ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.13 : (i) In the Present Value Multiplication Rule, let PV = present value, Ra = interest rate for first discount, A = duration for first discount; Rc = interest rate for second discount, C = duration for second discount. Let PV = [ 1 / (1 + Ra) ^ A ] [ 1 / (1 + Rc) ^ C ] where ^ is the symbol of power : 3 ^ 2 = 3 x 3, 2 ^ 3 = 2 x 2 x 2. (a) For discounts involving 8 % / year for 3 years and 10 % / year for 9 years, find the value of PV. (b) If Re = interest rate for third discount, E = duration of third discount, form a mathematical equation of PV as a function of A, C, E, Ra, Rc, Re. Note : Discounts are available in the purchase of certain biochemical engineering instruments. (ii) Let R = nominal interest rate related to growth rate of money, r = real interest rate related to growth rate of purchase power. If I = inflation, where the unit of R, r and I is %, find the mathematical relatonship of r as a function of R and I.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.13 : (i) (a) Let Ra = 0.08, A = 3; Rc = 0.1, C = 9. Then PV = [ 1 / (1 + Ra) ^ A ] [ 1 / (1 + Rc) ^ C ] = [ 1 / (1 + 0.08) ^ 3 ] [ 1 / (1 + 0.1) ^ 9 ] = 0.33666. (b) PV = [ 1 / (1 + Ra) ^ A ] [ 1 / (1 + Rc) ^ C ] [ 1 / (1 + Re) ^ E ]. (ii) r = R - I. 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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Question 43 - In a non-dilute absorber, the inlet gas stream consists of 8 mol % carbon dioxide in nitrogen. By contact with room temperature water at atmospheric pressure, 65 % of the carbon dioxide from a gas stream has been removed. (a) Find the mole ratio of carbon dioxide and nitrogen gases at inlet and outlet gas streams. (b) The Henry’s Law provides y = 1640 x for carbon dioxide in water. Find the mole ratio when x = 0.0000427. Mole ratio is y / (1 - y) for y.
In a furnace, 2 chemical reactions are happening – 1 mole of solid carbon reacts with 1 mole of oxygen gas to generate 1 mole of carbon dioxide gas; 1 mole of solid carbon reacts with 0.5 mole of oxygen gas to generate 1 mole of carbon monoxide gas. In a given process, 100 kmol of carbon is burned in a furnace. (a) Calculate the theoretical oxygen gas needed by assuming that all the carbon is burned completely to carbon dioxide gas. (b) Calculate the theoretical air needed by assuming that all the carbon is burned completely to carbon dioxide gas and there is only 21 % of oxygen gas. (c) Determine the amount of air required (in kmol) if 50 % excess oxygen gas must be satisfied for (a) and (b). (d) It has latter been found that 20 % of the carbon undergoes incomplete combustion resulting to carbon monoxide gas production. The rest of the carbon undergoes complete combustion. Calculate the total oxygen gas required stoichiometrically based on the actual process.
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