WRITTEN EXERCISES. 2. My tax is $37.80 at the rate of 4 mills on the dollar; required the property. Ans. $8400. 3. A's entire tax is $310.75; he pays for 3 polls at $2.25 each; the rate is 8 mills on the dollar; what is his property? Ans. $38000. 4. I have $12000 on interest, and my tax for money on interest is $33.07, at 24 mills on the dollar; for how much money at interest am I overtaxed? Ans. $2700. 5. A bridge was built by a certain town at a cost of $7580, which was raised by a tax on the property-holders of 31 mills on the dollar; the collector's commission was 24%; what was the valuation of the property? Ans. $2215564.49. NOTE. The collector's commission is included in the tax. 6. Mr. Mills paid one year .45% township tax, .3% county tax, .48% school tax, and 4 polls @ $1.25; his whole tax was $319.88; what was the value of his property? Ans. $24600. CASE III. 461. Given, the assessed value and the tax, to find the rate. 1. A tax of $6387.50 is to be assessed in a town; the real estate is valued at $345000, and the personal property at $477500; there are 420 polls, taxed @ $1.50; what is the rate of taxation ? SOLUTION. The entire poll tax is $1.50 multiplied by 420, which is $630; subtracting this from the whole tax, we have remaining $5757.50, the property tax; dividing $5757.50 by $822500, the amount of property, we have 7 mills, the tax on $1. OPERATION. $1.50x420-$630 $6387.50-$630=$5757.50 $5757.50$822500=.007 Rule. Divide the property tax by the amount of taxable property, the quotient will be the rate of taxation. NOTE. If there is a poll tax, subtract it from the whole tax before dividing. WRITTEN EXERCISES. 2. A's property is valued at $7580, his tax is $35: required the rate of taxation. Ans. .0046+. 3. A tax of $17250 is to be assessed on a town; the real estate is valued at $850000 and the personal property at $250000; there are 500 polls, each of which is taxed $1.50; what is the rate of taxation? Ans. $.015. 4. A market-house costing $7650, was built in a certain town, in which the taxable property was estimated at $804796, the collector's commission being 21%; what was the rate of taxation? Ans. .0097+. 5. In a certain school the expenses are as follows: salary of teacher, $500; fuel, $42.75; apparatus, $32.50. The school fund amounted to $125.25, and the rest of the expenses was paid by a rate bill; if the entire attendance was 7280 days, what was C's bill, who sent 4 pupils 90 days each? Ans. $22.25. MENTAL EXERCISES. MISCELLANEOUS PROBLEMS. 1. How much currency will $50 in gold buy, when gold is at a premium of 8%? 2. How much gold can be bought for $220 in currency, when gold is at a premium of 10%? 3. If I take 10% off and then another 10% off, what is the rate off? 4. What is the actual rate off, when I take 20% off and then another 20% off? 5. What is the difference between 10% off and 5 and 5% off? between 15% off and 10 and 5% off? 6. What is the difference between 20% off and two 10%'s off? between 10% on and 5 and 5% on? 7. How much is 10 and 10% on? 20 and 10% on? 20 and 5% on? 20 and 20% off? 20 and 20% on? 8. What is the difference between 15% on, and 10 and 5% on? between three 10%'s on, and three 10%'s off? 9. If an article is sold so as to gain on the cost, what is the gain per cent.? 10. I paid an agent $200 for selling a house for me, what did I receive for it, the rate of commission being 14% ? 11. What cost 5 shares of bank stock at 102, brokerage %? 12. Required the cost of 4000 U. S. 44's, at 1084, brokerage %. 13. A boy bought oranges at $3 a hundred, and sold them for 5 cents apiece; what per cent. did he gain? 14. A milliner sold some old-fashioned hats at $3.60, which was 25% below marked price; at what price were they marked? 15. A lady bought some canal stock at 80, and sold it at par, gaining $500; how many shares at $50 each? 16. I bought R. R. stock at 87, and sold at 1024, and gained $3000; how many shares at $100 each? 17. What sum must I invest in stock at 106, paying 8% yearly dividends, to realize an income of $1200? 18. What per cent. does stock, paying 6% dividends, yield, when bought at 90? 8% stocks at 120? 19. How much must pay for stock that pays 6% dividends, in order to realize 8% on my investment? 