6. A trader has molasses at 22, 25, 29, and 33 cents per gallon. How many gallons of each kind may he take to make a mixture worth 26 cents per gallon?

7. A trader has oils at $.95, $1.20, $1.42, and $1.60 per gallon, of which he wishes to make a mixture worth $1.25 per gallon. How many gallons of each kind may he take?

8. A trader wishes to mix 50 lb. of sugar at 7 cents per lb., and 30 lb. at 10 cents, with such quantities at 9 and 6 cents per lb. as will make a mixture worth 8 cents per lb. How many pounds of each may he take?

9. A trader wishes to mix 40 lb. of tea at 40 cents per lb., 30 lb. at 24 cents, and 50 lb. at 45 cents, with enough at 30 cents to make a mixture worth 35 cents per lb. How many pounds of the last must he take?

10. I have salt at 33, 37, and 50 cents per bushel. How many bushels of each kind may I take to make a mixture of 100 bushels worth 40 cents per bushel?

11. A farmer has oats worth 42 cents, barley worth 64 cents, rye worth 87 cents, and wheat worth $1.38 per bushel. How many bushels of each kind may he take to make a mixture of 200 bushels worth 75 cents per bushel ?

SECTION XV.

INTEREST.

166. Introductory.

WHEN a person hires an article of property of another, it is evident that, at the expiration of the time for which he hires it, he ought to return it, and pay for its use. Moreover, the sum paid for the use of the borrowed article should be proportioned both to its value and the length of time it is kept.

For instance, if I hire two houses, one of which is worth twice as much as the other, I ought to pay twice as much per year for the first as for the second. If the values of the houses are alike, and one is kept one half as long as the other, only one half as much ought to be paid for the first as for the second.

--

To the Teacher. It will be well to illustrate the above important principles by questions similar in character to the following:

If one man hires a horse to go a certain distance, and another hires one to go twice as far, how many times as much ought the second to pay for its use as the first pays? What would have been the answer to the above question, provided the second man had gone 3 times as far as the first? 4 times as far? 3 times as far? as far? as far? as far? &c. If the horses are hired by the hour, and the first man keeps his horse three times as many hours as the second keeps his, how many times as much ought he to pay for the use of it? What would have been the answer had he kept it 5 times as long as the second? times as long? 6 times as long as long long? &c.

as long as

Similar questions should be asked with reference to other objects hired, as houses, money, &c., till the principle is fully understood.

167. Definitions.

(a.) Money is very frequently hired, and the sum to be paid for its use is determined in accordance with the above principles. (See 177th page, Ex. 24, Note.)

(b.) Money thus paid for the use of money is called IN

TEREST.

(c.) The money used is called the PRINCIPAL.

(d.) The principal and interest added together form the AMOUNT, or entire sum due at any given time.

(e.) The interest of any principal is usually reckoned at a certain per cent, i. e., a certain number of one hundredths of that principal, for each year it is on interest. This per cent is called the RATE PER CENT, or simply the RATE.

NOTE. The term per cent, from the Latin per centum, originally meant by the hundred; but as it is now used in arithmetic, it means one hundredths. Thus 6 per cent means Too, or .06; 4 per cent means

Tʊ, or .04; per cent means To, or of Toʊ, or zoo; &c. This term may be applied to any thing else as well as money; and hence the definition (often given in the school room) "so many cents on 100 cents " is not a good one, any more than would be, so many bushels on 100 bushels, or so many yards on 100 yards. It is the more objectionable because scholars are sometimes led by it, and by being often called upon to use the term per cent in connection with money, to suppose that it has some necessary connection with cents, or with United States money

168. Legal Rate.

(a.) In most countries, laws have been passed regulating in some way or other the rates of interest.

(b.) Such laws are called USURY LAWS.

(c.) They commonly embrace the following particulars :First. They fix the rate which shall be paid when no special rate has been agreed upon by the parties. This is called the LEGAL RATE.

