 lbs. to a ton) does he buy ? 53. A commission merduint has consigned to him 5,000 lbs. of cotton, which he sells at 14e. a lb , and charges'2 % commission. With the net proceeds he buys cotton cloth, at 10c. a yard, charging 1J% commission for buying. How many yards of cloth does he buy ? 54. A commission merchant has consigned to him 5,000 barrels of fiour, which he sells at $5.60 a barrel, and charges U% commission; the expenses for frei^dit etc amounted to S250. With the net proceeds he buys sugar.' at ()Jc. a lb., charging ^% commission for buying. How much sugar does he buy, and what is the araoun't of his commissions *? |i-^.- CUSTOM HOUSE liUSINESS. 121 CUSTOM HOUSE BUSINESS. 253. Duties or Customs ,.re taxes levied by tlie Dominion Government on imported gooda. for revenue purposes and for the protection of home industry. 253. Duties are of two kinds, ad valorem and specific. 254. An Ad Valorem Duty is a certain per cent assessed or levied on the actual cost of the goods in the country from which they are imported, as shown by th mcome. -^ .uT^' t ^^^"^^ ^"^y '' ^ *^^ ^«^^^^ef^ a* a certain sum per ton, foot, yard, gallon, or other weight or measure without reference to the value. ^^ No^rK.-Upon certain goods both specific and ad valorem duties are 25«. A Custom House is an office established by the Dominion Government for the transaction of business relating to duties, and for the entrance and clearance ol orf^T'i TT? °^ ^"^"^ ^'' P^'^"^" ^* ^h^«h custom houses are established ; and it is lawful to introduce merchandise into a country only at these places. of f P^"f '^.P^^y^"''^ '' ^ certificate given by the Collector lb H .t'' ' requirements of law have been complied with, that the vessel has been properly entered. 25». An Invoice or Manifest is a statement made by the seller or shipper, giving a description of the same howmg actual cost, or value of such merchandise; show^g also, marks, numbers, quantity, charges, and other details IfcJi Ml 122 cunTOM iiousi: nusiNKss. 2«0. All invoicoH aro made out in tlio weights and moaHuros of tho oouutry from which the importation is madti. !S<(I. All invoices of merchandisi' suhjoct to an ad valorom duty, are made out in the currency of the country from whieh the importfition is made. 2«a. 'Alien the value of the foreign currency is fixed hy law the viiJue is to he taken in estimating the duties ; when the value is not fixed by law, the invoice nmst be acompanied by a consular certificate showing its value. a«:i. A Tariff is a schedule of goods, and the rates of import duties imposed by law on the same. a«4. Tho Free List includes classes of goods that are exempt from duty. a«.Ti. Tonnage is a tax levied upon a vessel independent of its cargo, for the privilege of coming into a port of entry. 2««. Allowances are deductions made in estimating Specific ])utie8, and are distinguished as Leakage, Breakage, Draft, Tare, etc. 2«7. Leakage, determined by gauging, is an allowance for the waste of liquids imported in barrels or casks. 2«.S. Breakage is an allowance made for loss of liquids imported in bottles. 20f>. Draft is an allowance mode for waste or impurities. 370. Tare is an allowance made for the box, bag, crate, or other covering of the goods. 271. Gross weight is the weight before any allowances are made. 272. Net weight is the weight after all allowances are mndf. r, CUSTOM HOUSE /lUSINKSS. paid an. f„„,«„ n.o.i,.;,:;:: I J "a " ^ .'h tiz 974. All Appraiser i« an nffirnr of tho cn»l„i„. «,!,„ Q«...w.„. „;-::r-r:,i:x;';a:7.t"z;r'°'''' 2. In case goodH are warcliouHi.,!. tliat in oJaimA^ h, fv • transferred bv Dronor nntrv ♦, 7 ,' ""^''^^'^ I'y the importer and within thirty days. Tho Droc«nH-^,f f^ , , ' *"*'" ''>' ''»«''on are paid over to the Receiver G La anVtav/" '^'"''f ^'^'"^"«-' ownerBhip. general, and may be recovered by proving a7«. A Custom House Broker is a person who makes buBiueas. He usually acts uniler the power of a„ attorney' 277. To find Specific Duty. Solution. T si/ f', "". ^^^ = ^^°'^^"^'- = «^°«^ quantity. Less 5% for leakage = _450 gal. •^•''''^"Sal. = Net .jua.itity. 20c. X 8o50 = 81710.00 = Specific dntv. V^IJ' Hi 124 CUSTOM HOUSE BUSINESS. 278. To find Ad Valofem Duty. Solution. 601b. X 120 = 60001b. = Gross weight. 81b. X 120 = OfJOlb. = Tare. 50401b. = Net weight. 9c. X 5040 = 8453.60 = Net value. »453.60 X .40 = S181.44 = Duty EXERCISE 68. Find the specific duty — « IK^'f^" to lu"^' °^?^^^' ^*«h weighing 480 lb., at Uc a lb., tare 78 lb. per hhd. * 2. On 360 doz. bottles of porter, duty 50c. a doz breakage 10%. j a wa., 3 On 250 chests of tea. each 75 lb., invoiced at 15c. a lb., duty 3|c. a lb. 4. On 120 bags of coffee, gross weight 148 lb each allowing 8 % tare, at 3k. a Ih. ^' 5. On 60 packages of figs, each 16 lb. weight, at 2+c per lb., tare 5%. &>«'«' ^a^- 6. On 897.120 lb. of bituminous coal at 75c. per ton 7. On an importation of 200 boxes of plate glass, each box contannng 20 plates 24 x 48 in. in size, at 25^. per SQ, It, ■*• ane!„no!;;:rbX,°' "'""■ '' '' -'■ '-■■ ™ »"- C VSTOM HO USE B VHINES^. Find the ad valorem duty— 11. On 16 tons of steel, invoiced at 18c. per lb., at 25 o^ 12. On 175 boxes of raisins, 18 lb. per box, at 17 % ^l^. On 650 doz. kid gloves, invoiced at $6.50 a doz., at 14. On 600 gal. sperm oil, of 42 gal. each, invoiced at 45c. a gal., at W ; 3^ o^ being allowed for lekkage! 16. What is the duty at 40°^ on an invoice o( French jewellery, amounting to 8,560 francs ? 16. What is the duty on an invoice of books from Vienna the value of which was 6,429 florins, at 38 y^. ^ to m 2Tfi^l'V^' ^."oJ °^ "" ^"'"^^ °^ '^^'^' ^"^ountinp to 43.256 sterling at 27 % allowing $4,866* to a pound ? 18. Find the duty on an invoice of woollen cloths from Germany valued at 8,437 Keichmarks, at 45 o^. 19. Wliat is the duty on 1,000 yd. of brussels carpet 27 m^ wide, mvoiced at 6s. 9d. per yd. ; duty 44c. per sq yd specific, and 35 % ad valorem ? ^' ^ 20. An invoice of woollen cloth, imported from England was valued at ^956 6s. If its weight was 684 lb how vXemT ' '"*^' '' '"'- ''' ''■ '^''''^' ^* ^^ % a^ 21. I imported from the United States 7,240 bush of corn and 17^ tons of hay. invoiced at $9.50 per ton. What amount of duties had I to pay, at 15c. per bush on the corn and 20 o^ on the hay ? ^ $309 7?' m^"'.!?'"^' "" '° importation of satin, is $309.70. What 18 the invoice of the goods ? 28. How much dutv must be paid on an importation of ^7,640 lb. of wool ipvni'nor! af "1 ^"'' -n ■ i of duty 18 10c. per lb. specific, and 11 o^ ad valorem if the rate r' i ! 126 CUSTOM HOUSE BUSINESS. 24. What is the duty and total cost of 2,500 pieces bleached calico, 38 yd. each in length, and IJ yd. wide; price fid. per yd., duty 4c. per sq. yd., and expenses at Liverpool ^65 10s. ? What is the amount of a bill of exchange at $4.87 to the M to cover the cost ? 25. Find the duty on 50 cases of tobacco, each weighing 60 lb., and 50,000 Havanna cigars weighing 55 lb , invoiced at $75 per M., the duty being 50c. per lb. specific on the tobacco and $2.50 per lb. specific on the cigars, and 25 % ad valorem on both. 26. Paid $22.40 duty on 100 bbl. of sugar, each weighing 220 lb., invoice,d at 8c. a lb., tare 4 %. What was the rate ? 27. Kequired the duty and total cost of 1 case of French silks, value 3,500 francs, duty 50% ad valorem; lease velvets, value 28,000 francs, duty 50%, expenses, cartage, shipping, etc., 625 francs, and commission 2^ %. 28. A merchant imported 80 pieces three-ply carpet, 76 sq. yd. in a piece, and paid $2,691.84 duty, at 16c. per sq. yd., and 30 % ad valorem. What was the invoice price per yd., in sterling money ? 29. A merchant imported 300 pieces of three-ply carpet, each piece containing 76 sq. yd., invoiced at 8s. 6d. per sq. yd., upon which he paid a duty of 17c. per sq. yd. specific, and 35 % ad valorem. What was the total amount of duty paid ? 30. Oil 40 cases of tobacco, each weighing 66 lb., and 20,000 Havana cigprs, weighing 200 lb., invoiced at $46 perM., the duty on tobacco being $.80 per lb., and on cigars $2^ per lb. specific, and 40 % ad valorem. 81. Find the duty at 33 % ad valorem, on 1 case cf shawls valued at ^42 Ss., 1 case of linens at £37 IDs., duty 40 % ; (CUSTOM BOUSE BUSINESS. ^^7 1 case prints at ^8 5s dnfv 9n o/ ■ • , ^I5s., commission 2/%: oonsuiri' '7^'"''^^ '^P^»«^« total cost in Canadian'm^ney ? " ''" ""^^^ '' *^^ avemgkg tielbTl* ^•''' '""P^'*"^ ^^ «^«^« ^^ shawls was paid with a bill of 2h ^ u '^^^°''"^- ^^^ ^"^^^^e the dollar. wLt 1/^ .T ' ^'"^^* "* ^'^^ ^^^««b to cost, after pa^n^orr ctrt^'/".? "'^^ '^^^ *^« ^^-^^ t^ y ng otiier charges to the amount of $75.80 ? 128 INHUHdNCB. p ■■ I' i|; n INSURANCE. !;^79. Insurance is a contract by which one party engages for a stipulated consideration to make up a loss which another may sustain. It is distinguished as Property Insurance, Life Insurance, Accident Insurance, ann Health Insurance. tsHO* An Insurance Company i8 a company or corpor- ation which insures against loss or damage. 2SI. Insurance companies may be classified according to principles of organization as follows: — 1. Stock; 2. Mutual ; 3. Mixed, or Stock and Mutual. 383* A Stock Insurance Company is one in which the capital stock is owned by the members of the company called stockholders^ They alone share the profits and are liable for the losses. The business of a stock company is managed by directors chosen by the stockholders. 3H:<. a Mutual Insurance Company is one in which the persons insured receive a share or division of the profits. 384. Non-participating policies, the holders of wnich do not share in the profits or louses, are issued by certain mutual and mixed companies. JNSUHANCE. 2«5. A Mixed Insura nro n 3S6. The Insurer or Tr«^« ~s the ..,, „.. a^^LsTS S;;:f; P-'^ -^'' 3Sy. The Policy ia th^ „ ^ '^ " '"''■ agreement of contract between ZJ""" '" ""' ™««» a'Bount\-n8u*edkdeSkefv If '"''.'" °"' '° '"'"'='' tl>e 'f urance ia effected. H^seat™;"'" "' "=^ *™" "- store are insured in po,iSro7;i,t,td"'"' '°"'' '" " 2S». An Open PoJirw • insurances may be entereLfc Tnv T\ ""^''^ ^^^Hional at rates and under condLtnl^ri'^on^"^ ^'^^'^ ^^ '-'' a»0. The Premium is the amount paid for f h. • 2»1. An Insurance A^^n. • ^surance. one or more Insurance Comn«n,-^ ^''T ''^' ^^Presents soliciting business. collectz^Zr' ""'^ "'*' ^°^ *^«^ in 2»->. An In. ^P''"'^'^'^^'^^J"«ti«gloses.etc. *="— An Insurance Brok«»r ,00 insurance for a compensation caLd 17'°" ^^" '^''^' siOQ. *^ """^ mailed brokerage or commis- t !■-: 1»0 FIRE INSURANCE. FIRE INSURANCE. I ; SIKS. Fire Insurance refers to insurance against loss or damage by fire. Losses may be total or partial. 394. Fire Insurance Losses are usually adjusted by the insurance company paying the full amount of the loss, provided that such loss does not exceed the sum insured ; if the policy, however, contains the "average clause," the payment made is such proportion of the loss ab the amount of insurance bears to the total value of the property. 295. The Term of Insurance is the period of time for which the risk is taken, or the property insured. S90. Short Rates are certain rates of premium charged by the companies when the term of insurance is less than a year. 39*7. In case a policy is terminated at the request of the insured, he is charged the "short rate" premium; if, however, it be terminated at the option of the company, the lower long rate will be charged, and the company refund the pvemium for the unexpired time of the policy. 29S. To guard against fraud, property is not usually insured for its full value, and no more can be recovered than the amount of actual loss. The party insured must also have an interest in the property insured. 299. Dwelling-houses and permanent property, about the value of which opinions differ, and which deteriorate in time, may generally be insured for from one-half to three- fourths their estimated value ; goods in store, at their cash value. Insurance companies usually reserve the privilege of rebuilding, replacing, of repairing damaged property. for MAlilNE INSUMANGE 131 MARINE INSURANCE. 300. Marine insurance refpr.. ^ • <»OI. Inland or Tran r>,,. »""on. otmerchandisewhileWt" "^^"^ ""'"' to insurance 'OS- as .he 3„n! in^'^feZ-lT,; f ..1^^ "' "" 308. Policies nn r,, "'"^a'aeoftheveosei. voyage, and o'vessltfrv "■' "?"' '»' " -'■'»- a04. Salvage is7n 1. „ ''' " " ' '^''^^ ""- casualties. ^ ""^ "^'Koes from marine ance company as soon as LL' '''"'* ""*^^^ *^^ ^"«"r- or other advice of shipm nt har>'"'''l'' '^" °^ ^^d^^^^ open policy. ^^^P^^"*' that it may be entered on the 306. Goods at sea may ffenei-«nv i.« • to 25% more than their cost or ,W '"'''''^ ^'°^ ^°^ cover the expenses of freiX ^ ' ^"''' ^° ^^^^^ to profits. ^^*' msurance, aiid a share of the 307. To find the coQf «f • insured, and per cent o?p%°'i„'— «^:^^ amount EXAMPLE._A house nn^ if . "»^"*S S^Ven. Solution. ««.S00 X .015 = $127.60. Multiply the amount of inmranre by the rn, Prermum, and the product u,U be the ^^ZZ^' '^ m 'i I .- i I r 182 MARINE INSURANCE. IIOH, To find the amount insured, the premium, and the per cent, of premium being given. P;XA5iri-K.— I paid $170 to insure a stock of goods for one year at a premium of 2%. For what amount was the policy insured? Solution. 2 % of amount of poHcy = 8170 Jo/ i< «« _ 170 100% 170 X 100 = »8,500. Ana. t= $8,500. Ans. ,'. Amount of pohcy or $170 -r .02 RULE. Divide the premium by the rate per cent, of jyremium, and the quotient will be the amount insured. 30!K To find the rate per cent, of premium, the premium and the amount of insurance being given. Example.— I paid §85 premium on a house insured for $6,800. What was the rate per cent, of insurance ? Solution. Cost of insuring $6,800 is $85 „ 85 $1 $100 6S00 85 X 100 6800"" li%. Ans, = .0125, or 1J%. Ans. .'. Rate or .•585 -r $6,800 rule. Divide the premium, by the mm insured, and the quotient will be the rate. 3IO. To find the sum to be insured that will cover both premium and insurance, in case of loss, the value of the property and the rate being given. Example.— For wliat amount must property worth $7,600 be insured, at 5 %, so that in case of loss, both the premium and the value of the goods may bo recovered ? MARINE INSURANCE. 133 Solution. To realize »95 we must insure «100 (Sine. - . , . '• »7,C00 or 100 9-) 100 X 7000 95 = *«'000 Ana. 100% - 50^ = 1,50^ »7,G00 - .9.-, == s,^_(,00. Ans. RULE. an. To estimate proportionate losses. »««„«,. How ,„„.. .,.„:„ e.ch ctp!r;™„ ^ ""■ ^> «» <>, ,«,„ M.500 Ontario Hu,„.,. ''°''"""'- 1.500 Phcenix. ^2^ Western. »7,500 = Sum insured. »6,000 ^ 7,500 = .80 - n., , , 2,500 X .80 = J2 000 ~ J^*^ °* ^«- "" *!• Ex. 1.500 X .80 = iZz ^^^^"-^^f""'-,.-,. Mutual. «.^oo X .80 = ,,800 : :: ^tz: ^ . RULE, ^«iv of uarreiB oi apples, worth $2.10 ner hnvr^i wi . and *5 adai«;l°:th™h^Ve' t;e'';Xa\^''^^"'""' policy ? ^"^ P*'^ ^0^^ survey and - ^ .ea„. at .,., .na anfth^'t— If ^^ ill : 1^1: 186 MARINE INSURANCE. If'i'. ;: tion the face of the policy will he fall indemnity for both the property and premium. Find the value of the house. 22. A factory worth $45,000 is insured, with its contents, for $62,500; $30,000 of the insurance is on the building, $12,500 on machinery worth $20,000, and $20,000 on stock worth $35,000. A fire occurs by which the build- ing and the machinery are both damaged, eacli to the amount of $15,000, and the stock is entirely destroyed. How much is the claim against the company, if tlie risk is covered by an " ordinary " policy ? How much if the policy contains the " average clau>e ?" 23. A merchant, owning a store worth $12,000, and goods to the same amount, insures them both for two-thirds of their value, at the rate of 50<:. on $100, through a broker who allows him a discount of 10% on the premium and retams 5% himself. How much does the insurance cost the merchant, what does the broker get, and what is the net premium received by the company ? 24. Three companies insure, at f of its value, a building worth $16,000. The first company takes ^ the risk at | of 1 % ■ the second, f of it, at i of 1 % ; and the third, the remainder, at f of 1 %. Find t!:: total premium ? XAXl'.S. 187 TAXES. •>l^. A Tax is the sum as'itptjqorl nn t-u^ or income of u„ individuS for Jo !. i ^'''°"' ^'^P'^*^ the valuation, ,ut usuaU T 1:; rjt r:;^'^"'- »' many mills ,m tl. ^ "^ * '""' »■• "« »15. I'M.perty is of two kin,l»,-Real and Personal tLf:a1;et" ,t~ " "" ^''"^^ ""f"-'^" «" -'-ate ing^?e;t:eto7:?ir ' t:'™: Lm' t '"''^''"" -"«- -nieipality. and thevaZt o" to "p^::'""" ^^ property. person s taxable taxlf" "" -°"'''"" '' " P^™" ^»"«>'«'' 'o collect the 188 TAXES. 321. To find the tax, the sum assessed and the rate of taxation being: given. Example. — The rate of taxation in a certain city was llj mills on the dollar. What tax was paid by a person whose property was assessed for «12.000? BoiiDTION. On $1 the tax is .001125. .-. " $12,000 " .001126 X 12000 - «186. Ans. BVhE, Multiply the sum assessed by the rate of taxation, and the product will be the tax. 332. To find the rate of taxation, the sum assessed and the tax being given. ExAMPLK 1.— In a oertiiin village a sohool-house is to be built at a cost of $5,725, to be paid by a tax upon the assessed property valued at #229,000. What rate of taxation will oover the oost ? Solution. On »229,000 there is a tax of $5,725. •« ji i< t< 6,725 229,000 a 2j|o. Ani. RULE. Divide the property tax by the sum assessed, and the quotient is the rate of taxation. Example 2. — A tax of #16,230 is to be assessed upon the village of Caledonia ; the valuation of the taxable property is §800,000, and there are 115 polls, to be assessed at #2 each. What will be the tax on the dollar, and how maoh will be the tax of Mr. Scott, whose property is ndned at $12,500, and who pays for 2 polls ? SOLUTIOH. 19 X 116 s «230. . Amount of pol . f»x. #16,230 - #230 5= #16,000. " property tax. #16,000 -i- #800,000 = .02. . Rate of taxation. #12,500 X .02 = #250. . Mr. Scott's property tax. #260 + #4 (2 polls) = #254. . " total tax. 323. To find the sum assessed, the rate of taxation and the tax being given. J'^XAMPLB. — The ta.\ on a certain property was #96.10, and the rate of taxation 7| mills on the dollar. For how much was the property aBBcBBed 7 '). 4 'I TAXES. SoiiDTION, »0.00776 is the tax on «1 .00776 189 f96.10 BVU. 96.10 .00776 's •12,400. Ana. MUMS* Solution. Tonu8e»97 net, »iro . must be Wied. 100 — - - " ™' °f ''-"er. It the agenfe com- mission IS 8%, delivery cl.arKes |6.80, and 5% charge i. iTounl'": 2;r*'n°' '™'"^ '° P-chasers/howTan; ermt::n':r:;iowedT" '"'' "^^ ^°"'' ^-^ "^ ™«' Mc, and 1,120 bushels of barley, at $1.78. Eequire.i charl $ 79 R^ ' ^^\''7«^'^«^«" being 2|o^, and the flour foi the consiguor, charging a commission of li°/ How mucli was still due the consignor ? ' ^" 8. An agent bought butter on a commission of 10°/ cheese on a commission of 6°/ and Paa« .« • V°' of 6°/ Tf h,-c « • / ^^^ °° * commiss on or & /o. If his commission for buying the butter was ^-n for buy, ,,, ^,^,^^^ ^^^^^^ ^^^ L' uying tt el i22 ness oV.."'" 25% additional for guaranteeing thTvtt ness of the eggs, what sum should the principal remTf t pay for purchases and charges ? P^^^^^Pal i emit to Bignmtrtht'"* ""' '" ''^ '''''' ^° N^^ Orleans a con- s gnment, the gross proceeds of which were S7 r.«q fi? ' charges being |323.50. and the commilstn \fr He •l-ected the agent to buy .sugar with the net proceeds and pay himself his commission for buying f2Ao7)Turnffh same. Whnf wna fK^ j. • -^ » '■^J/oJ out of the . .^"'^* ^^8 t»e amount luveated, and thp Ar^-nf. commission for both transactions ? ^'"^ ' 146 MISCELLANEOUS. I! i 10. Ad agent sold 2,000 bushels Alsike clover seed, at ^7.85 per bushel, on a commission of 5%; and 1200 bushels medium red, at $5.20 per bushel, on a commission of 2i%; taking the purchaser's 3 month's note for the amount of the sales. If the agent charges 4% for his guaranty of the notes, what amount does he 'larn by the transaction ? III. 1. A consignment of butter was sold for $1,570, of which $1,546.45 were the net proceeds. What was the rate per cent, of commission ? 2. An Australian buyer shipped 33,000 lbs. of coarse wool to a London agent to be sold on commission, and gave instructions for the net proceeds to be invested in ieather If the agent sold the wool at 18c. per 1'.., on a commission of 2% and charged 10% for the purchase and guaranty of grade of the leather, what was the amount of his com- missions ? 8. What are the net proceeds from the sale of 2 250 bbls of flour, at $6.25 a bbl., if the charges for freight and storage be 50c. a bbl., commission for selling 2% for guaranteeing paying 1^%? . ' 4. An agent sold, on commission, 1,750 bbls. of mesa- pork, at $16.50 per bbl., and 508 bbls. of short-ribs at $18 per bbl., charging $112.50 for cartage, and $6 55 for advertising. He then remitted to his principal $36 000 the net proceeds. Find the rate of commission. ' ' 6. A commission merchant received $1,640 with which to buy corn, after deducting a commission of 2^ %. What is the amount of his commission, and how many bushels of corn, at 62^c. a bushel, can he buy ? MISCELLANEOUS. ' , ,„ .n agen for collecfon, agredu,. tlmt, for .very .loilar sent lie agent succeeded in collecting but nv of the d„ht How much did the agent remit, hoi much com „it on dM he receive, and what wa» hi» per cent, of commissior? oarpetlritllt '"'1' "'T"^'' "" ''«^"'' ^«» -V- of mission, the freiglit amounted to S7.37 At wli-,f ™;„« pei^ard .ust the carpeting be so J to Lit Ip^^fTf in thLrar'-*"!'"^'" """'""' ''^''" '» ^« "vested m wheat, allowing him a commission of S'A for investing me uTs' "f fr "" ''"'•'^' "" ">« "'-'*• --i «" S^d months fh " . r; '"™"' '""^ ''°™8«. At the end of 4 months the agent sold the wheat at $1.10 per bushel on a commission of 6%. If I pa.d $850 for' he use of the money, did I gam or lose by the operation, and how much" for st^iT'T:?'™ "''I^*"' =""' " """"gnment of cotton ch»,;f:, .P*^' *" '•"■ ''•^'«'" *-d storage, and chaiges a commission of 2} %. What are the net proceeds ? 96r« of thrl r°'"'%°' * °°»=i«»'»»' of wheat was the r«tf J ■'«'.P';o<^eeds of a consignment of oats, and ne nrr /""Tr ™ '^'' ™' ^*^- ^he sum of the Xch $ 75 mT'- °"'^*''»'' commission, was $380, of How m, 1 ™l*"8''' '" *>"« consignment of wheat. oats? commission on the consignment of IV. each, and 6 dozen watches, invoiced at $85 each it the ad vabr^em dnty was B,% on the olocUs^ndt'^ o'n^he 14.3 MISCELLANEOUS. ^4^1 7 .°IT ^""^ '""^''^'^ ^ '^'^' °^ ^in«. and paid $482 du y, at $2 per gallon, leakage 10°^ allowed. How many gallons to each cask, had no leakage been allowed ? J-J'''^ f^^/^'^y o^ SoodB which had leen damaged; a^owance for damage is 24 o^, and tl.e duty was L/. What was the invoice price of the goods ? 4. An importer paid $825 duty on an invoice of silks, the duty being 24 o^. But damages of 15 o^ were allowed a the custom-house. What was the entire cost of the goods ? 4«o' IK '"^l' '"^i"'" ^""P^'*' ^^ ^^^«- °f «"8ar weighing llV .w^? .^^^ l^hds. of molasses containing 63 gals. each. What is the amount of the duties, if the sugar pay 3c. a lb. and the molasses 8c. a gal., an allow- rolLse?/ '° *^' '"^'' '^ '^°^' ""^ 2°^ °" *he 6 A liquor dealer receives an invoice of 120 dozen bottles of porter, rated at $1.25 per dozen. If 2 % of the bottles are found broken, what will be the duty at 24 % ? 7. A merchant imported 56 casks of wine, each contain- ing 36 gals. net. the duty at 80°^ amounting to $907 20 At what price per gallon was the wine invoiced ? ^'^!!1 "^"'^ ""^ ^° '"'''^^"^ °^ ^'e°«^ lace goods at 24 s^ was $132. an allowance of 12°^ having been made at the custom-house for damage received since the goods were shipped. What was the cost or invoice of the goods ? «i^o«n ?r"*'*/ ""^ ^"'^'°"^^' ^"^oiced at $1,654. co^ me J1,J80.50 m store, after paying the duties and $12.24 for treight. What was the rate of duty ? 10. A merchant imported 50 casks of port wine, each containing originally 36 gals., invoiced at $2.50 per gal He paid freight at $1.30 per cask, and duty at 30 s^ U""• i« $214 50 Af '^ ■' ™'*' " '*°^' ^"^'"8 " P^^'"'"'" »f profiVo, 20% .'""■ "'■" ""' "' '"' '"^ «»- *» """- » tataTlonnO ;rr,"''/"'"" i. at J of IS, « second takes $10 000, al } of 1 o/ ; a third, $13,000, at J of 1 « . a fourth, the remainder, at i of 1 -^ How much i. paii lor insurance ? *^ VII. 1 A town containing $541,->50 taxable real estate and 115 620 personal property, levies a tax of .009 ^z. if 2 0/ i^ 'he tax?''""'"'' "''* " *'' "'' ^"°""' '^^"-^ ^-- 2. In- a school section the valuation of the taxable pi^peity IB $752,400, nnd it is proposed to repair the school-house and ornament the grounds at an expense of 15 000. If old material sells for $673.70, what will be the rate per cent, of taxation, and what will be B's tax, whose property was valued at $9,400 ? 3 A tax of $11466, besides the cost of collecting at 2i %, 18 to be raised m a certain town. The polls, 660 in $1 270 000'^ '?H ^' "^'•, ^'^ '''' '^'^'^ ^'---'^ at $1,^70 000, and the personal property at $130,000 Deter- mine the rate, make an assessors' table for that rate, and nnd A R t,n,x fnr 9 do!]- tft.? ona ----,1 L ■ , - '•'"'""« , i'"""» -?^,uua lual estate, and |ii,40i3 per- sonal property ? v , va per 162 MISCELLANEOUS. 4. The cost of maintaining the public schools of a city during the year 1888, was $112,000, and the taxable property of the city was $44,800,000. How many mills on a dollar must be assessed for school purposes ? If 10 % of the tax assessed cannot be collected, how many mills on a dollar must then be assessed ? 5. The total assessed value of a town, real and personal, is $630,000, and the town expenses are $3,918.95. How much tax must be collected to provide for town expenses and allow b% for collecting? If the same town contains 810 polls, taxed $1.60 each, what vnll be the rate of taxation, and how much will be the tax of a man who pays for two polls and owns property assessed at $14,500 ? 6. A tax of $13,943.20 is assessed upon a town contain- ing 860 taxable polls; the real estate is valued at $2,708,000, and the personal property at $151,600 If the polls be taxed $1.26 each, what will be the rate of property taxation, and what will be the tax of Peter Parley, who pays for three polls, and has real and personal estate valued at $28,760 ? 7. The assessed value of a town is, on real estate, $1,197,500, and on personal property, $432,500. A poll tax of $.50 per head is assessed on each of 1,870 persons. The town votes to raise $8,000 for schools, $1 500 for highways, '^,500 for salaries, $1,000 lor support of poor, and $810 for contingent expenses. How much tax will a milling company have to pay on a mill valued at $46 500 and stock at $19,750? ' ' IIS IEEE ST. 153 INTEREST. 33tf. Interest ia money paid for the ..ae of money. 337. The Principal is the money for the use of which interest is paid. 33^. The Amount is the sum of the principal and interest. 3SO. The Rate is the per cent, of the principal paid for its use for 1 year, or a specified time. Note.— When the rate is given, it is to be understood in this work to mean rate per annum, unless otherwise specified. 330. Legal Interest is the rate fixed by law for cases in which no rate is specified in the agreement between the parties interested. In all the Provinces of Canada the legal rate is 6 %. 331. Usury is a higher rate than the legal rate. 332. In computing interest, a legal year is 12 months or 865 days. 333. Simple Interest is the interest on the principal only. ; 154 ACCURATE INTEREST. U i rf If- ACCURATE INTEREST, (12 months or 365 days to a year). 334. To find the interest on a sum of money for a given number of years, or fraction of a year, at a given rate. Ekample 1,— Find the interest on S650 for 2 years at 4 %. Solution 1 650 Principal •04 $26.00 Int. for 1 yr. 2 »62.00 " 2 yra. Solution 2. 16.50 is int. fgr 1 yr. 4 at 1% $26.00 «• •' <• a 4% 2 $52.00 " •• 2yrs. " 4%. Explanation. Interest for 1 year is 4% of the principal $C50 = $650 x .04 » *2(j.00, and the interest for 2 years is twice the interest for 1 year, or $26.00 X 2 = $52.00. Solution 3. $6.50 8 = 4x8 $52.00 Example 2.— Find the interest on $960 for 3 yrs. 4 mos., at 6%. Solution 1. Solution 2. ' Solution 3. -^6 6 $67.60 Int. for 1 yr. <>57.60 3i ^ $9.60 20 = 6 X 8J. •192.00 $192.00 •' " 3Jyr8.(3 yrs. 4 mos.) $192:00 Note 1-1 % of a number is found by removing the decimal point in the number, 2 places to the left. 2. The result will be the same in J .,:. 1, whether we multiply by 4 and then by 2, as in Solution 2, or by 8 (4 x 2), as in Solution 8. EXERCISE 72. Find the interest for one year of— $450 at 4i %. 6. $2,630 at 4^ %. $680 at 3 J %. 7. $4,920 at 5 %. 8. $5,000 at H% %. 9. $3,720 at ;}J %. 5. $1,720 at Ci%. 10. $4,080 at 44%. 1. 2. 8. $900at7i%. 4. $840 at 5 J %. H. $7,428 at 6* %. 12. $9,654 at 6 '%. 13. $7,851 at 6 J %. 14. $9,643 at 7%. 16. $5,430 at 6%. ACCURATE INTEREST. S'ind the interest and amount— TIMB. 2yr8. 2yr8. 6mo8. 5 yrs. Syrs. 3moB. 6 yrs. 7 yrs. 2 yrs. lOraoB. Syra. Omos. 4 yrs. 6mo8. 3 yrs. 8moa. 1 yr. 7 mos. 2 yrs. 4 mos. 6 yrs. Syrs. 2 mos. lyr. llmoa. 1 yr. 9 mos. 2 yrs 7 mos. 3 yrs. fJmoa. Syrs. 4 mos. Syrs. 7 mos. 6 yrs. 3mo8. 2 yrs. .")mos. 4 yrs. Gmos. 1 yr. 3 root!. 6 yrs. 2 yrs. 3J yrs. 4i yrs. a^yrs. H yra. 15& PBINCIPAL. hATH, 16. «600.00, 5%, 17. $700.00, 6%,' 18. $500.00, 7%,' 19. $950.00, p •', 20. «800.00, 9^' 21. $740.00. 8}% 22. $.1,320.00, 10%, 23. $960.60, 12°^, 24. $475.80, 6J%, 26. »3(j3.20, 2i%, 26. $1,020.00, 3|%, 27. $4,075.00, 6%', 28. $4,028.75, 4%,' 29. $4,026.00, 8%, 30. $270.36, 3J%.' 81. $840.00, 9%, 32. $100.00, 6%i 88. $900.00, 5%,' 84. $360 00, 7%i 35. $750.80, 4%, 86. $475.30, 3%,' 87. $328.00, 6J%* 88. 1474.90, 8J%,' 80. $640.80, 5J%, 40. $143.33, sjo^, 41. $360.96, 12%, 42; $796.00, 11%,' 48. $1,800.00, 13%,' 44. $1,080.00, 10%, 46. $894.00, 4i%, „,,,„. »85. To find the interest on a sum of monev for a given number of days, at a given rate. ExAMPiE l._Find the interest on $850 for 62 uays at 5 % bOLDTION 1. ' $8.50 . o Solution 2. «:ro"cn T i. * . CANCELLATION METHOD. $42.50 Int. for lyr. 8.60 x ? x 62 52700 62 866 ) 2635.00 ( $7 21 m 78 73 87.22. $7 72. 166 ACCUMATE INTEUEHI. ExPLA?rATrON. Sixty-two days is ^ of 1 year. The interest for 62 days is therefore ^ of the interest for 1 year, and this may be found by multiplying the interest for 1 year ($42.60) by 62 and dividing the result by 865, as in Solution 1, or by cancellation, as m Solution 2. Example 2. -Find the interest on »3,260 from April 16th. 1889, to June 18th, 1891, at 6 % per annum. (From April 16th, '89, to June 18th, '91, is 2 years and 63 days.) Solution 1. Solution 2. 32.50 X 6 X ^ == 33.66 Int. for 63 d». 354.50 X 6 X 2 = 390.00 " 2 yrs. »423.66 - ..yrs. 63 da »32.50 6 $195.00 2^ $423.66. Sa«. It is thp custom with banks when the time is given in months, to consider them calendar months in reference to the maturity of the paper, but even then they compute the discount by days. Time table, showing the number of days : From ant Day op To THE COBREBPONDINQ DAY Oi 1 Jan. 2 Feb. 3 Mar. 4 Apr. 5 May 6 June 7 July 8 Aug. 212 181 153 122 92 01 31 365 334 304 273 248 9 Sept. 243 212 184 153 123 92 62 31 365 a'J5 304 274 10 Oct. 273 242 214 183 158 122 92 61 30 865 334 804 11 Nov. 304 273 245 214 184 153 123 92 61 81 865 835 12 Deo. 884 303 275 244 214 183 153 122 91 61 30 see January ... Pobrnary... Max -in ...... April.. May 865 334 3>J6 275 245 214 184 153 122 99 61 31 31 365 337 306 276 245 215 184 153 123 92 62 59 28 305 334 ;«4 273 243 212 181 151 120 90 90 69 31 365 335 304 274 213 212 182 151 121 120 89 61 30 365 a34 mi 273 242 212 181 151 151 120 92 61 31 365 335 .304 273 243 212 182 181 1.50 122 91 61 ;m 3(')5 334 303 273 242 212 June July August September. October .... November . December. 1 1- How many days from May 13th to August 23rd ? EXPL.VNATION. Find " May in the column of montlis at the left ; and on the same line n.nder " August " find 92, which is the number of days from any dav in May to the same day in August. But August 23 is 10 days more than august 13, and 92 + 10 = 102 days. Ans. ACCURATE INTEREST. m Nora l.-If the required date be earlier in the month than the date from which time is counted, subtract the difference from the tabular number. 2. If in Leap Year, and the month of February be included in the time reckoned, add 1 day to the number of days found by the table. EXERCISE 73. Find interest on — PBIMCIPAL. X. »3.600, 2. »4,500, 3. $800, 4. »760, 6. W,S60, 6. $4,350, TIME. 65 da., 80 da., 90 da., 45 da.. 135 da.. 219 da., BATK. 5%. 7%. 8%. 6%. 3i%. PRINCIPAL. 7. $340.80, 8. $424.40, 9. $62.5.30, 10. $426.50, 11. «370.75, 12. $420.80, TISIB. 130 da.. 67 da., 48 da., 292 da., 73 da., 60 da.. BATE. 6%. Si%. 4%. 7%. 8%. Find the amount — PBINCIPAIi. 18. $542.00, 14. $684.00, 16. $960 00, 16. $1,100.00, 17. $1,186.20, 18. $1,260.48, 19. $1,040.25, 20. $1,097.76, 21. $976.80, 22. $896.84, 23. $1,272.24, 24. $1,284.96, 25. $1,200.00, 26. $989.00, BATB. 7%, «%, 9%, 10%, 11%, 12%, S%, 6%, 7%, 9%, 10%, 12%, 11%. 12%. TIME. From 1888, Oct. 27, to 1890, May 12. " 1887, Sept. 19, to 1889, June 1. •• 1882, Dec. 31, to 1892, Oct 1. " 1889, Jan. 1, to 1892, Deo. 20. " 1885, April 1, to 1886, July 28. " 1888, Aug. 31, to 1893,' Nov. 1. " 1890, Feb. 20, to 1891, May 10. " 1885, Mar. 15, to 1885, Jan. 16. *• IPPU June 19, to 1889, April 7. " 1887, Nov. 24, to 1887, Nov. 30. " 1891, Sept. 27, to 1892, Dec. 9. '• 1890, Dec. 8, to 1891, May 1. " 1888, Dec. 25, to 1890, May 28. " 1889, Mar. 21, to 189C June 30. 27. A note for $560.60, dated May 6th. 1881, was paid Dec. 3l8t, 1882, with interest at 7 %. What was the amount ? 28. If I have the use of $275 for 4 years 10 months from Jan. 12th, 1883, what aaonnt must I return to the owner, allowing 6 % interest, and what will be the date of maturity ? ■<-:l ''i V.^.l 158 AUCUBATE Uli'EREST. 29. Required the amount of $408.60 from Aug. 20th to Dec. 18th, 1886, at 10 % ? 30. What ip the interest on a note for $515.62, rln,ted March 1st, 1883, and payable July JOth, 1885, iit 7% ? 31. What is the value of a note of $65.76, due with interest for 1 year 2 months, at 6J%? 32. li a person borrow $875 at 6 %, what will be due the lender at the end ^1' 2 yep.rs 6 months ? 33. A man sold bis bou ifc and lot for $12,600 ; the terms were, $4,000 in cash on (■ tj'ivery,, $3,500 in 9 months, $2,600 in 1 year 6 months, aid the balance in 2 years 4 months, with 6% interest. What was the whole amount paid ? {I! SIX FEB CENT. METHOD. f.cy SIX PER CENT. METHOD. »37. The Six Per Cent. Method is formed on 9 basis of 360 days to the year and 30 days to the mouth. aHH. At 6% per annum the interest of $i. For 1 yr. 12 mo., or 860 da., is 6c. = .06 of the principal, lor^yr. 2 mo., or 60 cla., is Ic. = .01 of the principal. For ^jyr. 1 mo., or 30 da., is 5m. = .005 of the principal For ^ mo., or 6 da., is Im. = .001 of the principal. For ^ mo., or 1 da., is Jm. = .000 J of the principal. Hence the following — PBINCIPI.ES. »»». i. The interest of Si at 6% is half as many cents as there are months in the given time. 2. The interest of $1 at 6% is one-sixth as many mills as there are days in the given time. 8. The interest for 60 days at 6% is found by removing the decimal point two places to the lejt in the principal. 4. The interest for 30 days at 6% is found by removing the decimal point two places to the left in the principal and dividing the result by 2. 6. The interest for 6 days at 6% is found by removing the decimal point 3 places to left in the principal. 6. The interest for 1 day at 6% is found by removing the decimal point 8 places to right in the principal and dividing the result by 6. S40. To find the interest for anv number -' months j days '% 7o. 160 SIX PER CENT. METHOD. ExAMPLB 1.