7. A person possessed of £800 per annum devotes one-twelfth of his income to charity, and spends (on the average) £1, 15s. per day on other objects; how much does he save annually?

8. In a manufactory 15 per cent. or 90 of the employés are girls, and 20 per cent. are boys; there are 60 women, and the rest men; find how many boys and men are employed.

9. Of the boys in a school one-third are over 15 years of age, and one-third between 10 and 15. A legacy of £100 can be divided among them, by giving 10s. to each boy over 15, and 3s, 4d. to each of the rest; how many boys are there in the school?

Compound Interest.—Find the compound interest on £850 for 4 years at 5 per cent.

FIRST METHOD.-When the rate per cent. is given in a simple aliquot part of £100, as £4, £5, £2, 10s., £2, £10, £8, 6s. 8d., etc., the following easy method is employed:

£183 3 711 interest for 4 years.

Find the compound interest of £840 for 5 years at £8, 68. 8d. per cent. per annum.

The simple interest for 1 year is found and added to the principal; next, the simple interest for the second is found, which is also added to the principal, etc.

The fractions or aliquot parts arise in this way: To find the simple interest it has been shown that we must multiply by the number of years and rate per cent. and divide by 100. Instead of doing this, considering that we have in each individual case to find the interest for one year only, we multiply by the rate per cent. and divide by 100; but if the rate per cent. be divided by 100 first, and then the principal divided or really multiplied by the result, the same purpose will be effected. This is what is done in the above sums, 1. So in the first sum, instead of multiplying by 5 and dividing by 100, the same end is attained by dividing by 20; in the second sum, £8, 6s. 8d. 1 = ; hence, instead of multiplying by 83 and dividing by 100, the end is reached by a shorter method when we simply divide by 12, or multiply by 2, which is the same thing.

100

12

SECOND METHOD.-Find the compound interest on £854, 3s. 6d. for 4 years 5 months at £4, 5s. per cent. per annum.

£190 9 3.364 4 years 10 months.

(1.) The first year's interest is found and added to the principal.

(2.) With this principal the second year's interest is found and added to the second year's principal.

(3.) With this principal the third year's interest is found, and so on.

Lastly, each year's interest is added to find the whole gain.

EXERCISES.-LIII.

1. Find the compound interest on £1650 for 3 years at 5 per cent. per annum.

2. Find the simple and compound interest on £2000 for 3 years at 74 per cent.

3. To what will £850, 12s. 6d. accumulate in 4 years at 5 per cent. compound interest?

4. What interest will accrue to me on £500 left in the bank for 5 years at 3 per cent. per annum simple interest? Had the above sum been left at compound interest, how much more should I have had to receive?

5. Find the difference between the simple and compound interest on £100 for 5 years at 5 per cent. per annum.

6. A person has £17,350, for which he receives interest at the rate of 4 per cent. per annum. His expenditure is £500 a year, and the rest he puts out to interest each year at the same rate; what will be his property at the end of 4 years?

7. Find the difference between the simple and compound interest of £40, 13s. 4d. for 3 years at 4 per cent.

PROFIT AND LOSS.

THE aim of Profit and Loss is to show in mercantile negotiations, the gain or loss on any transaction; this gain or loss is generally calculated on each £100. It is always to the interest of the trader to know how much his profit is per cent., i.e., centum or hundred ; then if his dealings do not return sufficient interest for his money, considering the risks incurred, he can find an outlet for it in funds, bonds, etc., where, although the interest may be less, it is certain and regular.

Profit and Loss is that branch of arithmetic which treats of the gain or loss on mercantile transactions.

The resolution of such problems, as are given under the heading of Profit and Loss, require a little thought and common sense; they involve no difficulties that have not been already surmounted in former rules. In solving questions on

gain or loss, the pupil must be very careful to notice whether the gain is calculated on the selling price or cost price; there is a wide distinction in the following:

Suppose it be said that a tradesman's profits are 25 per cent., the question first arises, Is this 25 per cent. on the money laid out, or on the till takings, i.e., the money that comes in. If it be 25 per cent. on his money laid out, that is equivalent to 20 per cent. of the cash coming into the shop. Thus it will be seen that a wide distinction exists; there can be no doubt that all profit should be calculated on the money expended in the purchase of articles, and the cost of selling them, although it is convenient to know out of any given sum taken in commercial transactions how much is profit. The simplest mode to calculate this is as follows: if the tradesman marks his goods to gain 25 per cent., is profit; if 20 per cent., is profit; if 10 per cent., is profit; if 5 per cent., is profit. The way these fractions are obtained is as follows: 25 goes into 100 four times, add 1 to 4 is 5, the profit is ; 10 into 100 goes 10 times, add 1 makes 11, the profit is . Thus if profit is 20 per cent, the articles are sold for £120, the 20 is profit, 20 goes into the 100 five times, and once into itself makes 6, hence the profit is of the whole as above.

If a tradesman buy an article for 20s. and sell it for 24s., his profit is apparently t, or 20 per cent., on this single transaction, but the profit is not absolutely 20 per cent. There are other considerations to bear in mind, such as:

(1.) Capital sunk: when commencing business, it did not pay at first, a loss ensued; this was put down to capital, and has to bear interest.

(2.) Fixtures, repairs of same, shop expenses, assistance, gas, fuel, bad debts, deterioration of stock.

(3.) Booking debts, or the abominable credit system, is always a loss to the purchaser; the tradesman has to turn over his money, and to realise a due amount of interest and profit; hence if a man has a debt standing on any tradesman's books, he must expect to pay interest. This is seldom charged directly, but has to be paid in the shape of a higher price for goods, and no abatement for the ready money he does lay out.

(4.) Rent, taxes, and necessaries, i.e., if customers will compel tradesmen to keep extra carts, horses, etc., they must pay for them, the same as the public pay for the carriage and display of physicians, surgeons, etc.

In Profit and Loss the following equations always hold good: