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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.
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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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ENGINEERING MATHEMATICS - EXAMPLE 8.2 : In the US (United States), one barrel is equal to 42 US gallons and equivalent to 0.15898 cubic metres. One British barrel is equal to 36 Imperial gallons and equivalent to 0.163659 cubic metres. If an oil refinery in England sells 42 Imperial gallons of crude oil to a company in US, how much US gallons of crude oils has been sold?
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QUANTUM COMPUTING - EXAMPLE 32.4 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 2), X ≡ 3 (mod 3), X ≡ 4 (mod 5). X has positive values. (a)(i) List the values of these equations from 1 to approximately 40. (ii) Find the first smallest value and second smallest value of X. (iii) Guess the third smallest value of X. (b) Let X ≡ Aa (mod Ma), X ≡ Ab (mod Mb), X ≡ Ac (mod Mc). According to Chinese remainder theorem, X ≡ (Aa x Ya x Md + Ab x Yb x Me + Ac x Yc x Mf) [ mod (Ma x Mb x Mc) ]. (i) Show that Ma, Mb and Mc have the greatest common divisor of Ma x Mb x Mc. (ii) Find the values of Md, Me and Mf if Md = Mb x Mc, Me = Ma x Mc and Mf = Ma x Mb. (iii) Find the values of Ya, Yb and Yc if Ya = Remainder of (Md / Ma), Yb = Remainder of (Me / Mb) and Yc = Remainder of (Mf / Mc). (iv) Use Chinese remainder theorem to find X.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.12 : You, as an engineer, buy a piece of biochemical instrument to start a servicing business. The instrument has a useful life of 3 years, that costs $60k. The instrumental business generates $100k per year. The labor costs $50k per year. The $60k new instrument depreciates in its value evenly up to 3 years, thereafter the old instrument needs to be replaced by another piece of new instrument. (i) In the first year of this engineering business : (a) what is its starting cash? (b) calculate the depreciation value of the instrument. (c) find the operating profit generated. (d) what is the capital expense of the business? (e) calculate the cash from operation. (f) calculate the ending cash. (ii) Based on the income statement of the business in the second year : (a) find the capital expense of the business. (b) what is its starting cash? (c) calculate the depreciation value of the instrument. (d) find the operating profit generated. (e) calculate the cash from operation. (f) calculate the ending cash.
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A distillation column separates 10000 kg / hr of a mixture containing equal mass of benzene and toluene. The product D recovered from the condenser at the top of the column contains 95 % benzene, and the bottom W from the column contains 96 % toluene. The vapor V entering the condenser from the top of the column is 8000 kg / hr. A portion of the product from the condenser is returned to the column as reflux R, and the rest is withdrawn as the final product D. Assume that V, R, and D are identical in composition since V is condensed completely. Find the ratio of the amount refluxed R to the product withdrawn D. Hint : Solve the simultaneous equations as follow in order to find the answer (R / D) : 10000 = D + W; 10000 (0.5) = D (0.95) + W (0.04); 8000 = R + D.
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