— What iB the interest on 8460.7u for 1 yr. 3 moa. 21 dft. ate %? Solution 1. Int. on SI for 15 moa. = $.075. (Principle 1) " ' U " 21 " s .0035. (Principle 2) Int. on $1 for 1 yr. 3 moa. 21 da. = $.0786. /.Int. on $450.75 for 1 yr. 3 moa. 21 da. = $450.76 x .0785 = $35. 383876 Solution 2. 1 yr. 3 moa. 21 da. = 471 da. $4.5075 = Int. for 60 da. «31.5525 2.25375 = 1.126875 = .45075 = 420 30 15 6 $35.383875 = Int. for 471 da. (Prinoiplo 3) (60 X 7) (60 -f 2) (30 -f- 2) (Principle 6) Shorter Phocesb. $4.608 $31,556 2.254 1.127 .451 935.388 Note 1.— For buaineaa parpoaea it ia BufiSoiently exact to carry the work to mills, as in the shorter proceaa. 2, In this process when the decimal in the fourth places is less than 6 it is rejected ; when 5 or greater than 6, the figure in the third decimal place is increased by one, and the decimals to the right of the third decimal place are rejected. 341. To find the interest at any other rate than 6% by . this method, first find the interest at 6 %, and then increase or diminish the result by as many sixths as the given rate is wiits greater or less than 6 %. Thus, for 7 % add ^, for 8% add I- or \,for 4 % subtract f or -J, etc. EXERCISE 74. Find the interest at 6 % 1. $267.27 for 6 mo. 24 da. 2. $146.18 for 1 yr. 21 da. 3. $256.84 for 2 yr. 4 mo. 12 da. 4. $697.25 for 7 mo, 18 da. 6. $418.75 for 1 mo. 2o da. 6. $809.18for 2yr. 24da. 7. $38.90 for 1 yr. 1 mo. 6da. 8. $146.48 for 9 mo. 10 da. 9. $275.50 for 11 mo. 13 da. 10. $1,298 for 3 yr. 1 mo. 27 da. 11. $2,000 for 2 yr. 7 mo. 24 da. of— 12. $4,010 for 1 yr. 1 mo. 13 da. 13. $680 for 2 yr. 6 mo. 10 da. 14. $1,885 for 1 yr 7 mo. 7 da. 15. $468 for Syr. 6 mo. 1 da. 16. $1,000 for 11 yr. Imo. 20 da. 17. $645 for 4 yr. 4 mo. 6 da. 18. $500 for 3 yr. 1 mo. 27 da. 19. $895 for 5 yr. 11 mo. 11 da. 20. $1650 for 1 yr. 10 mo. 23 da. 21. $1,463 for 9 yr. 1 mo. 9 da. 22. $365 for 4 yr. 1 mo. 25 da. m* l». S SIX PER CENT. METHOD. Find the interest and amount — 161 PRINCIPAL. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 84. $1,080.50, »420.'25, «960.0O, »r)76.48, $645.00, $1,200.00, $1,200.00, $828.00, $972.36, $600.60, $1,165.17, $894.00, BATE 7%, 8%, 9%, 10%, 12%, 5%, 10%. 6%, 8%, 10%, 12%, 7%, TIME. 1 yr. 9 mo. 2yr. 9 mo. 3 yr. 4 mo, 3yr. 6 mo. 5 yr. 10 mo. 6 yr. 8 mo. 12 yr. 6 mo. 8 mo. 16 da. 17 mo. 18da. 23 mo. 14 da. 40 mo. 6 da. 14 mo. 17 da. PRINCIPAI, 35. $1,248.00, 36. $740.00, 37. $960.00, 38. $1,296,00, 39. $1,080.00, 40. $1,800.00, 41. $600.00, 42. $796.00, 43. $976.28, 44. $869.44, 45. $1,126.56, 46. $1,295.28. RATE 9%, 0%, 7%, 8%. 9%, 10%, 11%. 12%, 7%, 9%, 11%. 8%, Tina. 9 mo. 25 da. 1 yr. 9 mo. 15 da. 1 yr. 9 mo. 24 da. 2 yr. 3 mo. 9 da. 2yr. 9mo. 21da. 3yr.6mo. 16 da. 4 yr. 7 mo. 18 da. 5yr. lOmo. 6da. 7 yr. 9 mo. 27 da. 8yr.4mo. 17 da. 10 y.- 5 mo. 1 da. 13 yr. 4 mo. 29 da. 842. To find the interest for any number of days at 6^^ Example l.-Find the interest on $672 for 216 days at 6 %. Solution 1. $6. 72 = Int. tor 6 da. (Principles) $20.16 = '• 180 " " (60 X 3) 3.36 = .672 = 30 6 $24,192 = Int. tor 216 da. Solution 2. $672 ■036 4032 2016 •24.192. (60 4- 2) (Principl3 6) Explanation. By Principle 2, the interest on $1 tor 216 days = 36 mills = $.0.S6. .-. Interest on $672 tor 216 days = $672 x .036 -= $24,192. $2 Solution 8. . J"n! * J. ° ^-"^ = ^°*- *°'' 1 •'''• 'Principle 6) .-. $.112 X 216 = $24,192 = '. 216 da. Example 2.-Find the interest on $760.48 tor 174 days at 6 %. Solution. a ^ Shorter PRooKSi. f^('0 « . = Int. tor 60 da. (Principle 3) 7.005 180 " (60 X 3) .76048 II $22.05392 = Int. tor 174 da g " {Principle 5) 22.815 .760 $22,055. m « *• 162 SIX PER. CENT .VV'./ivrv EXERVi$E 711. Find the interest on- 1. »l,750.00, 2. *1,125.00, 8. 4. 6. 6. 7. 8. 9. 10. n. 12. 13. 14. »742.50, «900.00, $660.00, 8136.42, fl.OOO.OO, »2,000.00, 8351.00, »1,368.00, 893.00, 8550.00, 8842.50, 8800,00. 15. 81,725.00, 16- $125.00, 17. 83,741.85, for for for for for for for for for for 15 days, 24 days, 30 days, 95 days, 63 days, 33 d:iyp, 21 .I'lys, 12 C " B, 40 diys, ■ days, for 1 it days, for 75 d lya, 45 days, 27 days, 57 days, 55 days, 6 days, at (i%. at 7%. at 6 %. at7J%. at 8%. at 9%. at 10%. at 5%. at 1J%. at 3%. for for for for for at at at at at at at 6%. 7%. 6%. r.%. 9%. «%. 7%. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 84. 85,178.00, 8732.00, 81,174.51, 8340.00, 81,478.00, 82 150.00, 81,200.00, $1,500.00, 8420.00, 8360.00, 82,347.50, 81,11^.1'^, 81,300.00, 817,000.00. $195.50, 81,050.00, 81,560.00, for 9 days, at for 11 days, at for ' " V for 70 days, at for 80 dayp, at for 96 days, at for 53 days, at for 87 days, at for 41 days, at for 81 days, at for 18 days, at for 25 days, at for 13 days, at for 3 days, at for 33 lays, at fir 43 days, at for 44 days, at 9%. 6%. %. 10%. 6 %. 4i%. 6%. 7%. 6%. 6%. 7%. 8%. 6%. Bi%. 10 Vb. 7%. 7i% Find the interest in- PBINCU'AL 85. $36.61, 36. 850.00, 87. 897.86, 38. 8325.28, 89. 8154.75, 40. 8861.50, FBOM Nov. 11, 1891, Sept. 4, 1890, May 17, 1886, June 20, 1883, April 10, 1888. June 3, 1889, TO Deo. Jan. Dec. Sept. Nov. 15, 1893, 1, 1892, 90. 1803, 4, 1884, 24, 1888, Find the amount of- 41. 8450.80, 42. $1,500.00, 4a. 8127.36, March 6, 1893, May 5, 1894, Deo. 12. 1889, Marcr '5, 1890, T'oo 20, 1893, Jar. 20, 18C3, July 3. 1891, lUTK. 6%. H%. 7%. 8%. 6%. 6%. •5%. 4%. *^%. ACCURATE INTEREST. 168 ACCURATE INTEREST. (12 months or 365 days to a year.) 843. Since interest in Canada is reckoned upon a basis of 365 days to a year, the interest found by the " Six Per Cent. Method," which is based upon the supposition that 860 days make a year and 80 days a month, is not strictly accurate. 344. Since the year contains 366 days, the interest, found by the Six Per Gent. Method for 360 days to the year, is ^ or -^ part of itself too large. 345. In many States of the American Union interest is reckoned on the basis of 860 days to the year, and many people m Canada still reckon the interest on small amounts on this basis. 346. On account of the shortness of the Six Per Cent. Method, many accountants prefer to reckon interest by this me+hod, and to then make the necessary deduction of Jkr of 3lf. ^ BxiMPM— Find the accurate interest on $750 for 90 days at 8 %. Solution. *7.50 = Int. for 60 da. at 6 %. 3.75 75 30 6 (112.00 400 916.01' •16.00 ^ It 96 6%. " 96 " 8%. Art. 341. ift of »16.00 = »15.78. Aoouiate interest. EXERCISE 76. Find the interest at 6 % on— 1. »2,o00 for 75 days 2. 9750 for 48 days. 4. 94,626 for 47 days. 6. 98,360 for 78 days. 6. 94,780 lor 51 dayg. 7. 93,654 for 43 days. 8. 99,876 for 158 d»ys. 164 ACC URATE INTEREST. Find the interest and amount of — 9. »85000 10. $945.50 11. $378.08 12. »354.75 13. ?.->10.00 14. 9r,i-,.Q0 15. «450,00 IG. 8120.00 17. $353.00 for 63 days at 6 %. 18. «070.00 for for 33 days at 6 %. 19. 8785.00 for for 75 days at (J %. 20. 91,200.00 for for 130 days at G%. 21. 82,500.00 for for 03 days at 7%. 22. »1,935..50 for for 93 days at G %. 23. 82,136.88 for for 78 days at 5 %. 24. 81,000.00 for for 96 days at 7J %. 25. 82,000.00 for for 80 days at 10%. 26. 81,600.00 for Find the ijiterest of — PRINCIPAL. 27. 8450, 28. S720, 29. fOGO, 80. $540, 81. 8100, 82. 8900, 83. 8240, 84. 8333, 85. 8672, 86. 8G0, 87. 8000. 88. 8630, 89. 8480. 40. 8270, 41. 1386, From i< II n i< It TIME. Aug. 10 to Nov. 8, 1885, Jan. 25 to April 7, 1885, Feb. 3 to Mar. 19, 1884, April 8 to May 18, 1890, Jan. 30 to Mar. 6, 1892, Feb. 12 to Mar. 4, 1893, May 31 to Nov. 27, 189.5, Aug. 1 to Nov. 29, 1886, Feb. 28 to Oct. 25, 1880, June 19 to Nov. 10, 1881, July 4 to Oct. 20, 1889, Feb. 1 to Aug. 20, 1889, Jan. 21 to Dec. 2, 1891, May 10 to July 29, 1894, Oct. 13 to Deo. 12, 1895, 78 days at 5 %. 45 days at 7 %. 68 days ;it 5%. 93 days rt 8%. 75 days ;it 5%. 7ft days at 4%. 73 days at G >;{,. 146 days at 9 %. 219 days at 4^ %. lUTB. 6%. 7%. 8%. 9%. 4%. 7i%. 10%. 5%. H%. 12%. 3%. 5f%. 5%. 6%. 9%. 42. A person borrows $3,754.45, being the property of a minor who is 15 years 3 months old. He retains it until the owner is 21 years old. How much money will then be due at 6 % ? 43. A note for $710.50, with interest after 3 months at 7%, was given Jan. 1st, 1884, and paid Aug. 12th, 1886. What was the amount due ? 44. A speculator borrowed $9,675, at 6 %, April 15th, 1884, with which he purchased flour at $6.25 a barrel! May 10th. 1886, he sold the flour at $7f a barrel, cash! What did he gain by the transaction ? tat ACCURATE IN TK HE ST. 166 ^ 46 A man, engaged in business with a capital of |21 840 of i]I heal h he quit8 his business, and loans his money at b/tLTat / "^"^' '''' '' ''-' ^^ ' '-''' ' ^^"*^« 46 Bought 4.600 bushels of wheat at $1.12i a bushel payable m 6 months ; I immediately realized fo"r it $1 06 a bushel cash and put the money at interest at 10%. At the end of the 6 months I paid for the wheat. Did I gain or lose by the transaction, and how much ? befnT^iv^n.'^"'* *^' ^"""^^'' '^' '^'"' "'""' ^"^ '"^^^^^^ Solution 1 n.oo .04 .04 2i .09* 09J ) 44.80 _3 3 .28 ) 13440 ( 9480. Explanation. The interest on $1 for2yrR. 4 mos. at 4 % is $.0'.))^, therefore 844.80 must be the interest on as many dollars at^.ODJ is con- tained in 144.80 or $480. Ana. Explanation. The interest each year = 4 % of the principal, and for 2J years = 4% x 2J = 9i%ofthe principal, and therefore yj% of the principal = $44.80. days at'^sT" '"" ^'^ ""''* '""^ "' '""""' " *'' '' *^^ *°*^^^^* '^' ^6 Solution 2. 4% X 2i = <)i% 9i % of the principal = §44.80 .". the principal = 44 80 x = $480. 100 Solution. ^ , 5% X 3^^= 1^% 1^^ % of the principal = i^rym :. the principal ::= $45.60 x — ^ = $4,380. It^s EXPLA.NAT- ).\. Interest for each year = 5 % of the principal, and for TCdays = 5% X aV'ff = ItIj of the prin- cipal and therefore l^ % of the principal = #45.60. liULE;. Divide the ifiven interest by the interest on Bl th time and rate rth s given 166 ACCURATE INTEREST. • ^ li'i ' EXERCISE 77. Find the principal — RATE. TIME. INTEBK9T. BATB. TIMH. DITBRE8T. 1. 3i%, 1 yr., $45J. 7.6%, 7yra., $29.76. 2. 5i%, 1 " $41J. 8- 3J%, 4i " $94.50. 3. 4i%, i '• $25*. 9- 4%, 1|'« $68.25. 4. 3|%. i " $3f. 10. 4J%, ij.. 547.25. 5. 8< yo, i " $18. 11. 6 %, 5S " $170.00. 6. 2J%, 6 " $52*. 12. 3J%, 4|» $136.00. Find the principal — / INTEREST. B&TB. TIMH. 18. «42.70, 7%. From Jan. 1, 1886, to Sept. 1, 1887. 14. »197.80, 8%, 11 Jan. ] , 1887, to July 12, 1889. 16. $26.08, 6%, M Jan. 1, 1888, to Sept. 9, 1390. 16. e60.75, s%, (( Jan. 1, 1890, to Oct. 10, 1891. 17. $987.75, 9%, M Jan. 1, 1890, to -July 1, 1891. 18. $366.32, 10%, (t Jan. 1, 1888, to Oct. 18, 1890. 19. $90.06 + 11%, Solution. 100% + 5 X jj§ = 102^% 1^2Y*|(%of the principal = #2,235.60 /. the principal = 82,235.60 x ^^^ -= »2,190. Ana. 102^ Explanation. Interest for each year = 5 % of the principal, and for 152 days a 5% X M§ = 2,(ij o/^ of the princi- pal, ana tlierefore 102^j% of the principal = »2,235.(i0, the amount. BULE. Divide the given amount by the amount on given time and rate. for the '' -i EXERCISE 78. Bum must be put out at in! 1. 2 years at 4% to amount 2. 4 <( 0% 8. 6 K 2i% 4. 3 It 3% II 6. 10 tl 7% II 6. 8 « 6% II 7. 2i « 2% II 8. 3J It 6% II 9. 7J .1 8% tl 10. 4^ II 3% II 11. 9i tl 1% It 19. n II 5% It 13. .Syr 1 mo, at 4% tl 14. 2 yi . 5 mo. " 6% It 16. 3yr .7 mo. " 8% II 16. tyr O mo. •■•■ 3% t. 17. 2yr .2 mo. " 6*% II to $540. »2,'180.00. $2,760.00. «87.20. 8342.00. $616.00. $53.00. $120.00. $960.00. $1,353.00. $175.60. $360.00. $1,011 00. $114 .50. $386 00. 9945.00. $1,080 00. J, i 168 it ACCURATE INTEREST. 18. 1 yr. 6 mo at 3 J % to amount to $840.00. 19. 2 yr. 8 mo. " 8% <• »1,092.00. 20. 1 yr. 9 mo. " 10% <( »940.00. 21. 5 yr. 2 mo. " 12% ii $972.00. 22. 3 yr. 1 mo. " 6% (1 $1,185.00. 23. 45 da. " 6% u $1,470.80. 24. 16 da. " 73% (t $1,098.60. 25. 12 da. " H% (( $2,!»28.36. 26. 87 da. " 4% 0.00, 24. $l,0'.).j.OO, 25. $2,5)20.00, 26. $1,825 00, BATB. H%, 4%, 4J%, 5%, 5%, 4%, 5%. 4%, 6%, 7%, 8%, RATX. &%, 7J%, 3J%, 4%. INTEREST. $70. $136i. 72 m. 4il. $50. $78. $215J. $80.64. $144,853. $288.64. AMOUNT. $1,470.80. $1,098.60. $2,923.36, $1,812.40, PRINClPAIi. 12. $645.75, 13. $727.35, 14. $8iii;.40, 15. $'978.60, 16. $998.52, 17. $1,092.24, 18. $l,12;i.82, 19. $1,192.80, 20. $1,200.00, 21. $1,268.40, 22. $1,288.88, PBINCIPAL. 27. $4,3.S0, 28. $2,1'jO. 29. $2,5.55, 30. $3,285, RATB. 9%, 12%, 11%, 10%, 5%, 7%, 9%, 8%, 6%, 12%, 10%, KATE. 6% H%, 6%, 2i%, INTEREST. $206.64. *4] 8.954. $347,065. $518,658. $185,145. $338,958. $582,729. $751,464. $1,200.00. $1,208.40. $1,261,142. AMOUNT. $4,441.20. $2,246.70. $2,586.50. $3,318.75. 27. B. loaned $1,000 at 6% until it amounted to $2,000. What was the time ? 2H. Mr. Roper paid $48 interest. For what period did he pay it, the principal being $640, and the rate 5 % ? 29. Borrowed Jan. Ist. 1889, $00 at 6 %, to be paid as soon as the iuLt-reat amounted to one-half the principal. Whon is it due? 1 Ir 170 ACCURATE IHTEEESI. 80. May 18th a speculator bought 1,606 bushels of wheat at $1.00 a bushel. He afterwards sold the whole for $1,658.80 cash, his profit being equivalent to 6% per annum on the amount invested. What was the date of the sale ? 31. In what time will any sum of money double itself at 4 %, 5 %, 6 % 8 % and 10 % per annum ? »50. To find rate, when principal, interest, and time are given. I'JxAMPLB.— At what rate will »1,248 in 2 years 5 months prodaoa $135.72 interest ? Solution. 12.48 = Int. for 1 yr. at 1 % •80.16 = Int. for 2^yrs. at 1%. •30- IG ) ?135.72 ( 4 J 1% X 4J = 4J%. Ana. Explanation. The interest on ^ 1,248 for 2yrs. 5mos. at 1 % = $30.16, but the interest is 4J times as great as $30.16. .-. the rate per cent, is 4 J times 1% = 4i%. »136.72 1^135.72 jl,24'8;00 Solution 2. 100% = ^%. Explanation. eM-Jsioo^^'P'"^''"''^^^**"^"- tfun the interest is of the princi- pal for '2]5^ years ; this fraction divided by 2^ expresses what fraction of the principal the i'.terest is for 1 year ; this latter fraction is expressed as per cent, by multiplying by 100. ExAMPLB 2.— At what rate will 84,380 in 7C days, produce «46.60 interest ? 2A Solution 1. 143.80 a Int. for 1 yr. (365 da.) at 1 % #9.12= " 76 da. »tl% •9.12 ) •45.60 ( fi 1 % X S w 5 %. Ana. Explanation. Interest on 14,380 for 76 days at 1% = »'-•,.,•-..." ^- — %i.ree ngures. "a?me3s, we only extend A 176 COMLOUND INTEREST. Table. Ifrs., <» IMT ft. Iff (' ^ i ? 1 » 4 5 6 § 9 lO IB 11 1.) 16 17 18 10 'iO ai 23 2ii 27 2§ 29 30 31 32 33 34 3S 7 |M»r ct. 36 37 3§ 39 40 ].0(iOO 000 1.128(5 000 1.1910 IGO 1.2(524 770 1.3382 256 1.4185 191 1.5036 803 1.5938 481 1.6894 790 1.7908 477 1.8982 986 2.0121 965 2.1329 283 2.2(;09 040 2.3965 582 2.5403 517 2 6927 728 2.8.148 392 3.0l>.),") 9!i5 3.2071 3.55 3.3995 636 3.6035 374 3.8197 497 4.0489 846 4.2918 707 4.5493 830 4.8223 459 0.1116 8(57 5.4183 879 5.7434 912 6.0881 006 6.4533 867 6.8405 899 7.2510 2.53 7.6860 868 1.0700 000 1.1449 000 1-2250 480 1,3107 960 1.4025 517 1.5007 304 1.6057 815 1.7181 8(52 1.8,381 592 1.9671 614 8 per et. 2.1048 2.2521 2.4098 2.6785 2.7590 2.9521 3.1588 3.3799 3.6165 3.81596 520 916 450 342 315 638 152 32. "^ 9/: ■■ 4.1405 mi 4.4.304 017 4.7405 299 6.0723 670 5.4274 326 5.8073 529 6.2138 676 6.6488 3S4 7.1142 571 7 6122 550 8.1472 520 8.6360 871 9.1542 524 9.7035 075 10.28.-)7 179 8.1451 129 8.7152 708 9.32.53 398 9.9781 135 10.6766 816 1.0800 000 1.1664 000 1.2597 120 1 3604 890 1.4693 281 1.6668 743 1.7138 243 1.85119 302 1.9990 046 2.1589 250 2.3316 390 2.5181 701 2.7196 237 2.9371 986 3.1721 691 3.4259 426 3.7000 181 ;i. 960 195 4 .a57 oil 4 !i609 571 ii.()338 337 ..4365 404 0.8714 637 6.3411 807 6.8484 752 7.3963 632 7.9880 615 8.6271 0(54 9.3172 749 10.0626 569 9 |»oi- «;t. 10 per ct. 11.4239 12.2236 13.0792 13.9948 14.9744 422 181 714 204 578 10.8676 694 11.7370 8.30 12.6760 496 13.6901 336 14.7853 443 1.0900 000 1.1881 000 1.2950 290 1.4115 816 1.538(1 240 1.6771 001 1 8280 391 1.9925 626 2.1718 9.83 2.3673 637 2.5804 264 2.8126 648 3.0658 046 3.3417 270 3.6424 825 3.9703 059 4.3276 334 4.7171 204 5.1416 613 5.6044 108 6.1088 077 6.6586 004 7.2578 745 7.9110 8.S2 8.6230 807 93991 679 10.2450 821 11.1671 395 12.1721 821 13.2676 785 15 9681 17.2456 18.6252 20.1152 21.7245 718 256 756 977 215 14.4617 695 16.7633 288 17.1820 284 18.7284 109 20.4139 679 22.2612 250 24.2538 353 26.4366 805 288159 817 31.4094 200 1.1000 000 1.2100 000 1.8310 000 1.4641 000 1.6105 100 1.7715 610 1.9487 171 2.14.85 888 2.3579 477 2.5937 425 2.8531 167 3.1884 284 3.4522 712 3.7974 983 4.1772 482 4.6949 730 5.0544 703 5.5599 173 6.1159 .890 6.7276 000 7.4002 499 8.1402 749 8.9543 024 9.8497 327 10.8347 059 11.9181 765 13.1099 942 14.4209 936 15.8630 930 17.449i 023 19.1943 425 21.1187 765 23.2251 644 25.5476 699 28.1024 869 30.9126 805 34.0039 486 37.41143 434 41.1447 778 45.2592 656 COMPOUND INTEREST. 177 Notes 1 tj i. ^ 3. ^he amount for any nnmhfir «/ computed by finding theVXts of C ""' "' '° *^« ^'^^'^ '"^y be of years whose sum equal! the gtl tte'""" "' ''"^ *^° ""-^er. 4. To find the amoint of »„„ ■ multiply the principal by tCLZZr^ri ''^ °°™P°«"^ interest. 5. If the time contains part^T ^^ *''"" '^°'* ^"^t^- amount due for the full per ods and'to "th" "T.*^/ '' '^^'^ ^^^ ^he months or days. ^ ^' "'''* *° *^'3 add ita interest for the EXERCISE 81. 2 «ln " '''" "" °^ ' *«»» f« < years at 4 »/ a- 1640 /or 4 years M Sli- M7R t o '^" and IS days at 6 %. '^" * '^ '"' ^ ^''^ars 8 months 8 L*if at /;'. '"° '''"' ' ""O"*' "' ^i«i for S years ann„*r/" ' '"' ' """*'" "' ^«. Payable se.ni- *• ''^''"'O for 28 years at 7%. 7. $750 for 12 years af 8%. 8. $920 fur 8 years at 5%. 9- *2,600at6%,from Jan Ut isfyn . t 16th, 1894 *• ''^°"' ^""^ 3»«'. 1889. to Angnst coipoStL'st'?'"""""' °' *8,500for 6 years at 5% 12-Whatis.hean,„n„tof*l,850f„rl2yearsat7c,, IMAGE EVALUATION TEST TARGET (MT-3) A w A &?- &0 f/. 1.0 1.25 l^|2£ 12.5 li! lii 1312.2 1.4 10 1.6 Photographic Sciences Corporation 33 WEST MAIN STREET WEBSTER, NY. 14580 (716) 873-4503 iV iV ^^ o iV 1. ■v^^' ^ ^A^ 178 COMPOUND INTEBEST. I 'I I .\ *! It ■ 13. What is the compound interest of $1,469 for 15 years at at 3 %. 14. What is the compound interest of $2,500 for 24 years at 6 %. 15. What is the compound interest of $1,650 for 80 years at 8J %. 16. What is the amount of $1,800 for 8 years at 6 % compound interest, payable semi-annually ? 17. What is the amount of 1,500 for 2 years, at 12 % compound interest, payable quarterly ? 18. What is the compound interest of $5,000 for 2 years, at 6%, if the interest is due annually ? If the interest is payable half-yearly ? If the interest is payable quarterly ? 19. By how much does interest compounded semi-annu- ally exceed simple interest, on $400, for 2 years 6 months at7%? 20. What is the amount of $2,400 from May 1st, 1887, to Jan. 14th, 1890, interest compounded half-yearly, at 5%? What is the amount, if the interest is compounded yearly ? What is the amount, at simple interest ? 21. What is the compound interest on $7,325 for 2 years 2 months at 7 % ? 22. Find the compound interest on $8,833 at 8^ % semi- annually for 1 year 7 months. 23. What amount was due March 25th, 1886, on $1,612 borrowed Jan. 25th, 1885, with compound interest at IJ % quarterly ? 24. What is the amount of $4,616 at compound interest for 2 years 5 months at 8% ? 25. Find the amount of $3,500 at compound interest from Oct= 29thj 1888, to Nov. 15th, 1889, at 2% quarterly. I 3 COMP(>,JND INTEREST. 379 St 6 % ? °' °' ♦'•^«8 in 3 years 8 months ,4 4^5^. '^ "'^■1886. Interest compounded annuali; 29. w..t wm-^z^Serat irtssl"^^ ♦o Sept. 16th, 1893 at 10 <^ ;»,* V ' ^^^' amount 80. How much 'r^'^^l^^Zr^C^''''^'^ ' je-rs old, that, on arriving a^ 2,T . "■ "°° '« ^^ toe rate being 6-^ a. d tL f ' ! ""^ ''"™ ♦^^■«"'. annually? *"*""'' "'" '"terest compounded semi- To find the principal or present m,„,h , compound intereet, Aivide the ZT ^ ™ '"~™' "' *1 for the given tiZaJ . """""" '" "" """"" of interest J ^ " "" *"»"' ~«* <•« » .impU annuairfallT^^^^^^^^^^^ interest in 8 years ? i^'oauce $643.8466 compound 87. At what rate would $500 have f^ k. i amount to %\mQ la ;. ,n _ ,, ^® ^ ^ loaned, to pounded annually' ? ''^''' ^^' ^°*^^««' being com- 180 DISVOUNT. i r DISCOUNT. 354. Discount is an abatement or allowance made from the amount of a debt, a note or other obligation. 355. The term discount is often used without refer- ence to tme to imply an abatement at a certain rate per cent, on a price asked. 356. When Time enters in as an element, two kinds of Discount .are distinguished, viz.: True Discount and Bank Discount. 111. ft 'J' 1 ■*! I it TRUE DISCOUNT. 357. The Present Worth of a debt, note or other obligation, payable at a future time without interest, i» such a sum as, being placed at interest at a legal rate, will amount to the given sum when it becomes due. 358. True Discount is the diflference between any sum of money payable at a future time and its present worth, and is equal to the interest on the present worth. InnsTRATioN.— Suppose A. owes B. $106 payable a year hence without interest. The current rate of interest being 6 %, the present worth of the aebt is $100, because that sum would amount to $106 in 1 year at 6%. The true discount is «106-»100 or »6, which is evidently the interest on the present worth $100, for 1 year at 6 %. 359. To find the present worth and true discount, the face of the debt, rate per cent per annui6, and time being given. TRUE DISCOUNT. 181 •1.86olr r^e'^^fe %"' ''""°' "'''"' "^ *"« ^^-o-* of a debt of T 1 , SOLUTION. Interest on »1.00 for 6 years at 6%, o , .-. »l-36 has for its present worth »1.00 W. •• II LOO «1,360 M u *1.36 _100_x^l,860 "" 136 ■ i. Z)ertrf. the face of the debt' by the amount of 3(7 f .r, given time, and the quotient will L th ^^'* **' interest at 6 %. ° »l,781.40, due 4 years hence, Solution. ^ Interest on «1.0o,r 4 yars at 5 0^ = 9.20. »1.20 has for its discount $.20 .20 »1 »1,781.40 1.20 vm.^',) X 20 Oo 829G.90, discount. Divide the interest of the debt fnf th. - ij,. , ,, EXERCISE 82. Fmd the present worth and true discount^ 1. Of #475.60 at 7% due in 2 yr. 9 mo 2.0 »661.50at7%dnoin3yr.9r 3. Of $500 at 50^ due in 11 mo 6. Of «1,575 at 7 % due in 1 yr. 3 mo 1 *; ^a 6.Ofa860atCi%duein90da.""- 7. Of J678 40 at 44% due in 16 mo. '•S!e%2«-*'^i%aueinlyr.4mo, 10. Of 81,215.45 at 8% due in 219 da. ri.^ 182 TRUE DISCOUNT. h '-• fi., Find the true discount on— 11. $1,600 due in 3 yr. 6 mo. at %. 12. 83,550 due in 90 da. at 7%. 18. $4,960.76 due in 18 mo. at 6}%. 14. $960.40 due in 73 da. at 10%. 16. $625.13 due in 8 mo. at 7^^ %, 16. Which is the hetter. to buy flour at $8 a barrel, on 6 months' credit, or $7.60 cash, money being worth 8%? 17. What is the diflference between the interest and true discount of $1,650, at 6%, due in 8 months ? ^ 18. Which is worth the most, $640 in 12 months. $620 m 6 months, or $600 cash, money being worth 8% ? 19. Bought a farm for $2,964.12 ready money, and sold It agam for $3,665.20. payable in 1 year. 6 months. How much would be gained in ready money, reckoning true dis- count at 8 % ? 20. Having bought a house for $5,048 cash, I at once sold It for $7,000, to be paid in 18 months without interest. If money 18 worth 8 ^per annum, did I gain or lose, and now much ? 21 A man bought a flouring mill for $10,000 cash, or for $12,000 payable in 6 months, or $15,000 payable in 1 years months. He accepted the latter offer ; did he gain or lose, and how much, money being worth to him 10 %. 22. Goods to the amount of $510 were sold on 6 months- credit. If the selling price was $30 less than the goods cost and money is worth 6% per annum, how much was the loss and the per cent, of loss ? 28. A speculator bought 120 bales of cotton, each bale containing 488 pounds, at 9 cents a pound, on a credit of 9 months for the amount. He immediately sold the cotton for $6,441.60 cash, and paid the debt at 8% discpunt : how much did he gain ? . ''' TRUE DiavOUMT for 6 monlha ; «3 m lor ft t'^ /''"''' "' "" «"''" at 5%, for cash. Iflon^'rw frv '\r"™' '"^ ''"' much would the mereh.nf 1. , ** P^"^" ™""™' tow offer. """liant gam by aoceptbg the seller's 26. A merchant boneht a hiii „f „ j credit amoantiag to $1 jso What IS' ^ ' """"''' payment of the bill, If alWed 5* off ' **'° "^^"'"'^ i % a month ? * °'^' °'"'°<'->' being worth * monfhs.^dit^^fd'iSrdM''"' r™-' "' *^'^«'.» 10 «/. If from tl™' ™XtTtL'sa ' *' !•; "''"""» »' worth of hia debt at'a rTo'^^^^^^^tf '"^P^-' how much did he gain ? "'^«o"Q« of 8 % per anuum, at's^-ad^ero^'oVontst'" "f '°^ ' ■"""*'• ^ ^'^ " -Phaser a credit of on! vearjLf- ''"""""« '<• *<> P"'" ;„™-.Perannum7ZrrClt.::f"S': ^orlal^^ytsr f;ei%'i:^^^ "r • - ^-'^ " be gained in ready monev LI T ""^ "'"'^'^ ^^""^d How much. diseoS7a; tr :? t^^" «"' °' « ^ ' wWch a'^^adf Zoum o1 V:'tT "'."l' '^ *'■"««' ™ and a credit of 90 days ^n' fhet n^' pTi /" l'^ "''"^^• worth Si %, what sum should hp -i; ?*' """"^ » of the bill ten day;after ul pn^ctrr''' '" '"^ P*^'"™' Ibi BANK DISCOUNT. •■ > BANK DISCOUNT. 861. Bank Discount is a deduction usually made by banks for paying a note before it is due. This deduction ia the interest on the face of the note for the time it has ^Gra^J^' ^^^''^^'"S "^^^ thepernon who responsible for the payment of the note" " °^"^ ^° """"-'• ^^ ^ whtfn:::Ts7enTriT8ui^^^^^^^^ must be held by the pa/^ TntU it Lt due ^^^'^^^ '^ ^'^'^'^^^^^'^^'^ = '* «.e pt: or L t::™''^ "'^^^ ^^^'^ ^* ^ -^« P^y^ble t« the ... of Ha^e^srSi:;;r:ri::^z^:r^^ sequent endorser is not liable to a prior endomr "^ '"'^" *o«ayJ^ holder. Ti^ray "h^^^^^^^^^ responsible for payment. ^ ^°'^"'^'^'" ^"'i ^^ «»ch is 7. If the payee writes above his si(?natnr« 'rPn * xi_ , it is called .fun enaorse.nent. In tZcase 1 B n l""'" °'''' ^ " before he can negotiate it. ' ''''" ^^'^'"^ *° ^nd°"e it 8. If the payee writos above his signature ' Pav tn An , „ • termed a mtncaV endorsement ^ *° ^- ® ^^'-V- it is . Pi \i * 186 BANK DISCOUNT. 9 If the endorser does not wish to render himself liable for payment he should write. " Without recourse to me." above his name. This is called a qualified endorsement. 10. When a note is made payable to bearer it is negotiable without endorsement, delivery being all that is necessary. rn,!!; K° "f '"'f '°f ^^l ^''^ «* '"**°"*y of * note, the three days grace must be allowed after the time expressed, that is, it falls due on the third day after its term has expired. The day on which the note is dated is not counted in computing the date of maturity. 12 When a note becomes due which happens on the third day after the time expressed, it must be presented for payment during business hours at the place mentioned in it. If no place is stated it should be piesented at the maker's place of business or at his residence. it l!\u^Tl^ ^)\T^iV^''"^ *° P^y "• '^' P^°P^^ ^'""^^^ ^'^S made it IS the duty of the holder to give due notice to all the parties to it He may have it protested if he chooses. * 371. A Protest is a declaration in writing by a Notary Public, giving legal notice to the maker and endor- sers of a note of its non-payment. In Ontario a note must be protested on the day of its maturity, otherwise the endorsers are released from all obligation to pay the note. NoTKs 1. When a note becomes due on Sunday or a legal holiday, it must be paid on the day foUowing. ^ 2 The person paying a note has a right to a receipt, which is usually written on the back of the note. ="a.iijr 3. The person who pays a note has a right to it as his voucher, if it is negotiable, but not otherwise. 4. When a note is made payable with interest it bears interest from the isTart of 'tre di""^'' '""^ "^ '^^''"'''- '^ -»^ — ^^^ interest 6. When a note bears interest, the discount is computed on the face of the nou, with the interest added. 6. When the term of a note is given in months, calendar months are meant and no allowance is made for a deficiency in the number of days in any month. This being the case the student will see that four notes drawn at 2 months and bearing dates, Dec. 28, Dec. 29. Dec 30, Dec 31 respectively, will become due on the same day, viz. : Mar«5h 3rd, of next BANK DISCOUNT. 187 col7nllrtlri'^:l7:T^^^^^ of maturity is found by the note^nd the thZ ZTuL'^ ''Z'ZT' '' "^^ "^"^^ ^° day of maturity is found by count "nc I^V^t T "."^ "°°**''' '^^ ard the three days of grace! ^""^ *^* °°°»''«' °' <»lendar montha. »7a. Banks in discounting notes alwavs reckon dis- count for an exact number of days from the t^e o discounting to date of maturity. Thus on «. n^L T • July 5th, and discounted May' Jh'^e" t^mt f^Z? in June + 6 days in July . 41 Jayg. ' ''' JT8. To find the bank discount and proceeds of a P 1684. di";Ta,t;;r»f .r,T' '"°°°"' "" ^™°°'- -' - °°" <» Solution. The term of discount is 93 days Solution. The date of maturity is November 26th. The note beai>8 interest for 34 days. ^^■'^^ = Int. for (JO da. at 6%, " 30 " 3 J. " 34 « <> 1.875 .1875 .0625 2.125 .854 »2.479 = Int. for 34 da. at 7 %, f2 479 (360 da. int.) less ^ of #2.479 = »2.45 (actual int ) The amount of note at maturity is «376 + «2.45 = 8377 46 The note is held by the bank from Novembpr 1 9f h l.L or 14 days. November 12th until November 2eth. 111 •ii III i88 BANK DISCOUNT. = Int. for «0l 1,546. 19; they now discount nf «o/ n^. . "^*^^arawn $3,976.21 ,. a eo'day note f r ,5,6 /as' a 30 dTv"'.' T »1,546.19; a 20-day note for Llififis' '"'■''''/ °<"« '»•■ their credit at the bank What fs th, ' "'T'' °' "" '" baukaccount after they Ztl'ZZ:::^? "' ""'' m.0U47''"^\t'':--'' ""r" *-°°»' - overdrawn ; 1 ' ^ °°^ discount, at 6°/ n. on -g„ for »2,428.40,- a eO-day note for $6 3U 25 a 80 d'' "? for »1,120.60 ; a ao-day note for »4 son ',n f ^ ^ """* «1,560.50; Pr«,eede 0^ al t thei'r Tr ;d; a^L't 'f What is the condition of thB.V h!l '^ ''™''- receive the above or "lit,? '"""' """"J""' ""^"^ *^^ M $840, at lonth note Jounted at the bank' flour at ■day note, ^ the day msaction i. What ivhich he proceeds mted at vf much I it the I dis- iSS ? t'drawn 3te for ote foi- f all to f their 3rawn ' note 7 note )te for bank, ihey BANK DISCOUNT. ■HiXAMPLE For V,^ ■'•"ItS. *" ** %• '* may yield UM% Bank discount of 81 for 78,, ^T""""- »l for 78 days at 8 0^=8 016. »1 - ».016 a ft 984 „. 8 qs4 proceeds of »1. ».y84 = proceeds of $l »1 = .. 1 .984 »1,968 = «. 1,968 798?" ~ '^'OOO Ans. ij. . , BULB. EXERCISE 84. Find the faceo^ote or draft- Prockeds. ". What « .he r.e! r;"';"^™-"' "'^ ^ WOO ? •" Which, when discount of afc bank at 6% are $1,275 eeda 194 BANK DISCOUNT. : I 16. If a merchant wishes to draw t'^(\n(\ *. u , , w.at .^ .„, ,, ,,,, ,, „,^ X rrirr,': — Trtra: rTwteii^^e rrv""- ^■•^- face of the note ? !P^76.84. What was the =holt'Zr:"of l\'f?'-" " «» O"^™'- What if discounted aUJ^'aton:^;'" ^*^ ""' *» "-' ''^'". 20. James T. Fisher buys a WI? „f u ,. Montreal at cash uricf iTIh "erehandise in giv.s in pa,rn' h sit at IT"!"' f f «-«°' ""• mu»t be the face of the note ? ^*^°- ^''»' poXSroft^;rs.°L'„r"' '" ''"'' "-' "-- EXAMPLR.— A ')"oker buvs n 7rt ;i„ SoLnxioN. 70 day note = 73 days' time. Interest on $100 for 73 days at 10 % = »2 .". Amount of $100 = ^102. »102in 73 days gives »2 interest. .-. 100 "365 .. 39^ .. .*. Rate of discount = 9|i 0^. f^^ Example — What rate of interaat >. «..-^ u 70 days is discoanted at 10 % ? ^^' ''^*° '^ °°*« P»y»ble in fc bank, for ounting at • run, dis- t was the days, to oceeds of e. What act debt, odise in •90, and . What corres- i tiiHt his BANK DISCOUNT. li)5 d the Me in .. , Solution. rO day note = 73 days' time. Interest o„ ,^100 for 73 days at 10 ro = »2. .. Proceeds of IjlOO = ^93. ff '" '' <^^^^« gives $2 interest. .-. Bateofinterest=lOJjo^. ^^^ EXERCISE 85. 1- What rate of interp^f I'a r, .; j 1. 30dajs is discounted at 6%/ ' ''^'" " "°*« P^^^^^le in 2. A speculator discounted a note dup in Qa ^ per annum, what was the actual ll f- ? ^^^'' ^* ^^ °^ the sum invested ? ^*' °^ '"*^^^3* received on distuLVaT'lo7:erV" ' "?*'^ ^^*^-* ^-ce be interest? ^° ^"' """""^' ^^^^^^ will be the rate of rate of interest. "" *'' ^^«^' ^^at is the I li' 196 BANK DISCOUNT. or, I*tP = Principal; t ^ time; r = rate. P t r = Interest, or bank discount. Ptr 1 + tr = True discount. ^* '' ~ 1+17 "^ ^'fferenoe B. D. and T. D. tr. Simple interest on the true disoonnt. B. D. on 8100 for 1 yr. at 6% s T.D. " 44 ,. a 6 1.06 86 DiflFerenoe a S6 . 9 "- a 8J gg 1.06 *106 But »j^ is the simple interest on »_«_ for 1 year at 6%. = Simple interest on the true discount. 878. If the bank discount or simple interest on a sum of money for a given time and rate is J of that sum, then the true discount will be ^ of the sum. If interest = g of principal, then H is interest on »b. .-. »b (t... principal) + «a (i.e. interest) = #(a + b) = Amount »(a + b)" ""'"* "°''''°' '^^ "*• "^^ *'^'* ^^ " *^« true discount of .'. True discount is j- of principal. Thus: Simple interest on »100 for 1 yr. at 6 % « |6 f.e., the in orest is ^^ of principal. J.nen »6 is interest on flilOO. *•" Imn °* ^"°°'P*^ "^ *^ °' '°*«"»* = »106. Amt. .. »100 IS present worth of »106, and «6 is true discou.t of 9106. ■■• True discount = ^ of principal, f.*.. __6__ of principal. BANK DISCOUNT EXERCISE 86. 197 1. The interest is 2 ^f xu . . teewoe. fte interest ^n/dstunTLTs"'' ^/^ '"'^""" 2- The interest is Ss th?^- * ^'-xl ^e principal. «n^~.eis,.. Fi'n?th;::4r-' ^^ '"« -e tin.e ^' -ine interest is to j xi ',. . interest and discon "t i! !«". '5'^''"'^ ''^*™» *•■« ■"• If the interest"; y!fr ?""* "=' P"""P»1- ''s'Th^t.lt'''''"^'''"™"'"^ of Th;«n,„'„nTr$64a ^ZilV"^ '''*"' ""^ P^-oiP^I- 6. Tl>e diiference betw en b! ■?""""• o" a sum of money for li ° . '"''™' ^'^ ^e discount sum of money. * ^'"' "' 8% is 518. Find the -eivf;tts^ tt„\,fe'TomLrif' %*--» "<-»"" ha» a year to run. wiiat wZd h °' " ""^ ""ch true discount were deducted ^ ''"""™ '°' ""^ ™"' " 8- I have two notes CI both are discounted at 2o/o''„Vrt ™''[™'>™«n8 'o |88 ; at true discount, the entir. T ?} '''"=°"'"' *« "tiler feoe of the note » wh C k. t r™' ''"'"8 *^- ^^d the 9- The interest on, ^''.""'™"°ot was allowed. the discount Zth^ saZtT" %\ ' ^'"^ '^ ^'''' -" and rate per cent. ' "" " *^8'>- «■>9i"49 PARTIAL PAYMENTS. Example 2. SI, 000. rp , ,^ rn , Toronto, May 16th, 1881. ^°' James H. Ross. On this note were indorsed the following paymenta • September 20th, 1882 .. Vr^rrT October 25th, 1884 .. ..•..- " ^l;'''^. J"ly I'-th. 188C •• ''I'll September 20th, 1887 .. .. jjo in December 5th, 1888 . . .."'.."".. iqj'qq What remained due Miy 20th, 1889 ? Solution. Face of note InteresttoSept. 20th, 1882 (iyr" 128 da) »1.000.00 Amount of principal and interest at time of fi'.st pavmenr sT7,Sf First payment (Sept. 20th, 1882) IJ^-yment . . $1,094.56 Eemainder after deductmg first payment'.. ■".. -~? Interest from first payment to Oct. 25th, 1834 (2 yrs 'so da ) * ' ?S"!a Amount due at time of second payment . . [^ '"'^ ,, ^ Second payment (Oct. 25th, 1884) *1.082.44 Remainder after deducting second payment * ' .^'li Interes from second payment to Dec. 5th, 1888 (4 yrs. il d^ ") SVb Amount due at time of fifth pavment ' ^-^^^^ Third payment, less than interest due V^r AA *^'^^^'30 Fourth " #75.20 Surn^of third and fourth paymentsVles's'than int;3rest ^^^ Fifth payment"'..**.. *^'^7-30 Sum of third, fourth, and fifth payments '^^ Renminderafterdeductine third fourth nTi^fiwi, _j292.a0 BaUBcdM ..time of settleme-MMaySOlh, 1889) ..".. -jjjgj BULB. ,h?fT l-°'«^'' '*« ••"(«.( on the given principal from the dmeofthe note to the time of the Jim paLmt IfZ mment eguah or exceed, the interest due, sMraci. the Z m.„tfi0M the a„,.,un,. .,„, „,.„ „„. „,„^..„,,^^ "^ "^ ^Jf 200 PAliTIAL PAYMENTS. «»U: jrf;:r: 'zzai "t^ ••"'-"'• — '*« remainder Ja « J~i "''""'' "'" "■'""•'' S. Proceed in the mme manner vM ,u menu, until the date of .ettlement. "'matning pay. Bi EXERCISE 87. , 1- A note of $4,660, dated Jan. 22nd lfiS7 ^ . interest at 7 %, had payments indorsed unoJ'^ ' '''"''^ Jan. 10th, 1888, $2,000 • Au^ '^^T^Ll^T' '* ^^ ^«""^« .' IftftQ »''« 2 years from dat .-^ payme^t'oT*^:;' "'*''' '™^ »"'" 8 months from da. ; a plmeni o, «nn™ ""■'« ^ ^^ars 10 months from da e *S,„ "l*"" '"""""le 2 years maturity of the note? " "'"°'' '^""''"^'' ■!»