40 30 то 250 £Irish. 8 1 12 times £ Ster. OF THE SAME SUM EXPRESSED IN 27 $F.M.2 Suppose I have a sum in £ Sterling, which I wish to reduce to £ New England. I see, by the table, that any sum expressed in £ Ster. is, of the same sum, expressed in N. E. This I find, by looking for the given Currency, (which is Sterling,) in the upper line, and for the required Currency, (which is New England,) in the right hand column. Under the one, and opposite the other, I have the Fraction. Let the given sum be £6. Then I know that 6 is of the answer. If 6 is 1, 2 is 4. £2 is of 8£. Ans. It will be seen, that, in this case, we divided by 4, and multiplied by 3, which (§ LI.) is dividing by the Fraction. Hence, to reduce a sum from one currency to another, DIVIDE BY THE NUMBER FOUND IN THE TABLE, UNDER THE GIVEN, AND OPPOSITE THE REQUIRED CURRENCY. For similar reasons, the number under the required and opposite the given currency may be used as a multiplier. The numbers in the table may often be reduced to decimals with advantage. NOTE. It will usually be best to reduce shillings, pence, and farthings to a fraction of a pound, either vulgar or a decimal. It may perhaps be desirable that the pupil should commit to memory the numbers used in reducing the currencies of the U. S. to Fed. Money, and the contrary. The rest is only intended for reference. EXAMPLES FOR PRACTICE. 1. Reduce £4 N. E. to F. M. 2. Reduce 2£ 3s. 9d. N. E. to F. M. 3. Reduce £6 N. Y. to F. M. 4. Reduce £8; 4; 9 N. Y. to F. M. 5. Reduce £3; 2; 3 Penn. to F. M. 6. Reduce $152.60 to N. E. Ans. $13.3331. Ans. $7.2913. Ans. $15.00. Ans. $20.593. Ans. $8.30. Ans. £45; 15; 7.2. 7. Reduce $196.00 to N. E. 9. Reduce £35; 6; 8 Sterling, to N. E. 10. Reduce £120 N. E. to Can. 11. Reduce £155; 13 N. E. to Sterling. 16. Reduce 225; 6 N. E. to F. M. Ans. £58; 16. Ans. £47; 2; 2; 21. Ans. £450; 15; 6; 3. Ans. £56; 3. 17. Reduce £880; 15; 11; 1 Penn. to Ster. Ans. £528; 9; 6; 3. 18. Reduce £6,750 Irish to Geor. 19. Reduce £1,846 Ster. to Irish. Ans. £6,461. 20. Reduce £1,722; 18; 9; 3 N. E. to N. Y. Ans. £2,298; 5; 1. 21. Reduce £2,114; 1; 3 Can to F. M. Ans.$8,456.25. 22. Change £784; 5; 6; 2 Penn. to Geor. A. £487; 19; 10; 22. 23. Change £923 Sterling to Irish. 24. Change £4,000 Irish to Sterling. 25. Change £157; 8; 3; 3 N. Y. to N. E. 26. Change £1,654; 3; 8: 1 Penn. to N. E. 27. Change £947; 9; 4; 2 N. E. to F. M. 28. Change $1,444.66 to N. E. To N. Y. 29. Change $945.32 to N. Y. To Geor. 30. Change £1,846; 15; 4 N. E. to F. M. 31. Change $4,444-4444 to Sterling. 32. Reduce £1,000,000 Ster. to F. M. 23 อง To Penn. To Penn. To Geor. What is the value of 1£ Ster. in F. M. ? 34. What is the value of 1£ Irish in F. M.? 35. What is the value of 1£ N. E. in F. M.? 36. What is the value of 1 £ N. Y. in F. M. 37. What is the value of 1£ Can. in F. M. ? Scotch in F. M. ? Penn. in F. M. 38. What is the value of 1£ 39. What is the value of 1£ 40. What is the value of1£ Geo. in F. M. Ans. $4.444. Ans. $0.3701. Ans. $4.285. Hence we see that there are but two of the currencies, in which a pound can be expressed in Federal Money by a finite decimal. This is one of the disadvantages in their use. The following FOREIGN COINS have assigned to them the values, in FEDERAL MONEY, placed opposite to them, respectively. Shilling Sterling, Crown 5s. Sovereign, (a gold coin, $0.222 Re, of Portugal, $0.0012+ Testoon, 0.125 Milre*, 1.250 £,) 4.444 Moidore, " 6.000 Guinea, (21s. nearly out of use in England.) 