CASE III. 438. Given, the par value, and the brokerage, or the net proceeds, or entire cost, and the market value, to find the rate. 1. A broker bought Reading convertible coupon. 7's, par value $4000; his charge was $10; what was the rate of brokerage? SOLUTION.-The brokerage, $10, equals the par value, $4000, multiplied by the rate; hence, the rate equals $10 divided by $4000, which we find is .001, or %. OPERATION. =. = .001 $10 $4000 Rule I. Divide the brokerage by the par value, to find the rate. Rule II.-Divide the difference between the real value of the stock, and the net proceeds or entire cost, by the par value, to find the rate. WRITTEN EXERCISES. 2. A broker buys 110 shares of gas stock, par value $25 a share; his charge was $6.87; what was the rate of brokerage? Ans. 1%. 3. A broker, having purchased, according to order, $5600 Rhode Island 6's at 110, informs me that the entire cost is $6188; what brokerage does he charge? Ans. %. 4. I sent a draft for $21250 to a Detroit broker, to invest in Michigan 6's at 106; he remitted me a balance of $25; what rate of brokerage did he charge? Ans. %. INCOME FROM INVESTMENTS. 439. Investments in stocks, etc., may be made either for interest on the money or for the increase of capital. 440. There are Several Classes of stocks, viz.: those of Corporations, States, and the General Government. 441. Bonds are distinguished as Registered and Coupon Bonds. The Registered bonds are payable to order, and cannot be transferred without being indorsed. 442. The Coupon bonds have coupons or certificates of interest attached to them, which may be cut off and the inter est collected when due. 443. The principal bonds of the United States, called Government Bonds, are the following: The 4's of 1907, which are 4% bonds due in 1907. These bonds are both coupon and registered, and the interest is payable quarterly. The 4's of 1891, which are 44% bonds due in 1891, interest payable quarterly, both coupon and registered. The currency 6's, issued to aid in constructing several railroads to the Pacific. There are several series of these bonds, maturing respectively in 1895, 1896, 1897, 1898, and 1899. Government Bonds are so secure that they are much sought after for investment, and thus command a premium. This premium usually becomes smaller cach year, as the bonds approach maturity. When the interest on bonds is payable. in gold, and gold is at a premium, the income in currency is equal to the income in gold, plus the premium. During the civil war, and for several years afterward, gold was at a premium. 444. A Mortgage is a conditional conveyance of property as security for the payment of a debt. Should the interest not be promptly paid, the mortgage may be fore closed, and the property is then sold by the sheriff to the highest bidder, and the mortgage paid off from the proceeds. Property is usually not mortgaged beyond a certain part of its value, in order that the mortgagee may be secure from loss. A second mortgage is sometimes given, but this cannot be paid, in case of foreclosure, till the first is fully paid, and hence may not be a very good security. 445. A Ground-Rent is a fixed rent paid for ground, generally used for building purposes. It is a common practice in some cities, when a person wishes to build one or more houses, instead of buying the ground required, to agree to pay the interest on its value as rent, the contract to continue in force as long as the rent is regularly paid. Ground-rents are redeemable or irre deemable. Some cities, as Philadelphia, prohibit the issue of any more irredeemable ground-rents. Mortgages and ground-rents are not bought and sold at the Stock Exchange, but conveyancers are frequently employed in the transaction, as the title and condition of the property must be examined, and the necessary papers drawn up. Well-secured mortgages and ground-rents are in such high esteem as safe investments, that they are among the securities in which trust funds may be legally invested. NOTE.-In changing from one investment to another, there is often a little more realized from the sale of the first than will procure an exact number of shares of the second. In such cases the income will be calculated on the number of shares, without noticing the surplus. 446. The Quantities considered are: 1. The Amount Invested; 2. The Rate of Dividend or Interest; 3. The Income; 4. The Market Value of $100, or of one share; 5. The Rate of Income. CASE I. 447. Given, the amount of an investment, the mar. ket value, and the rate of dividend or interest, to find the income. 1. If I invest $5100 in 7% bonds at 85, what will be my annual income from them? SOLUTION. Since for 85 cents you can buy $1 worth of stock, for $5100 you can buy as many dollars worth of stock as $.85 is contained times in $5100, or $6000. The annual income on this is $6000×.07 which equals $420. OPERATION. $5100.85 $6000 $6000×.07 $420 Rule.