« "' 'he l»"«86":r^Ltse!Tf7 '"'^^ «'™">™^' •'-• «,200;I.e6.9th~;i '°n7\""^ ''"<'• IW. WhatwM dueM^r Ist'lsSQ^ ? . '"'' "*''■ *''«W. ^'*'^- ■^S''» -1^09, interest 5 % ? . /^' '^°o*eof$302.25, dated Au". 4th iftftT „ a a interest at 6^ °/ ho,! r, . '^ ' ^^°'' ^"^ (Imw ns 188S *-n T * • "^"'^aist, 1888, JIOO- Oef 7iTi ^uiy '^itiSs: '''"■ ^*«''' '''■ ^'-^ ''■e''am"o;:;t";:'o follows "Nov-'ard ''1^7' te^ T""™'^ ""^ -""-" - «S25. How much wfl» rf.,1 ., '.f ^""0; April 1st, 1889, money being worth ^f "' """"^ '» '""• May 8th. ISS,),' $1,600.00. n Three years after dat. T f^T"""' ^P"^" l»l, 1887. Sila„ Hopidns. "re tholLT^'H'" T.'" '"^ "^» »' received. Moasand sii hundred dollars, value 16. On the following note ... -. ^"' *'™'"'- iln».. A..,. , » """ ' ■' -'.omens n;er.i made as . „ — -^..^^niiig note '•■.( -.;. follows: Au.. 1st, 1833, ^850; :,:.- yrd, 18b,j $3,000; PARTIAL PdYMENTS. '.03 188!) ? ' * ' "• ^^^^ was tlio balance due Jan. 30tL, !^«,600.10 r, «. tl«usa„,I uve huuC-ed donL, wilh irfsfa, 6 r"' W. HiNDSON. 17. The following note was settled Oct ISth 7«ftM Tfiftft Tf ; ' ^^' ^"^ °ne of $200, Auril Ist S585.50. „ Six monllis aft»r ^.. t ' "«• ^^'- ^^86. Buchanan" „ order fiv.'h T^'"^ '" P^^ «° '^1-- dollar., va'lue re^dvecl ""'"' "^'t'^^ "■"' ''* 1^. MoHardy. 18. $500. Q ™ 17«« „ I . °^* IHOMAS, Feb 1 Iftftft interest at 7% """"'^^ '^*''' ^"^^' ^^^'^ Endorsed as follows. May 1, 188S. m!""" ''''''^^ Nov. 14, 1888, $S. April 1, 1889, $12. XT , ^Tay 1. 1889. $30. iicr ja^ch was due Sept. 16. 1889 ? 19. $5,000. Q^ Six „„„.h. after date I pro^rr;;,''^^^^'^^^- Endorsed, Oct. 1st, 1887, liOo'""" '^°"™- " Feb. 7lh, 1888, $45. « P™es8 of time, mav be paid in^r "'"""' ^"""^ ''°« »' different in one sum. ' '""'= ""^ >>« « be paid at onoe without ioL tdlttreditr ""^ "" most common dates used beinrtL«t^,*f'" "' '^" ^°°*1 -J^te; the the first day of the month otWrlTetd? r/'*'' *'^ ^^*«^* ^^ ^^^' month preceding the month ZT^s^LTalu' ''' '''' ''' °* *^^ -J. In Equation Tables Don Qi„t -, 8. Interest may be oaJu^atd at' n"v ^^ '''' '' *^'°" '°^ ^" °-™P^-- day basis, or a 365 day basis with'? P'"" °'°*- "^"^ ^^^^ «" a 36a that a uniformity in r'ate and m JZlTt' "^""' P^^^^^^"^' on^ throughout. "®' °* oomputmg mterest be observed 4. The student is recommended tn „v. accounts, that method being uniform r«-^°'' T '°'*^°^ °' «'l«a«ng and form of solution. ^ ^ regardmg choice of focal date, rate 3«8. Equation of ac«ount° '^pnpnrl^ „ ,, . principles : " ' ^'^P^^^^ apon the following _^- 206 EQUATION OF ACCOUNTS. h >i \h h >> I &i ri. .,i 1. The rate and time remaining the same. Double the principal produces twice the interest. Half the principal produces half the interest, etc. 2. The rate and principal remaining the same. Double the time produces twice the interest. Half the time produces half the interest, etc. 8. Hence, the interest on any given principal for 1 year, 1 month, or 1 day, is the same as the interest of $1 for oh many years, months, or days, as there are dollars in the given principal. 4. Hence, the interest on any given principal for any number of years, monfhi, or days, is the same as the interest for 1 year, 1 month, or 1 day, on as many dollars as is expressed by the product of the given principal multiplied by the given number oj years, months, or days. 88!!. The several rules in equation of accounts are based upon the principle of bank discount, for they imply that the discount of a sum paid before it is due equals the interest of the same amount paid after it is due. 390. To find the average time when the items are all debits or all credits, having the same date and different terms of credit Example. — A. bought a farm June 24th and waa to pay ^500 down, $800 in 2 months, $400 in 6 months, and $600 in 8 months. Find the average term of oredit and the equated time. Solution 1. By the interest method. Interest on $500 for mo. at 6 % = $0.00. ♦• 5300 for 2 " " = 3.00. ♦• $400 for 6 " " = 12.00. •• $000 for 8 " " = 24.00. i Amount of payments = $1,800 Interest = 39.00. Interest on $1,800 for 1 month at 6 % = $9'. $39 -f $9 = 4J. 1 mo. X 4^ = 4^ mo. the average term of credit. June 24th + 4^ mo. = Nov. 8rd, the equated time. p|*S' EQUATION OF ACCOUNTS. 207 Explanation. If we take June 24th aq tho +;.v, t would lose the interest of Loo for 9 '^?^™'"* "^ '^^ ^'^^ ^*^™«. A. »600 for 8 months, in allLtterest 'TTTV''' ' '"-"-' -^ use of $1,800, the amount of the debt for sn . T^''' ^"""^^ *° th« it would be equal to »39 and wtvt' T ^ *'"'" ''" *^^ ^^^''rest on and 4J months, from JuL 24th Jves'!;'""" ^'°"^ ^^° ^« ^i -o'^ths. could therefore pay the amounf of " 7T'^ t^^e Nov. 3rd. A Without loss of interest eithert:rms::if:;Vst*edi!:r '^ ^^^^ '''' P: ^ *i ■ "^'^'''' """^ Intekkst Method. The gmtient will b,- ,ke mJJZ 1, '""" '"■ Solution 2. By the product method. PRODUCT. „ _ nn -CJiPLANATION. : sSSr ?""»""><"• '"".n.. in prin- ITEMS. 500 300 400 1,800 X X X X TIME. Omo. 2 mo. Omo. 8 mo. = 2,400 mo. = 4^00 mo. 7,800 mo. 7,800 -5- 1,800 = 4J mo, interest on ^.300 for 2 months is the same as the interest on n tr 600 months; the interest on $400 for 6, nonths equals the interest on est on $600 for 8 months equals the inter!!: 2,"""**"' ' """^ ^^^ '"t«r- .ould therefore lose the Merest o'^?;*;? o^ ''^ "°""'^- ^• therefore be entitled to the use of »1,800 for su^h . T "' ^' ^°"'<^ on It would equal the interest on ,1 for'7;8;ornt;::r4rro:th^^^^^^ T\f u- 1 , -^^^^^ ^^'^ P^ODtJCT Method, MvlUply each item by its term of credit «.W ^- -. •urn of the vroduet. hy //,. <.„.^ J.y^.'"^'** ^*^ ^'^'^e the he the average term o^f cred^ ^ ^'"'"'' ''^ ^-^-'^^-'V/ 208 EQUATION OF ACCOUNTS. h i EXERCISE 88. 1. On a certain day A. bought a horse for $175 on 30 days, 3 cows for $120 on 45 days, 80 sheep for $250 on 60 days, and 6 tons of hay for $180 on 90 days. What is the average term of credit ? 2. Bought a ship for $30,000 ; the payments were $5,000 cash, $8,000 in 4 months, $7,500 in 6 months, $4,500 in 8 months, and the balance in a year. What is the average term of credit ? 3. Sept. 1st, 1891, I bought goods, as follows : $200 on 2 months' time, $400 on 3 months, and $450 on 4 months. What was the average term of credit, and the average date of maturity 9 4. On the first day of December, 1890, a man gave 3 notes, the first for $500, payable in 3 months ; the second for $750, payable in 6 months ; and the third for $1,200, pay- able in 9 months. What was the average term of credit, and the equated time of payment ? 5. Bought merchandise Jan. 1st, 1893, as follows : $350 on 2 months, $500 on 3 months, $700 on 6 months. What is the equated time of payment ? 6. Jan. 15th, I bought a bill of goods amounting to $900, $275 of which was on 30 days' credit, $300 on 60 days, and $325 on 90 days. What was the equated time of pay- ment? 7. James Hudson, June 12th, owes $317.75 due in 4 months, $216.38 due in 5 months, and $170 due in 6 months. Find the average time of payment and date of maturity. 8. Dec. bt. 1894, bought goods to the amount of $1,200, on terms as follows : 25% in cash, 30% in 3 months, 20% in 4 months, and the balance in 6 months. Find the equated time of payment. 5 on 80 days, • on 60 days, What is the I were $5,000 IS, $4,500 in i the average ^s: $200 on >n 4 months, average date gave 3 notes, B second for $1,200, pay- m of credit, Hows: $350 Qths. What ting to $900, on 60 days, time of pay- '.75 due in 170 due in i and date of it of $1,200, lonths, 20% , Find the EQUATION OF ACCOUNTS ^ 2(Kt 01 ^r^oo*' '7' ' P"''''''' ^''^'''^ ''' $8,500, paid cash $1,600, and gave notes, one for $3,000 navable in 2 years, and another for .$4,000. payable in 4 years' Pind the average term of credit on the notes JL^''''^i\^u "^ ^''^' ^P^" 20th amounting to $6^00. on the following terms: ^ cash, ^ in 4 months ^Xt^r ' ^^"^^' '' ^''^ ^^^-^ *^e;ti^ 11. A stock of groceries was purchased Jan. Ist, 1889 the purchase price payable as follows: i in 1 month, ^t' 8 months, i m 4 months, J in 5 months. When may th whole amount be equitably paid in one sum ? 12. William Owens bought a farm of 820 acres at SfiS per acre, i payable in cash, i in 1 year, J in 8 yeL' and the remamdar in 5 years Whn^ wn« fL „ 7 credit? average term of HiiZl J^ ^""^ *^^ average time when the items have different dates and different terms of credit all the items beingr on the same side of the account 5^600 on 6 months.' wl!ttC:;:ifZer '''''' '' ''''■ '''"" ''''' Solution 1. Interest method. DUE, ITEMS. Aug, 1, $350 Oct. 15, 400 Deo. 10, 4.50 Mar, 12, __ 600 Amount = $1,800 o Interest on 1,800 fori day at Go^ = $30 37.12i + 30 = 123| days. Aug. 1 + 124 days = Deo. 8. T*_-- . . , -Explanation. DAYS, 75 131 223 interest at 6 %, foo.oo, 5.00, 9.82i, 22.30. «37.12i iDtewBt. iilo EQUATION OF ACCOVNTS. Of »1,600 for such time as the interest will amount to «S7 T9i Bliown above for 124 dajg. amount to »37.12i, or as Hence the equated time is 124 days, after Au.. let or Deo. 3rd. I^UI-B FOB iNTKIiEST MkTIIOD. lake as the focal date the earliest due date. Find the n^t.-est on eachit^n fro,n the standard date to the da"f Z niatunty anddnide tkr su,n of the interests by the iJeZ of the sum of the items for 1 day dafet 'tf '"" '; ''"r"'"' '^''^^' -^'^'^^ '^' ^*"-^^-rd th Jn f'rr^' ^f' 'f P'^P^^'"^' ^dd this muuher to plment ''"""'' '"■" ''''' ^^"^^^^ ''^^^>f NOTHS l.~If the earliost or latest due date is the focal datP ifu v „ir°° '"°" "' """" "" '"™ '" "■•"•""■ ""'""i" ■»»"«'» ". Solution 2. By the product method. Assume August 1st as the focal date. DUB. ITEMS. TIME. Aug, 1, $350 X Oda. Oct. 15, 400 X 75 " Dec. 10. 450 x 131 " M-^r. 12, 600 X 223 '• «1,800 1800 ; 222750 ( 123J. PRODUCTS. 00. = 300.00. = 589.60. = 1,338.00. »2,227.^0, i Aug. 1 + 124 days a Deo. 8 ■'*♦ ' Ji(i!UdTl0N OF ACCOUNTS EXPLANAXION. This method of solntion may be exnln.;n«^ • given to Solution 2. Art. 89? "^'^^'"''^'^ '"^ » «anner similar to that Role FOR PitoDtjcT Method. 0/' each Lm. ^"'''^ ^^'^^ «'*^ '^^' ^^'^ of Maturity ^. Multiply each item by its mimhor ^/- ; u-ill be the average term of credit. *"''^^''** 3. Add this quotient to the foml ^n+. j ., he the equitakle date of paZn^ ''' ""''^ '^'' '•^•'«'' ^^^^ Solution 8. Interest method. Jr""^ the latest date, Marol, ,2th, ,889, as the ,o.». DOB. Aug. 1, Oct. 15, Dec. 10, Mar. 12, ITEMS. «850 400 450 600 DAT8. 223 148 92 INTEBE8T AT 6 %. 813.00|. 9.86f. 6.90. 00. Amount = ^],800 o Interest on $1,800 for 1 day at 0% = T^^^ ' ''"''""'*• 29-77J + 30=99idays. Mar.l2-99da. = Deo.8. Uarir • Explanation. Ma^mrrtttaVd:;: riirrei-r- °°*- ^^*^- -°- --. 223. 148. 92. and days respeo vl y If T. ^1^'^'''' °' ^"^'^ *° ^^ Mar. 12th. 1891. WilJiam GrLt wSd lo L th« 1* """^ °°* P^^"^ °°«' days, on »400 for 148 days. »450 Ir oo Zl '°*'"'*' ^'^ »^^« *«' 223 on Mar. 12th, 1891. The probLm then h'" "' * *°*"' '°*°^««* ^^ »29.77i time should Wm. Grant be allowed nteret .1'' 7'' ^^^* ''^^'^ oJ receive »29.77i interest ?- and v^^h f °° *^' ^''^^ ^^^^^ ^o »■ to tln.e at which the debt iTld b pt^Vo Z ^'°i: *^ '^ '' ^^^^ ^^ mtorcBt. would therefore be 99 davs ht ^ '"''*''"" P^^'*>' ^^"i'i lo» 1690. "^"^ '^'^y^ before Mar. 12th, 1891, or Dec. 3rd! 212 EQUATION OF ACCOUMS. Solution 4, By product method. Assnmo March 12th as the focal date. DUB. ITEMS. DAYS. PBODOOT Aug. 1. $350 X 223 s »78,050. X 148 = 69,200. X 92 = 41,400. X = 00. $1,800) 9178,650. Mar. 12, 1891-99 days = Dec. 3, 1890. Oct. 15. 400 Deo. 10. 450 Mar. 12. 600 Amount 81,800 Explanation. The namber of days is found as iu Solution 3 »400forr48C:;th S;sTo ;^^ '^ ' '^' ' ^ 92 days, or theLerest on »4M00 ortdav tL tot' l'^ ". '''° ''' « therefore the interest on ,1^50 o ^/ay. WetalXn .itr^' mine for how many days the interest on ftljoo ^11 tna 2 T I TX'TJr. ^^"^y--^-^ - fo-d to Kriayriitfore'th debt IS due 99 days before Mar. 12th. 1891. or dI 8«Jri890 EXERCISE C9. 1. A merchant bought goods as follows : Sept. 5 1890, a bill of $2:0 on a credit of 6 mos. No^- 11. " " 350 « fin 1 J^- «. " " 425 for cash. "'''^'^• What 18 the average date for the payment of the whole ? ^„^/?I;° ^' ^^T'" P»'-<'''i>8ed goods of Isaac 8. Smyth & Jm . !i'T, T^ •'"'^ ^"'' ^'^'OOO '" be paid Aug 18th ; the balance, $760, will become due Aug. 80th. It I™1 T'. " ''"«'' °°'^ '"' *''^ whole amount be drawn, payable in 8 months, tiat it may become due at the arerage date ? j "io uue ai EQUATION OF ACCOUNTS. 213 8. Bought goods as follows : Mar. 6, " ^25 '« fin^ What is the averaa^ ^o+ / ^ ^^^^ " '".^^'^^'^^^ date of payment? 4. When snail a note to setfclfl fh . „ • n^ade payable ? '"^^ *^« following account be Henry Field. rr, , Wawea li. Edwards, Dr. »250 00 100 00 300 00 420 00 »1070 00 " 25, '. u ; " 420.00 Apr. 4. <. . ^JT'- 61250 " 12, « . ^^ ^^f 210.25 6. The following items were sold n '"'''' -;«h- What is the average time fo'V "'''* °' ^^ ^^^^ whole amount? ^ ^ ^°^ **>« paym.-^nt of the ^f- 1. 20bbls.ex.fam.flour ^ «« .. 11, 500 bush iWo -^ u @ ^8-50 " 21 qnuii^^^'^^^a wheat " 135 ,, ^^'fbblg. Ontario flour « «?? 26, 100 bush, oats „ ^'^^ 7. Fznd the average of the following. '"^^ J^"e 8,Mdse.@ 3mos «in " 16, •• ^ clT $1,275.00 July 12, « . ^? ^^^^ 600.00 .. ^^ ^^y^ 820.87 Sept. 25, «« 3mo8. 145.68 $2,692.00 1^ •■ ( t',1 214 EQUATION OF ACCOUNTS. i. May 5, Mdse. @ (JO days " 16, " «« 30 " oune 10. Cash July 7, Mdae. (net) Aug. 14, " @ 60 days $600.00 8:)G.40 250.00 420.00 5;l8.28 ?2,204.68 9. A young man, having money advanced to help him pay his way through college, received : Sept. 1, 1888, $76. Feb. *15, 1890. |86. Feb. 15. 1889. §80. Sept. 20, 1890, $128. Aug. 31, 1889, $95. Aug. 80. 1891, $175. ^ What was the equated time at which he should date a single mterest bearing note for the whole sum ? 10. Five years from the date of the first loan, the above mentioned note was paid, with interest at 4%. What was the amount ? 11. What is the average time at which the following bills become due ? Feb. 10th, 1892. $400 on 2 months' credit • May 10th, 1892, $300 on 4 months' credit ; June 16th' 1892, $350 ; Aug. 6th, 1892, $150. ' 12 Find the equitable date for a single note given on the followmg bills for merchandise : June let, 1895 $20 Jaly 1st $30 Aug. Ist, $30, Sept. 1st, $20, each on 2 months' credit. 1 1 }u *^°''^^* ^''"^' °^ ^^''''' ^°^' ^ ^°" ^s follows : Mar nth $36. on 30 days' credit ; July 20th, $95. on 2 months- credit; Sept. 8th, $215. on 3 months' credit. What was toe average term of credit ? 392. To find the extension of credit to which the h^l?h^ * Tl ? '"^^"^^ ^^^" P^^ P^yn^ents have been tnade before they are due. l^ "^^^ «.«-,. I- . P^ !S>fJ50.86, and 30 days later lilPi i oq ».o«,. .hat extension ought he to have on'the halate ? 4. A person owes a debt of m Feb. 10 ' "y.'^^^'^> U " #()00 |»1,000 »700 *-^'"''""""^"""'™S-»o»nt by two .methods, •Jate. ®°*''"°'««"^''-«^-'«d from the standard whlTuet " "■' ''"'''™' "' '"^ '""owi-'g "ccoun, and 7. Find the average time nf «„ • account: °^ P*y^«« *he following Georoe Jenkins. 1891. »860 Jane 4 - ' $400 »540 9600 (»1,000 »700 Or. EQUATION OF ACCOUNTS. 221 .^ue of t M^Cacc'r /?' '"^ ^"^'"-' <" "=^ balance -Dr. W. T. Dawes. ^ ^ (Jr. 1890. , , ^-— __ draft, 60 da. Ugoo due"" ^'"' "" ""»"« °' «■» '""owing account «,<, „h„„ m if ! in t\ I { 'Mi I if- 222 EQUATION OF ACCOUNTS, nlliiZT " "' '"""°" "'.""^ '°"°™« »«'=°-' ■»- "^ 1889. Mar. 3 Apr. 24 May 1 " 30 Aug. 17 Samubl Peok & Son. To mdse. « CI $fiO $100 $150 fl)0 ^200 1889. Apr. 1 June 1 ^ug. 1 Oct. 1 By cash, It ii Cr. 9150 #loO $150 $90 w."„ dut"b;:'^uat:oof "" °' "■" ^"""-'-^ — '• ^■"'. Z>r. Walter L. Parker. l.s«9. May 11. July 1 Aug. 31 To mdse., 2 moa 30 da. 1P108.40 ^225.00 1280.80 5.' 87.50 1^. Fmcl wLen the tbllowiug account is due by equation : ^^' John Montgomery & Co. q^ ^y ^^"^ I $300 oO da. note (no interest), i $150 ^VE&AGING ACCOUNT S. dLES. 223 AVERAGING ACCOUNT SALES. 3J>3. An account sales ^a commission agent of «. ^ ,.^° account rendered by a a-i tte^net proceeds due the owner ' ""'""' "'""«^^' .-ro;, CO ™!3:s^:„™';^»^.f *'. -"«•• *--. .^ve«,,„,. oom*ti^n!foHli"tfeT '"'"''' " a-ttiition to the payment in ease of Stld^^^S"' "^ """ "^ "- ^sfr.to'ttX::,:::'"''-''''-. -^a,, adve. "■^e of payment of the same ' "''"'"'"'' ''"^ >" «=e oMreoL':izrtXt™?'*"''..°'''''-«-«''-8- »tthe«^„,,rf,,,„^^2 bvoth?/°?:f "" *'* ''^ «<"»« °/ »<.(« ,■ whiie some merchant. ? 1"'' *"^™«<' "^^ '«'"« "ate th^aeeonnt 3.1X0"" """"''™° "' "-^ 3. Of course the due date nf +»,„ -mH; ?h' tra^tgCreVrr"' «"- '= ">» "d credits, except inX „" T • ^'™« ''°"' """"^ *he commission and other Ij.:^:, "'''"'""^ «■« ^"'^ '•» I Jj: f^! Bi 'III [I K I thempToce'7s"f:d'?e.""'"" ^"^ «"'' ""d when __^^__^ SALES. CHAIiOES. I July l| FreiaJit I ■■ »'( srois".;-"-"-"..".."..- I ijiti ComuHS8ion,2Jo^on»5,cj20 - •' 150 00 * " ll ^^'^^i «779.00 Commercial balance " II »M41. 00 1 vi^j Solution. "'^^- ITEMS. BAVn •' '«• 2,170. « •'■''* S=P'"- 1,600. 80 "■^'*- M.920. .T=^*' J"lyl. »4o0.25 '^^^"^^TATGo^ •'"^>'l- 30 75' *-00. •>°ly4.- iso.oo' 2 •^*'- Sept. 7. 148.00. 68 •^^• -_ "* 1.67fi. T X ?77!).00. ,-- ^^^^^Oim ACCOUNT SALE,.' 3. Averaging sales and expenses fhav follows : Focal date July ist. ' ®^ ''°'' «*»nd as DUE. XTBM8. DAYS. product „™ ^- ^"^'-^ '^'^^O 68 402,560. — -ZI? _ 10,127 »S'1« ) 392,433 Net proceeds »5,141 due Jaly 1 + 7« ^ '^^^ *'™« "tgI^ ""'71 + 76 days = Sept. 16. BULE. ^. i^enrf the amount and the average date of th. IT EXERCISE 92. " ^*^® 01 payment ; 185 chesta tea at $45 on'aoJ°V ""• "»> 1889, coffee at $28, „„ 2 „o„ "h, nl^V 5'''- ^'"'' ^5 aaeks f. 50, 30 days; same r*285 h'lSf*' '''«= '"^ "' 2 months. Paid freight Dec 't?.?''' "' *'8-87 on storage, Dec, loth, $7 80 comm.W ^'f / "=■"•«»««. S6.40; ri.uL», commission, 2i%. 2. Same parties sold Senf i^f ;u«ar, at $.,2i,. Sept. 15th 25 4el ea"""".'' '•''" «•• M8 on 2 months ; October 2nd iatV, u T" ®^ "''- «' -•2 lbs. each, at $1.06 on /^ ." '"""•"'■ests Oolong tea -■•^ ".tober 16th. f^i°ht a„d° :■ '''^ ""arges ll' ranty 6«. °*' *'"' ™"»8« »86, commission paid *n Si ' 2^C AVEIUGLVG ,aaOU.,T S,L^s. Clinton McPherson 1 ««^^' ^^ '^*- Sept. 24 Fre,ol,t ca.iiUKs °' ® *^-^^' "-^^h- _ f'j j Cartage ' • Oct. 28 Cash IdvancP^ ■«■ •• ■ •• '■■■•• ^2 50 Nov. 15 Cooperage °"" -t .Z" •• •• 30.00 25|Commisfiou-4oV •• .." '■ ■■ 2,000 Oq July 15 500 barrels Hn^ ^ JJ^^^- A%'- 10/600 " „ " 7-00 »3,250.00 " 6.76 2,10000 I U 4,050,00 f-B. 10 j storage labor a . °^^««-'- p»:00 Commission on »9.4(f | fj ^ 11.26 ' N«' proceeds due%?,^-rage. i^^ 317 50 "^Pril 9 Sold Leonard Ra,i, ^^^s- 32 half chests o!!J^"'.^^'*22 '^8. @ l6o 1.325. @tiS°^°^g *«». 1.8051bl!S 480 = *^'««7 52 1.467.60 " 7 Son'°'- °" »«-000 @ u"r • p:625:02 Oonf''§''^«'g»^'°«^ labor' etn »90-00 Com. and guar, on fe.sls 02 @' W o^^.sj I Net proceeds due per average ^' -^ 883.62 •^"^y 17 100 bags DSmla^^ 86.05 »g8 peanuts, 30 daya, 69.60 I 767.60 J-e ^?| ?r?/rr'^^ @ 20f • ^ P^^ ro^^*' ^^"'^^ge and labor WBO.OO Commission on fLgisj^i-^g.- 825.50 ' Net prooeeds due --J^L^es^ 62 50 30.00 2,000 00 6.00 137.78 »3.250.00 2,100.00 4,050.00 ff9rioao6 31750 'i082J0 ^^^^■^GING ACCOUNT SALES. 4. Average ;^he following account Of sales: 227 '^'^ 'ount sales of 600 barrph ^f , . ' ^ ^""^'^ ""^ ^heir accotmt and risk. ^f74^|SoLD_To__| Dbsckiption. I Bar •'"Jy 6 Fox & Son 14 A. Eohr . ;; 16 H. Qaeen lo Clay & Co. New Mess. . . Prime Mess. New Mess... Extra Prime. »7.C0. 30 da. !«•;«, casli 17.60, 1 mo. 16 25, 2 mo. Chaboes. fa.'SSS™'™.*--'""'' ,_ .^®' ^*0'"ag? and insurance, 4;i50 -, Commission on $ ,at2i%, "■.. ^'"'^^ Total charges .. ,, Net proceeds, due as per average i - 4,067 62 UST^O 5i625^2 S83.62 700.00 85.05 69.60 ^57.60 il2.16 )5.80 >6.35 228 ACCOUNTS CUIUiENT. ACCOUNTS CURRENT. 3fl!>. An Account c mercantile Iranaaotions "tmj" f '*'""'''^ """^ ottbe «»3h balance dae at a cortat 71 ™ """''"■ *<"''''« "-e "• It is customarv fr.» t B. In the illnstrative examnio • aecounl at a g^^ f^^""^ '' "=« '"^ reciuired to settle an J0-Tofl„,t.eoa3.baia.ce„r„..ec„„„.,.^,,,„ ACCOUNTS CUlUiEHX. ord of the wing the 3r aoooant, of original a or agrer. nder their lually, or s seldom find only 160 days' uade. 'n open interest is th( tie an Jiven ae on Cr. jOO (40 100 229 »tn. DAYS. ITBMa Apr. 9 97 $650 T I ol ^^^ 1000 July 28 -13 _J260» »29i0" ^440 Bal. of items $470 PoLUTTON. INTEREST. »10.51 D0E. DATS. 17.50 Apr. 20 Aug- 14 June 1 86 -30 44 ITEMS. ?5on 940t 1000 «2440"' 360 days to year. «,-. v*u.uo Interest. Th *v J . Explanation. tothedisoounton1fl,260 aTys Thil'"'''''"/- ^^ "^^^'^ ^ -««S from the interest on the Or side or ad.T?''*u'"'^''*'^^^''«^^'^°°t«« '^'^'^^d adopted. '« *^« «ore convenient, and therefow ^'fircr^^ratre^^raieTtr^ may be found by calculat Jg « e in'elt "T^' '"^ ^* ^ ^'^^ ^^^ from the time it is due to the date o?s!,°° .' '^^■'^°«^ of the account mentis earlier than the average date T.' " '''' ^'^'^ of settle- ba ance of the account ; if la rlan h' ' * f ' ''''''''' '^'^ *be «■ The interest meth;d of fin^n? ^'^CaTT,''^*'' ''' *^^ ^"*--*- because i. gives the interest or dtcount on k '^''°' '" recommended stood, it is more satisfactory to those L who' '*''"' " " ^^^^'^^^ "'^der- than the product method aL wiZ . . ''°°°"''*' °""«^t are sent than any other method '^ '°*''''* **^'«« "« "««r. W. E. Telpobd in acct with A. T. Stewart. Cr, By mdse., 3 mos. " II " draft, 30 da. 840 9()0 800 16. Keduce the following transactions to the form of an account bearing interest at 6 %, and find the cash balance • ^l^sfn T' i??A^- ^°"^^* ^^^'^^ ^' ^' amounting to So r r>/ ''"^ °' ^'''^^' ^^y 6tb' - bill of $2,000. March 1st, 1890. C. sold a bill to D of $1 fi4n 1::^""' IT f. '''''' ^' ^''' ^^tb,a*bi?-of aeoo'; May 1st, a bill of $1,340; May 21st, a bill of $1 000 What was the cash balance June 10th, 1890? 17. What was the cash balance due July 20th, 1889, on the following account, at 7 % interest ? Dr. 0. W. Harrison in acct with L. Conqdon. 1889. Mar. 1 '• 20 Apr. 10 Mfty 2] For mdse., 8 mos. " 2 mos. *' 6 mos. 1 mo. 1889. »600 Apr. 6 760 " 20 410 May 1 600 " 22 By mdse., 3 mcx 2 mos. " 4 mos. " cash. $350 900 620 200 ^^^ STOllAQE. STORAGE. *i-. subj.t ttUeS Sir- "'• '"' '-^ --'-'^^ Xbe term storage is used also to desii?raf« fj,<. v, goods stored. aesignate the charges for keeping the Bates of storage may be fixed by aareemenf nf f V, sund^rwlf n'^'^.'* "^'^''^^^ '' ^ ^"'"^ ^PP^^^d *« ^a^es in which sundrv l>r. °^^^"^^S"«^-^« -re received, from wh ch sundry withdrawals or shipments are made- nn^ ii charges adjusted at the time of final wHhdrrwal '" 407. A grain elevator is a building erected for th. convenience of storing and shipping grain. ' 40S. Storage receipts, especially of rrrflins ovn ^ quently bought and sold under the lZZ^:Z^ receipts " or .« elevator receipts." as reprsenting T 11' value by current market reports. Note. -.When deposits or consicnmcnts anH nrUi ^ , ^ STORAGE. the 23,3 bet*?«^:'c"ftdwr„Tr,;'''''K«^"'''" «-"= have TCc at different dates, but none delivered •iiB» WSB ,11 delivered Dec 12th T,lu ? "'''"'" ™« n>««li«n- '»» pewod „, 30 d.,. .ve„.e'..„i\.:r;r. t'i™:t°iir •■^'- SOLUTION. The storage of 500 bbl8. for 08 davs - 9q nnn kk, , " ,. ^•' = 5,880 " .. . ..- M 200 340 id << = 4,400 = 6,120 BDLE. in the sloraae term nT ^ ''"'" ''» '*« "«"'''«■ o/ ./"y, EXERCISE 94. bul^h^LTlrir,''' 7;-'>°-- Ha, 15th, 2,500 storage ? ^ ^ °* °" <^ays average oatt.e ,. .„,y 16th. 40 head of e-at.e'. 'l ,"= C ' d.^ ed' 2^6 8T0RAQE. July 26th, and the charffPH wpt 7k^ i Nov 2nd '240 hhia , ^ct^7th, 160 bbls. potatoes; i^uv. ^na, 240 bbls. apples; Nov 24th fin kki„ • being 2Jo. pT; ba pe7fel7so ::;r ""' '"^ "'^"'^^ EX.MP.B.-A warehousernau received and delivered the following. KECEIVED. {. ""lug. Jan. 19. 300 bbls. ™ delivered. Feb. 24. 200 ■• ^f*'' »• 1^0 bbla. Mar. 8 IdO » f"^" ''' ^^^ " Al>r.21,400 " t^'- J' 1^0 " What was paid for storage at 2c. a bbl., for a pTriod ofso I storage, a aettlenaent having been made May 7th ? ^^' ''^'™«' First Method. Solution. From Jan. 19 to Feb. 9 = 21 dft • qnn KKi i. ^ . P.O. .... , ^r ,. , . , ,..^^„ ,, ^^ ^^ ^ _ __ .„ cu. .54 200 received. __ „ loO bbl. received. From Mar. 8 to Mar. 18 = 10 da • Ran h,y,^ „4. ^ * «_ , *^ 160 bbl. delivered. *x3mApr.4toApr.21 = i7dft • irnKw , . Apr. 21 'InnS • '"'"^^"^ "da - 2.C50 « „ . ^ 400 bbl. received. From Apr. 21 to May 7 a 16 da • R^n kki ^ . . May 7 '"^'^'f.^J^^^- fo"^ for 16da = 8.800 " ' £?P bbl. delivered. 8.4?00 bbl. for Iday » ^LJTl ua i,m" , ' 'J ^^ " U.0bhl.@2.aL.:^22.8;'SX'^- for each I was hie irehouse : potatoes ; onions ; was all e charge ds have following : STOBAOE, s average for Ida. I M 237 ^' ^^iltiphj the number of barrels hnlp^ .t. / .l Second method. Solution. delivbred. BBOBrVED. Jan. 19, 300 bbl. x 108 = 32 400 Feb. 24, 200 bbl. x 72 = 14 400 Mar. 8, 150 bbl. x Apl. 21, 400 bbl. X JPeb. 9, 150 bbl. Mar. 18, 200 bbl. Apl. 4, 150 bbl. May 7, 550 bbl. X 87 = 18,050 X 50 = 10,000 X 33 = 4,960 X « 0,000 60 = 9,000 16 = 6,400 62,200 2M0O '^^'^^^ 84,200 34,200 + 30 = 1,140. 1.140 bbl. @ 20. per bbl. = «22.80. Ooat of storage. EXERCISE 95. Jm !^V f\ "" "■" °'°™«« '=''»'8»' »« *"• per bbl for a BECEIVED. 1889._June 12, 200 bbla., potatoes. " 20, 160 » apples. " July 18, 60 .• turnipB " Aag. 2, 90 " oniona. DEIIVEBED. 1889.-June 17, 75 bbls. potatoes. " " 26, 126 " " 30, 90 ■' apnles. July 5, 60 '« " 25, 40 " turnips. Aug. 0, 20 «« a. What will be the storage chlrge, 'at tt^ner bM °7' a ter. oi thjrt, <,a,s average, in tb?M,ow1*; .Z 'all"; " Mar a Ri\ a 28, 190 " flour mar. 8, 60 •• potatoes. •• Anr ik rn <. " 60 " 29, 230 " flour. Jit 1 if .1 ii ! I ! I i' 288 3T0IUQB. Bist, 1889, at 2}c. per bbl., for 30 days ? BECEIVED. Jfi8!).-Aug. 17, 250 bbls. mdse. " 26, 90 '• '" Sept. 19, 200 •' '• Oct. 12, 800 " M " Nov. 18, 200 «« •• " Deo. 17, 400 " « DELIVEBED. 1889.-Aug. 23, 200 bbls. tadse. Sept. 26, 240 •• •• Oct. 13, 300 " •< " Nov. 20, 150 •' " " Deo. 26, 660 " " ^hh'h *.'^° i""^ *^^ ^^^^ S^^^^Se on goods received and delivered at different dates, when charges vli^ BECEIVED. Jan. 3, 160 bbl. Jan. 20, 200 bbl. Feb. 1, 300 bbl. DBLTVKRED. Jan. 23, 2.J0 bbl. Mar. 1, 400 bbl. How much must be paid for borage on the above at thereof?' "' '" '*°" "■''»^^"^°' 1" 4=, or part Sgldiion. DaU. Receiptt and Deliveriet. Jan 8, received 160 bbl. " 20, " 200 «• 350 bbl. in store. Jan. 23, delivered 260 bbl. f JJJ "'^ »*o.y«d 20da. or2 terms. So. = $12 00 "l^hhl . ■ • 8 da. on term, 6c. = 5.00 100 bbl. remauimg, Feb. 1, received 300 bbl. 400 bbl. in storti. Mar. l.deUvered400bbl. \lfo''^}-'^f^^^-orit,rins.l4c. = 914.00 ^ 8 " lie. = 33.00 Total cost of storage 964.00 STGRAQk. '£\ih EXERCISE 96. or part thereof, and S cente T'hh '/ *?''" ''"'*^"' 10 days, or part thereof? ^ "' '""^ ""bsequem EECEIViil). 1889.-.May 7, 350 bbl. flour " 26,160 " .. " June 15, 200 " «• 1869. DELIVERED. -May 26. 250 bb). flour. June 1, 100 " «• " 9, 100 •« .« " 30, 250 " I. 2. The receipts and deliveries nf <> r.^,.* • the foUo^g account wererfoJlta ""^''""^^ ™ REOEIVHD. 1889.— June 20, 350 bbl. pork. " Aug. 1, 260 " " " 26, 100 •« « Sep*. 12, 90 «• II It It DELIVERED. 1889.-July 10, 90 bbl. pork. " Aug. 15, 100 " 1. " 25, 250 •• " Sept. 10, 60 " 1. " " 20, 300 «• .1 ,usnt 10 day'^fplZtf r' ' ""'^ '" ^^^^ ="''- 8. Find the cashstorageon the following storageaooounf REOBrVED. 1889.-Sept. 2. 100 bbl. ^889 ^ToT' •■ — -1889.— Sept. 20, 100 bbl. •a .. 25, 200 Oct. 19, 350 " " 81, 160 «• Nov. 7. 200 •« 30, 100 <' Oct, 10, 100 «• " 20, 100 " 30, 100 " TJ,^ «« X . ^°''- ^' *^ remainder. 1*1. for eaeh .ub^e^ent te " orso d? ' "'/" "" thereof. ^ "° *** ^^ ^a^s or fraction 240 ^iSCELLANEOVS. MISCELLANEOUS. EXERCI5E 97. l. The interest on "tiii «n- i >>«»? 5 per oent. per „„„„J° *^,'J' f « ;««« of interest fcbe house ? ^^'^^^ ^^ the pnce asked for did I keep the money ? "" ip^571.25. How long 5. October 12th Iftfio t "heat, at $1.05 pW busLe Z, 7'^ ^''"^ '"'^''''^ "t P>-»fi'of 6%. On what date CL'^rT"' '"^ " «' » wa.e,.>„, . .„ ,, intererXttr;;;-^ ^^^^ o. December lith iftpo , »o„ey and bough. shi„g,e„'at $4Tn t"°'" ^"""^'-^ 17th, 1889, he sold the LJes!*f° ^Tj^'' ^'P"'"""'' .nterest, „„„„„„-„g .„ $3"? 2 60 'S!;""' '''""' """J « "^ shingles did he buy ? ^^ ■"»"? thousand 7 I loaned a bridge builder $17 goo f„, 10 « per annum, compound intll , , ""'" ^^a™. at tooka bond an,I moHCefol ' '.r^'"*"' ''""'erly, and Nothing having heen pafd „n" thV ftT" "''»'«-' how much „s re^uir^d iut'/stCLl^ """ ^■^-' MISCELLANEOUS. 24J for what amounts muTsu.h t ^T"'"^ ^y their father, that at the age otCn^^r^^lTT'' ^ "'"'^ '" ""^^ $12,500 ? '"^"'yone the boys may each have 4% interest, compounded oZl^ T """^"'^ *^^*' ^t his credit on the 5^0 IttaL H • ' '•'' "^^^ ^^ ^^'^^O tc was deposited ? ^ ''''' *^^' "^^J^'^*^- What sum 10. Having purchased July I'Jfh i ika u at $16 per barrel, on four montifered t t^'J ' '' '°''' days later, sold it at $17.50 per barr«l' ^^' ^'^^''' thirty six months' note Jhou iX^T w^^^^ money became due. he discointP^^h ! '° *^' P"'«^««« and paid his debt. Howrurwa^;redT ' ''''' '' ' '^' at i'% pe\~j:ti iz inr '-' "^- --^'- $851.60 in cash, which was 750/' T "'"^ ^"^ ^« Pa^d the remainder was paid ZmluLm' '^'""* ^"^ °^« ' interest at the rate of 10 r ^1, /."^ ^^^' ^^^''- ^■"^h settlement. ^°" "^'''^ '^' amount paid at final 12. Having bought a mill for «l!i9nnn t • - .000 on delivery and aJl u ^T^^' ^ Paid cash eight years without interest to \T 't "^^*^^^^ ^- secure the interest, wh ch was ,n u '^' ^^^^'''' ' *^ the rate of 7% P^r^^ll^ ^^^^^^^^ at bearing notes, without grace for So? v. "^'^'^nterest at the end of each six montl fn .1 ^'^' ^°' maturing ^our Of the notes ^r^t mTt^X^e^r 1^^, '' ^'^ no other payment was made nat^^ n ! '° ^"'' ^"'^ -chwasre,u[red^oTl;Vi:;irnTr ''''''' due M2 MISCELLANEOUS. «-'.. and pu. the m„„ "t 't fn';"'"'!"' '" " ^' '^'^O lo- Jones loaned $2 400 nf «o/ • -ounted .0 »8,000. k. wha fi^H t i^lT'' «"«' " lo. A man nvesterJ liift nnn • '^ 0' three ,.ar, thte t'S "• ,7"^-'' »' '"e end ™m mcladod investment and " 'I"''''" *22,880, „h,oh -nt. of interest did his testoe^Tp; 7"'" ^^'^ P» ^7. Sold an invoiVp nf /,»^ i ^;;e i.-ll was paid Zl LZ^sZT 'T "^"^^^' -^^t-' of purchase, with interest at 8 % "" '^.V'*" *^^ ^^*^ How much was the interest ? ^ '^' ^ ^""^ $1,963.46. IB8I; ^'^'s^^^^^^^^ M,v 1st. ^ent of $17,685. For 211 fu ^' ^^^^' ^^ ^^^ Pay- given? ^h^* ^a«e amount was the bond 19. What sum wilJ bn ^n^ t of $5,100, dated March 17th issTf ''*'' ^^^2, on a debt P^r annum, payable semilnnual 7^^'*'^^^* ^* ^ o^ '^^«"ts were made when due and n/' V^' ^"' ^^« P^^ were made ? """' ^""^ «« subsequent payments 20. A merchant sold a sfn^t «^ 1 "■•edit; the bill was ZpTil°liT^'''"-''''^'nor,m one days after it became d„e 1 l^. '"°"'""' '"^nty received a draft for $4,716 21 t ^"^ """' *>" ««"« thereon at the rate of 6 " p „{°' «" ">"'. »»■) interest goods. ^''- ^'"d the selling pfiee of the is $16.50 : ^shel, pay. i at $1.20 ^- At the in or lose t, until it " made ? the end •> which arly per credit; ihe date 963.45. »y ist, le pay. » bond a debt at 7% >pay- nents nth's mty. eller jrest the MISCELLANEOUS, 243 21. A tradesman who is ready to pIIow 5 »/ „ compound interest, for readv mnn , ^ P®"* annum, for two years. If he Vhar^edl fo 25 '^t''T ''''' ought the ready money pric; tolave bee"?'" '''' ^'^* 17,600, maturL ntLe ''''l'''\'^^^ of which wa. Which was not pafd^uTtlTe: f:;^ th ^^r^^' '^"^ purchase. If the notp ^rZ It . *^® '^'^^'^ o^ it« at nso^t'Xtatbi?'^ '"'' "' *™'-'» "-pet. "Old it at^iltrTd ."•"' """""''• """^ '»'»«liatei; 2<. On the 20th of Msroh Iflflo r i, « % interest , „„ Ap-1 5th i" ! ' J t '■°''''' *•«•««'• »' until December 20th im JlT. ^'/'^ "' ""^ """"ey With the re^aind^a fa ^ ^ jjoto T'l """""'^ but which, not being paid at If; ' "" ^"^"'^ !«. the $5,000 became due at IT T '''^'"'<"' °""l did I gain, both ZiZL \ * °' "*• ^ow much l««nof $5,000 betreaaeT*'"" """ "" *^ "^^ '"« 65."'un'; rZ:."""" -" *«^^-™ '» '« .ears at w;L*fhouMTl:!;„'i'i:'»*^''-'----nths, -ontha. reckoning Ir^eXcol^^ """ "" "" '» '-'- .^-"^t;^dr::;?r^;f:--r II -^i f 244 MISCKLLANKO US. 28, If $10 be allowed off a bill of $110 due eight montha hence, what should be the biii from which the same aum is allowed as four mouths' discount ? 29. How much may be gained by hiring money at 5 % to pay a debt of $6,400, due in eight months, allowing the present worth of this debt to be reckoned by deducting 5 % per annum discount ? 80. The discount on a certain sum due nine months hence is $20, and the interest on the same sum for the same time is $20.75. Find the sum and the rate of interest. 31. Havingboughtgoods to the amount of $2,431.80 cash, I gave my 60day note in settlement. If discount be at 7 %, what should have been the face of the note ? 32. A note dated September 1st, 1889, payable in 90 days, with interest at 7^ %, was discounted twenty-one days after date, at 10 %. If the proceeds were $690.62, what must have been the face ? 33. If, on a note made for $700, bearing interest at 6 %, and dated January 1st, 1889, $50 is paid on the first of every month, commencing February 1st, following the date, what is due January 1st, 1890 ? 34. F. J. Eamsay & Co. bought goods of John Hope & Co. as follows : July Ist, $150, at three months ; July 20th, $200, at four months ; August 16th, $303, at two months ; and October 4th, $250 at four months. Find the equated time of payment, and what would be due on the account March 15th foUowin g, at 6 % interest. 35. I owe $480 payable in ninety days, and $320 pay- able in sixtv davs. Mv creditor consents to an extensinn of time to one year, and offers to take my note for the MISCELLANEO US. 246 <•' 300 <« 150 le oncen..nd bears the following endorsements: June .th $12b 50; August 20th, $127.^5; November 17th $'0 What . due .ranuury Is, 188., ..okoning n.terl!! i.tt^^ 46. Bought of A. T. Stewart .1. Co.. the following hills $900 ; March l.th, 1888, $2,000 ; May lOth. 1888 $7.-.0 ' June 12th. 888, ,^-..000. F.nd -the present worth > a note drawn July 1st, in payment of the wh.le, disc^ounted MISCELLANEO VS. 247 i7. Bought goods at different dates, as follows : Aug. 16, amounting to $476, on 6 months' credit Sept. 10, « 600, " 6 Oct. 6, " 750, «« 4 u Nov. 1, «« 450, .. 3 » What sum will equitably discharge the whole debt November 10th, allowing true discount at 7 % ? 48. Purchased merchandise of W. Duncan & Co., as follows : Jan. 1, a bill amounting to $875.50, on 4 months' credit J«n-20. « 168.75, 6 ^^^•4. " 386.25, 4 Mar.U, « 14^60, 6 ^P^--7. " 386.90, 3 Wliat is the present worth of a note made May Ist, in payment of th. whole, discounted at 6%? 248 i'ERCENTAGE. PERCENTAGE. STOCKS. .ams n,te and o««.,io„, „. a singSivTduai.'" "' '"' 414. A Share is one of the eaual n«^fo • * capital ».ock of a corporation isTLeT " ''"'' '"' 416. A Certificate of Stock is a paper issued hv „ poration specifying the number of shal T th\ TJ" holder is entitled, and the par value <^ eTch sSar" "^ cerlmtte';''" "" ™'"' "' " """ " »" ™- --ed in the it rw'd^""'' ^^'"^ "' ''-" '^ ">' '- 'or which ar/j;a«ce; when tl.ey sell for less thpv .J,\ i'"^" 'm, or at aa ..or tr:rir ;roa: rr;™- --- cerlam percentage computed on the par value of' th",tcir STOCKS. 249 4ltt. A Preferred Stock is one which is entitled annually to a stated per cent, dividend out of the net profits before the common stock dividend is declared. 420. A Stock Broker is one who buys and sells stocks for others, on a commission called brokerag which is always a certain percentage computed on the par value of the stock purchased or sold. 421. A Stock Jobber is one who buys and sells stocks on his own account. 422. An Instalment is a payment of part of the capital. 423. An Assessment is a sum required of stockholders to meet the losses or the business expenses of the company. 424. The Gross Earnings of a company are its entire receipts from its ordinary business. 425. The Net Earnings is the remainder after all expenses are deducted. 