§ 138. The following general rule will be found applicable in casting interest on any sum of money, and for any period of time. It must, however, be remembered that this rule is restricted to interest at 6 per cent. per annum. RULE. Find the per centage of $1, for the given time, as in the preceding section. (§ 137.) Multiply the given money by this per centage written as a decimal, and point off decimals in the product, the same as in multiplication of decimals. (§ 88.) 1. What is the interest of $327.86, for 1 year and 6 months, at 6 per cent. per annum? EXPLANATION. 1 year and 6 months 18 months, and 1829, the required per cent. Therefore, $327.86 $29.5074=$29.507+, Ans. 9 per cent. is 9 hundredths, and properly expressed, .09. (§ 85.) 2. What is the interest of $256.81, for 2 years, 3 months, and 12 days, at 6 per cent. per annum? 2 years and 3 months-27 months=13 cents and 5 mills, or .135, the per centage for 2 years and 3 months; and 12 days÷6.002, the per centage for 12 days; and .135+ .002.137, is the per centage for the whole time. Therefore, 2 5 6.8 1 179767 25681 3 5.1 8 297. Hence, $35.18+, is the interest required. 3. Required the interest of $196.18, for 1 year, 10 months, and 18 days, at 6 per cent. Ans. $22.168. 138. What is the rule for casting interest? 4. Required the interest of $3786.97, for 2 years, 7 months, and 21 days, at 6 per cent. Ans. $600.234+. 5. Required the interest of $821.25, for 4 years, 6 months, and 24 days, at 6 per cent. Ans. $225.022+. 6. Required the interest of $87.90, for 3 years, 11 months, and 8 days, at 6 per cent. Ans. $20.773+. § 139. Whenever interest at any other than 6 per cent. is required, first find the interest at 6 per cent. as above, then divide the interest so found by 6, and multiply the quotient by the required per cent. The reason for this is obvious. Dividing the interest of any sum of money at 6 per cent. by 6, gives 1 per cent on the same money, and this multiplied by the given per cent. gives the interest required. 7. What is the interest of $358.50, at 8 per cent., for 2 years, 3 months, and 12 days? EXPLANATION. $358.50X.137=$49.114+=interest at 6 per cent; and $49.114÷6=$8.185+=interest at 1 per cent.; and $8.185×8=$65.480, Ans. 8. What is the interest of $150.67, for 2 years, 6 months, and 15 days, at 7 per cent.? Ans. $26.806+. 9. What is the interest of $280.75, for 3 years, 1 month, and 27 days, at 9 per cent.? Ans. $79.803+. 10. What is the interest of $456.12, for 1 year, 8 months, and 19 days, at 5 per cent.? Ans. $39.21+. § 140. When the interest of any sum of money, for a specified time, is ascertained, the amount due is found by adding the interest to the principal. 11. What is the amount of $382.16, for 5 years, 6 months, and 18 days, at 6 per cent.? The interest on the above sum, for the time and rate specified, is $127.259; and $127.259, interest+$382.16, principal $509.419, amount. 12. What is the amount of $636,93, for 2 years, 7 months, and 28 days, at 6 per cent? Ans. $738.626+. 139. How proceed when the interest is some other than 6 per cent? What is the reason for it? 140. How is the amount found? 13. What is the amount of $57.34, for 1 year, 4 months, and 27 days, at 6 per cent.? Ans. $62.185+. 14. What is the amount of $288.25, for 2 years, 2 months, and 14 days, at 8 per cent.? Ans. $339.11. In the following sums, the scholar will carefully observe when the amount, and when the interest only, is required. 15. What is the interest of $106.75, for 1 year, 11 months, and 6 days, at 6 per cent.? Ans. $12.383. 16. What is the amount of $731.82, for 3 and 9 days, at 7 per cent.? months, at 6 per cent.? and 8 days, at 6 per cent.? years, 2 months, Ans. $895.32. 17. What is the amount of $1693, for 2 years, 11 months, and 15 days, at 6 per cent.? Ans. $1993.507. 18. What is the interest of $860, for 4 years and 6 months, at 8 per cent.? Ans. $309.60. 19. What is the interest of $789.32, for 3 years and 8 Ans. $173.65. 20. What is the interest of $654.18, for 1 year, 2 months, Ans. $46.664+. 21. What is the amount of $539.72, for 2 years, 3 months, and 15 days, at 4 per cent.? Ans. $589.194+. 22. What is the amount of $18.63, for 2 years and 2 Ans. $19.84+. 23. What is the amount of $101.73, for 9 months and 12 days, at 6 per cent.? Ans. $106.51+. 