Five partial payments are endorsed on Smith's note: viz. Feu 1st, 1842, received seventy-five dollars. June 1st, 1842, received twenty dollars. August 1st, 1843, received twenty dollars. October 1st, 1843, received seven hundred and fifty dollars. Feb. 1st, 1844, received one hundred dollars. The balance of this note was paio June 1st, 1844. How much was it, by the legal rule?

COMPOUND INTEREST.

COMPOUND INTEREST is that which is paid not only for the use of the principal, but also for the use of the interest after it becomes due. The period of interest, that is, the term of time at the end of which interest is due, may year, a quarter, or any other term agreed upon. Whatever be the period, the following rule is applicable.

be a

RULE. Find the amount for the first period, and consider it the principal for the second period; find the amount for the second period, and consider it the principal for the third period; and thus proceed through the whole number of periods. Subtract the first principal

from the last amount, and the remainder will be the compound interest.

26. What is the compound interest of $100 for 3 years, at 6 per cent.; the interest being due annually?

27. What is the compound interest of 355 dollars, for 6 years, at 6 per cent. per annum ?

28. What is the compound interest of 250 dollars, for 4 years, at 7 per cent. per annum?

29. To what sum will 450 dollars amount, in 5 years, at 5 per cent. per annum, compound interest?

30. At compound interest, what will 600 dollars amount to in 1 year, at the rate of 6 per cent. a year, interest payable quarterly?

V.

DISCOUNT.

DISCOUNT is sufficiently defined in page 168; and we have now ouly to apply decimals to the operations.

RULE. Divide the debt by the amount of 1 dollar for he time, and the quotient is the present worth. Subtract the present worth from the debt, and the remainder will se the discount.

1. What is the present worth of 125 dollars, due in 18 months, when interest is 6 per cent. per annum?

$1 amounts to $1.09. 125 1.09 114.66+

=

2. What is the present worth of $456, due in 15 months, when money is worth 5 per cent. per annum ?

3. What is the discount on 3465 dollars for 6 months, when interest is 7 per cent. a year?

4. What is the present value of a note for 2448 dollars and 50 cents, payable in 8 months, when interest is 6 per cent. per annum ?

VI.
BANKING.

The interest on money hired from a bank is paid when the money is taken out. That is, the bank computes the interest on the principal of the note it receives, to the time the note is to be paid, deducts this interest from the principal, and advances the remainder to the hirer. Hence, bank interest is called discount; and the note received by the bank is said to be discounted.

Bank discount is always computed for three dayscalled days of grace-more than the time stated in the note for payment; and the hirer is not required to pay until the last of these three days.

1. Find the bank discount on $585 for 60 days and grace, (2 months,) at the rate of 6 per cent. a year.

2. What is the bank discount on 900 dollars for 90 days, and grace, at the rate of 6 per cent. a year?

3. How much is received on a note for 2540 dollars 80 cents, payable in 4 months, and grace, discounted at a bank, when interest is 4 per cent. a year?

4. A note for 452 dollars, payable in 7 months, and grace, is discounted at a bank, when interest is 6 per cent. per annum. What sum is received on it?

VII.

PROFIT AND LOSS.

The ascertaining what is gained or lost in buying and selling, and the adjusting of the price of goods so as to gain or lose a certain sum, or a certain per cent., come under the head of Profit and Loss.

How

1. Bought a piece of broadcloth containing 28 yards for 112 dollars, and sold it at 5 dollars 25 cents a yard. much, and what per cent., was my profit? (See Percentage, Art. III., Example 22.)

2. Bought 3 pieces of broadcloth, containing 28 yards each, at 5 dollars 25 cents a yard. At what price per yard must I sell it, to gain 20 per cent.?

3. Bought cloth at 4 dollars 60 cents a yard, which, not proving so good as I expected, I sold at 3 dollars 91 cents a yard. What per cent. did I lose?

