9. For how much must a note payable in 2 mo. be given to realize $1000 at bank, money being worth 6 per cent? Solution. - $1000, the money received, must be the difference between the face of the note and its interest for 2 mo. 3 da., i. e. it must equal the face of the note minus 2 0 3 o of it = 58.37 or 1:7% of the face of the note. Hence, the note must be given for 2008 of $1000, which is $1010.606. 10. For bow much must a note payable in 90 da. be given, in order that $2000 may be received on it at bank? 11. For how much must a note payable in 4 mo. be given, in order that $800 may be received on it at a New York bank, interest being 7 per cent? 12. For how much must a note payable in 3 mo. be given, so that when shaved at 2 per cent per month I may receive $1200 for it? 13. I owe $1000 payable in 3 mo. My creditor offering to deduct 4 per cent for cash, I pay him $500. How much is still due ? SOLUTION.-Since 4 per cent of the debt was to be deducted for cash, the cash payment would be 96 per cent of the part of the debt cancelled, and the part of the debt cancelled would be of the cash payment. Le of $500 = $520.83} = part of debt cancelled. $1000 = $520.83} = $479.163 still due. 14. I owed $1260 due in 4 mo. My creditor offering to deduct 6 per cent for cash, I paid $900 down. How much did I still owe? 15. I bought goods to the amount of $1500, and can pay for them by a note on 6 mo., or by cash at 6 per cent discount. Allowing that I pay $900 in cash, for how much must my note be given ? 16. I bought a lot of goods for $728.96, payable in 3 mo.; but the seller offering to deduct 4 per cent for cash, I got a note payable in 3 mo. discounted at bank for such a sum that the money received on it was just sufficient to pay for the goods. For how much was the note given? How much less money was required to pay the pote when due, than would have been required to pay for the goods at that time? 124. To find the Rate when the Principal, Interest, and Time are given. Note. — Problems like the following occur but rarely in business life. (a.) To solve them, we first find what part of the principal the given interest is, and then find from this what part of the given principal the interest for one year is, reducing the result to hundredths. 1. At what rate per cent must $324 be on interest to gain $19.44 in 1 yr. 2 mo. 12 da. ? Solution. — $19.44 = 1944 of $324; or the given interest is 1,9445 of the principal. If the interest for 1 yr. 2 mo. 12 da., or 432 days, is so much, the interost for 1 yr. or 360 da, must equal 269 of 944 of the principal = no or 5 per cent of the principal. Required the rate of interest when 2. $475.50 gains $38.04 in 1 yr. 4 mo. 125. To find the Principal when the Interest, Rate, and Time are given. Note.— These problems, like those of the last article, are of rare occurrence in business life. (a.) To solve them, we first find what part interest for the given time and rate is of the principal. The given interest being this fractional part of the principal, the principal must be the part of the interest expressed by this fraction inverted. 1. What principal on interest at 7 per cent will gain $88.536 in 1 yr. 4 mo.? Solution. — Since 1 yr. 4 mo. = 16 mo. = 15, or of a year, the interest must equal of 7o = of the principal. If $88.536 is of the principal, the principal must equal 15 of $88.536, which is $948.60. What principal on interest 2. At 6 per cent will gain $5.038 in 1 yr. 5 mo. 15 da. ? 126. Commission. (a.) Money received for services in buying and selling goods for others is called COMMISSION, and is usually reckoned at a certain per cent of the cost of the goods bought, or of the price of those sold. (b.) A merchant who makes it his business to buy and sell on commission is called a COMMISSION MERCHANT. 1. A commission merchant sold goods for me to the amount of $775.50, for which he charged a commission of 14 per cent. What was his commission, and how much ought he to remit to me? SOLUTION. — His commission = .011 of $775.50 = $11.632, and he ought to remit me $775.50 – $11.632 = $763.868. 2. A commission merchant bought goods for me to the amount of $573.25, for which he charged a commission of 2 per cent. What was his commission, and what sum must I remit to pay for the goods and commission? Solution. — His commission = .02 of $573.25 = $11.465, and I must remit $573.25 + $11.465 = $584.715. 3. I sold goods for R. & S. Ives to the amount of $3275.28, for which I charged a commission of 75 per cent. What was the amount of my commission, and how much money must I remit to them ? 4. I bought goods for John Munroe to the amount of $1500, charging him a commission of 3 per cent. What was my com mission, and how much money was required to pay for the goods and my commission ? 5. I sold for a manufacturer 9342 yards of cotton cloth at 9 cents per yard, 17250 yards at 10 cents per yard, and 5000 yards at 9 cents per yard. What was my commission at 2 per cent on the sales ? How much money ought I to pay him ? 6. I bought for a merchant a bill of goods amounting to $5172.75. What was my commission at 21 per cent? How much money ought he to send me to pay for the goods and my commission ? 7. John Williamson has sent me $3550 with which to buy flour, after deducting my commission of 2 per cent on the amount expended. What will be my commission, and how much ought I to expend for flour? SOLUTION.—Since $3550 includes the sum to be invested and the commission of 21 per cent, it must equal 1021 per cent, or 41 of the sum to be in. vested. Hence, I ought to invest 40 of $3550, which is $3463.415, and my commission ought to be at of $3550, which is $86.585. PROOF.--24 per cent of $3463.415 equals $86.585. 8. Thomas Simmons has bought a lot of goods for me, on which he charges a commission of 24 per cent. If $8520 is just sufficient to pay for the goods and his commission, what was the cost of the goods and what the amount of his commission? 9. I have bought a lot of furs at a commission of 10 per cent. The cost of the furs and the amount of my commission are together equal to $1376.65. What was the cost of the furs and what the amount of the commission ? 10. I sent $904.96 to my agent, directing him to expend it in corn, after deducting his commission of 1 per cent on the purchase. IIe purchased the corn at 50 cents per bushel. How many bushels did he buy? 11. I sent 15625 yards of sheeting to Brown & Rogers, Commission Merchants in New Orleans, directing them to sell it, and, after deducting all expenses, to invest the balance in cotton. They sold the sheeting at 12 cents per yard, for which they charged a commission of 4 per cent. They then invested the balance, after deducting a commission of 2 per cent on the purchase, in cotton, at 15 cents per pound. How many pounds of cotton did they buy ? 127. Insurance. (a.) Insurance is an obligation assumed by one individual or company to pay to another a certain sum of money on the occurrence of some contingent event. ILLUSTRATIONS. — My house is insured against loss by fire, when a company or an individual have agreed to pay me a certain sum in case it is burned within a specified period. My life is insured when a company agrees to pay to my heirs a certain sum in the event of my death. (b.) FIRE INSURANCE is insurance against loss by fire. (d.) HEALTH INSURANCE is an obligation to pay an individual a certain sum for each week that he may be sick. (e.) LIFE INSURANCE is an obligation to pay to some person a certain sum of money in the event of the death of the persun insured. (f.) The written certificate of insurance is called a Policy. (g.) The sum paid for insurance is called the PREMIUM. (h.) If property is insured, the premium is a certain per cent of the sum covered, i. e. of the sum for which it is insured, and is usually paid at the time of effecting the insurance. (i.) When health or life is insured, the premium is usually a given sum paid annually during the time for which the insurance continues. As its amount is calculated from tables prepared by the different insurance companies, it will be unnecessary to give examples in life or health insurance. 1. I had my factory insured for $10000, at a premium of 7 per cent, paying $1 for the policy. How much did the insurance cost me? ANSWER. — $1 + 7 per cent of $10000 = $701. 2. What would be the expense of getting a building insured for $1500, at a premium of 41 per cent, the policy costing $1? |