CHAPTER IX.

APPLICATIONS OF INTEREST.

77. Discount. When A owes B a sum of money which he must pay him at some fixed future time, and agrees to pay him at the present time instead, then during the interval B will have the use of this money, and will obtain interest for it, and at the time when the debt is due, will have received more than A owed him : he ought therefore to receive from A a sum less than the sum of the debt: this sum is called the present value of the debt, and the difference between this and the debt is called the discount.

The present value ought to be that sum of money which, if put out to interest till the time the debt is due, will amount to the sum of the debt: the rate of interest to be allowed depending upon the exigencies of trade.

78. In small transactions it is usual for the creditor to calculate the interest on the debt and return it to the debtor, instead of calculating the true discount. This is an advantage to the debtor; for suppose A owes B £100, due at the end of a year, and interest is reckoned at 5 per cent. per annum : then if B return A £5, or receives £95 for the debt, he will gain only £4 15s. interest on the £95 in the year, and will be a loser of 5 shillings. If, however, A were to give him this 5 shillings, or pay him £95 5s., B would gain £4 158. 3d. interest, and would be a gainer of 3 pence: if he received only £95 4s. 9d., he would be a slight loser, and in this way the exact discount could not be found.

79. In Art. 76, we showed how to find the principal which would reach a given amount in a given time, at a given rate per cent.: this is the same as finding the present value of a debt due some time hence at a given rate per cent. The discount can be found by subtracting the present value from the debt, or at once as follows:

Example. Find the discount on £225 11s., due six months hence at 8 per cent.

In half a year at 8 per cent. £100 would amount to £104, therefore the discount on £104 would be £4. Hence we have the Rule of Three sum, "If the discount on £104 is £4, what is it on £225 IIS.?"

80. In business transactions, when A purchases goods of B, he gives him a promissory note that he will pay him the value at a certain time agreed upon; if before the time has expired, B is in want of ready money, he takes A's promissory note, or bill, to a Bank, or Discount House, where he can receive its present value at the current rate of discount-this rate varies according to the state of the money market. Thus if A gave B a note on the 13th of March, 1866, promising to pay him £340 os. 9d. in 5 months; and on May 23rd B takes this to be discounted, and the current rate of interest is 7 per cent., he will receive the present value of £340 os. 9d., due 85 days hence: for the bill is due on August 13th, and from May 23rd to August 13th is 82 days: to these are added 3 days, called days of grace.

85

Now the interest of £100 for 85 days at 7 per cent. is

365

of £7 or £ 119, and to find the discount we have

73

81. Insurances.-At the present day insurances are made for all kinds of subjects: thus a man insures his life, his property against fire, hail, &c., his merchandise against loss at sea. In all cases the amount of the money paid for the insurance (called the premium) is calculated at a certain rate per cent., and will be found as in ordinary simple interest.

The deed of insurance is commonly called a policy of insurance. Example 1. A man 31 years of age insures his life for £1250 at the rate of £2 8s. 8d. per cent.; what is the amount of the annual premium?

Example 2. A man insures property worth £37 5fl. against fire at the rate of 9 centimes per cent., and has to pay a duty of 8 cents

:

per cent. what is the amount of his premium ?

Here 8 cents and 9 cents make 17 cents per cent.

82. In cases where the rate of insurance is high, as in marine

insurance, a man often wishes, in case of loss, to recover the premium as well as the value of the cargo. In such a case he requires to know at what price he must fix the value of his cargo.

Example. A person insures his cargo, worth £1003 158., at 82 per cent.; for what must he insure it so as to recover his premium in case of loss ?

If he insures his cargo for £100, he will cover the premium £81, + £914 of the value of his cargo: and we have the rule of three sum, "If a cargo worth £91 is insured for £100, for what must a cargo worth £10033 be insured ? "

83. The term rate per cent. will occur in many questions besides those mentioned, but in all the principle involved is the same, and they need no special mention in this treatise.

Example. A merchant buys 1260 qrs. of corn, one-fifth of which he sells at a gain of 5 per cent., one-third at a gain of 8 per cent., and the remainder at a gain of 12 per cent. If he had sold the whole at a gain of 10 per cent., he would have obtained £23 28. What was the cost price per quarter ?

more.

Suppose the cost price per quarter was 100 shillings, then his gain on of 1260 qrs. is of 1260 × 5, or 1260 shillings, his gain on of 1260 qrs. is of 1260 × 8, or 3360 shillings, and his gain on the remaining 588 qrs. is 588 × 12, or 7056 shillings, and his total gain is 11676 shillings.

But if he had sold the whole at a gain of 10 per cent., his gain would have been 12600 shillings, or 924 shillings more. But by the statement his gain was £23 28., or 462 shillings more.

Hence 94: 48% = 100

50

Ans. 50 shillings a quarter.

EXERCISE LXXI.

G

CHAPTER X.

SHARES AND STOCKS.

84. When a company is formed to make a railway, or carry on any extensive business, the capital of the company is divided into shares of £100, £50 or any other sum each. If the shares are £50 each, and a person takes 15 shares, that is subscribes £750 towards the capital of the company, he is said to have £750 of the company's stock. The value of a share will rise or fall according to the success of the undertaking, but it is still called a £50 share, though its actual value may be £80 or only £20. When the actual value of a share is the same as its nominal value, it is said to be at par, when above at a premium, when below at a discount.

The value of the shares of all the principal railways, &c., are reported in the newspapers every day. Thus, on Sept. 5, 1866, £100 stock of the Metropolitan Railway was worth £132, whilst £100 stock of the Great Eastern was only worth £32.

When the profits of a company are divided, which is generally the case at the end of each half-year, the dividends are calculated at so much per cent. on the original stock. Thus if a dividend is 3 per cent. for the half-year, a person will receive £3 for every £100 stock he holds, irrespective of the price he gave for it.

When a company wishes to borrow money, it generally creates preference stock, that is, a certain number of shares on which it guarantees a fixed dividend at so much per cent. It then sells this stock for the best price it can, sometimes more than its nominal value, sometimes less; sometimes such shares are called debentures, and are paid off at par at the end of a fixed period.

85. When the government borrow money to meet the extra expenses of great wars, &c., they create perpetual annuities; on every £100 stock of these annuities they guarantee a fixed rate of interest, generally 3 per cent., and then sell this stock for the best price they can they reserve to themselves the right of paying off the capital at par when they like. These stocks have various