NivaarExam PrepOfficial exam papers ↗

11-CS-1 Engineering Economics · May 2016

Question 1 of 5: Bank Rates, Simple vs Compound Interest

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — May 2016 — 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 questions follow; standard compound-interest factors are used and minor rounding is immaterial.

Question 1: Bank Rates, Simple vs Compound Interest (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) Effective Semi-Annual Rates

First the effective annual rates: A $(1+0.0825/366)^{366}-1 = 8.60\%$; B $(1+0.0825/12)^{12}-1 = 8.57\%$; C $(1+0.083/4)^{4}-1 = 8.56\%$. Then $i_{sa}=(1+i_a)^{1/2}-1$:

$$\text{A:}\ \boxed{4.21\%};\qquad \text{B:}\ \boxed{4.20\%};\qquad \text{C:}\ \boxed{4.19\%}$$

(b) Preferred Bank and Interest Earned

A saver prefers the highest effective annual rate, so Bank A (8.60%). Interest on $5,000 after 3 years:

$$F = 5{,}000(1.0860)^{3} = 5{,}000(1.28082) = \$6{,}404 \;\Rightarrow\; \text{interest} \approx \boxed{\$1{,}404}$$

(c) Nominal Rate for 1.4% Every Two Months

There are 6 two-month periods per year, so the nominal annual rate is $1.4\%\times 6 = \boxed{8.4\%}$.

(d) Compound (Bank A) versus 9% Simple (Bank D)

Bank D, simple interest: $F = 5{,}000(1 + 0.09\times 3) = 5{,}000(1.27) = \$6{,}350$, i.e. interest of $1,350. Bank A, compound: $F = \$6{,}404$, i.e. interest of $1,404. Since Bank A yields $54 more over the three years, no—keep Bank A: the compounding of 8.60% beats 9% simple interest. Note the margin is thin and it is horizon-dependent—over one year the 9% simple rate would win ($450 against $430), and the two break even at about 2.1 years; only beyond that does compounding put Bank A ahead.

← Paper overview