3d payment April 1, 1801 4th payment May 1, 1801. 12,00 30,00 How much remains due on said note the 16th of Sep tember, 1801? $cts. Principal dated February 1, 1800, 500,00 Interest to May 1, 1800, (3 mo.) 7,50 Amount, 507,50 Paid May 1, 1800, a sum exceeding the interest 40,00 New principal, May 1, 1800, 467,50 Interest to May 1, 1801 (1 year.) 28,05 Amount, 495,55 Paid Nov. 4, 1800, a sum less than the 8,00 12,00 30,00 50,00 445,55 10,02 interest then due, Paid April 1, 1801, do. do. New principa! May 1, 1801, Balance due on the note, Sept. 16. 1801, $455,57 The payments being applied according to this Rule, keep down the interest, and no part of the interest ever forms a part of the principal carrying interest. COMPOUND INTEREST BY DECIMALS. MULTIPLY the given principal continually by the amount of one pound, or one dollar, for one year, at the rate per cent. given, until the number of multiplications are equal to the given number of years, and the product will be the amount required. OR, In Table I. Appendix, find the amount of one dollar, or one pound, for the given number of years, which multiply by the given principal, and it will give the amount as before. EXAMPLES. 1. What will 4007. amount to in 4 years, at 6 per cent. per annum, compound interest ? 400×1,06×1,05×1,06×1,06 £504,99+or The same by Table I. Tabular amount of £11,26247 400 Whole amount=£504,98800 2. Required the amount of 425 dols. 75 cts. for 3 years, at 6 per cent. compound interest. Ans. $507,7 cts. + 3. What is the compound interest of 555 dols. for 14 years, at 5 per cent. ? By Table I. Ans. $543,86cts. + 4. What will 50 dollars amount to in 20 years, at 6 per cent. compound interest ? Ans. $160 35cts. 61⁄2m. INVOLUTION, Is the multiplying any number with itself, and tnat pro duct by the former multiplier; and so on; and the several products which arise are called powers. The number den ing the height of the power, is called the index or exponent of that power EXAMPLES. What is the 5th power of 8? 8 64 2d power, or square. 512 3d power, or cube. 8 4096 4th power, or biquadrate. 8 32768 5th power, or sursolid. Ana What is the square of 17,1? What is the square of ,085? What is the cube of 25,4? What is the square of 74 ? Ans. 292,41 Ans. ,007225 Ans. 16387,064 Ans. 20736 Ans. 52 EVOLUTION, OR EXTRACTION OF ROOTS WHEN the root of any power is required, the business of finding it is called the Extraction of the Root. The root is that number, which by a continual multiplication into itself, produces the given power. Although there is no number but what will produce a perfect power by involution, yet there are many numbers of which precise roots can never be determined. But, by the help of decimals, we can approximate towards the root to any assigned degree of exactness. The roots which approximate, are called surd roots, and hose which are perfectly accurate are called rational roots. A Table of the Squares and Cubes of the nine digits. Roots. 1 2 3 4 5 | 6] 7 81 9 Squares. 1 1|49|16| 25 | 36 | 49 64| 81 Cubes. | 1 | 8 | 27 | 64 | 125 | 216 | 343 | 512 | 729 EXTRACTION OF THE SQUARE ROOT. Any number multiplied into itself produces à square. To extract the square root, is only to find a number, which being multiplied into itself shall produce the given number. RULE. 1. Distinguish the given number into periods of two igures each, by putting a point over the place of units, nother over the place of hundreds, and so on; and if there tre decimals, point them in the same manner, from units tovaids the right hand; which points show the number of igures the root will consist of. 2. Find the greatest square number in the first, or left hand period, place the root of it at the right hand of the given number, (after the manner of a quotient in division) for the first figure of the root, and the square number under the period, and subtract it therefrom, and to the remainder bring down the next period, for a dividend. 3. Place the double of the root, already found, on the left hand of the dividend for a diviser 4. Place such a figure at the right hand of the divisor, and also the same figure in the root, as when multiplied into the whole (increased divisor) the product shall be equal to, or the next less than the dividend, and it will be the second figure in the root. 5. Subtract the product from the dividend, and to the remainder join the next period for a new dividend. 6. Double the figures already found in the root, for a new divisor, and from these find the next figure in the root as last directed, and continue the operation in the same manner, till you have brought down all the periods. Or, to facilitate the foregoing Rule, when you have brought down a period, and formed a dividend in order to find a new figure in the root, you may divide said dividend, (omitting the right hand figure thereof,) by double the root already found, and the quotient will commonly be the figures sought, or being made less one or two, will generally give the next figure in the quotient. 9 EXAMPLES. 1. Required the square root of 141225,64. 67)512 469 745)4325 3725 Reduce the fraction to its lowest terms for this and all other roots; then 1. Extract the root of the numerator for a new numerator, and the root of the denominator, for a new denomi nator 2. If the fraction be a surd reauce it to a decimal, and extract its root. PROELEM I. A certain General has an army of 5184 men; how many must he place in rank and file, to form tem into a save ? |