(3.) If $590 is due Sept. 11, the credit from the focal date is 39 days: hence the credit is equal to the credit of $1 for (39 da. × 590) 23010 days. (4.) If $100 is payable 9 mos. from Dec. 25, 1876, it becomes duc Sept. 25, 1877, and the term of credit from the focal date is 419 days: hence the credit is equal to the credit of $1 for (419 da. × 100) 41900 days. (5.) The credit of the sum of the payments, $1565, is equal to the credit of $1 for the sum of the credits of $1, or 105410 days. (6.) If the credit of $1 requires 105410 days to be worth a certain sum, then for the credit of $1565 to equal the same sum will require 13% of 105410 da., or 67 days, the average term of credit. (7.) The focal date, Aug. 3, 1876 +67 days=Oct. 9, 1876, the equated time of payment, from which time the $1565 should be at interest until paid. RULE.-I. Find the time at which each item becomes due. II. Assume the earliest date as the focal date, and find the term of credit from the focal date to the date when each item becomes due. III. Find the equated time of the several terms of credit, by the rule under ¶83. WRITTEN EXERCISES. 54. What is the equated time for the payment of the following account? 55. What is the equated time for the payment of the following bill? 1876. Jan. 10, To 214 yds. carpet @ $1.50 at 3 mos. Feb. 21, "450 yds. oil-cloth @ 80 cts. at 6 mos. Mar. 14, "10 doz. cane-seat chairs @ $20 at 4 mos. Apr. 1, "15 bedroom suits @ $25 at 3 mos. 56. Stuart and Co. sell to A. L. Williams the following bill of goods: Mar. 1, 1874, $450 at 4 mos.; June 4, $250 at 6 mos.; Aug. 13, $415 at 3 mos. What is the equated time of payment? 57. Loaned to A. B. Perkins, Mar. 5, $900; June 6, $450; Oct. 12, $375. What is the equated time at which the whole should have been paid? 58. A dealer sold me, March 15, $1600 worth of goods, to be paid for as follows: in cash, in 3 months, and the remainder in 6 months. When in equity should the whole be paid for in one payment? REVIEW.- What is the base of percentage in stocks? (17.) How are all premiums, discounts, brokerages, dividends, and assessments computed? What is insurance ?(18.) What is fire insurance? Marine insurance? What is a policy? (19.) An insurer or underwriter? (20.) What is a mutual insurance company? Who is the policy-holder? What is the premium? How is it estimated? Upon how much of the value of the insured property is insurance generally taken? Give the equivalent of the amount insured. Of the premium. Of the rate per cent. What is life-insurance? (21.) What is a life policy? An endowment policy? A continued premium life policy? A ten, five, or single payment policy? How is the premium computed? 59. I gave a note for $1400, to be paid in 12 mos., but in 6 months I paid $400, and in 3 mos. thereafter $400 more. When in equity should I pay the balance? = ANALYSIS.-(1.) If I pay $400 6 mos. before it is due, I am entitled to a credit of $1 for (6 mos. X 400) 2400 mos.; and, if I pay $400 3 mos. before it is due, I am entitled to an additional credit of $1 for (3 mos. X 400) 1200 mos., or in all 3600 mos. (2.) A credit of $1 for 3600 mos. is equal to a credit of $600 for ēdo 12 mos. +6 mos. 18 mos. Ans. of 3600 mos, or 6 mos., making the balance due 6 mos. after the original 12 mos., or 18 mos. from date. 60. A man borrowed $3600, to be paid in 9 months. At the end of 2 mos. he paid $600, at the end of 4 mos. thereafter he paid $800, and at the end of the 8th month he paid $1000. For how long after the expiration of the 9 mos. should he have credit on the balance? 61. On a note given July 5, 1875, for $930, payable in 12 mos., there was paid Aug. 5, $200; Oct. 5, $200; Dec. 5, $230. What is the equated time for paying the balance? REVIEW. What is a mutual life-assurance company? (22.) What is a tax? (23.) What is a direct tax? An indirect tax? A poll-tax? What is real estate? P'ersonal property? What is an assessor? A collector? What is the tax-rate? (24.) What are customs, or duties? (25.) What is tonnage? A custom-house? A port of entry? A collector of the port? A tariff? A clearance? A manifest? What is a specific duty? (26.) An ad valorem duty? (27.) What is draft? Tare? Leakage? Breakage? Gross weight? Net weight? What is interest? (28.) What is the principal? (29.) The rate per cent? (30.) The amount? (31.) * The pupil should remember that 1876 was a leap year. RATIO. 85. Ratio is the relation which one number bears to another of the same kind, and is found by dividing the given number by the one with which it is compared. Thus the ratio of 12 to 6 = 2; the ratio of 5 to 10==}. 86. The Terms of a Ratio are the numbers compared; and when taken together they are called a couplet. 87. The Antecedent is the first term of the couplet, and is the dividend or numerator of the fraction expressing the value of the ratio. 88. The Consequent is the second term of the couplet, and is the divisor or denominator of the fraction expressing the value of the ratio. Some teachers prefer the French method of expressing the ratio, in which the antecedent is the measure or divisor of the consequent, and make the ratio of 8 to 12 = 12 or . Either treatment will produce the same result in all questions involving the use of the ratio. 89. The Sign of ratio is a colon (:) or the ratio may be written as a fraction: thus, the ratio of 7 to 9 may be expressed either as 7:9, or 3. 90. Simple Ratio is a comparison of two numbers. 91. Compound Ratio is a comparison of the products of the corresponding terms of two ratios. 92. The Value of the Ratio is the quotient of the antecedent divided by the consequent. The numbers compared may be concrete numbers, but the ratio is always an abstract number. Thus in the ratio, 14 tons to 7 tons, 14 tons is the antecedent, and 7 tons the consequent, and 2 the ratio. 93. Since the value of the ratio is a fraction, it follows that its terms may be treated like those of a fraction: hence the following principles: 1. Multiplying the antecedent multiplies the ratio. 4. Dividing the consequent multiplies the ratio. 5. Multiplying or dividing both antecedent and consequent by the same number does not affect the ratio. 6. The product of two or more simple ratios is the ratio of their products: as, 3:4, and 5:6=5; then (5:6) × (3 : 4) = 15 : 24 = § = { × }• ORAL EXERCISES. 1. What is the ratio of 4 to 7? of 6 to 12? of 8 to 14? of 25 to 100? of 100 to 25? 2. What is the ratio of 6 to 18? of 18 to 6? of 7 to 7? of 25 to 6? 3. What is the ratio of $3 to $30? of 4 gal.: 12 gal.? Of 9 lbs.: 27 lbs.? 4. What is the ratio of 7 to 15? of 12:15? of 8 yds.: 12 yds.? 5. What part of 7 is 2? of 9 is 5? of $8 is $3? of 11 is 2? 6. Two is what part of 5? 6 is what part of 11? 27 is what part of 50? |