Ex. 1. A Bill for £77, drawn on the 8th of March, at 6 months, is discounted on the 3rd of June, at 5 per cent.: required the discount. The 6 months expire on the 8th of September; therefore the Bill becomes due on the 11th of September. From the 3rd of June to the 3rd of September is 92 days, and, therefore, to the 11th of September it is 100 days. The interest of £77, at 5 per cent., for 100 days, is found, by the method already taught, to be £1 1s. 14d., the discount required. The following example is one belonging to a class of cases of frequent occurrence in business. 2. A Bill for £500 was due Feb. 2, 1851 of this sum, £80 was paid, March 9; £115, May 15; £25, June 1; and the balance, namely £280, Aug. 14: what interest was due per cent.? at 1851, Feb. 2 Mar. 9 £ £ Due 500 × 35 = 17500 3)71545 See p. 160. 23848 1. What is the present worth of a Bill drawn on the 10th of January, 1852 (leap-year), at three months, for £1264 11s. 8d., at 4 per cent.? 2. How much cash must be received for a Bill for £218 11s. 8d., drawn on the 14th of August, at 4 months, and discounted on the 3rd of October, at 4 per cent.? 3. How much must be received for a Bill for £568 12s. 9d., dated April 27, at 7 months, and discounted June 3, at 5 per cent.? 4. What is a Bill for £1570 10s. 6d. worth on the 10th of January, supposing it to have been drawn at 5 months on the 30th of the preceding December: interest 3 per cent.? 5. A Bill for £39 5s. falls due on the 1st of September, but payment is offered on the 3rd of July preceding: what cash should be paid, the discount being at 5 per cent. ? 6. A Bill for £150, drawn 11th of July, at 3 months, was discounted Sept. 1st, at 54 per cent.: how much did the holder of it receive? 7. A Bill for £500 was due Feb. 2, 1851, of which £80 was paid on the 9th of March following; £115 on the 15th of May; £25 on the 1st of June; and the balance on the 14th of August: how much interest at 5 per cent. was due? NOTE. The present worth of the bills in the foregoing examples is what remains after deducting the banker's discount, which, as you have already been told (page 163), includes his profit, and is more than the true discount. The rule for this is as follows: As £100 increased by the interest for the time, that is, as the amount of £100 is to £100, so is the amount of the bill to its true present worth; as is obvious. enormous. If bills were drawn at a very long date, the banker's discount would be Thus, a bill of £100 at 20 years, allowing 5 per cent. (the usual rate), would produce nothing; for the interest, or banker's discount, would be just £100. And if it were not made payable till 40 years, the holder of it would have to give £100 to the banker to take it off his hands! The bankers' principle, therefore, when applied to such long periods, is manifestly unjust and absurd; but as bills are generally made payable within a few months, the banker's discount exceeds the true discount by no more than what may be considered a reasonable profit on the transaction. It must be remembered, too, that the discounter runs some risk, so that although long bills are apparently more profitable than short ones, yet bankers are less inclined to discount the former than the latter. (110.) BROKERAGE, COMMISSION, INSURANCE, &c. COMMERCIAL and money transactions are seldom conducted on a large scale, except through the agency of a third party, who is paid so much per cent. for his services. The sum of money engaged in the transaction, and the agent's per-centage being given, the whole allowance to the agent is, of course, computed in the same way as interest is computed, from which, indeed, it differs only in name, and in being generally free from considerations of time. If goods or merchandise be bought or sold through an agent or factor, the per-centage on the money is called Commission. If money be employed through an agent in discounting Bills, in the purchase of Shares in a trading company, or in the public funds or Stocks; or, if an agent dispose of such money interests for another, the per-centage he receives is called Brokerage; and he himself is a Bill-broker, a Share-broker, a Stockbroker, &c. Insurance is the name given to what is paid to an Insurance Office, at the rate of so much per cent. on the value of property exposed to loss by Fire, Shipwreck, &c. The parties who agree to compensate for the loss, are the Insurers (or, in the case of ships, Underwriters, from their undersigning the agreement); the party protected is the Insured; the money paid for the protection, the Premium ; and the parchment, which binds the parties to the contract, the Policy. Life Insurance, or Life Assurance, is of a similar nature it secures the payment of a specified sum when the assured dies, upon his paying so much per cent. per annum on that sum during his life, or a sum down, equivalent to the annual premium. Whatever be the name given to the agent employed, or to the service performed, it is plain, that the allowance on a specified sum of money, at a specified rate per cent., can involve no calculations different from those which come under the head of Interest: a few examples, therefore, will be all that need be given here, special rules being unnecessary. Ex. 1. A factor sells merchandise to the amount of £2575 17s. 6d., and charges 4s. per cent. for commission: how much is to be paid him? Here, the interest, or commission, at 1 per cent. is £25 15s. 2d. ; therefore, that at 4s. per cent. is a fifth part of this, or £5 38. 