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INTEREST for a year, may also be readily calculated by taking the interest on £1, according to the percentage table, page 94, and multiplying it by the number of pounds in the given sum.

Thus, to find the interest on £22, at 23 per cent., multiply 6d., the interest on £1, by 22, and the answer is Ils.: or to find the interest on £37, at 5 per cent., multiply 1s., the interest on £1, by 37, and the answer is 37s. £1, 17s. When there are shillings or pence in the given sum, take the proportion of the interest for a pound.

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INTEREST for a year at 23 per cent. on any number of pounds, may be readily found as follows:

Cut off the last figure of the principal, and divide the rest of the sum by 4; the quotient is the pounds of the answer: annex to any remainder, the figure that was cut off, and the half of this sum, reckoned as shillings-or if there is no remainder, the half of the figure that was cut off is the shillings and pence of the answer.

This process is merely a short way of dividing by 40-as 23 is the fortieth part of 100.

Example.-What is the interest on £437, at 23 per cent. ?

£ 4)43,7

10 18 6

Here we cut off the 7, and on dividing 43 by 4, the answer is £10, and 3 over. Annex to the 3 the figure cut off, 7, making 37, counted as 37s. and the half of this is 18s. 6d. The interest, therefore, is £10, 18s. 6d.

INTEREST for a year at 5 per cent. on any number of pounds, may be found as follows:

Cut off the last figure of the principal, and divide the rest of the sum by 2; the quotient is the pounds of the answer: if there is 1 over, annex to it the figure cut off, and this sum is the shillings of the answer; or if there is no remainder, the figure cut off is the shillings of the answer.

This process is merely a short way of dividing by 20-as 5 is the twentieth part of 100.

Example.-What is the interest on £276, at 5 per cent.?

£
2)27,6
£13 16

Here we cut off the 6, and on dividing by 2, the answer is £13, and I over: annex the 1 to the 6 cut off, making 16, which is the shillings of the answer.

II. TO FIND THE INTEREST FOR ANY NUMBER OF YEARS.

RULE. Find the interest for one year by Rule I. and then multiply the amount by the number of years.

Example. What is the interest on £162, 14s. 11d. for 2 years, at 3 per cent. ?

£162 14 11

3

100)488 4 9

4 17 72 180
2

Interest, £9 15 3

Here we find by Rule I. that the interest for one year is £4, 178. 73d. Too, which we multiply by 2, for the two years.

Exercises.-What is the interest on the following sums?

1. £847 16 8 for 2 years, at 3 per cent. Ans. £50 17 4

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III. TO FIND THE INTEREST FOR ANY NUMBER OF MONTHS. RULE.-Find the interest for a year by Rule I. and then take the,, or some other aliquot part of the amount, according to the number of months.

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Example.-What is the interest on £80 for three months, at per cent.? 4)£4

£1 Answer.

Here £4, the interest of £80 for 1 year, is divided by 4, as 3 months are of a year.

INTEREST at 5 per cent. may be conveniently found by reckoning the pounds of the given sum as so many pence, and then multiplying them by the number of months (interest at 5 per cent. being equal to ld. a £ per month).

Thus, to find the interest on £24 for 5 months, reckon the £24 as 24d.=2s., then multiply by 5, and the answer is 10s. If there are shillings and pence in the given sum, add the proportion of the interest for £1.

Exercises.-What is the interest on the following sums?

1. 187 16 10 for 5 months, at 4 per cent. Ans. £3 10 5 2. 1395 6 8 " 3

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IV. TO FIND THE INTEREST FOR DAYS.

RULE.-Multiply the principal by the number of days, and the product by twice the rate per cent.; then divide the result by 73,000 the quotient is the answer required.

NOTE.-INTEREST at 5 per cent. is found by multiplying the principal by the number of days, and dividing the product by 7300. This is merely an abridgment of the general rule.

Example.-What is the interest on £235, 10s. for 125 days, at 3 per cent.?

£235 10 125 29,437 10

6

73,000)176,625 0(£28 4 Ans.

Here we multiply the principal by the number of days, 125, and the product by twice the rate per cent., 6, and then divide the last product by 73,000 for the answer.

THE DIVISION BY 73,000 may be readily performed by the following rule, termed 'the third, tenth, and tenth rule:'

RULE. After multiplying by the number of days, and twice the rate per cent. write below the pounds of the product (the shillings and pence not being reckoned), of itself, of the third, and of that tenth; and add the four lines together: then cancel the two last figures; reckon the two next figures as so many farthings-less 1 farthing for every 25; the double of the next figure as so many shillings; and the rest of the figures as so many pounds. The whole forms the answer, and is nearly correct-there only requires a farthing to be subtracted for every £10 in the answer, to give nearly the exact interest.

Example.-Divide £357,200 by 73,000.

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357,200 = 119,066 = 11,906 = 1,190

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Ans. £4 19 10

Here, after adding 1-3d, 1-10th, and 1-10th to the sum, we cancel the two last figures of the total: we then reckon 93 as so many farthings -less 3, as there are 3 times 25 in 93, making 90, or 1s. 10d.; the double of 9 is reckoned as so many shillings, or 18s., and the other figure, 4, as 4 pounds. The answer is £4, 19s. 10d. which is about more than the exact sum.

