The present worth of any sum is the principal which would amount to the given sum if put out to interest now at a given rate until the sum falls due. This is required in the calculation of annuities. Discount is a percentage deducted from a debt or obligation of any kind paid before it is due. Interest is a percentage added to a debt or obligation of any kind paid after it is due. Firms doing business with each other always give discount or charge interest according to the time of payment. Hence discount for time is interest at a given rate for a given time-deducted instead of added. Bankers and Bill Discounters discount Bills of Exchange in exactly the same way. They deduct Interest on the Bill at the current rate for the number of days it has yet to run. In discounting such bills interest is reckoned on the three days of grace allowed before payment can be demanded, in addition to the currency of the bill. 17. Cash Discounts, Commission, Brokerage. Discount for cash is a percentage struck off a debt for prompt payment or ready money. Commission and Brokerage are terms to denote a similar percentage charged by an agent on sales effected for another. The agent is often termed a broker, factor, or commission agent. He is said to act for a principal. The question of time does not often enter into the calculation of such percentages. men Brokers are of many kinds, but they are all "middleengaged in effecting sales between parties directly or indirectly, and they all recoup themselves by charging a commission on the amount of sales. Bill-brokers, discount brokers, and bullion merchants meet at the Royal Exchange (on 'Change) for the negotiation of bills of exchange and the sale of bullion. Stock and share brokers, if members of the Stock Exchange, go there to buy of, or sell to, the stockjobbers. Colonial brokers engaged in the sale of tea, coffee, sugar and all colonial and foreign produce frequent the Commercial Sales Rooms in Mincing Lane. Brokers for corn and grain have their head-quarters in Mark Lane. Marine insurance and ship brokers frequent Lloyd's Room in the Royal Exchange to meet the underwriters. The term "underwriters" arises from the way in which a broker gets a ship insured. He fills up a blank policy of insurance and passes it to various insurance representatives in the room, each of whom accepts a portion of the proposed insurance and " underwrites" it accordingly. There is also a Coal Exchange, and in addition there are brokers of wool, fruit, fish, etc., each class having a recognised place of meeting. 1o. To find the present worth of a sum due in a given time, interest being at a given rate p.c. Find the compound amount of £1 for given time at given rate. Then the present worth is found by dividing the sum by this compound amount. Example. Present worth of £500 due 5 years hence at 4 p.c. .. present worth £500÷1.216653 = £410.963 (19s. 3d.). £1.000000 1.040000 1.081600 1.169859 46794 1.216653 1.2,1,6,6,5,3 | 500-0000 | £410-963 13 3388 1 1723 774 44 8 2. To find the discount on a bill for any number of mos. from a given date and cashed before maturity. Find date of maturity by adding 3 days of grace. Calculate the number of days the bill has to run from the day on which it is cashed. Reckon interest on bill for this number of days at current rate of discount. Subtract interest from bill. The answer is what the holder receives. Example 1. Bill for £312. 18s. 61d., 3 mos. date May 5, cashed June 3. Rate 28. Currency=92+3=95, date Aug. 8. 3.12926 5 2171 3 1293 2 1904 313 62 16 Discount = £1. 9s. 4 d. Cash for bill = £311.9s. 14d. 3,6,5 535.88 | 1-468 170 8 24 8 29 Example 2. Bill for £450. 8s. 6d., 2 mos. date March 4, cashed March 8. Rate 24 p.c. With grace time for discount=60 days. 60 × 23=165 4.50425 561 45043 27025 2252 3,6,5 743-20 | 2.036 132 22 3. Discount for cash is merely a case of percentages. Similarly any kind of brokerage or commission. The percentage is always struck off the debt or amount of sales. Example 1. Find net payment of bill for £651. 9s. 104d. Discount 2p.c. Example 2. Commission on sales to amount of £2561. 98. 4d. at 31 p.c. Example 3. £8645. 13s. 5d. 25.61466 76.8440 6.4037 £83.247 (4s. 11 d.). Brokeragep.c. on sale of stock to value of 86.45670 £10.807 (168.1ąd.). EXAMPLES. (Grace is always added.) 1. Discount bill for 3 mos. date Feb. 20 on March 10. Amount £612. 13s. 8d., rate 2ğ p.c. 2. Discount bill for 2 mos. date March 13 on March 20. Amount £715. 9s. 10d., rate 2 p.c. 3. Banker discounts bill for 4 mos. date May 9 on June 1. Amount £1000, rate 17 p.c. 4. Bill Discounter cashes bill for 3 mos. dated June 13 on July 9. Amount £579. 68. 7d., rate 31 p.c. 5. Banker discounts bill 2 mos. date July 4 on July 7. £651. 98. 6d., rate 3 p.c. 6. Banker discounts bill 60 days sight, seen June 5, on July 10. £1000, rate 13 p.c. 7. Merchant cashes bill 30 days date July 8 on July 10. £841. 78. 6d., rate 2 p.c. 8. Money-changer discounts bill 90 days sight Nov. 6 on Nov. 20. £1000, rate 13 p.c. 9. Banker discounts bill 3 mos. date Nov. 9 on Nov. 16. £541. 88. 9d., rate 23 p.c. 10. Banker discounts bill 4 mos. date April 6 on May 1. £852. 88. 6d., rate 21 p.c. 11. Commission at 3ğ p.c. on sales £1512. 8s. 9d., £1756. 10s. 6d., £2124. 88. 9d. 12. Brokerage atp.c., 1 per mille on bills for £956. 8s. 3d., £1020. 78. 6d. 13. Commission 1, 1, 1p.c. on inland bills for £712. 6s. 8d., £614. 9s. 10d., £10850. 14s. 6d. 14. Commission on sales at 31, 4, 21 p.c. to amount of £1164. 88. 5d., £3125. 10s. 6d., £5960. 12s. 8d. 15. Brokerage op.c. plus commissionp.c. on bill for £1856. 98. 4d. 19. Stocks and Shares. A Company is formed to carry on a business requiring considerable capital, by the issue of shares, which may be bought by those who think it a good investment. They thus become shareholders, and are in fact the proprietors of the business. Such a company is called a joint stock company, and is usually managed by directors chosen from the shareholders. At stated intervals (generally each half-year) the accounts are made up and the nett profit paid to the shareholders as dividends. A Firm differs from a company only in having a |