139. A school-house was insured for $15500 at 23%, $1.50 being paid for the policy and survey. What was the entire expense for insurance? 140. If the school-house named above was lost by fire, what was the net loss to the insurance company? 141. Suppose I buy 20 shares of stock originally worth $50 a share, at 10% discount, and sell at a premium of 8%, what do I make ? 142. A merchant sold some iron for $278, and made 15%. What should he have sold it for to make 25%? 143. When 75 shares of stock originally worth $100 a share sell for $7556.25, at what per cent above par does it sell? 144. If a company takes an accident risk of $ 8000 at 11%, and reinsures one half of it in another company at 11%, what will the first company gain if no accident occurs. 145. After losing 11% of his apples, a dealer has 133.5 bbls of apples left; if they cost him $2.50 per bbl., for what must they be sold per bbl. that he may lose nothing upon his purchase? 146. A broker bought insurance stock at 80, and sold it at 112. What per cent did he make upon his investment? 147. A broker sold 19 shares of stock for $1389.85, which was at 41% above par. What was the brokerage at 4% on the par value? 148. A factory is insured at the rate of $ 2 on $100. If the premium, with $1 for the policy, is $241, and the insurance is upon of the value of the property, what is the value of the property? 149. When an insurance stock, originally $100 per share, is quoted at 1023, how many shares can be bought for $ 8815, brokerage %? 150. If a watch sells for $ 60 at a loss of 22%, what should it have sold for to gain 30%? 151. The capital of a gas company is $ 200000, and the net earnings are $10746. What rate of dividend can the com pany declare, reserving a surplus of $2746 to meet future demands? 152. A vessel brought into port 12000 melons. 8% proved worthless, 10% of the remainder sold for 18 apiece, and the rest for 12 apiece. What was received for the whole? 153. At the sale of a piano, 20% was deducted from the retail price, and 5% of the balance for cash payment. If the retail price was $ 750, and the wholesale price $475, for what per cent advance upon the wholesale price was it then sold? 154. A regiment of 1000 men was reduced to 850 by sickness and battle, the loss by sickness being 50% as great as by battle. What was the entire per cent of loss? what by sick ness? by battle ? 155. I sold 250 lbs. of fish, gaining thereby $3.75, which was 42% of the cost. What was the cost? For how much pound was the fish sold? 156. A grain dealer's sales amounted in one year to $75000; of his receipts were for wheat, on which he made 10% profit, and the balance for other grains, on which he made 20% profit. What was the cost of the whole stock? 157. A broker bought stock at 8% premium, and sold it at 9% discount, and lost $510. How many shares originally worth $100 each did he buy? 158. Two horses were sold for $144 each; on one there was a gain of 20%, and on the other a loss of 20%. How much was the gain or loss on both? 159. What is the cost of 5 hhds. of molasses containing in all 2074 gallons, which was bought in Porto Rico at 429 a gallon, and on which is paid $45.75 for freight and carting, and 5 a gallon for duty, after deducting 12% for leakage? 160. A certain corporation wishing to increase its stock without multiplying the number of its shares, assessed the stockholders 40% on the par value of their stock, which was $500 per share. What was the par value of the stock after the assessment was made? SECTION XV. SIMPLE INTEREST. 526. A had the use of $300 of B's money for a year. At the end of the year he paid B for its use a sum equal to 7% of the money borrowed. What did he pay for its use? Ans. $21.00. 527. Money paid for the use of money is interest. 528. The money for the use of which interest is paid is the principal. 529. The sum of the principal and interest is the amount. In the above example, what is the interest? the principal? the amount? 530. Interest is reckoned at a certain per cent of the principal. It is, therefore, a percentage of which the bas is the principal. 531. The number of hundredths of the principal taken in finding the interest for one year is the rate per cent per annum, usually called the rate. NOTE. When a rate of interest is given, it is understood to be the rate per year, unless a different time is stated. 532. The rate of interest established by law is the legal rate. Interest at a rate higher than the legal rate is usury. NOTE. Debts of all kinds draw interest from the time they become due, but not before, unless it is so specified. Interest on interest unpaid when due is sometimes, though not usually, allowed. 533. Interest on the principal alone is simple interest. NOTE. The laws regulating rates of interest are frequently changed, but the following is a table compiled from official sources in 1877. 534. Table of Legal Rates of Interest, 1886. When two rates are given in this table, any rate not exceeding the highest is allowed, if agreed upon in writing. NOTE I. In this book, when no rate is mentioned or implied, 6% is understood. NOTE II. In reckoning interest, it is customary to consider a year to be 12 months, and a month 30 days. 535. In reckoning the months and days between two dates, take the entire calendar months as months, and then the exact number of days remaining. (See Art. 371.) NOTE. In computing interest for short periods of time, it is customary to take the exact number of days. 536. Oral Exercises. What is the interest a. Of $100 for 1 year at 7%? for 2 years at 3%? b. Of $300 for 2 years at 6%? at 8%? at 11%? at 12%? c. Of $400 for 3 years at 4%? at 10%? at 7%? at 8%? d. Of $40 for 3 years at 10%? at 5%? at 7%? at 6%? e. What part of a year's interest is the interest on any sum of money for 6 mo.? 2 mo.? 3 mo.? 4 mo.? 1 mo. ? f. At 5%, what is the interest of $ 600 for 1 year? for 6 mo. ? ? 4 mo.? 2 mo. ? 3 mo. g. At 9%, what is the interest of $100 for 1 year? for 1 mo. or 30 days? for 6 days? for 1 day? for 5 days? h. What is the amount of $100 for 4 years 6 months at 8%? i. What is the amount of $100 for 1 year 4 months at 5%? j. What is the amount of $200 for 3 years 3 months at 10%? METHODS OF COMPUTING INTEREST. 211 METHODS OF COMPUTING INTEREST. TO THE TEACHER. Two methods of computing interest are given in the following pages; but the teacher is advised to have pupils use but one. The method by aliquot parts will be found on page 308 of the Appendix. GENERAL METHOD. 537. ILLUSTRATIVE EXAMPLE. Find the interest of $840 for 4 y. 3 mo. 5 d. at 8%. WRITTEN WORK. $840 × 0.08 × 4 = $268.80 7 17.73 $840 × 0.08 × 95 360 3 Ans. $286.53 Explanation. The interest of $840 for 1 year at 8% is $840 × 0.08. The interest for 4 years is 4 times as much, or $268.80. 3 mo. 5 d. equal 95 days. The interest of $840 for 1 year being $840 × 0.08, the interest for 1 day is of this (Art. 534, Note II.), and for 95 days it is 95 times as much, or $17.73, which, added to $268.80, makes $286.53, the entire interest. 538. From the example above may be derived the following Rule. any 1. To find the interest at any per cent for number of years: Multiply the principal by the rate for 1 year, and that product by the number of years. 2. To find the interest for months and days: Change the months to days (Art. 535) and take as many 360ths of a year's interest as there are days in the given time. 539. This rule may be expressed by the formula: Interest = Principal Rate × Number of years. 540. Examples for the Slate. 1. What is the interest of $ 720 for 3 y. 7 mo. 6 d. at 8% ? 2. Of $472.30 for 2 y. 2 mo. 12 d. at 4% ? |