22. If the interest on a certain sum of money is $7.35 in one year, how much will it be for 5 months?

Ans. $3.367.

23. If the interest of $100 for one year is $6, how much is it for 10 months and 10 days? Ans. $5.163.

24. If a steam locomotive pass 18 miles in one hour, how far will it move in 50 minutes? Ans. 15.

Ans. 2.523.

25. If the interest of $100 for 12 months is $7, how much is it for 4 months? 26. What must I pay for 14 cords of wood, 128 feet in a cord, at 64 cents per foot?

Ans. $10.00.

PERCENTAGE.

112. THE term per cent. is an abbreviation of per centum, which means by the hundred.

Thus, 5 out of 100 is 5 per cent.

6 out of 100 is 6 per cent.

7 out of 100 is 7 per cent.

And so for other rates per cent.

Different rates per cent. are most conveniently expressed

by means of decimals.

Thus, 1 per cent. is the same as 0.01.

In many cases the rate per cent. is very concisely expressed by means of a vulgar fraction, as follows:

Suppose we wish 5 per cent. of $1122, we must take r of it; this is done by multiplying by the decimal 0.05.

OPERATION.

$1122.

0.05.

Ans. $56.10.

Hence, to find the percentage of any number, we have this

RULE.

Multiply the given number by the percentage expressed in decimals, and the product will give the percentage sought.

From what is per cent. abbreviated? And what does it mean? 5 out of 100 is what per cent.? 6 out of 100 is what per cent.? 7 out of 100 is what per cent.? What is the decimal expression for 1 per cent.? What for 2, 3, 4, &c., per cent. 1 Repeat the Rule for finding the per cent. of a number.

EXAMPLES.

1. What is 4 per cent. of $10000?
4 per cent, is 0·04.

per cent. is 0.005.

44 per cent. is 0.045.

OPERATION.

$10000

0.045

50000

40000

Ans. $450.000

2. What is I per cent. of $730?
3. What is 3 per cent. of 5789 pounds?

Ans. $7.30.

Ans. 14·6bu. Ans. $3.37635.

Ans. 173.67lb.

Ans. 164-15. Ans. $148.50.

4. What is 4 per cent. of 365 bushels? 5. What is 41 per cent. of $75·03 ? 6. What is 7 per cent. of 2345? 7. What is 30 per cent. of $495,? 8. A person laid out $222 as follows: he gave 21 per cent. of his money for calicoes; 15 per cent. for thread; 45 per cent. for silks; and the remaining 19 per cent. for broadcloths. How many dollars did he expend for each? He gave for calicoes,

Ans.

66

thread,

66

silks,

broadcloths,

$46.62.

33.30.

99.90.

42.18.

9. A merchant having 500 barrels of flour, sold at one time 25 per cent. of it, at another time he sold 20 per cent. How many barrels did he sell at each

of the remainder.

time, and how many remain ?

Ans.

The first time he sold 125 barrels.

75 barrels.

300 barrels.

The second time he sold
He has remaining

10. A farmer raising 1097 bushels of wheat, gives 10 per cent. of it for thrashing, 10 per cent. of the remainder

r flouring. What per cent. of the whole will he have Ans. 81 per cent.

ft?

11. A California miner having secured 15 pounds of old dust, finds it to lose 5 per cent. in refining; he then ;ives 6 per cent. for coining.

eceive after it is coined ?

How much ought he to

Ans. 13 8415 pounds 137b. 10oz. 1pwt. 23gr.

12. Suppose at each stroke of the piston of an air pump 10 per cent. of the air in the receiver is exhausted, what per cent. of the air will remain after the 1st, 2d, 3d, and 4th strokes, respectively?

113. INTEREST is money paid by the borrower to the lender, for the use of the money borrowed.

It is estimated at a certain rate per cent. per annum, that is, a certain number of dollars for the use of $100, for one year.

Thus, when $6 is paid for the use of $100, for one year, the interest is said to be at 6 per cent.

In the same manner when $5 is paid for the use of $100, for one year, the interest is said to be at 5 per cent. ; and the same for other rates.

The rate per cent. is generally fixed by law.

In the

New England States the legal rate is 6 per cent., while in the State of New York it is 7 per cent.

The sum of money borrowed, or upon which the interest is computed, is called the principal.

The principal, with the interest added to it, is called the

amount.

What is Interest? How is it estimated? What is the rate per cent. when $6 is paid for the use of $100 for one year? What is the rate per cent. when $5 is in the same way paid? Is the rate per cent. generally fixed by law? What is the legal rate per cent. in the New England States? What is it in the State of New York? What is the principal? What is the amount?

CASE I.

To find the interest on any given principal, for any whole number of years, at any given rate per cent.

Suppose we wish the interest of $365-50 for 3 years, at 7 per cent.

By the definition of interest money, it follows that the interest of $365-50 for one year, at 7 per cent., is 7 per cent. of $365-50; which by rule under ART. 112, we obtain, by multiplying $365-50 by 0-07. Performing the multiplication, we have $365-50×0.07=$25·585 for one year's interest, which, multiplied by 3, the number of years, will give us $76-755 for the interest of $365·50 for 3 years at 7 per cent.

Hence the following

RULE.

Multiply the principal by the rate per cent., expressed in decimals, and that product by the number of years; observing the usual rule for pointing off the decimal figures.