bonds or quantity of stock in the 4 per cents., will produce the same interest as a greater quantity of stock in the 3 per cents., and consequently be of the same value to the possessor in point of income.

150. The same view is taken of money advanced to Foreign Governments or to Trading Companies: and the computations necessary in all equitable transactions of this kind must depend upon the Rule of Proportion: and those of most frequent occurrence will be explained in the subsequent examples.

Ex. 1. How much money must be paid for £2400 in the three per cent. consols (consolidated annuities), at 89 per cent.?

Here, we have the following proportion :

and the operation may be conducted in the form below:

£2400

10×9-89

24000

9

216000

1200

21 4 8.0 0

that is, £2148 sterling will purchase £2400 of this stock when it is at 891 per cent.

If we reverse the operation, we may find the quantity of stock at 89 which will be purchased for £2148 sterling, as follows:

Ex. 2. A person invests £3000 in the three per cents. when they are at 901; what amount of interest will he receive half-yearly?

Here, £90 sterling produces £3 yearly or £1 half-yearly and therefore we have

:

Conversely, if a person wish to receive the last-mentioned sum half-yearly, he may invest £3000 in the three per cents. when they are at 90 for this purpose; since £. £. S. d. f.

£.

£.

1: 49.17.91.251:: 901: 3000;

but the same income might be acquired by the investment of a different sum of money in a different kind of stock, dependent upon the circumstances affecting it.

Ex. 3. At what rate will a person receive interest, who invests his capital in the 4 per cents. when they are at 104?

Since £104 sterling produces an interest of £4 annually, we have

Conversely, when the interest of money is £3.16s.11d. per cent., the equitable value of the 4 per cent. stock is £104 sterling.

Ex. 4. A person transfers £1000 stock from the 4 per cents. at 90, to the 3 per cents. at 72: find how much of the latter stock he will hold, and the alteration made in his annual income.

Here, a denoting the quantity of the latter stock, we have

is the quantity of stock in the 3 per cents. :

also £1000 at 4 per cent. gives an income of £40: and £1250 at 3 per cent. gives an income of £37. 10s.: therefore the diminution of his income £2. 10s.

From this example, it appears to be more advantageous to invest in the 4 per cents. at 90 than in the 3 per cents. at 72, as will be seen also from the circumstance of being greater than, which shews the reason at once.

151. Purchases and Sales of stock are made through Agents called Stock-Brokers at the rate of £ or 2s. 6d. per cent. upon the stock transferred: these agents are employed by both buyers and sellers, and the brokerage must therefore be added to the price of stock which is bought and subtracted from the price of that which is sold through them: and this is done by increasing or diminishing the current price of £100 stock by £1.

152. Stock-jobbing is dealing in the Stocks with the view of gaining money by the rise and fall of the market price and persons possessed of property may of course buy or sell stock, according as the price is likely to rise or fall, in the expectation of realizing a profit by the difference of price: but the practice of stock-jobbing may be explained as follows.

A agrees to sell to B, £1000 in the 3 per cents. for £870 to be transferred at the end of a certain time : A has indeed no such stock, but if its price on the day of transfer should be only 86 he may purchase what will enable him to fulfil his engagement for £860, and he will thus gain £10 by the transaction: on the contrary, if the price were 89, it would require £890 for the same purpose and he would then be a loser of £20. These are called time bargains or bargains for the Account, and are settled without the purchase of stock at all by payment of the difference: the buyers being known as Bulls pulling down, and the sellers as Bears forcing up, in the language of the Stock Exchange: but not being recognized by law, the principles by which this business is supported are merely a sense of honour or disgrace and the retention or loss of future credit.

153. It is the province of the Chancellor of the Exchequer to propose the terms of a Government Loan: and

if a person, asking 5 per cent. for his money, were to advance £1000 money, the nation would become indebted to him in £1666. 13s. 4d. stock in the 3 per cents. at par, because this sum produces the same interest. When the price of stock is above or below par, the calculations will be conducted as in the preceding pages; and in order to raise the immense sums that are frequently wanted, the Contractors or Subscribers are sometimes considered entitled to an advantage of one kind or other which is called a Douceur or Bonus.

Such stocks constitute what is termed The funded Debt; and whenever sums have been advanced to the government and have not been thus disposed of, they are styled The unfunded Debt.

Temporary loans are raised from time to time on what are called Exchequer Bills for single hundreds or thousands of Pounds, bearing a certain interest per cent. per day, from the days of their dates to the days when they are paid off.

Examples for Practice.

(1) What is the purchase of £5050 stock, at 853 per cent.?

Answer: £4311. 8s. 9d.

(2) If the 4 per cents. be at 82, what quantity of stock can be purchased for £821. 5s.?

Answer: £1000.

(3) A person invests £2000 in the 3 per cent. consols, when they are at 88: what annual income is he entitled to?

Answer: £67. 15s. 111}d.

(4) What sum must be invested in the 3 per cents. at 77 to produce an income of £120 a year?

Answer: £3100.

(5) A person investing in the 4 per cents. receives 43 per cent. interest for his money: what is the price of the stock?

Answer: 91%.

(6) How much stock can be purchased by the transfer of £1000 stock from the 3 per cents. at 72, to the

4 per cents. at 90: and what annual income will it produce?

Answers: £800 and £32.

(7) If I buy £650 stock in the per cents. at 903, and pay for brokerage: what does it cost me?

Answer: £588. 5s.

(8) What sterling money shall I receive for £1760. 16s. 8d. stock at 90%, and 1 per cent. commission? Answer: £1589. 3s. Od.

(9). If a person invest £650 in the stocks at 761, and sell it immediately at 77; find his gain by the transaction.

Answer: £10. 16s. 8d.

(10) A person having £10000 in the 3 per cents. sells out at 65 and invests the produce in the 4 per cents. at 82 find the change in his income.

:

Answer: £15. 3s. Od. increase.

(11) When a certain stock is at 97 a person possesses what would realize £879: find what quantity of another stock at 881 he ought to receive for it.

Answer: £996.

(12) The sum of the dividends on a quantity of 3 per cent. stock for 13 years was £3081: how much stock was there, and what will be its sterling worth when the fund is sold at 793 per cent. ?

Answers: £7900 and £6310.

IV. DISCOUNT OR REBATE.

154. DEF. Discount or Rebate is an allowance or abatement made upon a debt discharged before it is due, in consideration of ready money, the simple interest of money being reckoned at a given rate: and when the discount is subtracted from any proposed sum, the remainder is termed the Present Worth or Present Value.