42«. A Bond or Debenture is a written agreement to pay a sum of money, with a fixed rate of interest, at or before a specified time. The term is applied to the Dominion Provincial, County. Township, City, Town, Village, Eailroad Bonds, etc. NoTB.-Bonds or Debentures are named from the corporations wlio issue them, the rate of interest they bear, the date at which they are payable or from a combination of any of these. Bonds are also known, First Mortgage, Second Mortgage, etc.. Income Bonds, Consoki, Sinking Fund, etc. 427. Coupon Bonds are those having small certificate? attached representing the different instalments of interest payable at the times specified, and which are to be cut off when paid, as a receipt. N0TE.-1. Bonds are also issued without coupons, in what is known as ■ the registered form. In t . case the bond i. only payable to the regis- tered owner, or his assignee, and the interest is paid by cheque or in cash t» the owner or to his attorney. 250 STOCKS, 2. BondB are sometimes issued with coupons attached payable to bearer, but the principal of which may or may not be registered at the ohoioe of the owner. 4as. The principal United States government bonds are the ^'8 of 91, redeemable at tlie option ol the govern ment after Sept. Ist, 1891 ; 4'8 of 1907. redeemable at the option of the Government after July let, 1907 ; Refunding Certilicates of the denomination of $10, bearing interest at 4%, and convertible at any time with accrued interest into 4% bonds; Currency G's. issued to aid in the construction of Pacific railroads, payable in thirty years after date, and maturing at different dates fium 1895 to Consols are tne leading funded ?-curities of the F.nalish Government, bearing 3 % interest, payable half- vearly^ and redeemable only at the pleasure of the Government. The funded debt of France bears the title of Rentes bearing usually, interest at the rate of 5 % ' The German Empire has a funded debt bearincr 4°^ interest, known as 4 %, Imperial bonds. The funded debt of Austria is known as ihe Austrian Consols, the largest part of which bears 5% interest. Piussia has a debt which bears a nominal interest of 6 % ov5^%. The bonds are knon-a as Oriental Loans, and are below par. The boM.lK in Italy M,re called I^entes. and bear interest of 3%, or o%. STOCK EXCUANQE. 251 STOCK EXCHANGE. 43». Stock Exchanges are associations organized for buying and selling stocks, jonds, and other similar securities. 430. Quotations are usually made at so much percent. on the basis of a par value of $100 per share. 431. Stocks are usually bought or sold either "cash " " regular way," " seller three," " buyer three." NoTE.-l. A Stock sold -cash " is deliverable the day sold, a atook sold "reffiihir way " is deliverable next day, or if bought •■ rcnular xoay" is to be paid for the next day. '^ Seller three" means deliverable on either of three days at the option of the seller. " Buyer three " means the buyer can demand delivery within throe days, but must take and pay for it the third day. _ 2. Quotations are termed "flat" when the accrued interest is included in the price named. 3. Transacuons on any of the above terras carry no interest. 4. If the option is over three days, interoat on the sellinc; value of the Stock is paid by the buyer to the seller. 6. One day's notice is required of intention to terminate an option of » longer period than three days. 6. Should the stock pay a dividend during the pendency of a contract the dividend belongs to the purchaser of the stock, unless otherwise previously agreed. 432. Margin is cash or other security deposit. .1 witli a broker on account of either the purchase or sale of securities, ;uid to protect the uroker against loss, in case the market price of the securities. h')ar;ht or sold, varies so as to be against the interests of the customer. It ia usually 10% of the par value of the stock. Note— i. J Irokors charge interest on the amount fir lisl -.el by tlioin for " oarryiug the stock." ::62 STOCK EXCHANGE. direction. Incaseof the stock bo dot "t "^ '^°^" in the wrong the deposit of an additional aluntothtr''':rr* '^ '""^'^ ^°°<^ ''V stock to protect himself fromrsinfam ofT/" ''°^'' "^''^ ^^" *^« It is usually 10% of the parvaTueTSe sl^l "°"^ '^ '*^ '^'^^--^ price of the s J of ^^^:t^^ *° '^^"^^ *^^^ 2. A Bull is an opoiator who " > .Mi^n. * , , advance. He ■« eaid to be "C" , , ' * t^f °' f advance the price of the stock ofwhioht:;;,^"^^^.'" 8. Collaterals. Stocks, bonds, not«, or otl>er v«l„. g^ven .n pledge ae security, when =.„,„, '« borrowed 6 Short. When ol., has sold stock which he does not own hoping to realize a profit by buvins it „. ,. he is said to be " short." * P"''^^' tb^"^ ■'.^"^7!?.'°"*'^''^ ^^^^^ «^«»^es to the holder number o shares of stock at a specified price per share within a limited time (usuallv fhlrf,. a *^ '''*' P^^ ^"are, theUS"; hu;c:itt = :," r r specified price, within a limited time w«ho!u the !n ! " to purchase it. The holder of th^" ca 1" mn t."""" est. ^the purchase price Of the nsr.^^:;'- o protect the in the wrong Mtdegood by wiJi sell the as at! vanced "of stock. Bpress the ck for an ^Ih try to long-." ier value wed. epositing place on 3for9 the Ices not ' prices, i holder erein a ^ share, )ut the equired holder k at a igation inter- ay of i?i STOOK EXCHAmS. go.S 9. A 'Spread" ia a contract which secures to the holder .he pri-ic^ge of either buying or selling within a limited time, a number of shares of stock, at a snecified price without the obligations of taking or delivering it. 10. A "Straddle "is a contract which secures to the holder the prmlege of either buying or selling, within a limited Ame a number of shares of stock, not only at the price mentioned in the contract, but, also at the market price of the stocks at the date the privilege was purchased. 11. Puts, Calls, Spreads and Straddles, are privileaes not recognized by the Stock Exchange. 12. Cover, to "cover one's shorts." Where stock has Deen sold short and the seller buys it in to realize his profit or to protect himself from loss, or to make his delivery he 18 said to be " covering short sales." 13. Ex.-Div. or Ex.-Dividend. When the price of stock does not include, and the stock does not carry to the buyer a recently declared dividend. 14. Difference. When the price at which a stock is bargained and the price of the stock on the day of delivery are not the same, the broker against whom the variation exists, frequently pays the " difference " in money, instead of furnishing or receiving the stock. 15. Watering Stock is increasing the number of shares of an incorporated company without a corresponding mcrease of their value. This is usually done in the re-organization of a railroad or in the consolidation of two or more railroads. 16. A "Corner" is produced when one or more operators owning or controlling all the stock of a company are able to purchase^still more for either immediate or future „elivevy, from cne who is -' short." Wheu they demand the stock, the sellers are unable to find it in the market. STOCK EXCHANGE. sen;l/sIltT*^/ '^^''^ "'"'' '"•'^'^^'^'^^^ ^«r buying and the stock. ^ ''' "^' " ^^'«"'^^*^^ on the par vafue of '*»4. Given number of shar^G fho share. To find the stock, or vJ^e've!^''" ™'"^ "' =" by «s,000 Bank ot uZtTZllZlT' *" "'"'' """' '"''• "» '°P'"en W Solution. »200 = value of 1 share .-. ?8,000 = .. .. 3 ,^-_ _ rffeo"* = 40 shares. Solution. . ■*? 'J'"^^ represent «8,000 stock .. 1 share represents ^^ = jgOO stock. EXERCISE 9a What amount of etock i, represented by- Bank of Montreal, Toronto, Commerce, Hamilton, Imperial Bank, Dominion Bank, Standard Bank, II II II II II »200 »200 «50 8100 »50 »50 Find the par value of a share when- o: "r-irhtl^- represent !^- stock, (I ii << II M M It Merchants' Bank Ontario Bank <• Standard Bank « Western Assurance Co. top. S. & Invest. B. & L. Association " Dominion Telegraph " »7,o00 »9,000 «6,000 »12,000 »7,G00 «2,000 S5,500 •I <« M N It W y » '/■'" 8T0GK EXCHANGE. How many shares are represented by- 17. $8,500 stook Mernhniifj' n^.^ iSOo 18. »9,«00 19. $7,525 20. §2,640 21. $3,150 22. «3,175 23. £475 24. $G,400 Bauk of Montreal, Lon. & Can. L. & A., Western Aaauranco Co., Bank of Toronto, B. A L Association, Nortli-Wost Land Co., Imperial Bank, 99.Qn ■fri/O. ■S40. 1200. »25. £5. $100. Solution. Cost of 1 share =$121 + $J ^ jfiO|. " 60 shares = $121| x 60 = $7,275 Solution. Selling prico 1 share = $121 _ f j ^ jiaOf 60 shares = $120| x Go = $7 245 Solution. 60 shares cost $7,275 .*. l-8hare costs '^'^'^° « jigu »121J - »j brokerage = $121 = market va'ne Solution. 60 shares sold for $7,245 .'. 1 share sold for ^"^'^^^ - ji2oj »120i + ^ brokerage = »121 = market value SOLDXIO:. Cost, of 1 share = ,1121 + jU = j^igu »7,274 ^ ai21i = 60 flharl: aI * 1. 2. 3. 4. 5. 6. 7. 8. STOCK EXCHAmE. Example 6. -How SoLDTIOlt. B«oeipt8 from sale 1 share = fti2i .^ , EXERCISE 99. Fmd the amonnt of en ah .., • , 01 cash reyj^red to purcbasp- i%. 4%. J%. i%. i%- h%. 70 60 120 ;joo 45 90 110 36 MAR. VAT,, 110 75 35 140 220 206 105 80 a. 10. J'. 12. 13. 14. IS, 16. SHARES. 136 46 ISO 200 75 170 800 3G0 < Find the cash received from the sale o:- BBARI obtain 9200 SoLUTIOIf. . . „?- '°^"™« " -'"ved from 1 shar« 50 shares = 60 X 100 = 9^o;.sto:k.'^'^''^'^ 268 8T0CK EXCHANGE. ,w» ^^."^rSf " "" ""• "" ""■ '"'^»'' ■«■» « "— SoiiunoN. 40 shares yield an income of «240 .*. 1 share yields an income of 96 .'. rate per cent, dividend is 6 %. r.t.,^'ZZtlZr°'' '" '"'"'^ ^'""^ •»'^«> •*«*' ^^ the SoLtrrioN. »3,750 stock » 87J aharea 37J Rhares yield an income of »300 1 share yields an income of ^^^ 8"' .'. rate per cent, dividend « 8 % 87i 98 * EXERCISE 100. What income will be derived from— SHABBS. 1. 70 2. 120 8. 150 4. 66 DIV. 6%. 8%. 8HABE8. DIV. 6. 120 3 %. 6. 110 ^%, 7- 76 9%. 8- 126 8J%. What income will be derived from— 18. 14. 16. 16. STOCK. •6,000 •8,760 •4,400 »3,620 DIV. 7%. 3%. 5%. 17, 18. 19. 20. STOCK. •3,600 •4,600 •9,160 •4,376 DIT. 6%. 8%. IRABES. 9. 130 10. 146 11. 64 12. 87 21. 22. 23. 24. BTOOK. •4,100 •2,225 •4,520 $3,200 DIV. 6%. 7%. OIV. 6*%. 8%. H%. 6%. obtai-'"'"''^' "' '^^''' ""' ^'^* '^"^ ^««* be held to tNOOMa. DIT. 26. «800 6%. 26. $420 6%. 27. $600 2^%. 28. $520 4%. nroon. oiy. 29. ^64 4%. 80. $240 6%. 81. »620 8i%. 82= I860 ZNCOMX. DIV, 88. 1160 4%. 84. 1450 8J%. 86. »160 84%. ^Tfa. 36. $340 3i%. ft. .1 STOCK EXCHANGE. lit VVh,.t is the rate pe,. cent. „,divHe»d when- 25lj SIlARBg, 37. 60 88. 60 89. 90 40. 76 41. 84 INOOMB. yield 8276. " »S00. " »390. " »450. " »170, 47. is. 60. 61. 8HABES. 42. 86 48. 42 44. 80 46. 64 Whatia the mle per cent, of dividend when- ^^^' iNoomu »3,600 yields »24«. .„ »8«*0 " «182. i" " »226. ^* " »380. gg; " «n5. 56. IMCOHa. yield 5196. " »189. " 9.100. " mm. " »900. »2,250 »4,000 •2,800 STOCK. $4,500 97,r>50 $8,(i00 »3,275 «4,125 rNooux. yields 8135. " 84o3. " »301. " »131. " $330. 6316 Solution. i05j ' ^""^"^ ot shares bought. Art. 485. 6815 106^ X 8 ■ #860. Income. Art. 436. 860 Solution. -g- » 60, Namber of shares held. Art 436 105i X 60 - #6.816. Cash invested. Art. 485. 1. What otAsa. #4,210 #6,716 11.688 #3,624 6- #16,026 6. #7,988 7. #24,060 «• «10.189 1. 9. 8. 4. EXERCISE 101. income is derived from investinff^ BiTB. IfAlLviT. ».... ^ BiTB. «% 4i% 8% 6% 7% 9% 9% 7i% MAB.VAI,. BBOK. *%. *%. 106 96 70 110 160 920 240 140 i 0/ 4%. CASH. #8,510 #6,811 #23,070 #27.820 #6.049 I'i- #13.025 15. #15,785 16. #6.090 9. 10. 11. 12. 13. 4% «*% H% H% 9% 7% 10% 4i% HA3. VAt. BHOK. 106* i%. 96 85^ 140 130 226 76 1%. i%. i%. i%- 1%. i%. 260 8T0GK EXCHANGE. dele™-""'"'"" °' ""'" »-' ^ --ted in „,a„ fe INCOME. 1. $200 2. $270 3. $72 4. 8192 5. $700 6. $288 7. $900 8. $540 RVTB. MAB.VAL. BHOK. 5% 105 jo^. H% 95 3i% 70 6% 110 7% 150 8% 220 9 % 240 7i% 140 *%. i%. i% i%. INOOMB. 0. $320 10. $264 11. $1,500 12. $112 13. $288 14- »700 15. $700 16. $360 BATB. 4% 5i% 3i% 8% 7% 10% 4i% KAB. VAl, 106|. llOi 96 85J 140 130 225 76 BBOX. i%. i%. i%. i%. i%. i%. i%. *%. Solution, On $105 investment. $7 income is derived. " »100 .. 100 V _l_ aa. . A rate per cent == 6§ % ^ '""'""^ ^' ^^^^^^d. 439. To find how stock must be boucht «rh,Vh a given per cent, dividend fn rltir^ ' ^^'^^ P^ys cent. - n the investment ' *^'^^ * ^^"^^^ P^r a- ,, . Solution. Smce the mcome derived from 1 sir-re is «fi •« „ . .u of my investment for 1 share. ' ^^* therefore be 8% • inn 5 ""* f '^'^"'^"^'^ P"«e of 1 share = $6 •• -^^^^ " " •' Ton o = H^xQ:= $76. ^j^ EXERCISE 102. ^ What per cent, of my investment will be dflnv«^ / mvestmg in the— aenved from 1. 4 per cents at 120. 2. 6 <• 80. 8. 6 «• 110. ^- 3} " 90. 5. 8 per cents at 125. 6. 9 .. 175 7. 10 .. 225. 8. 12 ,, 2^Q_ 9. ^ per cents at 70 10. ^ u y yg- n. 5J .. 110. 12. 6 90. STOCK EXCHANGE. BBOK. i%. i%. i%. i%. k%. i%. i%. At what price must I buy stock which pays^ 13. 6% dividends to realize 9 o^ on my investment J 261 14. 4% 16. 5% 16. 8% 17. H% 18. 4^% 19. 7% 20. 9°^ 5% 6% 4i% 5% 3J% 4% 10% it u << Solution 1. Coat price of «100 of bonds = mo Polling " .. „ _ - ^^ m> = par value. Loss in 16 years = $20 "1 year = 5111 . J°'"'°° *^^°'^ year from $100 of bonds = $6 .. txani each year on $100 of bonds ^ $6 - «U - ftia On #120 invested, the income cleared 1 ^ ~ *'* /. On ?S100 •• „ 4a - rl ^ 100 , nu .-. ^^2i is derived from the investment. Solution 2. Eeceipts of §100 of bonds - siinn .,„ i Income <• T Z ^ ° l^' '''^'"^ ^* «°^ «* !« y^"8 ■ _ — - J6, gOper ye ar for 16 years Total receipts Cost - $196 at end of 16 years = 120 Gam on $120 investment = $76 for 16 years qaao/ *-\°^ " = «3§|for 1 year m % of mtere^t is derived from tl.e investment. sevfral J^afslo^rTn'^llH' Tl ^' '°"^^*' ^^'^^^ ^-^ d^-^^denu, .u rcanze a specified per centfon theinvest: Pi "'i f^'m HI im I 262 BTOOK BXOHANQE. Solution 1. By simple interest. Solution 2. By compound interest. If «6 income be invested at compound interest a« a .. year at 6%, the income at the end of in l n ° a^eoeived each (see Table of Annuities). ^'^" ^'" ^'°°«°t ^ #76.467 ' .-. Amount of WOO of bonds at end of 10 years - «17^ ^ar, . present worth of this amount for 10 years at 5 '/ ' ~ ^^^^^^' """^ '^« ♦n5.467 ^ $1.6289 + = $107.72 /Xs ^' °°°'P°""'^ ''''^^^^ ' EXERCISE 103. 1. What per cent, of the investment ib received «« mcome by purchasing C. P. R fl's af inK *^f «^^ecl as in tT^enty years ? ^ ^ ''•■"• ^ « »* 106. Payable at par 2. What per cent, income will be received if T k Domimon 4's at 112, payable at par in siZn ^rs p "' 8. Bought Intercolonial Railway bonds at 90 bearing 4 % mterest, having twenty-five years to run Wi f ^ cent. wiU be reali;ied if thev are imT.f I ''* ^^^ tuey are paid at par at maturity ? 4. What per cent, income will be aained fmm a^u j bought at 80. and payable at par i^ Cy yZsY '°"'"' «• In 1882, intercolonial 6'a, dae at i,»r in looo bought for 108. What interest win ,ht pr^ ? "^ """ _^'mWIKtJi--.,-" STOCK EXCHANGE. 6. If I pay 108 for Dominion 4\ havina fiffpp„ ^.„ , run what per cent, will I receive i I keep ^hertfl ^ mature, and they are paid at par? ^ ^'" *^'^ 7. At what price must 6% debentures, payable at mr in Hght years, be brought to realise 4 o, on t'heCestnfent; 8. Bought railroad bonds payable in five years and expect to reahze 7 % on the investment. What ml'.^j^, fiftL'?ears" thL' ^"' '"' ' °^ '^'^"^"^^^' ^^^^ --*-« in Wteen years, that my mvestment may yield 4°/? ^RnfK simple and compound interest). "^ ^^°*^ 10. What shall I pay for a bond of $500 having twelve years to run, with interest at 6%, in order to make iT an 8 % mvestment ? (Both methods). ^ 11. What must be paid for a $600 debenture, due in fivA yea.., with interest annually at 4 o^ so as to real e f? on the investmeut ? /^> "•a w realize 6 % EXERCISE 104 A^VTT """^ '^^^'^^^ '""^^'^ »*° Dominion Si's at 97f yield, brokerage J % ? * ^ 'LI »t°»k at 112, broterage i% in each ^t, Chat annual income IB secured ? ^aae, wnat Jt«*«o™ 1';!.°'' """" '<"■ *"!•« p» »"""■». is sold 4. How much must a gentleman invest tnr hi^ a u* in 7% bond, »en,ng at L, .„ sseu/eTh^ I'ltCj mcome of fsis ? t.iauai 'J I I '! ' W. tl 264 STOCK EXCHANGE. profit?* "^ '" P""^'"'^^ »■"' «»'e, what „ae ,h; net brokerage? ^"' *' »2*- ™at was the gain, less i| 7. Governments vieldina tOAn • interest, were sold aflOsTnAl '"'''"' ^ ^'^^ ^* 4% at $75 an acre Hoi 'anv ^'°'''^' ^"^^^^^^ '^ 1^" ^ now many acres were bought ? investment in it ? ^ realized on an ""»rt;r^t:trra;r^-»o.^ 13. If a man buys stock af i7o/ „u cent does he receive on H« n ! ^ ^ °'' P^"*' ^^at per dividend of s/' nn Z n '"r'*'"'"*' ^^ '^^ «*<^°k pays a ui og- ^ on Its par value ($100) ? 14. A man bought 8 shares of stock «f ioqs ^ keeping it eleven months received «T -f , ^' ''"^ ^^*^^ and sold the stock then atlO a' Wh^^"' '' ^' ^^ '^h-^' receive on his investment? ^'' """*• ^^'^ ^^ ''•mm»tlimmmmf STOCK EXCHANGE in. Md the latter at 98* Wh - ' "^ ""^ '°™<''- =" being worth 50^? *' ™''* ™' "^ S»'». ■""■"^y MKU''^eJr:fr8V';3^:'^r""r} *'^''^°'" tbe;a.e invested in C»2 Zt ItS"' ato"'^ ' " 15 % every two months ? '"^^' P^^^^^g '0%. What dll tht IVu^tt *°'- '"^ '"^=""^'" P"'-* 19- A man's income from $2,000 worth nf cf. i • ds« sen.,.an„„ah. What is the'per l^t t^, " ^^^ .Jihtit:reX'p:;°r;r*'*'*-"^''»«^^^ wh!n lirfwSI'si?""*"™"' '"'»' " "« ™.ue 22. Which is the more profitable investment . ,t„ l, . 120, paying 8 % annually, or a an J.„ . , ' '°* *' 6 % annually ? ■ ^ ""•^^*'' '«""' »' 90, paying «bov; p!™ h"o2be;:::„t\''r ''"',■ """■"■■"^ »' « -;«o,ane.prero:;:4:t^?;tu^rr°' fact ringtmptrt'';'''- '"? "^''' "' "'«'< '- » — *50 per sZ e ■ h t 'ft™ °' "'™'' "^» "'-«<' "' amounting to 75'°/ oil," "?"'« "^''^^ '"•stalments. declared. 'hoI nfu .^, ^ ^'^^ "f -" »' «.. was oent. on the actual cn-t, ■'"'""""• '■"^ »' "bat rate per !,1 1 )'l ',••-* • "S If; Yi 1 1 l-^i H ilijj 266 STOCK EXCHANGE. 26. The gross earnings of a stock company with j, capital of $3,500,000 are $420,000; their expenses are 60% of their gross earnings. What per cent, dividend can they declare, after putting aside $28,000 as a surplus ? 27. The receipts of a mining company in one year are $170,000, clear of all expenses. The company has a capital of $600,000, divided into shares of $10 each, reserving $50,000 as a contingent fund. What rate of dividend can It declare for the j ear \> what per month ? and how much can be paid on each share of stock ? 28. March 4th, deposited with my broker $500 margin, for purchasing 50 shares Canada Pacific K. E. stock at 92^.' The stock was sold March 28th at 96|. Allowing 6% interest on the deposit, and charging 6 % interest on the purchase, and \% brokerage, what was the net profit on the transaction ? 29. Sold " short " through my broker 200 shares Michi- gan Central at 90, and "covered" my "short "at 86f. Albwing ^% commission for buying and selling, what was my net profit ? 30. May 6th, I bought through my broker 300 shares of a certain stock at 93^, depositing with him $3,000 as " margin," for his security against loss by a fall of price. On the first of the following month, he sold them for my account at 95. How much does he owe me besides the $8,000, if he charges ^ % brokerage for each transaction, interest at 6% (for the exact number of days) on the money used in excess of my deposit ? 31. Three companies. A, B, and C, are to be consolidated on the basis of the relative market values of their stock. Thus, A's capital $1,000,000, Market value 100%; B's " $1,500,000, " 50 %i C's " $625,000, " 40%. li STOCK EXCHANOE. 267 The capital of the consolidated company is to be r2,000,000, in 20.000 shares of $100 each. What propor- tion and what amount of the capital should be allotted to each of the old companies ; and how much stock in the new company should the holder of 1 share of the stock of each of the old companies be entitled to ? 82. A customer deposited $500 margin with a broker November 28rd, who purchased for him 50 shares Michigan Central at 80. He sold the same stock November 80th. at 98. What was the gain, brokerage J %? 88. Aug. 80th, a broker purchased for the account of a coBtomer 800 shares of Eailroad Stock at 78. He deposited as a margin $3,000. On Sept. 22nd ,the stock was sold at 74|. What was the loss ? Interest 6%, and commission 84. May 10th, a speculator deposited with his broker $5,000 as a margin, and directed him to purchase for his account 600 shares i'ominion Saving & Loan, preferred at 90f. May 20th, the stock was sold at 94i. What was the gain ? Interest 6 %, brokerage i %. 35. Sept. 10th, I deposited with my broker $5,000 as margm, and he purchased for me 200 shares, C. P. E at 90^, 200 shares, Lon. & Can. L. & A. (half stock) at 122J and 200 shares Intercolonial Eailway Stock at 49|. The stocks on Sept. 80th were quoted as follows : C. P E 80^ Lon. & Can. L. & A., 120^, Intercolonial Eailway 4l|' How much should I have deposited with my broker to make my margm of 10 % good, and to cover commission of ^ % for buying and selling, and interest at 6 % ? If I had been unable to have made an additional deposit, and the broker had " sold me out," what would have been my loss ? 263 EXCHANGlw EXCHANGE. m^ffu,' f^'^'^T^u '' *^' '^'^'"^ ^^ ""^''^ merchants in distant places discharge their debts to each other without the transmissioH of money. gr!;?Tnd ?Tr!-'; ''"* ''■^' '^^^''^^^^ °"«^ ^- °^ Halifax «2,000 for hT], w of Hahfax owes D. of Toronto 82.000 for dry goods The effect a setting off or exchange of one debt for the other. 443. A Bill of Exchange is a written order, drawn by one party on another, to pay a specified sum of money to a party named therein, or to his order, or to bearer. 444. Bills of Exchange are of two kinds, viz. : Inland or Domestic, and Foreign. 445. An Inland Bill of Exchange is one which is drawn and made payable in the same country. 446. A Foreign Bill of Exchange is one which is drawn in one country and made payable in another couutry, 44r. Inland Bills of Exchange are usually called Drafts and are distinguished as Time Drafts and Sight Drafts. ' 448. A Sight Draft is one which is made payable upon presentation or on demand. 44». A Time Draft is one which is made payable at a certain specified time after date or after time of presenta- tion for acceptance. ' EXCHANGE. 269 450. A Bill of Exchange is negotiable when it may be transferred from one person to another by endorsement or assignment. ^ 451. The Rate of Exchange is the rate per cent, which IB computed on the Bill of Exchange. 453. The Course of Exchange is the current price paii in one place for bills of exchange on another place. •This price varies, according to the relative conditions of trade and commercial credit at the two places, between which exchange is made. amount of indebtedness to each other; and these, in turn, are largely dependent on "the balance of trade," or comparati;e amount of exports Gri'tT?" ":^' r^ ''"*^' '*^*^^ °"- C^reat Britain more ^hln Great Bntain owes the United States, which is likely to be the case IfTt has imported from Great Britain more than it has exported thithe oommaf/' '"' °'"°*7 "'" '^ ^" '^'"^"^' ^^ -» conse,uently command a premium. If. on the other hand, the balance of trade is in favor of the Urn ed States-that is, if the exports exceed the impor - on G e!rR > ' '^/"'°'*^' *° *'^ ^""^^^ «*^*-- *^« -PPly oT bills fall bll par "'' "°" '"''^ '""* *'^ ^^°^^-^' -^ -°^-ge will The premium for exchange on any country can not long exceed the ZL fr;'''T*''*'^^' formerchants'will transmit' 00^0 ply their indebtedness abroad, if it is cheaper so to do than to buy exchange 453. The Par of Exchange is the estimated value of the corns of one country as compared with those of another and 18 either intrinsic or commercial. ..f ^*; .?' ^"*""'^' ^^' °^ Exchange is the comparative value of the corns of different countries, as determined by their weight and purity. ^ Thus, according to the mint regulations of Great Britain and France £1 sterling xae.,«al to 25 fr. 20 cent., which is said to be the par ^tween i?il*".l^'"^«- ^-^-.^« ^«*-n the two countries is s'aid to be at dra^TT"/"-''"^"*'"''^ ^ttbisraie; that is, when a bill for £100 drawn m London is worth 2,520 francs in Paris, and conversely. When ''^M if ^ 270 EXGHANOB. London *„ „. ?ay . LuXultil ,r 'T' •"""■ '">■•■■" ta London and in (.,or ot P,ri° ' ^''°™'- '"'■•"geU againrt «.. ....«o„!n .0 rrd:'„'^:-;":,i,r„,»t:.rr'* "^ '^ 455. The Commercial Par of Exchano-A ,a +v, parative value of .he co.ns of diffolToounW t'dZ' m»ed by their nominal or market price '" .iVd-t-ttzi:^^" tnTd:.-""' rr'"' -»"» nBage, fluctuates. '^ ' ^ determined by commercial arat*' ifab^rXT af '" """ •' """■ '"^ '^™ "' ""« «. of ^- ^ ' °^ ** ^ premium, and below oar or at a discount, when sold for less than Uv LI INLAND Oh DOMESTIQ MXCHANOE. 271 INLAND OR DOMESTIC EXCHANGE 457. To find the cost of a draft at sight. Example 1--How munh mast be paid for a sight draft of «1,000, on the Bank of Montreal, at a premium of 1 J % ? Solution. U + $.015 a $1,016, oourse of exohanM .'. *1 coats $1,016 .'. »1,000 cost »1.015 X 1,000 = $1,016. Am. « . « Example U.-How much must be paid for a sight draft of $600. on llie BanJi ot Ottawa, at a discount of 1 % ? » «. uu Solution. $1 - $.01 = $.99, course of ezohangs .'. $1 costs $.99 .-. $600 cost $.99 X 600 = |594. Ana. 45H. To find the cost of a time draft. on Hamilton being in Toronto at 2^ % premium ? ^^^' Toronto, July 18th, 1889. Seventy days after sight, pay to J. S. Carson, or order. BIX hundred dollars, value received, and charge the same to my account. To Bank of Montreal. Hamilton. ^"^ ^^^^oi,- SoLDnoM. •1 f $.0225 = »1.0225, course of exchange fttmn:; ^^'l'' f '°^u"' °' '^ '"'' ^^ '^•••* «* (legal rate) $1.0105, oost of exchange of $1 ^ o s $1 coat $1.0105 'J600 " $1.0105 X 600 = $606.30. ■H ^>. IMAGE EVALUATION TEST TARGET (MT-S) k A A U.. A % ^ i$> 1.0 I.I no _. 1^ 1^ 2.2 IL25 i 1.4 20 1.6 Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 m \ qv \ :\ sS^ Ci^ 'S. 1 i 7==^ II 273 INLAND OB DOMESTIC EXOHANOM. C>u.hJ^T^''W^l^ *''" "°'* °^ ■* ^*^ ^^y«' ^^"^f* 0° the Bank of Quebec, Toronto, for «900, at a discount of 2^ %. Solution. 91 - ».025 = $.975, course of exchange .0104 + , bank discount of U (63 da.), at 6 % (legal rate) ».9b4b, cost of exchange of 81 $1 cost ».964o .-. »000 " 8.9646 X 900 = $868.14. EXERCISE 105. 1. Find the cost of a draft on Montreal for $1,100 at i of 1 % premium. ' 2. Find the cost of a draft on Winnipeg for $1,850 at i of 1 % discount. * 8. What is the cost of a draft on Chatham for $1,800 at 1J% premium? ' 4. Exchanged $600 in bank notes for gold at 5 % premium How much did I receive ? 5. Sold $875 uncurrent money at 2i% discount. How much did I receive ? How much did I lose ? 6. What was the cost of a bill for $240 on Belleville mi'- chased at 1^ % premium ? 7. Required the amount to pay for a draft to be remitted to Hart & Denton, Kingston, for $1,250, exchange at f "^ discount. ^ ^-^ 8. Shipped goods to Winnipeg, and received a draft for $2,500, which gave me a profit of 20%; sold the draft at H % premium. How much did I gain by both transac- tions ? 9. Bought goods for $1,250, and sold them at a profit of 25%; purchased a draft on Fredricton with the proceeds at a discount of f %. W^hat was the amount of the draft ? an the Bank of INLAND Oli DOMESTIC EXCHANGE. 273 10^ A commission merchant Bold goods, the net proceeds of which were $2,760. How large a draft can he buy tc S9 h' T^^""''''] h« P*y«2i% premium for the draft ? How large a draft if he purchases at 2^ % discount ? JLfa^^ *?' '''*u ^ ^ '^'^^* ^""^ ^^•^'^^' P^y^ble 30 days af^er sight, when exchange is i of 1 ^premium, and interest 12. Find the cost of a draft for $950, payable in 80 days, when exchange is at par and interest 4^ %. J!. ^'If *^r! ''''* ""^ ^ ^'^^* ^""^ *^^' payable 60 days after sight, when exchange is lot 1% discount, and inter! dai«'«f "'^ *\V°l* '^ * '^'^''^^^ $1,200, payable in 90 inTeres?7 oX"'*' " '"''"'' " * °' ' ^ P'^^^"-' -^^ 15. Find the cost of a draft for $810, payable in 90 days when exchange is at i of 1 o^ premium, and interest 5J% 16. Find the cost of a draft for $725, payable in 60 days when exchange is at i of 1 o^ discount, and interest 5 % at ^qo !I^* T'* t T^ ^° ^°'"""*^ ^'' a draft on Victoria 1011%? ^^'SOO. the course of exchange being * ^?*/ It '" ^''''°°*'' ^''"Sht a 60 days' draft on Mon- tti::;ttr'"*°^^^^""-^°^^'^*--*- ^^^-^^ 19 A broker in Montreal bought a 90 days' draft on Hahfax for $1,299 at ^ discount. He paid /% additiona" for brokerage. How much did he pay for the draft ? m^L!^^^^'^'"^''"' °''''^^°* ^" ^^°"^P«^ «°ld f°r a firm o ?19 9^0 \T'«°^«»* «f ««tton- The sales amounted 10 !pi2 240, and his commission was 6 % on the sales Ha nvnT ^ 7' r-mx.teu a oO days- dralt at f % discount for the proceeds due the firm. How much did the draft cost ? II ii; ii i.i 274 INLAND OR DOMESTIC EXCHANGE. 45tt. To find the face of a draft at sight. meroe ^^IV.TJ ^"' ''''•'' ''' ^ ''^''' ^^''^ °- *he Bank of Com- rneroe. Wmnxpeg. at a premium of | o^. What was the amount of it« SoUJTIOM. »1 + ».0075 = »i.0075, course of excliange $1.0075 is paid for #1 face 1 n h 1.0075 »652.86 '• '• ^^^'^-^ 1 OJ75 .-. Face of draft s ^648, f^ V,- ^^''" ^—^ commission merchant in Belleville wishes to reni.t to h.s employer at Halifax a sight draft pu«,hased with »7"o2.70 Z 18 the face of the draft, exchange at f % discount ? Solution. »1 - ».00625 = $.99376, course of exchange 9.99375 is paid for U face •1 " »« »—-L_ « .99376 »7,202.70 " «. «Z!?0^ .« .99376 .'. Pace of draft = $7,248. 460. To find the face of a time draft. ExAMPM l.-The cost in London of a 70 dav-J' draft on Ofta»o exchange J % premium, was »797.40. What was the ^ac^ of ^^1^7' Solution. »1 + ».00876 = «1.00876, course of exchange .012, bank discount of 91 for 73 da. at 6% •.99676 = cost of 91 •.99676 is paid for Jl faoe fl •799.40 » .99676 | 797.40 .99676 ^^aee of draft 5= iJtiOo. INLAND OR DOMESTIC EXGHANOE. .,-,- - 1 O Example 2.-A commission merchant in Stratford wishes to remit Ira dttunt ofi; ; "° '""''" "*' *^' ""■ '"''"'' '^'°^ SoiiDTlON. n - ».0076 = ».9925, course of exchange i0054 +, bank discount for 33 da. at 6% ».9871 = cost off! 8.9871 is paid for $1 iace f i_ «• .9871 ^ . »«87J0 .. .'.>871 Face of draft = »l,000. »1 »037.10 " 461. To find the rate of exchange on a sight draft 81 213?o'''''fTI.';;^''?°^' °* ^ "'^^' '^'^" *" ^^°"'p«« *«' »i'^oo ^«« Vl.^ld.dU. Find the rate of exchange. Solution. Cost = $1,213.60 Face T= $1,200.00 Premium = $13.50 $1,200 was purchased at a premium of $13.60 " «• tt ol3.50 $1 $100 1,200 13,50j^W0 ^ * 1,200 '** •■• Kate of exchange = 1|% premium. SoLnxioN. Face a $600.00 Oo8t = $694.76 Discount = $5.25 $Gp0 waa purchased at a discount of $5.25 11 u « 5.25 «00 .Bate of exchange "H:' '^\' r^*^^'^^^ - ^--*o drew otth mn.m oi 1:^0^^ thus realizing $508.75 from his dividend- how many shares did he own ? dividend, Ouet."^ T" *° ^J'" ^'""'^ '^=^^ *4.800 due him in draft or th" ""'' T "^^' ''' '^^^^ ^^ -^ King a draft for th s sum on Quebec au,l selling it at A"/ dis- .ount, than by having a draft on Owen Sound rem.ttd to t^im. purchased in Quebec for this sum at U p."m"um' .t!o?rifeX:;!r^^^^^ 50 Lt7rf ft!:>W»f- ^" P"°"P"^ ^^'^^^-^O' ^a« directed •o buy a draft with this amount, and remit it. The nrin 3ipal received $4.960 ; what was the rate of exchanged -'hl^'wai'th '''^'"^^°° Toronto for |5,000 cost $5,075 : "la^ was the course of exchange ? FOREIGN EXCHANGE. 279 FOREIGN EXCHANGE. 46a. Foreigm Exchange is the exchange which is 464. Direct Exchange is confined to the two places between which the money is to be remitted. ^ 465. There are always two methods of transmitting money between two places. Thus, if A. is to receive money let. A. may draw on B. and sell the draft ; 2nd. B. may remit a draft made in favor of A oate, eaoh bearmg the same date, payable to the same party _ The object of drawing Bills of Exchange in sets of three ,s to provide against loss in transmitting from one country to another. The bills are sometimes se"t by Afferent routes or by the same route at different dates «t::.rthi:r' "-' °""^- '"^ '=^^' ™^ ---^ -<• p- i, ■!: i ' ¥. Myni W I 280 FOREIGN EXCHANGE. SET OF EXCHANGE. ■£1,000. (J- X , lORONTO, July 23 IfifiQ order of U ^ ZLll"ty.''''Tl'''^' ^^^ '^ *^« value .ee.e., X:^^^^::^.^^^- To Brown. Shipley & Co., ^''^'' McDonald & Co. No. 179. ^«'^^<>°' England. ^^ (2.) i'1,000. „ To Brown, Shipley & Co., ^''^'' McDonald & Co. No. 179. London, England. /- (8.) ^1,000. ^ a- X n lORONTO, July 23 1880 value received, and charge the same to aoeou™ „f " "* To Brown, Shipley & Co., "^"^ MoDoNiin & Co. No. 179. ^"""J™. England. u.._ FOHEIQN EXGHANOE. 281 »ly 23, 1889. inge (Second , pay to the ds Sterling, iof ILD , aud the o a 'A w p l4 8 a So- ■d q S3 lo .•t-:«««qinu50"iqeiap!>5i3>mt£'«a) O (S o • :ee : : : =.o i : :SH ! ! : :■« I»3 1 : i =|i :|ai^ Sis-. t».-.*H t».3 E-iH&DC3> 284 m ,t FOREIGN EXCHANGE. 480. To find the cost of a foreign bill of exchange £ sterling? ^ '"'^'^' ""'"''^"S" ''^"^g 9'^°t«d at «4.86| tothe Solution. Cost of £1 _ $4.8,;j ,"i* iranoa, exoiiange being quoted at 6.18 ? Solution. 6.18 francs = $i 1 5.18 franc = «•"" "«"■ = «|^ = »400. An.. ., .. MoNTRRAL. Jul V 22nd 1889 At sight of this first of exchange (second^ aud third of same tenor and date unpaid), pay to the order of W R Telford, Montreal, four hundred and thirty-two pounds' value received, and charge the same to the account of. To Alex. Grant & Son.. ^' ^' ^""^^ ^ ^^• Liverpool, England. Solution. £9 s $40 X 1.095 840 x_1.09o 9 £1 = »^ £432 = Explanation. Since exchange on Liverpool is at 9^% premium, £9 will cost e4() X 1 095 X 4^9 premium, £9 will cos 54(M<^,095_>^J32^^2_jQ2.40 Ans. 840x1.095. Art. 475 EXERCISE 107. 1. Sold to a broker 480 English sovereigns at 4 86. I r'n /t currency when gold was quoted at 1.05^. How •nuch did I receive ? 4 "^"t I I FOREIGN EXCHANOE. 285 Jo ^" ^"'rtf purchased a bill of exchange on London at 3 days' sight, for AM88 IBs. 6d at 4 fiU wrr ' the cost ? ' ^^ ^•^^^' What was proceeds? . '"^^'^o© t^ What were the 6. What is the cost in F' -ston of « k;ii t , Eng for ^42^; fin a^ "n^ * '^^^^ °° London, xjiig., lor ±4J5 bs. 8d., at 9|>b premium ? 6 How much will a draft on Berlin for 2,400 marks cost, exchange being quoted at 94| ? ww^""?^*^ bill of exchange on Paris for 3,760.20 francs when exchange was 5.22^. What did the bill cost ? 8^ What is the cost in Toronto of a bill of exchange on mZ Til ? ™' "' """""'''• How much did I ™ni' ^"'^Z u '" °' ""•""'Se on Amsterdam for 1 440 go Idera Exchange 39*. What was the sum ob.aine'df « <»!; <• «="=''a"«e on Geneva, through a broker for 8 000 france at 60 days' sight. What were the ~8 of the draft, exchange being 6.20f , brokerage ix/ ^' "' a. "ar 711 ^ " ""' *" """' «'^^» '-- '<- Antwerp i%? ' (xvuichsraarks), at 94|, brokerage 286 FOREIGN EXCHANQE. ■■;•! i I 16. What are the prooeeds of a draft on Paris for 12 420 francs, at 5.19f, brokerage on exchange i%? 4Si. To find the course of exchange. .•„ 1 ,.^^'''-"1;^== l.-The coat of a bill of exchange on LiverDool for £Bnn inolud.ng a brokerage of i o^. was »2.443.05. What wa/the qlttion ? ' Solution. 100% + i% = 100i%. 100|%of cost of bill =$2,443.06 .'. Cost of bill _ 2,443.05x100 «„ ,,„ looi = ^^•^^®- .'. £600 are worth ?2,440 £1 is worth 2,440 _ - . qq . , 500 ~ '*■«». oonrse of exchange. E'""";^ 2.-The cost of a bill of exchange on Hamburg for 4 400 Solution. 100% + i% = 100^%. 100 % of cost of bUl = »l 057 32 .-. Cost of bill = »1.057.32 X 100 ., ,„ ioo| ~ ''^•"^®- A 4,400 marks are worth $1,066 1 mark is worth 24c. 24c. X 4 =r 96c. = course of exchange. Art. 478. EXERCISE 108. Find the course of exchange of a bill. 1. Face £,5,000, Cost «24,230.60,* Brokerage i %. 2. " £2,000, 8- '• 3,200 marks, 4. " 800 " 6. " 1,600 guilders, 6. " 3,600 " 7. " 1,854 francs, 8. " 866.20 " 9. " 2,200 reiohsmarks, 10. " 6,600 u It l> « il >l (• « (I »9,732.16, J765.66, » 184.23, »646.61, $1,680.76, «360.46, »72.09, »528.66, »1,321.66, K tl II II II II i%. i%. i%. *%. 