Each of the above rules becomes necessary under different circumstances. How ought interest to be cast on notes which have many endorsements? It seems obvious to the Author, that the only mode in casting simple interest, which is just to both the Dr. and Cr., is the following: Compute the interest on the whole amount of the Note, for the whole time; then cast the interest on each payment up to the time of general settlement, and add it to the sum of the endorsements. By the above rule, justice is done to both the lender and borrower. If the agreement is to pay annual interest, this is the same as Compound Interest, and will hereafter be explained. 4. If the principal is pounds, shillings, &c. multiply by the rate, and as this is a decimal, the two right hand figures must be cut off for decimal parts. The value of this fraction may be found by multiplying the decimals of a pound by the number of shillings in one pound, and adding the given shillings; the shillings are again to be multiplied by the number of pence in one shilling, &c.; in each case the decimals are cut off as before. EXAMPLE. What is the interest of 28 £. 10 s. 4 d. for 1 year? If at the end of a year the interest on a given sum is added to the principal, it becomes a part of it, and interest afterwards is necessarily cast on it. RULE. Find the interest of one dollar for the given time, and multiply that by the number of dollars, in the principal. Or, The compound interest at 6 per cent of any sum in Federal money, may be found by multiplying the sum by the following numbers. Multiply the given sum : "Point the product as in simple interest; it will then show the amount of principal and interest for the given number of years. Subtract the principal from the amount, and the remainder will be the compound interest. When there are months and days, first find the compound interest for the given years; then for the months and days cast the simple interest, which, added to the amount, will give the answer." A sum at compound interest will be doubled in 11 years, 10 months and 22 days. COMMISSION "Is an allowance of so much per cent to a factor or correspondent abroad, for buying and selling goods for his employer." BROKERAGE "Is an allowance of so much per cent to a person called a broker, for assisting merchants or factors in procuring or disposing of goods." INSURANCE "Is an allowance of so much per cent given to certain persons or companies, who engage to make good the loss of ships, houses, merchandise, &c. which may happen from storms, fire, &c." The method of working questions in these rules is the same as in simple interest, and needs no farther illustration. Discount is an allowance made for the payment of any sum of money before it becomes due, according to a certain rate per cent. agreed on between the parties concerned. If I am to pay A 100 dollars in one year, it is plain that I ought not to pay so much, if it is paid to-morrow. The present worth of any sum or debt due some time hence, is such a sum as, if put to interest for that time, at a certain rate per cent., would amount to the sum or debt then due. That an allowance ought to be made for paying money before it becomes due, if it is not on interest till after it is due, is highly reasonable; for if I keep the money in my own hands till the debt becomes due, I may make an advantage of it, by lending it on interest for that time; but if paid before it becomes due, it is giving that benefit to another. What is the discount of $846 for 6 months, at 6 per cent.? 1. "To find the discount, make a statement in the rule of three; As $100 or £., with its interest for the given rate and time, is to that interest; so is the given sum, to the discount required. And, 2. To find the present worth; As 100, with the interest for the given rate and time, is to 100; so is the given sum, to the present worth," SECTION XXII. PRACTICE. Before the introduction of Federal money, this rule was very convenient and useful, and hence its name. In the United States it is now seldom employed. But, as performing operations in it may be a useful exercise to the learner, it is thought best to introduce some of the prominent cases. Practice is a contraction of the rule of proportion, when the first term is a unit. When the price only is a compound number, the answer is more easily obtained, than when the price and quantity are both compound numbers. Example. What is the worth of 200 yards of cloth at 10 s. 6d. a yard? As 10 s. is a pound, if half the number of yards is taken, it will equal the number of pounds the cloth is worth at 10s. a yard. And as 6 d. is of a pound, if that part of 200 is taken, it will be the price at 6 d. a yard. These added together, will make the price of the whole. b) 200 100 105 £. Ans. An aliquot part of any number is such a part of it as, being taken a certain number of times, will exactly make that number. Hence the aliquot parts are used as divisors. GENERAL RULE. 1. Suppose the price of the given quantity to be 1 £. or 1 s. as is most convenient; then the quantity will itself be the answer at the supposed price. 2. Divide the given price into aliquot parts, either of the supposed price, or of another, and the sum of all the quotients will be the true answer required. Example. What is the value of 526 yards of cloth at 3 s. 101 d. per yard? 3 s. 4 d. is of 1 £. )526 In this example it is obvious that 526 £. would be the answer at 1 £. per yard; consequently, as 3 s. 4 d. is of a pound, part of that quantity, or 87 £. 13 s. 4 d., is the price at 3 s. 4 d. In like manner as 4 d. is of 3 s. 4 d., so o of 87 £. 13 s. 4 d., or 8 £. 15 s. 4 d., is the price at 4 d. And by reasoning in this way, 4 £. 7 s. 8d. will appear to be the price at 2d., and 10 s. 11 d. the price at d. Now as the sum of all these parts is equal to the whole price per yard, (3 s. 101 d.,) so the sum of the answers belonging to each price will be the answer at the full price required. And the same will be true of any example whatever. As the following cases are all founded on the principles involved in this general rule, this illustration will be sufficient to explain them." II. When the price is less than a penny. Divide the given number by the aliquot parts of a penny, and the quotient will be the answer in pence, which may be reduced to pounds." Example. What cost 4506 yards of tape at of a penny per yard? d. 2)4506 1126 12)33791 202817 14. I s. 7 d. Ans. 3379 III. When the price is an aliquot part of a shilling, divide the given number by that, and the answer will be the price |