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The nominal value of a share is the amount paid, when the stock was first created.

The real value is the sum for which a share will sell.

When stock sells for its nominal value, it is said to be at par.

When it sells for more than its nominal value, it is said to be above par, and when for less it is below par.

When stock is above par, it is said to be so much per cent. advance.

An Insurance Company, is a body of men, who in return for a certain compensation, promise to pay for the loss of property insured.

The written engagement they give is called a Policy. The sum paid to them for insurance, is called Premium.

Commission is a certain sum paid to a person called a correspondent, agent, factor, or broker, for assisting in transacting business.

Loss and Gain refer to what is made or lost, by merchants, in their business.

The calculations relating to stock, insurance, commis. sion, loss and gain, and duties, are performed by the rule for calculating interest, when the time is one year.

RULE.

Multiply the sum given, by the rate per cent. as a decimal. (See page 206.)

EXAMPLES.

STOCK.-1. What is the value of $350.00 of stock at 105 per cent., that is, at 5 per cent. advance ?

Ans. $367.50. The rate here is 105 per cent.=105 hundredths. The question then is, what is 105 hundredths of 350 ; or, mul. tiply 350 by 1.05.

What is the nominal value of a share? What the real value? When is stock at par? When above par ? When below par? What is an insurance ? Policy? Premium? What is commission ? Loss and gain ? What is the rule for performing these processes ?

2. What is the value of 35 hundred dollar shares of stock at $ per cent. advance ? Rate 1.0075.

Ans. $3,526.25. 3. At 112} per cent., what must I pay for $7,564.00 of stock ? Rate 1.125.

Ans. $8,509.50. 4. What is the value of $615.75 of stock, at 30 per cent. advance ?

Ans. $800.475. 5. What is the value of $7,650.00 of stock at 119 per cent. ?

Ans. $9,141.75. 6. What is the value of $1,500.00 of stock at 110 per cent. ?

Ans. $1,650.00. 7. What is the value of $3700 bank stock at 951 per cent., that is at 41 per cent. below par? Ans. $3,533.50.

INSURANCE.--1. What premium must be paid for the insurance of a vessel and cargo, valued at $123,425.00, at 154 per cent. ?

151 per cent.=.155, and the question is, what is .155 of 123,425.

Ans. $19,130.875. 2. What must I pay annually for the insurance of a house worth $3,500.00, at 14 per cent. ? Ans. $61.25.

3. What must be paid for the insurance of property, at 6 per cent., to the amount of $2,500.00? Ans. $150.00. 4. What insurance must be paid on $375,000.00, at 5

Ans. $18,750.00. 5. What premium must be annually paid for the insur. ance of a house worth $10,650.00, at 3 per cent. ; and a store worth $15,875.00 at 4 per cent. and out houses worth $3,346.00, at 5 per cent. ?

6. What premium must be annually paid for the insur. ance of a Factory worth $30,946.00, at 10 per cent. ; and 7 dwelling houses worth $875.00 each, at 8 per cent.; and 3 grist mills, worth $1,930.00 a piece, at 7 per cent. ; and one storing house, worth $9,859.00 at 6 per cent. ? Also, what is the average rate of insurance on the whole ?

7. If I pay $930.00 annually for insurance, at 5 per cent., what is the value of the property insured ?

930 is .05 of the answer ; 930-.05=$18,600 An. 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,

per cent. ?

2. In selling 50 hhds. of molasses, at 38 dollars a bhd., 1 gain 10 per cent. What is my gain? 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 four, 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 ?

COMMISSION.–1. If my agent sells goods to the amount of $2,317.46, what is his commission at 34 per cent. ?

Ans. $75,31745. 2. What commission must be allowed for a purchase of goods to the amount of $1,286.00, at 2 per cent. ?

Ans. $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 per cent. ?

4. A merchant paid his correspondent $25.00 commis. sion on sales to the amount of $1,250.00. At what per cent. was the conimission ?

He paid him to===.02=2 per cent. Ans. Duties.--Duty is a certain sum paid to government for articles imported.

