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23-CS-1 Engineering Economics · May 2013

Question 1 of 6: Effective Interest Rates

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Notes on this paper

National Exams — May 2013 — 11-CS-1 Engineering Economics. Open book; non-communicating calculator permitted. Any five of the six questions constitute a complete paper; all questions are of equal value. Fully worked solutions to all six questions are given below. Standard compound-interest factors are used throughout; minor rounding differences are immaterial.

Question 1: Effective Interest Rates (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Effective Quarterly Rates

Investment 1 (1% per month): a quarter is three months, so

$$i_q = (1+0.01)^3 - 1 = 1.030301 - 1 = \boxed{3.03\%}$$

Investment 2 (3% per quarter, compounded quarterly): the quarterly rate is already effective, $i_q = \boxed{3.00\%}$.

(b) Effective Annual Rates

$$\text{Inv 1:}\ i_a = (1.01)^{12} - 1 = 1.126825 - 1 = \boxed{12.68\%}$$
$$\text{Inv 2:}\ i_a = (1.03)^{4} - 1 = 1.125509 - 1 = \boxed{12.55\%}$$

(c) Which to Select

Investment 1 has the higher effective annual rate (12.68% > 12.55%), so RTC should select Investment 1 (it earns more per dollar per year).

(d) Monthly Rate for Indifference

Set the effective annual rate of Investment 1 equal to that of Investment 2:

$$(1+i)^{12} = (1.03)^{4} = 1.125509 \;\Rightarrow\; 1+i = 1.125509^{1/12}$$
$$i = 1.125509^{1/12} - 1 = 1.009902 - 1 \approx \boxed{0.990\%\ \text{per month}}$$

At about 0.99% per month, the two investments would yield the same effective annual return (12.55%) and neither would be preferred.

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