side 9 times 7000 £. or 63000£. and on the other, 15 times 10000£, or 150000£. which makes in all a sum of 213000£.

The third inerchant, having put in at first 10000. which remained in trade 12 months, and at that time having withdrawn the half of his fund, so that his stock was then only 5000. which remained 12 months in trade, has the same claim to the whole profit, as if he had put in for one month, on one side 12 times 10000. or 120000£. and on the other 12 times 5000. or 60000£. which amount in all to the sum of 180000£.

The question, therefore, is now reduced to one of simple fellowship, and may be thus expressed.

Three merchants formed a company for one month and gained 1755£.

The first put in
The second

each man's share of the gain?

we obtain the shares

585000: 1755::192000: to the gain of the 1st=576 585000: 1755::213000; to the gain of the 2nd➡639 585000: 1755::180000: to the gain of the 3d=540

NOTE. The first Ratio of each of these proportions, may be reduced to that of 1000: 3; and then taking away three cyphers from the right hand of

each of the antecedents, all these proportions are much simplified, and the first becomes 1: 3:192: to the gain of the 1st,=&c.

REMARK. When we have a great number of proportions, which commonly happens in the division of shares in a bankruptcy, if the two first terms after reducing them to their simplest expression, were still considerable, we could, to facilitate the calculation in the proportions, form a table of the products of each of these numbers, which would very much abridge the work.

We call a table of the products of a number, the different products of this number, by 1, 2, 3, 4, 5, 6, 7, 8, 9. To form this table, we write all the different products below each other on a loose sheet, which we have under our eyes, when we employ the number in question, as a multiplicand, or as a divisor; we also write at the left hand of each of the products of the table, the figure which has served as a multiplier.

RULE OF INTEREST.

By Interest, we mean the money due for a sum lent out, which is called the Principal. The chief object of the rule of interest, is, to determine the money due according to the conditions of the loan.

Interest may be either simple or compound: It is simple, when it proceeds only from the principal. It is compound, when to the interest of the principal, are superadded the interests upon interests.

The rate of Interest is fixed at so much per-cent per-annum, as at 3, 4, 5, 6, &c. per-cent; which means that for 100£. lent, an interest is demanded per-annum, of 3, 4, 5, 6, &c.

SIMPLE INTEREST.

We must distinguish two cases: the first, when the loan is for one year; the second, when it is for more or less than one year: but in this 2nd case, the question may be begun to be solved as in the first, and then by the multiplication of complex numbers, it will be easy to come up to the result demanded.

First Case; the rule is solved by this proportion, if 100£. gain so much interest per-annum, how much will the sum lent gain during the same time.

QUESTION. It is required to tell the interest of 7450£. for one year, at 4 per-cent per-annum.

We shall say; if 100£. gain 4£. how much will 7450£. gain and then we shall have 100£.4£;; 7450£: to the interest required,=298£•

Second Case, Question. What is the interest of 8474£. 8s. 4d. for 7 years 10 months and 18 days, at 5 per-cent per-unnum?

To solve this question, we must first find the interest of 8474£. 8s. 4d for one year; we find it by this proportion, 100£:5£::8474 £. 8s. 4d:x; and dividing the two first terms by 5, we have 20:1:: 8474£. 88. 4d: x=423.£. 14s. 5d. the interest for one year; now multiplying this sum by the number of years and parts of years, (being the time that the

loan remained out at interest) the product will evident. ly give the solution of the question.

REMARK. When the loan is in dollars, and the interest is at 6 per-cent, as the law rates it in this country, the simplest method then to be pursued, is, to find at first the interest of the sum for two months, which is obtained by separating with a dash at the right hand of the number, the two first figures, which we count as cents, and the other figures of the same number express dollars. This method is easily comprehended, since the interest for a year at 6 percent, is reduced to 1 per-cent for 2 months, that is to say, to the hundredth part of the loan. For example, the interest of 3457 dollars, for two months, is 34 dollars and 57 cents.

* The month is supposed to consist of 30 days.

Third Question. A man pays his creditor 500£, both for principal and interest, at 6 per-cent, for 10 years. What was the principal ?

This question differs from the preceding, but it may be solved by an almost similar method, by saying, since the interest of 100. is 6. per annum, the interest of 100. for 10 years will be 60. thus the interest and the principal of 100. for 10 years, will be 160. then it is evident that we have this proportion; 160. the principal and interest of a hundred pounds: 100:500. the principal and interest: to the principal required, which we find =312£. 10s.

We can vary questions of this nature very much, but we shall always solve them with ease, by the same principles just employed.

COMPOUND INTEREST.

As to questions of Compound Interest, we can resolve them by means of the rules above, by taking each year successively, the interest of the sum due at the end of the preceding year.

Algebra directs us to a very easy method of solving questions of Compound Interest,

RULE OF DISCOUNT.

Discount is an allowance made upon a sum of money, the payment of which is demanded before it becomes due.

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