Ex. 3. What is the difference between the simple interest of £10000 for 1 year, at 6 per cent. per annum, and the C.I. of the same sum for a year, taken quarterly? The simple interest of £1000=100×6= £600. Difference £613. 12s. 84d.-£600 £13. 12s. 81d. 284. EXERCISES IN C.I. 1. Find the C.I. of £640 for 5 years, at 3 per cent. per annum. 2. Which is the most advantageous to receive for the value of a house, £5000 ready money, or £5750 in 3 years, sup posing the interest compound, and the rate 5 per cent. per annum ? 3. An engineer, whose salary is £150 a year, puts in the Savings Bank every year one-tenth of his stipend. How much will he have in 6 years, the rate of interest being 3 per cent. per annum ? 4. Required, the C.I. of £9375, at 10 per cent. per annum, for 3 years 8 months. 5. What is the rate per cent. per annum on a principal lent at 1 per cent. quarterly, C.I. 6. Find the amount of £819. 4s. in 4 years, at 12 per cent. per annum, C.I. 7. Required, the difference between the simple and compound interest on £1460. 18s. 9d. for 5 years, at 4 per cent. per annum. 8. What will be the amount of 6 payments of £1200, put yearly into a bank for 6 years, at 10 per cent. per annum ? 9. How much must be put to C.I., at 4 per cent. per annum, to make the sum of £33955. 13s. in 5 years ? 10. What principal, lent at C.I., at 6 per cent. per annum, will amount to £2050. 10s. 8d. in 3 years? 11. If a boy, 14 years old, has a legacy of £2000 left to him. How much will he have to receive at the age of 21, the legacy increasing, at C.I., at the rate of 5 per cent. per annum ? 12. Determine the C.I. of £15000, at 4 per cent. per annum, for 3 years? 13. During 5 years a person puts £1000 each year, at C.I., at 4 per cent. per annum. How much will he have to receive, at the end of that time? DISCOUNT. 285. Discount is an money before it is due. a bill of £3000, which a banker in order to have it discounted. find what he will deduct, and what he will pay to the holder of the bill, if the rate of interest be 6 allowance made upon the payment of To explain this, let us suppose that is to be paid in 1 year, is taken to It is required to per cent. The holder of a bill is evidently entitled to receive a sum, which being added to its interest for 1 year, would amount to £3000, the value of the bill. But since £100, at 6 per cent., amounts to £106 in 1 year, it follows that £106, due 1 year hence, is of the same value as £100 ready money. The present worth of the bill is, therefore, £2830. 3s. 9d., and the discount £169. 16s. 3d. We have, then, the present worth the given sum-the discount; And the discount=the given sum-the present worth. 286. This method of calculating discount, though the true one, is not that employed by bankers and merchants; it is customary to charge as discount the interest of the sum for the given time, which gives the discount too large, and, consequently, the present worth too little, by the interest of the true discount. Thus, if a banker discounted a bill of £3000, at 6 per cent., he would deduct the interest of that sum for 1 year, which is £180, exceeding the true discount by £10. 3s. 9d., which is the interest of £169. 16s. 3d., and the present worth is £3000-£180 £2820. Therefore, by this transaction, the holder would lose £10. 3s. 9d., which sum the banker would gain. 287. The bankers' method is supposed to be preferred, as involving less intricate calculations; and when the time is short, and the sum small, as it is generally the case in real business, the difference between the results found by the two methods is but trifling, and the easier method, though false in principle, may be adopted; but when the time is long, and the sum large, the error is too considerable to be allowed for the sake of easy calculation. 288. Discount is mostly applied to the payment of bills, which are stamped documents, given by buyers to sellers, by debtors to creditors, and under many other circumstances, both as security for money due, and as a means of obtaining the immediate use of cash, not payable till a given time. If such a bill be presented to a banker, before the time fixed for payment, and he accepts the security of the person promising payment, or of the holder of the bill, he will discount it, or pay its present value at once, deducting the interest for the time it has to run. 289. When a bill is drawn to run a certain time, three days are allowed after the expiration of the term before the bill is presented for payment. Thus, a three months' bill, dated May 1st, would be nominally due on the 1st of August, but legally on the 4th of August. These extra days are called days of grace. 290. When articles are paid for at the time of sale, or shortly afterwards, tradesmen allow a discount of 5 per cent., which is the same as 1s. per £1 from the amount. For example, in settling an account of £24. 14s. 8d., most tradesmen would allow £1. 4s. 6d., viz., 24s. for the £24, and 6d. for the 14s. 8d. The discount may consist of odd shillings and pence over a certain sum in pounds, but it is generally in the shape of a percentage. This allowance is the interest of the debt, and not of the present value, and will be to the payer's advantage: it thus differs in principle from the bankers' discount. Ex. 1. Required, the present worth of a bill of £486. 18s. 8d., drawn March 25th, at 10 months, and discounted on June 19th, at 5 per cent. Here, from June 19th to January 25th, are 220 days; with the three days of grace, 223 days. By bankers' discount: ...the interest of 100 for 365 days is 5, ..the interest of 100 for 223 days is 223 × 5 or 33. 365 73 ..the interest of £486. 18s. 8d., the amount of the bill, for £486. 18s. 8d. x33-or £14. 17s. 6d. 223 days is = 100 ..present worth £486. 18s. 8d.—£14. 17s. 6d.=£472. 1s. 2d. nearly. By true discount : 103 are worth now 100, ..the present value of £486. 18s. 8d. is = £472. 10s. nearly. £486. 18s. 8d. x £100 103 Ex. 2. What is the present worth and discount of £550. 10s. for 9 months, at 5 per cent. per annum? 193.75 ⚫83 =£530. 12s. Old. ..£550. 10s,-£530. 12s. 04d, £19. 17s. 114d.=discount. Ex. 3. What would a banker gain by discounting, on July 8th, a bill of £447. 12s. 6d., dated June 23rd, at 6 months, at 5 per cent. per annum? Counting 6 months and 3 days from the 23rd of June, we find the bill to be due on the 26th of December: from the 8th of July to this date there are 171 days. |