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Geometry. 250. SOME INTERESTING FACTS ABOUT SQUARES, TRIANGLES, AND HEXAGONS.
1. Four equal squares may be so joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 90°. Four tinies 90°
degrees. 2. Six equal equilateral triangles may be so joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 60°. Six times 60° degrees.
NOTE.—Cut from paper 6 equal equilateral triangles and join them as shown in the figure.
3. Three equal hexagons, may be so joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 120°. Three times 1200 degrees.
NOTE.—Cut from paper 3 equal hexagons and join them as shown in the figure.
4. Since every regular hexagon may be divided into six equal equilateral triangles, * as shown in the figure, it follows that the side of a regular hexagon is exactly equal to the radius of the circle that circumscribes the hexagon.
* See Observation, page 149.
251. MISCELLANEOUS REVIEWS. 1. Find the interest of $250 from Sept. 5, 1896, to Jan. 17, 1898, at 6%.
2. Find the amount of $340 from April 19, 1895, to Oct. 1, 1896, at 6%.
3. Find the amount of $500 from May 20, 1897, to Feb. 28, 1898, at 5%.
4. Find the amount of $630 from July 1, 1896, to Nov. 1, 1896, at 7%.
5. Find the amount of $800 from Jan. 1, 1897, to Jan. 25, 1897, at 6%.
6. If a 60-day bill of $400 is discounted 2% for cash, how much ready money will be required to pay the bill?
7. Find the amount of $392 for 60 days (two months) at 6%.
NOTE -Observe that $392 is the answer to problem 6. The result of problem 7, then, is the amount that the goods mentioned in problem 6, would cost at the end of 60 days if the purchaser borrowed the money at 6% to pay for them. Compare this result with $400. How much does the purchaser of the bill save by borrowing the money at 6% to pay the bill instead of letting the bill run 60 days and then paying $400 ?
8. Find the cost of goods, the list price being $46, and the discounts “50 and 10 off and 2 off for cash.”
9. My remuneration for selling goods on a commission of 40% amounted to $56.20. How much should the man for whom the goods were sold receive?
NOTE. - $56.20 is 40% of the selling price of the goods. The man for whom the goods were sold should receive 60% of the selling price When goods are sold on a commission of 40%, what the agent receives equals what part of what the employer receives ? What the employer receives is how many times what the agent receives?
K. The sum of all the angles of 6 triangles equals how many right angles ?
252. When a man borrows money at a bank he gives his note for a specified sum to be paid at a specified time and he receives therefor, not the sum named in the note, but that sum less the interest upon it from the time the note is given to the bank officials to the time the note is due.
253. The acceptance of a note by the bank officials and the payment of a sum less than it will be worth at maturity* is called "discounting the note." '
254. The proceeds of a note is the sum paid for it. rule, the notes discounted at a bank are those which bear no interest, and the date of discounting is usually the same as the date of the note, though not necessarily so.
EXAMPLE Find the discount and proceeds of the following: $800
JACKSONVILLE, ILL., Jan. 10, 1898. Sixty days after date I promise to pay James Rice or order, eight hundred dollars, value received.
ARTHUR WILLIAMS. Discounted at 6%, Jan. 10, 1898.
From the date of discount to the date of maturity it is 60 days. Interest of $800 for 60 days $8.00.
Proceeds of note = $800 – $8 $792.
Observe that the bank receives the interest on $800 for two months at 6% for the use of $792 for two months. The actual rate of interest is therefore a little more than the rate named.
* The date of maturity is the day upon which the note is legally due.
255. PROBLEMS IN BANK DISCOUNT.
CHICAGO, ILL., Apr. 5, 1898. Thirty days after date I promise to pay to the order of John Smith, three hundred seventy-five dollars, at the Union National Bank. Value received.
JAMES WHITE. Discounted April 5, at 6 %. Find proceeds.
AURORA, ILL., March 10, 1898. Sixty days after date I promise to pay to Wm. George, or order, four hundred fifty dollars, at the Old Second National Bank. Value received.
FAY D. WINSLOW. Discounted March 10, at 7 %. Find proceeds.
WAUKEGAN, ILL., Feb. 9, 1898. . Ninety days after date I promise to pay to the order of John Mulhall, two thousand three hundred dollars, at the Security Savings Bank. Value received.
CHAS. WHITNEY. Discounted Feb. 9, at 7 %. Find proceeds.
SERENA, ILL., Jan. 20, 1898. Sixty days after date, I promise to pay to John Parr, or order, five thousand dollars. Value received.
HARRY BROWN. Discounted Jan. 20, at 7 %. Find proceeds.
BOSTON, MASS., April 12, 1898. Sixty days after date I promise to pay to W. J. Button, or order, three thousand five hundred dollars. Value received.
HARRY WILSON. Discounted Apr. 24, at 6 %. Find proceeds.
Promissory Notes. 256. THE DISCOUNTING OF INTEREST-BEARING NOTES.
Whenever a note is presented at a bank to be discounted, its value at maturity is regarded as the sum upon which the discount is to be reckoned. When the note is not interest bearing, its face value* is its value at maturity. In the discounting of short-time notes at banks it is customary to find the exact number of days from the date of discounting to the date of maturity, and to regard each day as 1/360 of a year.
AUSTIN, ILL., Jan. 1, 1898. Six months after date I promise to pay to the order of N. D. Gilbert, seven hundred fifty dollars, with interest at the rate of six per cent per annum.
O. T. BRIGHT. Discounted at a bank, May 10, 1898, at 7 %.
Value of the note at maturity$772.50
TOPEKA, KANSAS, Dec. 10, 1897. Five months after date, I promise to pay to the order of J. C. Thomas, five hundred forty dollars, with interest at the rate of six per cent per annum.
HIRAM BAKER. Discounted at a bank, April 1, 1898, at 7 %.
EARLVILLE, ILL., Feb. 1, 1898. Six months after date, I promise to pay to the order of Wm. R. Haight, three hundred twenty-five dollars, with interest at the rate of six per cent per annum.
Chas. Hoss. Discounted at a bank, June 1, 1898, at 7 %.
* The face value, or “face," of a note is the value shown upon its face-the sum of money expressed in words in the body of the note.