Table, SHOWING THE AMOUNT OF $1 FROM 1 TO 20 YEARS, AT 21, 3, 5, 6, AND 7 PER CENT., COMPOUND INTEREST. Years. 2 per cent. 3 per cent. 5 per cent. 6 per cent. 7 per cent. Years. 23 1 1.025000 1.030000 1.050000 1.060000 1.070000 1 2 1.050625 1.060900 1.102500 1.123600 1.144900 3 1.076890 1.092727 1.157625 1.191016 1.225043 4 1.103812 1.125508 1.215506 1.262476 1.310796 4 5 1.131408 1.159274 1.276281 1.338225 1.402552 5 6 1.159693 1.194052 1.340095 1.418519 1.500730 6 7 1.188685 1.229873 1.407100 1.503630 1.605781 7 8 1.218402 1.266770 1.477455 1.593848 1.718186 8 9 1.248862 1.304773 1.551328 1.689478 1.838459 9 10 1.280084 1.343916 1.628894 1.790847 1.967151 10 11 1.312086 1.384233 1.710339 1.898298 2.104852 11 12 1.344888 1.425760 1.795856 2.012196 2.252191 12 13 1.378511 1.468533 1.885649 2.132928 2.409845 13 14 1.412973 1.512589 1.979931 2.260903 2.578534 14 15 1.448298 1.557967 2.078928 2.396558 2.750032 15 16 1.484505 1.604706 2.182874 2.540351 2.952164 16 17 1.521618 1.652847 2.292018 2.692772 3.158815 17 18 1.559658 1.702433 2.406619 2.854339 3.379932 18 19 1.598650 1.753506 2.526950 3.025599 3.616527 19 20 1.638616 1.806111 2.653297 3.207135 3.869685 20 7. What is the compound interest of $400, at 6%, for 20 years and 6 months? - SOLUTION. Amount of $1 for 20 years $3.207135; interest of $1 for 6 months = $.03; $3.207135 X .03 $.09621405 = interest of amount for 6 months; $3.207135 $1$2.207135 compound interest of $1 for 20 years; $2.207135+ $.096214 = $2.303349 = compound interest of $1 for 20 years and 6 months; and $2.303349 X 400 = $921.3396, or $921.33+ = compound interest of $400 for 20 years and 6 months. 8. What is the amount of $100, at a semi-annual compound interest of 21%, for 10 years? Ans. $163.86+. 9. What is the amount of $50, at 7 % compound interest, Ans. $380.61+. for 30 years ? Here, find the amount for 20 years, and then the amount of that sum for 10 years, by aid of the table. REVIEW EXERCISES. 1. If on settlement with a merchant I give my note for $5400 payable in 6 months, with 6 % interest, how much must be paid when the note becomes due? Ans. $5562. 2. A certain sum lent at 6 % produced $250, between July 5, 1865, and December 6, 1866; what was the sum? Ans. $2935.42+. 3. My money at interest doubles itself, I find, in just 14 years; what is the rate per cent.? Ans. 7%.. 4. On the 15th of July, 1866, I paid $65, the interest due on a note of $250, at 6%; from what date did the interest commence? Ans. March 15, 1862. 5. How much more is the bank than the true discount on $800, for 3 years, 4 months, and 18 days? Ans. $27.80+. 6. Having a gold watch to sell, one man offers $220 payable in two years, and another offers me $200 cash in hand; which is the better offer, and how much? Ans. $200 cash in hand, by $3.58+. 7. I have received a note dated April 10, 1866, for $500, payable six months after date; required when it becomes due, the time to run if discounted Aug. 11, and the proceeds at 6%. Ans. Due Oct. 10 | 13; time to run, 63 days; proceeds, $494 75. 8. How much more is the compound than the annual interest of $1300, at 6 %, for 4 years? Ans. $1.13+. REVIEW QUESTIONS. What is the Present Worth of any sum? (302) The Discount? (302) The Rule for finding the present worth? (303) What is a Promissory Note? (306) The Face of a Note? (306) Days of Grace? (306) Bank Discount? (307) Rule for finding bank discount? (308) RATIO AND PROPORTION. 320. Ratio is the measure of the relation of two like quantities. It is determined by dividing the first quantity by the second. Thus, The ratio of 6 to 3 is 2, or of $8 to $2 is 4. 321. The Terms of a ratio are the two quantities compared. The ANTECEDENT is the first term of the ratio. The CONSEQUENT is the second term of the ratio. 