12. A 1-inch cube of metal is heated until its edge is increased to 1.004 in. By what per cent is its edge increased? By what per cent is the area of its surface increased? By what per cent is its volume increased?

13. The length of a steel rod is increased .000007 of its length for each degree of increase in temperature. By how much is the length of a steel rod 30 ft. long increased if the temperature is increased 100°?

14. Show that a round barn 60 ft. in diameter and a rectangular barn 36 ft. by 78 ft. have practically the same floor space.

15. Find the number of board feet of siding for each of the barns in the previous problem, if it is 18 ft. to the eaves in each case. Do not consider the gables. Find the cost of the siding in each case at $35 a thousand feet.

16. The following data were taken from Bulletin No. 143 of the Illinois Agriculture Experiment Station.

The amounts of certain kinds of materials for a round barn 60 ft. in diameter and for a rectangular barn with a plank frame 36 ft. by 78 ft. are as follows:

Find the cost of the materials for each barn if the framing timbers cost $30 a thousand feet, the sheathing, siding, and flooring $30 a thousand feet, and the shingles $5 a thousand. The cost of materials for the rectangular barn is what per cent more than the cost of materials for the round barn? Find the cost of a concrete floor for each at 18¢ a sq. ft.

Exercise 103. Percentage

1. Read the per cents equivalent to the following: .25, .07, 6, 35, 489, .0003, .001, .07, .81, 6.502, .5%.

3 3 5

2. Read the equivalent per cents:,,, t, §, 1, §, 7, I, I, I, I, 17, 18.

3. Read the equivalent decimal fractions: 17%, .6%, 9.4%, 200%, 1568%, .001%, %, 4%, 3%, 3.004%.

4. A grocer buys eggs at 32¢ a dozen and sells them for 36¢ a dozen. What per cent of the cost does he gain?

5. If he buys eggs at 20¢ a dozen and sells them at the rate of 10 for 20¢, what per cent of the cost does he gain?

6. A buys a house for $2450. He sells it to B, losing 10% of the cost. B gains 10% of what the house cost him by selling it to C. Did C pay the same for the house as A? If not, how much more or less?

7. A hat is marked to sell at 25% above cost. The marked price is $6. The hat is sold for $5.50. Find the per cent of gain or loss on the cost.

8. An article that costs $9 is sold for $11.50. Find the per cent of gain on the cost. Find the per cent of gain on the selling price.

9. At a fire sale the prices were marked down 121%, to the nearest 5¢. Find the sale prices of articles which before the fire had sold for the following prices: $8; $12.50; $6; $25; $3.25; $7.75; $2.50.

10. An accident policy for $5000 costs $29 a year. What is the rate of premium?

11. In July, 1865, it took $100 in paper currency to buy $39 in gold. The paper currency was worth what per cent of its face value in gold? How much currency was needed to buy $100 worth of gold?

12. From 1860 to 1865 prices increased 117%, that is, an article that cost $1 in 1860 cost $2.17 in 1865. At that rate, an article that cost $1 in 1865 cost how much in 1860?

The data in the following problems were taken from a report of the Superintendent of Insurance of Illinois for a

recent year.

1. The following table gives the amount of insurance, the premiums paid, and the losses paid on certain classes of buildings. These figures are for the whole state.

Find the rate of insurance per $100 on each class of buildings. Do you see any causes for the differences?

Find the ratio of the losses to the premiums for each class of buildings. On which class of buildings is the insurance the most profitable for the insurance companies? What per cent of the premiums was returned to the policy holders in each case?

2. The average rate of insurance in Norway in a certain year was 11.7¢ per $100. The average rate in the United States in the same year was $1.037 per $100. Find the cost of a policy of $5000 in each country at these rates. Do you know some of the probable causes for this difference in rates?

3. Find the rates of insurance in your neighborhood on the classes of buildings mentioned in problem 2. How do these rates compare with the rates found in that problem?

Exercise 105. Stocks and bonds

1. In its annual report for a recent year the United States Steel Company showed gross sales of $1,205,000,000, which were 41% more than for the preceding year. Find the sales for the preceding year to the nearest million dollars.

2. The net earnings of the United States Steel Company for this year, after deducting Federal taxes, were $224,219,564. The Federal taxes were $223,465,435. What was the total of the net earnings including Federal taxes? What per cent of the total net earnings was paid for taxes?

3. At this time United States Steel common was selling at 90 and preferred for 109. Can you suggest any probable cause for this difference in price?

4. The following bond quotations are from the New York stock market :

Find the rate of income on the investment paid by each kind of bonds bought at the price quoted, brokerage 1%. Which investment yields the highest rate of income?

5. Find the cost of 10 $100 bonds of each of the kinds mentioned in the previous exercise, allowing 1% brokerage. 6. Find the cost of $1000 worth of U. S. Liberty 41s at the price quoted above, brokerage 1%.

7. How much must be invested in City of Paris 6s as quoted above to secure an annual income of $750, brokerage 11%?

8. Name some differences between stocks and bonds.

9. Find the gain if 1400 shares of Union Pacific are bought at 118 and sold for 120, brokerage % for buying and the same for selling.

98. Investments. The principal things to be considered in making an investment are its security and the rate of income it yields.

Many investments are advertised to yield large rates of income. These investments are often unsafe. If they offered good security and high rates of income, it would probably not be necessary to advertise them. But many persons with small sums to invest are attracted by the large incomes promised by "get-rich-quick" schemes, and invest in the hope of getting something for nothing.

Exercise 106

The investments offered in the first 8 of the following exercises were found in the advertisements or the market reports of daily newspapers. At the time these investments were offered money could be put out at interest with good security at 6%. State which of these are probably safe investments, and which offer as good or a better rate of income than lending money at 6%.

1. An oil company stock, par value $1 a share, is offered at $1.50 a share, and promises dividends " at the rate of 24% annually on par."

2. Another oil company offers "oil stock that pays 12% a year."

3. I am in a position right now to deliver shares of Motor Car Corporation at a price which affords the buyer an immediate profit of 15 per cent."

4. Farm mortgages bearing 6% interest are offered for sale.

5. "50% profit. Established manufacturing company offers a profit of 50% and return of principal within 12 months to a limited number of investors."

6. United States 34% bonds may be bought at par.