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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QUANTUM COMPUTING - EXAMPLE 32.7 : If | ± > = 0.707 ( | 0 > ± | 1 > ), prove that | Ψ (t = 0) > = | 0 > = 0.707 ( | + > + | - > ).
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Question - Chemical Engineering Material - In crystal material, hexagonal crystal system could form 4-digit index in certain direction of solid. For [1(-1)0] direction in the hexagonal crystal systems of particular catalyst applied in fume removal of incinerator, what is the four-digit index for this direction? Hint : The transformation equations between the 3-digit [h’k’l’] and the 4-digit [hkil] indices are : h = (1/3) (2h’ – k’); i = - (h + k); k = (1/3) (2k’ – h’); l = l’. A. [(-1)100] B. [1(-1)00] C. [(-1)000] D. [00(-1)(-1)] E. [(-1)0(-1)0]
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