11. A draft on Dublin for ^6860 co«t H,786. What was the course of exchange ? i- »' u. wnat rse of exchange. nge. Art. 478. FOREIGN EXCHANGE 287 of exchange ? ^^^ "^^ course of brokerage? ''™™'' "' ««hange, exclusive An'tr?for rnVr'"''''"^ *°^ '"'"'^'^S^. '»' " •'raft on of ISnge ? '™"" "" *'"• Wha. was the oourte e^chan«e. "o chargerb^e^Xtjr.at/""™ "' 4Sa. To find the Face of a Foreign Bill of Exchange Example 1 A hill r^( ^ u -^^"tiiigc. »1194.94 when exchange 1 4 88 wrat'^lr^*"' ^"^'-^- -«* s waB4.«s. What was the face of the bill? SOLDTION. $4.88 — cost of £1 •1 91194.94 = 1 4.88 . £111)4.99 ^ *^88- = ^244.875. »,. „ = -£244 I7s. 6d. Pace of bill . BXAMPLB 2. Thfi nna> «* o u-ii , SOLCTION. ».96 = cost of 4 marks. (Art. 478). " -1 •96 .. 4x«70 -9S- ExAHPLKft TV, .7 2,400 marks, Face Of bill. ' Solution, ••»1 = cost of 6.18 francs. 618x600 " 91 e 9670 » = 2,690 francs, Face of bUl. 2H8 FOREIGN EXCHANGE. li 35 . W liilli EXERCISE 109. mingham, EngJaud, exchange being at 8% premium for sterling ; required the face of the bill ? P'^'"^""^ f^^ VVhat was the face of the bill ? ^unency. 6. What will be the face of n hJli «» ti i bein« ,„„eed at 9., and itr, Tufdrri^T^Br-^' 6. An agent m Boston, havinc $7 fiqfi ^n ^, w Jjiverpool. What is the face of the bill vohinh i,« 9. A trader m London. Eng.. wishes to invest £2 600 in 10. G. B. Smith & Co., Toronto, instructed their airent at Berlin o draw on them for a bill of goods of 4 500 marks, exchange at 97^ brokerage i %. What dL A pay in Canadian money for the .oodf ? ^'^ ^^'^ FOREIGN aXOHANGE. 289 FOREIGN CIRCUITOUS EXCHANGE. If A. is to receive money from r iu^ u t^ may draw on B., and B. draw on C ^nlT ^- '"■ ^• B., and C. remit to B. ; 8rd B ^'d ^w ot c "' T °" to A. -^ "^""^ o"^ <^-i and remit If A. is to transmit to C. through B l«fc a .v, to B., and B. remit to C • 2nd a "'"'^ ""^^i* draw on B.; 3rd. B may' draw ot a"' T' '' ^" ^"^ ^• 5.400 francs, by rer:iZ7 :: aIZmJ^ T. ''"^°' '''" ^ ^-« ^^ stivers, and thence to Pads at t^Tratt 0^28 «t ""'*! °* '^ "^^^^ ^- ^0 much Canadian money was required ? '" '°' ' ''•'^'^««- Ho.. SoLU I ION. 28 stivers = 3 francs • is ^^^^ , , 5|400 franca fi.400 X 28 ^. 3 stivers _ 5.400 X 28 ,. 5 Stivers . 6.400 X 28 X 21 o ■ . . y oenta o a; 10 = »1,058.40. Ans. n I 296* K'OHKHS:^ JiiXVHAUGs:. Explanation. To rednco francs to etiverB. multiply by V. beoanse there are M times as many stivers as there are francs. ^ To reduce stivers to cents, multiply by ^, because there ar... U times as many cents as there are stivers. t* times A , ^^™^ '^-"^ Montreal merchant remits r,r,,^m Uorms to ^sterdam by way of Londou and Paris, at a tixne wi.e. tlu/l" h,.,^ of Montreal on London is »4.885 for £1, of London on Paris o^l francs for £1, and of Paris on Amsterdam is 212 francs forloiVo,!;; i per cent brokeraKe bei„, paid in London and in Paris. How ma y' dollars will purchase the bill of e:ccliange ? ^ 100 florins = 212 francs 26.4 francs = £1 66.880 florins x 65.880 X 212 X 801 . ioolTioo ^^''"^ g 65,! "0 X 212 X 801 X 801 100 X aou X 26.4 X 800 Solution. /212 ^ 1004\, • Vloo '^ looj^™"'=^ = ^^°"°- »4.885 = £1. _ 65,880 X 212 x 801 , Tm^rm — *'^°°"- _ f 65,880 X 212 x 801 x 801 lOU X 800 X 26.4 X 800 = 1^ 55,880 X 212 X 801 X 801 X 4 885 100 X 800 X 26.4 X 800 = ip22,840.634 + Ana. Explanation. To reduce florins to franos. multiply by ^^ x m, because there ar. (212 ^ lOOiv ,. ^^^ 100 «*" iOO 100 / ^®^ ** ™°'°y "*°^^ «•« *l»ere are florins. To reduce francs to £. multiply by (_^^ ^ l^i ). ^^^^ ^,^^ are /' 1 V 100^ ... V254 ^ loo y *'™^^ *« "*°y £ ''s there are francs. ^.^«^"= 8— A banker in New York remits 1f3,000 to Liveruool hv t sTsMvS; ? *' ''' ''^'"" P^' '^ ""^-^ = «-"- to Amsterdam >^t 86 stiv^ per 2 marcs; thenoe to I iverpool at 2^0 stivers per^S fnf T. ^r,'°°°^«*«'^i"«°«'ney wiUhe have in hankatTiverpoS and what will be his gain over direct exchange at 10 % premhin 7 ' re are >^ times e ar.j f^ times i80 Uoiins to the (jxcluiiii»e Paris is 26.4 r lOOfloiins; How many I florin. cs. X 801 X 801 25.4 X 800" ! 801 X 4 885 i X 800 FOREIGN EXGHANQB. 281 220 stivers 2 maros 186 francs 5 francs 40 cent SOLDTION. £1 36 stivers 100 maros 91 93.000 « 3,000 X 640 , — 100 — ^'*°«' 3,000 X 640 X 100 100 X 185 marcs. marcs. • *T§Tr = 1 stiver. . 'iA stivers = 1 marc. . HI marcs = 1 frano. •"• iJS francs = 81. 3,000 X 540 . •• ^ francs. ^^ 8,000 X 540 x_100 10(r>ri85 8,000 X 54 X 100 x 85 . f 8,000 X 540 X 100 X 3 5 100 X 185 X 2 X 320 " 9 (V X m) = £1 " ^^^'^ "'■ ^- ^^'^°"-*°"» exchange. ... 93.000 = £-1^ X A X m = £618 12B. 9d. Direct exchange £82 188. 6d. Gain. Ana. EXERCISE 1ia 8.000x64 X 100 X 35 .. iOO X 186 X 2 -«*»^«" Be there are >aase there S times as rorpool, by IBS per #1 ; msterdam « per £1 Liverpool, m? 1. When exchange at New York on Paris is 6 francs 16 centimes per |1, and at Paris on Hamburg 2^ frlnc per marc banco, what will be the arbitrated price in New York of 7,680 marc bancos of Hambur- ? 2 The exchange at Paris upon London is at the rate of 26 francs 70 centimes for ijl sterling, and the exchange at 3 An agent in Boston, having $7,636.80 due his employers England, is directed to remit by a bill on Liverpool. What is the face of the bill whih hi «!« pu^hase^for this .oney, exchange .^^^^ 292 ^OBEIQN SXCH^Qjii, ^r "\ 120 franc" WhatTth "" ^""^ »» "J florins for and P^, ™'" " '"^ """"^ o'^-'tange between London per £1 ; what ie the arhitr.t!^ ™"°' *^ centimes Phi.ade.phia »d'ttr;:rSr;loTf *''''' ""'-" -deti^TXtt S:: th"™^ " '^'"^'' »' ««.^^« hi» agent in Jndo"' X" ^^T'"^""^ '; "^ ^^^^ '» serving hia comaieei "Ti r on T^ „'" ''"""• exchange on London i. Z • i . """ '^™" "«■"'• « London* and N^es i |i^ „?/f™'.r *"» -t^^etween ■"an realize from hL be^LT? ' ''°" """"■ "^"^ «"« Toronto and Hamhnr^If i. L ' 'Change between exchange botwSn Toronto an'd r, °T ''' ' ""•"=• ^"^ that between LondonTnd Paris .^ 26 ? '' *"»'«*!! that of Paris on HambuL 7, I7 f f""' '" ^^ '" "■<' what wa, sh„n,d r^^Z!Z^ ^» ff -- B. «-^oX:hth'r:"^rlrto?h^^^'-''^ pay» the requisite sum to bisTroker atTf • T =' exchange between London and P„Ts '' 1 1^7" ""';'' *'" and between Paris and at b * , ^^-^^ '™°e' fo'*], rouble. TheremitLnl- i', '■"""■8 ^'^ ''»■'■<'« for 1 franc, for £1 TAZT T"^ ""'" '"^ «"«= »'e 25.85 broker gainlrtehytheTel^;' ""'''»■ ^""'"-s the ult.TX^rLo^lt^-„ron-paTs;? 12 florins florins for Q London 8 at 9f % centimes between ■ $8,720 made to Naples, ent. If between loes the FOREIGN EXCHANQE. francs 25 centimes ner ti . a ^^^ to a guilder. The LhlnL ut '° t'^^t^rdam. 40 cents at the same time 25 fra"^' t^'Z'^ ^^-"«e and England advantageous, the direct exoh^t '^ '" ^^^ most through Amsterdam? ^'' ^' *^^^"g^ i^aris, or 10. When the cours* «/ ^. Paris is 9id. per frl and ttT '^*""° ^^^^ and Prnssian thaler, and 24 5 thf Tl^'' m^s'^hnt to 1 and 25 Austrian florins to 12 fi v '^^"«*--- Aorins, London merchant owe" one'n Vel"'*!? '"^^^^'-^^ ^ " l^e more advantageous to rem^^ I "''' ^'T '"^"*«' ^i» and Vienna, or dirocfc to YeXK^' ""^^ °^ ^^"«' ^e^^i^. eguivHlent to 4s 2d ? ' '"^^i^^^^^S a du.,u to be i 2,400 •etween . The br ^1 ; L; and 3. Bj r rsburg . He n the or A'], for 1 25.35 !S the •0 in is, 5 II ',., 1 til! fh Jit ulul i III ■i I litll! 294 JUT/0. RATIO. 485. Ratto is the relation between two members of the (6 ?9;. '^'' '^^''' "^ ' *° ^ ^« (9 + 6) ; the ratio of 6 to 9 is 4«6. The Sign of ratio is the colon ( • ) Jhe^ra^ioof9to6 is expressed 9:6, or 9.6, or a,s a 4«7. The Terms of a ratio are the numbers compared. 488. The Antecedent is the first term, or the dividend or, If expressed a^ a fraction, the numerator. 48». The Consequent is the second term or the dmsor. or. .f expressed as a fraction, the denomLor 4»0. The two terms together form a Couplet. 491. A Direct Ratio is the quotient of the antecedent ' divided by the consequeni. antecedent 4»3. An Inverse Ratio or Reciorocal Raf.v^ • .u quotient of the consequent divided by rrnte^Tdrnt" "' H,.*rV^"r T ""'P<>'"«»eing illus- r V'Ct of the by eif'y,r extreme SIMPLE PROPORTION. SOLUTION. » X «<. ,6 . 9, „o. required. Pri„oipl. a. E„„.. .._„ . ,^. „, .„^„ ^_^,, ^^ ^^^^ _^^ ^ ^^ ^ ^^ ^^ SOLUTION. the:<^.r.xx~p'«i;i;trtoT„:s.' "^"^ ""■" """ "•°" ■•■ 6 1b.. .-Ulb.. :,-Met8. :re,„l„a„,„, ^•■•"^"'""'""'-"f''-«1.3i.A,.. PH„oi,.,e3, SOLUTION. .•.«».. re,.,„a , or 5 „,„ = »-iH =.= a.,. A.,. P™„ip,.,. or, r.;r, ^ ' "•" ■■■■ '' '^y <"»= -^-^^ - -hat will 68 gallon, 18. If 6i buah. of oals cost $3. what will 9* bush, cost t 14. What will 87.6 yd. of cloth cost, if If yd. cost ».42 ? 16. If by soiling $1,600 worth of drv ™n,1. t • $276.40, what amount must I sell to sa,7»l!^?, ' T ^^1«^ What will n*,b. of tea cost, if 8 lb. 12 oz. COS. I Ho:^.^n;";:t^sUU'sr:ftr;"--^^^^ money at SOc a lb ? "" °""x6 SIMPLE PROPORTION. Bnominations, 299 20. If wall paper be 20 inches wide. I shall need 7 rolls to paper a room How many rolls will suffice if the piper be 24 inches wide ? If 30 inches wide ? ^ 21 If $760 will yield $120 interest in a certain time What interest will $600 yield in the same time ? Btl!* LT^' T^""'' '*'P m^^Bme^ | yard, counts 1.200 steps from his house to his office. How many steps C his son have to take, whose step measures ^ yd ? ' hrtt IV*'\ '"^'' °° ^^^'^ «^^P °°°««°^es daily n lb bread, their bread will last 6i months. How much wm each man get per day if it is to last 6^ months ? miks wm' t'h?/ /? P^f -trians is as 5 : 4. How many miles will the first travel in the same time in which the second travels 84^ miles ? ^ cos?? "^^ '''' ''*' '' ^''^ ^'^ ^ ^«^«' ^^^* ^i» 5 acres Sf^L%i:r;t:r ^" -''-' '- ---- 27. If If yards of velvet cost $6^ what will 9 yd. cost ? 28. A farmer sowed 8 bush, of buckwheat on 2| acres How much would he need for a field containing 4 /a!res ^ 29. f of a sum of money is $800. how much is | of it ? bOO COMFOUND PROFOJiTlON. ■'■> j 'I IS I * 1 M ' if''^ III COMPOUND PROPORTION. Thus 3 :4) 6 : 9[ •••• 14 : 28 is a proportion ooiriposed of a compound and a -mple ratio, and may be expressed. 3 x 6 : 4 x 9 •• U • 2« to a simple proportion, 18 : 36 ;: 14 .• 28 ^ '• 1* • 28, equivalent M an tfca. ' ■ ' '""™ " » ««"«. "ill dr., 15 too. COMi-QUND PBOPQRTIOif. 301 18* cause : 2nd CMse ::'l8t effect : 2nd effect or Ut effect : 2nd effect := 1st cause : 2nd cause. bow j„xJ^m'.„'33r'6i::r "' °"" '° •^^•^- SOLUTIOM. . let cause: 2nd cause :; Ist eflfect : 2nd effect. 12 . ^„. . t iuu. euecii. ^ horses : 20 horses I 7 ' days : 16 days | :•* 1 24 bush. : No. bush, required. /. No. bush, required = ^0 x ]6 x 24 , .„ ^ , 4 X 12 — * ^''" °°sh. Ana. Prin. 3. Solution. Ijicause__^_jndcau3e ^^st^^fect_^^„, effect. 2 workmen : 3 workmen 5 days : No days required 24 yards 3 feet 2 feet 30 yards. 4 feet. 8 feet. -J. f \ a leei : a feet th, „eL. *' '^"°"" "J- "■« P™i»"' »' tte given p.rt, ^ Hence, required time = HJL5J1_?Ox4 x 3 —3^24-3^-3-3^-^ ~ * "^^y^- ■^°»- Prin. 2. EXERCISE 112. 1. 8:9 \l]' 40:«. 8. 6 480 : X ) 30: 15; -84: 21. 14:12;-|66:54. 7:28) «0:80. 5. Five olerka nafi 9fi nniV^x. «« • , »«™c ,ate, how r^ ^^pe;;^,! SVu" e" in lo dav! ^ 802 COMPOUND PROPORTION. 6. Six lamps consume 2 gallons of petroleum in 8 days How many lamps will consume 3 gallons in 12 days ? 7. Two workmen dig a ditch of 24 yds. in length and 8 ft. m width in 6 days. How long will it take 8 workmen to dig a ditch 30 yds. long and 4 ft. wide ? 8. Eight persons spend $296 on a journey of 7 days How long will $300 last 7 persons at that rate ? 9. If a block of marble 5 ft. long, 3 ft. wide, 2 ft. thick weighs 4,850 lb., what will a block weigh measuring 7 ft. in length, 4 ft. in width, and 8 ft. in thickness ? 10. Ten cwt. of merchandise cost $2^ freight for 245 miles. What will 6 cwt. cost for 210 miles ? 11. If $700 at interest amounts to $770 in 15 months, what sum must be put at the same rate to amount to $845 m the same time ? 12. From the milk of 20 cows, each giving 18 qts. daily 16^ cheeses of 50 lb. each are made in 42 days. How many cows, giving but 16 qts. daily, will be needed to make 88 cheeses of 60 lb. each in 28 days ? 13. Being asked to find the number of bricks in a wall 10 ft. high, 922 ft. long, and 16 in. thick, I found that a part of the wall, 4 ft. high, 4 ft. long, and 16 in. thick contamed 448 bricks. How many in the whole wall ? 14. If $750 gain $202.50 in 4 years 6 months, what sum will gam $155.52 in 1 year 6 months ? 15. If it require 1,200 yds. of cloth { wide to clothe 500 men, how many yards which is | wide will clothe 960 men ? 16. If by travelling 6 hours a day at the rate of 4^ miles an hour, a man perform a journey of 540 miles in 20 days, in how many days, travelling 9 hours a day at the rate of ^a "^ — S'H noiirj '^iW lie travoi 600 miles ? COMPOUND PROPORTION. ml fz s^Twtr aid's ft r" 7"''^ «° -''^ " o""" houTB each, if 6 m n can df » L T '" ^^ '■^^^ "' 8.2 i8«.io„ga„ds;rwMr.:r,d«o'L^:r'' "'^' -'^ $600 for 6 month^ H„!"''°'^' f*"" '" « "'°""=s. and III 1 :!' bU4 DlSXmBUTlVE PROPORTION. DISTRIBUTIVE PROPORTION. n.f rt f?*"!^"**^^ ^'^ P^'^*"^^ Proportion is the method of dividing a number, or quantity, into parts which are proportional to given numbers. 510. The principle of this rule can be applied to the solution of numerous questions of a practical nature, such as determining the profits and losses of partners in trade apporionmg shares of participators of prize money, find.no the relative proportion of ingredients requisite to form a given quantity of a compound, apportioning taxes, school rates, averaging, etc. Example 1.— Divide $600 amcng A. B C and D «« ti..* .u ■ shares may be in the proportion of 3. 4 6 and 6?' ' ^* '^"^ Solution 1 3 + 4 + 6 + 6 = 18 18:3 :: «C00 : A.'s share 18:4 :: 9600 : B.'b share 18:5 :: »600:C.'B share 18: 6 :: «600 : D.'B share A.'s share =s JlOO B.'s share = %l'6^ C.'s share = ftl66f I^.'s sbare s $200. iliXPLANATION. Altogether there are 18 shares, of which A. gets 3. B 4 O 5 T) ft .„^ theprohlen.thenbe,ornes:lfl8sharesrepresen^»600^^^^^^^ by 3 shares ? by 4 shares 'i by 5 shares ? by 6 shares ? These gfve rise to the preceding proportions. *«»« give rise to Solution 2. A. 3 shares is shares » «600 "' * " .*. 1 share = ^ A. gets 3 shares = i^ x 8 .-s «100 B. gets 4 shares = fi/^ x 4 = »133J, C.6 D.6 Total 18 shares. etc mSTRIBVTIVE PROPORTION. 805 Solution 3. etc ^ "^' '"'* •• A of «600 = Jissi. A. 3 shares B. 4 •• C. 6 '• D. 6 •• Total "IsTharea. SOLCTION. A.'8 Share = A.'b share B.'8 share = A.>8 share + $300 Total , 3 times A.'s sharrT^SOo" .. 8 times A.'s share + 5800 =,2,000 = ?1,200 • A.'s share = P400 B.'s share = mo + $300 = ,700 C.8 share =,700 + » 00 = ,900. EXERCISE «3. wv de |2,S00 mlo parts proportional to 2, 8 7 « 8. Dmde »8,470 into parts proportional to J *.' Lj * 4;rpCi:non?rorrf"-"^^^^^^^^^^^^ of each are contained in l.^ll^oCniowdlr^ ''™"^' o. Ihe sides of a trianele arp «« q j /. the ,en«t,s of the sides is^.soTarl:' L^rsit '""' "' together. ' *""* ^' ^' "^"«^ as A. and B. -ond. and the fonr.h S^tt'tn '^'elr™ """■ ""' 'Jill Ill i! ao6 DISTHIIiUTIVE PKOFOliTION. 8. If C. has twice as much money as B., and if $12 he taken from A.'a money, it will be equal to | of B.'s ; how much has each, the sura of their moneys being $645 '? 9. A man left his property to be divided among his 3 sons in proportion to their ages, which are 21, 18, and 12 years. The share of the youngest is $1,440. What was the value of the property ? 10. A., B., C, and D. commenced business with a capital of $18,500 ; A. invested $800 less than B,, and C. invested $1,000 more than A., and D. $900 less than C. ; how mu(th did each invest? 11. Divide 560 into parts, so that the second may be 4 times the first. 12. A force of police 1,921 strong is to be distributeu among 4 towns in proportion to the number of inhabitants in each ; the population being 4,150, 12,450, 24,900, and 29,050 respectively. Determine the number of men sent to each. 13. Divide 450 shares of stock among 3 persons, in pro- portion to the number of shares owned by each ; A. holds 400, B. 200, and C. 300; how many shares will each receive ? 14. A piece of land of 200 acres is to be divided among 4 pe^ons, in proportion to their rentals from surrounding property. Supposing these rents to be ^£500, ^6350, £800, and £90, how many acres must be allotted to each ? 15. If § of A.'s money, and | of B.'s equal $900, and | of B.'s is twice f of A.'s, what sum has each ? 16. A father divided $18,500 among 3 children, so that the portion of the second was greater by one-half than that of the first, and ^ the first was equal to ^ of the third ; wliat w.as the share of each ? if $12 be i.'s ; liOW M5? mg his 8 i, and 12 ^bat was fARTNERSHIf. ao7 PARTNERSHIP. a capital . invested low much aaay bf 4 stributeu iabitants ,900, and neu sent s, m pro- A. holds vill each 3 among rounding iO, £800, I? 0, and I , so that ban that e third; persons, who eSthI .» ^7?"°" "' ""> »' »«« tbem. for the p«Ce „f ^rrT ' "''"' °' '""»'• "' ''" <" called a Partner. ^"^^•'^dnal of the association, is ^l^. Partners may be classified as- ' 1. Active partners. 2. Silent or dormant partners. 8. Nominal partners. 4. Special partners. 51S. A Silent or Dormant p=,* interest in the business hTi. T^" " °"' """o '"'= an partner. ''™^»». but .s nnkno™ to the public as a to t' tetf^ttnf^t'SThe /" "'7"°™ "^'^ »-« pecuniary interest L its bules, ' ""''°"' ""»« ""^ ■'\W 808 PABINERSHlt. ffi'l Vii ! 518. In an ordinary partnership, each member is liable to the full extent of his means for the liabilities of the firm ; but in a joint stock company, each shareholder is liable only for the amount of his unpaid capital. This explains the meaning of the term *' Limited;' which is added to the names of companies, as for example, " The Canada Publishing Co." (Limited). 519. Capital is the money or property invested in the business. 530. The Resources or Assets of a firm consist of the property it owns and the debts due the firm. 531. The Liabilities of a firm embrace all the debts or obligations due by the firm to its creditors. 533. The Investment is the aggregate of the iuoney or property jointly contributed by the partners. 533. The Net Capital is the excess of the Assets or Besources over all Liabilities. 534. The Net Insolvency is the amount which the liabilities exceed the resources. 535. The Net Investment of a firm is the difference between the total sum invested and the total withdrawals. 53G. The Net Gain is the excess of the gains over the losses, during a certain time. 537. The Net Loss is the excess of the losses over the gains, during a certain time. 538. A Partnership Settlement is an adjustment of the partners' accounts setting forth the net investment, liabilities assumed, withdrawals, gains, losses, and showing his net capital or net insolvency at closing or settling the partnership's interests. PARTNERSHIP. ne?f*a:,tit:^;«4-; Loss When each Z time. ^"^ employed for the same period of Example, — A and S tn a B.»»,00O; ll„, ,.,„,a 52,000 ™<,'''"'""?'P: A. (aml.hrf ,:,.ooo, SoLnuo A. -8 capital = 3,000 ^•'« " = _M00 . . /°*^' " = »8,000 •• R^"'''::^''^^*^^^^"r I of capital. .. A. B share of gain = 3 Of 52.000 = 8700. = I of «2,000 = $1,250, Total gain (82,000) = ^M or'i of capital = .5 of can'* , .. A.S share of gain , ,3,000'x .25 ^tIo ' ^"^ = 95,000 X .25 = Si,2oO. tu8 over ises over EXERCISE 114. 1. A. and B. buy a store which rents for ^o^n A. advanced $3,500, B S4 ftnn • ^ '^^^^ * ^'^^r ; each receive? . ^ '^^^' ^^^ "^"c^i rent should «hat was each one', share of tie gito ?''''''"'''*'''''''''• 5. The net gains of a, B nnri p »"" kept, what has been ll'Z o^iS^mL T™' "''"« Partne. „ apportioned rX^-^rCLtrell a "sin^ rr tSrr^s r,if r •- '» year. Nine months before dissoEn „. '". ™° invinrsv,i.':rB*i?:rr"^™'''''.'- ^ .v-"..i. of 6 mnnfhl a" • f ^''S'-iug $u,4U0. At the end Of 6 months A. increased his investment by $1,500 ■\m i 3 ii d'if 816 PARTNEliSHIP. and B. withdrew $900 ; one year before the expiration of the partnership, each withdrew $1,000, and six months later each invested $500. The net loss was $2,400. How much should be sustained by each, if the partners receive credit for interest at the rate of 6 % on all investments, and are charged interest on all sums drawn out, and the loss be sustained in proportion to average investment ? 22. April 1st, 1884, Craig and Cowan commenced business as partners, Craig investing $8,000, and Cowan $6,000 ; six mouths later each increased bis investment $1,500; and on Jan. 1st, 1885, Allan was admitted as a partner with an investment of $2,400. On Oct. 1st, 1885, each partner drew out $1,500 ; on Apr. 1st, 1886, Craig and Cowan each drew out $1,000, and Allan invested $6,000. On Jau. Ist, 1889, it was found that a net gain of $37,500 had been realized. What was the share of each, if by agreement Craig, at final settlement, was to be allowed $1,200 per year for keeping the books of the concern ? 531> To find the net gain or loss, the net resources or the liabilities of a partnership. Example 1. — A. and B. commenced business with a capital of ^10,000 cash ; merchandise as per inventory, $5,000 ; bills payable,- $1,500. At the end of the year they had cash $6,500 ; merchandise as per inven- tory, $5,400; bills receivable, $3,200; debts owed by firm, $650. What was the net gain or ious of the firm ? Solution. ASSETS AT COMMr.M'KMRNT. Cash . . . M'dse . . Total .\ssi;t8 . Liabilities Mot Capital . ^10,000 5.000 i: 15,000* 1,500 . .. i..l3,500 Net gain = $U,450 ASSETS AT CLOSE. Cash $6,500 M'dse 5,400 Bills receivable .. .. 3.200 Total Assets $15,100 Liabilities ))50 Net Capital $14,450 - $13,600 = n,950. PARTNERSHIP. gj„ !«-. ? «"!" ?"~^' "-""^ ^- "^ P'^'^t"^'-^. A. sharing % of the gain or loe. MMl B, I. A. invests «5,000, and B. »-2,350. At the end of the yej tholr monroee and liab'Uties are as follows : merchandise on hand aa per inventory. «2.000; real est.te. «7.000 ; cash on hand and in bank. »U82; due on personal accounts, «1,640.25; bills receivable, »1,000- Wis payable. $800; owing by the firm to sundry persona, N,47l.6». What 18 the amount of net resources belonging to each partner ? Solution. BB80URCES. M'dse. on hand . . , »2,000.00 Real estate 7,000.00 Cash on hand and in bank .. 1,632.00 Personal account 1.640.25 Bills receivable 1.000.00 Bills payable »800.00 Personal accoun -i 4,471.69 g5.27(.6 9 Present wort!', »7,900.56 Less investments 7fl.''i0 00 Total net gain ; "555066 § of »550.66 = »367.04, A.'s share of gain, i of $650.56 = $183.52, B.'s " A.'s investment = 86,000.00 A.'s gain . . . . . 867.04 A.'s present worth «6,867.04 B.'s investment = $2,350.00 B,'s gain . . . . sb 183.62 B.'s present worth «2,533.6a Present worih as before .. ., $7,900.66 53a. To find each partner's interest, when eacli partner is allowed to withdraw a certain sum, and when no interest account is kept. Example.- A. and B. are partners, each invested $6,000, and »greed to share the gains and losses equally. A. drew out $1,200 and B 11,000, R^qnired their galTjs at the end of the year, their booki inowmg the following result : i'm Pf PARTNEESHIP. BISOUROia. OasU $7,000 Mdse. per inventory . , 7,200 Bills receivable 2,400 Debts due firm as per ledger 6,000 Total resources . . . . #21,600 Net capital at olosing, 921,600 - 94,600 A. invested 96,000 A. withdrew 1,200 A.'s credit balanoe 94.800 B. invested 96.000 B. withdrew 1,000 95,000 LUBILimSS. Debts firm owe as per ledif er 9i 000 Bills payable , 1,600 Totalliabilities 94,600 917,000 B.'s credit balance Net gain of firm . . A.'s i net gain = 93,600 B.Bj " = 98,600 9^800 »7,200 PBOor. A. in^'ested.. A. withdrew .. A.'s } not .r'ain 96,000 . 1.200 94,800 3,600 A.'s net capital at olosing $8,400 $8,400 + 98,600 =s 917,000, firm's net capital B. invested 96,000 B. withdrew 1,000 $5,000 B.'sjnetgain 3,fit B.'s net capital at olosing 98,600 533. To find each partner's interest, when one or more partners are allowed a fixed salary and no interest arcoimt is kept. Example.— A., B. and C. entered into partnership Jannary let, 1809. A. invested 914,000, B. 914,000, and C. 928,000. A. to share ^ of the gains and losses, B. J, and C. J. A. was to receive a salary of §1,000 per year, B. 91,200. anJ C. 9600 for services. A. drew out 91.300, B. ♦900, and 0. 91i800. What was each partner's interest in the firm Jan- uary lat, 1S90, when their resources were 9108,000, and their liabilities >i;{7(HX>? i t ( 1 BAllfiTERSUlP. HesonroeB Ijiabilitiea Firm's net capital A.'b investment $14 000 ^-^s^l"? 1,000 »15,000 Less amoont withdrawn .. 1,300 A.'s oredit balance 819 $108,000 27,000 981.000 B.'b investment #14,000" B.'s salary j'aoo ei3,700 $15,200 900 Less amount withdrawn B.'s credit balance C.'s investment $28,000 C.B salary 'epo »28,600 1,800 $14,300 Less amonnt withdrawn . . t54,800 $26,200 O.'b credit bal. $26,800 O.'sigain ., 13,100 O.'b net capital $39,900. $26,800 Firm's net gain A.'s credit bal. $13,700 I B.'s credit bal. $14,300 ' A.'s J gain .. 6,550 B.'s t gain .. 6,550 A. '8 net capital 120,250 I B.'s net capital 820^850 PROOF. A.'s net capital $20,250 B-'s " 20,850 O.'s " 39,900 Firm's uet capital $81,000 534. To find each partner's interest at the end r' the year or close of partnership when amounts with- fnowed."' ''''''^''' '"' ^"'^'^^^ '' ^^^^^-^ *nd ExAMPLK._A. and B. entered into partnership January 1st 188q and agreed to share the gains or losses equally. A. Lested $6 and' c1" J i ?oz r°^.''''*°'' ^"' ""°"^'^ ^% °" b" investment and wa. cL6-6«d 6% for the sums withdrawn. A. drew as follows- Mnr.h T' $300; July 9th, $250; September 10th, $200; Dec Zr" 1^1,15^' B dr«w. Apnl 17th, «100; August 4th, $400; November 23 d m^ TVhat was each partner's interest in tl,e ^usiaess Januarv 1st 1800 S rewawes and liabilities beinj: as follows : ' ^*' Si i 820 PARTNERSHIP. iils ., :'i ^li 1 V BES0URCE8. Cash Personal debts due firm Bills receivable . . M'dse. as per inventory 0. P. R. Railway Stock Total resources .. $1,800 8,000 700 18,000 3,000 520,500 LIABILITIES. Personal debts firm owe . . $5,760 Bills payable 250 Total liabilities $6,000 .. $20,500 $26,500 Firm's net capital $6,000.00 900.00 $5,100.00 $360.00 ae..'?.^ 3.B3.G7 $6,433.67 Boi.CTION. A.'s amount withdrawn $900 ; average date July 7th. From July 7th to January 1st = 178 days. B.'s amount withdrawn $750; average date August 27th. From August 27th to January Ist = 127 days. A.'s investment Less withdrawn Int. on investment for 1 year , . Less int. on JjQOO for 178 da. at 6% A.'s credit balance ]"| 77 B.'s investment $7,250.00 Less withdrawn 750.00 $6,.';00.00 Int. on investment for 1 year . . $435.00 Lessint. on$750forl27da. at6% 16.66 419.34 B.'s credit balance $6 919 34 Firm's net capital $20,'500.00 A.'s credit balance $5,433.67 ^•'^ " 6,919 34 $12,353.01 Firm's net gain A.'s credit balance . . $5,433.67 A.'s i gain 4,073.49^ A. 'b net capital .. .. $9,507.16J Firm's net capital $20,500 $8,146.99 B.'s credit balance. . . . $6,919.34 S-'sigain 4,073.49i B.'s net capital .. #10,992.83 J EXERCISE 116. 1. At the expiration of a year from the commenceniont of their business, Baker, Morgan &. Co., after taking an account of stock, find the amount of merchandise, as per inventory, to be $17,450; cash on hand, $10,250; debts due the firm, $11,300 ; amount of firm's indpl.tidn'^aq PAli'lNi^U^Uillj ^U fin,! V; ""' °' ""^ 4™' "''ii net capital and Rain • and ind eaoh partner's share of the latter tl„. T-! ' sba™, of capital bci„g a, follows: J Bake ssX";* Morgan, $5,000 ; and J. Murray, $3,000 ' ' ' ®- resources beincr %^k fton T!, "^ ^^"^' ^^""'^ one-third of the losses. Duff hdrew t'lr."' "'IT time of the partnership Fry ^I Hon a'T "°^ *^^ At close of business hp'irr^ ' ' '"^ ^'^^* ^^,000. mrlse ^14 7ftr ! resources were: cash, $3,540- Tble $f6n;^f '■ »f««' acceptances, and accounts rceiv.' aoJe, ;pi6,250; real estate, $28,500 Th^v nx^-n^ ^T outstanding notPR «s io^ ^^^'«^w- itiey owed on their BESOUROKS. ^f'^^^^^^ «3,475 Mdse.permventory 6,150 IiIABItilTIES. Bills payable Rent, eto. «3,000 700 ~ „ ■ *^ ^«niory 6,150 Rent etn '"'""" TotJr^t";;;;:::::: 55lf i ^""'"•^'"«.. » 822 PARTNERSHIP. 5. At the time of closing business, the resources of a firm were: cash, $931.60, mdse., per invontory, $18,196.25; notes and accounts due it, $8,164; interest on same, $211.50; Veal estate, $11,150. The firm owed, on its notes, acceptances and hills outstanding, $7,142, and interest on tho same, $848.50; and there was an unpaid mortgage on the real esta-e of $2,500, with interest accrued thereon of $88.60. If the invested capital was $22,500, what was the net solvency or net insolvency of the firm at closing, and bow much has been the net gain or net loss ? 6. The firm of A. & B. formed t, partnership Jan. Ist for 1 year, investing $8,000 e.ic-h. They were to have 6% interest on their capital and be charged fi % on sums with- drawn. The gains or losses v.ere to be shared equally. April 4th, A. drew out $500, July 10th, $400, and Sept. 5th, $200. 13. drew out May 6th, $700, Aug. 12th, $300, and Oct. 4th, $400. What was each partner's net capital on closing, the net gains being $3,850 ? 7. Johnston and Atkinson became partners April 1st, 1888, under an agreement that each should be allowed 6 % simplo interest on all investments, and that, on final settlement, Johubton should be allowed 10% of the net gains, before other division, for superintending the business, but that otherwise the gains and losses be divided in propor- tion to average investment. April 1st, 1888, Atkinson invested $18,000, and Johnston, 14,000 ; Jan. 1st, 1889, Atkinson withdrew $5,000, and Johnston invested $3,000 ; Aug. ist, 1889, Atkinson withdrew $1,600 ; Dec. 1st, 1889, the partners agreed upon a dissolution of the partnership, having resources and liabilities as follows : RBBOUBOES. Gash on liand 9 1,101 05 Accounts receivable.. 16,405 60 Bills receivable 2,650 00 Interest 287 41 Mdfe.aa per inventory 9,716 55 LIABILITIES. Bills payable »6,620 00 Outstanding accounts . . 1,246 50 Rent due 1,200 00 PARTNEIiSmP. Q„. If, of the accounts receivable, onlv 80»/ r,i-nv„ .„ i, what has been the net gain or os" ? mZl '°}'^«°'t' gain o,. loss of each partner? What ih'r'f ""^ i..8oivency at dissolution ? What is 1 L T' "'' each ? '^® "*^* insolvency of invtMngl^ual'ut'wrth' "-""""'"'"I' '- « years, re.eivei°ntels luh; rlt eToTtr *■■" '''°'' ^'""' charged interest at the sal rate on ,V""" '".l"'"' '" and .he gains or losses shown « fin 1 ^^IT^''''^^' .oned according to average net inve^ 1:". T e/mrths" after the formn h'nn rtf fV. l ,. -^uree months A. invested 3«,jr„f.:-„d-„ftet:t:'i*''?';'''' o»t $500 On closing the affa.rs o the 8,^ ^t ,' ""^ stajement was made: net eain t\Tni^ ™^ What was each partner's share of the gain 1 »• A. and B. became partners for one vear • i ,„ i- f of thecaijital and R ». "'""^ ™«' y«ar , A. investing gains or losses Shan he . "S^ment being thai the net m4 Zt :"d harrr'' r""'''°« '» "^'-S' interest per ar^rorurltCtran^tr ''i ' rzrfittdr "''™ ""'"^™™ ^tXtr 1191 4ftn , *^ resources: mdse., per inventorv !ii2],460; real estate. |15,000 • cash iTi qkh I /^ receivable, $13,146 60- m^^Z' ''*'^' *1'960 ; bills $519.25; accou'nts du^ iClTl 2^^ ^ 'Y ""^^' I1.3S0; deliver, wagons and h^rsfs | ^0 *^^^^ were : mortgage on real estate. $7,000 interest on ' accrued, $210; notes outstanding $2fiQ?n .' ' "*''' ^^^"^^^- It ^« found that 38*0^ of the .' I ff if^ 824 PAUmKlismP. accounts due the firm are uncollectable. If the firm's Josses (iuriiif,' the year liavn been $12,000, how much was invested by each partntn-? What is the present worth or net inaohciicy of the firm, and of each partner, at closing? 10. Sills and JoneH l)ecaine partners July Ist, 1886, undnr a S-year's contract, which provided that Sills should have $1,500 each year for superintending sales, and that Jones should have $1,000 each year for keeping the books of the concern, and that these salaries should be adjusted at the end of t ach year, and before other apportionment of gains or losHcs was made. July 1st, 1886, each invested $12,500. Six months later, each increased his investment $5,000. July Ist, 1887, Sills drew out $3,600 and Jones drew out $3,000. Oct. 1st, 1887, Sills withdrew $1,000 and Jones invested $2,000. July Ist, 1888, each drew out $1,600. At the expiration of tlic time of the contract, the resources exceeded all liabilities by $17,280. What was the gain of each, and the present woitii of each *? 11. A. and B. commenced business as partners. A. invested $20,000, and B. $10,000, A. sharing § and B. J of the gains and losses. No interest account was kopt. A. drew out $1,700, and B, $2,150. Their assets at the close of the year consisted of — cash, $4,200; bills receivable, $8,800; mdse., $26,000, and personal deles, $16,000. 10% of the personal debts are considered bad. Their liabilities are— bills payable, $3,250; personal accounts, $11,250. If B. should retire from the firm, how much ought he to receive ? 12. On January 1st, 1889, A. E. Brock, W. McMa.ter and H. Crawford entered into a co-partuirship. Brock was to i.ivest ^ of the capital and share |- of the gains. McMaster was to invest ^ of the capital and share | of the gains, fiuu via — iuiu -.-£4= 5v iiivSd!( 5 Oi itU'c uap::.u,i iiiiu miaru f- Oi PARTS KUSniP. tne gains. Interest at the ratP nf mo/ be allowe., to each p„Hoer luW h "Ir,! l';::;™, "> proportion ; and internaf of h '^^ *^^^" ^^'^ cl.ar,e.l each ,.rZTl fail , IT' T,'- ' ""' '" "^ A. E. Brock. " p. ;; J°°«i«. " 1.600 Ang. 17. .. ^800 Total withdrawn «U,400 l«89.-jan. 1, Jnv^i^ jl2;oo5 ^r-18' " 4.800 Oct. 20. .. _e^ooo Total investment J42.800 Dr. I889:^jmy 28. Dre\r3^ir~iri-26o " ^-- 't. " .00 " Total withd, , ja.800 W. MoMabter. Cr. l^p^n. I, inveated $^ ,)0 « J ^^' " ».600 ^^y^l' '• J,200 Total investment $28,800 $12,000 1,200 *1.'^,200 >;' iff 826 BANKRUFTCY. BANKRUPTCY. 935. Bankruptcy is the formal acknowledgement in accordance with the law, by a person or firm, of inability to pay indebtedneBS. 536. A Bankrupt is a person who is insolvent, or unable to pay his debts. 537> After the assets of a bankrupt have been applied to meet bis liabilities, he still remains liable for tbem unless discharged, or unless a compromise has been effected with his creditors. 33S. The Assets of a bankrupt are his entire property. 53$l. The Liabilities of a bankrupt are the debts and obli^utious due by him to his creditors. 540. The Net Proceeds are the assets less the expense of settlement. They are divided among the creditors according to their claims. The claims of a certain class of creditors, as employees and others, are paid in full up to a certain amoant. These are called "Preferred Credi- tors." 541* An Assigrnee is a person appointed in accordance with the law, to take charge of the bankrupt's property, to make collections of debts due the estate, and after deduct- ing the expenses of the assignment, to pay such proportion of the debts due the creditors as the available assets will allow. BANKRUPTCY each creditor receive ? s^uienB were «430. Hdw much did Solution. TiTABITiima. iBSXTS. Cash Eeal eatate .. Mdse Personal aoooants.. Total Less expenses . . Net assets.. R.E. Walker &0o. .. 5,000 ^•^°y^«*oo ^^ ^"^^ «24,900 • • •• - .. »6.474 8,000 4,000 _1^ .. »14,374 430 .. $13,944 *i2 400 "■ !:«'•'"« = •''■ '' '' %• «<« on dollar. t'fl '' -^^ = *^'^*4 0° bills payable 817^0 X M = «9^ to A. Boyle & Oo »24,900 813.944 ''I EXERCISE in. 1. A bankrupt owes A. $»,600, B. $4,600 and n «« onr, Ins assets are $6,950, and the expe JesTS'.*, 'Z' what per cent, and how m„„h ..Laoh credZ rS ' 2. J. Gould & Co. failed wifh lioKij;*- *800000. The assets oFti^^t^t^lZZ'Z '" much should each cre.litor receive! th!/i ^ "^ sum was allowed J. P. Hume * rn u ' ^'^ "■"" »17,814, ..e expenses of s^ L'^ $Mm '*"" ™' -d-ha ™$f,^;i reL;°ixt':T/::r '''^'^■ of the amount distributed t^ ...d't-f" ™ f "' ™' ' « how much did a creditor reoeiVe on 'ksfoT ""' ""'• *"' 828 BASKllUPTOY. 