Week 3 Tutorial ETC2430 with solutions.pdf

Week 3 Tutorial ETC2430 with solutions.pdf - ETC2430 Week 3...

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1 ETC2430 Week 3 Tutorial NB In each question where you need to use a formula to calculate the answer, be sure to: state the relevant formula / formulae. state the relevant values of each of the parameters that make up the formula. E.g. n=5, i=5.5%. you can then use a spreadsheet (or calculator) to calculate the answer. This is how you will be expected to show answers to these kinds of questions in tests and exams (except you won’t usually need to complete the last step in an exam). A. Background First, take some time to construct and test your own calculations spreadsheet, based on the Week 2 Lecture Spreadsheet . Next, work through the examples in the Week 2 Lecture spreadsheet Examples sheet . B. Exercises 1. $4,600 is invested at time 0 and the proceeds at time 10 are $8,200. Calculate A (7,10) if A (0,9) = 1.8, A (2,4) = 1.1, A (2,7) = 1.32, A (4,9) = 1.45. Solution Representing the initial investment, proceeds, and accumulation factors on a diagram, we have: Since $4,600 accumulates to $8,200 in 10 years, we know:
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2 𝐴(0,10) = 8,200 4,600 = 1.7826 Using the principle of consistency: 𝐴(0,10) = 1.7826 = 𝐴(0,2)𝐴(2,7)𝐴(7,10) => 𝐴(7,10) = ଵ.଻଼ଶ଺ ஺(଴,ଶ)×ଵ.ଷଶ where A (2,7) = 1.32. We can find A (0,2) using the principle of consistency again: 𝐴(0,9) = 𝐴(0,2)𝐴(2,4)𝐴(4,9) => 𝐴(0,2) = ஺(଴,ଽ) ஺(ଶ,ସ)஺(ଶ,ଽ) = ଵ.଼ ଵ.ଵ×ଵ.ସହ = 1.1285 So: A(7,10) = 1.7826/(1.1285x1.32) = 1.1967 Check with Exercises spreadsheet 2. If the rate of simple interest is 𝑖 % per year, state the interest paid to the investor on investment capital of C after n years. Answer : The interest paid will be: 𝐶 𝑖 𝑛 . 3. If the rate of compound interest is 𝑖 % per year, state the interest paid to the investor on investment capital of C after n years. Answer: The interest paid will be: 𝐶 [(1 + 𝑖 )^n − 1] 4. Show how to convert between nominal interest rates and effective interest rates. Answer : If you are moving from an effective rate 𝑖 to an equivalent effective rate ( 𝑝 ) paid 𝑝 thly, then the formula linking to two is: 𝑖 (௣) = 𝑝[(1 + 𝑖) ଵ/௣ − 1] 5. A 91-day treasury bill is bought for $98.83 and is redeemed at $100. (i) Calculate the annual effective rate of interest from the bill.
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