7. What sum must be invested in the 3 per cents. at 94 to produce & quarterly income of £8.?

8. What amount of Stock must be purchased in the 4 per cents. at 93 to produce a quarterly income of 9 guineas?

9. Sold Stock at 723 for £461, 10s. ; what was the Stock sold?

10. Sold £9003 Stock for £1200, 16s. ; required the price per cent.? II. If the 2 per cents. are at 96, what sum must be invested therein to produce an annual income which, one year before it is due, is worth £7, 6s. 6d. after being discounted by a banker at 23 per cent.?

What was the sum received?

What was the Stock sold?

12. Sold £364 Stock at 924 per cent. 13. Sold Stock at 833 for £203, 17s. 14. If £650, 13s. be given for £550, 11s. Stock, what was the price per cent.?

15. If £225, 9s. Stock be sold for £125, 5s., what was the price per cent.?

16. A person sells out £350, 14s. Stock from the 3 per cents. at 128; what does he receive, and what difference does he make in his income by investing the proceeds in 3 per cents. at 144?

17. £800, 16s. Stock was sold out of the 23 per cents. at 873, and invested in railway 5 per cent. preference shares at 12 per cent. premium. What was the difference in the income derived?

18. I invest £1270 in 3 per cents. at 923, and, selling out after allowing the interest to accumulate for 2 years, I find myself richer by £147, 10s. ; at what price did I sell out?

19. If I invest £2800 in the 3 per cents. at 92, what is my income, and how much per cent. do I get for my money?

20. What is the price of the 34 per cents. when £3930 invested in them produces an income of £130 per annum?

21. Which is the better investment-the 3 per cents. at 901, or railway shares at 114, paying a half-yearly dividend of £2, 5s.?

22. I have £2400 Stock in the 3 per cents. ; I sell out at 90, invest the money in debentures, paying 53 per cent., purchasing them at 111; what is the difference in annual income?

23. I lay out £1270 in the per cents. at 92; after allowing the simple interest to accumulate for 2 yrs., I sell out at 93, and invest the sum in debentures at 104, paying 4 per cent. What is my income? (Fractions of a penny may be neglected.)

24. Is it better to invest in 3 per cent. Stock at 833, or in shares at £233 each, on which a dividend of £7, 13s. 4d. is paid annually? If you have invested £1000 in the 3 per cents., and exchange it into the other security, what difference will it make in your income?

25. A person invests £4095 in the 3 per cents. at 91; he sells out £3000 stock when they have risen to 933, and the remainder when they have fallen to 85? What does he gain or lose by the transaction? If he invests the produce in 43 per cent. Stock at 102, what is the difference in his income?

26. A has stock in the 3 per cent. Consols which produce him £300 a year. He sells out one-half at 92, and invests the proceeds in the South Devon Railway when a £50 share is worth £23. What dividend per cent. per annum ought the South Devon Railway to pay so that he may increase his income £50 per annum by the transaction?

27. A buys 200 shares in the South Devon Railway, for which he gives £100 a share. When they are paying 2 per cent. he sells out at £46 a share, and invests the proceeds in 3 per cent. Consols at 92. Find the difference in his income in consequence of the operation.

28. A person invests £6825 in 3 per cents. at 91; he sells out £5000 Stock when they have risen to 932, and the remainder when they have fallen to 85. How much does he gain or lose by the transaction? If he invests the produce in 4 per cent. Stock at par, what is the difference in his income?

29. What must a person have invested in 3 per cents. at 90§ if a transfer of of his capital to the 4 per cents. at 115 would increase his income by £7?

30. A person invests £6200 in the 3 per cents. at 891, and pays incomesax at 10d. in £1; when the Stock rises to 92 he sells out, and invests the proceeds in £50 Railway Shares, which yield an annual dividend, clear of income-tax, of 3 per cent. What is the difference in his income?

31. A certain railway pays an annual dividend of £3, 10s. a share. A person bought 12 shares at such a price that they yielded 5g per cent. on his investment, and when the price had risen £5, he sold out and invested the proceeds in 34 per cent. Stock at £85. Find the alteration in his income.

