cent.?-2175 17550 per cent.?-225, 65 per cer per cent.?-2625. per cent.?-285. 100 per cent., or to double my money ?-30. A. $2,31.

7. Bought 100 tierces of rice, each tierce weighing 300 lbs net, at 64 cents per lb.-1875; 30 pipes of wine for $1,12 per gallon-425250; 3 hhds. of rum for 90 cents per gallon-17010; 40 barrels of flour for $7 per barrel-300; and 40 bushels of salt for 7 s. 6d. or $1,25 per bushel-50: how much must all the said articles be sold for, to gain 50 per cent., being 150 per cent. on the first cost? A. $9971,40.

1 LXVII. TIME, RATE PER CENT., AND AMOUNT GIVEN, TO FIND THE PRINCIPAL.

1. What sum of ready money, put at interest for 1 yr. 8 mo. at 6 per cent., will amount to $220?

The amount of $1 for 1 year and 8 mo. is $1,10; then, $220 $1,10-$200, Ans.

RULE. Q. How, then, would you proceed, to find the principal?
A. Divide the given amount by the amount of

$1 at the given rate and time.

2. What principal, at 6 per cent., in 5 years, will amount to $650: In this example, in dividing $650 by $1,30, we annex two make the decimal places in the divisor and dividend equal.

ciphers to 509, to (see ¶ LVI.)

.4. $500

3. What principal, at 6 per cent., in 1 year 2 mo., will amount to $642? A. $600.

4. What principal will amount to $691,50 in 2 yrs. 6 mo. 15 da., at 6 per cent.? A. $600.

5. A correspondent has in his hands $210, to be laid out in goods; after deducting his own commission of 5 per cent., how inuch will remain to be laid out?

It is evident, that the commission which he received, added to the money laid out, must make $210; hence $210 may be considered the amount, and the money laid out the principal; consequently, the question does not differ materially from the foregoing. In such questions as these, in which time is not regarded, the amount of $1 is the rate per cent. added to $1.

It will be recollected, that 6 per cent. is 6 cents on 100 cents, or $1, 5 per cent., 5 cents; the amount, then, of $1, at 5 per cent., is 5 cents added to $1, making $1,05; then, $210÷$1,05= $200, Ans.

A

6. A factor receives $1040 to be laid out in goods, after deducting his own commission of 4 per cent.; how much does his

commission amount to?

The sum laid out, found as before, is $1000; then, 1040-1000-$40, commission, the Answer.

7. A factor receives $2100, from which he wishes to deduct his commission of 5 per cent.; what will his commission amount to? A. $100.

DISCOUNT. 1. William owes Rufus $1272, to be paid in 1 year, without interest; but Rufus, wanting his money immediately, says to William, I am willing to allow you 6 per cent., the lawful interest, if you will pay me now; what sum ought William to pay Rufus?

It is evident that he ought to pay just such a sum as, put at interest, would, in 1 year, amount to $1272; or, in other words, such a principal as would amount to $1272. This question, therefore, is solved in the same manner as the preceding. $1272 $1,06 $1200, the Ans.

Q.. What is an allowance made for the payment of a sum of money before it becomes due, called?

A. Discount.

Q. What is the sum called, which, put at interest, would, in the given time and rate, amount to the given sum or debt?

A. The present worth.

Q. In calculating interest, what would the present worth be called?

A. The principal.

Q. What would the given sum, or debt, be called?

A. The amount.

Q. What is the discount of any sum equal to ?

A. The interest of its present worth for the same time.

Q. As operations in discount are substantially the same as in the preceding paragraph, what is the rule, which was there given, that 18applicable to discount?

RULE. A. Divide the given sum, or debt, by the amount of $1, at the given rate and time; the quotient will be the present worth.

Q. How is the discount found?

A. By subtracting the present worth from the given sum or debt.

Note. It will be recollected that, when no per cent. is mentioned, 6 per cent. is understood.

2. What is the present worth of $133,20, due 1 yr. 10 mo. hence? A. $120.

PROOF. 3. What is the amount of $120 for 1 yr. 10 mo. (Perform this example by the rule for calculating interest.) A. $133,20.

A

A. $60.

4. What is the discount of $660, due 1 yr. 8 mo. hence? PROOF. 5. What is the interest of $600 for 1 yr. 8 mo.?

A. $60.

6. What is the discount of $460, due 2 yrs. 6 mo. hence ?

A. $60.

7. What is the present worth of $1350, due 5 yrs. 10 mo. hence? A. $1000.

8. Bought goods to the amount of $520, on 8 mo. credit; how much ready money ought I to pay as an equivalent? A. $500. 9. Bought goods in Boston, amounting to $1854, for which I gave my note for 8 mo.; but, being desirous of taking it up at the expiration of two months, what sum does justice require me to pay? A. $1800.

10 What is the discount of $615, due 5 mo. hence?

A. $15.

11. What is the present worth of $1260, due 10 mo. hence?

A. $1200..

12. What is the present worth of $1272, due 2 yrs. hence, discounting at 3 per cent.? A. $1200.

13. What is the present worth of $51,50, due 6 mo. hence?→ 50. Of $204, due 4 mo. hence ?-200. Of $13000, due 5 yrs. hence?-10000. Of $9440, due 3 yrs. hence ?-8000.

A. $18250. 14. What is the present worth of $515, due 6 mo. hence?500. Due 1 yr. hence?-485849. Due 15 mo. hence ?-479069. Due 20 mo. hence ?-468181. Due 4 yrs. hence ?-415322. A. $2348,421+.

¶ 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 cent. 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.

LXIX. THE PRINCIPAL, INTEREST, AND TIME, BEING GIVEN, 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.? A. Divide the given 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 nio., 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 game as in the foregoing examples.

It has been remarked, that 6 per cent. is 6 cents on 100 cents; that is, the interest is T of the principal; which, written decimally, is‚06; 5 per cent. is 8,05; 25 per cent. is,25; that is, the rate 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;=,2525 per cent., the Answer.

Ο

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 gailons 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 18 12121 per cent., that is, the third place is so many tenths of 1 per cent. ; thus, 1 per cent. is,01, and per cent. is ,005, 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.