20. I bought Phila. 6's at a rate by which I realized 5%; what did I pay for them? 21. What will be the annual premium of insurance, at 1%, on goods valued at $2000? 22. I paid $8 for insuring $400; what was the rate? Paid $16 for insuring $1000; what was the rate? REVIEW PROBLEMS. 1. The list price of a lot of ginghams is 20 a yard; if I buy them at 20% off and sell at 25% on, what is my gain per yard? Ans. 94. 2. Bought French merinos at $1.15 a yard, and marked them cln, my key being. "Charleston;" what was my gain % if I sell the goods at the marked price? Ans. 3019%. 3. Mr. Behmer bought mining stock ($50) at 9% premium, and sold it at a loss of $5 on a share; at what rate was it sold? Ans. 1% disc. 4. An agent sold 150 barrels of flour, charging 2% commission, and 24% guaranty; the net proceeds due the consignor were $1143; for how much was the flour sold per barrel ? Ans. $8. 5. I exchanged $5000 U. S. 6's at 108 for 30 shares of stock of Bank of North America ($100); what did I pay for the latter? Ans. 180%. 6. Mr. Albert received in April a stock dividend of 10 shares in a mining company and another of 21 shares in November; he then owned 231 shares; what were the rates of dividend? Ans. 5% and 10%. с SIMPLE INTEREST. 462. Interest is a percentage on a sum of money for its use a certain time. 463. The Principal is the sum on which the interest is computed. 464. The Rate of interest is the rate per cent. on $1 for a certain time. The usual time is one year. 465. The Time is the period during which the money is on interest. 466. The Amount is the sum of the principal and inter est. 467. Simple Interest is the interest on the principal only. Compound Interest is the interest on both the principal and interest. 468. Legal Interest is interest at the rate fixed by law. The rate varies in different states, as follows: 469. Usury is a rate of interest greater than the law allows. Various penalties are attached to the taking of usury in different States. The legal rate in England and France is 5%; and in Ireland, Canada, and Nova Scotia is 6%. In notes, contracts, accounts, mortgages, etc., when no rate is specified, the legal rate is understood. Notes draw interest after they become due, though interest is not mentioned in them; and interest is reckoned on book accounts after the expiration of the term of credit. 470. The Quantities are five: 1. The Principal; 2. The Interest; 3. The Rate; 4. The Time; 5. The Amount. NOTE.-In Computing interest it is customary to reckon a month as of a year, and a day as 3 of a month. In dealing with the U. S. Government, each day is of a year. CASE I. 471. Given, the principal, the rate per cent., and the time, to find the interest or the amount, MENTAL EXERCISES. 1. What is the interest of $80 for 2 yr. 6 mo. at 6%? SOLUTION.-6 months equal or of a year, which with 2 yr. equals 21, or years. At 6 per cent. for 1 yr., 18 of the principal equals the interest, and for 2 or 3 yr., times 180 or 15 or 23 of the principal equals the interest, 2% of $80 equals $12. What is the interest of 2. $60 for 6 yr. at 5%? 3. $40 for 4 yr. at 5%? 4. $30 for 5 yr. at 4%? 5. $600 for 2 yr. 3 mo. at 8%? 6. $300 for 4 yr. 6 mo. at 6%? 7. $240 for 3 yr. 9 mo. at 8%? 8. $330 for 7 yr. 6 mo. at 1%? 10. What is the interest of $300 for 5 yr. 3 mo. 18 da. at 10%? 11. What is the interest of $500 for 2 yr. 2 mo. 12 da. at 5%? 12. What is the amount of $50 for 2 yr. 8 mo. at 6 per cent.? REMARK.-We find that or of the principal equals the interest, of the principal equals the amount; } of $50-$58. hence 13. What is the amount of $600 for 7 yr. 6 mo. at 6 per cent.? 14. What is the amount of $300 for 8 yr. 10 mo. at 6 per cent? COMMON METHOD. 1. What is the interest of $2400 for 6 yr. 7 mo. 15 da., at 7%? SOLUTION.-By reduction, we find that 6 yr. 7 mo. 15 da. equals 6 yr. At 7%, .07 times $2400 equals the interest for 1 year, which is $168; if the interest for 1 year is $168, for 63 yr. it is 63 times $168, which by multiplying we find is $1113. Hence the following Rule.-I. Multiply the principal by the rate, and that product by the time expressed in years, to find the interest II. Add the interest to the principal to find the amount. |