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The current one-year spot rate is 5%, two-year spot rate is 5.5%, and three-year spot rate is 6%. You invest in a three-year zero-coupon bond today. Suppose that the two-year interest rate one year from now turns out to coincide with what investors expect it today (based on expecta!ons hypothesis). What is your rate of return from inves!ng in this three-year zero-coupon bond for a year? Answer options: None of the above 6% 5.5% 5% 5.67%

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Propose an efficient Synthesis for each of the following transformations. a b c d e f g.

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What continuous uniform series of cash flows over 7 years can be paid out of a fund having $20,000 at the present (or time 0) if interest is 10 percent compounded continuously?

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Explain why aromatic rings like benzene tend to undergo substitution rather than addition reactions (even with the presence of multiple C=C).

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Consider a suburb in which commute trips to downtown can be made either: by driving (alone) in a car; or by bus. Commuters make choices based solely on monetary considerations. The suburb is home to 200 (rich) people who derive a daily benefit of $60 by commuting. These folks value their time at $30 per hour, whether traveling inside a vehicle or waiting at a bus stop. The suburb is also home to 250 (poor) people who derive a daily benefit of $40 by commuting and who value their time (traveling or waiting) at $10 per hour. Round-trip time spent each day commuting by car is 0.5 hours. The only out-of-pocket cost for commuting by car is a highway toll, t, is to be paid in each direction. Round-trip time spent commuting by bus (waiting + riding time) is 1.5 hours. The fare each way is $2, such that round-trip fare is $4. Bus commuters do NOT pay toll, ?. Sketch the demand function for commuting by bus, $D_B$, as a function of the highway toll, $?$. Your sketch must be legible (i.e. readable). Include on your sketch dimensions (i.e. numeric values) of $D_B$ and $?$ at points where the function changes - such as at the minimum value of $?$ for which everyone commutes by bus.

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b) A firm's production function is given by $Q = 100KL$. Unit capital and labour costs are £2 and £1 respectively. The firms is contracted to provide 5000 units of output and aims to fulfil this contract at minimal cost. Write down the Lagrange function for firm's optimization problem. Check first and second order conditions using the Hessian matrix and solve for $K$ and $L$. What does $\lambda$ signify in the Lagrange function?

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(1 point) Find all solutions to the system $x_1 - 3x_2 = 0$ $x_1 - 3x_2 = -3$ by eliminating one of the variables. $(x_1, x_2) = $ Help: If there is a solution $(a, b)$, enter your answer as a point $(a,b)$. If there is a free variable in the solution, use $s_1$ to denote the variable $s_1$. If there is no solution, type no solution.

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Exercise 5-17 (Algo) Future value; solving for annuities and single amount (LO5-4, 5-9) Parents want to accumulate $75,000 to be used for their child's college education. The parents would like to have the amount available on December 31, 2029. Assume that the funds will accumulate in an account paying 8% interest compounded annually. Answer each of the following independent questions. Required: 1. If they were to deposit a single amount, how much would they have to invest on December 31, 2024? 2. If they were to make five equal deposits on each December 31, beginning on December 31, 2025, what is the required amount of each deposit? 3. If they were to make five equal deposits on each December 31, beginning on December 31, 2024, what is the required amount of each deposit? Note: For all requirements, use tables, Excel, or a financial calculator. Round your final answers to nearest whole dolar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. Amount $ 51,045 2. Annuity amount $ 18,784 3. Annuity amount $ 17,393

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2. A SOFC is operated with an anode exit flow of 2 g/s (hydrogen and water vapor) and an inlet of pure hydrogen. If the cell is operated at 0.75 volts and delivers 10kW of power, determine the following: (Total points: 10+15=25) a. The mass flow rate into the anode gas chamber. (Points 10) b. The mass flow rate into the cathode chamber if 20% oxygen utilization is desired. (Points 15) $m_{a,in}$ Anode Gas Chamber $m_{a,out}$ = 2 g/s $m_{c,in}$ Cathode Gas Chamber $m_{c,out}$ Figure P2: Flow Diagram of the SOFC

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Deliverables: Use engineering format, solve the following problem. Scan and upload it on Canvas. You are welcome to do this with 1 other person, make sure both names are on the engineering paper to receive credits. Problem: Find the current, voltage drop, and power dissipation for each of the resistors in the circuit. 3? 2? 10? 24V 6? 4?

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