When interest is at 3 per cent. the rate is 3 ; But, by law in England, interest ought not to be taken higher than at the rate of 5 per cent. Interest is of two sorts; Simple and Compound. Simple Interest is that which is allowed for the principal lent or forborn only, for the whole time of forbearance. As the interest of any sum, for any time, is directly proportional to the principal sum, and also to the time of continuance; hence arises the following general rule of calculation. As 100l is to the rate of interest, so is any given principal to it interest for one year. And again, As 1 year is to any given time, so is the interest for a year, just found, to the interest of the given sum for that time. OTHERWISE. Take the interest of 1 pound for a year, which multiply by the given principal, and this product again by the time of loan or forbearance, in years and parts, for the interest of the proposed sum for that time. Note, When there are certain parts of years in the time, as quarters or months, or days: they may be worked for, either by taking the aliquot or like parts of the interest of a year, or by the Rule of Three, in the usual way. Also to divide by 100, is done by only pointing off two figures for decimals. EXAMPLES. 1. To find the interest of 230l 10s, for 1 year, at the rate of 4 per cent. per annum. Here, As 100: 4 :: 230l 10s: 91 4s 43d. Ex. 2. To find the interest of 5471 15s, for 3 years, at 5 per cent. per annum. As 100 5 :: 547-75: Or 20: 1: : 547-75: 27-3875 interest for 1 year. 3 I 82-1625 ditto for 3 years. 20 $ 3.2500 12 d 3.00 Ans. 821 3s 3d. 3. To find the interest of 200 guineas, for 4 years 7 months and 25 days, at 41 per cent. per annum. ds ds As 365 : 9.45 25: l 210/ 840 105 9.45 interest for 1 yr. 9.45: 5: 6472 73) 47.25 (-6472 345 530 19 4. To find the interest of 4501, for a year at 5 per cent. per annum. Ans. 221 10s. 5. To find the interest of 715l 12s 6d, for a year, at 4 per cent. per annum. Ans. 321 4s Od. 6. To find the interest of 7201, for 3 years, at 5 per cent. per annum. Ans. 108/. 7. To find the interest of 355l 15s for 4 years, at 4 per cent. per annum. Ans. 561 18s 43d. Ex. 8. To find the interest of 321 5s 8d, for 7 years, at 41 per cent. per annum. 9. To find the interest of 170l, for 1 per annum. 10. To find the insurance on 2051 15s, 4 per cent. per annum. cent. per annum. Ans. 91 12s 1d. year, at 5 per cent. Ans. 121 5s. for Ans. 21 1s 13d. of a year, at 11. To find the interest of 3191 6d, for 53 years, at 33 per Ans. 681 15s 91d. 12. To find the insurance on 2071, for 117 days, at 43 per cent. per annum. Ans. 1 12s 7d. 13. To find the interest of 171 5s, for 117 days, at 4 per cent. per annum. Ans. 5s 3d. 14. To find the insurance on 712 6s, for 8 months, at 72 per cent. per annum. Ans. 35l 12s 34d. Note. The Rules for Simple Interest, serve also to calculate Insurances, or the Purchase of Stocks, or any thing else that is rated at so much per cent. See also more on the subject of Interest, with the algebraical expression and investigation of the rules at the end of the Algebra, next following. COMPOUND INTEREST. COMPOUND INTEREST, called also Interest upon Interest, is that which arises from the principal and interest, taken together, as it becomes due, at the end of each stated time of payment. Though it be not lawful to lend money at Compound Interest, yet in purchasing annuities, pensions, or leases in reversion, it is usual to allow Compound Interest to the purchaser for his ready money. Then con RULES.-1. Find the amount of the given principal, for the time of the first payment, by Simple Interest. sider this amount as a new principal for the second payment, whose amount calculate as before. And so on through all the payments to the last, always accounting the last amount as a new principal for the next payment. The reason of which is evident from the definition of Compound Interest. Or else, 2. Find the amount of 1 pound for the time of the first payment, and raise or involve it to the power whose index is denoted by the number of payments. Then that power multiplied by the given principal, will produce the whole amount. amount. From which the said principal being subtracted, leaves the Compound Interest of the same. As is evident from the first Rule. per annum, Here 5 is the 20th part of 100, and the interest of 11 for a year is or05, and its amount 1:05. Therefore, 1. By the 1st Rule. S d 1st yr's princip. 2. By the 2d Rule. 1.05 amount of 11. 1.05 36 0 0 1st yr's interest. 39 13 9 3d yr's interest. / 875-1645 2. To find the amount of 501, in 5 years, at 5 per cent. per Ans. 631 16s 31d. annum, compound interest. 3. To find the amount of 501 in 5 years, or 10 half-years, at 5 per cent per annum, compound interest, the interest payable Ans. 641 Os 1d. half-yearly. 4. To find the amount of 501, in 5 years, or 20 quarters, at 5 per cent per annum, compound interest, the interest payAns. 641 2s Old. able quarterly. 5. To find the compound interest of 370l forborn for 6 Ans. 981 3s 41d. years, at 4 per cent. per annum. 6. To find the compound interest of 410l forborn for 21 years, at 41 per cent. per annum, the interest payable halfAns. 481 4s 11d. yearly. 7. To find the amount, at compound interest, of 217, forborn for 24 years, at 5 per cent per annum, the interest payAns. 2421 13s 44d. able quarterly. Note. See the Rules for Compound Interest algebraically investigated, at the end of the Algebra. ALLIGATION. ALLIGATION. ALLIGATION teaches how to compound or mix together several simples of different qualities, so that the composition may be of some intermediate quality or rate. It is commonly distinguished into two cases, Alligation Medial, and Alligation Alternate. ALLIGATION MEDIAL. ALLIGATION MEDIAL is the method of finding the rate or quality of the composition, from having the quantities and rates or qualities of the several simples given. And it is thus performed: * MULTIPLY the quantity of each ingredient by its rate or quality; then add all the products together, and add also all * Demonstration. The rule is thus proved by Algebra Let a, b, c be the quantities of the ingredients, and m, n, p their rates, or qualities, or prices; then am, bn, cp are their several values, and ambn + cp the sum of their values, also a+b+c is the sum of the quantities, and if denote the rate of the whole composition, then a + b + c xr will be the value of the whole, conseq. a+b+c xr = am + bn + cp, and r = am + bn + cp ÷ a + b + c, which is the Rule. Note, If an ounce or any other quantity of pure gold be reduced into 24 equal parts, these parts are called Caracts; but gold is often mixed with some base metal, which is called the AHoy, and the mixture is said to be of so many caracts fine, according to the proportion of pure gold contained in it; thus, if 22 caracts of pure gold, and 2 of alloy be mixed together, it is said to be 22 caracts fine. If any one of the simples be of little or no value with respect to the rest, its rate is supposed to be nothing; as water mixed with wine, and alloy with gold and silver. VOL. I. 18 the. |