RULE.*-Multiply each person's stock by the time of its continuance; then divide the quantity, as in Single Fellowship, into shares, in proportion to these products, by saying, As the total sum of all the said products, Is to the whole gain or loss, or quantity to be parted, To the correspondent share of the gain or loss. EXAMPLES. B 1. A had in company 501 for 4 months, and в had 60l for 5 months; at the end of which time they find 241 gained : how must it be divided between them? Here 50 60 5 Then, as 500: 24:: 200: 93 91 12s A's share. and as 500 24: 300: 14% = 14 8 = B's share. pay of 2. C and D hold a piece of ground in common, for which they are to pay 541. c put in 23 horses for 27 days, and d 21 horses for 39 days; how much ought each man to the rent? Ans. c must pay 231 5s 9d, D must pay 30 14 3 4. Three persons, E, F, G, hold a pasture in common, for which they are to pay 30 per annum; into which E put 7 oxen for 3 months, F put 9 oxen for 5 months, and G put in 4 oxen for 12 months; how much must each person pay the rent? Ans. E must pay 5l 10s 6d 159. F of 11 16 100, it 12 12 72. 4. A ship's company take a prize of 1000l, which they agree to divide among them according to their pay and the time they have been on board: now the officers and midshipmen have been on board 6 months, and the sailors 3 months; * The proof of this rule is as follows: When the times are equal, the shares of the gain or loss are evidently as the stocks, as in Single Fellowship; and when the stocks are equal, the shares as the times; therefore, when neither are equal, the shares must be as their products. ^ the the officers have 40s a month, the midshipmen 30s, and the sailors 22s a month; moreover there are 4 officers, 12 midshipmen, and 110 sailors; what will each man's share be? Ans. each officer must have 231 28 5d 02. each midshipman 17 6 9 3. each seamen 6 72 043. as a Ex. 5. H, with a capital of 10001, began trade the first of January, and, meeting with success in business, took in partner, with a capital of 1500/, on the first of March following. Three months after that they admit к as a third partner, who brought into stock 2800l. After trading together till the end of the year, they find there has been gained 1776/ 10s; how must this be divided among the partners ? Ans. H must have 4571 9s 41d. 571 16 81. I 747 311. 6. x, y, and z made a joint-stock for 12 months; x at first put in 201, and 4 months after 201 more; v put in at first 301, at the end of 3 months he put in 201 more, and 2 months after he put in 40/ more; z put in at first 601, and 5 months after he put in 10/ more, 1 month after which he took out 301; during the 12 months they gained 501; how much of it must each have? Ans. x must have 10l 18s 6d 3489. 22 8 1 017. 16,13 4 0. SIMPLE INTEREST. INTEREST is the premium or sum allowed for the loan, or forbearance of money. The money lent, or forborn, is called the Principal. And the sum of the principal and its interest, added together, is called the Amount. Interest is allowed at so much per cent. per annum; which premium per cent. per annum, or interest of 1001 for a year, is called the rate of interest : :-So, When When interest is at 3 per cent. the rate is 3; 4 per cent. 5 per cent. 6 per cent. 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 calcula-tion. As 100 is to the rate of interest, so is any given principal to its 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 : 9l 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. 3 182.1625 ditto for 3 years. 20 s 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. ι ds 9.45: 25: l 5:·6472 73: 9.45: 5 73) 47.25 (-6472 345 530 19 9 1.3120 4. To find the interest of 4501, for a year at 5 per cent. Ans. 22/ 10s. per annum. 5. To find the interest of 715 12s 6d, for a year, at 41 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. 1087. 7. To find the interest of 355l 15s, for 4 years, at 4 per cent. per annum. Ans. 561 188 43d. 8. To find the interest of 321 5s 8d, for 7 years, at 41 per cent. per annum. Ans. 91 12s 1d. 9. To find the interest of 170l, for 11 year, at 5 per cent. per annum. Ans. 127 58. 10. To find the insurance on 205l 15s, for of a year, at 4 per cent. per annum. Ans. 2l is 13d. 11. To find the interest of 319 6d, for 53 years, at 33 per cent. per annum. 12. To find the insurance on 2071, for cent. per annum. 13. To find the interest of 171 5s, for cent. per annum. Ans. 681 15s 91d. 117 days, at 43 per Ans. 1l 12s 7d. 117 days, at 43 per Ans. 5s 3d. 14. To find the insurance on 7121 6s, for 8 months, at 7 per cent. per annum. Ans. 35l 12s 31d. 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. 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 |