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? each officer must have 231 2s 5d 0.939each midshipman Ans. each seaman 92 69 17 6 9 3173. Ex. 5. H, with a capital of 1000/, began trade the first of January, and, meeting with success in business, took in 1 as a partner, with a capital of 1500/, on the first of March following. Three months after that they admit K as a third partner, who brought into stock 2800/. 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 457/ 9s 44d 6. x, y, and z made a joint-stock for 12 months; x at first put in 20%, and 4 months after 20/ more; Y put in at first 301, at the end of 3 months he put in 20/ more, and 2 months after he put in 40/ more; z put in at first 60%, and 5 months after he put in 10/ more, 1 month after which he took out 30/; during the 12 months they gained 50/; how much of it must each have? Ans. x must have 10/ 18s 6d 3499. 22.8 1 077. 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 100/ 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. 4; But, by law, 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 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 230/ 10s, for 1 year, at the rate of 4 per cent. per annum. Here, As 100: 4 :: 230/ 10s: 91 4s 43d. Ex. 2. To find the interest of 541 15s, for 3 years, at 5 per 3. To find the interest of 200 guineas, for 4 years 7 months and 25 days, at 4 per cent. per annum. 210/ 840 105 ds ds 4. To find the interest of 4501, for a year, at 5 per cent. per annum. Ans. 22/ 10s. 5. To find the interest of 715 12s 6d, for a year, at 4 per cent. per annum. Ans. 321 4s 03d. 6. To find the interest of 7201, for 3 years, at 5 per cent. per annum. 7. To find the interest of 355/ 15s for 4 years, at 4 per cent. per annum. Ans. 108/. Ans. 56/ 18s 44d. 1 Ex. 8. To find the interest of 321 5s 8d, for 7 years, at 44 per cent. per annum. Ans. 9/12s 1d. 9. To find the interest of 1701, for 1 year, at 5 per cent. annum. per annum. Ans. 12/155. 10. To find the insurance on 205/ 15s, for of a year, at 4 per cent. per annum. Ans. 2/ is 13d. 11. To find the interest of 3191 6d, for 5 years, at 33 per cent. per Ans. 68/ 15s 9d. 12. To find the insurance on 1077, for 117 days, at 4 per cent. per annum. Ans. 1/ 12s 7d. 13. To find the interest of 17/ 5s, for 117 days, at 43 per cent. per annum. Ans. 5s 3d. 14. To find the insurance on 712/ 63, for 8 months, at 7 per cent. per annum. Ans. 35/ 12s 3žd. 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. from the first Rule. As is evident EXAMPLES. d 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 1/ for a year is or '05, and its amount 1.05. 1. By the 1st Rule. Therefore, 1:05 amount of 11. 1.05 1.1025 2d power of it. 1.1025 1.21550625 4th pow. of it. 720 / 875.1645 20 S 3.2900 12 d 3.4800 41 13 £875 3 34 the whole amo'. or ans. required. 2. To find the amount of 501, in 5 years, at 5 per cent. per annum, compound interest. Ans. 637 16s 34d. 3. To find the amount of 50/ in 5 years, or 10 halfyears, at 5 per cent. per annum, compound interest, the interest payable half-yearly. Ans. 64/ Os 1d. 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. 64/ 2s Old. 5. To find the compound interest of 370/ forborn for 6 years, at 4 per cent. per annum. Ans. 98/ 3s 44d. 6. To find the compound interest of 410/ forborn for 24 years, at 4 per cent. per annum, the interest payable halfyearly. Ans. 48/ 4s 114d. 7. To find the amount, at compound interest, of 217, forborn for 24 years, at 5 per cent. per annum, the interest payable quarterly. Ans. 242/ 13s 44d. Note. See the Rules for Compound Interest algebraically investigated, at the end of the Algebra. ALLIGATION. |