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 25 5d 0 1999 each midshipman 17 6 9 each seaman 6 7 2 0143 3175 Ex. 5. H, with a capital of 10001, began trade the first of January, and, meeting with success in business, took in 1 as a partner, with a capital of 15001, on the first of March following. Three months after that they admit k as a third partner, who brought into stock 2800l. After trading together till the end of the year, they find there has been gained 17761 10s; how must this be divided among the partners ? Ans. H must have 4577 9s 4d 571 16 87 747 3 114 I K 6. x, y, and z made a joint-stock for 12 months ; x at first put in 201, and 4 months after 201 more ; y 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 101 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 jol 18s 6d 3419. 22 8 1 07 16 13 4 0. Y Z 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 :-$o, When When interest is at 3 per cent. the rate is 3; 4; 5; 6 per cent. 6; 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 suni, 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 1001 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 2301 10s, for 1 year, at the rate of 4 per cent. per annum. Here, As 100 : 4 :: 230l 10s : 91 4s 4 d. 4 3.20 Ex.2. To find the interest of 5471 15s, for 3 years, at 5 per cent. per annum. As 100 : 5 :: 547075 : 3 years. or 3. To find the interest of 200 guineas, for 4 years 7 months and 25 days, at 4į per cent. per annum. ds I ds 1 5 : 6472 5 73 ) 47.25 (•6472 345 9:45 interest for 1 yr. 530 4 19 •7875 ditto 1 month. ditto 4 years: 1 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 45 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. 56/18s 4d. cent. per annum. 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 15 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 1d. 11. To find the interest of 3191 6d, 'for 5 years, at 3per 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 6s, for 8 months, at 74 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. 1 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 ca culate 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. .S 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 d 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 97 3d yr's interest. 1875.1645 20) 833 9 91 4th yr's princip. 20 41 13 54th yr's interest s 3.2900 £ 875 3 34 the whole amo'. 12 or ans. required. d 3:4800 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 d. 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 4 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 2 years, at 5 per cent. per annum, the interest payable quarterly. Ans. 2421 13s 44d. Note. See the Rules for Compound Interest algebraically investigated, at the end of the Algebra. ALLIGATION. |