A Practical and Theoretical System of Arithmetic

rated bank, and sell them at 93 per cent. advance, what will be my profit, the shares having cost me $50 each? Ans. 351.56.

12. When a share of the United States Bank stock sold for $112, the nominal value being $100, what were $2000 of that stock worth? Ans. $2250.

Here the advance is 12 per cent.

13. If $100 of stock in an Insurance Company, sell for $96, what are $1200 of the stock worth?

The stock is 33 per cent. below par.

Ans. $1159.50.

DISCOUNT.

DISCOUNT is applicable only to demands not drawing interest, and to notes on which the interest is paid in advance, whereon the drawer receives a sum, which, at the customary rate of interest, will amount to the face of the note in the specified time.

The problem then of Discount is, from the rate, time, and amount, to find the principal.

This is solved by the Rule of Three. We take any sum-for convenience, 1 dollar, or 1 pound-and find its amount at the given rate, and time; and then say, as this amount is to the given sum, (which is also amount,) so is 1 dollar to the principal or present worth of the sum in question.

1. For example; a note for $246 is payable 2 years hence, and not on interest. If it be paid now, what is its present worth?

The interest of $1 at 7 per cent. is .07, and for 2 years .14. Adding this interest, we have the amount $1.14. The statement would be ;

Amount. Amount. Prin.

1.14 : 246 : : 1 : A.

But the third term is constant, being always unity. We may therefore omit it.

RULE. Divide the given sum by the amount of $1 for

If we take the present worth or principal, and cast the interest for the given time, we shall obtain for amount the original sum.

2. If a note for $925 be payable without interest, 1 year 8 months hence; what is its present worth at 6 per cent.? Ans. $840.91.

3. If I buy goods in Montreal, to the amount of £615 15s. on a credit of 7 months; how much ought to be deducted, if I pay down, discount being 4 per cent. per Ans. £15 15s.

annum ?

4. What is the present worth of $756, one half payable in 6 months, and the other half in a year, discount at 7 per cent. ? Ans. $718.49. 5. What is the discount on $ 600, payable in 4 years,

at 5 per cent. per annum?

Ans. $100. 6. What is the present worth of a legacy of $1200 to be paid when the legatee comes of age, he being 16 years old; discount 6 per cent. per annum? Ans. $923.07.

EQUATION OF PAYMENTS.

THIS rule teaches us to find a mean time for the payment at once, of several debts due at different times, so that no loss of interest shall be sustained by either party.

RULE. Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time for the payment of the whole.

1. If I owe my neighbor $100 payable in 6 months; $120 payable in 7 months; and $160 to be paid in 10 months; when can the three sums be paid at once, without loss to either of us?

The interest on $100 for 6 months int. on $ 600 1 mo.

Adding these products together, we find, that the interest on $3040 for 1 month is equivalent to the interest of the several sums for their respective times of payment. But $380 is the sum actually to be paid; and the question is, in what time it will produce the same amount of interest, that $3040 does in 1 month. If stated it would stand,

princ.

mo.

380 :: 3040 :: 1 : A.

But the third term being

always unity, may be omitted, and the sum of the products be merely divided by the sum of the payments.

3040-380=8.

Ans. 8 months. 2. If $400 are now due, $400 payable in 4 months, and $400 in 8 months; what is the equated time for paying the whole? Ans. 4 months.

3. A man bought a farm, and agreed to pay of the price down, and the residue in three equal annual instalments; what is the equated time for paying the whole at once? Ans. 18 months.

4. A owes B $600 to be paid in 2 years from the date of the note; but at the expiration of 6 months, A agrees to pay $150, if B will wait enough longer for the balance to compensate for the advance: how long ought B to wait? Ans. 6 months

5. If $750 are to be paid of it in 1 years, of it in 2 years, and the residue in 2 years; what is the equated time of paying the whole at once? Ans. 233 months. 6. If of a sum of money be now due, in 4 months, and the residue in 8 months; what is the equated time of payment? Ans. 3 months.

PROFIT AND LOSS PER CENT.

WHEN Commodities are bought and sold again, it is often desirable to know the profit or loss per cent.; or, at what price they must be sold to gain a certain per cent.

1. If I buy factory cotton for 2s. per yard, and sell it at 2s. 8d.; what do I gain per cent.?

Here, the gain is 8d. on 2s., or 24d., and expressed fractionally, it is 24 If this fraction be reduced to a decimal and carried to hundredths, (that is, to 2 places of decimals,) it will express the per cent.

3)100

Ans. 33 per cent.

2. If I buy broadcloth at $ 3.44, and sell it at $4.30 per yard; what is the profit per cent. ?

$4.30 .86 .43 172) 4300(25 per cent

Sold for

3.44 1.72

.86

344

860

3. Bought cloth at 624 cts. per yard, and sold it at $1; what is the profit per cent.?

.375

5)300

Ans. 60 per cent.

RULE. Make the cost of the article the denominator, and the gain or loss the numerator of a fraction, and if there are decimals, make the number in both the terms equal: then

reduce the fraction to its lowest terms, annex two ciphers to the numerator, and divide by the denominator.

4. If a merchant buy broadcloth at $5.50 a yard, and sell it at $ 6.60 a yard; what is his profit per cent.? Ans. 20 per cent.

5. A man bought 500 sheep at $2.25 a head, and his expenses in the purchase were $75. He sold them again at an average price of $ 3.40 per head; what was the profit per cent. on his investment? Ans. 41 per cent. 6. A grocer bought tea at 6s. a pound, but in consequence of a fall in the price of the article, is obliged to sell at 5s. 4d. per pound; what is his loss per cent. ?

Ans. 11 per cent. To know how a commodity must be sold, in order to gain or lose so much per cent.

RULE. Make a fraction of the per cent, and reduce it to the lowest terms: then take the parts of the purchase price indicated by the fraction, and add or subtract them according as it is gain or loss per cent.

7. If I buy Irish linen at 2s. 3d., how must I sell it per yard to gain 25 per cent.?

25 per cent. is 25.

s. d. 1)2 3

6 3

Ans. 2s. 9d. 3 qr.

8. If I buy rum at $1.05 per gallon, how must it be sold to gain 30 per cent.?