ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.15 : Based on Time Discounting of Money, let y = x / (1 + r) ^ n, where ^ = power, r = interest rate for the period in decimal value, n = number of periods, y = current value, x = future value. According to Present Value Addition Rule, the present value of a set of future payments is equal to sum for present value of each of the payments. In an engineering business, 3 future payments are to be made : $100 after 1 year; $500 after 2 years; $200 after 3 years. (a) Form an equation of y as a function of r. (b) Find the value of y in 5 decimal places if r = 8 %.
ACCOUNTING AND FINANCIAL ENGINEERING - ANSWER 34.15 : (a) First future payment : n = 1, x = $100. Second future payment : n = 2, x = $500. Third future payment : n = 3, x = $200. Then total y = sum of x / (1 + r) ^ n = 100 / (1 + r) + 500 / (1 + r) ^ 2 + 200 / (1 + r) ^ 3. (b) When r = 8 % = 0.08, y = 100 / (1 + 0.08) + 500 / (1 + 0.08) ^ 2 + 200 / (1 + 0.08) ^ 3 = 680.02845 (5 decimal places). 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 36 - For a mixture of benzene (B), toluene (T) and xylene (X), the equation applies where x for B, T and X will sum up to 1. The equation of x for each component is x = (L / V + 1) (F) / (L / V + K). The data of F for each component are : 0.5 for B, 0.35 for T, 0.15 for X. The data of K for each component are : 1.98 for B, 0.76 for T, 0.24 for X. When x for B + x for T + x for X = 1, find the values of (a) L / V; (b) x for each component of B, T, X respectively. You may use Excel program - Data : What-If-Analysis for Goal Seek to perform the iterative calculations.
PROCESS DESIGN - EXAMPLE 21.2 : The names of the flow streams could be represented by : H1 for first hot stream, H2 for second hot stream, C1 for first cold stream, C2 for second cold stream. Data of supply temperature Ts in degree Celsius : 150 for H1, 170 for H2, 30 for C1, 30 for C2. Data of target temperature Tt in degree Celsius : 50 for H1, 169 for H2, 150 for C1, 40 for C2. Data of heat capacity Cp in kW / degree Celsius : 3 for H1, 360 for H2, 3 for C1, 30 for C2. (a) Find the enthalpy changes, dH for all streams of flow H1, H2, C1 and C2 in the unit of kW. Take note of the formula dH = (Cp) (Tt - Ts). (b) Match the hot streams H1 and H2 with the suitable cold streams C1 and C2 to achieve the maximum energy efficiency.
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BIOCHEMICAL ENGINEERING INSTRUMENTATION - EXAMPLE 29.6 : In infrared spectrum, one of the factors affecting peak location is the mass of the atoms. The stretching frequency of a bond connected to a lighter atom will be greater than the same bond connected to a heavier atom. (a) For halogens like florine (F), chlorine (Cl), bromine (Br), iodine (I) and astatine (At), what is their IUPAC group number? Hint : The proton numbers for F, Cl, Br, I and At are 9, 17, 35, 53 and 85 respectively. (b) For the compounds of H-F, H-Cl, H-Br, H-I and H-At, which one has the lowest stretching frequency and which one has the highest stretching frequency? State the reasons.
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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.10 : Let D be the random outcome of rolling a dice once. A new dice has values of D* = D - 3.5. There is a total of n rolls of a dice. (a) Find the variance for D* by using the formula 6 V = [ D* (D = 1) ] [ D* (D = 1) ] + [ D* (D = 2) ] [ D* (D = 2) ] + [ D* (D = 3) ] [ D* (D = 3) ] + [ D* (D = 4) ] [ D* (D = 4) ] + [ D* (D = 5) ] [ D* (D = 5) ] + [ D* (D = 6) ] [ D* (D = 6) ]. (b) Calculate the standard deviation of D* as a square root of V. (c) Another new dice has values of D** = kD*. (i) Find the value of k so that D** has a standard deviation of 1. (ii) Find the values of D** for each outcome of D = 1, 2, 3, 4, 5 and 6, when the standard deviation is 1. (iii) Given that the average score of a dice is 3.5, find the equivalent, new and improved model of a dice, Sn in term of n and D**. (iv) Find the expected value of D** as the average of D**.