159. In what time will a sum of money double itself, simple interest at 5%? 6%? 8% ? and 10% respectively? Ans. 20, 163, 124 and 10 years. 160. What is the rate of interest when $120 is paid for the use of $600 for 3 years and 4 months simple interest ? Ans. 6% 161. What principal at 6% simple interest will amount to $6900 in 2 years and 6 months ? Ans. $6000. 162. In what time will a sum of money treble itself at 5%? 6%? 8%? 10%, simple interest ? Ans. 40, 331, 25, 20 years. 163. A steamboat whose rate is 12 miles an hour sails up a river whose current is 4 miles an hour, returning in 15 hours; how far up the river did the boat go ? Ans. 80 miles. 164. A and B engaged a piece of work. A can do it in 8 days, and 3 in 12 days; how long will it take them both to do it? Ans. 44 days. 165. A can do a piece of work in 1 day, B in f and o in 4 day; how long will it take them all working together to do it ? Ans. } day. 166. A tank has two pipes for supply and one for discharge; the first alone will fill it in 9 hours and the second in 12 hours, and the third will discharge it in 8 hours ; in what time will the tank be filled with all the pipes in operation ? Ans. 14 hours. 167. A boy driving geese to market, sold to his first customer one-half of what he had and one-half a goose more : to the second and third customer he sold in like manner, without killing a goose, when he had none left ; how many had he at first ? Ans. 7 geese. 168. What is the cost of excavating a ditch 1 mile long, 6 feet wide, and 3 feet deep, at 40 cents per cubic yard ? Ans. $1408. 169. A rectangular lot of land is 80 rods in length 40 rods in width; how many acres does it contain ? Ans. 20 acres. 170. A triangular lot has one side 40 rods long, and a perpendicular line from the opposite corner of the lot to this side 16 rods; how much land does it contain ? Ans. 2 acres. 171. A house valued at $15000, and furniture $3000, is insured for f of its value at 11%; what is the premium? Ans. $180. 172. What per cent on the value of a house, is a premium of $24 on $960, which is the value of the house? Ans. 15%. 173. The principal is $900, the time 2 yr. 4 mo. 20 da., and the interest $150.50; what is the per cent ? Ans. 7%. 174. The principal is $1350, the interest $225.75, the rate 7%; what is the time ? Ans. 2 yr. 4 mo. 20 da. 175. Paid $850 in currency for gold at 61% premium ; how much gold was received ? Ans. $800. 176. Goods sold at 10% gain for $3300; what would have been the gain per cent if sold for $3600 ? Ans. 20%177. At what rate must I buy 7% bonds, in order to realize 10% on the investment? Ans. 70% 178. In a sale of damaged goods for $1200, the loss was $300; what was the rate per cent? Ans. 20%. Yr9 . Bought a farm for $12000, on condition that 15% is to be paid in cash, 23% in 6 months, 17% in 12 months, 30% in 18 months, and the balance in two years; how much was the last payment? Ans. $1800. 180. Sold goods for $2500, which was $300 more than cost; what was the gain per cent ? Ans. 131% y 181. What per cent of 35 is 3 ? Ans. 84%. 182. What per cent of 3 is 35 ? Ans. 11663%. 183. What is the amount of a 6% note for $1040, with interest from April 1st, 1875, to August 21st, 1878? Ans. $1251.463. 184. BALTIMORE, MD., Jan. 1st, 1876. - Three months after date, I promise to pay to John Smith or order, Five hundred dollars, for value received. JOHN JONES. What was due on this note April 16th, 1877? Ans. $531.25. 185. BALTIMORE, MD., Jan. 1st, 1876. Three months after date, I promise to pay Peter Post or order, One thousand dollars, for value received, with interest ; how much interest is due on this note July 21st, 1877? Ans. $933. -186. What is the value of a note for $1200, due 2 yr. 6 mo. previous to this date, at 6%, simple interest ? Compound interest payable annually and also semi-annually ? Ans. At simple interest, $1380 ; compound interest, annually, $1388.77; compound interest, semi-annually, $1391.13. 187. Date of note April 1st, 1872, for $1000, at 6%, payments July 16th, 1873, $200; April 1st, 1875, $300; April 16th, 1876, $400. What is due July 1st, 1877? Ans. $331.57. 188. A note for $1000, dated April 1st, 1872, due in 3 years, with interest at 6%, payable annually, is endorsed as follows: Oct. 1st, 1873, $300 ; Jan. 1st, 1874, $200; what is due April 1st, 1875 ? Ans. $648.296. 189. A note for $500, dated April 1st, 1875, due m 3 years, with interest at 6%, payable annually, is endorsed : April 1st, 1876, $130 ; Oct. 1st, 1876, $100; Oct. 16th, 1877, $100. Jan. 1st, 1878, the note is discounted in bank, without grace, at 8%; what sum is received from the bank ? Ans. $232.76. NOTE.- In the last two examples, as the interest is only due at the end of the year, the payments made during the year should bear interest until the settlement at the end of the year, and this method is called the Merchants' Rule, which is decidedly the most just method. 190. What is the difference of the amounts of $2000 at 6% for 12 years at simple, and at compound interest ? Ans. $584.394. 7191. 191. What is the amount of $2000 at 6% simple interest for 20 years, also at compound interest ? Ans. Amount at simple interest, $4400; at compound interest, $6414.272. 192. What is the compound amount of $1000 for 20 years 3 months ? Ans. $3255.243. NOTE.—When there are months or days, in compound interest, take from the table for the years and on this compound for the months or days, as you would from the table ; for 6 months multiply 1.03, when at 6%, and accordingly other times and rates. ᅥ 193. The length of a rectangle is 128 feet and its breadth 96 feet; what is the length of its diagonal ? Ans. 160 feet. 194. The length of a rectangle is 2 feet and its diagonal 90 feet; what is its width ? Ans. 54 feet. 195. A merchant of St. Louis has a debt of $6000 to pay in New York. Direct exchange is 13% premium on New York, but on New Orleans funds there is a discount of 3%, and at New Orleans the premium on New York is 1%; what advantage is the circuitous route? Ans. $75.221 gained by the circuit. 196. A house valued at $12500, is insured for its value at 5%; for what sum is the policy drawn so as to include the premium? Ans. $105268. 197. If I purchase a city bond at 90% which bears 8% interest, what per cent do I get on my investment? Ans. 88% 198. A merchant being asked at what per cent profit he sold his goods, replied šof my selling price is 25% less than cost ; at what per cent profit did he sell, goods ? Ans. 12% aprofit. 199. In the ruins of Persepolis are two columns standing upright; the one is 70 feet above the plane and the other 50 feet; in a straight line between these columns is a small statue 5 feet high, the head of which is 100 feet from the top of the higher and 80 feet from the top of the lower column. What is the distance between the tops of the columns ? Ans. 143.54. 200. What is the rate per cent, when the amount is the principal that had been at interest 3 years ? Ans. 83% 7 |