When duty is at a certain rate on the value, it is said to be ad valorem, in distinction from duties imposed on the quantity.

An Invoice is a written account of articles sent to a pur. chaser, factor, or consignee.

In computing duties, ad valorem, (or ad val. as it is commonly written,) it is usual in custom houses to add one tenth to the invoice value, before casting the duty. This makes the real duty one tenth greater than the nominal du. ty. It will be equally well to make the rate one tenth greater, instead of increasing the invoice. What is duty ? When are duties ad valorem? What is an invoice ?

1. Find the duty on a quantity of tea, of which the in. voice is $215.17, at 50 per cent.

Ans. $118.3435=$118.3434. In this example we may add, as directed above, one tenth of 215.17, to 215.17. Thus, 215.17+$21.517= 236.687. Then 236.687X50=$118.3435.

Or we may add to the rate .50, one tenth of itself=.05 : thus, .50+ .05=55. Then, 215.17X.55=8118.3435, as before.

2. Find the duty on a quantity of hemp at 13} per cent., of which the invoice is $654.59. The second of the above modes is recommended. Another might be used, viz, : to find, first, the duty on the invoice at the given rate, and add to it one-tenth of itself. Thus, 654.59 X 131=$88.36965.

Ans. $97.206615, 3. What is the duty on a quantity of books, of which the invoice is $1,670.33, at 20 per cent. ? Ans. $367.4726,

EQUATION OF PAYMENTS. Equation of payments is a method of finding a time for paying several debts due at different times, all at once; and in such a way that both creditor and debtor will have the same value, as if the debts were paid at the several times promised.

For if a man pays a debt before it is due, the creditor gains; if he pays it after it is due, the debtor gains.

In how many months will $1 gain as much at interest as $8 will gain in 4 months ? Now as the $1 is 8 times less than 8, it will require 8 times more time, or 8X4=32 months.

In how many months will the interest on $9 equal the interest on $1 for 40 months ?

Supposing a man owes me $12 in 3 months, $18 in 4 months, and $20 in 9 months. He wishes to pay the whole at once ; in what time ought he to pay?

$12 for 3 months=$1 for 36 months.
$18 for 4 months=$1 for 72 months.
$20 for 9 months=$1 for 180 months.

$50

288 months.

What is Equation of payments ?

Now it appears that it will be the same to him to have $1 for 36, for 72, and for 180 months, as it would to have the 12, the 18, and the 20 dollars for the number of months specified.

He might therefore keep $1 just 288 months, and it would be the same as keeping the $50 for the number of months specified. But as the whole sum of money lent was $50, he may keep this only one fiftieth (3b) of the time he might keep $1. Therefore divide the 288 months by the 50, and the answer is 53 months.

RULE FOR FINDING THE MEAN TIME OF SEVERAL PAYMENTS.

Multiply each sum by the time of its payment. Divide the sum of these products by the sum of the payments, and the quotient is the mean time.

A man is to receive $500 in 2 mo.; $100 in 5 mo. ; $300 in 4 mo. If it is paid all at once, at what time should the payment be made ?

A man owes me $30n, to be paid as follows: { in 3 months; in 4 months; and the rest in 6 months ; what is the mean time for payment ? Ans. 44 months.

RATIO. The word ratio means relation ; and when it is asked what ratio one number has to another, it means in what relation does one number stand to another.

Thus, when we say the ratio of 1 to 2 is į, we mean that the relation in which 1 stands to 2, is that of one half to a whole.

Again, the ratio of 3 to 4 is $, that is, 3 is 4 of 4, or stands in the relation of to the 4. So also the ratio of 4 to 3 is f; for the 4 is 4 thirds of 3, and stands to it there. fore in the relation of fa

What is the relation of 11 to 12 ? of 12 to 11 ?

When therefore we find the ratio of one number to an. other, we find what part of one number another is.

Then the ratio of 4 to is f; that is, 4 is 4 sixths of 6. The ratio of one number to another, then, may always

What is the rule for performing it? What is ratia ?

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