THE DIVISION by 7300, in the case of 5 per cent. is performed in the same way as that by 73,000, only, instead of cancelling the two last figures as above, cancel merely the last figure.

Exercises.-What is the interest on the following sums?

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7. What will £328, 16s. 11d. amount to, at 2 per cent. interest, from January 7 to March 29 ? *

8. Find the interest on £584, 11s. August 17, at 3 per cent.?

9. What will £816, 17s. 63d. amount from June 14 to September 25?

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Ans. £330, 15s. 22d. 402030 34d. from February 21 to Ans. £10, 12s. 74d. 200 to, at 43 per cent. interest, Ans. £826, 19s. 32d. 39263 14s. 6d. from August 10 to Ans. £12, 16s. 114d. 41275

10. What is the interest of £875, December 14, at 44 per cent. ? 11. What is the interest of £697, 8s. 54d. from June 17 to December 31, at 5 per cent.? Ans. £18, 16s. 5d.

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*NOTE.-In exercises 7 to 11, we require to calculate, in each case, the number of days from the one given period to the other. The following is the method of calculating the number of days-as, for instance, from January 7 to March 29— Jan. 24

Feb. 28
Mar. 29

Ans. 81 days.

Here we take the remaining days in January after the 7th, then the days in February, and the days in March up to the 29th, and add them all together. The day reckoned from is not counted, but that to which we reckon, is counted.

V. TO CALCULATE THE INTEREST ON SUMS OR DEBTS WHEN PARTIAL PAYMENTS ARE MADE.

A partial payment of a debt is made, when part of the principal is repaid after a certain time, leaving the balance at interest for a longer period.

RULE.-Multiply each sum or balance due, by the number of days that it lies at interest, and add together the different products; then multiply the sum-total by twice the rate per cent. and divide the result by 73,000.

Example.-A sum of £300 was borrowed on March 16; of which £50 were repaid on April 7, £100 on July 16, and the balance, including interest at 4 per cent., on October 11; how much will the last payment amount to?

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Here £300 lies at interest from March 16 to April 7, that is, 22 days; we therefore multiply 300 by 22. On April 7, £50 were paid, and the balance, £250, lies at interest from April 7 to July 16, that is, 100 days; we therefore multiply 250 by 100. Again, on July 16, £100 were paid, 16 to October 11, We now add the

and the balance, £150, lies at interest from July that is, 87 days; hence we multiply 150 by 87. products, and multiply their sum, 44650, by 8, twice the rate per cent. and then divide the product by 73,000; the interest is £4, 178. 10 d. to which we add £150, the balance due at July 16; and the sum, £154, 17s. 10d. is the amount of the last payment.

Exercises.

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1. A person borrowed £500 on February 2: he repaid of this sum on May 15, on August 1, on November 11, and the remaining, together with the interest, on December 31. Required the amount of the last payment, Ans. £140, 6s. 102d. 2. Required the interest at 33 per cent. on £320, due on September 11, 1846, of which £116 were paid on November 23, £50 on December 21, £100 on January 19, 1847, £30 on February 22, and the balance on May 11, Ans. £3, 16s. 6d. 1

3. I lent £456 to a friend on March 14, and received as partpayment, £66 on April 30, £130 on July 11, £120 on August 15, £100 on October 19, and the balance on November 30; how much interest have I to receive, at this last date, at 3 per cent.? Ans. £6, 13s. 02d. 181

VI. TO CALCULATE THE INTEREST ON ACCOUNTS-CURRENT.

AN ACCOUNT-CURRENT is an account in which is drawn out, in Dr. and Cr. (Debtor and Creditor) columns, a statement of the transactions that have taken place between two parties.

Example.-Required the interest at 4 per cent. on the following account-current to June 30.

Dr. Mr J. SIMPSON, in Account-current with R. Duff.

Cr.

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This account is drawn out by R. Duff, and sent to J. Simpson on June 30. On the left or Dr. side are written all the sums that Simpson owes to Duff; and on the Cr. side the sums that Duff owes to Simpson. Interest at 4 per cent. is then calculated on the account, as below; and as Duff finds that Simpson is due him £3, 8s. 24d. of interest, he enters it on the Dr. side. He next adds the Dr. side, and finds the amount to be £1696, 19s. 94d.; then the Cr. side, which amounts to £1543, 11s. 4d. The difference between these, £153, 8s. 5d. is entered on the Cr. side, to balance the account, and then transferred to the Dr. side of a new account, shewing that J. Simpson is owing R. Duff £153, 8s. 5§d.

INTEREST on the account is calculated as follows:

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73,000) 248,936 Interest, £3 8 2

As the account is supposed to be settled up to June 30, the interest is calculated according to Rule V. page 100, on all the sums on both sides of the account, up to that date: as, for instance, on £360, 14s. 9d. from January 18 to June 30, or for 163 days; and so on. The products of the Dr. side are placed in one column, and of the Cr. side in another; each column is then added, and the smaller of the two sums deducted from the greater; the interest is then calculated on the difference; and the Dr. products in this case being the greater, the interest is entered on the Dr. side of the account

current.

In multiplying the sums by the number of days, the shillings and pence of the products have, for convenience, been left out.

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