4. A grain firm failed with liabilities amounting to $24,500. The assets were: cash, $1,080; real estate, $8,260; notes on hand, $1,170. The expenses of settling were 2% of the assets. How much should W. H. Hull & Co. receive, whose claim against the firm was $6,308.50 ? 6. A manufacturer failed, owing A. $12,260, B. $18,850*, and C. $14,560 ; his assets were $28,850, and the expenses of settling were $1,250. He owed $850 to employees who were to be paid in full ; what per cent, and how much did the other creditors receive ? 6. The real estate of a bankrupt firm was sold by an assignee for $24,000, goods in store for $12,244. There were collected on notes due the firm $4,214, and on personal accounts $5,346. The total liabilities of the firm were $54,067.50, and the expenses of settling $1,850. How much on the dollar can be paid, and what should Howard Bros, receive, whose claim is $12,480 ? 7. A. Reid's claim against a bankrupt firm was $7,200, and J. Taylor's 70 % of that of A. Reid's. After the expenses of the assignment were deducted from the assets, there remained $18,260. The total liabilities were $24,480. How much did A. Reid and J. Taylor respectively receive ? 8. A firm failed with liabilities amounting to $26,125. The assets of the firm exclusive of real estate were $ 1,52 1 25. The assignee obtained for a warehouse and three building lots the sum of $15,675. The expenses for settling the bankruptcy was $237.60. W. Alexander's claim against the firm was $8,642; J. Moblo's, $3,191 ; R. A. Harrison's, $2,897; D. McGregor's, $2,383.50; W. Ayer's, $1,982. How much did each of these creditors receive ? AN.\U1T1£:3. 829 ANNUITIES. ai^ll'i^r" ^"""^ '^ »~ -l^-h "^g- and »ds depends upon soJlLl^tZZTrl T' individual or his arrival at acerZlgr L fet 11T pen^n, dowers, leases, etc., belonf to tJs elaHi An?i;fsltr?e;^,t:S- - '»— 548. A Deferred Annuity or an Annuity in Reversion 18 one that begins at some future time it m«v ) . f Bpociiied time, or at the occurrence Z;!"!' ""^ 349. An Annuity in Arrears or Forborne is one on which the payments were not made when due S50. The Amount or Final Vain* «* ^ .0 ,,m.a all xiB payments with interest on each will amount at its termination ^' ; B f!l 880 ANNUITIES. 551. The Present value of an Annuity is the sum which at tb given rate of interest, will amount to its final value. Note 1.— The present value of a deferred annuity is that principal which will amount, at the time the reversion expires, to what will then be the present value of the annuity. 2. The present value of a perpetual annuity is the sum whose interest equals the aimuity. 3. Annuities am their values are computed by simple inteiest or by compound interest. .152. To find the amount of an annuity at simple interest when the time and rate are given. Example — What is the amount of S500 annuity for 6 years at 6 % ■imple interest ? Solution. ANNUITY. »500 + 600 + 500 + 600 + 600 + INT. H'iO = 1)0 = ()0 = ;{0 = = AJIT. ?(;2o 590 660 630 600 Amount $2,800 Explanation. The interest on $600 for 1 year at 6 % = $30. The first annuity is not due until the end of the first year, and hence draws interest for only 4 years = $120. The second is not due until the end of the second year, and hence draws interest for only 3 years, etc. 553. To find the present worth of an annuity at simple interest. /' Example. — What is the present value of an annuity of $600 for 6 years, when money is worth 6% simple interest? Solution. By the preceding example the final value of the annuity is $2,800. The Dreseut worth of $2,800 due in 6 years at 6 % = }gg. of $2,800 a $2163.846. 'v- EXERCISE 118. 1. What is the amount of an annuity of $150 for 8 years, when money is worth 6 % simple interest ? loso interest ANNVITIES. until the expiration of the ^hSiZr', "■""° »»?'"'' interest at tLt?on't;«lnlVr^"'= ^'''"^'"^'^ 4 A lady baa $300 a year left to her for 10 years Wh.t « .ts present cash value, at 7% simple interest ™'" «. What is the present worth of an annuity nf %Rnn , * years, money being worth 6% simple ^Z^f *'*"' '"' Syear^alsTl""'? """""^ "' *"» '-™»' «<• m o years at « % simpie interest ? 6yLf wt!"^ "^ *"^ '°'" '' y^"™ " » "version for years. What .s its present worth, simple interest at 6 %l ml ail 332 ANNUITIES AT COMPOUND INTERKST. ANNUITIES AT COMPOUND INTEREST. 554. The labor of computing the values of annuities at compound interest is greatly dimniished by the use c.f Uie following tables. The tables are always used in practice. Table 1, Amount of $1 annuity at compound interest, from 1 year to 40, inclusive. 1 2 3 4 B 6 7 8 8 10 1.000 000 2.030 000 3.090 900 4.183 (;27 5.309 136 6.468 410 7.062 462 8.892 330 10.159 100 11.463 879 13.807 796 14.192 030 15.617 790 17.086 324 15 18.598 914 20.156 881 21.761 688 23.414 435 25.116 868 26.870 374 28.676 486 30.536 780 32.4."ia 814 34.426 470 36.459 264 38..553 042 40.709 631 42.030 923 45.218 8:50 47.675 416 50.002 678 52..'iU2 759 55.077 841 57.780 177 60.462 0S2 1.000 oon 2.035 000 3.106 225 4.214 943 6.362 466 6.650 152 7.779 408 9 031 087 10.308 196 11.731 393 13.141 992 14.601 !)02 1G.U3 030 17.070 986 19 295 681 20.971 030 22.7U5 016 24.499 691 86.357 180 28.279 682 30.269 471 32.328 B03 34.460 414 36.666 .523 38.949 857 41.313 102 42.759 060 46.290 627 48.910 7!»9 61.622 077 63.271 944 66.174 22.': 09.169 449 72.234 2;i3 76.401 260 54.429 471 57.3,14 502 60.341 210 63.453 152 66.674 013 70.007 603 73.4,57 869 77.02S 895 80.724 900 84.6S0 2,8 1000 000 2.O10 000 3.121 600 4.216 464 5.416 3?3 6.632 975 7 898 2y4 9.214 226 10.582 795 12.006 107 13.486 851 15.02T 805 16 020 833 13.291 911 20 023 588 21.824 .531 2.3.097 512 25.015 413 27.671 229 29.778 079 31.969 202 34.247 970 36.017 889 39082 604 41.645 908 44.311 74.'i I 47.084 i'.U 49.967 583 52.966 286 56.084 938 1.000 000 2.050 000 3.1.-)2 500 4.310 125 5.525 631 6.801 913 8.142 008 9.549 109 11.02(> ,664 12.577 893 14.206 787 15.917 127 17.712 9.'!3 19.59.H 032 21.578 561 23.657 492 25.840 ;)C6 28.132 385 30.5;-J9 004 33 065 954 85.719 252 I Sf* .505 214 41 l:)0 475 44 .-,01 999 47.727 099 I 59 .328 335 62701 469 66.209 527 69.857 909 73.052 225 77.598 814 81.702 246 85.970 336 90.409 150 95.025 616 .51.113 451 i4.R«9 126 68.402 6K3 62.322 71'3 66.438 848 70.760 790 75.298 829 80.063 771 85.000 959 90.320 307 g5.aS6 323 101.628 139 107.709 546 114.095 (yiS\ 120.799 7V4 1.000 roo 2.000 000 3.1S3 600 4.374 010 5.037 093 6.975 319 8.393 838 9.897 408 11.491 SI6 13.180 795 14.971 6 3 16.869 941 IS.Ssa 138 21.015 000 2:3.275 970 25,670 528 iW 212 880 30.905 653 I 33.7.59 992 36.7a5 591 39.992 727 44.,392 290 46 995 828 50.815 577 64.864 612 .59.156 883 0:3.705 706 6i.528 112 73 639 798 79.058 186 84.801 677 90.89fl 778 07.343 105 104.1b3 755 111.434 780 119 120 867 127.26)? 119 ia5.904 200 145.058 458 154.761 966 1.000 000 2.070 000 3.214 900 4.439 9 13 6.750 739 7.153 291 8.054 021 10 2.59 803 11.977 989 13,816 448 15.783 699 17.888 461 20.140 613 22,.550 48H 25.1S9 022 I 27.888 0,54 I 30.840 217 i 33.999 0.33 I 37.378 9- 5 40 995 492 I 44.865 177 I 49.005 7.^9 ' 53.4.36 141 i 5^ 176 671 63.249 030 I 68,070 470 74.. I .S3 823 80.097 091 87 346 ,529 94.460 786 102.073 041 110.218 1,54 118,9.33 25 128.2,-i8 76 . 138.236 878 148.913 460 100.337 400 172.501 020 185.610 892 199.635 112 ANNUITIES AT COMPOUND INTmEST. 33B Tabui a. Yrs 3%. 6 7 8 8 ID 11 12 *i«i. U.U.)1 ( 13|Tl0.6;Jl • 14 11,2X, t 15 I 11.937 i 0.970 874 1.9W 470 2.828 GU 3.717 01)8 4.579 707 6.417 191 C.230 283 7 Ol'J 092 7.780 109 8.630 203 9.252 624 9.951 004 9.55 U7o 935 12.561 102 13.100 118 33.7.'>3 518 14.323 799 14.877 476 15.415 024 15.930 917 16.443 608 16.935 542 17.413 148 17.876 842 ia327 031 18.764 108 19.188 455 19.600 441 3i%. 0.966 184 1.899 C94 2.801 6.17 3.073 079 4.515 052 5.328 553 6.114 .514 6.873 9.56 7.CU7 &7 8.316 G05 9.001 551 9.603 334 10.31)2 7,38 10.920 ,520 11.517 411 12.094 117 12 651 321 13.189 682 13 709 837 14.212 403 14.697 97i 15.167 125 15.P20 .110 16.0.'.8 368 16.481 515 5%. 20 000 428 20.338 7fi6 20.705 792 21.131 837 21.487 220 21.832 252 22.167 235 22 492 462 22.808 215 23114 772 16.890 352 17.285 365 17.667 019 ia035 767 18.392 045 0.961 ,5.38 1.886 095 2.775 091 3.629 895 4.461 622 6.242 137 6.002 (165 6.732 745 7.435 3:i2 8.110 896 8.760 477 I 9 385 074 9.985 6^8 10.563 123 11.118 387 11.652 296 12.165 669 12.659 297 13.133 939 13.590 328 14029 160 14.451 115 14.8,56 812 15.216 903 15.022 080 18 736 276 19.068 865 19.390 208 19.700 684 20000 661 20.291 494 20.570 525 20.841 087 21.102 500 21.366 072 15.982 769 .16.329 586 16.663 063 16 9S3 715 17.292 033 17.5as 494 17.873 5.52 18.147 616 18.411 198 18.664 613 la 908 282 19.142 579 19 367 864 19684 485 19.792 774 0.9.-2 381 1.K59 410 2.723 218 8.C45 951 4.820 477 6.075 693 6.786 373 6.46.) 213 7.107 822 7.721 735 8.306 414 8.863 252 9.393 573 9.898 611 10.379 668 10.8;<7 770 11.274 066 11.689 .587 12.0a5 321 12.462 210 12 821 153 iaic:i 003 13 18s 574 13.798 642 14.093 945 6%. 70/ 0.913 yjc, ].8;i3 393 2.073 012 3.105 106 4.212 364 4.917 324 5.,5,S2 381 6.209 7(4 6 801 692 7.300 087 7886 875 a383 844 a852 083 9.294 984 9.712 249 10.105 895 10.477 200 10.827 603 11.158 116 11.409 421 0.931 579 1.808 017 2.024 311 8.387 209 4.100 105 Yi-s. 1 2 3 4 5 14.275 185 14.643 034 14.898 127 15.141 074 15.372 451 15.592 811 16.a)2 077 16.002 ,519 16.192 204 16,?74 194 16.546 852 16.711 287 16.867 893 17.017 041 17.159 086 11.764 077 12.011 583 12 ;i03 379 12 5)0 358 12.783 356 13.00.! 166 13 210 ,534 13. 106 164 13.590 721 13,764 831 13,929 086 14.084 043 14.230 230 14.36H m 14.498 246 14.620 987 14.736 780 14.846 019 14.949 075 15.046 297 4.766 537 I 6 5.3S9 286 7 5.971 295 8 0.515 22.S e 7.023 577 10 7.408 609 7.912 671 8.357 &S.5 8.715 452 9.107 HftS 9.446 032 9.703 200 10.059 070 10.335 578 10.693 997 lO.aSS 527 11 (101 241 11.272 187 11.409 334 11.653 583 11.825 779 11.986 709 12.137 111 12.277 674 12.409 oa 12531 814 12 616 ,555 12.7.53 790 12,a54 009 12.947 672 13.035 208 13.117 017 13.193 473 13.264 928 13.331 709 in-. ii i 384 ANNUITIES AT COMPOUND INTEREST. 55«. To find the final value of an annuity by compound interest . years af 5™ ^■~^^"'* '' *^' ^"''' ^"'"^ °^ ^° *°°°'*y °^ »^00 for 6 Solution. By Table 1 the final value of an annuity of . fl„„, , , 81, at 5 % for 6 years = er,.801913 Nn":. wr" '^'^nuity of §500 = 6.801913 x 600 = »8400.;.o65. A K, rT " P'^y™^"*^ ^"-^ «^a *^. .-. A Binku,j» fund of U has a present worth of y^ =.. ^11.638461. for •he required time at 6 %. ' Looking in Table 2, Art. 656, in the column C.% we finrt th» „oare«t number less than UMSm. to be 11.4H9421, the prusent worth T» annuity for 20 years. v»«u ut »i 20 years is therefore the luitnber of whole years required. Af^ain : The amount of the debt »l,-,,000 at 3% compound interest for20year8 = »48 1(V7 40 The amount of a sinking fund »1,300 at 6% compound intercut .. ,. =■ t7,R?1.27 Balance due at end of 20 years = U286.1d BULB. Divide the debt by the pircn sinking fund, and the quotient will be the present worth of $1 annuity for the given time. Look for this number in Table 2, Art. 655, in the colum.n denoUng the given rate, and opposite in the column 0/ time will b(; found the number of whole years. Notes l.-If the exact number is not found in the column, take the years standing opposite the next smaller number. 2. To ascertain the balance due at the end of the number of whole years find the difference between the amount of the debt, at the given rate, for the time taken, and the amount of the sinking fund for the same time and rate. «**uo EXERCISE 120. 1. If a railroad company sets apart an annual sinkinff tuud of $20,000, and loans it at 5% compound interest What will be its amount in 12 years ? 2. What will be the amount in 16 years of a sinking fund of $12,000, yielding 4 % compound interest ? 3. What sum must be set apart annually to rebuild a bridge costing $30,000, estimated to last 17 years, allowinc f^INKWO FUNDS. 889 4 A railroad company bought $10^000 worth of rolling 5. A man buys a farm for $5,000, and agrees to pay for ah T ''" '"""'' -stalments. What is the a.nount o each payment, mo., y be..^, worth 6 % compound interest ? S'^LmT^ "' y^^^ " '"'^ '^"^'"8 f"°^ bonds at 6 "^ for $200,000, payab!^ .. 10 .ars. If at compound interest Trt Lrr b "?^ "' ^^"' ^"""^"^ '° --' -merest ad prnicipal when due ? _ 8. If the funded securities were drawing an annual income of 4% compound inlerest, by how much wouTthe reTu"c^r"°"' '° "■"' """"P*' "" ""''-' "*«« ^« 9. With the above reduction, what sum would be needed .™„ally as a eu,kinK fund to pay the amount when due at „,?,!>, rv,'" ""^ "^ ""^ payments. How man^ raitld t^'-lm' ''"'"/ ^'''""''■•'o»»e costing $12,000, and " e est Z '"^' '° f ? '" " •■ """""S « « """P'-'-i h J ti'o Z "*"^ "''°'* y«"» »«' " «9«i« to oancel the debt? What will be the b«l»nee then due? I s I ri I km. 340 QliOUND UEm-S. GROUND RENTS. 564. Ground Rents is a term applied to lease? of building lots, the rent of which is considered equal to the interest on the valuation of the land. The payment is generally secured by a claim on the building erected on the land occupied. 565. When the party who 1-ents the ground has the privilege of purchasing it, the Ground Rent is said to be redeemable ; otherwise, it is irredeemable. The renter of the land usually erects buildings thereon in his own right and pays a specified sum quarterly, semi-annually, or yearly, for the use of the ground. In some cities the issue of irredeemable ground rents is prohibited. 566. Building lots are sometimes sold at so much per foot frontage ground rent. Thus, a lot valued at $4,000, with a frontage of 20 feet, drawing interest at 8 %, is'said to be worth $16 per foot. The interest on $4,000 for 1 year at 8% is $320, which, being divided by 20, the num- ber of feet on the front, gives $16 as tha price. V,nen a 6% ground rent yields the owner $180 per year, the value of the gi-ound is estimated at $3,000, since $18«> is the interest on $3,000 for 1 year at 6 %. EXERCISE 121. 1. What is tb'^ capitalized value of ground, which at 5 % ground rent, fieldiz the owner $600 per year ? OROVND RENTS. 841 •v^tyfyjyj, leased at a ground rent of 8 % ? rent of 7 x *^^'''°" "'"' f^^S » grouDd investment ? ^"^ ^ '^^^^^« ^^m my 7. The annual income received nn « fto/ per share. ^0,^4 ,^^,"1^ be' r^tT ""°'' " *«« 8. Find the pr^^sent worth of a ground renf of ft«y lot valued at $4,500. to commence^n 3 Va- .n/tof'h ' continue 16 years, if monev be worth 6 /^ ^J interest, "" ^^ compound ' ]ih II ^ I i I 842 LIFE mSUBANCM. LIFE INSURANCE. if »«7. Life Insurance is a contract by which a com- pany (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. 56M. The principal kinds of policies issued by Life Insurance Companies are the following : Ordinary Life Limited Payment Life, Endowment, and Annuity. 5«». An Ordinary Life Policy is one on which 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. 570. A Limited Payment Life Policy is one on which the premium is 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 aelected period. The policy is payable on the death of the insured. 571. An Endowment Policy is one which is payable to tbe person insured, if he survives a certain number of years, or to his heirs, if he should die before the expiration of such period, in consideration of certain regular payments from the person insured. 573. An Annuity Policy is one which secures to the holder the payment of certain hum of money every year during his lif.^-time. It is secured by a single payment. .'57:5. A Non-Forfeiting Policy is one which does not become void on account of non-payment of premium. 574. The Surrender Value of a policy is the amount of cash which the Compauy will pay the holder on the surrender of the policy. It is the legal reserve less a c&rtaiu per cent, for cxpuuBeB, LIFE INSVUANOS. S7il. The Reserve of Life lusuranoe Policies i« fh. present value of the amount to be paid at dea h le s he present value of al. the net pren,i„„. to be paid' ^ Z pany IS tl^al sum on har i which invested at a given rat of merest together with future premiums on existL h:^Z'dt"'lt'' T"'""' 1 "''^""' »''«^»«°- X' s':r Hrcies^ra;!"."' '"^ ^"^-^'^ — "' '-^ or^wsoltl^^rir'' ": ""^ '•""'' f°-' «>« insurance ,;.ari:;,r'"'" " ^ ^'"'' — %.-mi.annually.„, 5M. The Premium consists of three elements- l.l The Reserve, or that portion of each premium whfch musi thernnfau::::^:^ ~:/"' ^-'' -"'^ ="- "' 3rd. Loading, or a certain per cent, to be added to the net premium to cover the general expenses of the bus ness and to provide against unusual contingencies. ^' 57 J. The Sum Insured is the sum which is payable contract.""'"' ""''^ *'^ ^°"''^^°"« mentioned Tthe a.f ?at oTti^H °^ ^°''^""'^ ""' ^^^^'' «^°^^"8 *he aver- age rate cf deaths m every ten thousand persons. u-hth ^''P^^^^f ^^" i« t^e average number of years £es:e^rmpira::i!:do^ni'zs^^^ marxr;n'fn.r -^ "^'^^ bear, aud a loading or maigin lor expenses. ^ ■< 1 1 ti. 1 ; » ■ ,■ I j r 1 ■- i I. i Life. \\ 844 LIFE insura: ns. 5S3. Expectation of Life. The following table shows the dumber living, the num- ' '^« expecfcatioa or duration of life of each from the Combined Experience ber dying, an in(livii 848 MISCELLANEO US. MISCELLANEOUS. EXERCISE 123. I. 1. Which is the better investment, a $3,000 7 % bond or a house which rents for $240 a year, taxes being $30 60 and annual repairs $40 ? o -r , 2. A person exchanges 250 shares of 6% stock, at 70 for stock bearing 8%, at 120; what is the difference in niB income ? 8. A gentleman has been receiying 12 % on his capital m Canada. He goes to England to resi^Ie, and invests it in the 8 per cents, at 94f, and his income in England is to UM^T^^ ""^^ ^'' '"'°°'' '" ^^"^*^^' *^' ^ ^''""^ ^^"^^ 4. Find the alteration in income occasioned by shifting £3,200 stock from the 3 per cents, at 86f, to 4 per cent! stock at 114| : the brokerage being | %. 6. Suppose a railroad stock, actually worth $100 a sha- a to be " watered " by the issue of a stock dividend of 20 % to the stockholders, what would the watered stock be worth ? 6. A person bought stock at 95^ and after receiving the half yearly dividend at the rate of 7% per annum sold out at 92f and made a profit of $37.60. How much stock did he buy ? 7. At what price must U. S. 4^'s be bought, to yield the mtercst on the investment that 5 % bonds will at 110 ? What amount of the latter bonds (par value) must bo Bold at lOS, leaving brokerage out of account, that with the proceeds a sufficient amount of 4^'s m^y be bought, at par, to yield a eenii-aunual income of $364.60 ? MISCELLANEOUS. 8. A person invests the proceeds of a note for $9 607 50 m 6% stock at 91, brokerage i%. Pi„d hj, ^Jj Jfj iustifj"; Sd 'oTsTr^'if'tr"™' """'"^ ''™"' u , , ""'" o' ^f/o, If there were no ureferenp*. hi"' ."'."" ^'•^■'^ "' "=« »«-k consists TZ shares, which are guaranteed 5% per annum, the o^dirrv shareholders receive onlv 8 % wLt i« ii,. l , ""'"""^y of stock? ""'JfO/*). What 18 the whole amount 10. A gentleman has $25,000 of Bank of Commerce worth ttj"'^] * f ''™' "' «*• ^"^ -"Tis sToct alios wv .■""• "'"' '■"'''= '■» ^'""'of Toronto stock at 205, which pays a dividend of 12% Wh»f difference in his income after allowing his ag nt i «Im mission for each transaction ? K "' t % Com- at 1.M, and $19,850 in Bank of Toronto stock at 198 oav- /re Ld'°'S heT' "" *^ °'' "■' -°™' Of 'sS elr and th. 1 « '"'T.F*'" * ''»'f-y'>"Iy dividend of bJA and the latter a half-yearly dividend of 6i% find his total moome for the half-year. "' "t %. und , Jv ^"'r '"™""' ' ""'»" ™" i° Bank of Commerce stock, which 13 at 120, and pays 4f % half-yearly divrndT and 62i per cent, more than that sum in Dominion Bank stock, which IS at 180, and pays ^ % half-yearly divMeads his income from both investments is $222.60 Find the amount of money invested in eaoh kind of stock. n. ^"' '? =!'•::"• ^- ft ■» *«»«• »■"! May 1st $800 more. 0. pu. ,„ ,,00, and July 1st $400 more. At the end of the year the profits were $876. How shall it he divided ' m I 1360 ATlSani.j.^NEOVS. 2. A. B. fi'M C. commence business; A. puts in 250 firkins of bufter. B. puts in $2,500, and C. $4,100. Their profits amounted to $2,210, of which A. took $560. How much was his butter a pound, and *o y -, ->uch were B and C. entitled ? 8. A building worth $28,600 is insured in the ^tna for $3,200, in the Western for $4,200, and in the Mutual for $6,600. It having been partially destroyed, the damage is set at ?1> 10,500. What should each company pay ? 4. A. had $3,800 at interest for 60 days ; B. had $4,100 at interest for 46 days; and 0. had $4,960 at interest for 70 days. They received $162 interest money. What did each get, and what was the rate pt r cent ? 5. A. and B. formed a partnership Jan. Ist, 1889. A. put in $6,000, and at the end of 3 months $900 more, and at the end of 10 months drew out $300 ; B. put in $9,000, and 8 months after $1,500 more, and drew out $500 Dec.' 1st. At the end of the year the net profits were $8,900. Find the share of each. 6. Two persons commence trade yith the same amount of money. The fi. mau pends . . % of hit money yearly, and the second spends a sura equal to 26 % of what both had at first. At the end of the year they both to•■ ^- '^-^W- f« " J1.485 for his. Bequired. B.'s stock and C.'s time. 10. On the 1st of January, 188!», James Wilson opened a hardware store with a stock of tl7,200- on th! Ist „^ April, Joseph Brooks entered into pa'r.ilhip wi„ h m and advanced $12 000; on the let of'juiy, Abraham Mm"; put in goods to the amount of .^Ifi.oOO; on the 1 of January 1890, when the balance sheet was e.hiWted there appeared a net profit of $8,060. To how much wa^ each partner entitled ? ^^^" 11 A., B. and C. engaged in business. A nuts in «4nft ll t 7?"^, "T "' '"* ^■"' "' « ">""*s' B. put n end of 6 rn^t";. "r "T" °"'"""''' <" "' -P"al at th^ end of 6 months ; 0. puts in $200 at the end of everv $rZ Wb"^' '^ "•" »' '"» y^^'^ 'hey have »aS $6 700. What share of the profits should C recer !„ addition to 25 % of the total profit for mana^.' ' "! business? manag.aii iue ]^' tv A*""^ "• '''™"* » P»ftaer8hip for 2 years • A put™ »,0,000, B. $5 000, and C. $2,600; i, JSZ^^ti tha C. should receive $1,500 a year for superintendirthe busmess. A. drew out $1,000 at the end of »oh „ar ' for on, year and at the end of 18 months put in $16 S T:^^- .""".I"- ^. "' 'h^ "-i of each'ou^ttr. 'T eacVoTe's'storr"" '" "•* ^"^ ™' *'''^""- ^1""^'" I r ^--11 !J62 MlSiJELLANEOUa. m. *io A^"''^' ®° Winnipeg bought at |% premium for $12 000, was sent to an agent to pay for cotton purchased at 2J % commission ; what was the value of the cotton ? 2. A commission merchant in Peterborough wishes to remit to his employer in Belleville $512.36 by draft at 60 days ; what is the face of the draft that he can purchase wi^th this sum, exchange being at 2^% discount, interest I /of _ 3 Shipped to Liverpool, 2.000 barrels of flour, which cost m Montreal $4.60 per barrel ; it was sold at il 18s Cd per barrel, when the premium was 8^%; how much was the gain ? 4. A grain dealer bought 10,000 bushels of corn, at 88# eta. a bushel. He sent it to London, where it brought 28s 9d. a quarter, when the premium was 9^°^; the cost of transportation was 12^ cts. per bushel ; how much was gained ? 5. A person in Bajrrie received £1,000 sterling, from Jingland, when the premium was 9%. He put it out at interest for 9 months. 18 days at 6°^ per annum; to now much did it amount ? 6. A merchant sent his agent in London 425 bales of cotton weighing 356 lbs. apiece, which cost him 9i cents a lb.; the agent paid §d. a lb. for freight, £43 for car- tage sold It at 8d. a lb., and charged ^% commission. If the merchant sells a bill of exchange for the amount, at 10*%, will he make or lose by the operation. How mrch ? ' Bmium for purchased cutton ? wishes to Iraft at 60 purchase t, interest tvhich cost 1 188. 6d. much was •n, at 88f i brought H%; the ow much ng, from it out at aum ; to bales of 9^ cents for car- mission, amonnt, How MISCELLANEOUS. u... OoJ 7. Received from my corrospondent in New York $6,150 U S^currency, with instructions to deduct my commission worth i'l n?i ?' T^'""^'' ^" ^^"^'^i^" Tweeda worth $1.08i per yard. How many yards should I send uim, gold bemg quoted at 115 ? 8. An importer bought 1,565 yards of silk, at 6s. 6d per yard ; paid ^7 12s. for freight, 25°^ duties, and remitted . a bill on London at 9^% premium; how must he sell it 7% fnTeresT? "'''''*^'' '" '''^'' ^ ""*^' ^^*°^' ^"°''^^° 9. Exchange between Paris and Amsterdam being at the rate of 2 francs 20 centimes to the guilder, that between London and Paris at the rate of 26 francs 80 centimes to the £ and that from New York on London at 1 000^''°?^"""' 7^^^ ""^'^ ^' ^^' ^«^* °^ » remittance for 1.000 guilders from New York to Amsterdam by bills of exchange through London and Paris ? T ^^; ^ T'u*°' '"^ ^^'''^^^ ^'«^e« *o pay ^8,000 in London Exchange on London is 9^°;^ premium; on Pans. 6 francs 26 centimes per $1 ; and on Amsterdam 40 cents to a guilder. The exchange between France and Eng and at the same time is 26 francs to £1, and that of Amsterdam on England 12^ guilders to £1, Which is the most advantageous, the direct exchange, or through Pans, or through Amsterdam ? ^ 11. A Hamilton meichant, owing 2,400 florins in Ams- terdam can buy exci^ange on that city for 41^. Is it bet er for him to do so, or to remit to London, and thence to Am8terdam.-exchange on London being 4.87 in Ham- ilton exchange on Amsterdam being 12 florins to tb« pound sterling in London, and brokerage for purchasing, tne exchange m London being i of 1 % ? '»ji I f W ili<> 1J51 MISCELLANEO US. 12. A banker in Toronto remits $10,000 to Liverpool as follows : First to Paris, at 5 francs 40 centimes per $1 ; tbence to Hamburg, at 185 francs per 100 marcs ; thence to Amsterdam, at 17J stivers per marc ; tbence to Liver- pool, at 220 stivers per £ sterling; bow mucb sterling money will be bave in bank at Liverpool, and wbat will be bis gain over direct exchange at 10 % premium ? IV. 1. Allowing 6% compound interest on an annuity of $200 wbicb is in arrears 20 years, what is its present amount ? 2. Wbat is tbe present wortb of an annuity of $500 for 7 years, at 6 % compound interest ? 8. Find tbe annuity wbose amount for 25 years is $16,469.35, allowing compound interest at 6 %. 4. Tbe present wortb of an annuity to be continued 10 years at 6 %, compound interest, compounded annually is $7,360.08. What is tbe annuity ? 6. A man bought a farm for $4,500, and agreed to pay principal and interest in 4 equal annual instalments ; bow mu(«b was the annual payment, interest being 6 % ? 6. A man bought a piece of property for $10,000, and agreed to pay principal and interest in 3 equal annual iq- stalnwnts. How mucb was tbe annual payment, interest being 7 %? '7. A father bequwatbed (his «ion, ,11 .yaars jof «ge, « 6 % ammity cff ?$2;500, to begin in -8 t^aexB «nd ieontmue 10 yeare; irhttt wwiiid be 4be amount nrfaan :iibe .wii mas 21 years old ? MISCELLANEOUS. baDk. the compound interest of which, at 5 ^/o pavabTe Bemi-annually, shall discharge his annual ^r.mL7 9 A man died leaving $5,000 to be divided between his three sons, aged 13, 15, and 16 jears respect veh in such a proportion that the share of each be ^p't at simple interest at 6% should amount to the same sum when they should arrive at the ageof 21. How Zh wa" each one s share ? 10. A man paid annually $10 for tobacco from the age s heir? WhaT ''' ^'"r ''I ''''' '' '^'^ $^'«^« '- n s heirs. What sum mi<;ht he have left them had he at the end of each year at 6 % compound interest ? . vi' ^ T-^f^' °^ ^^'^^^' '"^P^^'^'^1^ i" 5 years at $200 a year with interest at 6"^ on the unpaid principal is sold what IS Its value allowing the purchaser 8% for his money ^ 12. A mortgage on a farm is payable in four equal annual instalments of $1,000 each. When the first instal ment fans due the mortgagor offers in part payment $2 00 m 6% municipal debentures upon which interest is due and which mature in one year. What balance in cksh BhouW the mortgagor demand in exchange for the Jort gage, money being worth 10%? ""« mort- Ji^TM 856 POWERS AND MOOTS. POWERS AND ROOTS. «S«. A Power of a number is the nimber itself or the pro duct ofequal factors, each of .Mob i, tbat uumbt ■inus, 8 18 a power of 2, since 8 = 2x2x2 ««!' It^ ^'^^ ^^"^^^ '' *^^ """'ber itself; 5««. The Second Power is the product of a number taken tmce as a factor, and is called a Square. lUus, 16 IS the square of 4, since 16 = 4 x 4 ta k*!!?; ™"' T" " '"» I'''"'""' »f' » "»«">» Th„l 7« • !! "' \'°'"°''' *"'' *" """^d » Cube, ibos. 126 18 the cube of 6. since 125 » 6 x 5 x g sJ^'k'*,""'" '" "'" "' ""^ '9""' fe"'"" of a number of a!„*;,«r! ^'""^ """" " »™ "' '"^ '- ^'"' '•'-- Thus, 7 is the square root of 49, since 49 - 7 x 7 l^' U' "" '"^ ""'* '■' 848, since 843 -7x7x7 pW before . number, indicates that its root is to be the^'r^df .?' "■?"? "' ""' ''°°' '' ""^ ««"« P'^^'d above the iad.cal s.gn to denote what root is to be taken. When iNoiK.— The names of the roota are derived frr pawers. and are denoted by the indices of tTe radl, a """^P'^^^^"^ ^Thn^B^N^ denotes the square root of 9. the V-9 denote, the onbe root .«^w ^ f ^"^^'^ ^^"^'^^ '' °"« ^^°«« «a«t «q"are root can be found ; as 9, 16, 86, etc. 5!>6. A Perfect Cube is one whose exact cube root can be found; as 27, Gl, 216. etc. SQUARE HOOT. 857 SQUARE ROOT. 597. Extracting- the Square Root of a number is th« ^, NoxK.-The student should memorize the squares of the first nine ^^The squares of 1. 2. 3, 4, 5, 6. 7. 8. 9, are respectively 1. 4. 9. 16. 25, 86. 5«8. To extract the square root of a number. Example l.-Extraot the square root of 6,625. Process. U6 66 I 26 (76 49 726 725 Explanation or the Method. Separate the given number into neriods nf +«,^ « , at the nnits' figure. periods of two figures each, beginning Find the greatest square in the first narin/I ikr\ ™u- i. • .„ it under 66, also write the root of 4q v. u ^ ^' ^^'"^ '' ^^' ^"^ P^^ required root. ^^' "^^'"^^ '" 7, as the first figure in the the root already foundTT). wi^i^.lt H ''^ '"''^"' ^''^'^' ^^^*^ *-- ?m'^« ? ^^ "■ ^'"°^^ ^'^^^ -^ 1"°tient '5). A.^ W 5'l^r^.;^!';;^' 'Jr, '' r ^•^^ --^ «H- of the root. leaves no Lainde;. ' ' "°'' '"'^'^"^'^^'^ '''"" the dividend (725). 75 is the required root, ExAMPM 2.-Extract the square root of 6.838.226. Process. ( 6 I 83 I 82 I 25 (2616 4 283 1-276 782 521 26126 2r)126 358 SQUARE ROOT. fl JIM kl Explanation op the Method. Find the greatest square in the first period m\ whiVh , -a 4 ;. , • wli?Jves 4°' "'' ''^''^'^' ^'''^' "^^*^ *^^°« *^« -* -'-^y ^ound (2). Divide 28 by 1, which gives 7 as a quotient. A&x 7 to 4, yivinji 47, also place 7 as the second fi„n..„ f *u multiply 47 bv 7 wi,;,o. „; , .r> ^ ^^°°'^° °""ie of theroot.and We next try G as the second figure of the root. Alhx 6 to 4, giving 40 ; and place 6 as the seconr, fiihe;^9Upwi^g ri^es vfill |,e expr^fppd ia^a.phprtened form. The convejw-oftthe pr.eaeding, rule m^^t,l?)8,trixe : If the area of a ^dangle be divided by aside, the quotient will be the other tide, or if -the tquare rmt of , the arm of a square be extracted, the result wiU be the length of upside. • trapezoid is llel eidp.s- i straight line square. vhose sides are INATION. D, let A B be J 8 inohes. Let 3 5 equal parts, , and let A D be divisions each, iw through these •resented in the s, each of whose V inch. In each horizontal rows I, and hence the is 8 inches. ATION. J^ple 1. lit will be the distance between the™ bemfg?,:^" ""' """^-O-"''' Example.— Find tnp opposite sides are 10 feet in lengtVandtLeT'."'' °°^ ^^'^ °^ -»^o- 8o.nxxoK "''^"•''^ '^'"^^" "-- 6 feet. 10sq.ft.x6 = 60sq.ft. Ans It i„ ^""™°'' Ans. It „ proved in Euclid, Book I, p,o- lelogram is equal to the area of a recti?.? '^' !^* '^' '"''" "^ ^ P^''^'- same altitude, and hence the solSt'n gif ""^' '*"' ^°^ °^ '"^^ between them befng^ven P^P^"'^^*^"^^ distance sides bdTe'fe/Jnl lo'feTand^tlT'"'' ^'^ '^"^''«°* **>« P^^'^'lel them 6 feet. *' """^ *^^ Perpendicular distance between SOLCTION. RULE. tly a shortened re of the length le brea4t^. ;d fprm. rue : the quotient e area of a fa.Mide. ? 'I I B68 TRIANGLES. TRIANGLES. 034. A Triangle is the space enclosed by three straight lines. 685. Triangles are named according to their sides, and also according to their angles, as follows : Equilateral. Isosceles. Soalene. '. Right-angled, 626. An Equilateral Triangle has its tliree sides equal. 627. An Isosceles Triangle has only two sides equal. 628. A Scalene Triangle has all of its sides unequal. 639. A Right Angled Triangle has one of its angles a right angle. ^ «»0. The Base of a triangle is any side ai a triangle upon which a perpen- dicular is let fall from the opposite angle. 63]. The Altitude of a triangle is the length of the perpendicular let fall from an angle on the opposite side or the opposite side produced. NoTB.—Dotted lines represent the altitude. 682. To find the area '^f a triangle. Example l.-Pind the ar. f a triangle whose base J3 16 feet, and whose altitude is 9 feet. Solution. (16 sq. ft + 2) X 9 = 72 sq. ft. ^lil.-tXuLES. bijy 13 16 feet, and KXPLANATIOM. BULB. Multiply one.half the bate hj, the aUitu,U. ^^ The ^..owmg rule is al.o necessary when three sides »re RULE. SoLUTIOSf. (12 + 16 + 18) -H 2 := 23 2^ - 12 = 11 VW8 = 94.1 sq. ft. An. «»3. /^ is proved in Euclid, Book I, proposition 47 th \ In the accompanying figure, if A ±J C be a triangle having a right ^ngle at C. the area of the square described on A B is equal to the sum of the areas of the squares described on A C and B C. .ii 870 TRIANOLBS. EzAHFLB 1. — If the base of a right angled triangle be 8 *jet, and the perpendioalar be 6 feet, what is the length of the hypothenoM • Solution. In the preceding figure, sq. onAB = 8x8 + 6x6 = 100 Bq. ft. .-. A B = y^ToO = 10 ft. Ans. Example 2. — The hypothennse of a right angled triangle is 6l> fpet and the perpendioalar is 28 feet, find the base. Solution. 35 X 85 = sq. on the base + 28 x 28 A sq. on the base s 86 x 35 - 28 x 28 = 441 :. the base > ^"441 ^ 21 ft. Ana. 634. To find the area of a trapezium. A trapezium may be divided into two triangles by joining two opposite comers, and hence it is only necessary to find the areas of the two triangles and to take their sum. Example. — Find the area of a trapezium whose sides are 10 feet, 11 feet, 12 feet, and 15 feet, the length of the line joining opposiuo «omers being 18 feet. Solution. Area ABC » A CD Area A B G D = VlSx7x6x5«€1.46. (Art. 689V * V^jv X 9 X 6 x 4 » 64.06. (Art. 632.) . 61.48 + 64.06 at 125.54Bq. ft. /*.na POLYGONS. «7i POLYGONS. tingle ia 6b fnet BULB. MuUiply the perimeter (sum of nil *h. -^ v . Solution. Perimeter = 8 ft. x 6 = 48 ft Area «.,B.x?|2?.,6,.j„^^,^ is made «p ^f 6 ^^feti^iru h" 'r''"^ ' "'"°'' "n.o> the. a,u»re of a .ide. "" ® " •<8» 872 THE CIRCLE. THE CIRCLE. 636' A Circle is a plane figure bounded by a curve line called the circumference, every point of which is equally distant from a point called the centre. «3T. The Diameter of a circle ip a line drawn through the centre, and terminated at both ends by the circum- ference. 638. A Radius is a straight line drawn from the centre to the circumference and is equal to half the diameter. Note —From the definition of a circle, it follows that all the radii are equal ; also, that all diameters are equal. 63tf. Principles. 1. The circumference = th/i :iainetfir 3.1416 nearly. 2. Therefore the diameter = tUv ctrcumTerence + 3, 141G nearly. 3. The area of a circle = the square of the radius x 3.1416 nearly. 4- The area of a circle = the circumference x half the radius. 6. Thertfore the radius of a circle = aq. root of (the area + 3.1416) nearly. Note.