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884. 425 + 99 is 1 less than 425 + 100; 425 + 999 is 1 less than 425 + 1000.
885. 565 - 99 is 1 more than 565 – 100; 1424 - 999 is 1 more than 1424 - 1000.
7. 4 bbl., 300 lb. each, @ 5$. 9. 84 = 4. 8. 18-44
10.75 @ $ 79 (or $80). 892. 4. Find I and annex cipher. 13. See Art. 791. 893. See Arts. 792, 716, 717, 714.
26. Multiply by 36, by subtracting 4 times the number from 40 times the number; multiply by 45, by subtracting 5 times the multiplicand from 50 times the multiplicand.
900. It may be necessary for the teacher to supplement the information given the pupils in connection with the demand notes in Art. 877. The present note is payable at a fixed time, and the place of payment is specified; but it does not bear interest. If, however, it is not paid at maturity it bears interest from that time at the legal rate.
While savings banks loan money only on good security, generally real estate, banks of deposit will advance money on a note, if the officers feel certain that it will be paid at maturity. When William Brown & Sons present the note for discount, they endorse it by writing their name on its back. This transfers the ownership of the note to any subsequent holder, and also makes the endorsers liable for the amount in case the maker fails to pay it at maturity. The discounting bank thus has two parties upon whom to depend for the money.
The sum charged by the bank for this service is the interest on the face of the note for the time it has to run. This sum is called the discount, as it is deducted from the sum named in the note; and the difference — called the avails or proceeds — is given to the owner of the note.
When the above note is due, it is sent to the Park National Bank for collection. If Thomas Tierney, or some other person, does not pay the money before the close of banking hours, the note is protested; that is, a notary public certifies that payment has not been made, and notifies the endorsers, William Brown & Sons, of their liability.
901. In states in which days of grace are no longer allowed, the pupils should not employ them even in calculating discount on notes made in places that still have days of grace. Two answers are given to each problem in discount, one including days of grace; the other, enclosed in parentheses, in which days of grace are not employed.
902. These exercises are nothing more than examples in interest, except that in some states, three days are to be added to the time mentioned.
Deducting the discount from the face of the note gives the proceeds.
903. As will be seen in Art. 906, the exact number of days is taken for periods less than a year.
904. Pupils should be led to see that banks are entitled to interest only for the number of days they have to wait for repayment. A failure to understand this, leads to frequent mistakes. Many careless scholars find the difference in time between the two dates named in the example, — from Feb. 27 to March 9, in 25, — disregarding entirely the time for which it is drawn.
Instead of explaining how to calculate the discount on the notes given in Art. 905, the teacher should permit the class to attempt to ascertain the result by themselves. In case of a failure to obtain the correct answer, a discussion of the matter will lead to a proper understanding of the principles involved.
906. 1900 is not a leap year. See Arithmetic, Art. 1303, Time Measure.
907. Find the total number of meters in the first twelve pieces, and ascertain their value at the price named. Do the same for the remaining four pieces. Reduce the total number of meters in the sixteen pieces to yards, by multiplying by 39.37 and dividing the product by 36.
908. See Arithmetic, Art. 758.
910. In 641 x 119, the product by 4 is found by multiplying the product of 4, already ascertained, by 4.
912. 8. A yard is 36 in. If ribbon is 36 in. long, its width must be (144 - 36) in. to contain 144 sq. in.
14. Some pupils will say without reflecting, 200% — not seeing that the profit is equal to the cost, 100%.
15. 1% of $ 1500.
29. The thoughtful teacher must determine for herself just how much time she can afford to waste in giving the pupils a number of useless facts about taxes, brokerage, commissions, bonds, etc., etc. The time allotted to arithmetic should be spent chiefly in developing “power" in her scholars. If the latter can correctly apply mathematical principles in ordinary problems suited to their present experience, they will not find it difficult in later life, after they understand the conditions, to solve such new problems as come up.