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and charges 2 per cent. commissior. How much money must he pay to his principal ?
Ans. 15802:50. 4. A sends to B, a broker, $3605 to be invested in stock: B is to receive 3 per cent. on the amount paid for the stock. What was the value of the stock purchased ?
Since B is to receive 3 per cent., it is plain that $103 of A's money would purchase $100 worth of stock. Hence, the amount expended for stock must be 18 of $3603= $3605:1.03=$3500. Ans.
NOTE.-In such cases as the above, when the given sum includes the factor's commission, and we desire to know what amount he must invest for his principal, so that the balance may be his commission on the amount invested, we must divide the given sum by the percentage of the commission increased by a unit. Thus, dividing #3605 by 1:03, the quotient is $3500, which is the sum invested.
5. A factor receives $60112, and is directed to purchase cotton at $289 per bale : he is to receive 4 per cent. on the money paid for the cotton. How many bales did he purchase ? $60112-1•04=$57800 amount paid for cotton. ,
$57800 --$289=200, number of bales. 6. The par value* of 125 shares of bank stock was $100 per share. What is the present value, if the stock is worth 18 per cent. above par? Ans. $14750.
7. What is the value of 50 shares of bank stock, the par value of which was $200 per share, on the supposition that it is 12 per cent. below par, or, that it is worth only 88 per cent of its par value ? Ans. $8800.
* By par value is meant the original cost or estimated value of stock. When it is worth more than its original cost, it is said to be above par, when it is worth less than the original cost, it is said to be below par.
8. A bank fails, and has in circulation $108567. It can pay only 13 per cent. What amount of money has it on hand ?
122. INSURANCE is a contract, by which an individual or company agrees to restore the value of ships, houses, or goods of whatever kind, which may be destroyed by the perils of the sea, or by fire.
The security is given in consideration of a certain sum of money called the premium, which is paid by the owner of the property insured.
The premium is always estimated at a certain rate per cent. on the value of the property insured.
The written agreement of indemnity is called a policy. What is Insurance? What is premium? How is the premium estimated ? What is the policy?
It is obvious that the foregoing rules under Percentage and under Commission, may be employed for finding the insurance premium.
1. If A gets his house insured for $1800, at 41 cents on $100, what will be the amount of the premium?
Ans. $738. 2. An insurance of $12000. was effected on the ship Ocean, at a premium of 2 per cent. What did the premium amount to ?
Ans. $240. 3. I effected an insurance of $5230 on my dwellinghouse and furniture for 1 year, at of 1 per cent. What did the premium amount to?
Ans. $19.6125. 4. What is the amount of premium for insuring $34567, at 60 cents on $100 ?
Ans. $207.402. 5. What would be the premium for insuring a ship and cargo, valued at $46370, from Boston to Liverpool, at 21 per cent. ?
LOSS AND GAIN.
123. Loss AND Gain is a rule by which merchants discover the amount lost or gained in buying and selling goods. It also assists them in adjusting the price of their goods so as to lose or gain a certain per cent. What is Loss and Gain ?
1. Bought 300 yards of broadcloth at $2.25 per yard, and sold the same at $3.50 per yard. How much was gained ?
$3.50 price of 1 yard.
$375.00 whole gain. 2. A merchant bought 320 barrels of flour at $5 per barrel, but he finds he must lose 10 per cent. in the sales. How much will he receive for the whole ?
The whole cost of 320 barrels is $5 x 320=$1600.
Since he loses 10 per cent., one dollar's worth must sell for 90 cents.
0.90 Ans. $1440.00 what he receives. 3. Suppose I buy 25 cords of maple wood at $2.50 per cord, and sell it so as to make 25 per cent. What must I receive for the whole ?
The whole cost of the wood is $2.50 x 25= $62:50.
Since I make 25 per cent., one dollar's worth must sell for $1.25.
1.25 31250 12500
Ans. $78.1250 what I receive. 4. Bought a house and lot for $1400, and sold it for $1200. How much per cent. did I lose ?
$1400 cost of house.
$200 what I lost on $1400. Hence, folob==0:144=144 per cent.
5. Bought 225 gallons of molasses for 26 cents per gallon, and sold the whole for $64:35. What did I gain per cent. ?
The whole cost of 225 gallons is $0.26 x 225= $58:50. The whole gain is $64.35 – $58:50=$5.85. Since $5.85 is the gain on $58-50, it follows that the gain on $1 will be found by dividing $5:85 by 58.5. Performing the division, we have $5.85-58.5=0.1 or 0.10, that is, the gain is 10 per cent.
From the foregoing examples we are able to deduce the following principal
RULES. . I. The total gain or loss is the difference between the first cost and the selling price.
II. The first cost multiplied by 1, increased by the gain per cent., or by 1 decreased by the loss per cent., considered as a decimal, will give the selling price.
III. The whole gain or loss divided by the first cost, will give the gain or loss per cent.
6. Bought 75 pounds of coffee at 10 cents per pound. At how much per pound must I sell it so as to gain $3 on the whole ?
Ans. $0·14. 7. Bought 25 hogsheads of molasses, at $18 per hogshead, in Havana ; paid duties, $16:30; freight, $25; cartage, $5.50 ; insurance, $25.25. What per cent. shall I gain, if I sell it at $28 per hogshead ?
Ans. About 34 per cent. 8. If I buy broadcloth for $3.50 per yard, how much must I sell it at per yard so as to gain 25 per cent. ?
Ans. $4 371. 9. If I buy cloth at $3.50 per yard, how many must I sell it at per yard so as to lose 25 per cent ? Ans. $2:621.
10. A person bought a city lot for $800, and sold it so as to gain 40 per cent. How much did he sell it for ?
Ans. $1120. . 11. A house which cost $3000 was sold for $2400, What per cent. was lost?
Ans. 20 per cent. .12. A house which cost $2400 was sold for $3000. What per cent. was gained ? Ans. 25 per cent.