50. The prime cost of a purchase is the sum paid by the agent for the goods or property. The gross cost is the prime cost plus the commission and expenses incident to the purchase. 51. An account purchase is a detailed statement made by the agent to his principal, showing the cost of goods or property bought, the expenses attending the purchase, and the gross cost. 52. The commission or brokerage is usually computed at a certain per cent. of the gross proceeds of a sale or the prime cost of a purchase. In some cases, however, it is computed at a certain price per unit of weight or measure; as, so much per ton, per bushel, or per barrel. Examples in commission are solved by the rules of percentage. Either the gross proceeds or prime cost is the base; the net proceeds is the difference; the gross cost is the amount; the commission is the percentage; and the rate of commission is the rate per cent. The remittance from the principal to the purchasing agent, including both the investment and the commission, is an amount. The following rules are derived directly from the principles of percentage: 53. Rule.-To find the commission, multiply the prime cost or gross selling price by the rate of commission. Formula. Commission = cost or selling price × rate of commission. EXAMPLE. A real estate agent sells a house and lot for $4,375 and receives 2% commission; what is the commission and what are the net proceeds? SOLUTION.-Commission = selling price X rate = $4,375 X .02 = $87.50. Ans. Net proceeds = $4,287.50. Ans. = selling price - commission = $4,375 $87.50 54. Rule.-To find the prime cost or gross proceeds, the commission being given, divide the commission by the rate of commission. Formula. Prime cost or gross proceeds = commission rate of com mission. EXAMPLE.-An agent received $319.50 commission for selling apples; if the rate of commission charged was 14%, what was the selling price of the apples? = SOLUTION.-Selling price or gross proceeds = $21,300. Ans. = $319.50 .015 55. Rule. To find the prime cost and commission, the remittance from the principal being given, subtract from the remittance the expenses of the purchase, if any, and divide the remainder by 1 plus the rate of commission. The quotient is the prime cost. Subtract the prime cost from the remainder and the difference is the commission. EXAMPLE.-A principal sends his agent $21,611 with orders to buy cotton after deducting his commission and other charges; the agent paid $124.30 for freight, $51.70 for cartage, $15 for insurance, and deducted his commission of 2%. (a) How much remained to invest in cotton? (b) What was his commission? SOLUTION. The expenses are first deducted. $21,611 - ($124.30 +$51.70 +$15) = $21,420, which is the sum of the prime cost and commission. According to the rule, (a) Prime cost = $21,420 ÷ (1 + .02) Ans. (b) Commission = = $21,420 1.02 = $21,000. = $420. Ans. $21,420 $21,000 NOTE.-When a charge is made for guaranty, add the per cent. of guaranty to 1 plus the rate of commission, and proceed as above. EXAMPLES FOR PRACTICE. 56. What is the commission (a) If the gross proceeds are $300 and the rate of commission is 34%? (b) If the gross proceeds are $9,375 and the rate of commission is 2% ? (c) If the prime cost is $831.75 and the rate of commission is 14% ? (d) If the prime cost is $960 and the rate of commission is §%? What are the net proceeds (e) If the gross proceeds are $340, rate of commission 3%, other expenses $4.30? and (f) If the gross proceeds are $6,375, rate of commission 4%, and other expenses $32.50? (g) If the gross proceeds are $195.40, rate of commission 1%, and other expenses $7.45? (e) $325.50. Ans. (f) $6,087.50. (g) $185.02. What is the prime cost if (h) The gross cost is $520 and the rate of commission is 4%? (i) The gross cost is $1,606 and the rate of commission is %? (1) The gross cost is $843, the rate of commission is 2%, and the expenses of buying are $27? Ans. (h) $500. 1. An agent receives $13 commission for selling $650 worth of goods; what rate of commission does he charge? Ans. 2%. 2. A commission merchant sold a quantity of wool for $4,650; he charged 2% commission, 2% guaranty, and the transportation, storage, and other expenses amounted to $184. How much should he send his principal? Ans. $4,256.75. 