2. Find the interest on the following account to 31st Dec., allowing 5 per cent. when the balance is due to the bank, and 4 per cent. when due to A. Sharp. Dr. Mr. A. SHARP's account-current with the LEITH BANK, Cr. CASE VI. To find the interest on bonds or bills, when partial pay. ments are made at intervals greater than a year. RULE. Add the interest duc at the time of the first payment to the principal, and deduct the payment from the amount, the remainder is a new principal, to which, in like manner, add the interest due at the next payment, and deduct the payment; and so on. EXAMPLE. A bond for £1140 was due 14th March 1815; of which £465 were paid on 2d Feb. 1817, and £206 on 12th August, 1818; find the amount due 20th May, 1820, when the account is to be settled. Borrowed on bond 13th September 1816, £900; of which I paid 1st August 1817, £70, and 14th Jan. 1819, £210. The account is to be settled 9th February 1820; what sum will then be due ? DISCOUNT. Discount is the allowance that ought to be made for receiving payment of a sum of money before it is due. The present value of a sum of money due at a future period, is such a sum as, if lent on interest for that period, at the rate proposed, would amount to the sum then due. RULE. Find the amount of £100 at the proposed rate, in the given time; then," As the amount is to the interest of £100, so is the debt to the discount:"-Or, "As the amount is to £100, so is the debt to its present value. EXAMPLE. What discount ought to be allowed on receiving present payment of a debt of £500, due 4 years hence, interest at 5 per cent.? 100 4x5= 20 120 20: £500 £83 6 8 Ans. Remarks. The Rule gives the true discount of a sum of money due at a future period, that is, it gives the interest of the present value of that sum, or of the money which should be presently paid for it; but bankers, merchants, &c. (as is stated in Interest, Case III.) do not compute in this way; they always charge such a sum for discount as is equal to the interest of the whole bill for the time it has to run: thus, for the present payment of a bill of £105, due a year hence, they would deduct the interest of £105, that is £5:5, and pay the holder of the bill £99:5; whereas the true discount is only £5, and the present value £100. 2. When goods are sold on credit, and discount is allowed for present payment, the general practice is to allow the purchaser double interest for the length of credit: thus, if the goods are sold at 3 months, 2 per cent. is allowed for cash; if at 6 months, 5 per cent.; and so on. 3. The true discount of any sum at 5 per cent., for any number of months, may be found by a single division; thus, for 1 month, divide the sum by 241; and for any number of months, the divisor may be found by dividing mentally 240 by the number of months, and then adding 1 to the quotient. Thus, for 3 months, the divisor is 1+(240÷3)=81; for 8 months, it is 1+(240—8) 31; and so on. • EXERCISES. 1. What discount ought to be allowed on receiving present payment of a debt of £375: 10, due 3 years hence; reckoning inerest at 5 per cent. ? K 2. What ready money is equivalent to £150: 16:4, payable 3 months hence; allowing interest at 5 per cent. ? 3. What ready money is equivalent to £89: 15, payable 1 year 146 days hence; reckoning interest at 3 per cent.? 4. What discount ought to be allowed on receiving present pay. ment of a debt of £117: 12, payable 219 days hence; reckoning interest at 3 per cent.? EQUATION OF PAYMENTS. In order to find the average or mean time at which two or more sums of money payable at different times may be discharged at once, without injury to either party, men in business use the following RULE. Multiply each debt by the time it has to run, then divide the sum of the products by the sum of the debts, the quotient is the time at which all the money ought to be paid, nearly. EXAMPLE. A. owes to B. £25 payable 1st Dec., £50 on 2d Feb., £100 on 25th March; and £125 on 15th May: on what day ought all the money to be paid at once? 117 days after Dec. 1. is 28th March. Ans. EXERCISES. 1. Bought goods payable as follows: £50 on the 1st May, E64 on the 4th June, £86 on the 1st August, and £90 on the 5th Sept.: find the mean time for paying the whole at once. 2. Sold to A. B. goods payable as follows; £70 on 1st January, £110 on 2d March, £80 on 5th May, £120 on 20th July, £48 on 27th Sept., and £52 on 7th Oct.; find the mean time for paying the whole at once. 3. A debt was to be discharged thus: one-fifth in ready money, one-fifth at 3 months, one-fifth at 4 months, one-fifth at 6 months, and the rest at 8 months; find the time for paying the whole at once, 4. A. is indebted to B. in the sum of £750, which was to be paid thus: £250 at the end of 1 year, £100 at the end of 2. years, and £400 at the end of 4 years; at what time ought the whole to be discharged in one payment? THE BUYING AND SELLING OF STOCK. CASE I. To find the value of any quantity of stock. RULE. As £100 is to the proposed quantity of stock, so is the price of £100 of stock to the value of the proposed quantity. Note. Stock is bought and sold through the medium of brokers, who receive per cent., or 2/6 for every £100 of stock which they buy or sell. It is obvious, that the expense of brokerage must be added to the cost of any quantity of stock which is bought; but deducted from the value of what is sold. EXAMPLE. Sold £600 three per cent. consolidated annuities at 633 per cent., how much have I to receive, allowing per cent. for brokerage? £1,00 £6,00 :: £63. 