INSURANCE.

§ 251. INSURANCE is an obligation assumed by a company, or an individual, to pay for the loss or damage of property by fire, shipwreck, or other casualty.

The Policy is the certificate of insurance issued by the Insurers, sometimes called the underwriters, to the person insured.

The price or Premium paid for insurance is usually a specified percentum on the amount insured.

EXERCISES.

1. What would be the annual premium of insurance on a house, valued at $3500, at 1 per cent.? Ans. $35.

2. What would be the annual premium of insurance on a manufactory, valued at $20000, at 1 per cent.? Ans. $300. 3. What would be the insurance on a shipment of goods amounting to $5200, from New York to New Orleans, at 14 per cent.? Ans. $65.

4. What would be the insurance on a ship and cargo, from New York to Liverpool, the ship being valued at $30000, and the cargo at $42000, at 13 per cent.? Ans. $1260.

5. The annual insurance on a paper mill, at 2 per cent.. amounts to $165.50. What is the value insured?

Here the amount of percentage is given, to find the basis of percentage. (§ 250). Ans. $8275.

6. The policy of insurance on a shipment of cotton, at per cent, costs $75. What was the amount insured?

Ans. $10000. 7. A gentleman procures an insurance on his house and furniture, valued at $7500, at per cent. per annum. What is the annual premium to be paid? Ans. $46.875.

8. The annual insurance on a manufactory, at 14 per cent., amounts to $250. What is the amount insured? Ans.

9. What would be the cost of insurance on a store house, valued at $5000, and a stock of goods amounting to $7500.50, at 24 per cent.? Ans.

Re

10. A steamboat is valued at $35000, and the proprietors of it obtain an insurance on of its value, at 34 per cent. quired the amount of premium to be paid? Ans. $853.125. 11. An upholsterer has his warehouse, valued at $8000, insured to the amount of of its value, at 1 per cent. per annum; and $10000 worth of furniture insured at 13 per cent. per annum. What does he pay for insurance annually? Ans. $271.

DUTIES.

§ 252. DUTIES, in commerce, are certain charges, imposed by Government, on articles imported from foreign countries. These duties are paid in the Custom Houses established in the several ports of entry of foreign trade.

A specific duty is a specified charge on the quantity; as on a yard, pound, gallon, &c., of the article.

An ad valorem duty is a specified percentum on the cost of the articles in the country from which they were imported (Ad valorem is a Latin phrase which signifies, according to value.)

An invoice is a written statement of articles and their cost.

Tare, Draft or Tret, and Leakage, are allowances made for the weight of the box or cask, &c., containing the articles; or for waste, leakage, &c., before the duty is computed.

12. What would be the amount of duty on an invoice of broadcloth amounting to $5465.75, at 30 per cent.?

Ans. $1639.725. 13. What would be the amount of duty on an invoice of philosophical instruments, amounting to $30200, at 25 per cent.? Ans. $7550.

14. The duty on a box of goods, at 12 per cent., amounted to $65; what was the amount of the invoice? Ans. $520. 15. A lot of cutlery was purchased in Sheffield for $575.182. What would be the amount of duty on it at 9 per cent.? Ans. $54.642'.

16. An invoice of Irish linens paid a duty of $330. What was the amount invoiced, the duty being 33 per cent.?

Ans. $1000.

17. A quantity of ready-made clothing was purchased in Paris for $1534.12. What would be the amount of duty to be charged, at 15 per cent.? Ans. $230.118'.

cent.?

18. An invoice of silk was purchased in Canton for $12000.25, what is the amount of duty to be paid, at 10 per Ans. $1200.025. 19. The duty on an importation of iron, at 20 per cent., amounted to $15000. For what sum then was the iron purchased abroad? Ans. $75000. 20. What would be the amount of duty to be paid on 3 cwt. 3 qr. 20 lb. of steel, purchased at $21.12 per cwt.,-at 9 per

cent.?

Ans. $7.46'.

-ONE GIVEN NUMBER A PERCENTAGE ON ANOTHER.

RULE L.

§ 253. To find what PERCENTUM one given number is of another.

Divide the number which is made the percentage by that which is made the basis of percentage. The quotient will be the ratio of percentage; and this quotient multiplied by 100, will produce the required rate per cent.

EXAMPLE.

To find what percentum $9 is of $150.

9÷150.06, the ratio of percentage;

and .06×100=6, the required rate per cent. (§ 247). This Rule follows from the preceding one. (§ 249). Proportion. $150 : $100 :: $9: the required rate per cent.

TAXES.

§ 254. TAXES are contributions in money, imposed by Government on property, and frequently on persons, for public purposes.