-I. Divide the amount invested by the market value, to find the par value. II. Multiply the par value by the rate to find the income. WRITTEN EXERCISES, 2. What annual income would I receive from $16050 invested in U. S. Pacific R. R. 6's at 107 ? Ans. $900. 3. If I invest $5631.25 in 6% bonds at 112, what is my annual income from this investment ? Ans. $300 4. I invested $5280 in United Companies of New Jersey, stock costing me 132, dividend 10%; what was my annual income from this investment? Ans. $400. 5. Miss Brown has invested $8475 in 54% railroad bonds at 113, interest payable semi-annually; what will be her semiannual income from this investment? Ans. $206.25. 6. A conveyancer sold a lot 25 ft. front and ground rent, redeemable on payment of $1500; ground-rent at 6% ? 50 ft. deep on what is the Ans. $90. 7. Mr. Tompkins bought on ground-rent a lot 75 ft. front by 90 ft. deep, valued at $87.25 per foot front; what would be the ground-rent per foot front at 6%? Ans. $5.231. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 8. I made $5000 by a speculation, and wishing to invest it permanently, I bought $2000 6% bonds at 1173, and invested all the romainder possible in 44% bonds at 1104 (denominations as low as $50); what surplus remained, brokerage %, and what was the annual income? Ans. Sur., $50.75; In., $225.75. 9. Mrs. Warner has $10,000 railroad 6's, quoted at 103; would she increase or diminish her annual income if she should sell them and buy with the proceeds 7% bonds at 110? Ans. Increase, $58. 10. When gold was at a premium of 12 %, Mr. Barton conveyed a lot on a 6% ground-rent, payable in gold, and redeemable on payment of $4500; at what sum in currency must it be made redeemable to realize an equivalent rent, and what is the ground-rent in currency? Ans. $5062.50; Rent, $303.75. CASE II. 448. Given, the income, the rate of dividend, and the market value, to find the amount invested. 1. When 5% gas bonds are selling at 110, how much must be invested to produce an income of $550 ? SOLUTION.-Since $1 of stock gives an income of $.05, to give an income of $550 it will require $550÷.05, or $11000; $11000 of stock at 110% will cost $11000X1.10, or $12100. OPERATION. $550÷.05-$11000 $11000X1.10-$12100 Rule.-I. Find the par value of the stock by dividing the income by the rate. II. Multiply the par value by the market value of 1 share, to find the amount invested. WRITTEN EXERCISES. 2. A real estate dealer buys a 6% ground-rent of $300 per annum at par; what does it cost him? Ans. $5000. 3. A house subject to a ground-rent of $75 at 6% was sold for $5750; what was its value? Ans. $7000. 4. What sum must I invest in 6% street railway bonds, at 119, to secure an annual income of $600, brokerage %? Ans. $11975. 5. What sum must be invested in Kentucky 6's, at 103, to yield $786 a year, brokerage %? Ans. $13525.75. 6. When 44% government bonds are selling at 105, what sum must I invest in them to secure an income of $900, brokerage %? Ans. $21050. *7. If I sell $8000 Ohio 6's at 118, and buy sufficient Georgia 7's at 103 to yield $560 income, how much shall I have left, brokerage % on sale and purchase? Ans. $1160. 8. What must be the market value of Georgia 6's to realize 7% on the investment? What must I pay for Reading coupen 7's, to give an income of 63% ? Ans. 85; 103. SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed. 9. When gold was selling at 115, what must be paid for 6% gold Dearing bonds to realize 7% on the investment? Ans. 984. 10. What must be the market price of 5 % bonds, so that, brokerage%, I may realize 4% on an investment? Ans. 1243. 11. I bought a lot 50 ft. front and 85 ft. deep, at a ground rent of $5.40 per ft. front; what would be the cost of the property, the ground rent being 6% of it? Ans. $4500. 12. How many shares of North Pennsylvania R. R. ($50) at 49, must be sold, that the proceeds, invested in Pennsylvania State 6's, at 115, may give an income of $600, brokerage being charged on sale and purchase? Ans. 237 shares; $8.37 surplus. 13. Mr. Jackson sold $15000 Union Pacific 7's at 101, and invested part of the proceeds in Illinois 6's at 117, sufficient to produce an income of $750, and deposited the remainder, (brokerage %), in bank; what was his bank deposit ? Ans. $412.50. 14. I had some California 7's, which brought me in an income of $546, but preferring an investment nearer home, I decided to exchange them for Philadelphia 6's; if the California bonds were worth 117 and the Philadelphia 105, how much must I add to my investment to secure the same income, brokerage not considered? Ans. $429. |