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find the interest of the following sums, for the proposed times, and at the rates per cent per annum, respectively assigned.
£ a d
31. 214 8.0 for 1 year and 4 months, at 5 per ct, per an. 32. 927 48 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 .......... *9 months at 34 per ct. per an. 35. 816 9 8 for . . . . . . . . . . 11 months at 6 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 33 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 7% months at 4 per ct. per an. 40. 870 176 for 3 years and 11 months at 64 perct. per an.
CAse 6th–To find the interest of 100l 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 or fourpences—but if the interest thus found should be 6s. 1d. or more, subtract lå. for every 6s. 1d. or or thereof, and the remainder will be the exact interest required.
Demonstration.— If the year consisted of but 360 days, the interest of 1001 would be 4d. per day; 6l make exactly 360 groats or 4 pences, and as 5 days are or of a year, therefore, the rule is manifests - Grample.
41. What is the interest of 1001 for 95 days, at 6 per cent. per annum ?
* 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 interests 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 be readily effected, by subtracting the dividend o'r thereof, and cutting off 4 figures for decimals, or which is the same thing, dividing by 10000.
42. Find the interest of 1001 for 43 days, at 6 + ct. *ah. ” 43. Find the interest of 100t for 135 days, at 6 + ct. *an.? 44. Find the interest of 100l for 168 days, at 6 p. ct. p an.? 45. Find the interest of 100l for 247 days, at 6 p. ct. *an.?
Case 7th.--To find the interest of 100l for days, at 5 per cent. per annum ? The days divided by 73 will give the exact interest required. For 5! is or of 1001, therefore, 11 per cent. is the interest of 20l for a year, or is the interest of 100l 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.
46. Find the interest of 100l for 146 days, at 5 per cent per annum ?
2,002 20 0} Correction, #
£2 00 47. Find the interest of 100l for 47 days, at 5 yet y an.” 48. Find the interest of 100l for 193 days, at 5 to ct. *an. : 49. Find the interest of 100t for 297 days, at 5 to ct, r 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 y, 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 100l in the remainder 4d., and proportionably for odd parts, this gives the interest in shillings too much by the or thereof, therefore, from the interest thus found, subtract lid. for every 6s. 1d. the remainder will be the true interest, which divided by 20, gives pounds.
Demonstration.—If the year consisted of but 360 days, at 6l 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 *r 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 20x300= 6000 the answer by this division is therefore found in pounds and decimals of a pound, too much by the or part as before.
50. Find the interest of 317. 15s. 0d. 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;
£ s d 61. 835 12 6 from January 1st to February 4th. 62. 945 l7 6 from June 6th to August 25th, 63. 841 94 from July 9th to September 15th. 64. 735 50 from May 1st to August 10th. 65. 1141 34 from April 9th to September29th.
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 10l therein, if the interest should be so much and the remainder will be the interest required true to the nearest farthing.
* The above rule is best illustrated by an example, Let the interest of £145 12s. 6d. for 97 days, at 34 per cent per annum be required. Then by compound proportion,
...herefore, by the omission of the cipher in each term, 73000 becomes 7300, which is the second part of the rule.
The exact correction is 4s. in each 175l, 10# farthings in each 10l, or loor farthing in each pound.
The reason of this rule will be evident, if from 7300, or 73000 one *25th thereof, be subtracted, with the first there will result a remainder of 7008, which being divided by 7000, will give 1+torol for the interest. -
Now the interest of 100l for 73 days is ll, therefore, the interest by the rule is row of a £ in each pound too much, which is 1-pyr farthing; from the second, there will result a remainder of 70080, which divided by 7000 will give 10, #3,1 for the interest. Now the interest of 100l for 2 years or 730 days is 101, therefore, the interest by the rule is rol too much, which is exactly 10+ farthings.
Gramples. Find the interest of 1145l 17s.6d. at 5 and at 6% per cent per annum, for 215 days.
36 s d £ s d 1145 176 1145 17 6 215 215 w 5725 Product as before, 246363 1145 - 13 double rate, 2290 3203719 17 6 188 12810876. “;s 7,0000)307,461024 7000).236,50848 43,923
Find the interest of the following sums for the several times, and at the rates respectively assigned. ar d- Days 66. 448 17 6 for 74 at 5 per cent. per annum. 67. 773 19 8 for 64 at 5 per cent. per annum. 68. 847 13 4 for 52 at 5+.per cent. per annum. * 69. 473 12 6 for 31 at 5% per cent. per annum. 70. 175 6 8 for 44 at 53 per cent. per annnm.
* To divide by 25 is to multiply by 4, because 4 is the 25th part of 100.
+ In the first example the correction is 37 farthings; for each pound a farthing, for each 10te farthing, and for the odd shillings and pence, an additioual farthing, being nearly another pound.