II. Divide 1 dollar multiplied by the interest on the stock by the given rate, and the quotient will be the price of $1 of the stock. EXAMPLES. 1. If I buy 7 per cent stock at 121 per cent discount, what is the rate per cent on the investment? 2. At what rate of discount must I invest in 8 per cent stock in order to yield me 10 per cent? 3. The stock of the Erie Railroad is at 62 per cent if it pays semi-annual dividends of 21 per cent, what would be the rate of interest on an investment ? 4. The bonds of the Illinois Central Railroad Company, which bear interest of .7 per cent., are worth 87 per cent., and the charge for brokerage is per cent.: what would be the interest on an investment in these funds? 5. If the par value of a stock is $100, and the interest 7 per cent., what is the discount when an investment yields 12 per ct.? 6. The stock of the Hartford and New Haven Railroad is at a premium of 20 per cent: reckoning the interest on money at 6 per cent, what will be the interest on an investment in this stock? 244. Which is the best investment? 1. I invest $1250 in State Stocks bearing an interest of 6 per cent, and a premium of 15 per cent. I invest the same amount in State fives at 12 per cent discount: which will yield the larger interest? 244. How do you find which is the best investment? x .06 = .0521 + X= 52 pr. ct. Find the rate of interest on the second investment (Art. 243). The comparison of these two rates will show which is the more profitable stock. .88 $1 х .05 x=.0568 + 68 x = 588 pr. ct. 2. Which is the best investment, to buy sixes at par, or sevens at 107 ? 3. Which will yield the larger profit, 8 per cent stock at a premium of 20 per cent, or 5 per cent stock at 80 per cent? 4. If I invest $2000 in state stocks at 5 per cent, at par, and the same amount at 6 per cent, at 90, what will be the difference of the proceeds of the investments at the end of 5 years? PROFIT AND LOSS. 245. PROFIT or Loss is a process by which merchants discover the amount gained or lost in the purchase and sale of goods. It also instructs them how much to increase or diminish the price of their goods, so as to make or lose so much per cent. 1. Bought 325 bushels of wheat at $1,37 a bushel, and sold it at $1,45 a bushel: what was the profit? ANALYSIS.-We first find the profit on a single bushel, and then multiply by the number of bushels, which is 325: the product is the profit. OPERATION. $1,45 sold per bushel. ,08 profit on 1 bushel. then, 325 ×,08=$26,00 profit. 2. Bought a piece of broadcloth containing 36 yards, at $2,75 per yard; it proving damaged, was sold at a loss of $18: for what was it sold per yard? 245. What is Profit or Loss? How do you find the entire profit or loss? How do you find the profit or loss on unity? ANALYSIS. Find the cost, which is $99; then subtract the loss $18, and then divide by the number of yards: the quotient will be the answer: hence, OPERATION. $2,75 × 36 = $99 Loss I. When the entire profit or loss is required: 18 36)81($2,25 Find the profit or loss on unity and multiply it by the number which shares the profit or loss. II. When the profit or loss on unity is required: Find the entire profit or loss and divide it by the number which shares the profit or loss. EXAMPLES. 1. Bought 9 barrels of sugar, each weighing 250 pounds, at 7 cents a pound: how much profit would be made if it were sold at 8 cents per pound? 2. If in 3 hogsheads of molasses which cost $68,04, one-third leaked out, what must the remainder be sold for per gallon to realize a profit of $2,52 on the whole? 3. A farmer bought a flock of 360 sheep; their keeping for 1 year cost $0,75 a head; their wool was worth 1 dollar and 25 cents a head, and one-fourth of them had lambs, each of which was worth one-half as much as a fleece: what was the profit of the purchase at the end of the year? 246. Given the per cent of the gain or loss, and the amount of the sale, to find the cost. 1. A grocer sold a lot of sugars for $477,12, which was an advance of 12 per cent on the cost: what was the cost? ANALYSIS.-1 dollar of the cost plus 12 per cent, will be what that which cost $1 sold for, viz., $1,12: hence, there will be as many dollars of cost, as $1,12 is contained times in what the goods brought. OPERATION. 1.12)477,12 246. How do you find the cost when you know the per cent and the amount of sale? 2. Mr. A. bought a lot of sugars, but finding them of an inferior quality, sold them at a loss of 15 per cent, and found that they brought $340: what did they cost him? ANALYSIS.-1 dollar of the cost less 15 per cent, will be what that which cost 1 dollar sold for, viz., $0.85: hence, there will be as many dollars of cost, as .85 is contained times in what the goods brought. OPERATION. .85)340 $400 RULE.-Divide the amount received by 1 plus the per cent when there is a gain, and by 1 minus the per cent when there is a loss, and the quotient will be the cost. EXAMPLES. 1. I sold a parcel of goods for $195,50, on which I made 15 per cent: what did they cost me? 2. Sold 78cwt. 3qr. 14lb. of sugar, at 8 cents a pound, and gained 15 per cent: how much did the whole cost? 3. A merchant having a lot of flour, asked 331 per cent more than it cost him, but was obliged to sell it 121 per cent less than his asking price; he received for the flour, $7.015 a barrel : what did it cost him? 4. A dealer sold two horses for $472,50 each, and gained on one 35 per cent, but lost 10 per cent on the other: what was the cost of each, and what was his gain? 247. To find the selling price of an article so as to gain or lose a certain per cent. 1. A grocer bought 12 barrels of sugar, for which he paid $18,50 a barrel: what must he sell it for to yield him a profit of 15 per cent? ANALYSIS. Since the amount for which the sugar is to be sold exceeds its cost by 15 per cent., that amount added to the cost will give what it must be sold for. When there is a loss, subtract. OPERATION. $18,50 × 12 = $222 33.30 15 per cent RULE. Add the percentage to the cost, when there is a gain, and subtract it when there is a loss. EXAMPLES. 1. A farmer sells 375 bushels of corn for 75 cents a bushel; the purchaser sells it at an advance of 20 per cent: how much a bushel did he receive for the corn ? 2. A merchant buys a pipe of wine, for which he pays $322,56, and he wishes to sell it at an advance of 25 per cent : what must he sell it for per gallon? 3. A man bought 3275 bushels of wheat, for which he paid $3493,334, but finding it damaged, is willing to lose 10 per cent.: what must he sell it for per bushel? 4. If a merchant in selling cloth at $4,70 a yard, loses 6 per cent. on its cost, for how much must he sell it to gain 14 per cent.? 5. If I purchase two lots of land for $150,25 each, and sell one for 40 per cent. more than it cost, and the other for 28 per cent. less, what is my gain on the two lots? 6. Bought a cask of molasses containing 144 gallons, at 45 cents a gallon, 36 gallons of which leaked out at what price per gallon must I sell the remainder to gain 10 per cent. on the cost? 7. A person in Chicago bought 3500 bushels of wheat, at $1,20 a bushel: allowing 5 per cent. for waste in measuring and transportation, and 3 per cent for freight, and 2 per cent commission for selling, what must it sell for per bushel in New York that he may realize 40 per cent net profit? 248. Given the gain or loss to find the per cent. 1. Bought a quantity of goods for $200, and sold them for $170 what per cent did I lose on the purchase? 247. How do you find the selling price of an article so as to gain or lose a certain per cent ? 248. How do you find the percentage when you know the gain or loss? |