24. What is the interest of $66.66, for 1 year, 9 months, and 18 days, at 6 per cent.? Ans. $7.199+. 25. What is the amount of $288.40, for 2 years, 10 months, and 6 days, at 7 per cent.? Ans. $345.935+. months, at 3 per cent.? TO COMPUTE INTEREST FOR DAYS ONLY. § 141. Interest at 6 per cent. per annum is cent per month, or 1 mill for 6 days, allowing 30 days to each month, since cent=5 mills=.005, and 30÷5=6, the days required for $1 to gain 1 mill. Hence, part of the days during which any sum of money is on interest, will be the interest due on each dollar of principal in mills. Therefore, RULE. Multiply the principal by 1 sixth part of the days during which the money draws interest. If the principal consist of dollars only, the product will be mills, (§ 91 ;) if it consist of dollars and cents, it will consist of hundredths of mills, and must be reduced to dollars, OBS. If preferred, at any time, the scholar may multiply by the whole number of days, and divide the product by 6, with the same result. 26. What is the interest of $426, for 18 days, at 6 per cent.? OPERATION. 18 days÷6=3, the number of mills of interest each dollar draws during 18 days; therefore, 426×3== 1278 mills $1.278, Ans. 27. What is the interest of $3672, for 69 days, at 6 per cent.? Ans. $42.228. 28. What is the interest of $2087.96, for 42 days, at 6 Ans. $14.615+. per cent.? 29. What is the amount of $59.40, for 90 days, at 6 per cent.? Anş. $60.29+. 30. What is the amount of $257.93, for 45 days, at 6 per cent.? Ans. $259.864+. 31. What is the interest of $88.52, for 36 days, at 6 per cent.? Ans. $0.531+. 32. What is the interest of $69.56, for 32 days, at 8 per cent.? Ans. $0.494+. 33. What is the amount of $288.75, for 18 days, at 4 per cent.? Ans. $289.327+. 34. What is the amount of $375, for 27 days, at 6 per cent.? Ans. $376.687+. 35. What is the amount of $480, for 40 days, at 6 per cent.? Ans. $483.20. 36. What is the interest of $356, for 63 days, at 6 per cent.? Ans. $3.738. 37. What is the interest of $596, for 18 days, at 7 per cent.? Ans. $2.086. 141. What is the rule for casting interest for days only? What is the reason for it? What may be done if preferred? NUMBERS AND THEIR RELATIONS TO EACH OTHER. § 142. Numbers, when we regard their numerical value only, bear a certain relation to each other. Of any two given numbers, the smaller one may be so repeated, that the amount of these repetitions shall just equal the larger, or, such a portion of the larger may be taken as shall just equal the smaller. The relative value of numbers thus ascertained, is called their ratio. It is obvious that numbers, to be thus compared, must be considered merely as numbers, representing no particular objects; or, if representing objects of a particular kind, they must agree in kind. An obvious and important relation represented by numbers, is that of quantity and value. By this we mean, that the greater the quantity of any given article, the greater its value, and the less the quantity, the less the value. To represent quantities and their relative value is then an appropriate use of figures. Thus, if the price of a single yard of cloth be $1, the price or value of 2 yards is $2; of 3 yards, $3; of 4 yards, $4, &c.; that is, in whatever ratio the quantity increases, the value increases in the same ratio. Hence, having the value of a single object, we readily determine the value of any like objects, by repeating that value as many times as' there are units in the number representing the objects. 1. If 1 yard of cloth cost $3, what will 3 yards cost? Ans. 3 times $3, that is, $9. What will 4 yards cost? Ans. $12. What will 6 yards cost? Ans. $18. 2. If the price of 1 pound of butter be 12 cents, what is 142. What is said of the relation of numbers? What of the smaller of two numbers ? What is the relative value of numbers called? How must numbers, to be compared thus, be considered? If they represent objects of a particular kind, what is said of each? What is another important relation represented by numbers? What is meant by this? What is the appropriate design of figures? In what ratio does the value of any quantity increase? Having the value of a single object, how do we determine the value of any number of like objects? |