flour: 25 barrels at $5}; 50 at $54 ; 90 at $5; 100 at $47; 400 at $5. His store rent was $10 per week; clerk hire, $12 per week; insurance on his flour at the rate of of 1 per cent. per week. What price per barrel will cover all expenses, and afford 10 per cent. profit on the outlay, if sold within the week? Ans. $5'54+. 77. A tax of $2000 is assessed upon a certain town, of which $400 is raised by poll-tax, that is, by a tax raised on the citizens by the head, without regard to property, and the remainder on the inhabitants, in proportion to the amount of their real and personal property. The number of taxable citizens is 800, and the whole amount of taxable property in the town is valued at $400,000. How much is the tax per cent. on the property, and what has a farmer to pay on 2 polls in his family, and property to the amount of $1500 ? Ans. of 1 per cent. and taxes $7. per cent. SHORT PROCESSES FOR THE CALCULATION OF SIMPLE INTEREST. Exemplification for the Black-board. 56 • 2 56.2.6 156•26 6 *100.1 100•1•6 6 Suggestive Questions. What does 56 represent in the second perfect ratio ? What part of the principal do you find in the third perfect ratio ? What does the 2 represent ? the 6 ? By what, then, must the hundredth part of the principal be multiplied to give the interest for any number of years ? Form a rule, then, to find interest for one or more years : Multiply the - part of the · by the and the or by their product. Exercises for the Slate or Black-board. 1. Find the interest of $24 for 6 per cent., by inspection, without any statement. Ans. $7620. years at 5 per cent. 2. Find the interest of $64 for 7 years at 6 per cent., by inspection, without statement. Ans. $26-88. 3. Interest of $345 for 3 years at 5 per cent., by inspection, without statement. Ans. $51.75. II. When the interest is for one or more months. Exemplification for the Black-board. 1. What is the interest of $61 for 8 months at 6 per annum ? 64.8 64.8.6 6 100.12- 1.12.6 Suggestive Questions.—What does the '64 represent in the second perfect ratio ? Ans. The part of the What does the 8 represent ? the 6? Form a rule, then, by which to find interest for months : Multiply the part of the - by a fraction in its lowest terms, of which the product of the and — of — forms the numerator, and 12 the denominator. Exercises for the Slate or Black-board. 1. Find, by inspection, without statement, the interest of $245 for 9 months, at 4 per cent. per annum. Ans. $735. Suggestive Questions.-What is the numerator of the mul. tiplying fraction in this problem ? the denominator ? To what integer is the fraction equal ? 2. Find, by inspection, without statement, the interest of $336 for 8 months, at 6 per cent. Ans. $1344. 3. Find the interest of $27 for 11 months, at 7 per cent. Ans. $1673. 4. Find the interest of £12 10s. 5d. for 7 months, at 6 Ans. £0 8 9+ III. When the interest is for one or more days. Exemplification for the Black-board. 1. What is the interest of $384 for 16 days, at 6 per annum ? 384.16 384.16.6 6 100•360 1. 36.6 Suggestive Questions.- What does 384 represent in the per cent. per cent. second perfect ratio ? the 16 ? the 6 ? the 36 in the denominator ? Why not 360 ? See the principal in the numerator. What is the fraction in its lowest terms by which the thousandth part of the principal is to be multiplied ? Give a rule for finding interest for days. Multiply the part of the - by a fraction in its lowest terms, whose numerator is the product of and the and whose denominator is 36. per cent. per cent. Exercises for the Slate or Black-board. 1. What is the interest of $450 for 18 days, at 5 per cent. ? Ans. $112. 2. Find the interest of $220 for 25 days, at 6 per cent. Ans. $.916. 3. Find the interest of $324-50 for 24 days, at 6 Ans. $1.298. 4. Find the interest of £365 for 16 days at 5 Ans. 16s. 24d. IV. When the Time consists of two Determinate Fractions, or of an Integer and one or two Determinate Fractions. Exemplification for the Black-board. 1. What is the interest of $420 for 2 years, 4 months, and 18 days, at 6 per cent. per annum ? $4:20.12= =5040 Int. for 2 y. by Case I. 4:20:44=2= 8.40 Int. for 4 m. by Case II. 42040=3= 1·26 Int. for 18 d. by Case III. $60.06 Int. for 2 y. 4 m. 18 d. Exercises for the Slate or Black-board. 1. What is the interest of $3475 for 9 months and 12 days, at 6 per cent. per annum ? Ans. $163-325. 2. Find the interest for the same sum and time at 7 per cent. Ans. $190-545. 3. Find the interest for the same sum and time at 5 per cent Ans. $136-104. 4. Find the interest of $0.73 for 1 year and 8 months, at 6 Ans. .073. 5. Find the interest of $7342 for 1 year, 4 months, and 15 days, at 6 per cent. Ans. $605*715. per cent. per cent. Ans. 4 6. Find the amount of a bond for $875.49 for 5 years, 8 months, and 18 days, at 6 per cent.; also at 7 and at 5 per cent. $1176-78 at 6 Ans. $1226-82 at 7 per cent. $1126-74 at 5 per cent. © The three rules that have been developed above may all be comprehended in one, as follows: The interest for any given sum may be found by multiplying its part by a fraction in its lowest terms, whose numerator is the product of the and, and whose denominator is 1 for years, 12 for months, and 360 for days. 1. Find the simplest form of the fraction for multiplying the principal when the time is 8 months and the rate 6 per cent. 2. Find the simplest form when the time is 5 months and the rate 7. 3. When the time is 3 months and the rate 8. 4. When the time is 36 days and the rate 6. 5. When the time is 20 days and the rate 7. 6. When the time is 6 days and the rate 6. D The rate of interest is generally fixed by law in the several States of the Union. As in most of these it is six per cent., it may be well to seek for a still more simple rule for calculating interest for months and days when the rate is uniformly of that amount, as follows: Exemplifications for the Black-board. For Months. 1. Find the interest of $500 at 6 per cent. for 4 months. 500• 4 •6 6 100•12.6 Ans. j. Ans. 4. Ans. . Ans. 78 Ans. iy. Or, cancelling only the principal and the permanent terms of the ratio, 5.00.4.1 6 1.00.2-6 Suggestive Questions.-What is the multiplying fraction in the last formula? What part of the 4 months is ? If the per cent. number of months was 6 what would be the fraction ? Will the fraction, then, for any number of months be always equal to half the number of months ? Give, then, a rule for finding the interest for months at 6 Multiply the -- part of the principal by the number of months. For Days. 2. Find the interest of $568 at 6 per cent. for 24 days. 568. 24 .6 6 100.360.6 per Or, cancelling the principal and the permanent terms of the ratio, 5-68.24.1 6 1.00.60.6 Suggestive Questions. What is the multiplying fraction in the last formula? What part of it would be different if the number of days were altered ? Would the fraction, then, always be or of the number of days ? Give, then, a rule for finding the interest both for months and days, at 6 cent. ? Multiply the — part of the principal by — the time when it consists of months, and by - of the time when it consists of days. Exercises for the Slate or Black-board. 1. Calculate the interest of the following sums, as above, at 6 per cent. per annum. Brought over, $2.271 $100 for 60 days $36 for 2 years 50 for 30 75 for 18 months 25 for 90 32 for 3 27-50 for 75 « 27 for 4 72-75 for 25 89 for 11 Carried over, $2-271 Total, $15.028 2. Find the interest of £300 for 2 years, 8 months and 15 days, at 6 Ans. £48 15s. 3. Find the amount of $221675 for 3 years, 7 months and 6 days, at 6 per cent. Ans. $269•647. per cent. |