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WHEN THE PRICES OF Goods ARE GIVEN, TO FIND

WHAT IS THE RATE PER CENT. OF GAIN OR Loss,

1. A merchant bought cloth for $1,20 a yard, and sold it for $1,50; what was the gain per cent.?

In this example, we are required to find the rate per cent. The process, then, of finding it, is substantially the same as in the foregoing examples.

It has been remarked, that 6 per cent. is 6 cents on 100 cents ; that is, the Interest is Too of the principal; which, written decimally, is ,06; 5 per cent. is To=,05; 25 per cent. is mor=,25; that is, the rate may always be considered a decimal carried to two places, or 100ths. In the last exanıple, by subtracting $1,20 from $1,50, we have 30 cents gain on a yard, which is on of the first cost ; =,25=25 per cent., the Answer.

RULE. How, then, do you proceed, to find the rate per cent. of gain or loss?

A. Make a common fraction, by writing the gain or loss for a numerator, and the cost of the article the denominator ; then change it decimal.

to a

2. A merchant bought molasses for 24 cents a gallon, which he sold for 30 cents; what was his gain per cent. ?

A. ,25=25 per cent. 3. A grocer bought a hhd. of rum for $75, from which several pallons having leaked out, he sold the remainder for $60; what did he lose per cent.?

In this example, the decimal is ,2; which, carried to two places, is ,20 = 20 per cent., the Answer.

4. A man bought a piece of cloth for $20, and sold it for $25; what did he gain per cent. ? A. 25 per cent.

5. A grocer bought a barrel of flour for $8, and sold it for $9; what was the gain per cent. ?

As two decimal places only are assigned to the rate per cent., ,125 is 12-=124 per cent., that is, the third place is so many tenths of 1 per cent. ; thus, 1 per cent. is 901, and 3 per cent. is ,005= Pb, or 1 of 1 per cent.

A. 124 per cent. 6. A merchant bought a quantity of goods for $318,50, and wld them again for $799,39; what was his loss per cent. ?

A. 6 per cent. 7. What is the gain per cent. in buying rum at 40 cents a gallon, and selling it at 42 cents a gallon?-5. At 44 cents 10. At 46 cents ?-15. At 50 cents ?-95. At 54 cents ?-35. At 60 cents ?-50. A. 140 per cent

8. Bought a hhd. of molasses, containing 112 gallons, at 28 cents a gallon, and sold it for $,286 a gallon; what was the whole gain, and what was the gain per cent. ?

A. $2,912, and the gain ,l=10 per cent. 9. Bought flour at $9"a barrel, and sold it for $10,80 a barrel; what was the gain per cent. ? A. 20 per cent.

10. If I buy a horse for $150, and a chaise for $250, and se: the chaise for $350, and the horse for $100, whät is my gain per cent.? A $,125=12}, per cent.

11. If I buy cotton at 15 cents a pound, and sell it for 164 cents, what should I gain in laying out $100? A. $10.

12. Bought 20 barrels of rice for $20 a barrel, and paid for freight 50 cents a barrel; what will be my gain per cent. in selling it for $25,6216 a barrel ? A. 25

per

cent.

LXX. The PRINCIPAL, RATE PER CENT., AND

INTEREST BEING GIVEN, TO FIND THE TIME. J. William received $18 for the interest of $200 at 6 per cent.; how long must it have been at interest ?

The interest on $200 for 1 yr. at 6 por cont. is $12; hence $18+12=1,5 =lf years, the required time, Ans.

Q. What, then, is the RULE?

A. Divide the given interest by the interest of the principal for 1 year at the given rate ; the quotieni will be the time required, in years and decimal parts of a year.

2. Paid $36 interest on a note of $600, the rate being 6 per cent.; what was the time? 4. 1 year.

3. Paid $200 interest on a note of $1000; what was the time, the rate being 5 per cent. ? A. 4 ycars.

4. On a note of $60, there was paid $9,18 interest, at 6 per cent.;. how long was the note on interest ?

A. 2,65 yrs. =2 yrs. 6 mo. 18 da.

COMPOUND INTEREST.

4 LXXI. 1. Rufus borrows of Thomas $500, which he agrees to pay again at the end of 1 year, together with the interest, at 6 per cent.; but, being prevented, he wishes to keep the $500 another year, and pay interest the same as before. How much interest ought he to pay Thomas at the end of the two years?

In this example, if Rufus had paid Thomas at the end of the first year, the intorest would have been $500 x 6= $30, which, added to the principal, $500, thus, 500+30,=530, the sumn or amount justly due Thomas at the end of the first year; but, as it was not paid then, it is evident, that, for the next year, (20 year,) Thomas ought to receive interest on $530, (being the amount of the first year.) The interest of $330 for 1 year is 530 X 6=$31,80, which, added to $530, =561,80, 'the amount for 2 years; hence, $561,80 - $500 $61,80, Compound Interest, the Answer.