— The fraction 3f is commonly used in place of the decimal 8.1416, and is near enongh for common practical operations, and will be naed iu tliis work. THE CIRCLE. e circum- 378 7 feet P^""^^^ '- ^^^* ^^ *^« »--'erenoe of a circle whose radius is ScLniioN, 7 ft. X 2 = 14 ft. diameter, 14 ft. X 3^ . 44 ft. Ans. (Pri„. i., ^.r^J^r '■ ^^-'--^-nce of a circle is 176 feet. What i. the Solution. 176^.3t_66(t. An.. (Prin. 2.)- Solution 1. 14 ft. ^ 2 = 7 ft. the radius. 7 X 7 X 3f = 154 sq. ft. Ans. (Pri„. 3.) Solution 2 « >■ J - IM .q. a An,. (Pri„. 4., Solution. Radius = VeTeni = ,4 .X ,„,. . J4 ft. X 2 - 28 f^ fL I . ^^""- "•' . ■ *• ^^^ diametei'. «•- I- X u = S3 ft. the cironm,vr<,uof. (Pria. l.k ■*"'■ Ill ■ Km It n I ! 874 MISCELLANEOUS, MISCELLANEOUS. EXERCISE 125. 1. How may acres in a piece of woodland 220 yards in length and 40 rods in width ? 2. How many square miles in a township 6 miles and 40 chains square ? 8. How many square feet in a floor 20 feet long and 6 yards wide? , 4. Find the surface of a pane of glass measuring 37* inches long and 23 inches wide. 5. How many square yards in the four walls of a room IP ft. 6 in. high and 80 feet in compass ? 6. A rectangular pavement, 60 ft. 9 in. long and 12 ft. 6 in. wide, was laid with a central hne of stone 5 feet widd at $1.76 a rnnning foot ; the sides were flanked with brick at 80 cents per square yard. What did the paving cost ? 7. How many square feet in a surface 24 feet long 20 feet wide? How many in another surface of half these dimensions ? 8. Two fields contain 10 acres each ; one is in the form of a square, the other is 4 times as long as it is wide. What would be the difference in expense of fencing them at $2.26 per rod ? 9. If the fence were built 4^ feet high, of boards 8 inches wide, the lower one raised 2 inches above the ground, and a space of 3 inches between the boards, how many square feet of boards would be required for both fields ? MISCELLANEOUS. o76 10. How many more for one than for the other ? J^ith!Z ° wT^. ''"*''"^"^ ' ''''' '' ' ""^^^ aa long M u 18 broad. What is its length and breadth ? 12. How many bricks 8 inches long and 4 inches wide will pave a yard that is 100 feet by 50 ? is'LZ\!l ^^^ IT '" ''" ' ^^'^'"^^ ^« ^^^^ ^-« --^ 19 leec wiae, at $1.60 per square yard ? 14. I have a box without a lid; it is 6 feet long 4 feet wide, and 3 feet deep, interior dimensions. How manv :?rbtv' ^^" ^'^ " '''' *^ ""^ *^« bottom^Lrei 15 Find the area of a rhomboid whose length is 1 yd. i ft. 6 in., and whose width is 2 ft. 3 in. 8 fL't. ' WhlTLt atrr ^^ '' "• ^ ^"•' ^^^ ^*« ^^«*"^^ .»,^^ ^r.rr^ ^"'' '° * P^^''^ «^ 'and in ;he form of a rhomboid, the base being 8.76 ch. and altitude 6 ch? 18. A man bought a farm U8. rods long and 160 rods wide, and agreed to give $32 an .ere. What did the firm J!*btlTo'V''*'°'"'"'''"°'^^"' "^^^^"^•^^ 1.000 imks by 100. How many acres does it contain ? ^ 20. How many square feet in a board 16 feet lona 18 mcheswide at one end and 26 inches wide at the o^her are e 1.8 aud 14b feet, and the altitude 69 feet 1 :i 1 i ^ i fi J7G M ISC ELLA NEO US. 22. One side of a quadrilateral field measures 38 rods • the side opp,)«itH and parallel to it measures 26 rods and the distance betwoeu the two sides is 10 rods. Find the area. 23. The parallel sides of a trapezoid measure respectively 8* feet and 6 inches ; the perpendicular distance between them 18 2 feet. What is the area ? 24. Find the area of a trapezium whose diagonal is 168 and one perpendicular 42, the other 56. 25. Find the area of a trapezium whose diagonal is »5 tt. 6 in., and the perpendiculars to this diagonal 9 feel and l^ feet. 26. How many acres .n a quadrilateral field whose, diagonal is 80 rods, and the perpendiculars to this diagonal 20.453 and 50.832 rods. ? 27. What is the base of a triangle whose area is 156 square feet, and its altitude 12 feet ? 28. What is the base of a triangle whose area is 144 acres and its altitude 60 rods ? 29. Find the base of a triangle whose area is 5 280 square yards, and altitude 240 yards. 30 What is the area of a triangle whose three sides are 13, 14, and 15 feet ? 31. What is the area in acres of a triangular field whose three sides measure f.spectively 47, 58, and 69 rods ? '32. What is the area of a triangle whose base is 24 feet and altitude 16 feet ? 33. The base of a triangle is 28 inches and the altitude lb inches ; what is the area ? ures 88 rods ; i 26 rods, and Is. Find tlie e respectively ance between igonal 18 168, ' diagonal is agonal 9 feel field whosfc this diagonal area is 156 area is 144 ea is 5,280 ee sides are field whosa rods? e is 24 feet be altitude MISCELLANEOUS. o„„ oil 34 A board 16 feet long is 22 incl.es wide at one end. and tapers to a point ; what ia the valu. at U cents a square foot ? .a 86. Find the area of a triangle whose base is 12 ft 6 in and altitude 6 ft. 9 in. ' ' 86. Whose base is .5.01 chains and altitude 18 14 chains. 87. What is the cost of a triangular piece of land whose base IS 15.48 ch. and altitude 9.07 eh. at ^60 an acre? 88. At $.40 a square yard, find the cost of paving a triangular court, its base being 105 feet, and its altitude 21 yards ? 89. Find the area of a circular pond, its circumference being 200 chains. 40. The distance around a circular park is 1^ miles. How many acres does it contain ? 41. How much land in a circular garden that requires 84 rods of fencing to inclose it ? 42. Find the difference in cost at 871 cts. per rod between fencing a square field of 10 acres and a rectangular field 82 rods wide of the same area. 48. Draw a square containing 81 square inches ; inscribe a circle m this square. What is the superficies of this circle in square inches ? 44. A cow is tethered to a post driven in the centre of a lot 100 feet square ; the tether is just long enough for her to reach the fence. How much of the surface of the field IP she unable to crop ? ' iii If:* I '\ m 878 MISCELLANEOUS. '■.'li ! '' f 46. If the diameter of an iron column is 3 ft. 5 in., what is the circumference ? If the girth of a tree is 5 ft. S in., what must be its diameter ? 46. If the equatorial diameter of the earth is 7,925 miles, how long in miles and rods is the equator ? 47. The distance from the centre of the hub of a wheel to the outer edge of the felly is 15 inches. How long must the tire be ? 48. It the length of an oar from the thole- pin to the end of the blade is 6 feet, how many feet would the end of the blade travel in the water during 6,000 strokes, each describing an arc of GO^ ? (60° » * of the circumference.) 49. If the circumference of a circular pond is 628.318 rods, what part of a mile must I row to pass from shore to shore across the centre of the pond ? 60. If a horse is tethered to the middle post of a fence, from which he can graze out into the field in a curved line 78.539314 feet long, how long is the tether ? 51. What will be the circumference of the largest circle that can be drawn on a sheet of paper 12 inches wide and 18 inches long ? ''1 t ft. 5 in., what is 6 ft. 9 in., SOLIDS. 379 •th is 7,925 tor? b of a wheel )w long must n to the end te end of the rokea, each 3umference.) d is 628.318 om shore to ; of a fence, curved line irgest circle es wide and SOLIDS. 640. A Solid is that which has length, breadth, and thickness. «41. A Prism is a solid whose bases are similar, equal, and parallel polygons, and whose side^ are parallelograms. 643. Prisms take their names from the forms of their bases, as triangular, rectangular, pentagonal, hexagonal, etc. 643. A Cube is a rectangular prism whose faces are all equal squares. 644. A Cylinder is a circular body of uniform diameter whose ends are equal and parallel circles. 645. The Altitude of a prism or cylinder is the perpen- dicular distance between its bases. Triangular prism. Rectangular prism. Pentagonal priem. Hexagonal prism. Cube. Cylinder, 880 SOLIDS. ©le. To find the convex Burface of a prism or cylinder. Suppose a block of the shape of one of the preceding prisms to hav. been fitwd with a piece of paper so as to exactly cover its convex surface Now If the paper be unrolled it will be found to be the shape of a rect angle, one side being equal to the height, and the other side equal to ihe perimeter of the base. Hence, the following rule. BtJIiE. i. Multiply the perimeter (mm of all the sides J of th « base by the altitude. 2. To find the entire surface, ada the areas of the haset to the convex surface. - ™ . ^^""^^ ^■. ^^°^ *h« "O"^^'^ surface and also the entire surface of a rectangular prism whose ends are ,5 inches by 7 inches, and whost altitude is 12 inches. * Solution Perimeter of the base = (5 + 7 + 6 + 7) in. = 24 in. Altitude = 12 in. .-. Convex surface = 24 sq. in. x 12 = 288 sq. in. Again, area of base = 7 sq. in. x 5 = 35 sq in .-. Entire surface = 35 sq. in. + 35 sq. in. + 238 sq. in. =' 358 sq. in ExAMPL.. 2. Find entire surface of a cylinder the diameter of whc^e base is 14 inclieB, and whose altitude is 20 inches. Solution. Perimeter of base = 14 x 3f = 44 in. .-. Convex surface = 44 sq. in x 20 = 880 sq. in. Again, area of base = 7 x 7 x 3| = ].04 sq in' .-. Entire surface = (154 + 154 + 880) sq. in. = ii8S sq. in. «47. To find the volume of a prism or cylinder RULE. Multiply the area of the base by the altitude. E^™-1. Find the volume of a rectangular prism whose bas. 18 4 inches by 6 inches, and altitude 10 inches. Solution. Area of base = 6 sq. in. x 4 = 24 sq in Volume = 24 cub. in. x 10 = 240 cnb in SOLIDS. the diameter of rism whose bast 381 EXPI,ANATI0N. 24 squares into which the b ^« '""f^^^^^^' corresponding to t:,^ blocki will there J^be itch LVlin'h '11'''''^'^ °^ ^^ese small Hence the part cut off wm con rn%4 Lbi^hrs 10 ^^t " *''=' '''''■ cut off the Whole b,oe., ... u. wh " S:;- ri^::::^^-'^'^ ^^ a4 cub in. X 10 = 240 cub. in. 12 inches ? mchas, and whose aUitu.le is Solution. Area of base = Vir^mrm = 27.^12 + sq -'n Volume =27.712cub.in.xl2.332.,4cu1 :n. Example. 3. Find the volume of b rvlinria,. *.i j- ba« iB 14 inches and altitude 20 Sche, ' ""' "' "'"^^ Solution. Area of base = 7 x 7 x 3f = 154 sq. in. = 154 cub. in X 20 = .JOSOoub.ia. Volume 64S. A Pyramid is a solid whose base is a pob-.on and whose sides terminate in a point called the vov^,^. 649. A Cone is a solid which has a circle for its base and terminates m a point called the vertex. 650. The Altitude of a pyramid or cone is the perpen- dicular distance from the base to the vertex. 651. The Slant Height of a pyramid is the distance from the vertex to the middle point of any side of the base 653. A Frustrum of a pyramid or cone is the part whicli IS left after the top is cut off by a plane paralleMo 653. The Altitude of distance between its ends. to IX ustrum is the perpendicular Mil ft,! 382 SOLID-. In li „ . . 654. The Slant Height 6f a frustrum of a pyramid is the distance between the middle points of two parallel sides of one of its faces. Pyramid. Cone. Frustrum of a pyramid. Frustrum of a cone. 655. To find the convex surface of a pyramid or cone. , BULB. J, Multiply the perimeter by one-half the slant height. 2. To find the entire surface add the area of the base to the area of the convex surface. Ejcample 1.— Find the entire surface of a pyramid whose basd ia a square side 6 inches, and whose slant height is 10 inches. Solution. Perimeter of base = 16 in. Convex surface = 16 sq. m. x ^ = 80 sq. in. Area of base = 4 sq. in. x 4 = 16 sq. in. .-. Entire surface = (80 + 16) sq. in. = 96 sq. in. Example 2. — Find entire surface of a cone, the diameter of the base being 14 inches, and slant height 30 inches. Solution. Perimeter of base = 14 in. x 3;^ = 44 in. Convex surface = 44 sq. in x ^ = 660 sq. in. Area of base = 7 x 7 x 8;^^ =154 sq. in. Entire surface = (660 + 154) sq. in. = 814 sq. in. 056. To find convex surface of a frustrum of a cone or pyramid. RULE. 1. Multiply one-half the sum of the perimeters of the ends by the slant height. 2. To find ike entire surface, add the areas of the ends to the area of the convex surface. SOLIDS. 383 a pyramid or Lim of a cone rs of the ends height is 20 inXs '° '"^ '' ^"°^'^' "^"^ ^^^°«« '^^^^ SOLCTION. Perimeter of ends = 7 in v qj. _ oo • ■> . . tin X 3| = 22 in., and 14 in. x 3f ^ 44 in Convex surface - Z^"* + 22\ . ^ - ^ ___ ^ sq. ,n. X 20 = 660 sq. in. Areaofsmallerend = ^ x t; x v- - ^ai.r, ■ AreaofIargerend = 7.^:3t:ilM:rn. Entire surface = (660 + 38^ + 154) sq' in. = 852J sq. in. 65r. To find the volume of a cone or pyramid. - EULE. MuUtply area of the base by me-third the altitude. Solution. 7 X 7 X 3f (area of base) x 4^ = 1232 cub. in. oy?frS*d.^° ^""^ ^^^ """^"""^ °^ *^^ *''"^^^"'" °^ a ^«ne or RULE. area Of fl) "" ^ ^^^ ^ ^ - *' ^'^^-^ ' A ' stands for the ana h for the perpendicular height. diametl":rT7^ft"l* M^'r^ ? *'j '^^^^""^ °^ ^ --• -^-« -^ meters are 7 feet and 14 feet, and whose altitude is 12 feet. Solution, Areaofsmallerend = J x 5 x 3f = 38J sq. ft. Area of larger end = 7 x 7 x 3i = 154 so " Volume = (154 + 38* + VlsiTrari) x 12 x J = 1078 cub. ft. cufvp*;,,."^ ^^^'^''^ °'" ^^"''^ '' ^ '^"^ terminated by a cuive surface, every part of which is equally distant from a point within, called the centre. 660. The Diameter of a sphere is a straight line drawn through its centre and terminated at both ends by the sur- face. ,1 m I',? 8«4 SOLIDS. «6I. A Hemisphere is one-half a sphere. ««2. The Radius of a sphere is a strai^'ht line drawn from its centre to any point in its surface. ««». To find the surface of a sphere. RULE. Muhiphj the square of the diameter bjj 3f . 7 feet ? Example.— What is the surface of a sphere whose dian«>te: it Solution. 7 X 7 X 3f = 154 sq. ft. Ana. 4I04. To find the volume of a sphere. RULE. Multiply the cube of the diameter by 3|, and divide the result hy 6. ExAJT'>T^.— What is the vohime of a sphere whose diameter if f f e"t«: fs CISTERNS AND BINS. 66«. To find the number of gallons in a cistern. RDLB. Find the volume in cubic inches and divide the resuU by 231. ti' 8"- ^ • bin 4 feet by 6fee, SoLUTioa. Volurne - 4 X 6 X 8 X 1,728 cub. in. .. No. bushels - 4 X 6 X 4 X 1.728 x 2160.42 . W bush. n.arly. nil V I- B86 OAUOINO OF CASKS. GAUGING OF CASKS. «67. Gaugring: is the process of finding the capacity or volume of casks and other vessels. NorE.-A oasK is equivalent to a cylinder, having tne same lengtn and a diameter equal to the mean diameter of the cask. ««». To find the mean diameter of a cask (nearly). R0LB. Add to the head diameter §, or, if the staves are but little curved, I of the difference between the head and buna diameters. «6S>. To find the volume of the cask in gallons. RULE. Multiply the square of the mean diameter by the length (both in inches), and this product by .0034. ExAMPU.-How many gallons in a cask whose head diameJK.f is 34 mohes, bung diameter 30 inches, and length 34 inches? SoiinxioN. Mean diameter s {24 + (;50 - 24) x §} =28 in. Capacity = 28 x 2d x Hi x .0034 = gO.tis'gal. fcXt'RCISE 126. 1. What is the solidity of a triangular prism who&o length is 12 feet, and one of the equal sides of one of its equilateral ends is 3 feet ? 2. How many gallons of water would a cylindrical boilej sontain if 25 inches high and 12 inches in diameter ? OJUOING OF CASKS. 887 diameter. ' ^ '"' ^'^^ *"^ ^^ inches in 4. A sphere 8 inches in diameter is placed in a cnl,Jp„i i whose interior dimensions are 8 inches Hnw ^''■' space is left ? -^""^ """^^ ^at'^it it it* i«^"7." ?'^^.^"«^1 tank which contains 160 gallons • It 18 6 ft. 6 m. m diameter. How deep is it ? 6. How many square feet of canvas will be reonirpri f cover a cylinder Ifii fo^f ;„ • I oe required to long ? * '° circumference and 26 feet 7. How many square inches of surface in a stove pine 22 inches m circumference and 12 feet long ? ^ ^ 8. What is the convex surface of a loff 2S foof ,« • ference and 18 feet long ? ^ ®'* '" '"'""°^- 9. What is the convex surface of a ovlfn^^r q f . i and IHeet in dia.et» . Wb.t is it^eTttTuie:;'™^ feefintlt^f ^ ""'"" "' * '»« ^^ '-' """« and 2 Jny X^tfefntt'^esl'^r': '"^'T '" high ? '° diameter and 3 feet who!;™lr2,"" r'r'^ "' » '""drangular prism .h"se !«:: Lfb: istLm i* 'i*-'" ^^--'^ square? » i- « le teet, and whose base is 80 feet height 16 feet ? °'""""'« *'««*»" '""h «de, and slant «; ii' Ki m^i 888 OAUaiNQ OF CASKS. i ' n Mii 16. What ig the convex surface of a cone, the diameter of whose base is 7 feet and its slant height 12 feet ? 17. What is the entire surface of a triangular pyramid whose slant height is 25 feet, and each side of the base 10 feet ? 18. What is the entire surface of a right cone, the diameter of the base and the slant height being each 40 feet ? 19. Find the cubic feet in a log 80 feet long and 2 feet in diameter at the larger and 1 ft. 10 in. at the smaller end. 20. Find the cubic contents of a pyramid, base 300 feet square, and altitude 80 feet. ' 21. How many cubic feet in a circular mound 48 feet high, and having a diameter of 86 feet at the top, and d circumference of 471.24 feet at the bottom ? 22. How many cubic miles in the earth, supposing it to be a perfect sphere 8,000 miles in diameter ? 23. How many barrels of oil in a tank 60 feet in diameter if the oil is 5 feet deep ? (40 gal. to the barrel.) 24. A monument in the form of a square pyramid, is 2 ft. 10 in. square at base, and 11 feet high ; at 175 pounds to a cubic foot what is its weight ? 25. What are the contents of a round log whose length is 20 foet, diameter of larger end 12 inches, and smaller end 6 inches ? 26. The altitude of a frustrum of a pyramid is 27 feet, the ends are 4 feet and 8 feet square ; what is its solidity ? 27. What are the contents of a pyramid whose base is 144 square feet, and its altitude 83 feet ? 28. Find the solidity of a sphere whose diameter is 12 inches. OAUaiNO OF CASKS. 389 basTisT^esr f'! ""T'' ''' ^°"« *^« ^'^^ of whose Ociae 18 1,865 sq. feet, and its altitude 36 feet ? 80. Find the convex surface of a frustrum nf o «« base 80 feet, and of the upper base 16 feet. 31. What will it cost to gild a ball 12 inches in diameter at 10 cents a square inch ? "i»uieiei, inclt^n^'*'"'^?''^ ^""'^'^ "^*'^^ ^»i*«d States is 18 J mches in diameter and 8 inches deep; how many cubio niches does it contain ? f . "w many cubio 38. How many square yards in the convex surface of a frustrum of a pyramid, whose bases are heptagons each Bide of the lower base being 8 feet, and of the uppe" base 4 feet, and the slant height 65 feet ? 84. Find the contents in gallons of a cask whose length inches" ' ""' '""^*^^ ''' '^' ^^^^ diameterVa 36. Eequired the contents in gallons of a rectangular cistern 4^ feet long, 3^ feet wide, and 6 feet deep. ^ lJ!'i7T aV^" '°"^'°*' ^ «^"°"« of * «^«k 36 inches long.xts head diameter 26 inches, and bung diameter 82 24^Lh "'' r"^ °:- """' ^° " '"^^ ^'^ose head diameter is fnchest "' ""''" '' "^'"' ^"^ i*« '-^^^ 34 38. What is the volume of a cask whose length is 40 mches the diameters 21 and 30 in. respectively ? ft fin 7. ""?/ f^Tl '"^ ^ '^'^ ^f '^'^^^ ^"rvature, 3 ft. 6 m. long, the head diameter being 26 inches, the buns diameter 31 inches ? o «. lue uung till i'i i It :| MEASUAMME^l OF CAUeElLiHi. MEASUREMENT OF CARPETING. «70. Carpet is isoUl by the linear yard, and i8 of variou& widths. The more common widths are 27 inches and 86 inches. 671. In determining the number of yards of carpet that will be required to cover a room, it is first necessary to decide whether the strips of carpeting shall run lengthwise of the room or crosswise. Economy in matching usually decides this. 672. In determining the length of each strip of carpet, allowance must be made for waste in mulching. 673. To find the number of yards of carpeting required for a room of given dimensions. ExAMPLB 1.— How many yarda of carpet 27 inches wide will be required for a rectangular room 21 feet long and 18 feet wide, if the stripa run lengthwise and no waste in matching 1 SoIiDTION. 18 ft. = 216 in. 216 -f 27 — 8, No. strips of carpet. 1 strip is 21 ft. or 7 yds. long. 8 strips are, 7 yds x 8 = 56 yds Ana. ExAMPiiE 2. — How many yards of carpet 36 inches wide will hp. required for a rectangular room 20 feet 6 inches long, and 16 feet 9 inches wide, if the strips run crosswise, and 4 inches per strip be allowed for matching ? Solution. 16 ft. 9 ii3. T)' in. 201 in. -r ••'^ V ■ . imeB and 21 in. remaining. .". It will take ;: Kii:... '>*. '"^'pit. Lengthof et>.d> ^t-.-. 1 iv 20 ft. 6 in. :- 4 in. = Oft. 10 in. 1 strip is 20 tt: 10 i:; long. 20 ft. 10 in. X 6 = 125 ft. or 413 yds. Ana. MEASUREMENT OF CAItPETUfQ. 9H -t. ' ' .i ■ EXERCISE 127. » 1. A rectangular room 26 ft. 3 in. long, and 10 ft. 6 in wido, ,B to be covered with carpet 1 yard mr.e. Which way of the room should the strips run that there may be the least turned under or cut off from one sid. of a breadth ? 2. In No. 1, if the strips were 16 ft. 6 in. long, how many strips would be required ? 8. In No. 1, if the strips were 26 ft. 3 in. long, how many would be required. 4. In No. 1, if the strips wer^ 16 ft. 6 in. lon^, and there was no waste in matching, how many yards would it take ? P. In No. 1, if the strips w,n-e 26 ft. 3 in. long, and there were no waste in matching, how many yards would it take ? 6. How many yards of carpeting 27 inches wide will be required for a room 17 ft. 6 in. by 15 ft. 5 in., if the strips run crosswise, and 7 inches be wasted in matching each strip ? 7. A room is 15 feet by 17 ft. 6 in., and the carpet is f of a yard wide. What must be the length of the strips to have the least waste ? How many strips will be required ? 8. In No. 7, how many yams oi carpet would be required if there were a waste of 8 inches in matching each strip, except the first ? Why should there be no waste in the first strip ? 9. Find the cost of carpeting a room 22 ft. 8 in. by 18 ft. 4 in. if the carpeting be 27 inches wide, and cost $1.80 per yard, there being a waste of 8 inches per strip in matching, the strips running lengthwise. 10. A parlor 20 feet by 17 feet is carpeted with a carpet 1 yard wide, at $1.20 per yard, surrounded wi^'^ a rarp^t border 1 foot wide, at 75 cents a yard. Find the cal cost. ^^■;|l i'' 1 ^^^^n '1 '' ill ^^Hlin n 1 ^^nil' 1 ^ Bfti ll ^H|| 1 1 ^^^^Hiii 1' ! " ^^^^^^^^^1 1 . i ^^^^^^^^^1 1 { if J ) ^^^^^^■Kffi 1 li' i ^^^^^^^■Mtt'f ( 1 ^HM|]i !', ^^^^BMI ^^1 ', 1 ^^^^Hii ' w' li ■ ! ^^^^ffil fi' , ^^nli ' ill! ^^■i^V '' ' !i ! ■ iif ■; 1 1 ; ; ^^B^H if >l 1 ' ■ I ' : ^■11 i \ \f9 ^^^^^^^^^^■HH^Bnfe^HHHfe!! 11 ill ^fPinE: ' > 1 I ' 1 ^^^^■m iM '» , ^{'jll 1 1 ,'i ^^^Hp 1 i 1 I ^■l ,.' '' If 1 ' ^^h|'|^ '„, ll . 1 ii i ^■i' Wm' ' ^^■Ijh:' M m ^-^-'N i ,jl 1 ^^■lifi '• ; 1 1 ^^^^^^^H ^^H^F ■A s'T '1 392 MEASUREMENT OF CARPETINO. 11. Find the cost of carpeting a room 28 ft. 10 in. long, by 17 ft. 8 in. wide, with carpet f of a yard wide, at $1.80 per yard, if the strips run lengthwise of the room, and 9 inches per strip be wasted in matching. 12. Find the cost of the carpet for a stair of 17-12 inch steps, each rising 8 inches, at 90 cents a yard. 18. Find the cost of the stair carpet at $1.20 a yard, for a flight of stairs of 22 steps, 11 inches wide, with Tin lea rise, allowing 1 yard extra at the top. 14. Find the cost of covering the floor of a hall 24 feet long by 8 feet wide, with oil-doth 4 feet wide, uo waste in matching. ' MEASUREMENT OF WALL PAPER. 8i)B MEASUREMENT OF WALL PAPER. «74. Wall paper is sold by the roll, any part of a roll being count'jd as a whole roll. 675. Canadian and American wall papers are 18 inches wide, and have 8 yards in a roll. For convenience wall paper is done up in double rolls of 16 yards. «76. In estimating the number of rolls necessary for a certain room, paper-hangers ascertain the height of the room and its perimeter, making an allowance in the peri- meter of 3 feet for each door or window. «77. The exact cost of papering a room can be ascer- tained only by taking account of the number of rolls of paper actually used in doing the work. H7H, To find .ae number of rolls of paper required for a room. Example 1.— How many rolls of wall paper will be required for the walls of a rectangular room 20 feet by 16 feet, with a 12 foot ceilin» there bemg one door 3 feet 8 inches ^vide, and 2 windowa each 4 feet 2 inches wide ? Solution. Perimeter of room is (20 ft. + 16 ft.) x 2 =72 ft. Width of door, 3 ft. 8 in. Width of 2 windows (4 ft. 2 in.) x 2 = 8 ft. 4 in. 12 ft. Peiii:ieter after dednoting width of door and windows = 60 ft 60 ft. = 720 inches. 720 in. -f 18 in. (width of paper) a 40, number of strips. 1 strip is 12 ft. long. 40 strips are 480 ft. or 100 yds. long. 100 yards -^ 8 yds. (No. yds. in a roll) 20, No. of rolls. Ana. 14 ' u \ 394 MEASUREMENT OF WALL PAPER. Example 2.— Find the cost of the wall paper at 80 cents a roll and bordering at 7 cents a yard for a room 18 feet 9 inches long by 16 feet 5 inches wide, with the ceiling 10 feet 9 inches above the base boards, allowing for 2 doors each 3 feet 8 inches wide, and 3 windows each 3 feet 6 inches wide, also an allowance of 9 inches on each strip for matching. (In reckoning the cost of die bordering no allowance is made for the doors and windows.) Solution. Perimeter of room is (18 ft. 9 in. + 1(5 ft Sin.) x 2 = 70 ft. 4 in. Width of doors (8 ft. 8 in.) x 2 = 7 ft. 4 in. Width of windows (3 ft. 6 in.) x 3 = 10 ft. « in. 17 ft. 10 in. Perimeter of room after deducting width of doors and windows ■ 52 ft. 6 in. 52 ft. 6 in. = 630 in. 630 in. -f 18 in. = 35, No. of strips. T(i allow for matching, the paper will cut into strips of (10 ft. 9 in. + 9 in.) = 11 ft. 6 in. in length. One roll will practically cut into 2 strips. .-. No. of rolls = 35 -=- 2 = 17J .'. It will take 18 rolls 1 roll is worth 80 cents .'. 18 rolls are worth 80 cents x 70 ft. 4 in. = 24 yds, nearly 1 yard is worth 7 cents .-. 24 yds. are worth 7 cents x 24 = 51.68, Oost of border. $16.08. Total cost. 18 = $14.40, Cost of wall paper. EXERCISE 128. 1. How many strips of paper will go around a room 18 feet by 24 feet ? 2. How many strips of paper are required for a room 30 feet by 24, if there are 4 windows and 2 doors ? (Art. 676.) 3. How many rolls will paper a ceiling 24 feet by 18 feet ? 4. How many double rolls are required for a hall 21 feet long and 13 feet high, with a cornice 1 foot deep ? 6. Find the cost of the paper for a room 86 feet by 24 feet and 11 feet high, with a cornice 1 foot deep, and a wainscoting 2 feet deep, at 50 cents per double roll. MEASUREMENT OF WALL PAPER. 3■' I 896 MEASUREMENT OF SAW-LOOS. MEASUREMENT OF SAW-LOGS. 679. TABLE OF LUMBER AND LOG MEASUREMENT. Showing net proceeds (fractions of feet omitted) of logs in 1 inch boards, deducting saw kerf and slabs. The length will be found in the left hand column, and the diameter in inches on the head of the other columns. (X ~a C-. ii 4- i; i; i-i o 2 O Diam. 10 t'oo©«oeo«oco(X)OOOo-q-q-.ae»050icnc;'Oii«>-*».it>.*.tao:to Diam. 11 i^oa>i!oaoi^oo:toaoi<^oo>coaori^oc:K>coi<^octcoaoi(^o tw-ab05i5lC-Jt>S«fll>8C;i-'O5(-'O»h-'C:(— C5I— '0»)-'ai0 Diam, 12 Diam. 18 ICtOiaWbSl-'H-l-'l-'l-il-'H-ll-'h-'l-'k-l-'h-h-'l-'l-i ici-'i-'©©eooDa-ic:o:cnc-T*kj«ii;tCh-i-'00«ooDOO-J05C5 Diam, 14 bSbStStCitOtOtCbSMtOI-'l-'MI-ih'H-'l-il-'l.-'l-'Mf-'K' 0SM0:tat>SUl(0«St6(Ot<9lOMt>UI-'MI-'l->l— h-'MI-'h-il-'l-' tOI-'0!000~a-q050il*^MtCH-'©50(Z)CC^Cn©-J(X>(OOI->tOWl4^VlOi~Jao«CO)-'tCMl(^C}lC:-}CX>0© Diam. 15 Diam. 16 CUv>:Ci:WWOSCUCi:tOI>9tStOtOI>StStOtStOMI-'l-'l-'l->l-'l->l-'.^ X ~00l-'©OQ0-J050lt^C«t>St-'©«3.it..tU.euwMwo:cuo:uscot«totct>stobstci-'h-'i-'i-'i-'i->i-> i*-'.ci-'©eoooC5 0ii*>.cui-'Occc»cr;«'i*»t»:i-sotrQo^eni«^osio Diam. 18 ©;r-jO!Oii«to©«oa)OsoiWbs©«DOD05mwi«t-'oaDr;oiitk c;bOiXrf>k©a:tcaoK^oa:h-'a>c»eow©owtficnM:>cAl>St!£>tiil-^'H-> ti 0< ii 4)1 Oi -a o *» ts H- ;-. © iK 00 bO tf IX Oi iC>. 09 h-' O0035C;iC0b0©W-JOli*>.|jS©5C-*« ( . t>S tn i4>>. isS 55 © is 00 tC C5 © Diam. 20 lASUREMENT. of logs in 1 inch 11 be found in the hcas ~q Oi CC Dium, 10 W W OS -J *>. H- Diam. 11 4^ lb. >;^ 00 l*»© Diam. 12 OS C "J< 1- CnO Diam. 18 ~J 05 05 W :< to to 05 © o o to en to ce © qs liiMMMMliiiiillii Diam, 26 Diam. 27 totoo>a.totoo>.;.g S^a£:^S2S£;gg5as-gfes|fe o.t.oeo:Qotoq>H.o>ogg^>feo;3^g>^;^^oowto^|^ Diam 30 Diam, 31 ssisigiSsiHiiiiisiiggiaiii iiiiiiiiiiiiiiiiliiiiiigiss 6Sl— (-'(-•(-'►-'MI-l.-lH'h-Mt-ll-ll-l Diam, 32 Diam. 33 iiiiiiiiiiiiiiiipiiggsssgg .---._-_ — . — ^- *^^ *— ^^v ^- — f— ^J i«i u_i _^ _. ^ — Diam. 34 Diam 35 I.! n , I i ;i ! I Jin Ml,:; i'l 1 ! 898 MEASUREMENT OF SAW-LOOS. 6WO. Tn some parts of Canada saw-logs are bought and sold by the Standard, in other parts with reference to the number of feet of inch lumber which they will produce. 6S1. A Standard Log is 12 feet long and 21 inches in diameter, and will produce 1,085 feet of inch lumber. 6^3. The measurement of a log is always taken at the small end and between the bark. HHS» To find the number of standards in a given number of saw-logs. Example 1. — How many standards are there in 4 saw-logs, each 12 feet long, the diameters of which are 16 inches, 20 inches, 22 inches and 25 inches respectively ? Solution. 16a = 256 2i,2 = 400 22a = 4S4 253 = 625 Sum = 1,765 1,765 -5- 21» = 1,765 .f 441 = 4. No. standard Ana. ExaM"i,e 2.— How many standards are there in 5 logs, each 16 feet long, the dicuneters of which are 18, 20, 21, 24, and 30 inches respec tively ? Solution. 188 = 324 20a = 400 212 = 441 243 = 576 302 = 900 Sum = 2,641 2,641 -r 441 = 6 nearly. No. of standards 12 feet long. 16 = IJ times 12 .*. No. of standards = 6 x IJ = 8. Ans. EXERCISE 129. 1. How many standards are there in 6 saw-logs, each 12 feet long, the diameters of which are 12, 18, 20, 25, 28 and 28 inches respectively ? s in a given • ,A',^'"',^'"^^ standards are there in 6 I0.8 each IS feetlong, the dian,eter» of vfiich are 14, 20. 22 24 a 1 % inches respectively? " 3 What is the side of the largest square niece of tirah.r winch ...,e sawn fro. a log. the L.et'er l^l^Z 4 From the Table, Art. 679, lind out the quantity of inch lumber that can be sawn from the following : 3 logs 10 feet long, diameters 15. 20 and 32 inches respectively. 4 " IR « 18 and 24 2 .. :: .. " 16. 20. 22 and 80 " ^ ^^ " 20 and 26 6 A man wishes a piece of timber 18 inches sauare what . t^he diameter of the smallest log from :hi:hTmay 11^ 400 MEASUREMENT OF LUMBER I MEASUREMENT OF LUMBEK. 6H4. Lumber, as the term is used here, includes all kinds of sawed boards, plank, scantling, joists, etc. 6S5* A foot of lumber, or a board foot, is the unit of measurement. It is 1 foot long, 1 foot wide, and 1 inch thick. 686. The term scantling is given to lumber 3 or 4 inches wide, and from 2 to 4 inches thick. Joist is usually from 2 to 4 inches thick, and from 6 to 16 inches wide. Lumber heavier than joist or scantling is called tii^'hPT. A. broad piece of lumber thicker than a board, — usually from 1^ to 4 inches thick, is called a plank. 657. All lumber less than one inch in thickness is con- sidered inch lumber in measuring. 658. In measuring the width of a board a fraction greater than a half inch is called a half, and if less than a half it is rejected. Thus a board 5^ inches wide would be considered 6 inches wide, a board 9* inches wide would be considered 9 inches wiao. 689. The price of lumber is usually quoted at a certain rate per thousand feet, board measure. 690. To find the number of board feet or feet of lumber in a board, plank, joist, etc Example 1 Find the number of feet of lumber in a board 14 feet long, 12 inches wide, and 1 inch thick. Solution. (14 X 12 X 1) -r 12 = 14 feet. Ana. ME AS V HEME M OF LUMBER. 401 Solution. (16 X 14 X 3) -M2 = 56 feet. Ans. r.ULE. iJ/«W/.Zy the length infect by the mdth and thickness in inches, and dunde the product Uy 12, and the re^uZ Z the number ofboardjeet of lumber. I !l skness is con- i at a certain EXERCISE 130. 1. Find the number of feet of lumber in 24 boards 14 feet long and 10 inches wide. " 2. Find the cost of tty 2-inch plank 16 feet long and 10 inches wide at $18 per thousand, ^ 3. How many square feet are therp in fhn o., t * board 16 feet by 9 inches ? ^' ''''^^'' °^ ^ 4 How many feet of lumber are there in a board 12 feet long, 6 inches wide and 1 inch thick ? 5. How many feet of lumber are there in ih. tu-' Pieces of ^d:„g, 12 feet l„„g, 4 inches wide, f inch thiok 14 beams 20 feet long, and 9 inches souare Ifi .!. *, ' 2 inches by 4 iaohes, 16 feet long. ' ' '°"'"'"«' 6. How many feet of lumber in a 140 ni»,...„f a- each 12 feet long, 6 inches wide, and " Lh tWck ? """*■ 14 feeXT""""'" '^ """^ " ^'^"'-^ 2x4 scantling th!ns»d' "" "="' "' '•'=» ''^' °' '»"">" «t 120 per 4k 'ft, i-i . li 402 MEASUREMENT OF LUMUhli 9. Find the cost of 1^ inch flooring required to lay a floor 42 feet by 24 feet at $24 per thousand. 10. Find the cost of flooring a bridge 320 yards long by 20 feet wide with 8 inch oak planks, at $22 per thousand. 11. If 2 X 4 studs are used, and they are placed 16 inches apart, from centre to centre, how many feet of lumber are there in the studding of a wall 20 feet long and 12 feet high? 12. How many 12 foot boards 6 inches wide are required to put a wainscoting 3 feet high around a kitchen 12 feet by 16 feet, allowing for 2 doors, each 3^ feet wide ? 13. Find the cost of the lumber for two floors of a house 24 feet long and 18 feet wide, if the lower floor is 1^ inches thick, and the upper floor 1 inch, at $20 a thousand. 14. A barn is 64 feet long and 40 feet wide, and 20 feet high to the eaves; the gables are 8 feet high, and the rafters 22 feet, 6 inches long. Find the number of feet of inch boards necessary to inclose the two sides, allowing for two doors 12 feet by 16 feet. 16. In No. 5, find the number of feet of lumber in the ends and gables. 16. In No. 5, find the number of feet of luinl)er required to sheet the roof. 17. In No. 5, find the cost of the lumber for the doors at $20 a thousand. 18. In No. 6, find the cost of the 2 inch plank needed for the floor at $24 a thousand. 19. If 4 X 5 rafters are used, and they are placed 30 inches apart, from centre to centre, how many feet of lirmbuf are thers in the 20 foot rafters of a double roof 40 feet long ? il nber in the MEASUHEMJUNX OF Ll'MBER, 403 20. Find the price of the following u\n «f i u per thousand :- ^ommng bill of lumber at $24 120 2-inch plank 10 inches wide. U feet lona 125 boards 10 inches wide, 16 feet long '* 80 2 X 4-nich scanthn,.. 14 feet long. 50 3 X 4inch " 12 u ^ 120 3 X 10-inch joist, 16 feet lonT between the sf^s ? '^"''' '°'* '"'™*"'' '>-'' «■■ i«ol' in No T^^lll "°^= "'-'' '» "-^ - sheeting ,he roof of lumber will be required? ' ""'' """^ ""^'^ '^^' Je\o!:Lra%re°/o'retM; ""-'" '-^ --'- fa"'l8''dooTeaeh''7%'7'." '"'*'■* "-»-<" "- wideftbe fal X;;fJ,,t'J^^,\-^3^ ^-' « -^es feet. "®' ^* ^3<^ per thousand %■ Ir. ^; i ll 404 MSASUEEMENI OF SIIINOLINO. MEASUREMENT OF SHINGLING. 691. Shingles are sold by the bunch, each bunch con- tains a quarter thousand. A bunch of shingles is 20 inches wide, and has 25 courses on each side. Dealers will not sell a part of a bunch. 0»a. Ordinary shingles have an average width of 4 inches, and are generally laid 4 inches to the weather. «»3. Allowing for waste, 1000 shingles will cover a surface of 100 square feet (a square of shingling), 4 inches to the weather ; laid 4J inches to the weather, 900 shingles are required. EXERCISE 131. 1. How many shingles are there in 24 bunches ? 2. How many bunches are there in 15^ thousand ? 3. How many thousand are there in 48 bunches ? 4. Laid 4 inches to the weather, how many square inches are covered by the exposed part of one shingle ? 5. How many shingles are required for a roof having a surface of 2,400 square feet ? 6. How many bunches of shingles will shingle a roof 32 feet by 24 feet ? 7. How many shingles are required for a double roof 36 feet long, with 20-foot rafters ? 8. Find the cost of laying a double roof 48 feet long, rafters 24 feet long, with shingles 4 inches to the weathrr at $3.20 per thousand. 