32. Having a legacy of £7823, I hesitate between investing it in 2 per cents. at 73, or 5 per cents. at 134, but finding that in the latter investment they deduct 13d. in the £1 from all yearly dividends, I decide on the former. How much do I gain or lose per annum by this choice?

33. I bought an estate, which let for £450 per annum at 28 yrs. purchase; how much Stock must I sell out of the 3 per cents. at 96 to pay for this estate, and how much more interest per cent. do I get by the estate than by the Funds?

P

PROFIT AND LOSS.

118. The Profit or the Loss on the sale of articles is not generally expressed in commercial transactions by the difference between the cost price and the selling price, but by the ratio which this difference bears to the cost price, which ratio is generally expressed as so much per cent.

Thus, if a man purchased coals at 30s. a ton, and sold them at 368. a ton, he would not express his gain as being "6s. on the sale of a ton of coals," nor as being "6s. on an outlay of 36s.," but as being ( of, i.e.) "20 per cent. on his outlay," meaning thereby that, selling his coals at 36s. a ton, he gained £20 on every £100 he laid out.

Whenever a gain or a loss is expressed as being so much per cent., it must always be considered as being calculated upon the original outlay, and not on the selling price, unless so expressed.

In all questions of Profit and Loss there are three things to be considered, viz.

1. The Prime Cost, or Cost Price, which is the sum originally given for the article.

2. The Retail Price, or Selling Price, which is the sum for which it is sold by the original purchaser.

3. The Gain or Loss Per Cent., which is the difference between the cost price and the selling price.

Ex. If an article were purchased for 20 shillings and sold for 22 shillings, we should say that 20s. was the prime cost, 22s. was the selling price, and 2s. was the gain.

Here it is plain that if the gain on 20s. was 2s., the gain on 100s. at the same rate would be 10s., i.e. 5 times as much, because the principal is 5 times greater.

The same thing may be stated in a proportion, thus

As 20s. the gain on 20s. :: 5 times 20s. : the gain on 5 times 20s., i.e. 20s. : 28. :: 100s. the gain on 100s.

Now, although "per-centage" signifies literally "for a hundred," it is usual to consider it as applying particularly to £100; so that, to take the above example, if an article be purchased for 20s. and sold for 22s., we say that the gain was 10 per cent., i.e. at the rate of £10 gained for every £100 laid out in the original purchase; therefore we see that—

Hence the reason of the following rule

RULE. To find the PER-CENTAGE of gain (or loss, for loss may be considered as a minus gain) on the sale of an article, multiply the fraction which expresses the ratio of the gain to the cost price by 100.

Ex. Bought an article for £3, 10s. and sold it for 4 guineas; what did I gain per cent. by the transaction?

The truth of the following proportion is also apparent―

£100+ gain p. c. when a gain is effected, or,

Cost price selling price: £100 £100 - loss p. c. when a loss is

Hence the reason of the following rules

sustained.

RULE 1.-To find the SELLING PRICE of an article to gain a given per-centage, multiply the cost price by 100 increased by the rate per cent., and divide the product by 100.

Ex. Bought goods for £11, 7s. 1d.; find the selling price to gain 6 per cent.

RULE 2.-To find the SELLING PRICE of an article to lose a given per-centage, multiply the cost price by 100 diminished by the rate per cent., and divide the product by 100.

Ex. Bought goods for £120, 17s. 6d.; find the selling price to lose 133 per cent.

cost price x (100 – 13}) £120, 17s. 6d. × 863
100
100

=

RULE 3.-To find the COST PRICE of an article when a gain of a certain per-centage has been made, multiply the selling price by 100, and divide the product by 100 increased by the rate per cent.

Ex. Sold goods for £5, 10s. 3d., and gained 8 per cent. on my outlay; what was the cost?

RULE 4.-To find the COST PRICE of an article when a loss of a certain per-centage has been sustained, multiply the selling price by 100, and divide the product by 100 diminished by the rate per cent.