4.666 Joanese, " 8.000 Marc Banco of Hamburgh, 0.333+ Livre of France, 0.185 Pistole of Italy, 3.200 Franc Rix Dollar of Austria, 0.778 Rix Dollar of Denmark and Switzerland, 1.000 Five franc piece, " 0.937 Rix Dollar, of Sweden, 1.037 Real of Plate, of Spain, 0.100 Rix Dollar*, of Prussia 0.778 Real of Vellon, 0.050 Florin, 0.259+ Pistole, 3.60 Ducat, of Sweden and Dollar, Prussia, 2.074 • Those denominations which have the asterisk, [as the Pistole of France, and the Milre of Portugal,] are merely nominal; that is, they are represented by no real coin. In this respect, they are like the Mill in Federal Money. We sub. join a very few, EXAMPLES FOR PRACTICE. 1. In 300 Milres, how many dollars? Ans. $375.00. 2. In $900, how many Gold Ducats of Holland? Ans. 112. 3. In 3,000 Francs, how many dollars ? Ans. $562.50. 4. In 2,876 Pistoles of Spain, how many dollars? Ans. $10,353.60. 5. In $600 how many Moidores? 6. In 3,842 Rupees how many dollars? 7. In 1,945 Pagodas how many dollars? 8. In $2,955 how many Francs? NOTE. The above examples belong to the rule commonly called Exchange. CALCULATIONS OF CENTAGE, INCLUDING STOCKS, PROFIT AND LOSS, INSURANCE, COMMISSION, Duty, interest AND DISCOUNT. LXXIV. Men in business find it often necessary to calculate, at what rate they are gaining, or the contrary; that is, how great a part their profit or loss is, of the sum laid out. For this purpose, they usually culculate how many hundredths of the sum expended, they have lost or gained: and this num er of hundredths is called the rate per cent. of their loss or profit. Cent. is a contraction from the Latin word centum, which means hundred. Rate per cent., then, means rate by the hundred. When we speak therefore, of a gain of 5 pr. cent. on any sum, we mean a gain of 5 hundredths of that sum.Thus, 5 pr. ct. on $20, is of $20. So 8 pr. ct. on $312, is of $312, &c. Various calculations are made by hundredths; that is, by a rate per cent. The most important are embraced under the following heads. PROFIT AND Loss, which terms explain themselves. STOCKS, which is a general name for the capitals of banking, trading and insurance companies; and for funds established by government. Persons owning stock aro called STOCKHOLDERS. It sometimes happens, that stock rises; that is, that stockholders can dispose of their right to it, for more than was originally paid. Stocks sometimes, likewise fall, and then they will not command their original value. A fund is established by government, when they borrow money, on condition of paying annual interest, until they see fit to discharge the debt. INSURANCE, which is an allowance made to a company, who agree to make up any loss by fire, storms, &c. COMMISSION, which is an allowance made to a broker or factor, or an agent or correspondent, for assisting in procuring and disposing of goods. DUTY, which is a tax, required by governments to be paid on the importation, exportation, or consumption of goods. INTEREST, which is an allowance made for the use of borrowed money; or for debts of any kind, remaining unpaid after they are due. DISCOUNT, which is an allowance made for the payment of money before it is due; or for advancing money on notes, bills, &c., payable at a future day. These subjects will be severally examined. RATE PER CENT. IS PROPERLY EXPRESSED BY A DECIMAL FRACTION. For it is always a certain number of hundredths. Thus, when we speak of 3 pr. ct., we mean 3 hundredths,=.03, and so of any other number. Thus, 1. How is 1 pr. ct. written? A. .01. 