2. If Missouri State 6's are 16% below par, what sum must be invested in this stock to obtain an income of $960?

3. I have an investment in Virginia 6 per cent. bonds, which brings me an income of $630, and I wish to sell, and invest the proceeds in United States 5 per cents.; if in the market, the Virginia bonds are 15 % below par, and the United States bonds 3 % above par, what sum must I add to the investment to secure the same income? Ans. $4053.

4. How many shares of canal stock at 60 % must be sold, in order that the proceeds, invested in the California State 7's at 96 %, may yield an income of 840? Ans. 192 shares.

5. A capitalist invested equal sums in the United States 5 per cents., and the Maryland 5 per cents., purchasing the former at a premium of 4 %, and the latter at a discount of 5%. The income from both investments was $2487.50; how much money was invested in each kind of stock?

CASE III

Ans. $25000. 24.700

492. To find what per cent. the income is of the investment, when stock is purchased at a given price. 1. What per cent. of my investment shall I secure, by purchasing the New York 7 per cents. at 105 %?

OPERATION.

.07 1.05

=

63 %

ANALYSIS. Since $1 of the stock will cost $1.05, and pay $.07, the income is 1763 % of the investment. Hence the

RULE. Divide the annual rate of income which the stock bears by the price of the stock; the quotient will be the rate upon the in

vestment.

EXAMPLES FOR PRACTICE.

1. What per cent. of his money will a man obtain, by investing in 6 per cent. stock at 108 %? Ans. 55 %.

2. What is the rate of income upon money invested in 6 per cent. bonds, purchased at a discount of 16 %? Aus. 74. 3. Panama railroad stock is at a premium of 344 %, and the

charge for brokerage is 1%; what will be the rate of income on an investment in these funds, if the stock pays a dividend of 8% annually? Ans. 6%.

4. Which is the better investment, to buy 5's at 70 %, or 6's at 80 %?

5. Which is the more profitable, to buy 8's at 12 %, or 5's at 75%?

6. If a railroad company, whose capital stock is $24182400, pays $1722996 in a dividend to the stockholders during a certain year, what per cent. on the investment will a man receive who holds shares purchased at 79% %? Ans. 813 %

CASE IV.

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493. To find the price at which stock must be purchased, to obtain a given rate upon the investment.

1. At what price must 6 per cent. stock be purchased, in order to obtain 8 per cent. income on the investment?

OPERATION.

$.06.08 $75

ANALYSIS. Since $.06, the income of $1 of the stock, is 8% of the sum paid for it, we have,

(449), $.06.08$.75, the purchase price. Hence,

RULE. Divide the annual rate of income which the stock bears by the rate required on the investment; the quotient will be the price of the stock.

EXAMPLES FOR PRACTICE.

1. What must I pay for Government 5 per cents., that my investment may yield 8 %? Ans. 62 %.

2. At what rate of discount must the Vermont 6 per cent. bonds be purchased, that the person investing may secure 61% upon his money? Ans. 4%.

3. What rate of premium does 7 per cent. stock bear in the market, when an investment pays 6 % ?

4. A speculator invested in a Life Insurance Company, and received a dividend of 6 %, which was 83% on his investment; at what price did he purchase? Ans. 72 %.

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494. Profit and Loss are commercial terms, used to express the gain or loss in business transactions.

495. Gains and losses are usually estimated by some rate per cent. on the money first expended or invested.

Hence

I. Profit and loss are reckoned as percentage upon the prime or first cost of the goods as the base.

II. The selling price of the goods is amount or difference, according as it is greater or less than the prime cost.

EXAMPLES FOR PRACTICE.

1. A merchant bought cloth for $3.25 per yard, and gained. 8% in selling; what was the selling price?

the gain, which added to the cost gives $3.51, the selling price. Or, since the rate of gain is 8 %, that which cost $1 will bring $1.08, and the selling price will be 1.08 times the buying price. Hence $3.25 x 1.08 3.51, the selling price.

2. A jobber invested $2560 in dry goods, and realized $384 net profit; what was the rate per cent. of his gain?

OPERATION.

$384 $2560 = 15 %

ANALYSIS. According to (Prob. II, 450), we divide the gain, $384, which is percent

age, by the cost, $2560, which is the base, and obtain 15 15 %, the rate of gain.

3. A produce dealer sold a shipment of wheat at a loss of 5 %, realizing as the net proceeds, $8170;

OPERATION.

