paratively little value, unless it leads pupils to the employment of this device throughout all of their work. Besides preventing a pupil from making a very serious mistake in an ordinary computation, the habit of careful reading that is necessarily formed by the scholar that is not satisfied with a simple guess, will tend to make his methods simpler and more accurate. He will learn to apply to the apparently more difficult numbers of the written problem the processes employed in solving the comparatively simple “mental” questions. While all of the pupils should not be expected to give the same answer to each of these examples, they should gradually approach more and more closely to the correct result. 1. 480 is what per cent of 960 ? 982. The teacher that is allowed any discretion should omit all problems relating to Bonds and Stocks. The average grammar-school pupil cannot be made to understand the subject without the expenditure of more time and energy than should be given to a topic that he will learn by himself when he grows older if he gets the proper foundation. If, however, the course of study requires that this topic be taken up, the teacher should aim to interest the pupils by making some local corporation the basis of the work. A certificate of stock should be obtained, or at least a copy made, which might be placed upon the blackboard. · The proie build and equinha, for instance The scholars should be led to see that large undertakings, such as the construction of a railroad, the building of water-works, and the like, require more money than any individual might have, or would care to risk. It then becomes necessary to interest a number of persons that will be willing to invest more or less money in the new enterprise. It is found, for instance, that $ 50000 will be needed to build and equip the street railroad mentioned in 1. The projectors divide this amount into 500 shares, each of which represents a one-five-hundredth interest in the profits. It may happen sometimes that it is considered advisable to interest people of small means, and who are unwilling to take a $100 share. In these cases the original (par) value of the shares may be fixed as low as $10 each. When the par value is not given, it is understood to be $100. In the distribution of profits, the owner of 10 shares is entitled to 3% of $ 2000, or $ 40. 2. These profits are generally distributed annually, semiannually, or quarterly. Before the time comes for “declaring" the dividend, the directors of the company meet and determine how much money shall be thus distributed. It may be considered advantageous to reserve a portion of the profits for the purchase of new cars, or for the extension of the road, etc.; so that the amount distributed at any time does not necessarily include all that has been gained. The dividend is generally announced as a per cent of the capital, which in this case is $50000; so that the semi-annual dividend is 4%, equal to 8% per year. 3. The owner of a $100 share, on which he receives $8 per year, is not likely to be willing to sell it for $100 if he can obtain only $4 per year interest on that sum of money deposited in a savings bank. The person desirous of obtaining stock after it is reasonably certain that the railroad is going to prove successful, will have to pay more than $100 per share. Mr. H. pays $150 per share, or 150% of the par value. 4. Mr. H. receives 4% dividend on $3000, or $120. From the savings bank he would obtain 2% on $4500, or $90. 5. The $120 semi-annual dividend is 2% on the $4500 invested, equivalent to 51% per year. 6. The words “per cent ” are not used in stating the price of stock. A $ 100 share at 1642% is worth $1641; 30 shares are worth $1641 x 30. 7. Assuming the par value of each to be $ 100, the first pays $6 per year on $150, or 4%; the second pays $7 per year on $175, or 4%. The par value of $100 is assumed for convenience; a par value of $50 would make the cost of a share of gas stock 150% of $50, or $ 75, and its annual dividend would be 6% of $50, or $3, the rate on the amount invested being 4%. 8. The buyer of stock at 125 wishes to receive 4% of $ 125, or $5. As the dividend is based on the par value ($ 100), the rate must be 5% per year, or 21% semi-annually. 9. [937% of ($ 50 x 17)]+[1024% of ($10 x 143)]. 10. A person that desires to buy stocks is not always likely to know where he can find any for sale; so he goes to a stockbroker, who makes a business of buying and selling stocks on commission. This commission is a small per cent of the par value, the charge of {% for buying or selling a share of the par value of $100 being 1216, whether the actual value of the stock be $150 or $50. This broker receives, therefore, % of [($50 x 17) + ($10 x 143)]. 11. A bond is a note issued by a corporation, and is generally secured by a mortgage on its property. It is a much larger document than the note of an individual, and frequently contains at the bottom a number of “coupons," one for each half-year's interest, upon which is engraved the date when due and the sum payable. A 10 years' U.S. 4% coupon bond for $ 1000 would have 20 coupons, each worth $20 when due. At the expiration of each 6 months, the holder of the bond cuts off the proper coupon and presents it for payment. A “registered” bond contains no coupons, a check for the interest being mailed to the owner. Although the railroad company in this example receives only $95 for each $100 bond, it promises to pay $4 interest per year, and $ 100 at the end of 20 years. In considering the rate of interest received by the owner of such a bond, it is not customary to complicate the example too much by requiring the pupils to take into account the additional $5 above the cost received when the bond is redeemed at the end of 20 years, although buyers of bonds include it in their calculations. For our purpose, at present, it will be sufficient to assume that the purchaser of one of these $100 bonds receives $4 on each $95 invested, the rate being 400 = 95, or 41%. 12. Omitting the question of redemption, at which time the purchaser for $116.50 would receive only $100, the rate is 400 = 1161, or 3281%. The holder of a U. S. bond knows that the face value of the bond will be paid in full at maturity, and that the interest payments will be made on the dates when due; in the case of the bond of a railroad, or the like, there is always the possibility that something may occur to prevent the company from meeting its obligations. 13. The rate of income from stocks may vary at each dividend period, depending upon the amount of business done, etc.; the rate of income from bonds is fixed as stated on their face. Bonds are redeemed at the time specified; there is no reason why a successful company should sell out and divide the proceeds among its stockholders. When, however, the property of a corporation is sold, the claims of bondholders and all other obligations must be satisfied before the stockholders receive anything. 14. The stock-broker's fee is called brokerage, or commission. 15. A cotton-mill obtains material through a cotton “ factor”; property is purchased through a real estate agent; a grocer may buy butter, eggs, etc., from a commission merchant, the seller in each case remitting the amount received to the owner after deducting his fee, or commission. 16. The base in insurance is the sum for which the property is insured; in taxes, it is the assessed value of property; in brokerage, it is the par value of stocks or bonds; in commission, it is the sum for which goods are bought or sold; the principal is the base upon which interest is calculated; the face of the note is the base in bank discount; in commercial discount, the gross price is the base in the first instance, the base for each subsequent discount being the successive remainders left after the deduction of the previous discounts; in stocks and bonds, the base is the par value. 17. The assessed value of property is the value for purposes of taxation, and is fixed annually by officers chosen for this duty, generally called assessors. 18. 21% of assessed value (x) = $540; assessed value = $24000. This is of the actual value, or 663%. For various reasons, the assessed value is placed below the sum that would be realized by the sale of the property under favorable conditions; but care is taken that all property is assessed upon the same basis. 19. If all property were assessed at its actual value, the same amount of taxes would be produced by a lower rate. To obtain $540 taxes on property assessed at $36000, the rate would be 11%. 21. 1674 ft. = 558 yd.; 558 yd. = 51 yd. = 1116 half-yd. =-11 half-yd., which gives 101 rd. and 5 half-yd. = 101 rd. 21 yd. = 101 rd. 2 yd. 1 ft. 6 in. 22. $8575 - $245 = 35 = number of shares. Quarterly dividend = 21% of ($ 100 x 35). |