4. Bought 1250 barrels of flour for 6250 dollars. At what price per barrel must I sell it, to make a profit of per cent.?

per

5. Bought wheat at 75 cents a bushel; at what price bushel must I sell it, to gain 20 per cent.?

6. A merchant received from Lisbon 180 casks of raisins, containing 80lb. each, which cost him 2 dollars 18 cents a cask. At what price per cwt. must he sell them, to gain 25 per cent.?

7. If I sell sugar at 8 dollars per cwt., and thereby lose 12 per cent., what per cent. do I gain or lose, by selling the same at 9 dollars per cwt.?

VIII.

PARTNERSHIP.

PARTNERSHIP is the union of two or more individuals in trade. The company thus associated is called a firm and the amount of property, which each partner puts into the firm, is called his stock in trade.

When each partner's stock is in the firm an equal length of time, the profit or loss is shared in proportion merely to each one's stock. But when the stock of the several partners is employed unequal terms of time, the profit or loss is shared in proportion both to stock and time.

1. A, B, and C entered into partnership, and the stock of each was in the firm one year. A put in 240 dollars, B 360 dollars, and C 120 dollars. They gained 350 dollars. What was each partner's share of the gain?

Solution. The whole capital $720. A's stock was $240, and he must have 240 of the gain. B's stock was $360, and he must have 360 C's stock was $120, and he must have 20. Observe the following statement.

720

2. W, S, and L formed a connexion in business. W put into the firm 2500 dollars; S 2000 dollars; and L 1500 dollars. The stock of the several partners was in trade the same term of time, and they gained 1500 dollars. What was each partner's share of the profit?

3. A, B, C, and D traded together one year. A put in 800 dollars, B 500 dollars, C 300 dollars, and D 150 dollars; but by misfortune they lost 350 dollars. What loss did each partner sustain ?

4. Three merchants bought a ship, for 8000 dollars A paid 2850 dollars, B 1980 dollars, and C the rest. In her first voyage she cleared 6400 dollars. How much of the profit had each partner?

WHEN THE TIME IS UNEQUAL, We compute on the prin ciple, that $1 for 2 months is equal to $2 for 1 month. For example, A, B, and C traded in company; A put in $200 for 3 months, B $180 for 5 months, and C $70 for 10 months: they gained $132. Now we say, that A's $200 for 3 months was the same as $600 for 1 incnth; B's $180 for 5 months the same as $900 for 1 month; and C's $70 for 10 months the same as $700 for 1 month; therefore the relation is the same as if A had put in $600, B $900, and C $700, all for an equa. term of time. These sums added together make $2200; therefore, A had of the gain, B 200 These fractions, reduced, are 22 22 6 22, 22, and 72. $132 is $6; then A had 6 times $6, B 9 times $6, and C 7 times $6.

2200

2200'

and C 700 2200 1of

22

RULE. Multiply each partner's stock by the time it was in the firm; make each product the numerator of a fraction, and the sum of the products a common denominator; then multiply the whole gain or loss by each of these fractions, for each partner's share.

5. A, B, and C traded in company. A put in 400 dollars for 9 months, B 300 dollars for 6 months, and C 200 dollars for 5 months: they gained 320 dollars. What was the gain of each?

6. X, Y, and Z formed a partnership. X put into the firm 500 dollars for 18 months, Y 380 dollars for 13 months, and Z 270 dollars for 9 months; but they lost 818 dollars 50 cents. What was the loss of each?

7. Gould and Davis entered into partnership for one year. Gould's stock, at first, was only 500 dollars, but at the end of 5 months he put in 150 dollars more. Davis's stock, at first, was 600 dollars, but at the end of 9 months he took out 200 dollars: at the end of the year, it was found they had gained 682 dollars 50 cents. What was the gain of each partner?

8. Three farmers hired a pasture at 60 cents for the season. A put in 5 cows 4 cows 5 months, and C 9 cows 6 months. did each pay ?

dollars 50 months, B 8 What rent