Second. They forbid persons to receive interest at more than some given rate.

Third. They impose penalties for their violation.*

(d.) Any excess over the rates allowed by these laws is called USURY.

(e.) In most states of the Union, the legal rate is also the highest rate allowed by law, even on special contracts. The exceptions to this are named in the following statement of the legal rates of interest in the several states.

(f) In New York, South Carolina, Georgia, Michigan, and Wisconsin, the legal rate of interest is 7 per cent per year.

*It may not be amiss to remark that the laws regulating the rate of interest are very often disregarded, while the penalties for their violation are seldom imposed. Very few men continue long in business without paying or receiving interest at more than the legal rate. Money, having, like every thing else, a variable value, will bring what it is worth at the time it is sold or let, and it seems as impossible to regulate by law the price which shall be paid for its use, as to fix by law that which shall be paid for the use of any other article of property.

(9.) In Alabama and Texas, it is 8 per cent per year. (h.) In Louisiana, it is 5 per cent.

(i.) In California, it is 10 per cent.

(k.) In all the other states, the legal rate is 6 per cent per year.

(1.) By special agreement of the parties, interest may be charged at the rate of 8 per cent per annum in Florida, Mississippi, and Louisiana; at the rate of 10 per cent in Arkansas, Illinois, Michigan, Iowa, and Ohio; at the rate of 12 per cent in Wisconsin and Texas; and at the rate of 18 per cent in California.

(m.) On debts in favor of the United States, interest is computed at the rate of 6 per cent.

(n.) In each state, interest is reckoned at the legal rate of that state, unless otherwise specified.

(0.) In the United States, it is customary, when reckoning interest, to regard a year as 12 months, and a month as 30 days. But in England, the year is regarded as 365 days, and the number of days in the months considered are reckoned as in the calendar.

(p.) In England, the legal rate is 5 per cent.

169. Interest for 2 Months, 200 Months, &c., at 6 per

cent.

(a.) If the interest of any sum for one year is 6 per cent of that sum, for of 1 year, or 2 months, it must be of 6 per cent, or 1 per cent of it.

(b.) Therefore, at 6 per cent per year, the interest for 2 months is 1 per cent, or .01 of the principal, and may be found by removing the decimal point of the written principal two places towards the left.

Thus, the interest of $75 for 2 months is $.75; of $364.30 is $3.643, &c., &c.

What is the interest of each of the following sums for 2 months?

7. What is the amount of each of the above sums for 2

months?

(c.) If the interest of any sum for 2 months is .01 of that sum, its interest for .1 of 2 months, which is 6 days, must be .1 of .01, or .001 of it.

(d.) Therefore, at 6 per cent per year, the interest for 6 days is .001 of the principal, and may be found by removing the decimal point three places to the left.

Thus, the interest of $987 for 6 days is $.987; of $439 is $.439; of $8763.72 is $8.764; † or, carrying the values no farther than cents, the interest of $987 is $.99; of $439 is $.44; of $8763.72 is $8.76; &c.

What is the interest of each of the following sums for 6 days?

8. $586

9. $930

10. $67
11.

$36.75

12. $1473.87 13. $142

14. What is the amount of each of the above sums for 6 days?

(e.) If the interest of any sum for 2 months is 1 per cent of that sum, its interest for 100 times 2 months, or 200 months, must equal 100 times 1 per cent, or 100 per cent of it, which is the sum itself.

(f.) Therefore, at 6 per cent per year, the interest for 200 months, or 16 years 8 months, must equal the principal.

Thus, the interest of $47 for 200 months is $47; of $37.84 is $37.84; of $23 is $23; &c.

What is the interest of each of the following sums for 16 yr. 8 mo., or 200 mo. ?

*The denominations below mills need not be given in the answer. In deed, those below cents need not be given, if, when there are more than 5 mills, 1 be added to the number of cents.

+ Since $.00072 more than of a mill.