Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 Excerpt: ...D. By logarithms, Log a = log p + t log R. where a = amount. p = principal. t = time or number of payments. R = (l + r) = amount of £1 for one period. Illustrative Example.--Find the compound interest and a mount on £2000 for four years @ 5 j0. First by method A. £2000 P,. 100 Ii = (yof 2000 or 5%). 2100 Poor A,. 105 I 2205 P3or Aj. 110-25 1,. 2315-25 P4or A,. 115-7625 1,. 2431 '0125 A4 = amount required..'-Compound interest required = £4310125. Second by method B. 1-05 = amount of £1 for one year. 1-05 525 105 1-1025 105 55125 11025 1-157625 105 5788125 1157625 1-21550625 2000 2431-01250000 Compound interest required = £431-0125 and amount required = £2431-0125. 1 21550625 = 4th power. Thirdly by method C. The only variation in this method is that the 4th power 1-21550625, or the amount of £1 for given time at given rate, is obtained direct from interest tables. The rest of the work is identical with method B. Fourthly by method D, or logarithms. Log a = 1ogp + t log R. Log p = log 2000 = 3-3010300 tlogR =-0847572.-. log a = 3-3857872 and the number answering to this log is 2431-012..-. required amount = £2431-012. SCALES OF NOTATION. In the Common Notation ten (10) is the radix or root of the scale, but any other number may form the radix or base of a scale. Thus we have the binary with 2 as radix; ternary with 3 as radix; denary or decimal with 10 as radix; duodenary or duodecimal with 12 as radix, and so on. In any scale of Notation every digit is necessarily less than the radix (or K), and the number of them including 0 is equal to B. The most valuable scale of Notation after the denary is the duodenary, which has 12 for its radix, but two new signs are required to express ten and eleven. They may, of course...
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