3. An agent received $550.50 to buy potatoes after deducting all expenses; he paid $26.50 for drayage, $32 for barrels, and charged 2% commission for buying. How many bushels did he buy at 60 cents per bushel? Ans. 800 bu. 4. A commission merchant has consigned to him 400 barrels of flour which he sells at $4.75 per barrel, and charges 2% commission; with the net proceeds he buys sugar at 64 cents a pound and charges 2% commission for buying. (a) How many pounds of sugar does he buy? (b) What is the amount of his commissions? 5. A New York agent received $1,134 with which to purchase hats. If he charges 3% commission and 2% additional for guaranty of quality, how many dozen hats can he buy at $13.50 per dozen? Ans. 80 doz. 6. A commission merchant sold 2,500 bushels of wheat at 64 cents a bushel and a quantity of corn at 23 cents per bushel; the rate of commission on each sale was 13%, and the total commission was $35,084. How many bushels of corn were sold? Ans. 1,760 bu. INSURANCE. 57. Insurance is a contract by which one party, the underwriter, or insurer, agrees, for a consideration, to make good a loss sustained by another party. 58. Insurance is of two kinds, property insurance and personal insurance. Property insurance includes fire insurance (indemnity for loss or damage by fire); marine insurance (indemnity for losses at sea); transit insurance (indemnity for loss of, or damage to, merchandise during transportation); stock insurance (indemnity for loss of live stock); and accident insurance (indemnity for breakage of fragile materials, as plate glass, etc.). Personal insurance includes life insurance, which secures the payment of a certain amount to a specified person at the death of the party insured, or after the lapse of a specified time; accident insurance, which secures the payment of a certain sum in case of accident to the insured; health insurance, which secures the payment of a weekly sum during sickness; and insurance against the dishonesty of employes. 59. The policy is the written contract between the insurance company and the party insured; it contains a description of the property insured, the conditions upon which the insurance is taken, and the amount to be paid in case of loss. 60. The premium is the amount paid to the insurer for assuming the risk of loss or damage. The premium is a certain per cent. of the amount of insurance, as 5%, 3%. The rate of premium depends upon the nature of the risk and upon the length of time the insurance has to run. It is customary to speak of the rate of premium as the cost per $100 of insurance; as 60 cents per $100, $1.20 per $100, etc. 61. In property insurance, all computations are based on the rules of percentage. The amount of insurance is the base, the premium is the percentage, and the rate of premium is the rate. 126D-13 62. Rule. To find the premium, multiply the amount of insurance by the rate of premium. (Art. 14.) Formula. Premium amount of insurance X rate. EXAMPLE.-A house and furniture are insured against fire for $3,250, the rate of premium being %, or 75 cents per $100 per year; what is the yearly premium? SOLUTION. 3% = .0075. Using the rule, Premium = $3,250 X .0075 = $24.37. Ans. 63. Rule. To find the amount of insurance, divide the premium by the rate of premium. To find the rate of premium, divide the premium by the amount of insurance. EXAMPLE 1.-What amount of insurance can be obtained for $137.50, the rate of premium being 55 cents per $100? SOLUTION.-Rate = .55 100 = .0055. Amount of insurance premium rate = $137.50 ÷ .0055 = $25,000. Ans. EXAMPLE 2.-A warehouse and contents together valued at $13,500 is insured for two-thirds of its value; if the premium is $78.75 what is the rate of premium? 64. 1. A store and contents valued at $16,400 is insured for three-fifths of its value at 14% premium; what is the cost per year of Ans. $110.70. insurance? 2. A premium of $162.50 is paid for the insurance of a steamer worth $32,500, which is insured for four-fifths of its value; what is the premium, in cents, per $100? Ans. 62 cents per $100. 3. A stock of goods is insured for two-thirds of its value; the premium paid is $43.75 and is at a rate of 75 cents per $100. What is the value of the stock of goods? Ans. $8,750. |