EXAMPLES. 1. What will be the compound interest, at 7 per cent, of $3750 for 4 years, the interest being added yearly? $3750,00 principal for 1st year. $3750x7÷100= 262,50 interest for 1st year. $4012,50×7÷100= 4012,50 principal for 2nd 4293,37+principal - 3rd $4293,37 x7-100= 300,53+interest 3rd 4593,90+principal - 4th $4593,90 × 7÷100= 321,57+interest 4th "" 4915,47+amount at 4 years. 2. If the interest be computed annually, what will be the interest on $100 for three years, at 6 per cent? Ans.$19,101+. 3. What will be the compound interest on $295,37, at 6 per cent, for 2 years, the interest being added annually? Ans. $36,50+. 4. What will be the compound interest on $500 for one year, at 8 per cent, the interest being computed quarterly? Ans. $41,21+. Q. What is Compound Interest? Give the Rule for computing Compound Interest? COMMISSION AND BROKERAGE. § 162. Commission is an allowance made to a factor or commission merchant for buying and selling. Brokerage is an allowance made to dealers in money or stocks. The allowance made is generally a certain per cent, or rate per hundred, on the moneys paid out or received, and the amount may be determined by the rules of simple interest. EXAMPLES.' 1. What is the commission on $4396 at 6 per cent? 2. A factor sells 60 bales of cotton at $425 per bale, and is to receive 2 per cent commission: how much must he pay over to his principal ? Ans. $24862,50. 3. A sent to B, a broker, $3825 to be invested in stock: B is to receive 2 per cent on the amount paid for the stock: what was the value of the stock purchased? 75 PROOF. Commission on $3750, at 2 per cent= 4. A factor receives $708,75, and is directed to purchase iron at $45 per ton: he is to receive 5 per cent on the money paid: how much iron can he purchase? Ans. 15tons. 5. Messrs. P, W and K buy 200 shares of United States stock for Mr. A. They pay $197 per share, and are to receive one-fourth per cent on the money they advance: how much must A pay them for the stock? Ans. $39498,50. 6. Messrs. P, W and K receive $28750 to be invested in stock. They charge 21 per cent commission on the amount paid: what is the value of the stock purchased ? Ans. $28048,78+. 7. The par value or first cost of 167 shares of bank stock was $200 per share: what is the present value, if the stock is at a premium of 25 per cent, that is, 25 per cent above par. Ans. $41750. 8. What would be the value of the stock named in the last example, if it were at a discount of 10 per cent? Ans. $30060. 9. One hundred shares of United States Bank stock is worth 18 per cent premium: the par value being $200 per share, what is the value of the stock? Ans. $23700. 10. A bank fails, and has in circulation bills to the amount of $267581. It can pay 91 per cent: how much money is there on hand? Ans. $25420,194. 11. Sixty-nine shares of bank stock, of which the par value is $125, is at a discount of 8 per cent: what is its value? Ans. $7935. Q. What is commission? What is brokerage? How is the allowance generally made? How is the commission or brokerage found? How do you find the amount of stock to be purchased when the broker receives a certain per cent on the amount purchased, as in Example 3? INSURANCE. § 163. Insurance is an agreement by which an individual or a company agrees to exempt the owners of certain property from loss or hazard. The written agreement is called the policy. The premium is the amount paid by him who owns the property, to those who insure it, as a compensation for their risk. It is generally so much per cent on the value of the property insured. EXAMPLES. 1. What would be the premium for the insurance of a house valued at $5500 against loss by fire for 1 year, at per cent. By dividing by 100, we have the insurance at 1 per cent. The half, is the insurance at half per cent. { 55,00. $27,50. 2. What would be the premium for insuring a ship and cargo, valued at $37500 from New York to Liverpool, at 31 per cent? Ans. $1312,50. 3. What would be the insurance on a ship valued at $47520 at per cent: also at per cent? Ans. $237,60.-$158,40. 4. What would be the insurance on a house valued at $14000 at 11 per cent? Also, at 2 per cent? At per At per cent? At per cent? cent? Ans. $210.-$105.-$70.-$46,66+$35. 5. What is the insurance on a store and goods, valued at $27000, at 21 per cent? At 11 per cent? At per cent? At At per cent? At per cent? At 2 per cent? Q. What is insurance? What is the policy? What is the premium? How is it generally reckoned? DISCOUNT. § 164. If I give my note to Mr. Wilson for $106, payable in one year, the present value of the note will be less than $106 by the interest on its present value for one year: that is, its present value will be $100. note. The amount named in a note is called the face of the Thus $106 is the face of the note to Mr. Wilson. The present value of a note is that sum which being put at interest until the note becomes due would increase to an amount equal to the face of the note. Thus $100 is the present value of the note to Mr. Wilson. The discount is the difference between the face of a note and its present value. Thus, $6 is the discount on the note to Mr. Wilson. RULE. As 100+ interest of $100 for the given time, is to 100, so is the face of the note to its present value. EXAMPLES. 1. What is the present value of a note for $1828,75 due in one year, at 4 per cent per annum ? 100 4,50 interest of $100 for the time. 104,50 100 :: 1828,75: Ans. 100 104,50)182875,00($1750. Ans. $1750. 2. What is the present value of a note for $1290,81 discounted for four months, at 6 per cent per annum ? 5. What is the present value of hence the interest being computed annum? Ans. $1265,50. $800, due 4 years at 5 per cent per Ans. $666,66 6+. NOTE. When payments are to be made at different times, find the present value of the several sums separately and their sum will be the present value of the note. 4. What is the present value of a note for $3500 on which $300 are to be paid in 6 months; $900 in one year; $1300 in eighteen months; and the residue at the expiration of two years: the rate of interest being 6 per cent per annum ? Ans. $3225,83+. 5. What is the discount of £1500 one-half payable in 6 months and the other half at the expiration of a year, at 7 per cent per annum? Ans. £74 8s 63d+. 6. What is the present value of $2880, one-half payable in 3 months, one-third in 6 months, and the rest in 9 months at 6 per cent per annum? Ans. $2810,08+. Q. What is the face of a note? What is the present value of a note? What is the discount of a note? How do you find the present value of a note? When payments are to be made at different times, how do you find the present value? |