Ex. 2. To find the interest of 5471 15s, for 3 years, at 5 per cent. per annum. As 100 : 5 :: 547.75 : 3 20 12 or 3. To find the interest of 200 guineas, for 4 years 7 months and 25 days, at 45 per cent. per annum. ds 1 ds 1 5 : •6472 5 73) 47.25 (6472 345 9:45 interest for 1 yr. 530 4 19 37.80 6 mo = { 4.725 ditto 6 month. 1 mo ő •7875 ditto 1 month. .6472 ditto 25 days. ditto 4 years. 1 9 1.3120 4. To find the interest of 450l, for a year, at 5 per cent. per annum. Ans. 221 10s. 5. To find the interest of 7151 12s.6d, for a year, at 4, per cent. per annum. Ans. 321 4s 0 d. 6. To find the interest of 7201, for 3 years, at 5 per cent. per annum. Ans. 1081. 7. To find the interest of 3551 15s for 4 years, at 4 per cent. per annum. Ans. 56l18s 4d. Ex. 8. To find the interest of 321 5s 8d, for 7 years, at 44 per cent. per annum. Ans. 9/ 12s ld. 9. To find the interest of 1701, for 1 year, at 5 per cent. per annum. Ans. 121 155. 10. To find the insurance on 2051 15s, for of a year, at 4 per cent. per annum. Ans. 21 1s 11d. 11. To find the interest of 3191 6d, for 5 years, at 3 per cent. per annum. Ans. 68/ 15s 9 d. 12.' To find the insurance on 1071, for 117 days, at 4. per cent. per annum. Ans. 11 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 7121 65, for 8 months, at 7 per cent. per annum. Ans. 351 12s 3 d. 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 inuch 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. Rules.--1. Find the amount of the given principal, for the time of the first payment, by Simple Interest. Then consider 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. EXAMPLES. 1. To find the amount of 7201, for 4 years, at 5 per cent. per annum. Here 5 is the 20th part of 100, and the interest of 1l for a year is zo or .05, and its amount 1•05. Therefore, 1. By the 1st Rule. 2. By the 2d Rule. 1:05 amount of 11. 20 ) 720 0 0 1st yr's princip. 1:05 36 0 0 1st yr's interest. 1.1025 2d power of it. 20) 756 0 0 2d yr's princip. 1:1025 37 16 0 2d yr's interest. 1.21550625 4th pow. of it. 20 ) 793 16 0 3d yr's princip. 720 39 13 92 3d yr's interest. 1875.1645 20) 833 9 9 4th yr's princip. 20 41 13 54th yr's interest s 3.2900 £ 875 3 3 the whole amo'. or ans. required. d 3.4800 12 2. To find the amount of 501, in 5 years, at 5 per cent. per annum, compound interest. Ans. 637 16s 3 d. 3. To find the amount of 501 in 5 years, or 10 halfyears, at 5 per cent. per annum, compound interest, the interest payable half-yearly. Ans. 641 Os Id. 4. To find the amount of 501, in 5 years, or 20 quarters, at 5 per cent. per annum, compound interest, the interest payable quarterly. Ans. 641 2s 0.1d. 5. To find the compound interest of 3701 forborn for 6 years, at 4 per cent. per annum. Ans. 98/ 3s 4 d. 6. To find the compound interest of 4101 forborn for 24 years, at 41 per cent. per annum, the interest payable halfyearly. Ans. 481 4s 11 d. 7. To find the amount, at compound interest, of 2171, forborn for 25 years, at 5 per cent. per annum, the interest payable quarterly. Ans. 2421 13s 4 d. 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 um, bn, cp are their several values, and am + bn + cp the sum of their values, also a + b + c is the sum of the quantities, and if r denote the rate of the whole composition, then a + b + c X r will be the value of the whole, conseq. . a + b + cxr=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 Alloy, 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. K the the quantities together into another sum ; then divide the former sum by the latter, that is, the sum of the products by the sum of the quantities, and the quotient will be the rate or quality of the composition required. EXAMPLES. 1. If three sorts of gunpowder be mixed together, víz. 50lb at 12d a pound, 441b at 9d, and 261b at 8d a pound; how much a pound is the composition worth? Here 50, 44, 26 are the quantities, 9 = 396 120) 1204 ( 10ro = 1036 Ans. The rate or price is 1035d the pound. 2. A composition being made of 5lb of tea at 7s per lbs 9lb at 8s 6d per lb, and 14 lb at 5s 100 per lb; what is a lb of it worth? Ans. 6s 10 d. 3. Mixed 4 gallons of wine at 4s 10d per galt, with 7 gallons at 5s 3d, per gall, and 9: gallons at 5s 8d per gall; what is a gallon of this composition worth? Ans. 5s 4 d. 4. A mealman would mix 3 bushels of flour at 35 5d per bushel, 4 bushels at 5s 6d per bushel, and 5 bushels at 4s 8d per bushel; what is the worth of a bushel of this mixture ? Ans. 4s 7d. 5. A farmer mixes 10 bushels of wheat at 5s the bushel, with 18 bushels of rye at 3s the bushel, and 20 bushels of barley at 2s per bushel: how much is a bushel of the mixture worth? Ans. 35. 6. Having melted together 7 oz of gold of 22 caracts fine, 12oz of 21 caracts fine, and 17 oz of 19 caracts fine : I would know the fineness of the composition ? Ans. 20%} caracts fine. 7. Of what fineness is that composition, which is made by mixing 31b of silver of 9 oz fine, with 5lb 8 oz of 100% fine, and ilb 10 oz of alloy, Ans. 765 oz fine. ALLIGATION |