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THE RATE PER CENT., INTEREST, AND PRINCIPAL BEING
GIVEN, TO FIND THE TIME.
Rule.- Place the interest of the given principal for one year opposite 12: then opposite the given interest will be the answer in months and decimals of a month. Or, place the interest of the given principal for one year opposite 365: then opposite the given interest will be the time in days.
Example.--Gave 87,5 cents at 7 per cent. for $50.00 : how long did I have it?
The interest of $50.00 for one year, is $3.50. Place 3.50 opposite 12: then opposite •875 is the answer, 3 months.
Gave 24 cents at 7 per cent. for the use of $50 : how long did I have it?
Place $3.50 opposite 365: then opposite 24 is the answer, 25 days.
RULE. -Place the principal opposite fig. 1 : then opposite the rate per cent. added to 100, on the fixed part, is the amount for one year.
Place this amount opposite fig. 1 : then opposite the same point is the amount for two years. Place this last amount opposite 1: then opposite the same point is the amount for 3 years, &c.
Example. What is the compound interest on $5.00 for 5 years at 6 per cent ?
Place 5 opposite 1: then opposite 106, (the por cent. added to 100,) is $5.30, the amount for 1 year. Now place $5:30 opposite 1: then opposite 106 is $5.62, the amount for 2 years. Now place $5.62 opposite fig. 1: then opposite 106 is $5.95. the amount for 3 years. Now place $5.95 opposite fig. 1: then opposite 106 is $6:31, the amount for 4 years. Now place $6.31 opposite fig. 1: then opposite 106 is $6.69, the amount for 5 years.
LOSS AND GAIN.
Bought a hogshead of molasses for $60: for how much must I sell it to gain 20 per cent. ?
RULE.—Place 20 opposite 1: then opposite 60 is what must be added to the original cost to gain said per cent., viz... 12: which added to 60=72.
Bought cloth at $2.50 per yard; but, being damaged, I am willing to sell it so as to lose 12 per çent. How must I sell it per yard ?
Place 12 opposite 1: then opposite $2.50 is 30, the amount to be deducted from $2.50, which will leave 2:20, the answer.
Bought cloth at 50 cents per yard: sold it for 10 cents advance from cost. What per cent. did I make?
Place 10 opposite 50: then opposite 1 is 20 per cent., the answer.
ANOTHER METHOD.-Place the original cost opro. site 1: then opposite the rate per cent. added to 100, is the answer.
Example.-Bought corn at 50 cents per bushel : at how much must I sell it to gain 20 per cent. ?
Place 50 opposite 1: then opposite 120, is 60 cents, the answer.
Bought cloth at $2 per yard, and sold it at $3 per yard: what per cent. did I make ?
Place 2 opposite 1: then opposite 3 is 150, 50 per cent., answer.
RULE OF THREE, OR PROPORTION.
Rule.- Place the second term opposite the first : then opposite the third term, is the answer.
Example.If 2 yards of cloth cost $4.00, what cost 8 yards ?
Place 4 opposite 2: then opposite 8 is 16.
NOTE.-All numbers of yards at that rate, are now on the scale, and may be determined without moving the circular.
At of a dollar per yard, what cost 4 yards?
Place 7 opposite 8: then opposite the given num. ber of yards, is the answer.
If 1 ton of hay cost $3.00, what cost 900 pounds?
Place 8 opposite 2000, (the number of lbs. in a ton :) then opposite 900 is the answer; and so of any other number of pounds.
RULE.-Place the whole gain or loss opposite the whole stock: then opposite each man's share of the stock is his share of the gain or loss.
Example.-A invested $30, B invested $20, and they gained in trade $12: what is each one's share of the gain?
Place 12 (the whole gain) opposite 50 (the whole stock): then opposite 20 (A's stock) is $4.80; and opposite 30 (B's stock) is $7.20.
TO EXTRACT THE SQUARE Root.
RULE.-Move the given number around until it is opposite the same number which is opposite 1; and that number is the answer sought.
Example.—What is the square root of 42 ?
Move 42 on the circular around until it comes opposite 6:48. Now 6:48 is opposite 1: hence that
1 is the square root of 42.
TO EXTRACT THE CUBE Root.
RULE.—Move the given number around until it comes opposite a number, the square of which at the same time is opposite 1; and that number is the root sought.
Example.-- What is the cube root of 27 ?
Move 27 around until it comes opposite 3: at that time 9 is opposite 1: hence 3 is the answer.
TO APPORTION TAXES.
RULE. Place the whole tax to be raised, found on the circular, opposite the whole valuation : then oppo.
. site each man's valuation, is his tax.
Example.— A tax of $1.500.00 is levied on a val. uation of $200.000.00: what is a man's tax whose valuation is $700.00 ?
Place 1500 opposite 200.000 : then opposite 700 is $5.25, the answer.
1550 days have been sent, and $33.20 tax is to be raised: how much is each man's tax ?
Place 33-20 opposite 1550 : then opposite the days each man has sent is his tax.
A has sent 28 days: his tax is 60 cents.
Opposite 70, the number of days B has sent, is his tax, $1.50; and so of every other man's tax, without moving the scale.