$1.00.05 = .95

8170.95 $8600, Ans.

what was the cost?

ANALYSIS. According to (Prob. V, 453), we divide the net proceeds, $8170, which is difference, (448), by 1

minus the rate of loss, or .95, and obtain the base, or prime cost, $8600.

4. A merchant pays $7650 for a stock of spring goods; if he sell at an advance of 20 % upon the purchase price, what will be his profits, after deducting $480 for expenses? Ans. $1050.

5. Bought 320 yards of calico @ 15 cents, and sold it at a reduction of 24%; what was the entire loss?,204

6. A dealer having bought 30 barrels of apples at $3.50 per barrel, and shipped them at an expense of $5.38, to be sold on commission of 5 %, what will be his whole loss if the selling price is 10% below the purchase price? Ans. $20.60 7. Bought corn at $.50 a bushel; at what price must it be sold to gain 33 per cent. ? 66.66788

8. Bought fish at $4.25 per quintal, and sold the same at $4.93; what was my gain per cent.? Ans. 16 %. 9. Bought a hogshead of sugar containing 9 cwt. 44 lb., for $59; paid $4.72 for freight and cartage; at what price per pound must it be sold to gain 20 per cent. on the buying price?

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10. A wine merchant bought a hogshead of wine for $157.50; a part having leaked out he sold the remainder for $3.321 a gallon, and found his loss to be 5 per cent. on the cost; how many gallons leaked out? Ans. 18.

11. Sold a farm of 106 A. 3 R. 30 P. for $96 an acre, and gained 18 per cent. on the cost; how much did the whole farm cost? Ans. $8700.

12. A lumberman sold 36840 feet of lumber at $21.12 per M, and gained 28 per cent. ; how much would he have gained or lost, had he sold it at $17 per M? Ans. $18.42, gained.

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13. A speculator bought shares in a mining company when the stock was 4% below par, and sold the same when it was 28 % below par; what per cent. did he lose on his investment? 14. A machinist sold a fire engine for $7050, and lost 6 per cent. on its cost; for how much ought he to have sold it to gain 12! per cent.? Ans. $8437.50. 15. Sold my carriage at 30 per cent. gain, and with the money bought another, which I sold for $182, and lost 121 per cent.; how much did cach carriage cost me?

Ans.

{ First, $160; Second, $208.

16. Gafney, Burke & Co. bought a quantity of dry goods for $6840; they sold of them at 15 per cent. profit, at 18 per cent., at 20 per cent., and the remainder at 333 per cent. profit; how much was the average gain per cent., and how much the whole gain? Ans. 21. % gain; $1482, entire gain. 17. If I buy a piece of land, and it increases in value each year at the rate of 50 per cent. on the value of the previous year, for 4 years, and then is worth $12000, how much did it cost?

18. A Western merchant bought wheat as follows: 600 bushels of red Southern @ $1.80, 1200 bushels of white Michigan @ $1.621, and 200 bushels of Chicago spring, @ $1.25. He shipped the whole to his correspondent in Buffalo, who sold the first two kinds at an advance of 20 % in the price, and the balance at $1.20 per bushel, and deducting from the gross avails his commission at 5 %, and $254.60 for expenses, returned to the consignor the net proceeds. What was the rate of the merchant's gain? Ans. 4%.

19. A broker buys stock when it is 20 % below par, and sells it when it is 16 % below par; what is his rate of gain?

20. A man has 5 per cent. stock the market value of which is 78%; if he sells it, and takes in exchange 6 % stock at 4 % premium, what per cent. of his annual income does he lose?

21. A machinist sold 24 grain-drills for $125 each. On one half of them he gained 25 per cent., and on the remainder he lost 25 per cent.; did he gain or lose on the whole, and how much? Ans. Lost 200.

22. Bought land at $30 an acre; how much must I ask an acre, that I may abate 25 per cent. from my asking price, and still make 20 per cent. on the purchase money? Ans. $18.

23. A salesman asked an advance of 20 per cent. on the cost of some goods, but was obliged to sell at 20 per cent. less than his asking price; did he gain or lose, and how much per cent.?

24. A Southern merchant ships to his agent in Boston, a quantity of sugar consisting of 200 bbl. of New Orleans, each containing 216 lb., purchased at 5 cents per pound, and 560 bbl. of West india, each containing 200 lb., purchased at 5 cents per pound.