This mode of computing interest, although strictly just, is not authorized by law.

Q. When the interest is added to the principal, at the end of ! year, and on this amount the interest calculaied for another year, and 60 on, what is it called ?

A. Compound Interest.
Q. How, then, may it be defined ?
A. It is interest on both principal and interest.
Q. What is Simple Interest ?
A. It is the interest on the principal only.

Hence we derive the following

RULE.

Q: How do you proceed ?

A. Find the amount of the principal for the Ist year, by multiplying as in Simple Interest; then of this amount for the 2d, and so on.

Q. How many times do you multiply and add ?

A. As many times as there are years: the last result will be the amount.

Q. How is the compound interest found ?

A. By subtracting the given sum, or first principal, from the last amount.

More Exercises for the Slate.

2. What is the compound interest of $156 for 3 yrs ?

$156 = given sum, or first principal.

6

9,36 = interest and 156

= principal, added together. 165,36 = amount, or princig ior 20 year. ,

6

9,9216 = compound interest 2d year,

and
165,36 principal 2d year, added together.
175,2816
= amount, or principal for 3d

year,
6

10,516896
= compound interest 3d

year,

and
175,2816 =principal 3d year, added together
185,798496 = amount.
156

= first principal subtracted. Ans. $29,798 rejecting the three last figures, as of trifling value

3. Wliat will be the amount of $500 for 4 years, at compound interest ? A. $631,2387 +:

4. What is the amount of $500 for 4 years, at simple irterest ? A. $620.

5. What will be the amount of $700 for 5 years, coinpound interest? A. $936,757 10 +

6. What will be the amount of $700 for 5 years, at simple interest ?

A. $910. 7. What will be the amount of $1000 for 3 years, at compound interest ?-1191016. $1500 for 6

years?-21277780. $2000 for 2 years ?-224729. $400 for 7 years ?-601452.

A. $6167,4468+. 8. What is the compound interest of $150 for 2 years ?-1854 $1600 for 4 years ?-4199631. $1000 for 3 years ?-191016. $5680 for 4 years ?-1490869. $500 for 3 years ?-95508.

A. $2215,89676+. 9. What is the compound interest of $600,50 for 2 years, at 2 per cent. ?-242602. At 3 per cent.?-365704. At 4 per cent. ?490008. At 5 per cent. ?-615512. At 7 per cent. ?-870124 . At 10 per cent. ?-126105. A. $384,50.

10. What is the difference between the simple interest of $200 for 3 years, and the compound interest for the same time?

A. $2,2033o. 11. What is the compound interest of $600 for 2 years 6 months ?

In calculating the compound interest for months and days, first find the amount for the years, and on that amount calculate the interest for the months and days; this interest, added to the amount for the years, will be the interest required.

A. $94,38,4 +. 12. What is the compound interest of $500 for 3 yrs. 4 mo.?

A. $107,41815 to 13. What is the difference between the simple and compound interest of $200 for 3 yrs. ?-22032. For 4 yrs. 6 mo.?-60702. For 2 yrs. 8 mo. 15 da. ?-17706. A. $10,044.

As the amount of $2 is twice as much as $1, $4, 4 times as much, &c., hence, we may make a table containing the amount of the l£, or $1, for several years, by which the amount of any sum may be easily found for the same tiine.

TABLE, Showing the amount of 1£, or $1, for 20 years, at 5 and 6 per

cent., at compound interest. 5 per cent. 6 per cent.

5 per cent. 6 per cent. 1,05000 1,06000 1,71033 1,89829 2 1,10250 1,12360 12 1,79585 | 2,01219 3 1,15762 | 1,19101 13 1,88564 2,13292 4 1,21550 1,26247 14 | 1,97993 2,26090 5 1,27628 | 1,33822 15 2,07892 | 2,39655 6 1,34009 | 1,41851 16 2,18287 | 2,54035 7 1,40710 1,50363 17 | 2,29201 2,69277 8 1,47745 | 1,59384 18 | 2,40661 2,85433 9 1,55132 | 1,68947 19 | 2,52695 3,02559

10 1,02889 1,79084 20 1 2,65329 3,20713 14. What is the compound interest of $20,15 for 4 years, at 6

per cent. ? By the Table, $1 at 6 per cent. for 4 years, is $1,26247, X $20,15= $25,438, amount, from which $20,15 being subtracted, leaves $5,288 t.

15. Wliat is the amount of $10,50, at 5 per cent. for 2 years ?115762. For 6 years ?-140709. For 8 years ?-155132. For 16 years 7-218286. For 17 years ?-240661. For 20 years 7-278595.

$114,91416 +, Anus.

Years.

Years.

11

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