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• 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?

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?

Ans. $10,353.60.

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 calculate how many hundredths of the sum expended, they have lost or gained: and this number 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, 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 are

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

1. How is 1 pr. ct. written? A. .01. 2 pr. ct.? A. .02. 7 pr. ct.? ct. ? 9 pr. ct. ?

ct.? A. .03. 4 pr. ct.? 5 pr. ct.? 6 pr. ct.?

12 pr.

3 pr. 8 pr.

11 pr. ct.? A. .11.

pr. ct. ? 17

2. How is 10 pr. ct. written? A. .10 or .1. ct.? 13 pr. ct.? 14 pr. ct. ? 15 pr. ct.? 16 pr. ct.? 18.pr. ct.? 19 pr. ct. ? 20 pr. ct.? 21 pr. ct. ? 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.? 181 pr. ct.?

We sometimes speak of pr. ct., pr. ct. &c. These expres. 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.,,,, ↓, †, †, 11, 21, 92, 161, 71, 82, 9, 154, and 23 pr. ct. Ans. .0075, .002, .003, .008, .003, .00142857, .0016,

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.015, .025, .0975, .16125, .0725, .091, .08375, .15142857, and .023.

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6

8.

6. Express, 8, 6, 6, 77, 73, TT, 4, 25, 314, 191, 1, 3, 41, 1872, 563,8, 96222.

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

.08.

left, a unit is added to the rate, and, by this 43.44 means the amount of the allowance, and of $43.44 543 the given sum is obtained. This is often

$586.44

convenient.

§ 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 AT PAR. When it will bring more in market than its nominal value, it is said to be ABOVE PAR; when not so much, BELOW PAR. When stock is above par it is said to be at so much per cent. ADVANCE.

EXAMPLES.

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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 1191 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

7. What is the value of $2,500 of stock at 20 pr. ct. advance? A. $3,000.00

8. What is the value of $6,000.00 of stock at 15 pr. ct. advance ? A. 6,900.00

9. What is the value of $9,854.25 of stock at 113 pr. ct.? A. $11,135.3025

NOTE. Stock is bought and sold by even shares. We have given some examples in which the shares are not regarded, as affording a better exercise. 10. What is the value of $823.00 of stock at 4 pr. ct. advance ? A. $855.92

11. What is the value of $1,976.44 of stock at 111 pr. ct.? 12. What is the value of $366,000.00 at 114 pr. ct.? 13. What is the advance on $600.00 at 6 pr. ct. advance? A. $36.00

14. What is the advance on $5,460.00 at 116 pr. ct.? COMMISSION. 1. If my agent sells goods to the amount of $2,317.46, what is his commission at 3 pr. ct.? A. $75.31745 2. What commission must be allowed for a purchase of goods to the amount of $1,286.00, at 21 pr. ct.? A. $32.15 3. What commission shall I allow my correspondent for buying and selling on my account, to the amount of $2,836.23 at 3 pr. ct.? 4. A merchant paid his correspondent $25.00 commission on sales to the amount of $1,250.00. At what pr. ct. was the commission? 25 He paid him 050-180.02=2 pr. ct. Ans. 5. If $76.25 be paid as commission on $3,900.00, what pr. ct. commission is allowed?

6. A factor receives $988.00 to be laid out in goods, after deducting his own commission at 4 pr. ct. What sum did he lay out for his employer?

He evidently ought only to receive commission on the money laid out. Then, as the money laid out is of itself, and the commis. sion, the money laid out, together with the commission, must be Then, $988 is 1.04 times the answer.

$950 Ans.

988÷1.04=

7. I remit $2,963.75 to my correspondent to be laid out for me, directing him first to deduct his own commission at 3 pr. ct. What was his commission, and what remains to be laid out?

INSURANCE. The written contract or obligation which binds the parties, is called POLICY. The sum paid for insurance, is called PREMIUM.

1. What premium must be paid for the insurance of a vessel and cargo, valued at $123,425.00, at 153 pr. ct.?

15 pr. ct.=.155, and the question is, what is .155 of 123,425. A. $19,130.875.

2. What must I pay annually for the insurance of a house worth $3,500.00, at 1 pr. ct. ? A. $61.25. 3. What must be paid for the insurance of property, at 6 pr. ct., to the amount of $2,500.00 ? A. $150.00.

4. What insurance must be paid on $375,000.00, at 5 pr. ct.? A. $18,750.00. 5. What premium must be annually paid for the insurance of a house worth $10,650.00, at 3 pr. ct.; and a store worth $15,875.00, at 4 pr. ct.; and out houses worth $3,846.00, at 5 pr. ct.?

6. What premium must be annually paid for the insurance of a Factory worth $30,946.00, at 10 pr. ct.; and 7 dwelling houses, worth $875.00 each, at 8 pr. ct.; and 3 grist mills, worth $1,930.00 apiece, at 7 pr. ct.; and 1 storing house, worth $9,859.00, at 6 pr. ct.? Also, what is the average rate of insurance on the whole ? 7. If I pay $930.00 annually for insurance, at 5 pr. ct., what is the value of the property insured?

Here 930 is .05 of the answer; 930÷.05 $18,500 Ans. 8. If I pay $6,849.00 for insurance, at 3 pr. ct., what is the value of the property insured? A. $228,300.00. 9. If $978.00 be paid for insurance, at 2 pr. ct., what is the value of the property insured? A. $48,900.00. 10. If $765.00 be paid for insurance annually, at 5 pr. ct., what is the amount of property insured?

11. If $1,000.00 be paid, annually, for insurance on $20,000.00, what is the rate of insurance ?

A. 5 pr. ct.

12. If $288.00 be paid for the insurance of $48,000.00, what is the rate of insurance? A. 6 pr. ct.

13. If $975.35 be paid for insurance on $19,507.00, what is the rate of insurance ?

14. If $1,200.00 be paid for insurance on $12,000.00, what is the rate pr. ct.?

PROFIT AND LOSS. 1. Sold a bale of goods at $735.00 by which I gain at the rate of 6 per cent. What sum do I gain? Ans. $44.10 2. In selling 50 hhds. of Molasses at 38 dollars a hhd., I gain 10 What is my gain. per cent. Ans. $190.00 3. In selling 25 bales of cloth, each containing 27 pieces and each piece 50 yards, a merchant gained 20 per cent. on the cost, which was 10 dollars a yard. What did he gain, and what did he sell the whole for? Ans. Gain $67,500.00. Whole $405,000.00

4. A merchant gained at the rate of 15 per cent, in selling the following articles: 6 hhds. of brandy for which he paid $1.50 per gal.; 7 barrels of flour, cost 11 dollars a barrel; 2 quintals of fish, cost 4 cents a pound; 16 hhds. of molasses, cost 56 cents per gal. and 25 bls. of sugar, containing each 175 lbs., cost 9 cents per lb. What was his gain on the whole, and what did he receive in all ? Ans. Gain $241.5345. Sold for $1,851.7645.

5. A merchant purchased a large amount of cotton contained in 1,899 bales, each containing 194 lbs. at 13 cts. pr. lb. ; but the price suddenly falling he was obliged to lose 8 per cent. on the cost. What did he lose, and how much did he obtain for his cotton ?

6. A merchant laid in 634 pieces of broadcloth, each piece containing 85 yds., for which he paid 7 dollars per yd.; and 537 pieces of Russia sheeting, at $10.25 a piece; but they were so much in

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