The Theory of Finance Being a Short Treatise On the Doctrine of Interest And An

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occurs instead of a in the second term of the denominator. From it /o= -0024998. We therefore have by formula A. I= -0525714 B. I= -0524963 C. I= -0524457 D. I= -0524998 the true value of i being -0525.
54. Formula C gives a better value than formula A, and, if we examine the processes by which the formulas were deduced, the reason becomes apparent.
Equation (32) is obtained from equation (33) by multiplying by (i+p)> """it^ ^^^ result of a loss of accuracy. If in the expansion 2 1 6 Theory of
...Finance, [chap. It.
of 1 — {(l+y)+/)}~*^ we denote the coefficients of the ascending powers of p by ^, /, and w, so that^= {l-(l+J)-''}, Z=?i(l4-7)-^^^+'\ and ^^ ^^+l) ^^_|. J^-(n+2)^ equation (32) will take the form 'mp^-{-{a—r)p—{k—aj) = 0, or say xp'-^yp-z=0 (40) where x—m, y=(a^l), and z=(k—aj), and equation (33) will take the form or [m+i-j, y+(^a-l + ^-^)p-(h-aj)=0 which is seen to be the same as ). )f%-^fy+{y^j}-^-o ..... (41) ^Equations (40) and (41) are simply equations (34) and (37) so displayed that they may be compared, and they show us that in equation (34) we neglect part of each power of p.


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