for flouring. What per cent. of the whole will he have left? Ans. 81 per cent.

11. A California miner having secured 151⁄2 pounds of gold dust, finds it to lose 5 per cent. in refining; he then gives 6 per cent. for coining. How much ought he to receive after it is coined?

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 and the same for other rates.

per

cent.;

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.

EXAMPLES.

1. What is the interest of $573.15 for 5 years at 6 per cent. ?

Ans. $120.

2. What is the interest of $600 for 4 years at 5 per cent.? 3. What is the interest of $725 for 8 years at 4 per cent.? Ans. $261. 4. What is the interest of $149 for 5 years at 2 per cent.? Ans. $14.90. 5. What is the interest of $225.25 for 10 years at 4 per cent.? Ans. $90.10. 6. What is the interest of $311.30 for 11 years at 10 per cent.? Ans. $342-43. 7. What is the interest of $501.50 for 2 years at 31 per cent.? Ans. $35.105.

CASE II.

To find the interest on any given principal, for any given time, at any given rate per cent.

Suppose we wish the interest of $126 for 3 years 5 months and 15 days, at 7 per cent,

15 dys.

66

of 1 mo. 3675-15 days'

Ans. $30-5025=3 yrs. 5 mos. and 15 days' int

Hence the following

RULE.

Multiply the principal by the rate per cent. expressed in decimals; the product will give one year's interest, which, multiplied by the number of years, will give the interest for the tine expressed in years. Then find the interest for the months and days by means of aliquot parts, as in Practice.

EXAMPLES.

1. What is the interest of $39-42 for 1 year, 5 months, and 11 days, at 7 per cent. ?.

NOTE. We have not extended our work to more than three places of decimals, but have added 1 to the third place whenever the fourth decimal figure would be 5 or greater.

2. What is the interest of $47.13 for 7 months and 21 days, at 7 per cent.? Ans. 2.118.

Ans. $5.621.

3. What is the interest of $321.21 for 3 months and 15 days, at 6 per cent.? 4. What is the interest of $270 for 2 months and 8 days, at 7 per cent. ?

Ans. $3.57. 5. What is the interest of $404-44 for 1 year, 5 months and 4 days, at 7 per cent.?

Ans. $40-422.

6. What is the interest of $99.99 for 11 months and

29 days, at 5 per cent. ?

Ans. $4.986.

7. What is the interest of $37.50 for 6 months and 10 days, at 6 per cent. ?

Ans. $1.287.

8. What is the interest of $49.49 for 8 months and 8 days, at 7 per cent. ?

Ans. $2.386.

CASE III.

To find the interest on any given principal for any given time at 6 per cent.?

The interest on $100 for one year, at 6 per cent., being $6, it follows that the interest on $1, for one year, is $0.06; and since 2 months is of a year, the interest on $1, for two months, is $0.01; again, since 6 days is of 2 months, when we reckon 30 days to each month, it follows that the interest on $1, for 6 days, is 80-001. Hence, if we call half the number of months, CENTS, and one-sixth the number of days, MILLS, we shall obtain the interest of $1 for the given time, at 6 per cent.

The interest of $1 being multiplied by the number of dollars in the given principal, will obviously give the in