13. What per cent. is 10% of 50% ?

Ans. 5%.

14. A merchant lost 5% of his capital by the failure of one debtor, and 41% of the remainder by the failure of another, and then had $7258 left: what was his capital?

Ans. $8000.

15. A gentleman having a certain amount of money, deposited 90% of of it in bank, and then had $1625 on hand: what was the amount of his money?

16. Bought 100 shares of railroad stock at 95% of its par value, $100 per share: what did it cost?

17. What per cent. of 5 kilogrammes is 50 grammes ?

Ans. 1%.

18. What is 5 per cent. of 3 hectares?

Ans. 15 ares.

19. The sum of two numbers is 300, which is 150% of the greater number: what is the less number?

INTEREST.

300. Interest is the sum paid for the use of money. It formerly meant the use of money.

301. The Principal is the sum, or base, on which the interest is computed.

302. The Rate is the number of units per hundred, or per cent. of the principal paid for its use for any given time, usually per annum.

303. The Amount is the sum of the principal and interest. 304. Simple Interest is interest upon the principal only.

305. Compound Interest is interest upon both principal and interest, compounded at certain periods of time when the interest becomes due and remains unpaid; as, annually, semiannually, and quarterly.

306. Annual Interest is simple interest on interest payable annually and overdue, as well as on the principal.

307. Legal Interest is the rate allowed by law, and varies in the different States.

308. The taking of any more than the legal rate is, in most of the States, an offence called usury, which is prohibited under various penalties.

309. In many States a certain rate is fixed by law, to be allowed on all contracts when no particular rate is specified, while a higher rate may be taken by special agreement between the parties.

TABLE.

Showing the legal rates of interest, and the rates allowed by special agreement. in the several States and Territories of the Union.

310. Interest is usually reckoned upon the basis of 360 days to the year, and 30 days to the month. This practice is not strictly correct, although sanctioned by almost universal usage, and in some States by legal enactments. Thus, the interest of $500 for 18 days, at 6 per cent., computed by this method, is of $30, the interest of $500 for one year, or $1.50. If 365 days be reckoned a year, it will be of $30, or $1.47%}, which is or less than $1.50, the amount found by reckoning 360 days to the year.

CASE I.

311. To compute interest for years and months.

It is obvious, from the fact that interest is certain per cent. of the principal per annum, that, if the principal be multiplied by the rate expressed as hundredths, the product will be the interest for one year. This product, multiplied by the number of years, will be the interest for any given time. Hence the following

RULE.-I. Multiply the principal by the rate per cent., and the resulting product by the number of years and fraction of a year; or, take aliquot parts of one year's interest for the months.

II. Or, multiply the rate per cent. by the time expressed in years, and the principal by the product thus obtained.

EXAMPLES.

1. What is the interest of $750, for 4 years and 6 months, at

6

per

cent. ?

750 × .06 × 4 = 202.50 Or, .06 X 4 X 750202.50

Ans. 202,50.

2. What is the interest of $475, for 3 years, at 5 per cent.? 3. Find the interest of $184.25, for 4 years and 3 months, at 7 per cent.

4. Find the interest of $240.50, for 1 year and 6 months, at & per cent.

5. What is the amount of $3416.40, for 2 years and 10 months, at 6 per cent,?

6. What is the amount of $716.40, for 3 years, at 9 per

cent. ?

7. What is the amount of $1840.37, for 2 years and 3 months, at 7 per cent.?

CASE II.

312. To compute interest for months only.

At 6 per cent. for one year, or 12 months, the rate is one half per cent. a month, for 6 is one half of 12. time is given in months, one-half of the expressed as hundredths, is the rate per Hence the

Therefore, when the number of months, unit for that time.

RULE.-Multiply the principal by half the number of months, expressed as hundredths; the product will be the interest at 6 per cent.

NOTE. -For any other rate than 6 per cent., increase or diminish the interest so found by as many sixths of itself as the given rate is greater or less than 6. Thus, for 8%, add, or; for 7%, add ; for 5%, subtract f.

EXAMPLES.

1. What is the interest of $640, for 10 months, at 6 per cent.? Ans. $32.

SOLUTION. 640 X .05 = 32.

2. What is the interest of $375.48, for 9 months, at 6 per

cent.?

SOLUTION. 375.48 × .04, or .045

Ans. $16.90.

16.8966.

3. Find the interest of $1137.50, for 14 months, at 7 per cent.

4. Find the interest of $19.75, for 11 months, at 8 per cent.

5. What is the amount of $3264.50, for 18 months, at 6 per cent. ?

6. What is the amount of $244.60, for 28 months, at 7 per cent.?

7. What is the interest of $200, for 7 months, at 6 per cent. ? 8. What is the amount of $1000, for 6 months, at 7 per cent. ? 9. Find the interest of $189.75, for 7 months, at 6%. 10. Find the interest of $130.50, for 8 months, at 7%. 11. Find the interest of $240.18, for 6 months, at 9%.

CASE III.

313. To compute interest for days only.

As shown by Case II, the interest of $1, for one month, at 6 per cent., is one half a cent, or 5 mills. Hence, for 6 days (of 30 days), it is of 5 mills, or 1 mill, and for 1 day, of a mill. And, since mills are thousandths of a dollar, when the time is given in days, one sixth of the number of days, expressed as thousandths, is the rate per unit for that time. Hence the following

RULE.-Multiply the principal by one sixth of the number of days, expressed as thousandths; the product will be the interest at 6 per cent.

NOTE. When it is more convenient, to avoid fractions in the multiplier, multiply by the number of days, and divide by 6. The result will be the interest in mills. Therefore, point off three decimal places, in addition to the number in the multiplicand.

EXAMPLES.

1. Find the interest of $945, for 18 days, at 6 per cent.