9. Find the cost of shingles for a double roof 36 feet long, rafters 21 feet long, at 60 cents a bunch, if the shingles are laid 4^ inches to the weather. 10. At $3.60 per thousand, find the cost of the shingles for a roof of a building 60 feet long, 40 feet wide, having a gable 12 feet high, and the rafters having an IS-inch heel. FJiNVLWO. 106 FENCING. EXERCISE 132. roils long, if the posts are placed 8 feet apart ? fi.l!i!n°''r^"-'' ''°'*' ^'' '"1"^^^^^ f«^ * fence around a fiel.i 40 rods square, if they are placed 8 feet apart ? If aid, if they are placed 8 feet apart ? 4 Find the cost of the posts for a rence around a garaen plot 250 yards by 220 yards, if the posts are placed 6 fee" apart and cost 10 cents each. 6. In No 4, how many 2 x 4 scantling. 12 feet long will be required for the 2 stringers of the fenc^ ? ^ iy. ^; ^^^u' ^' ^°^ *^' '°'^ °^ 2 ^ 4 Bcantling, 16 feet long hat will be required for the 2 stringers of th fence, if th^ lumber is worth $18 ppv thousand. 7. How many feet oi mmuer are required for a 10-inch base board around the field in No. 2 ? rod®- i^""" "^l"^ ^"i"'^ ^''^'^' ^'' ^^-l^^^^d for a fence 40 rods long, If the pickets are placed 2 inches apart ? 9. How many 2i-inch pickets, placed 2 inches apart are required for a fence around a garden 200 yards by 150 10. How much lumber 40 rods long, consisting of 6 rounds of 6-inch l)oard7? is there in a common board fence 406 FENCING. 11. What will it cost to fence 5 miles of railway, both Bides", with 6 rounds of 6-inch boards, at $12 per thousand feet? 12. What will it cost at $10 per thousand to fence a field 40 rods by 60 rods with 1 round of 12-inch boards, and 5 of 6-inch boards ? 13. What will be the cost per mile to fence a railway with 5 strands of barbed wire, which weighs 1 )b. per rod, at 8 cents a pound ? 14. Find the cost of a quarter mile of fence with the posts 8 feet apart, a 12-inch base, a 2 x 4 rail at top, and 4 strands of barbed wire ; the posts cost 10 cents each, the lumber f 12 per thousand, and the wire at 7 cents a pound. ^A pound stretches 10^ feet.) MKASUUKME.M OF lUlNTl.SQ, ETC. 407 ; MEASUREMENT OF PAINTING, KALSO- MINING AND PAVING. « nH r*- '^^- "If °^ "^eaBurement of painting, kalsomining, and paving is the square yard. EXERCISE 133. I. How many square yards of painting are there in a floor 30 feet by 28 feet ? f g «.re mere m a 2 Find the cost of kalsomining the ceiling of a hall 64 feet long and 36 feet wide, at 20 cents a square yard 8 What will it cost to paint a close board fence 6 feet high around a lot 36 yards long by 24 yards wide ? 4. What will it cost to paint a house 36 feet bv 30 feet s^uatyrrdT '""'^ '''''''' '' '' ''''' ^*/« -*« ^ 5. What will it cost to kalsomine a room 20 feet bv 18 feet and 10 feet high, at 7 cents a square yard ? "^ hv^o//"? *^,r'* ""^ P*"^*'"^ ^ '^^"'^^^ roof 44 feet long by 24 feet, at 12 cents a square yard. ^ 7. What Will it cost to tuckpoint the front of a brink house 36 feet long and 22 feet high, allowing for halHhe openings which form one quarter of the surface, $1.25 per square yard ? f w-^-^o per 8 Find the coBt of paving a street half a mile long and 60 feet wide, at 30 cents a square yard. 1 '■ ^'f, f^l ™" "' """"«! " "'"«' one-eighth of a mile long and H chains wide, at 25 cents per square yard [. eet wide, formea around the outer edge. Find the cost of gravelling the walk, at 16 cents a equf'; yard d 408 MEASUREMENT OF LATHINQ AND PLASIERINQ, f fl f "i ^1 1 M *? H" I i II ti MEASUREMENT OF LATHING AND PLASTERING. 695. Laths are sold by the bunch. There are 50 laths in a bunch, each lath being 4 feet long and IJ inches wide. They are usually laid about three-eights of an inch apart. 6t>6. Allowing for waste, contractors reckon that a bunch of laths will cover 3 squarie yards of surface. 607. Lathing and plastering are estimated by the square yard. Only one-half the surface of openings is allowed. 6!>H. To find the cost of lathing and plastering a room of given dimensions. Example. — A rectangular room 24 feet by 18 ft. 9 in., and 10 ft. 10 in. high. The base board is 10 inohea high ; there are two doora 8 feet by 4 ft. 3 in. each, and three windows 6 ft. 4 in. by 4 feet each. Find the cost of lathing and plastering the walls and ceiling at 30 cents a square yard. Solution. Perimeter of room = (24 ft. + 18 ft. 9 in.) x 2 = 85 ft. 6 in. Height of walla above base board - 10 ft. 10 in. - 10 in. = 10 ft. Area of walla = 85 ft. 6 in. x 10 ft. = .. .. .. 855 sq. ft. Area of ceiling = 24 ft. x 18 ft. 9 in. = 45 aq. ft. Total groas area = 1,305 aq. ft. Area of 2 doors = (8 ft. x 4 f t.3 in. ) x 2 = 68 aq. ft. Area of 3 wintlowB = (6 ft. 4 in. x 4 ft.) x 3 = 76 sq. ft. Total area of .'oors and windows = 144 aq. ft. Half of 144 sq. ft. ia allowed s= - 72 sq.ft. Net area to be lathed and plastered a 1,233 sq.ft. 1,233 sq.ft. = 1.37 sq. yds. 1 8(1. yd. ia woi'th 30 cents. 137 aq. yds. are worth 30 cents x 137 = $41. 10. Ans. 1 1 MEASUREMENT OF LATIUNG AND PLASTEIUNO. 409 EXERCISE 134. 1. Including one of the spaces between the laths, how many square inches does one lath cover ? 2. How many square feet will a bunch of laths cover? a. How many bunches of laths will be required for a wall 86 feet long and 12 feet high ? 4. How many bunches of laths will be required for the ceihng of a room 82 feet by 28 feet ? 6. How many bunches of laths are required for the walls and ceihng of a room 15 feet by 18 feet, and 9 feet high ? 6. How many bunches of laths are required for a hall 84 feet long. 52 feet wide, and 24 feet high, allowing for 4 doors and 10 windows, each having an average surface of 82 square feet. Art. 696. 7. At 80 cents a bunch, find the cost of the laths for a room 20 feet by 24 feet and 15 feet high, there being 8 wnidows and 2 doors, each 8 feet by 4 feet. 8. At 25 cents a bunch, find the cost of the laths for a room 24 feet by 16 feet and 10 feet high, allowing for a door 8 feet by 3 ft. 6 in., and a window 7 feet by 4 feet. 9. How many square yards of plastering are there in the ceiling of a room 60 feet bv 32 feet ? 10. How many square yards of plastering are there in the walls and ceiling of a room 86 feet by 24 feet and 12 feet high ? m.lO. Ana. 11. Allowing of yards of piasterin feet high. an 18-inch base-board, find the numbpr in a room 86 feet by 80 feet and 14 1 ml 1 i ^^^^^K^^B '^H in V I 1 . [ 410 MEASUREMENT OF LATHING AND PLASTERING. 12. Find the cost of plastering the ceiling of a room 36 feet by 32 feet, at 9 cents per square yard. 18. Find the cost of plastering the walls and ceiling of a room 18 feet by 24 feet, 12 feet high, at 12| cents a square yard. 14. At 15 cents a square yard, find the cost of plastering the walls and ceiling of a room 21 feet long, 14 feet wide, and 12 feet high, with 4 openings, each 8 feet by 4 feet. 16. At 12^ cents a square yard, find the cost of plaster- ing a room 20 feet by 16 feet and 12 feet high, with an 18- inch base, and having 4 openings, averaging 82 square feet each. 16. Find the cost of lathing and plastering a room 16 feet bj 18 feet and 12 feet high, with laths at 30 cents a bunch, and plastering at 16 cents a square yard. 17. Find the cost of cementing a circular cistern 8 feet in diameter and 9 feet high, at 8 cents per square foot. MEASUREMENT OF STONE-WOliK. ^n MEASUREMENT OF STONE-WORK. «9». A cord of stone is of the same size as a cord of wood. In estimating stone-work no smaller part than quarter-cords is allowed. •TOO. A cord of stone will make about 100 cubic feet of wall. TOI. In estimating the cost of mason-work, it is customary to take the outside measurement of the wall, and make no allowance for openings, except they are large! 7«2. It takes about three bushels of lime and a cubic yard of sand to lay a cord of stone. T03. Stone-work is usually estimated by the perch. •704. A perch of stone- work is 1 rod long, 1^ feet thick and 1 foot high. It contains 24| cubic feet. EXERCISE 135. 1. How many cubic feet of stone are there in a pile 38 feet long, 6 feet wide, and 4 feet high ? 2. How many cubic feet of stone are there in wagon-box 9 feet long, SJ feet wide, and IJ feet high ? What part of a cord does it contain ? 3. How many cords of atone are there in a pile 20 feet long, 8 feet wide, and 3 feet high ? 4. In No. 3, how many cubic feet of wall will the stone build ? 6. How many cords of stone will build a wall 200 feet long, 6 feet high, and 8 feet thick ? 6. How many cords of atone will build a wall 60 yards long, 6 feet high, and 18 inches thick? How many perch of stone-work in the wall ? 412 MEASUREMENT OF STONE-WORK. V.'3 7. Find the cost of the stone in a wall 42 feet long, 8 feet high, 18 inches thick, at |6 per cord. 8. How many cords of stone are required for a cellar 86 feet long, 80 feet wide, if the wall be built 8 feet high, and two feet thick ? Find the cost ot the mason work at 60 cents a perch. 9. How many cords of stone are required for the founda- tion of a bank barn 60 feet long, by 36 feet wide, if the foundation wall be 7 feet high and 8 feet thick ? Find the cost of building the foundation at 60 cents a perch. 10. At 60 cents per perch, what is the cost of the s >ne- work for the basement of a house which has an outside perimeter of 160 feet, the wall being 8 feet high and 20 inches thick ? 11. How much lime and sand will be required for the mortar of an 18-inch wall 8 feet high, under a house 40 feet by 80 feet ? 12. In No. 9, find the cost of the material at $6 per cord for the stone, 80 cents a bushel for the lime, and $1.20 per cubic yard for the sand. 18. A stone house is 86 feet by 24 feet ; the cellar walls are 9 feet high and 3 feet thick ; the walls of the ground floor are 12 feet high and 2 feet thick ; the walls of the second floor are 8 feet high and 18 inches thick ; the gable walls are 7 feet high and 12 inches thick ; find — 1st. Number of perches of madon work in the building, and cost of labour at $1.10 a perch. 2nd. Cost of the stone at $5 a cord. 8rd. Cost of the lim^ at 35 cents a bushel. 4th. Cost of the sand at $1.10 per cubic yard. MEASUREMENT OF BRICK-WOHK. MEASUREMENT OF BRICK-WORK. 418 i •705. Bricks vary so much in size and style, that to give the exact dimensions of the different styles is impracticable. Ordinary bricks are 8 inches long, 4 inehos wide, and 2A inches thick. ^ T06. It is sufficiently accurate, in making an estimate of the number of brick needed for a certain work, to reckon iO bricks to the cubic foot laid dry. 707. In half-bnck walls, such as in veneering wooden houses, each brick, with the mortar required to lay it, has an external surface of 8^ x 3, or for about every 26 square inches of surface. 708. In single-brick walls, each brick, with the mortar required to lay it, has an external surface of 4* x 8, or one brick IS required for about every 13 square inches of surface. 70». In a brick-and-a-halfwaM, a brick is required for about every 8f square inches. 710. In doable-brick walls, a brick is required for about every 6i square inches of surface. 711. In estimating material, corners are measured once, and allowance is made for doors and windows. In estimating labor, the corners are measured twice, that 18, the outside measurement is taken, and allowance is usually made for one-half the openings. EXERCISE 136. 1. A pile of ordinary bricks is 8 feet 6 inches high, 14 feet long, and 15 feet wide. What is the pile worth at $8 per thousand ? 414 MEASUREMENT OF BRIGK-WOBK. ) M 2. How many bricks are there in a wall 36 feet long, 12 feet high, und half a brick thick? 3. How many bricks are required to veneer the front of a house 18 feet wide and 25 feet liigh? 4. How many bricks are require! for a single brick partition between two houses, 40 feet deep and 24 feet high ? 5. How many bricks are required to build a house 80 feet by 24 feet, and 18 feet high, with single brick walls ? 6. How many bricks are required for a dou!>le brick wall of a basement, 48 feet by 32 Axit, and 10 feet high ? 7. What will it cost to lay the brick of a house 40 feet by 82 feet, and 21 feet high, with a flat roof and double walls, at $2.75 per thousand ? 8. Find the cost of the brick in the wall around a garden, 400 feet, by 200 feet, 6 feet high, and a brick and a ha,lf thick at $7 per thousand. 9. At $8 per thousand, find the cost of the brick in the front walls of a terrace block, 120 feet long and 22 feet high. There are 6 doors, each 8 feet by 3|, and 20 windows, each 8 feet by 4 feet, the wall being a brick and a half thick. 10. How many bricks will be required for a house 40 feet by 80 feet ; the basement walls are 8 feet high and 2 brick thick, one door 4 feet by 6 feet ; the ground floor is 11 feet between the floors, and the walls a brick and a half thick, 2 doors and 4 windows, each 8 feet by 3^ feet ; the second floor is 10 feet high between the floors, and the the walls one brick thick, 6 windows, each 8 feet by 3^ feet ; the gables are 10 feet high and half a brick thick. I iii. i '\ METRIC SYSTEM OF MEASUREMENT. 415 THE METRIC SYSTEM OF MEASUREMENT. t.e;;jtLS3r :;^^:^-^S - --- -^^ a„. niiiiii'iiti#niiJ^iJ,i[,j,, [i i'„[jj^^ am each of which fa sub-dlvldedTmoiSLr' "*^*''°" '"*" '» C««/m./«^. whlte-and.black strips. T^ZlXlTll't '""^.r »' ^"'"° ^y the small illustration. complete A^^/r* can be easily constructed from this t J^^; ''^® "®*''1<^ System (pronounced Met'-ric) is a sys- tem of weights and measures expressed in the decimal scale. It IS now legal in nearly all civilized counS i Z^^l'^-V" ^"°"'" ^^ ^«* °f ^-^^^on Parltment in 1886 (chap 104, sec. 21), and all contracts based upnraJe T,::tT '' ^'"- '' ""^ ^^^^"-^ - *^e Un^^ Stat Sat !'' ThlT r °' f ^'^"'^^^ ™«*- ^--J^ed to all the btates This system of measurement is used in all countnP^. for scientific purposes on account of its exactneL a„T ^ many countries it is used for ordinary purposes. ^'nr?84S in F^nt """"^ '^^^ ^^^ *^^ ^"^^ -- ^- -m-n - Metric System of Measurement, is a bar of platinum 39 37 inches long. This length was chosen because ft wlssup!^ to be one ten-millionth ( Wa... or .0000001) of a quartr^f he earth's circumference measured by a line passinJ through Paris. France, from the equator^to the pole' Thf 416 METRIC SYSTEM OF MEASUREMENT. it: L&l!it ! original bar, or metre, was made by Boraa in 1.795 at Paris, where it is carefully preserved, accurate copies being fur- nished to the governments of all civilized nations. Its length being nearly 3 ft. 3| in., the metre may be remembered as the rule of the three threes. 714. The Standards used in a general scheme of meas- urement are called Units. Thus, the Metre in France forms the foundation and starting-point of every measure in existence. 715. All the Units of measures are derived in a simple manner from the Metre. Thus : The Metre is the unit of Length. It is a bar 39.37 inches long. The Ar (or Are) is the unit of Land Measure. It is a square whose side is 10 metres. 1 Ar = 119.6 sq. yds. The Litre (Leo-ter) is the unit of Capacity, ii is a cubic decimeter ; that is, a cube whose edge is a deciu) etre long. A Litre •= 1.76 pint. The Gram is the unit of Weight. It is the weight of a cubic centimetre of water. As the terms used in the Metric System are derived from the Greek, Latin and French languages, we have thought it best to give them English spellings, dropping the iinal "me" in "gramme," etc. 716. The Metre is sub-divided always into tenths, hundredths, thousandths, &c., or decimal parts, thus : Decimetre (dm) Latin decem, ten=iVor .1 metre (m). Centimetre (cm) " eentum, hundred=Tb or .01 metre. Millimetre (mm) " mllle, thousand=TTiW or .001 " The names of these lower denominations are formed by prefixing Latin numerals (deci, centi, milli,) and writing the abbreviations (dm, cm, mm,) -without Capital letters. All the compound names are accented on the first syllable thus, tril' limetre. Therefore : 1 metre=10 decimetres =100 centimetres = 1000 mm. 1 decimetre = 10 ceiitimetr63= 100 mm. 1 centimetre — 10 mm. V\ METRIC SYSTEM OF MEASUHHl^ENT, 417 717. Multiples of the Metre are as follows: Decametre (Dm) Greek Deka, ten-lO metres Hm. Km. Mm. Mg.n) W/M CapTtoUett™ f ""^^ ''''' -■"^brevlatlons (Dm, 718. A person who wished to buy 125 metres of cloth would not ask for .^1 hectometre, 2 decametres, 5 metres ' any more than a Boston merchant would tell a person who owes h.m ,25.90 that his bill is 2 eagles, 5 dolla.^. 9 dils: 719. Comparative Lengths are as follows: 1 >r Inches. Feet. Yards lM3tre= 39 37079 3.2808992 i oSg'l 1 r)oc,metre= 3.93708 .3280899 loJS Centimetre= .39371 .032809 oioS 1 Mxllxmetre= .03937 .0032809 .SS 720. The Metre, like the yard-stick, is used in measur ing cloth and short distances; the Kilometre is used Tn measuring long distances. ^ 721. Since, in the Metric System, 10, 100, 1000, etc., units of a lower denomination make a unit of a higher denominf tion, It follows that any one of the metric mLures maTbe expressed m terms of another measure by simply moving the decimal pomt to the right or left. "^"vmg are ciphers in the multiplier. ^^^ "^ ^^'^« are ciphers in the divisor. ^^ "** '^«''« Thus, 12 465,687- may be written as Kilo-metres by observmg that MiUi-metres are changed to metres by Ly^ 418 MMTKIC SYSTEM OF MEASUREMENT. ing the point threfi places to the left, and metres are changed to Kilo-metres by carrying the point three places furtheB, making in all six places. Therefore 12,4(i5,G87"'°' - 12.465687*" RULE.— First count the number of places needed to convert the given measuren into terms of the principal unit ; then the number needed to convert the principal into the required units. Before adding or subtracting, the quantities must be written in the same unit of measure. 722. MEASURES OF LENGTH. 10 millimetres, marked mm. are 1 certimetre, marked cm. 10 centimetres) 10 decimetres, 10 metres, 10 dekametres, 10 hektometres, 10 Kilometres, ti It It cm. dm. m. Dm. Hm. Km. 1 decimetre, 1 metre, 1 dekametre, 1 hektometre, 1 Kilometre, 1 MyriametrOi ti t( It ti it It dm. m. Dm. Hm. Km. Mm. 723. To Reduce 3.825 m. to cm. Solution. — To reduce metres to centimetres, multiply by 100. Write 3825, and place the decimal point between 2 and 5, two orders farther to the right tnan it is in 3.825. Ans. 382.5 cm. 724. To Reduce 1025.5 m. to Km. Solution. — To reduce metres to kilometres, divide by 1000. Write 10255, and place the decimal point between 1 and 0, three orders farther to the left than it is in 1025.5. Ans. 1.0255 Km. 725. To Reduce 2.15 Dm. to centimetres. Solution. — To reduce dekametres to centimetreSj mul- tiply 10 X 100 = 1000. Write 215 and annex a cipher. Ans. 2150 cm. LAND OR SQUARE MEASURE. 726. The Are is the unit of Land measure (or Area). It is legal at 119.6 sq. yds. The Are is the principal unit of" MMTHIC avuTEM OF MSASUKEMUNT. 419 surface of small plots of land. The area of a farm is ex- pressed in Hektarg ; of a country in square Kilometres. Tahle. 100 oentiares, marked ca., are 1 Are, marked a. 100 ares •' a., •• l hektar " Ha. 727. An Are is 100 square metres, marked ml The Hektar is nearly 2^ acres (2.47), 728. For measuring other surfaces, squares of the metre and its subdivisions are used. 1. Reduce 897.8 a. to hektars. ^' " 3'8 a. to square metres. A.-3.978 Ha. A.— 380 ra». MEASURES OF CAPACITY. . 1^' ^^^ ^*^'*® '' '^^ ""'^ "' capacity. It is legal at 1.0567 quarts, Liquid n a-e. Table. 10 centilitres, marked cl., are 1 decilitre, marked dl. 10 decilitres, " dl., " i litre " i 10 litrei, '« 1., « 1 dekalitre " Dl 10 dekalitres, " Dl., " i hektolitre " Hi". 730. The measures commonly used are the litre and the hektolitre. The litre is very nearly a quart ; it is used in measurmg milk, wine, etc., in moderate quantities The hektolitre is about 2 bu. ^ pk. ; it is used in m^asurino- grain, fruit, roots, etc. in large quantities. " 731. For measuring wood the Stere is used ; it is a cubic metre ( = 35.316 cub. ft.) MEASURES OF WEIGHT. 732. The Gram is the unit of Weight; it is legal at 15.432 grains Trt)y. ^ w 420 733. METRIC SYSTEM OF MEASUREMENT. Table. 10 milligrams, marked mg., are 1 centigram, marked eg. 10 centigrams, ' eg., ' 1 decigram dg. 10 decigrams ' ' dg., " 1 gram, g- 10 grams, ' ' g. ' 1 dekagram, Dg. 10 dekagrar.s, ' L>g., " 1 hektogram. Hg. 10 hektograms, ' Hg., ' 1 kilogram, Kg. 10 kilograms, " Kg., ' 1 myriagram, Mg. 10 myriagrams, " Mg., ' 1 quintal, Q. 10 quintals or 10()0 kilograms are 1 Metric ton, marked M.T. 734. The weights com- monly used are the ' Gram, Kilogram, and Metric ton. The Gram is used in mixing- medi- cines, in weighing the precious metals, and in all cases where great ex- actness is required. The Kilogram, ( commonly called the "Kilo"), is the usual weight for Grocer- ies and coarse articles generally ; it is very nearly 2| lbs. Avoir. The metric ton is used for weighing hay and other heavy a rticles; it is about 204 ftp, more than our ton. 1 KiIoMri'.Tni=inf»> 2-i-ntTi«. lexnct oize), coininonly imUuU tlie " Kilo." 735. Legal and Approximate Values are as follows: Denomination. Legal Value. Approximate Value. Metre 39.37 inches 3 ft. Sf inches. Centimetre 89371 " finch. Kilometre '. 821 37 mile % mile. Square Metre 1.196 sq. yards 10| sq. feet. METRIC SYSTEM OF MEASUREMENT. 421 Legral and Approximate Values (continued). Denomiuation. Legal Value. Approximate Value ^V-- 119.6 sq. yards 4 sq. rods. H«ktar 2.471 acres 2i acres ?"^-^«^- 1.308 cub. yds 35V cub e: ^^™ 2759cord j .^rd. ^i^re 1.0567 quarts \^f^ liquid quart. !?"^*°"*^« 2.8375 bushels "^''i'^busr^sTpk. ?!T 15.432 gr. Troy 15i grains. ^'^^^^^^ 2.2046 lb. Avoir 2rpounds ■ IT. 204 lbs. Metric Ton (or tonneau) . .220-1.6 tb. " ^^^^^ o•2759ocord.....■.■■;;:.■.^■■.■."^^.■.^cord. 736. The legal value is used in solving the foUowinff examples. ® 737. MISCELLANEOUS EXAMPLES. 1. How many yards, feet, etc., in 4 M.? Solution. — In one metre there are 89.37 in. ; in 4 metres there are 4 times 89.37 in., which are 157.48 in. ; 157.48 in. reduced to integers of higher denomina- tions are 4 yds. 1 ft. 1.48 in. OPEKATION, 39.37 4 12)157.48 3)13 ft. 1.48 in. 4 yds. OPERATION. 1ft. 2. What is the value of 36 ft)s. in kilograms ? Solution.— In one kilogram there are 2.2046 fts. ; in 86 lbs. there are as many kilograms as 2.2046 are contained times in 86, which are 16.329+. 3. What is thft value of 20 Km. ? 4. How many hektars in 160 acres? 2.2046)36.0000(16.329 + 22 046 13 9540 13 2276 72640 66138 65020 44092 209280 198414 12.4274 miles. 64.75 + Ha. 422 METRIC SYSTEM OF MEASUREMENT. 5. What is the value of 49 m. ? 9 rd. 4 yd. 3.13 in. 6. How many hektolitres in 42 bu. ? 14.8 + HI. 7. How many square yards in a roll of paper 9 m. long and 5 m. wide? 5.382 sq. yd. 8. The five-cent piece weighs 5 grams; how much will 100 such pieces weigh? .5 Kg. 9. Ten litres of a certain liquid weigh 92 Kg. ; what is the weight of a decilitre ? • .92 Kg. 10. One hektogram of goods costs ?5.35 ; what costs one kilogram ? 153.50 11. A piece of money weighs 10 g.; how many such pieces in a bag weighing 1 Kg. ? 100 12. A hektolitre of wheat costs 16.25 ; what is the price of a dekalitre ? $.625 13. A hektolitre of wine costs $25.10 ; what is the price of a litre? *.251 14. A kilogram of wool costs $1,875 ; what is the cost of 100 kilograms ? $187.50 15. A litre of wine weighs 880 g. ; what is the weight of a hektolitre? 88 Kg. 16. Add 45 kilograms, 4 hektogranis, 5 dekagrams; 35 kilograms, 8 dekagrams, 7 grams; and 45 hektogranis, 4 grams. 85.041 Kg. 17. A wine merchant sold 1270 litres, 487 litres, 1563 litres, 1000 litres, and 2345 litres ; how many hektolitres did he sell ? 66.65 HI. 18. A vase, weighing 24.67 hektolitres, contains 18.79 hektolitres of liquid ; what is the weight of the empty vase ? 5.88 HI. 19. From n barrel coritaining 117 litres of wine, 42.75 litres leaked out : how much remained ? 104.25 1. METRIC SYSTEM OF MEASUREMENT. 423 20. How much will 135.60 m. of cloth cost at «1 IG a '"^'^*'' $157,290 21. A grocer bought 3845 Kg. of sugar at 19 cents a kilo- gram ; how much did it cost ? 173Q 55 22. Bought 25 hogsheads of wine, of 225 litres each, at the rate of $.156 a litre ; how much did it cost ? 0877.50 23. What is the cost of 21 pieces of cloth of 42 m. each at 15.69 a metre? ^^^^^^^ 24. I have in article that sells for 26 cents a pound : how much i 'orth a kilogram ? 1 573 ^ 25. .\ .an bought 25 lbs. of tea at II.8J a pound : he exchanged it for five times its weight in coffee, which he sold at 0.86 a kilogram ; did he gain or lose by the bargain and how much? «a7r ' 26. How many metres of carpeting, .75 m. wide, will cover a floor 8 m. long and 5 m. wide ? 53.33 + ^ 27. I paid 813 for a barrel of vinegar containing 140 1. • I lost 22 1. by leakage, and sold the remainder at 20 cents a litre ; how much did I gain ? ^jo (jq l!:i|lil'>B 424 INSTITUTE OF CHARTERED ACCOUNTANTS. INSTITUTE OF CHARTERED ACCOUNTANTS. ORGANIZATIOX. 738i This InstitUDe, Avhich re- ceived its charter from the Ontario Legislature iq 1883, com- prises in its membership the leading Accountants of Canada. The chief aim of the Institute is to raise the standard of account- ancy; and in order to increase the knowledge, skill and profi- ciency of its members, it is empowered to establish classes, lectures and examinations ; to prescribe tests of competency; to grant diplomas entitling members to use the distinguishing letters F.C.A. (Fellow of the Chartered Accountants); and to affiliate with any other similar bodies for mutual benefit. AFFILIATION. 730. Business Colleges a,nd other Educational institutions having a department devoted to the study of Accounts may become affiliated with the Institute, and may conduct the Intermediate Examinations in connection therewith, on terms fixed from time to time by the Council. INSTITUTE OF CHARTERED ACCOUNTANTS. 425 740. Students-at-Accounts, of the age of 16 years or over, are admitted to registration under two classes: (l) Primary Students and (2) Intermediate Students or Book- keepers. Such Students are entitled to attend the meetings of the Institute and take part in discussion of papers. Students may form an Association for the better advance- ment of their studies and professional knowledge, and for making recommendations to the Council affecting their ioin^t interests. 741. The Primary Examination required of students on entrance comprises Business Composition and Correspond- ence, Spelling and Punctuation, Arithmetic, Penmanship, Wementary Book-keeping, Common Latin Terms and Roots British and Canadian History, Geography, Stenography (the last optional). This examination may be conducted in any affiliated institution, or the Council may waive this examina- tion on students showing that they have passed one equiva- lent, or have had practical experience at accounts which mav be deemed equivalent. The object of the Primary Examina- tion IS to reasonably ensure that future candidates for membership shall be men of good general education, the Council holding the view that the comparatively slow progress made hitherto, towards obtaining recognition from the public 6f the claims of accountancy to be considered as a profession, has been due in no small measure to the superficial character of the education deemed to be uecrssary to fit a man for intelligently undertaking the duties of an account- ant, or even of a book-keeper (understood in the sense of one versed in one branch only of accountancy). While it may be true that every accountant will find his own level, on the ground of natural ability alone, it is equally certain that the accountant who has had the initial advantage of a good general education, supplemented by a judicious course of ^raclounSl? Jr f ' ''"^!«.°' profession, will out-distance efse beTng equlr "' "'* '"' *''" advantages, everything 426 INSTITUTE OF CHARTERED ACCOUNTANTS. ;ir^ 742. The Intermediate Examination is open to any one who has registered as a Stadent-at- Accounts, 19 years of age or over, after one year from passing the Primary or equivalent Examination. The Intermediate Examination comprises Mercantile Arithmetic, Negotiable Instruments, Book-keeping, Auditing, Shareholders' and Partners' Accounts, Insolvency. This examination may be held in afdliated institutions. Ev«ry person passing the Intermediate Exam- ination is entitled to a Certificate to that efTect, ?.A setting forth in suitable terms his attainments as a book-keeper. The Intermediate Examinations are intended to afford to students who desire to take up accountancy as a profession, an opportunity to test their general progress in professional knowledge, to enable the Council to form an estimate of their capabilities, and to advise upon and direct, so far as may be, their course of preparation for the Final Examination, which qualifies for admission to membership as an Associate. There is the further intention to provide recognition of the attain- ments of those candidates who do not purpose attempting the Final Examinations, but desire to have the Certificate of the Institute of competency to undertake the duties of a book- keeper. The scope of the Intermediate Examinations, therefore, will, generally speaking, be limited to a thorough comprehension of the duties of one required to undertake the duties of chief book-keeper in a first-class business. 743. Final Examinations. Any person who has passed the Intermediate may apply for membership in the Institute, and if of the age of 21 or over, the Council will set a Final Examination comprising Book-keeping, Auditing, Insolvency, Joint Stock Companies, Mercantile Law, Partnerships and Executorships. This Final Examination shall be held in Toronto, and any who pass, upon being admitted to the Institute by ballot, fhall receive a Certificate of membership, and right to use the appellation "Chartered Accountant," and to be styled " Associate." INSTITUTE OF CHARTERED ACCOUNTANTS. 427 "F. C. A." 744. A Chartered Accountant who has been in continuous practice as such for three years after admission as a member may be admitted a "Fellow of the Chartered Accountants" upon passing the tests, viz. : (i) Known standing and repu- tation as a Public Accountant, and (2) a thesis upon some subject to be approved by the Council. Upon passing these tests a "Diploma of J^ellowship" is issued to the candidate giving him the right to use the letters " F.C.A." ' 745. Every Commercial Student should aim to secure membership in this Institute of Chartered Accountants, and to pass through tho various grades above outlined till the goal is reached-the high honors and privileges of a "Fellow of the Chartered Accountants," upon whom the stamp of this honorable Institute is placed in the letters " F.C.A " In order to help our readers to reach this end, the above information is given and the following Examination Papers are quoted 428 MERCANTILE ARITHMETIC. MERCANTILE ARITHMETIC. i'hi ' ••'h Problems set for Candidates in Intermediate Examina- tion, Institute of Chartered Accountants, May, 1897. 1. A nail manufacturer has 8 grades of nails which he wants to net him per keg $2.75, 82.80, $2.85. He desires to make a list of prices to sell at 50%, 10%, 5% discount to net the above prices. Give the list prices and show how it is worked out. 2. A Trustee invests $4,000 in Ontario Bank stock at 80, paying 6%. and *1,000 in Dominion Bank stock at 200 paying 10%. After two years he sells the former at 86 and the latter at 180. What rate of interest has he received during the period of investment and how lias the value of the capital changed ? 3. Convert £855 5s. lOd. into currency, exchange being 9.78. 4. Convert $750 into Francs, Sterling exchange being at 9J, 25i Francs representing £1 Sterling. 5. Find the equated time of paying the balance of the following account on basis of 860 days to the year. Interest, 6%. ■ 1896 Feb. 9 By Cash, $100 Mar. 2 By Cash, 50 1896 Jan. 3 Jan. 20 Mar. 1 Mar. 14 Apr. 9 May 7 Goods 4/m, " 2/m, " 1/m, Net, " 8/m, " 2/m, $175 75 125 50 200 100 $725 $315 Apr. May By Cash, By Cash, Balance, 60 200 315 $725 May 7th, Balance, Adjust the interest and state vhat amount is due in Cash May 7th. 6. A merchant has a line of tweeds which he is selling in 50 yd, ends, for $75 per end, a profit of 25% on cost. His clerk, in order to make quick cash, sales, sells for 16% cash discount. What advance over cost did he net ? MERCANTILE ARITHMETIC. 439 7. A note of S500, dated April Ist, 1895, payable July Ist 87 F^r*^ with interest at 6% was discounted May 1st at 8%. Find the proceeds. laterest on basis of 360 days to the year. 8. A Board of School Trustees desire to issue Debentures to th« amount of 82 500. Interest 5% payable annually IstTnua * each year, he whole amount with interest to be paid in five equa^ annual payments. Divide the amount into five debentures' one to mature each year. ^ui-uiea, one to « A ^'"^ ^l^"""^ *"'°"°* °^ ^*°^ debenture numbering them 1 2 d, 4, 5, and the amount of coupons due each year. ' ' 1 at 80c. per lb. 1 " 75c. 1 " 50c. 1 " 60c. 1 " 25c. 1 " 20c. He desires to make 1 chest of a blend containing all these fo^st" lOOy ""'^^r ''■ "'^^' "i" ^^^^ ^^^ - advance ova costs of 100%. Find how many pounds of each he must use. 10. If the profits are divided in proportion to the Capital invest- ed and the time it was employed, at the end of a year what Tofit, f '';. f n'"'''' '^'^"^' investment and share of the pronts from the following accounts. Net profit $500. Jno. Eoberts Harry Jones . ^'- ^^- Dr. Cr Apr. 1, $2,000 I 1 Jan. $4,000 May 1, $300 | Jan. 1, $2 000 Aug. 3,000 Sept. 1, 1,000 Problems set for Candidates in Intermediate Examlna tion, Institute of Chartered Accountants, Nov. 1895. MERCANTILE ARITHMETIC. 1. A merchant buys a sort of wine at $2 per gallon, and another a. ,i.o0 per gallon. At what price must he sell a blend of 7 parts of the former and 8 parts of the latter to realize 20 percent, profit? 480 MEhCANTlLE ARITHMETIC. 2. You manage an estate, and receive as your remuneration 5 per cent, of the net amount paid to the beneficiaries. Taxes, re- pairs and sundry expenses in a given year are $540. Your com- missions amount to 8850. Find the gross revenue of the estate. 8. Find the present value of 13,250 due 8 years and 6 months hence at 4 per cent, per annum. Show working. 4. Average the following account : Jan. 20.— Merchandise, 80 days $150 00 27.— " 4 months 100 00 Feb. 15.— " net 150 00 Cr. $400 OO Feb. 10.— Cash 75 00 Balance $325 00 5. A certain stock pays a semi-annual dividend of 8 j^ per cent What is it worth to an investor who wants a return of 4i per cent, per annum upon his investment ? 6. Convert $1,000 into sterling at ten and one-half per cent. 7. Find the cost of papering a room 30 x 22 feet, and 12 feet high, with paper 18 inches broad, costing eighty cents per roll of 12 yards, deducting 20 yards of paper for window and door spaces. 8. A merchant imports as follows : 850 yards sheeting at 5 cents ; 1,400 yards flannel at 13 cents. The duty on sheeting is 20 per cent, ad val., and 5 cents per lb. (9 yards to 2 lbs.) ; the duty on flaunel is 30 per cent. (4 yards to the lb.) Packages are charged at $4. Freight $6.50. Cartage $1. Find the cost per yard of each laid down in his warehouse. 9. An insolvent estate realized, after payment of expenses, $1,840.72. The claims to rank are as follows : A, $8,400.60; B, $1,847.85; C, $890.96 ; D, $870.42 ; E, $391.80; F, $102 ; G, $84.58. Prepare a dividend sheet showing the rate per cent, and the amount coming to each. 10. You are being charged interest monthly at 7 per cent, per annum on an overdraft at your bankers. They offer to discount your bills at three months at 6^ per cent, per annum. Which is the more profitable transaction, and by how much ? leration 5 Taxes, re- lour com- e estate. I 6 months 00 00 00 00 00 00 I per cent •n of 4^ per ' cent. and 12 feet per roll of oor spaces. mts per lb, 4 yards to Cartage ^rehouse. expenses, ,400.60; B, a, $84.58. t. and the ir cent, per discount Which is