WRITTEN PROBLEMS. 5. Mr. C owns 250 shares of bank stock, and receives as his semi-annual dividend $1125: what was the rate? Ans. 41%. 6. A company whose capital is $500000 earns $26500: if they declare a dividend whose rate is expressed by a whole number, what is the rate, and what the surplus? Ans. Rate, 5%; surplus, $1500. 7. Suppose a company with a capital of $2000000 earns $265000, what rate of dividend can it declare if $15000 is placed aside as surplus? Ans. 121%. 8. The earnings of a company whose capital is $400000 are $86500, and the expenses $12500: if a surplus of $12000 be reserved, what dividend can be declared? Ans. 15%. CASE VI. To find the Amount of Stock, the Premium and the Investment being given. ORAL EXERCISE. 1. How much stock can be bought at 10% premium for $880? SOLUTION.-At 10% premium, stock is worth $110 per share; hence, for $880 as many shares can be bought as $110 is contained times in $880, or 8 shares. 2. What amount of stock can be bought at 5% discount for $1900? 3. How many shares of canal stock at 20% discount can be bought for $1640, par yalue being $25 a share? 4. When Reading Railroad stock is 12% above par, how many shares can be purchased for $8400, par value of shares being $50 each? WRITTEN PROBLEMS. 5. When bank stock is at a premium of 43%, how many shares can be purchased for $12570 ? Ans. 120. 6. I invested $13125 in railroad stock at 871⁄2, and sold it at 91: how much stock did I own, and what was my gain? Ans. Stock, $15000; gain, $525. 7. If stock is bought at 31% discount, and sold at a premium of 21%, and the gain is $258.75, what is the par value of the stock? Ans. $4500. 8. If a capitalist buy $9040 worth of stock at 113, and after receiving a 5% dividend sells at 111, how much does he make, and how much stock did he buy? Ans. Made, $320; had $8000 stock. SECTION IX. COMPARISON OF GOLD AND CURRENCY. ORAL EXERCISE. 1. How much currency can be bought for $200 gold when gold is at a premium of 13% ? SOLUTION. When gold is at a premium of 13%, $1 in gold is worth $1.13 in currency, and $200 in gold is worth 200 times $1.13, or $226 in currency. 2. When gold is at a premium of 10%, how much gold may be bought for $132 currency? SOLUTION. When gold is at a premium of 10%, $1 gold is worth $1.10 in currency, and $132 in currency is worth as much gold as $1.10 is contained times in $132, or $120. 3. When gold is at a premium of 15%, how much currency can you buy for $40 in gold? 4. When gold is at a premium of 121%, how much currency can be bought for $120 in gold? 5. How much gold at 12% premium can be bought for $560 currency? 6. How much gold at 8% premium can be bought for $1080 currency? For $648 currency? For $270 currency? WRITTEN PROBLEMS. 7. What is the value in currency of $2740 gold at a premium of 113% ? Ans. $3051.675. 8. What is the currency value of $6500 gold at a premium of 137% ? Ans. $7401.871. 9. Bought goods for $4850, payable in gold: what must be paid in currency when gold is at a premium of 161% ? Ans. $5638.121. 10. When gold is at a premium of 13%, what is the value in gold of a $1 bill? Ans. 885 cents. 11. Paid for a gold watch $220 currency when gold was at a premium of 75%: what was the gold value of the watch? Ans. $125.714. 12. I imported some silks for which I paid in currency $7695 when gold was at a premium of 12%: what was the gold value? Ans. $6840. SECTION X. INTEREST. 222. Interest is a certain percentage paid for the use of money. It is reckoned at a certain rate per cent. for each year. 223. The Principal is the sum on which the interest is paid. 224. The Rate is the percentage paid per annum. 225. The Amount is the sum of the principal and the interest. 