Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

Exam. 7. Required the interest of £429 - 17 - 4, from June 29, 1841, till Feb. 12, 1842, at 5 per cent. per annum.

The number of days from the 29th of June, till the 12th of February following, is found, by the method shown in page 72, to be 228; and the interest of £429 17 - 4 for a year, computed (by Rule I.) to be £21-9-10. Then, as 365 days: 228 days :: £21-9-10 £13-8-61, the interest required.

It will readily be seen, that this and all similar questions may be wrought by compound proportion. The terms will be arranged thus::

As £100

: £5

365 days: 228 days}::£429 - 17 - 4 : £13 - 8 - 64, answ.

Exercises. Find the interests of the following sums, for the proposed times, and at the assigned rates per cent. per annum :—

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors]

38. Required the interest of 15 guineas from March 17, 1840, till January 26, 1842, at 6 per cent. per annum

39. What is the interest of £53 - 6 - 8, from June 14, 1841, till Sept 22, 1843, at 4 per cent. per

annum

1 15 2

5 9 12

RULE III. To find the interest of a given sum for any number of days: Multiply the principal by twice the rate, and the product by the days, and divide the result by 73,000.

The division by 73,000 may be performed by the following rule :Below the dividend write one third of itself, one tenth of that third, and one tenth of that tenth, rejecting shillings and remainders: then add the four lines together, divide the sum by 100,000 (or cut off five figures), and reject a farthing for each £10 in the result.*

*The exact correction is a farthing for £10 - 8 8-41. The reason of this process will appear from performing the operation indicated in it on 73,000, the result being 100,010. Now 10, the excess of this above 100,000, is contained in it 10,001 times, and 10,001 farthings are £10 - 8

The tenths will be obtained by setting the figures one place to the right hand, and rejecting the last of them.

Exam. 8. What is the interest of £372 - 10 - 10, from February 12, till December 17, 1840, at 41 per cent. per annum?

1840 being a leap year, the number of days is found to be 309; and the product of this, of the given principal, and of 9 (twice 4), being found, as in the margin, is £1036077, which being divided by 73,000, the quotient is £143 101, the interest required. The division by 73,000, by the second mode, will stand as in the margin, below the answer as found by the first method. After cutting off five figures, we have £14 remaining to the left. Then, according to the method shown in page 225, we divide the number expressed by the next two figures by 5, and obtain for quotient 3 shillings, with the remainder 4. Prefixing this to the next figure, we have 44;

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

and rejecting 2, for a twenty-fifth of 44, we have remaining 42 farthings, or 10d. We then correct the result by rejecting one farthing, and we find the same result as before.

The reason of the rule will be evident from the operation by compound proportion, if, instead of £100 and the rate per cent., their doubles be employed. Thus, we should have, in this exercise :

As £200 £9

365 days: 309 days}

:: £372-10-10: £14 - 3 - 101;

[ocr errors]

and, in working this by the rule for compound proportion, we should multiply together the principal, the days, and twice the rate, and divide the product by 365 x 200, or 73000.

When the rate is 5 per cent., since the double of 5 is 10, we merely divide the product of the principal and the days by 7300.

Exercises.

£ S. d.

40. 648 15 6 from June 2, till Nov. 25, at 5

Mar. 23, Nov. 2, 6

[blocks in formation]

41. 14 0

0

[merged small][merged small][merged small][ocr errors][merged small]

19 0 6

[blocks in formation]

45. 66 8 0 May 6,

46. Required the interest of £14 for 3 years and 122 days, at 6 per cent. per annum

2 16 0

Aug. 21,

-5

1 1 5

The following rule will be found easy and useful in interest and discount:

RULE IV. To find the interest of a given principal for any number of days, at 4 per cent. per annum: (1.) Multiply the principal by the days: (2.) to the product add one tenth of itself: (3.) from the sum take four times the same product, wanting the last three figures: (4.) divide what remains by 10,000 (or cut off four figures); the quotient will be the answer nearly. (5.) When the interest is large, reject a farthing for each £10 contained in it.

For other rates than 4 per cent. increase or diminish the product of the principal and days, by the method. of aliquot parts, and then proceed by the rule.

Exam. 9. Required the interest of £8985 - 14, for 12 days, at 4 per cent. per annum.

