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23-CS-1 Engineering Economics · December 2018

Question 1 of 5: Accumulated Value of Four Saving Plans

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Notes on this paper

National Exams — December 2018 — 11-CS-1 Engineering Economics. Open book; non-communicating calculator permitted. Any four of the five questions constitute a complete paper; all questions are of equal value. Fully worked solutions to all five follow; standard compound-interest factors are used and minor rounding is immaterial.

Question 1: Accumulated Value of Four Saving Plans (25 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) $100/Month, 12% Compounded Monthly

Monthly rate $i=1\%$; a 12-payment ordinary annuity:

$$F = 100(F/A,1\%,12) = 100(12.682503) = \boxed{\$1{,}268.25}$$

(b) $100/Month, 12% Compounded Quarterly

The compounding (quarterly, 3% per quarter) differs from the payment period (monthly), so first find the effective monthly rate: $i_m = (1.03)^{1/3}-1 = 0.990163\%$. The rate must be carried into the factor unrounded—rounding it to 0.9902% first shifts the answer by several cents:

$$F = 100(F/A,0.990163\%,12) = 100\left[\frac{(1.03)^4-1}{0.00990163}\right] = 100(12.67557) = \boxed{\$1{,}267.56}$$

(c) $1,000 Once, 12% Compounded Continuously

The deposit is made at the end of month 1 and grows for the remaining 11 months $(=\tfrac{11}{12}$ yr):

$$F = 1{,}000\,e^{0.12\times 11/12} = 1{,}000\,e^{0.11} = \boxed{\$1{,}116.28}$$

(d) $60 Increasing $5/Month, 12% Compounded Monthly

Arithmetic gradient at $i=1\%$, 12 months. Equivalent uniform amount $A = 60 + 5(A/G,1\%,12) = 60 + 5(5.38145) = \$86.9073$:

$$F = 86.9073(F/A,1\%,12) = 86.9073(12.682503) = \boxed{\$1{,}102.20}$$
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