6. What will $2000 amount to in 4 years, at 7 per cent., Compound Interest? Ans. $2621,59,2m.

7. What is the Compound Interest of $400, for 31 years, at 5 per cent.? Ans. $90,69,8m.

ENSURANCE, COMMISSION OR FACTORAGE, BROKERAGE AND BUYING AND SELLING STOCKS.

Q. What are Ensurance, Commission or Factorage, Brokerage, and Buying and Selling Stocks?

A. They are allowances made to Ensurers, Factors, Brokers, and Buyers, at a stipulated rate per

cent.

RULE.

Q. How do you find the Ensurance, Commission, or Brokerage, on any given sum?

A. The given sum must be multiplied by the rate per cent., and the product divided by 100, the same as in finding the interest of any given sum for one year only.

ENSURANCE.

NOTE. Ensurance is a premium, at a certain per cent., allowed to companies and persons, for securing or indemnifying against loss of property, such as houses, ships, merchandise, &c., which may happen from fire, storms, &c. The writing by which the contract of indemnity is binding upon the parties, is called the policy. The average loss is 5 per cent, that is, if a person having his property ensured does not suffer damage or less exceeding 5 per cent., he must bear it himself, and can not call on the ensurers.

EXAMPLES.

1. What is the ensurance of $3250, at 3 per cent.? Ans. $97,50.

EXPLANATIONS.

3

In this example, you multiply by 3, the rate per cent., and divide by 100, or, rather, you cut or 3250 point off two figures at the right hand, precisely as in obtaining the Simple Intercst on any given sum for one year.

97,50c. Ans.

2. A house, valued at $4000, was ensured against fire for 41 per cent. a year; how much ensurance did the owner pay annually? Ans. $180.

3. What is the ensurance of a ship and cargo, valued at $87564, at 141 per cent.? Ans. $12477,87c.

4. What is the ensurance of a store of goods, valued at $7296, at 3 per cent.? Ans. $255,36c.

COMMISSION OR FACTORAGE.

NOTE.-Commission or Factorage is an allowance of a certain per cent. from a merchant to his factor, or correspondent, engaged in buying or selling goods, &c.

EXAMPLES.

1. What is the commission on $1500, at 24 per cent.? Ans. $37,50c.

2. What is the commission on $6000, at 13 per cent.? Ans. $105.

3. What is the commission on $3948; at 5 per cent.? Ans. $197,40c.

4. What is the commission on $1200, at 64 per cent.? Ans. $78.

BROKERAGE.

NOTE.-Brokerage is an allowance of a certain per cent., to any person or persons who assist merchants or factors in buying and selling goods, &c

EXAMPLES.

1. What is the brokerage upon $3000, at 1 per cent.? Ans. $45.

2. A broker sold goods amounting to $4500, at 24 per cent.; what was his demand against his employer? Ans. $112,50. 3. If a broker sells goods to the amount of $7500; what is nis demand, at 34 per cent.? Ans. $243,75c.

4. What is the brokerage upon $5162, at 2 per cent.? Ans. $38,71,5m.

BUYING AND SELLING STOCKS.

NOTE. Stock is a name given to the capital, or funds of banks, trading companies, or of a fund established by governments, &c.; and the buying and selling of certain sums of money in those funds, the value of which often varies, are very usual.

EXAMPLES.

1. What is the value of $400 of stock, at 106 per cent.? Ans. $424.

EXPLANATIONS.

400

106

The sum to be purchased must be multiplied by the rate per cent., as in Simple Interest, whether the stock be above or under par; that is, if $100 of stock be worth more than $100 of money, or less than $100 of money; you $424,00 Ans. must proceed precisely as in Simple Interest,

multiply by the rate per cent., and divide by 100, or, rather, cut off two figures at the right hand, and the figures at the left will show the value of the stock in money.

2. What is the value of $3000 of bank stock, at 75 per cent. ? Ans. $2250.

3. What is the value of $6500 of capital stock in the United States Bank, at 112 per cent ? Ans. $7280.

4. What is the value of $1000 of bank stock, at 95 per cent.? Ans. $950.

SINGLE RULE OF THREE DIRECT.

Q. What is the SINGLE RULE OF THREE DIRECT? A. The Single Rule of Three Direct teaches, by having three numbers given to find a fourth, which shall have the same proportion to the third, as the second has to the first.

EXPLANATIONS.

The Single Rule of Three is merely an application of Multiplication and Division, as it is principally performed by those two rules in its operation. It is divided into two parts; the Rule of Three Direct, and the Rule of Three Inverse. On account of its extensive usefulness in the solution of nearly every mathematical inquiry, and also in the transaction of business, it is often called the Rule of Proportion, or, the Golden Rule of Proportion. The Rule of Three is so called, because three terms or numbers are given to find a fourth; and the principle upon which the rule is founded is this, that the result of any effect varies in proportion to the varying part of the cause; thus, the quantity or number of any article or articles, is in proportion to the money paid; and the space which is gone over by a uniform motion, is in proportion to the time. The sign of proportion is this, which should

be placed between the numbers thus, 3 6 8 16, and should be read thus, as 3 is to 6, so is 8 to 16. This is, you will readily perceive, very plain; for it is evident, that 16, the fourth term, bears the same proportion to 8, the third term, that 6, the second term, bears to 3, the first term.

Two of the given numbers, the first and second, are called terms of supposition, and the other term, the third given number, is called the term of demand. The terms of supposition are generally known by being preceded by if, suppose, &c. The term of demand is generally known by being preceded by the words, how much, how many, how far, what will, what cost, &c. When the third term is greater than the first, and requires the fourth term, or answer, to be greater than the second; or, when the third term is less than the first, and requires the fourth term, or answer, to be less than the second,

the sum belongs to, or must be worked by the Rule of Three Direct.

The Rule of Three Direct is much more useful for practical purposes, and in the transactions of business, than the Rule of Three Inverse, and is easily distinguished from it by the preceding conditions of the question; that is, whether more requires more, and less requires less; or, whether more requires less, and less requires more, &c.

All the following rules are worked by, and strictly belong to the Rule of Three Direct: Discount, Loss and Gain, Barter, Practice, Tare and Tret, Single and Double Fellowship, Alligation, Annuities, and also Double Rule of Three; for, as was stated on pages 139 and 140, these rules have different names, applicable to the different kinds of business to which they are applied, without involving any new principle in their operation, being all worked by the simple or fundamental rules only, as will be obvious to the learner on examination.

RULE.

Q. How do you state the terms in the Rule of Three Direct?

A. The term of supposition, which is of the same name or kind with the term of demand, must be written for the first term; and the remaining term of supposition must be written in the second place, which must always be of the same name or kind with the answer; and then the demanding term must be written in the third place, which must always be of the same name or kind with the first term.

Q. How do you work the different terms?

A. If the first and third terms are of different denominations, you must first reduce them to the lowest denomination mentioned in either; and if the second term stands in different denominations, you must also reduce it to the lowest denomination mentioned in that term. You must then multiply the second and third terms together, and divide their product by the first term, and the quotient will be the