7 6: Remarks. The Stocks, or public funds, are the debts of Government, for which interest is paid from revenues set apart for that purpose. A creditor of the public, or stockholder, cannot demand payment of the capital he has lent; but the interest of it is always regularly paid: and he may obtain money for what is due to him when he pleases, by tranferring his property in the funds to another. When he does so, he may sometimes obtain more, and at other times be forced to accept less, than it cost him; as the prices of the stocks are liable to considerable fluctuation from a variety of causes. The method of raising supplies for the state by borrowing money from individuals or public bodies, and levying taxes for the payment of the interest, is called the Funding System; and the loans thus raised are called the National Debt. Loans have been sometimes raised on annuities for a limited time, these are called terminable annuities; but the general practice is to raise loans on interest, and these are called perpetual annuities. The debt for which perpetual annuities are granted is called the redeemable debt; and the other is called the irredeemable debt. The different funds are also distinguished according to the terms on which they were established: thus, some are called the 3. per cents, some the 4 per cents, and some the 5 per cents. The greater part of the public debt is vested in two large funds, bearing interest at the rate of 3 per cent. of the nominal capital, called the 3 per cent. consolidated, and the 3 per cent. reduced annuities. The first of these arose from the uniting of several funds, formerly kept separate; the other received its name from the reduction of the rate of interest of capitals which before were at 4 per cent. To both considerable capitals, created by subsequent loans, have been since added. The annuities in the 3 per cent. consolidated capital, (and also the 5 per cents.) are payable on the 5th January and the 5th July; those in the 3 per cent. reduced, (and also the 4 per cents.) on the 5th April and 10th October. The person possessed of stock on the day of payment receives interest for the preceding half year; and therefore a purchaser during the currency of the half year, has the benefit of the interest of the stock he buys, from the last term of payment to the time of transfer. New loans are payable by instalments at stated periods; and they generally comprehend several kinds of stock, which, when the loan is in progress, are all assignable together, and their united value is called Omnium. The annuities for fixed terms now existing (called Long Annuities) all termi nate in January 1860. Loans are called a funded debt, when taxes are appropriated for paying the interest; sums raised by Government for which no provision has been made, are called the unfunded debt: of the latter description are Exchequer, Navy, and Ordnance Bills. Exchequer Bills are bills issued from the Exchequer. They are mostly for £100 each, and bear interest at the rate of from 2d. to 3d, a-day. Some are for £1000 each, and bear interest at the rate of from 2d. to 3 d. a-day on each £100. Navy Bills are bills issued from the Navy Office, in payment of stores for ships, dockyards, &c. They are made payable at 90 days; after which they bear interest, if not discharged. Ordnance Bills, or Debentures, are issued from the Ordnance Office, for payment of stores, &c. for that department. The capitals of the Bank of England, and of the East India and South Sea Companies, are also termed Stocks; and they are transferable like Government funds, but the dividends vary according to the success of the respective companies. India Bonds, are bonds issued by the East India Company of £50 and £100 each, bearing interest at the rate of 5 per cent. 1. Find the cost of £1200 three per cent, consolidated annuities, bought at 79 per cent. 2. Find the proceeds of £800 three per cent. reduced annuities, sold at 80 per cent. 3. Find the cost of £425 navy 5 per cents, bought at 1061 p. cent. 4. Find the proceeds of £1450 India stock, sold at 241 per cent. 5. Find the cost of £55 long annuities, bought at 19 years' pur. chase, brokerage per cent. on the value. 6. Bought £3000 stock in the 3 per cent. cons. when at 63, and sold out when at 673; what did I gain? 7. Bought £6000 stock in the 3 per cent. red. when at 627, and sold out when at 614; what did I lose? CASE II. To find how much stock may be bought for a given sum. RULE. Increase the given rate by ; then, As that sum is to the given purchase money, so is £100 to the quantity of stock. EXAMPLE. How much stock at 65% will £4734 purchase? EXERCISES. Ans. 1. How much stock at 844 will £6178: 18 purchase? 2. How much stock at 68 will £1638 purchase? |