322. The relation of antecedent to consequent may be indicated by writing, or the sign of division, between two numbers. Thus, 6 3, or 63, indicate the ratio of 6 to 3. The sign is an abbreviated form of÷, and has a like meaning. Some few American authors determine ratio by dividing the consequent by the antecedent, after the old method of La Croix, which has become quite obsolete in the country where it originated. 323. A Simple Ratio is a single ratio of two terms. Thus, 8: 2 expresses a simple ratio. 324. A Compound Ratio is the product of two or more simple ratios. Thus, (65) × (2 3), or X, expresses a compound ratio. 325. From the definition of ratio, follow the PRINCIPLES. 1. Ratio can only exist between quantities of the same name and kind. 2. The ratio is equal to the quotient of the antecedent divided by the consequent. What is Ratio? Terms of a ratio? The Antecedent? The Consequent ? How may the relation of antecedent to consequent be indicated? What is a Simple Ratio? A Compound Ratio? Give the first Principle. The second. 3. The antecedent is equal to the product of the consequent and ratio. 4. The consequent is equal to the quotient of the antecedent divided by the ratio. Also, since ratio may be expressed by a fraction : 5. The ratio is not changed, if both the antecedent and consequent are multiplied or divided by the same number. Exercises. Write the ratio of 1. 3 to 5. Ans. 3: 5. | 4. 3×2 to 4 X 3. Ans. (3 × 2): (4 × 3). 13. Reduce the ratio 6: 30 to its smallest terms. 14. Reduce to a simple ratio 8 × 3: 6 × 2. Ans. f. 15. Reduce to a simple ratio & × 2: & × 12. Ans. 30 16. Find the ratio of 6 h. 20 m. to 2 h. Ans. 3. 17. If the antecedent is 15.6 and the ratio 6, what is the consequent? Ans. 2.6. 18. If the consequent is and the ratio, what is the antecedent? Ans. . PROPORTION. 326. A Proportion is an equality of ratios. Thus, 8 216 4 is a proportion. The equality is generally indicated by writing :: between the ratios. Thus, 8 2 16 4 indicates a proportion, Give the third Principle. The fourth. The fifth. What is Proportion? How is the equality generally indicated? and may be read, the ratio of 8 2 is equal to the ratio of 16 to 4, or 8 is to 2 as 16 is to 4. 327. The Terms of a proportion are those of its ratios. The EXTREMES are the first and fourth terms. The MEANS are the second and third terms. A PROPORTIONAL is any one of the terms. A MEAN PROPORTIONAL is a term repeated between the other two. Thus, In 12 6 6 3, 6 is a mean proportional. PRINCIPLES. 328. 1. In every proportion the product of the means is equal to the product of the extremes. 6×2 4 X 3 and by For, in the proportion 6: 3 :: 4 : 2, since the ratios are equal (Art. 326), we have § 4. Now, these equal fractions reduced to equivalent fractions having a common denominator, give 8x2 dropping the common denominator, 6 × 2 = 4 X 3. 2. Either extreme is equal to the product of the means divided by the other extreme. Hence, 3. Either mean is equal to the product of the extremes divided by the other mean. 4. The fourth term is equal to the quotient of the third term divided by the ratio of the first to the second. Exercises. Find the missing term in 1. 27: 3 :: 54: (). Ans. 6. 15. ::: 15: ( ). Ans. 12. 2. 12 yd. 4 yd. : $9 Ans.. (). 6. (): 4 Ans. $3. 7. $1.50: $7.50 :: () : 3 bu. Ans. bu. 3. 20 rd. 25 rd. :: (): $10. 4. 5: ( ) :: 16: 32. Ans. $8. 8. 2 gal. 2 qt. :( ) :: $4: $.80. Here, in example 8, the 2 gal. 2 qt. must be reduced to an equivalent single denomination before proceeding to find the missing term. What are the terms of a proportion? The Extremes? The Means? A Proportional? A Mean Proportional? The Principles ? |