same thing, 100 representing the present worth, 21 will represent the discount, and 121 the given sum. And the quantities themselves will be proportional to their representative numbers.

N.B.-In ordinary practice, the discount deducted from the amount of a bill, for payment before it becomes due, is calculated in the same manner as simple interest on that amount for the given time; so that the present payment is less than in strictness it should be at the given rate of interest.

Among bankers and merchants, a bill due nominally on a certain day, is legally due three days afterwards. These are called days of grace.

When the time is reckoned in months, calendar months are intended; and if in so reckoning a bill should fall nominally due on the 31st of a month having only 30 days, it is to be considered as due on the 30th,

For instance a bill drawn on June 12th at four months, would fall due nominally on Oct. 12th, but legally on Oct. 15th; so that if discounted on Aug. 4th, there would still be 72 days before it became due.

Ex. (2) Find the true discount on a bill for £889 48. 3d. drawn July 7th at three months, and discounted Aug. 12th, at 5 per cent.

The bill falls due on Oct. roth, and from Aug. 12th to Oct. 10th, there are 19+30+10, i, e. 59 days.

Exercise 69.

(1) Find the present worth of £2416 10s. payable at the end of 7 years, at 5 per cent. simple interest.

(2) Find the present worth of £4261 6s. 9d. due at the end of six years, at 4 per cent.

(3) Find the discount on £783 5s. 6d. due in 4 years, at 3 per cent.

(4) What is the present value of £3334 128. 5d. due in 7 years, at 4 per cent.?

(5) Find the difference between the simple interest and discount on £2000 for 5 years, at 3 per cent.

(6) What does a banker gain by deducting simple interest instead of discount on a bill of £899 2s. 4d. payable in 75 days, at 6 per cent.?

(7) Find the present value of £500 due in 11 months, at 5 per cent.

(8) Determine the value on February 15th 1866 of a bill of £1620 78. 6d. drawn on February 1st at 10 months, at 51⁄2 per cent.

(9) Find the difference between the simple interest and discount on a bill of £1401 88. 11 d. drawn on July 1st at 100 days and discounted on August 1st, at 5 per cent.

(10) Find the present value at 4 per cent. compound interest of £7030 8s. due in three years.

(11) At 5 per cent. compound interest, find the present worth of £275 12s. 6d. due in two years.

(12) What is the difference in the present value of £1000 due in 4 years, at 5 per cent. simple, and 5 per cent. compound interest?

CHAPTER XII.

STOCKS.

86.-THE National debt of a country is an accumulation of debt, consisting of money borrowed at various times by the Government, on which an annual interest is paid out of the taxes of the country.

Considered with reference to the creditors as an investment for money, any portion of the debt is called Stock, and a creditor for any sum is said to hold so much stock.

Considered from the same point of view, the debt is spoken of as the Funds, and a creditor is said to have money invested in the funds. For instance, a person to whom the Government owes £1000 is said to hold £1000 stock, or to have so much in the funds; and is entitled to receive interest upon it.

A holder of stock may dispose of his stock to another person, and in that case the price per cent. at which he disposes of it is called the price of stock. The price of stock varies from day to day, and depends upon a variety of circumstances, such as the rate of interest which can be obtained from other investments, the abundance or scarcity of money in the country, the approach of the dividend day (i. e. the day on which the interest is paid), &c. Thus if the price of stock on a given day is 89, or as it is commonly expressed, if the funds are at 89, the meaning is that £100 stock costs on that day £89 of money; or that if 100 be the representative of any quantity of stock, 89 will represent the corresponding value in money.

If the price of stock is 100, it is said to be at par; if above 100, at a premium; if below 100, at a discount; the premium or discount being the excess or defect from 100.

Thus 99 would be per cent. discount, 101 would be 11 per cent. premium.

The interest is paid at a certain per centage on the stock, and gives the name to each particular stock, as 3 per cents., India 5 per cents., &c.

It must be noticed that to any buyer of stock, the amount of stock he has bought remains unchanged so long as he holds it, and the interest he receives upon it each year remains constant, but its value in money (i. e. supposing he were to sell it) is liable to continual variation.

The name Stock is also applied to the capital of railway and other trading companies; but in such investments the annual interest is not generally fixed, but fluctuates with the profits and expenses of each year. The capital of a trading company is often considered as consisting of shares, the original value of which is in some £100, in some £50, in some £20, &c., and the value of stock at any time is then estimated by the current price per share.

The purchase and sale of stock is conducted through the agency of stockbrokers, who receive a brokerage per cent. on the stock both from the buyer and seller. The brokerage varies slightly with the kind of stock; for the funds it isper cent. (i. e. 2s. 6d. on £100).

It will be seen that the effect of brokerage will be to increase the price of stock to the buyer by, and on the other hand to diminish by the amount which the seller will receive per cent. for his stock. But in working ordinary examples, the brokerage need not be taken into account unless specially mentioned.

87.-In all questions on stocks, we may employ the principle of representative numbers, which has been before used; such numbers being always proportional to the quantities they represent. They are as follows:

100 being the representative of any amount of stock, the price will represent its value in sterling money, and the rate per cent. paid by the stock will represent the interest upon it.

The application of the principle will be easily seen in the following examples.

Ex. (1) How much will be received for £1350 stock if sold at 89%?

100 89: £1350.

I

100

X X1350=£1206 11s. 3d. Ans.

715
8

Ex. (2) What amount of stock at 84 for £1878 138. 6d., brokerage to be paid

may be bought per cent.?

Ex. (3) What income will be derived from £4675 3 per

cent. stock?

100 3 £4675

3

140 25

20

5'00

£140 5s. Ans.