the Stock he wishes to buy, he may bring the Bank Bills to discount. The Bank discounts these Bills by creating a Credit, or Debt, in his favour; which is a Negative Quantity, exactly like a Bank Note. The customer then gives the bank a cheque on his account-that is, he releases the bank from the Debt it has created and that Debt released, then becomes increase of Capital This is the way in which the Capital of all Joint Stock Banks is increased, and it may go on to any extent without any payment in Money

In a precisely similar way, when great public loans are contracted for, a very large portion of them is always created by means of Credit. The customers of a Bank wish to subscribe to a loan. They bring it a batch of bills to discount. They draw cheques against the deposits created on the discount of these bills. These cheques may be paid into the credit of the great contractors, at their bankers, and transferred an indefinite number of times, without ever being required to be discharged in money; they may, in fact, be discharged by being cancelled against other Credits

CHAPTER VII

THE THEORY OF BANKING DISCOUNT

1. Profits made by a Loan of Money are made in two ways— (1) By advancing the complete sum, and waiting till the end of the year for the Profit. This is termed Interest

(2) By retaining the Profit at the time of the advance, and advancing the difference. This is termed Discount

But there are two ways of making Profit by Discount

1. According to the ordinary works on Algebra, the sum advanced should be such a sum as improved at the given interest should amount to the given sum at the end of the time

The sum so advanced is called the Present Value of the given sum

This species of Discount is used in certain branches of commerce and it may be called Algebraical Discount But this species of Discount is never used in Banking

In Banking the full sum charged as Profit is deducted, and the difference only is advanced: thus, if a Banker discounts a Bill at 5 per cent.: he gives his customer a Credit for £95, and receives £100 at the end of the year

The Profits made by Interest and Algebraical Discount are identical

But the Discount used in Banking is evidently more profitable than Interest and Algebraical Discount: because the Banker receives a profit of £5 on the advance of only £95 instead of £100

:

So long as the rates are low there is not much difference but as these increase, the difference increases at a very rapid ratio: as may easily be seen

If a person lends £100 at 20 per cent. Interest, he advances £100, and at the end of the year he receives £120 which is a Profit of 20 per cent.: if he discounts a Bill for £100 at 20 per cent., he advances only £80, and at the end of the year he receives £100 which is a Profit of 25 per cent.

If he lends £100 at 50 per cent. interest, he advances £100: and at the end of the year he receives £150 or his Profit is 50 per cent.

If he discounts a Bill at 50 per cent., he advances only £50, and at the end of the year he receives £100: i.e., he makes Profit at the rate of 100 per cent.

cent.

So, discounting a Bill at 60 per cent., is Profit at 150 per

If a person lends £100 at 100 per cent. Interest he advances £100, and at the end of the year he receives £200 or his Profit is 100 per cent.

If a person discounted a Bill at £100 per cent. he would advance Nothing: and at the end of the year he would receive £100 or his Profits would be Infinite

On Banking Discount

2. It is somewhat strange that this kind of Discount is entirely overlooked by Algebraists. We shall now trace the relation between Profits made by Interest and Banking Discount: as this kind of Discount may be termed

To find the Amount of a given Sum in any time at Simple Banking Discount

- rP Let r'

=

=

=

=

Amount of Principal and Discount

Interest on P£ for 1 Year

Sum actually advanced =

P (1 − r)

Profit by way of Banking Discount on each £ of sum actually advanced

Which is the relation which Banking Discount bears to Interest and all Problems in Banking Discount may be solved by for in the Problems in Interest, both Simple

1

substituting and Compound

These two Equations will enable us to solve any question in the subject

3. Adopting the Formula for calculating Interest and Banking Discount, we have the following

Table showing the Profits per cent, and per annum at Interest and Banking Discount

A consideration of this Table will show how Bankers' profits increase when Discount becomes high; and also what discounting a Bill at 50 and 60 per cent. (which we occasionally hear of in Courts of Law) means

וי

To find in what Time a Sum of Money will double itself at Simple Banking Discount

4. The General Formula is

Hence a sum of money will double itself

At 5 per cent. Simple Interest in 20 years

Discount in 19 29

5. The Difference in Profit in trading by Interest and Discount being connected by this relation, may be exhibited by either of the following figures