ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.13 (CORRECTION) : (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 relationship of r as a function of R and I.
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ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.13 (CORRECTION) : (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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CHEMICAL MATERIAL BALANCE - EXAMPLE 2.1 : Two methanol-water mixtures are contained in separate tanks. The first mixture contains 40.0 wt % methanol and the second contains 70.0 wt % methanol. If 200 kg of the first mixture is combined with 150 kg of the second, what are the mass and composition of the product? The symbol of weight percent is wt %.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.20 : Assume an engineer buys a $1 bond in period T while the nominal interest rate is R. The inflation rate at T + 1 is anticipated to be I. (a) If the bond is redeemed in period T + 1, how much money will the buyer engineer receive, in term of R, which is not affected by inflation? (b) Find the present value, PV of the proceeds from the bond, in term of R and I. (c) If the bond is redeemed in period T + 1, calculate the real growth or real value of the money that the buyer engineer will receive, in term of r = real interest rate, which is affected by inflation. (d) From the answers in (b) and (c), find the values of x, y and z in the following Fisher equation : (1 + x) = (1 + y) / (1 + z), in term of r, R and I.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.1 : (i) In the pricing of engineering bonds, 3 sets of data for Portfolio Value, Probability, Senior Tranche and Junior Tranche are : $2000, 81 %, $1000, $1000; $1000, 18 %, $1000, $0; $0, 1 %, $0, $0. By assuming independent defaults, find the price for : (a) Senior Tranche; (b) Junior Tranche. (ii) Assuming statistical independence of the values in the sample, the standard deviation of the mean (S) is related to the standard deviation of the distribution (s) by : N x S x S = s x s, where N is the number of observations in the sample used to estimate the mean. In a drug development project, let s = 1. Find the value of S if such a similar project is performed 100 times.
ENGINEERING ECONOMY - EXAMPLE 7.3 : There are 2 alternatives of investment. Choice 1 : A trader offers you an investment opportunity where your investment of A$15000 presently will be A$18000 after 4 years. Choice 2 : A bank offers you 5 % annual return for your initial investment of A$15000. Question a : What is the equivalent bank payment after 4 years? Question b : By using the concept of equivalence in engineering economy, which is the better choice, between 1 and 2, that will be more profitable after 4 years?
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QUANTUM COMPUTING - EXAMPLE 32.8 : In quantum computing, a quantum state is given by S = a | 00 > + b | 01 > + g | 10 > + d | 11 >. (a) Find S in term of | 0 > and | 1 > etc. (b) The probability of getting x is P(x). For S = 0.5 | 00 > + 0.5 | 01 > + 0.5 | 10 > + 0.5 | 11 >, find P(0) and P(1). Hint : P(00) + P(01) = P(0) = a x a + b x b, P(10) + P(11) = P(1) = g x g + d x d.
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