ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.21 : The cost of building a biochemical processing plant is increasing due to inflation. Let I = inflation rate, R = nominal interest rate, r = real interest rate. According to Fisher Equation, (1 + r)(1 + I) = (1 + R). According to General Inflation Equation, R = r + I. (a) By assuming that both r and I are fairly small, prove by mathematical calculations that complicated Fisher Equation could be simplified into the General Inflation Equation. (b) By using 2 first order Taylor expansions in the linear approximation, namely 1 / (1 + x) ≈ (1 - x), (1 + x)(1 + y) ≈ 1 + x + y, show by mathematical calculations that (1 + r) = (1 + R) / (1 + I) could be approximated by r ≈ R - I.
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ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.21 : (a) Let (1 + R) = (1 + r)(1 + I) = 1 + r + I + rI, R = r + I + rI. When r ≈ I ≈ fairly small, R ≈ r + I (proven). (b) Let 1 / (1 + I) ≈ (1 - I), then (1 + r) ≈ (1 + R)(1 - I) ≈ 1 + R - I, then r ≈ R - I (shown). The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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