£8985 - 14

12

107828 - 8

10783

118611

431

11,8180

Here the product of the principal and days is £107828 nearly, and the tenth of this (found by setting each figure one place nearer the right-hand side, and increasing the unit figure by 1, because 28 is nearly 30) being added to it, the sum is 118611. After this, we multiply 107 by 4, and increase the product by 3 (carried for 4 times 8, the first of the figures cut off). The result, 431, is then subtracted, and the remainder, 118,180, di- £11 - 16 vided by 10.000, in the way pointed out in the last example. The quotient is £11 - 16 - 4}; £11 - 16 from which, because it is nearly £10, a farthing is subtracted, and the remainder, £11 - 16 - 4, is the interest required. Had the rate been 5 per cent. we must have increased £1078288, by one fourth of itself, and then have added to the result one tenth of itself, &c.

4

4, answ.

With respect to the reason of this easy and expeditious rule, the reader who has studied decimal fractions will find, by the last rule, that the interest of £1, for 1 day, at 4 per cent. per annum, is £8÷73000, or £0001096, nearly, or £00011-£0000004, nearly : and it will appear, on a little consideration, that the operation by the rule is nothing else than multiplying by 00011 and 0000004,

*The following method of finding interest for days at 6 per cent. per annum may be found useful, when the interest to be found is not very large :-Divide the product of the principal and days by 100; take one third of the quotient for shillings, and one sixth of the remainder for farthings; and from the sum thus obtained reject a penny for each six shillings contained in it; the remainder will be the interest required, nearly. Another correction may sometimes be made, by adding to the result obtained by the preceding part of the rule, a penny for each six shillings contained in the first correction; or a penny for each £20 in the entire interest will give nearly the same correction.

and taking the difference of the results. The correction is necessary, because the decimal £0001096 is not the exact interest of one pound for a day.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

The computation of interest, on accounts current, affords a useful application of the preceding principles. An ACCOUNT CURRENT Contains a statement of the mercantile transactions of one person with another, when immediate payments are not made. It is usually written on two pages, marked Dr. and Cr. (Debtor and Creditor), in the manner of a Ledger account, the left-hand page containing the payments made by the merchant who furnishes the account, and the other what is paid to him. At the foot of this page and the next, there is a specimen of this kind of account; and the following is the method of computing the interest on it, at 4 per cent. per annum:

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

For rightly understanding this computation, it is necessary to consider, that the account is made up till the 10th of December, and the interest calculated on it till that date. We place in a column, as above, all the sums on the debit side, and then all those on the credit side, prefixing to both their dates. To the former, also, we prefix the word to, and to the latter by, for the sake of distinction. We next find, successively, the number of days between Feb. 10 and Dec. 10, between Feb. 25 and Dec. 10, &c., and place them in the next column. A debit column and a credit one (marked Dr. and Cr.), are then formed, and all the sums on the debit side are multiplied by the corresponding number of days, and the products are placed in the debit column. In like manner, the products of the sums on the credit side, by the days which follow them, are placed in the credit column. The sums of the two columns are then taken, and the debit side is found, by subtraction, to exceed the other side by 45336; which, by means of Rule IV. (or of Rule III.), gives £4-1941, the interest due on the entire account. This is placed on the debit side of the account; and then the sum of all on the credit side is taken from the sum of all on the debit side, and the remainder £106 - 13 - 101, is placed on the credit side, as the sum due by the person to whom the account is furnished. It is scarcely necessary to say, that the last two lines, in Italics, form the answer of the account.

The pupil ought not only to perform the computation of the interest on the following accounts current, but also to write the accounts out, in proper form, on a sheet of paper, after the manner of the specimen given at the foot of this page and the preceding. The answers are in the lines which are printed in Italics,

Exer. 54, 55, 56. Required the principal and interest due on each of the following accounts current, till the date at the end of each, the first at 6, the second at 5, and the third at 6 per cent. per

annum.

Dr. 1842 |

Mr. J. Fox, in Account Current with S. BELL.

May 19 To goods
Aug. 23 To tea

Oct. 4 To goods
Nov. 18 To sugar
1843 To balance

[ocr errors]

......

......

Jan. 18 of interest Š

...

£ s. d. 1842

512 12 6 June 13 By cash

273 8 0

186 10 0
272 5 0

10 4 11

£1255 0 5

Cr.

£ s. d.

400 18 0

680 0 0

[blocks in formation]

Nov. 8 By wheat
Dec. 1 By bill

[blocks in formation]

Current with CHARLES CAULFIELD, Belfast.

1842

new account

[blocks in formation]

Mar. 24 By amount of flour

[blocks in formation]

April 6

By cash

347

Sept. 26 By bill on Cavan & Co., Dublin

200

Dec. 10

By balance to your debit in a new account_106

[blocks in formation]

£821

5 2

« ΠροηγούμενηΣυνέχεια »