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74

THE DOUBLE RULE OF THREE.

EXAMPLES.

1. If a principal of $100 gain $6 interest in one year, what will $500 gain in 8 months ?

Statement and operation.
$ P. $ P.
100

500
12 m.

$ int. 1200 4000 :: 6

6

8 m.

12,00)240,00

$20 Ans. In this question, the answer required is interest, therefore 6 dollars interest must be the third term. As $500 will gain more interest in 8 months than $100 will in 12 months, the $500 must be placed for the second term, and the $100 for the first, &c.

2. If 7 men can reap 84 acres of wheat in 24 days, how many men can reap 100 acres in 10 days?

Ans. 20 men. 3. If 12 men earn £8 8s. in 8 days, what will 21 men earn in 15 days?

Ans. £27 11s. 3d. 4. If 225 buskels of oats be eaten by 20 horses in 30 days, how many bushels will suffice 50 horses 16 days ?

Ans. 300 bushels. 5. If a family of eight persons expend $360 in 9 months, how much will serve a family of 18 persons 12 months ?

Ans. $1080. 6. If the wages of 4 men for 7 days be $8.68, how many days must 14 men work for $43.40 ? Ans. 10 days.

7. If the carriage of @cwt. 128 miles, cost $12.80, how far may 12cwt. be carried for $24? Ans. 160 miles.

8. If 5 men make 300 pair of shoes in 40 days, how many men will make 900 pair in 60 days? Ans. 10 men.

9. If 16 compositors set 150 pages of types, each page consisting of 48 lines, and each line of 50 letters, in 3 days, of 10 hours each, how many compositors will be required to set 500 pages of 72 lines each, and 45 letters in a line, in 6 days, of 8 hours each?

Ans. 45 compositors. 10. If $400 gain $14 in 7 months, what is the rate per $100 for 12 months ?

Ans. $6.

the year:

INTEREST. INTEREST is an allowance made by the borrower to the lender, for the use of money. It is rated at a certain number of dollars for the use of each hundred dollars, or pounds, for one year; and in the same proportion for a larger or less sum; or for a longer or shorter time. The interest of $100 for one year, or that which is paid for the use of $100 for one year, is called the rate per cent. per annum. In New York the legal rate is 7 per cent. ; in Pennsylvania and most of the other States the legal rate is 6 per cent. per annum; that is, $6 for $100, or 6 cents for 100 cents; or thus, išo=.06 per annum.

When the rate per cent. is established by the law, the interest is called legal, or lawful interest. When there is no mention made of the rate per cent., it is understood to be the legal rate.

Per cent., or per centum, means by the 100. Per annum means by
Principal is the sum lent.
Amount is the principal and interest added together.

Interest, Commission, Insurance, Buying and Selling Stock, &c.; any thing that is rated at so much per cent., is calculated by either of the following

RULES. 1. Multiply the principal by the rate per cent., and remove the deci. mal point in the product two figures to the left hand (which is dividing by 100); and if there are not so many figures in the product, supply the defect by prefixing ciphers and the sign of dollars, for the interest of one year, or commission, &c. Or,

2. Multiply the principal by the rate per cent., written as a decimal fraction, and place the decimal point in the product as directed in multiplication of Federal money, for the interest of one year, or commission, &c. When the interest for two years or more is required, multiply the interest of one year by the number of years, for the interest required.

Since at 6 per cent., the interest of 100 cents or $1 for 12 months is 6 cents, half as many cents per dollar as there are months, so we have the following:

3. Multiply the principal by half the number of months, and remove the decimal point in the product two figures to the left hand, &c. (as above), for the interest required. Or,

4. Take the product of the principal and days for a dividend.-Divide 365.25, the number of days in a year, by the rate per cent. for a divisor; and the quotient arising from these two numbers will express, in cents or a decimal of a cent, the interest required.

In compliance with custom, I will give other modes of computing interest for days, in which the year is rated at 360 days, and the months at 30 days (which gives an error of $.0875 too much on $100 for one year.)

5. Divide the product of the principal and days by 6, for the interest in mills. REMARK.-Banks use this mode of computing interest.

aand;

76

INTEREST., 6. Multiply the principal by half the number of days, and divide by 30, and remove the decimal point in the quotient two figures to the left

and if there are not so many figures in the quotient, prefix ciphers and the sign of dollars, for the interest required.

Note. Find what fractional part of a month half the number of days re, and reduce the fraction to its lowest terms; thus, for four days, one malf=%=imo.; and 10 days={mo. &c. What is the interest of $50 for 30 days ? For 6 days? Thus, $50 Or thus, $50

$50
30da.
30

of 30 days={=}
6)1500

Ans. 250 m, Ans. by rule 6th 25 c. Ans. by rule 5th

250 m.
And, $50

$50
=1

and 4 of 6 da.=j&=id Ans. by rule 5th 50 m. (By rule 6th.) Ans. $.05 c. When the rate is either more or less than 6 per cent. add or subtract. Thus, to find the interest at 7 per cent., add of the interest at 6 per cent. to itself; the sum total will be the interest at 7 per cent. Or, the Given rate will be a given part of 6 per cent. ; thus, 5 per cent. will be

as much as 6 per cent.; and 7 per cent. Z as much, &c. To get or of any number, wé multiply by the numerator, and diide by the denominator.

