2. A broker sold goods to the amount of $6000, at 1 per cent; what was his demand against his employer? Ans. $60. 3. A broker made sale of goods to the amount of $3000, at per cent, what was his demand? Ans. $15. 4. A broker bought goods to the amount of $1000, at 1 per cent; what must he receive for his services?

ENSURANCE,

Ans. $17,50 cents.

Is a premium, at a certain per cent, allowed to persons and offices, for indemnifying against loss of property of any description, such as houses, ships, merchandise, &c. which may happen from fire, storms, &c.

Policy is the name given to a writing by which the contract of indemnity is binding upon the parties.

If the person having his property ensured suffer damage or loss not exceeding 5 per cent, he must bear it himself, and cannot call on the ensurers, the average loss being 5 per cent.

The premium is paid to the ensurers, by the ensured who receives the amount of his ensurance in case of loss from fire, from storms, &c. unless he has broken his policy or indemnity, by his own wrong. The method of operation is the same as in Simple Interest for one

year.

$1500

EXAMPLES.

1. What is the premium on 1500 dollars, at 8 per cent ? Ans. $120. The learner will understand, that if the en8 surers indemnify against loss to the amount of $120,00 1500 dollars, in case of loss, they must pay the person having his property ensured, the 1500 dollars, and the ensurers receive 120 dollars, whether there be loss or not.

2. A man's house valued at 4000 dollars, was ensured against fire for 13 per cent a year; what ensurance did he pay annually? Ans. $60. 3. What is the ensurance of a vessel and cargo, valued at $90146,46cts. at 8 per cent? Ans. $7662,44cts. 9m..

10

BUYING AND SELLING STOCKS.

Stock is the name of the capital of trading companies, or of a fund established by government; the value of which frequently varies.

The operation of the work is the same as in Simple Interest; thus if bank or other stock be worth 75 per cent, 100 dollars stock would be worth 75 dollars; and 1000 dollars stock would be worth 750 dollars, which is obtained by multiplying the stock by the per cent; the product is the worth of the stock.

$

50=1)1500 dollars.

EXAMPLES.

1500

1. Required the value of 1500 dollars of bank stock, worth 75 per cent? Ans. $1125. NOTE. In the last op,75 eration, we multiply by 7500,75 cents, because $1 is worth only ,75 cents, and in the first operation we take parts.

25) 750 or thus,

375

$1125

10500

$1125,00

2. What is the value of 500 dollars of stock, at 95 per

cent?

Ans. $475. 3. What is the value of 200 dollars of stock, at 107 per cent? Ans. $214.

What is the value of 1500 dollars of bank stock, at 60 per cent?

COMPOUND INTEREST,

Ans. $900.

Is that which arises from the principal and interest added together, as the interest becomes due; and for this reason it is called Compound Interest.

RULE.-Find the amount of the given sum for the first year the same as in Simple Interest, which will be the principal for the second year; then find the amount of that principal for the second year, and that will be the principal for the third year; and so on, for any number of years. From the last amount subtract the given principal, the remainder will be the compound interest.

This Rule is founded on the following principle:

That interest becomes due at the end of each year, at which time it becomes a part of the principal, if it remains in the hands of the borrower; this is not, however, allowed by law; yet in purchasing annuities, pensions, or leases in reversion, it is usual to allow Compound Interest to the purchaser for his ready money.

NOTE.-In our rule we have considered the interest to be due annually, and then becoming a part of the principal; but other periods of time are sometimes reckoned, as half-yearly, quarterly, &c. and then

the interest is computed, for every six months or for every quarter of a year, and at the end of each period, becomes a part of the principal; carrying interest for the next period.

EXAMPLES.

1. What is the compound interest of $1000, for 3 years, at 7 per cent?

6

1

Ans. $225,04cts. 3m.

NOTE. The learner will perceive, that compound interest is casting interest, at the end of each year, on the amount.

1 1 4 4,9 0 Amount at the end of the 2d year.

7

8 0,1 4,3 0

1 144,9 0

1225,0 4,30 Amount at the end of the 3d year. Principal deducted.

1000

$225,0 4,3 0 Compound Interest of $1000 for 3 years.

2. What is the compound interest of $750 for 4 years, at Ans. $196,85cts. 7m.

cent?

per 3. What will $250 amount to in 3 years, at 7 per cent, compound interest?

Ans. $306,26cts. 4. What will £50 amount to in 5 years, at 5 per cent per annum, compound interest? Ans. £63 16s. 31d.

QUESTIONS ON INTEREST.