2 pr. ct. ? A. .02. 3 pr. ct.? A. .03. 4 pr. ct.? 5 pr. ct. ? 6 pr. ct.? 7 pr. ct. ? ct.? 9 pr. ct. ? 8 pr. 2. How is 10 pr. ct. written? A. .10 or .1. 11 pr. ct.? A. .11. 12 pr. ct. ? 13 pr. ct.? 14 pr. ct. ? 15 pr. ct. ? 16 pr. ct.? 17 19 pr. ct.? 20 pr. ct.? 21 pr. ct. ? pr. ct.? 18 pr. ct.? 181 pr. ct.? These expres 3. How is 99 pr. ct. written? A. .99. 100 pr. ct.? A. 1.00 or 1. 101 pr. ct.? A. 1.01. 102 pr. ct.? A. 1.02. 115 pr. ct.? A. 1.15. 125 pr. ct.? 137 pr. ct.? 149 pr. ct.? 156 pr. ct.? We sometimes speak of pr. ct., pr. ct. &c. sions signify a hundredth, of a hundredth, &c. Hence, when we speak of a fraction pr. cent., we mean a fraction of a hundredth, and the fraction may be reduced, and the result placed next below hundredths, or, in other words, written with two cyphers on the left. 4. Express pr. ct., decimally. .125. Prefix two cyphers, and it becomes .00125 Ans. 5. Express decimally the following rates.,,, }) 1, 1, 1, 11, 21, 92, 161, 71, 82, 9, 15, and 23 pr. ct. Ans. .0075, .002, .003, .008, .003, .00142857, .0016, .015, .025, 0975, .16125, .0725, .091, .08375, .15142857, and .023. 5 8 6. Express, 3, 6, b, 77, 15, 1, 4, 257, 314, 191, 17, 34, 41, 187, 563, 96223. In order to find a number of hundredths of any sum, we have only to multiply by the decimal expression for those hundredths. Thus, to find 3 hundredths of $50, we multiply $50 by .03; to find 9 hundredths of $50, we multiply $50 by .09, &c. Hence, to calculate an allowance of a certain rate per cent. on a given sum, MULTIPLY THE SUM BY THE RATE PER CENT. EXPRESSED DECIMALLY. Thus, what will an allowance of 8 pr. ct. on $543 come to? $543 On the right, I multiply by 8 pr. ct.=.08, $543 1.08 and obtain the allowance required. On the left, a unit is added to the rate, and, by this means the amount of the allowance, and of $43.44 the given sum is obtained. This is often convenient. 43.44 543 $586.44 .08 § LXXV. STOCK. Stocks are usually bought and sold in shares. These shares are some definite amount, as 50 or 100 dollars, &c. usually 100. The amount of a share is its NOMINAL VALUE. The REAL VALUE of stock is the sum for which a share will actually sell. When stock sells for exactly its nominal value, it is said to be When it will bring more in market than its nominal value, it is said to be ABOVE PAR; when not so much, BELOW par. stock is above par it is said to be at so much per cent. ADVANCE. AT PAR. EXAMPLES. When 1. What is the value of $350.00 of stock at 105 pr. ct., that is, at 5 pr. ct. advance? A. $367.50 The rate here is 105 pr. ct.=105 hundredths. The question, then, is, what is 105 hundredths of 350; or, multiply 350 by 1.05. 2. What is the value of 35 hundred dollar shares of stock, at pr. ct. advance? Rate 1.0075 A. $3,526.25 3. At 112 pr. ct., what must I pay for $7,564.00 of stock ? Rate 1.125 A. 8,509.50 4. What is the value of $615.75 of stock, at 30 pr. ct. advance ? A. $800.475 5. What is the value of $7,650.00 of stock at 119 pr. ct.? A. $9,141.75 6. What is the value of $1,500.00 of stock at 110 pr. ct.? A. $1,650.00 |