Questions.-What is interest? How is it rated ? What do we understand by the rate per cent.? Per annum? Principal ? Amount? How is interest computed for one year ? For a number of years ? For months ? What are he three different modes given for computing interest for days ? &c. &c.

MENTAL EXERCISES. What is the interest of $6 for 4 months ? $4 for 8 months ? $8 for 6 months ? 350 for 12 months; for 6 months? $1 for 2 years? $10 for 6 months ? $100 or 9 months ? $60 for 6 months ? $20 for 12 months ? $16 for 2 months ? 350 for 12 months ? &c.

EXAMPLES. 1. What is the interest of $100 for 3 years, 3 months, and 25 days, at 6 per cent. per annum?

Thus, 1 of 25da.=12.5da. Or 3y. 3mo.=39mo.

$100 39;2=19.5mo. Thus, $100 principal.

$100 .06 rate or ratio.

3,0)125,0

$19.50 $6.00 int. for 1 y.

.41fC.

.414 3.25 number of y: Or, 40mo. -2=20mo.

Ang. $19.91fc. 19.50 int. for 34 y.

$100 .41 c. do. 25 da.

$20.00

$100

-..08} 1 of 5 da = 45=ts $19.91sc. Ans.

Ans. $19.91c.

5 days' interest 8fc. In this example the interest for the days is a fraction of a cent too much.

2. What is the interest of $75 for one year, at six per cent. per annum ?

$75 principal Or, thus, $75 principal
6 rate per cent.

.06 ratio

277 days $125 prin.

Ans. $4.50 interest.

Ans. $4.50 interest. 3. A received of B his note for $125, dated January 1, 1832, on demand, with six per cento interest. Required the amount, October 3, 1832, inclusive. Jan. 31

6)365.25 Feb. 29

60.875 divisor March 31

1385 April 30

3324
May 31
June 30 60.875)34625.000($5.68114 Ans.
July 31

304375
418750

da. da.
Sept. 30
365250

Or, As 60.875 : 277 :: 125 Oct. 3

535000

487000 days 277

48000
60875

Aug. 31

4. What is the interest on a bond of £537 10s. for five years, at six per cent. per annum ?

Ans. £161 5s. 5. What is the amount of $100 for 20 months, at 6 per cent. per annum ?

Ans. $110. 6. What is the interest of $50 for three months, at 6 per cent. ?

Ans. 75 cts. 7. What is the amount of $400 for two years, at 64 per cent. per annum ?

Ans. $452, 8. The value of a certain ship and cargo is $8560—what is the insurance, at 35 per cent. ?

Ans. $2996. 9. What is the deduction on a prize in a lottery, of $1000, at 124 per cent. ?

Ans. $125. 10. Calculate the interest of $35.25, from February 10, 1832, to January 1, 1833, inclusive.

Ans. $1.89177. 11. What is the interest of $260 for 20 days, at 6 per cent. ?

Ans. 85cts. 4 m.184.

G2

INTEREST.

per cent. ?

78

12. What is the amount of one dollar for 12 years, at six per cent. per annum ?

Ans. $1.72. 13. What is the duty on 2cwt. 3qrs. 18lb. of iron, at 21 cents per pound?

Ans. $8.15. 14. What is the interest of $225 for four months, at six

Ans. $4.50. 15. What is the interest of $215.65 for five years five months and six days, at six per cent. ? Ans. $70.3019.

16. What is the interest of 85 cents for six months, at six per cent. ?

Ans. $.02,55. 17. Calculate the interest of 75 cents for four months, at six per cent.

Ans. $.015, or 1łcts. 18. What is the amount of $66for one year, at five per cent. per annum?

Ans. $69.825. 19. What is the interest of $146 for 146 days, at five per cent. per annum?

Ans. $2.918–105. 20. What is the interest of $125 for 30 days, at six per cent.?

Ans. $.616+ or 61 cents 6 mills + 21. I require the interest of ten thousand cents for 1461 days, at six per cent. per annum.

Ans. $24. 22. What is the interest of $10 for 10 days, at six per cent. per annum ?

Ans. $.01,6+ 23. Required the amount of a note of hand for $16.50, for one year, at six per cent.

Ans. $17.49. 24. I require the interest of one dollar for 19 days, at six

Ans. $.00,3121+ 25. Find the interest of $1740.40 for three years and nine months, at six per cent. ?

Ans. $391.59. 26. Required the value of a twenty dollar bank note, which is 27 per cent. below par.

Ans. $19.50. 27. Required the value of $2195.50 United States' bank stock, at 125 per cent.

Ans. $2744.37,5. 28. Required the interest of $44 for 8 months, at six per cent.

Ans. $1.76. 29. What is the amount of $12.08 for two years and three months, at six per cent. per annum ? Ans. $13.71,08.

In computing interest on notes, &c.

On this subject we have no special acts of Assembly.In the state of Pennsy'rania, Chief Justice M’Kean, in 1785, fixed the following i ale fur calculating interest, (laid down in 1st Dallas, page 124) viz.

per cent.

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