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I LXVIII. TIME, RATE PER CENT., AND INTEREST
BEING GIVEN, TO FIND THE PRINCIPAL. 1. What sum of money, put at interest 1 yr. 8 mo. at the rate of 6 per cent., will gain $20,60 interest? The interest of $1 for 1 yr. 8 mo. = 10 cts.; then $20,60 --- $,10= $206, Ans.
RULE. Q. How, then, would you proceed ?:
A. Divide the given gain or interest by the interest of $1 at the given rate and time; the quotient will be the principal required.
2. A certain rich man has paid to him every year, $48000 interest money; how much money must he have at interest? or what principal will gain $48,000 in 1 year, at 6 per cent. ?
A. $800000. 3. If a man's salary be $12000 a year, what principal at interest for 1 yr. at 6 per ceni. would gain the same?
A. $200000. 4. Paid $45, the lawful interest on a note, for 2 yrs. 6 mo.; what was the face or principal of the note ? A. $300.
1 LXIX. THE PRINCIPAL, INTEREST, AND TIME,
BEING GIYEN, TO FIND THE RATE PER CENT. 1. If I have $2000 at interest, and at the end of the year
I should receive $120 interest, what rate per cent, would that be?
The interest of $2000 at 1 per cent. for 1 year, is $20; therefore, $120 - 20 =$6, that is, 6 per cent., the rate required.
RULE. Q. How, then, do you proceed to find the rate per cent.
iven interest by the interest of the given sum, at 1 per cent. for the given time; the quotient will be the required rate.
2. If I receive $60 for the use of $600, 1 yr. and 8 mo., what is the rate per cent. ? A. 6 per cent.
3. If I pay $200 for the use of $2000 for 2 yrs. 6 mo., what is the rate per cent. ? A. 4 per cent.
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 Tøy of the principal; which, written decima'iy, is ,06; 5 per cent. is To=,05; 25 per cent is =,25; that is, the rata may always be considered a decimal carried to two places, or 100ths. In the last example, by subtracting $1,20 from $1,50, we have 30 cents gain on a yard, which is of the first cost ; P =,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 to a decimal.
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 gallons 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 = 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 = 121 per cent., that is, the third place is so many tenths of 1 per cent. ; thus, 1 per cent. is ,01, and 1 per cent, is 9005=1, or of 1 per cent
A. 12 per cent. 6. A merchant bought a quantity of goods for $318,50, and sold them again for $299,39; 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?-25. At 54 cents ?-35, At 60 cents ?-50. A. 140 per cent,
8. Bought a hhd. of molasses, containing 112 gallons, at 26 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 sell the chaise for $350, and the horse for $100, what is my gain per cent.? A $,125=12 per cent.
11. If I buy cotton at 15 cents a pound, and sell it for 10% 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 $25,621 a barrel ? A. 25 per cent.
I LXX. THE PRINCIPAL, RATE PER CENT.,
INTEREST BEING GIVEN, TO FIND THE TIME.
1. William received $18 for the interest of $200 at 6 cent. ; how long must it have been at interest?
The interest on $200 for 1 yr. at 6 per cent. is $12; hence $18; 12= 1,5 =l5 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 quotient 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? A. 1 year.
3. Paid $200 interest on a note of $1000; what was the time, the rate being 5 per cent. ? A. 4 years.
4. On a note of $60, there was paid $9,18 interest, at 6 per cent.; how long was the note on interesi ?
A. 2,55 yrs.
=2 yrs. 6 mo. 18 da.
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 ho cay Thomas at the end of the two years?
In this example, if Rufus had paid Thomas at the end of the first year, the interest would have been $500 X6=$30, which, added to the principal, $500, thus, 500 + 30, = 530, the sum 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, (24 ycar,) Thomas ought to receive interest on $530, (being the amount of tho first year.) The interest of $530 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 Anstoer.
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 1 year, and on this amount the interest calculaied for another year, and so on, what is it called ?
A. Compound Interest.
Hence we derive the following
Q. How do you proceed ?
A. Find the amount of the principal for the 1st 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 resul: 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.
9,36 = interest and
=principal, added together.
9,9216 = compound interest 2d year,
= principal 2d year, added togethor. 175,2816 = amount, or principal for 30 year.
10,516896 = compound interest 3d year, and
first principal subtracted, Ans. $29,798 rejecting the three last figures, as of trifing value.
3. What will be the amount of $500 for 4 years,
at compound interest? A. $631,238% +:
4. What is the amount of $500 for 4 years, at simple interest ? A. $620.
5. What will be the amount of $700 for 5 years, compound interest? A. $936,757, +.
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 com. pound interest ?-1191016. $1500 for 6 years ?-21277786. $2000 for 2 years ?-224720. $400 for 7 years ?-601452.
A. $6167,44616+. 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. $2215,89616t. 9. What is the compound interest of $500,50 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 ceni.?-870124. At 10 per cent. ?-126105. A. $384,50.