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Investments.

1. The dividend on certain stocks being prospectively for all time, 8% per annum, how much shall one pay per share (par value $100) in order to realize 6% on the investment?

2. The current rate of interest continuing to be 6% for all time, would an 8% bond running 20 years be worth as much as the 8% stock mentioned in Problem 1 ?

3. The dividend on certain stocks being prospectively for all time, 5% per annum, how much shall one pay per share (par value $100) in order to realize 6% per annum on the investment?

4. The current rate of interest continuing to be 6% per annum for all time, would a 5% bond running 20 years be worth more or less than the 5% stock mentioned in Problem 3?

5. How much, including brokerage, * must one invest in 8% stocks at 38% premium in order to have an annual income of $1000 ?

6. How much, including brokerage, must one invest in 4% stocks at 28% discount in order to have an annual income of $1000 ?

7. A man invests (not including brokerage) $27,500 in bank stock at a premium of 10%; if the stock yields a semiannual dividend of 3}%, what is his annual income?

8. U.S. 4's, due in 10 years are bought at 8% premium. (a) What would be the cost (not including brokerage) of twelve $100 bonds? (b) What is the annual income on the twelve bonds ?

9. To secure 5% on the investment, how much can one afford to pay for stock that yields an annual dividend of 6%?

10. To secure 5% on the investment, how much can one afford to pay for stock that yields an annual dividend of 4% ?

*Stocks are often bought or sold through a broker. The commission for transacting the business is called the brokerage. The usual brokerage is f of 1% reckoned on the par value, or 124¢ per $100 share.

Investments.

1. What is the average per cent of annual income on a 20-year 6% bond bought at a premium of 20%?*

2. What is the average per cent of annual income on a 20year 4% bond bought at a discount of 5% ?

3. What is the average per cent of annual income on a 25. year 5% bond bought at a premium of 2% ?

4. What is the average per cent of annual income on a 10year 5% bond bought at a discount of 2%?

5. At what price must 6% 10-year bonds be bought to yield an average annual income of 5%? +

6. The converse of the foregoing problem is as follows: What is the average per cent of annual income on a 10-year 6% bond bought at a premium of =%? I

7. At what price must 4% 10-year bonds be bought to yield an average annual income of 5%?

8. The converse of the foregoing problem is as follows: What is the average per cent of annual income on a 10-year 4% bond bought at a discount of -%? $

9. If a man pays $1500 for a city lot from which he receives no income, but upon which he pays a tax of $20 a year (the first tax being paid exactly one year after purchasing the lot) for how much must he sell the lot immediately after paying his tenth annual tax, in order to realize 6% compound interest on his investment, regarding the amount paid for taxes as a part of the investment ? ||

* A $100 6% bond bought for $120, in 20 years yields (20 times $6) $120 less the $20 of premium paid; or, $100. The average yield per year then is ($100 = 20) $5. $5 is what per cent of $120 the amount originally invested ?

† A $100 6% bond in 10 years amounts to $160. One dollar in 10 years at 5% amounts to $1.50. It will take as many dollars to amount to $160 as $1.50 is contained times in $160.

# Put the premium at which the bonds described in Problem 5, must be bought, in place of the dash.

$ Put the discount at which the bonds described in Problem 7, must be bought, in place of the dash.

| In solving this problem use the table on page 298.

Investments.

per month.

1. A house cost $5500. The average annual necessary expenditures are: Repairs, $120; taxes, $52; insurance, $12.50. The house rents for $35 a month.

What per cent, net, does the owner realize on the investment ?

2. A house cost $1000. The average annual necessary expenditures are: Repairs, $25; taxes, $12.75; insurance, $6.40. The house rents for $10 a month. What per cent, net, does the owner realize on the investment?

3. A house rents for $25 per nionth, and the owner pays $60 for taxes, insurance, and repairs. On what sum does the house pay a net profit of 5% per annum ? 4. Three flats that cost $8500 rent for $35, $30, and $25

If the flats on the average are vacant 12 of the time and if the annual cost of repairs, insurance, taxes, water, fuel, and janitor services is $565, what is the net income on the investment ?

5. A farm cost $10,000 including buildings that are valued at $3000. If the farm and buildings rent for $600 per annum, and the owner pays annually for repairs $62, taxes $55, and insurance $13; and if the annual depreciation on the value of the buildings is equal to 2% of their original value, what is the net per cent of income on the investment?