A poll or capitation tax is a tax on the person, without regard to property. A tax on property is sometimes specific, that is, a specified sum on certain articles; but it is most commonly ad valorem, or a specified percentum on the value.

EXERCISES.

21. A person paid a tax of $52.88 on $3525.50 worth of property; at what rate per cent. was the tax assessed? Ans. 1 per cent. 22. The property of a town amounts to $50000, and the citizens resolve to tax it to the amount of $1125, for public improvements. At what percentum must the tax be laid? Ans. 2 per cent. 23. Allowing a gentleman to pay a tax of $1379.163, on property amounting to $82750, at what rate per cent. is the tax assessed? Ans. 14 per cent.

24. A citizen pays taxes as follows, viz: for three polls at $1.25; on a carriage $10; on silver plate valued at $500, 3 per cent.; on $15000 of other property, & per cent. amount of tax does he pay?

What Ans. $141.25.

25. The taxable polls in a State amount to 325830, and are assessed at $1.12. The landed property in the State is valued at $38400000; at what percentum must the land be taxed, that the revenue from both sources may amount to $462558.75 ? Ans. per cent.

A Required Number, increased by a Percentum of itself, equal to a Given Number.

RULE LI.

$ 255. To find a number which, increased by a specified PER CENTUM OF ITSELF, shall be equal to a given number.

Divide the given number by 1 plus the ratio of percentage : the quotient will be the number required.

EXAMPLE.

What number, increased by 5 per cent. of itself, is equal to 210?

The ratio of percentage is .05; and 1+.05 is 1.05.
Then 210 1.05-200, the number required.
Proportion. 100+5: 100: 210: the number required.

The reason of the Rule is evident from considering that, as the required number multiplied by 1+ the ratio of percentage, would be increased by the specified percentum of itself, and thus be equal to the given number; so the given number divided by 1+ the ratio of percentage, will give the required number.

In the example, 200×1.05=210, which is 200 increased by .05 of 200; then 210-1.05 gives 200, the required number.

COMMISSION.

§ 256. COMMISSION is a compensation to an Agent, Factor, or Commission Merchant, for buying or selling for another; and is usually reckoned at a certain percentum on the amount of purchase or sale. BROKERAGE is a commission charged by Brokers, or dealers in money, stocks, &c., on the amount of exchange, purchase or sale, which they effect for another.

EXERCISES.

26. An agent receives $500 to purchase goods-himself to retain a commission of 2 per cent. on the amount of purchase. What is the amount of purchase to be made?

Ans. $490.196'.

27. A factor receives a remittance of $1200 to purchase cloth, at a commission of 14 per cent. on the purchase. What will be the amount of purchase? Ans. $1185.185'.

28. A commission merchant sold goods amounting to $1785.814; at a commission of 1 per cent. What sum must the merchant pay to the owner of the goods?

Ans. $1759.025'. 29. An agent is intrusted with $450 to purchase iron. His commission being per cent. on the purchase, how many tons of iron can he buy at $30 per ton? Ans. 14.888' T.

30. A, as factor for B, sells 50 bales of cotton, averaging 450 pounds, at 7 cts. per lb.-commission 1 per cent. With the proceeds A purchases for B, a supply of provisions,-commission per cent. on the purchase. What sum is expended for provisions? Ans. $1649.71'.

A Required Number, diminished by a Percentum of itself, equal to a Given Number.

RULE LII.

$257. To find a number which, diminished by a specified percentum of itself, shall be equal to a given number.

Divide the given number by 1 minus the ratio of percentage; the quotient will be the number required.

EXAMPLE.

What number diminished by 5 per cent. of itself, is equal to

190?

The ratio of percentage is .05; and 1-.05 is .95.

Then, 190.95=200, the number required.

Proportion. 100-5: 100 :: 190: the number required.

The reason of the Rule is evident from considering that, as the required number multiplied by 1 minus the ratio of percentage, would be diminished by the specified per centum of itself, and thus be equal to the given number; so the given number divided by 1 minus the ratio of percentage, will give the required number.

In the example, 200×1-.05=190, which is 200 diminished by .05 of 200; then 190-1-.05 or .95-200, the required number.

STOCK.

§ 258. STOCK, or Capital, is money or other property employed in any way to produce a profit; as in manufactures, banking, &c. Bonds of the Government are also called Government Stock.

The stock of a Company is divided into shares, usually of $100 each; and the owner of one or more shares is called a Stockholder.

The nominal value, or par value of a share of stock, is its first cost, or the sum originally invested in it.

Stock is said to be above par, at a premium, or an advance, when it sells for more than its nominal value; and below par, or at a discount, when it sells for less than its nominal value. The rise or fall of stock is expressed by a percentum on its nominal or par value.