226. Legal Interest is the rate of interest fixed by law. When more than the legal rate is charged it is called Usury. When in contracts, etc. no rate of interest is mentioned, the legal rate is always understood. The following are the legal rates in the States named: Delaware, Maryland, New Hampshire, Pennsylvania and the United States courts....... Connecticut, New Jersey, New York.............. Alabama...... Idaho, Montana.. Wyoming....... 6% 7% 8% ...10% ..12% In most of the other States the rate is not definitely fixed, but is variable. In some also any rate can be fixed upon, if stipulated in writing. 227. Simple Interest is that which is reckoned upon the principal alone. 228. Compound Interest is that which is reckoned upon the principal, and also upon the interest as it comes due. SIMPLE INTEREST. 1. GENERAL METHOD. ORAL EXERCISE. 1. What is the interest of $100 for 3 yr. at 6% ? SOLUTION.-At 6%, 15, or 5% of the principal, equals the interest for 1 yr., and for 3 yr. 3 times, or of the principal; of $100 equal $18; hence the interest of $100 for 3 yr. at 6% is $18. 2. What is the interest of $200 for 1 yr. at 5% ? 3. What is the interest of $600 for 3 yr. at 7% ? 4. What is the interest of $450 for 2 yr. at 5% ? 5. What is the interest of $320 for 2 yr. at 6% ? SOLUTION.-If the interest for 1 yr. is 6% of the principal, for 2 yr. it is 2 times 6%, or 12% of the principal; and 12% of $320 is $38.40. 6. What is the interest of $90 for 8 yr. at 5% ? 7. What is the interest of $66 for 10 yr. at 6% ? 8. What is the interest of $350 for 7 yr. at 6% ? 9. What is the interest of $24 for 2 yr. at 16% ? 10. What is the interest of $240 for 3 yr. at 15%? 11. What is the interest of $120 for 6 yr. at 7% ? 12. What is the interest of $250 for 6 yr. 6 mo. at 6%? SOLUTION.-6 yr. 6 mo. equal 61 yr. If the interest for 1 yr. is 6%, for 61 yr. it is 6 times 6%, or 39%; 39% of $250 is $97.50. 13. What is the interest of $120 for 3 yr. 8 mo. at 6%? 14. What is the interest of $360 for 6 yr. 3 mo. at 8%? 15. What is the interest of $500 for 7 yr. 2 mo. at 6%? 16. What is the interest of $600 for 3 yr. 7 mo. at 5%? 17. What is the interest of $12 for 2 yr. 9 mo. at 10%? 18. What is the interest of $750 for 3 yr. 5 mo. at 7% ? 19. What is the interest of $150 for 2 yr. 3mo. 18d., at 5% ? SOLUTION.-18 d. equal 18, or 3 of a month; hence, 3 mo. and 18 d. equal 33, or 18 mo. of a month equals of of a year, which is of a year, and 18 mo. equals 18 of 12, or 18, or 1% of a year; hence, 2 yr. 3 mo. 18 d. equals 21% yr. If the interest is 5% for 1 yr., for 2 yr. it is 2 times 5%, or 111%; 11% of $150 is $17.25. 20. What is the interest of $300 for 6 yr. 2 mo. 12 d., at 6% ? 21. What is the interest of $270 for 3 yr. 7 mo. 6 d., at 5% ? 22. What is the interest of $300 for 3 yr. 24 d., at 15% ? 23. What is the interest of $600 for 1 yr. 6 mo. 20 d., at 9% ? 24. What is the interest of $250 for 1 yr. 1 mo. 6 d., at 10% ? WRITTEN PROBLEMS. 1. What is the interest of $620 for 6 yr. 3 mo., at 6% ? Ans. $232.50. SOLUTION. $620 .06 37.20 64-6 yr. 3 mo. 223.20 9.30 Analysis.-6% of $620 is $37.20, the interest for 1 yr., and for 6 yr. 3mo., or 6 yr., the interest is 6 times $37.20, or $232.50. 232.50 RULE. To find the simple interest, multiply the principal by the rate expressed decimally, and this result by the number of years. 2. What is the interest of $225 for 6 yr. 8 mo., at 6% ? Ans. $90. 3. What is the interest of $75 for 3 yr. 4 mo., at 5% ? Ans. $12.50. 4. What is the interest of $630 for 6 yr. 4 mo., at 7% ? Ans. $279.30. 5. What is the amount of $315 for 3 yr. 7 mo., at 8% ? Ans. $405.30. NOTE. To find the amount, add the principal to the interest. 6. What is the interest of $625 for 2 yr. 3 mo. 12 d., at 6% ? Ans. $85.621. |