What is interest? A. An allowance or premium of a certain per cent for the use of money. What is the principal? A. The money lent. What is the amount? A. The interest and principal added together. What is the rate? A. The per cent paid by the borrower to the lender for the use of money. What is meant by per cent? A. It means a certain number of dollars for the use of a hundred dollars, or a certain number of cents for the use of one dollar, or one hundred cents? What is the per cent in the New England States? A. Six.— What is the per cent allowed by law in New York? A. Seven. How many kinds of interest are there? A. Two, Simple and Compound.What is Simple Interest? A. That which arises from the principal

only? How do you cast the interest on any sum for one year? A. Multiply the interest for one dollar by the number of dollars, and the product will be the interest for one year; or, multiply the given sum by the interest of one dollar, and the product will be the interest for one year. Why should that give the interest for one year? A. Because it is plain, that the interest of one dollar repeated by the number of dollars, must give the interest on the whole number of dollars. Is this the most convenient way of casting interest? A. It is not, the best method of casting interest is, to multiply the given principal by the interest of one hundred dollars, and divide the product by one hundred. Why divide the product by 100? A. Because the product is one hundred times too much, the multiplier being the interest of one hundred dollars instead of the interest of one dollar. When you have computed the interest for one year, how do you compute it for a number of years? A. Multiply the interest of one year by the number of years, and the product will be the interest for the whole number of years. What general rule may be given to cast interest on a sum for any number of months? A. First multiply by the per cent, and the product will be the interest for one year, then divide the interest of 1 year by 12, and the quotient will be the interest for one month, and the interest for one month multiplied by the number of months, gives the interest for the whole number of months; but the better way is to take aliquot parts of the interest of a year for the months. What gen eral rule may be given to compute interest for any number of days?A. Divide the interest for one year by 12, and the quotient will be the interest for one month, then divide the interest for one month by 30, and the quotient will be the interest for one day, and one day's interest multiplied by the number of days, will give the interest for the whole number of days; but the better way is to take aliquot parts of a month for the days. How is the amount obtained? A. By adding the principal to the interest. How do you cast interest on bonds in the state of New York? A. Compute interest to the time of the first payment, and from the amount subtract the payment, and the remainder will be a new principal, upon which cast interest till the time of the next payment, and from the amount again subtract the payment, and so on, till the time of settlement; but if the payment be less than the interest, at the time it is made, cast again on the same principal, and so continue to do, till the amount of payments exceeds the interest, and then subtract the sum of the payments from the amount of the note or bond at that time. On what principle is the computation of interest founded in the state of New York when partial payments are made? A. On the principle that interest is due whenever a payment is made, and that the payment must first go to pay the interest, and then to discharge the principal. What is Commission or Factorage? A. It is a premium or an allowance of a certain per cent, to a factor engaged in buying and selling goods for his employer. How is the work performed? A. The same as in Simple Interest. What is Brokerage? A. It is a premium allowed, at a certain per cent, to per sons assisting merchants or factors in sales and purchases. How is the work performed? A. The same as in Simple Interest. What is Ensurance? A. It is a premium of a certain per cent allowed to per

sons and offices indemnifying against hazard or losses of different kinds. What is Compound Interest? A. It is reckoning interest upon interest; or at certain periods of time, the interest is incorporated with the principal, and draws interest. How do you proceed in the operation of the work? A. Compute interest on the given sum, the same as in Simple Interest, from time to time, as the interest becomes due, each time making the amount a new principal for the next period of time. Is compound interest allowed by law? A. It is not; yet it is usual to allow compound interest in purchasing annuities, pensions, or leases in reversion."

THE SINGLE RULE OF THREE.

The Single Rule of Three is properly an application of Multiplication and Division; for on those two rules it principally depends. It is generally divided into two parts, viz. the Rule of Three Direct and the Rule of Three Inverse or Indirect. It is sometimes called,. and very properly too, the Rule of Proportion, or the Golden Rule of Proportion, on account of its extensive usefulness, in the transaction of business, and in the solution of almost every mathematical inquiry. The rule is founded on this obvious principle; that the magnitude or result of any effect, varies constantly in proportion to the varying part of the cause; thus the quantity of articles purchased, is in proportion to the money laid out; and the space gone over by a uniform motion, is in proportion to the time.

This is the sign of proportion, which is placed between numbers thus, 4:8:: 5: 10, and read thus, as 4 is to 8, so is 5 to 10.

The Rule of Three is so called, because three terms or numbers are given to find a fourth, which, in the Rule of Three Direct, shall bear the same proportion to the third, as the second bears to the first, thus, 4 is to 8: as 5 is: to 10.

It is obvious that ten, the fourth term, bears the same proportion to 5, the third term, that 8, the second term, bears to 4, the first term. Two of the given numbers, are called terms of supposition, and the other the term of demand. The terms of supposition may generally be known by being preceded in most cases, by words like these, if, suppose, &c. The term of demand is generally preceded by words like these, How far? What cost? What will? How many? How much? &c.

RULE OF THREE DIRECT.

The Rule of Three Direct is far more useful in business than the Rule of Three Inverse, and may be distinguished from it by the conditions of the question. When the third term is greater than the first, and requires the fourth term or answer, to be greater than the second, it belongs to the Rule of Three Direct: or when the third term is less than the first, and requires the fourth term, or answer, to be less than the second, it belongs to this rule.

RULE FOR STATING.

Write down for the first term, that term of supposition which is of the same name or kind with the demanding term. Place the remain