DISCOUNT. Discount is a deduction allowed or charged for the present payment of a sum of money due at a future period. The allowances of Discount are either, 1. A fixed sum agreed upon, without any consideration of either time or a rate per cent. 2. A per centage upon the Principal. 3. The Interest upon the Principal for the intervening time. 4. The Interest upon the sum actually paid, for the time it is paid in advance. As the first species of Discounts requires no calculation, and as the calculations of the second and third sorts have been shown under the Rules of Per Centages and Interest, we shall give here only the Rule for the fourth sort of Discounts, observing, that in this country, this plan is rarely ever practised except in the calculations of the present worth of Life Insurances and Annuities. RULE. For calculating Discount as the Interest upon the Present Worth. Find the Interest upon £ 100 for the given time, and add it to £ 100; then say, as this amount is to the Interest, so is the Principal to the Discount, or, as this amount is to £ 100 so is the Principal to the Present Worth. EXAMPLE. To find the Present Worth and Discount on £ 500 for year at 5 per cent. per annum. The Interest on £100 for year is £ 21. EXERCISES. Ex. 1. Find the net amount of £ 639 14 5, allowing for Discount 7 per cent. Ex. 2. Find the net amount of 30 bales of Cotton, Gross weight 84 cwt. 2 qrs. 17 lb., Draft 1 lb. per bale, Tare 4 lb. per cwt., the Net weight being sold at 11 d. per lb., with a Discount of 13 per cent. for Cash in 1 month. Ex. 3. Find the net amount of Spanish Wool, which was sold for £ 1164 17 6, allowing a Discount for 8 months at 5 per cent. Ex. 4. Find the net proceeds of a Bill of Exchange for £600, due the 21 st of May, and Discounted the 17 th of April, at 5 per cent. Ex. 5. Find the net proceeds of the following Bills of Exchange, Discounted the 1 st of March at 4 per cent., allowing also a Brokerage of per cent. 2 Bills each for £ 747 11 6 due April 17. Ex. 6. Find the Present Worth of £ 750 for 1 year at 3 per cent. per annum, allowing for Discount the Interest upon the Present Worth. Ex. 7. If I buy a lot of Goods for £ 153 12 on the 1 st of March, how much must I sell them for on 27 th of May to clear the Interest upon them at 5 per cent. per annum, and make a profit of 7 per cent. upon the Principal and Interest, clear of a Discount of 10 per cent.? Ex. 1. £ 591 14 11 3. 1126 0 10 PRODUCTS. Ex. 2. Net weight 9113 lb. 5. Bills £ 3795 3 0-Days 47, 64, and 71 days. Discount £18 11 4-Selling price £ 185 13 3 EQUATION OF PAYMENTS, OR AVERAGE TIMES OF PAYMENT, An equated or average time of payment, is a time at which the Interest upon the whole of several sums of money is equal to the amount of the Discounts upon the separate sums for the separate times they have to run. RULE. Multiply each payment by the number of years, months, or days, which that payment has to run. Then say, by the Rule of Three, If the amount of all the payments require 1 year, &c., what will the amount of the products require? The answer to which statement will be the equated time required. N. B. When particular days are specified, it is usual to reckon the time of each payment from the day on which the first payment becomes due; then the first payment will not require any multiplication, and the whole amount will be reckoned due at the end of the number of days in the equated time, calculated from the day of the first payment. EXAMPLE 1. On March 2 nd, £ 300 is due; on March 18 th, £ 350 is due ; and on April 17 th, £ 550 is due. It is required to find an average time of payment for the whole sum. From March 2 to March 18 is 16 days to April 17 is 46 days EXAMPLE 2. To find an average time of payment for £ 600 due in 2 months, £ 300 due in 3 months, and £ 1100 due in 6 months. Ex. 1. What is the average time of payment for the following sums due in the following manner? viz. Ex. 2. On what day are the following sums due on an average? Ex. 3. 200 bags of Pernambucco Cotton Wool were sold on the following days, at three months credit, on what day were the amounts due upon an average? Ex. i. 4 months 12 days. Ex. 2. April 25. 3. Amounts due Sept. 1, Sept. 27, and Nov. 21. Average day, October 19. THE STOCKS. The Stocks, or public Funds, are the Capitals on which certain Annuities payable by Government are calculated. The valuations of Stock are made per centages, in which the given rates, reckoned in pounds and fractions of a pound, are the prices of £100 Stock; varying according to the rate of the annuity, (or, as is it called, the Interest,) and to the supply of the market. Stock is bought or sold through the medium of a broker, whose usual charge is 1-8 th, or 2 s. 6 d., per cent. ; but it is to be observed, that if the 1-8 th per cent. on the quantity of the Stock does not amount to 1 s., it is charged at 1 s., as it is the custom of Stock Brokers not to take less than that sum. EXAMPLE 1. To find the cost of £ 680 Stock, at 83 per cent. To find the net proceeds of the sale of £ 564 13 10 Stock at 85 per cent. £ S. d. |