16. What is the interest of 4607 15s for 1 year at 6 per ct 17. What is the interest of 4601 15s for 1 year at 5§ v ct 18. What is the interest of 7417 12s 6d for 1 yr at 51 ct 19. What is the interest of 8931 16s 8d for 1 yr at 44 ct Find the interests of the following sums for 1 year at the given rates per cent per annum? CASE 5th. To find the interest of any sum for years and months, at any rate per cent. Find the interest of 100 for the given time, per case 3d. and take such parts of the given sum, as the interest found may be of 1007, and the quotient or sum of the quotient, arising from dividing the given number by denominator or denominators of the aliquot part or parts will be the interest required. Where there are fractions thus produced, it will be best to find the interest of the given sum for 1 year, which multiply by the number of years, and add proportionably for the months. Examples. 30. What is the interest of 4691 10s. for 2 years and 9 months, at 6 per cent per annum ? 24×6=134 1469 10 Or thus, 10 To 46 19 2= 11 14 9 4 13 10 £63 7 74 6 2817 0 2817 0 3m. 704 5 100)6338 5 £63 7 74 Find the interest of the following sums, for the proposed times, and at the rates per cent per annum, respectively assigned. 31. 214 8.0 for 1 year and 4 months, at 5 per ct. per an. 32. 927 4 8 for 2 years and 9 months at 44 per ct. per an. 33. 491 7 6 for 1 year and 8 months at 5 per ct. per an. 34. 395 13 4 for 35. 816 9 8 for *9 months at 31⁄2 11 months at 6 per ct. per an. per ct. per an. 36. 475 16 8 for 3 years and 5 months at 34 per ct. per an. 37. 297 15 6 for 2 years and 7 months at per ct. per an. 38. 279 18 4 for 1 year and 10 months at 5 per ct. per an. 39. 654 15 0 for 2 years and 74 months at 4 per ct. per an. 40. 870 17 6 for 3 years and 11 months at 6 per ct. per an. CASE 6th. To find the interest of 1001 for days; at 6 per cent per annum. Divide the given number of days by 3, and the quotient will be the interest in shillings, the remainder, if any, will be groats fourpences-but if the interest thus found should be 6s. 1d. or more, subtract 1d. for every 6s. 1d. or thereof, and the remainder will be the exact interest required. or Demonstration. the interest of 100% would be 4d. per day; 61 make exactly If the year consisted of but 360 days, 360 groats or 4 pences, and as 5 days are of a year, therefore, the rule is manifest: Example. 41. What is the interest of 1001 for 95 days, at 6 per cent. per annum? 3)95 £1 11 24 *The interest of any sum for months, is readily found, by multiplying the principal, months and rate together, and dividing the last product by 1200. To find the interest of any sum for weeks, multiply the principal, weeks, and twice the rate continually together, and divide the last product by 10400. This division may he readily effected, by subtracting the dividends thereof, and cutting off 4 figures for decimals, or which is the same thing, dividing by 10000. T 42. Find the interest of 1001 for 43 days, at 6 pct. ↑ an. ? 43. Find the interest of 100 for 135 days, at 6 pct. p an. ? 44. Find the interest of 100% for 168 days, at 6 45. Find the interest of 100% for 247 days, at 6 ct. p an.? ct. an.? CASE 7th. To find the interest of 1007 for days, at 5 per cent. per annum ? The days divided by 73 will give the exact interest required. For 5l is of 100%, therefore, 17 per cent. is the interest of 201 for a year, or is the interest of 1001 for 73 days; whence the rule is manifest. This division by 73 may be much shortened, thus, multiply the days by 4, and put down the product two places removed towards the right hand, which subtract from the days, and divide the remainder by 7000, this will give the interest in pounds and decimals of a pound, from the value of which subtract one farthing for each pound therein, remainder will give the interest true to the nearest farthing.* When the rate is any other than 5 or 6, the interest may be found at either of these rates, which ever best answers, and to or from this interest, to add or subtract proportionably for the excess or deficiency. Examples. 46. Find the interest of 1001 for 146 days, at 5 per cent per annum ? 146 7,000)14,016 2,002 2001/ Correction, £200 ct an.? ct. ¥ zn. ? 47. Find the interest of 1007 for 47 days, at 5 48. Find the interest of 100 for 193 days, at 5 49. Find the interest of 100% for 297 days, at 5 ct. за an.? CASE 8th. To find the interest of any sum of money for days, at 6 per cent per annum. * A full demonstration of this rule will be given a little farther on: Multiply the given sum or principal by the days, divide the product decimally by 6000, and find the value of the quotient by inspection, from which subtract. the remainder will be the interest in pounds, shillings and pence. When the sum is small, multiply the given sum by the days, which divide by 300, annexing for every 1007 in the remainder 4d,, and proportionably for odd parts, this gives the interest in shillings too much by the thereof, therefore, from the interest thus found, subtract 1d. for every 6s. Id. the remainder will be the true interest, which divided by 20, gives pounds. Demonstration. If the year consisted of but 360 days, at 61 or 120 shillings per cent per annum, the interest would be exactly 4d. per day or 4d. for each pound for every 100 days; therefore, when the pounds and days are multiplied, every 100 in the product will be fourpences, and as three fourpences make a shilling, it is divided by 300 for shillings, and as 5 days are of 365 days or a year, the interest so found, is by this part too much, and therefore, must be subtracted. This being evident, the former rule must be equally apparent, as 20×300= 6000 the answer by this division is therefore found in pounds and decimals of a pound, too much by the part as before. Examples. 50. Find the interest of 2171 15s. Od. for 94 days, at 6 per cent per annum ? Find the interests of the following sums of money, for the days assigned respectively, at 6 per cent per annum? 61. 835 12 6 from January 1st to February 4th. 10th. CASE 9th. To find the interest for any sum of money for days, at any rate per cent per annum. Multiply the principal, days, and twice the rate, continually together, and divide the product by 73000. When the rate per cent is 5, the interest is found by simply dividing the product of the principal and days, by 7300.* The division by 73000 or 7300 may be performed by the following rule: Multiply the last product or dividend by 4, put down the product two places removed towards the right hand, which subtract from the dividend, and divide the remainder by 70000, or, if the rate be 5, divide by 7000, neglecting the two last figures, in either cases the quotient will be the interest nearly in pounds and decimals of a pound. From the value of this decimal subtract one farthing for each pound, and an additional farthing for each 10/ therein, if the interest should be so much and the remainder will be the interest required true to the 1 nearest farthing. *The above rule is best illustrated by au example, Let the interest of £145 12s. 6d. for 97 days, at 34 per cent per annum be required. Then by compound proportion, That is, as 36500 145 12 6 x 97: :3 Multiply first and third terms each by 2. And we have 73000 145 126 x 97:7: the interest, which is the rule. Therefore, by the omission of the cipher in each term, 73000 becomes 7300, which is the second part of the rule. |