6. To make 5% on the investment, how much should be paid for a house that rents for $30 a month, if repairs, taxes, and insurance average $125 per

annum ? 7. Land that cost $70 per acre and rents for $4 per acre pays what

per

cent on the investment, if the average annual cost of fencing and taxes is 70 cents per acre?

8. Land valued at $80 per acre rents for $5 per acre. If the assessed value is one fifth the actual value and the taxes amount to 41% of the assessed value, and the average annual cost of fencing is 40 cents an acre, what per cent of the actual value does the land annually yield its owner ?

“ Marking Goods." In many mercantile houses, the cost of goods is indicated by a private mark upon each article. The characters used may be ten letters, each letter standing for a figure. To aid the memory of those using the mark, the letters employed may be those of some “key word,” as follows:

Purch a s e d
1 2 3 4 5 6 7 8 9

Any letter of the alphabet not in the key word may be used to represent zero. This makes it more difficult for a customer or a competitor to interpret the private mark than it would be, were a word of ten letters used, the tenth standing for zero. According to the above plan $1.25 is puh; $2.40 is ucx or ucy or ucz; $2.05 is ukh or ugh or ulh.

In giving the answers to the following, write the cost in letters employing the key word given above; write the selling price in figures.

1. Men's rubber boots; list, $4.20; discount, 33%. (a) Cost? (b) Selling price to make a profit of 33%?*

2. Since the discount in Problem 1 is 333% and the expected profit 331%, why is not the selling price the same as the list price?

3. Men's arctics; list, $2.00; discount, 25 and 10%. (a) Cost? (b) Selling price to make a profit of 333% ?

4. Women's buckle gaiters; list, $1.75; discount, 40%. (a) Cost? (b) Selling price to make a profit of 33} %?

5. Men's plow shoes; cost $15 per case of 12 pairs. (a) Cost per pair? (b) Selling price to make a profit of 40%?

6. If a 36-pair case of Oxford Ties cost $75.60, (a) what should be the cost mark on each pair, and (b) what the selling price, if the rate of profit is 33}% ?

7. Shoe polish; list, $10 per gross, actual cost 650 per bottle; selling price, 104 per bottle. (a) What was the per cent of discount? (b) What was the per cent of profit ?

* In giving the selling price of articles worth one or more dollars each, wake the right hand figure a zero or a five. To do this, mark above rather than below the given per cent of profit. For $3.41 mark $3. 45; for $2.17 mark $2.20, etc.

Estimates.

LATHS.

NOTE.—A lath is 4 feet long and 11 inches wide. Laths are laid about g of an inch apart. Hence 1 bunch, 50 laths, will cover (including the spaces between them) a strip 4 feet wide and 50 times 14+% inches long. Such a strip contains a little more than

square feet. Making large allowance for defective laths and wasted pieces, builders calculate that a bunch of laths will cover 3 square yards.

1. Estimate the laths necessary for two rooms, walls and ceilings, the rooms being 15 ft. by 16 ft. and 14 ft. by 18 ft. with ceilings 10 feet above the floors. Make no allowance for windows and doors in the making of this estimate. In practice, if the openings are numerous or large and

large and "close figures" are required, such allowance may be made. In such cases it is best to make the computation as though there were no openings and make the proper deduction from the amount obtained.

2. Estimate the laths necessary for the walls of a 5-room house, the entire length of wall, including closets and halls, being 163 feet, and the height of wall being 8 feet, an allowance of 200 square feet to be made for openings.

3. Estimate the laths necessary for 6 ceilings the dimer. sions being as follows: 12 by 133, 12 by 14, 10 by 117, 9 by 13, 41 by 10, and 4 by 6.

SHINGLES.

NOTE.-Shingles are of variable widths; but in buying and selling and in making estimates, each 4 inches in width is counted as 1 shingle. A bunch of shingles is 20 inches wide; so there are 5 shingles in each course. There are 25 courses in each end of the bunch; hence there are

shingles in one end of the bunch and shingles in the entire bunch. Four bunches are 1000 (1 M.) shingles. When shingles are laid “41 inches to the weather,” each shingle may be thought of as covering a space 4 inches by 4] inches, or 18 square inches. So 8 shingles are required for each square foot to be covered. To cover 100 square feet (1 square) 800 shingles will be required. But since there is always some waste and often short measure, builders

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