04d. In such small per-centages it is not worth while to take account of the odd pence in the sales; so that dividing £2575 17s. by 5, for the per cent., and disregarding the pence in the quotient, we may proceed as in the margin. In the next example, too, the 9d. may be omitted in finding the broker's charge, which would be 14s. 5d. :.£5 38. Commission. 2. How much money will purchase £575 108. Bank Stock, worth 131 per cent., and how much must be paid to the Stock-broker, who charges per cent., that is, 2s. 6d. per cent., on the stock purchased? Here, to find the purchase-money, it is plain, 14,38 12 that we shall only have to 182,72 2 6 add to £575 10s., the in terest of it at 31 per cent.: this interest will be best found by taking 32 per cent., and deducting per cent., as in the margin: the purchase-money is thus 20 found to be £758 4s. 5d., and the broker's claim, 14s. 4 d., which is of £575 10s., divided by 100. NOTE. Those who purchase stock, purchase nothing more than a claim to a certain amount of interest, payable half-yearly. Stocks are of different kinds, not only as to the names they bear, but as to the rate of interest paid to the purchaser. If stock yield a high rate of interest, it is proportionally dear; and more than £100 in money must be given for £100 stock, when the interest the latter yields is more than can be got for £100 in money. Although property in stock cannot be taken out, it can always be sold out with but little trouble. The prices of stock, of whatever kind, varies from time to time, sometimes rising and sometimes falling, like other purchasable commodities; the fluctuations, however, are usually inconsiderable, except when the tranquillity of the country is in danger; funded property then becomes insecure, and stocks fall in proportion to the alarm. 3. A cargo, worth £3800, is to be insured at 5 per cent. : for what amount must the insurance be effected, so that, in case all should be lost, the owners may recover both the value and the premium paid? For an insurance for £100, a premium of £5 must be paid; this being deducted, leaves £95; so that an insurance for £100 can cover a loss of only £95: therefore, to find what insurance can cover a loss of £3800, we have the proportion, £95 £100 :: 3800: £4000, the amount to be * The half of this is 4th of £575.10s. insured. And in this way is the insurance to cover loss and premium always to be found; namely, as £100 diminished by the rate £100 value of the property: the sum to be insured. If there be any other per-centage, as for commission, policy, &c., it must be deducted from £100 in the same way. Exercises. 1. What is the commission on £3698 12s., at 34 per cent.? 2. If a person sell out £600 stock, when the price of it is 833 per cent., how much will he receive after paying per cent. on the stock sold for brokerage? 3. What amount must be insured to cover £1880, together with the premium of £5 5s. per cent., 5s. per cent. for the policy, and per cent. for commission? 4. What amount must be insured on £1938 12s. 6d. at 53 per cent., so as to provide also for the premium? 5. What is the commission on £876 5s. 10d. at 33 per cent.? 6. What is the brokerage on £372 7s. 4d. at 4s. 6d. per cent. ? 7. How much must be given for £912 14s. stock, at 1273 per cent.? 8. Required the brokerage on the purchase of £11675 17s. stock, at per cent. 9. What will it cost to purchase £7391 14s. 9d. stock, the price being 861, and the brokerage per cent.? 10. Find the expense of insuring a cargo worth £850, at £2 12s. 6d. per cent., policy duty 5s. per cent., and commission per cent. (111.) COMPOUND INTEREST. ALL the preceding calculations respecting interest proceed on the supposition that the interest is actually paid when due. If, however, the interest be withheld for any time, then this interest so withheld becomes a new principal, and itself produces interest. The whole interest thus accumulated in any time is called compound interest; while that which arises solely from the original principal, and which has been the subject of the preceding articles, is, for distinction, called simple interest. An example will be sufficient to show you how compound interest may be calculated; but as the work, though made up of very easy and obvious steps, becomes I |