23-CS-1 Engineering Economics · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2015 — 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 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.
The nominal annual rate is the stated periodic rate multiplied by the number of compounding periods in a year. Bank A quotes 6% per six-month period and compounds twice a year; Bank B quotes 3% per three-month period and compounds four times a year:
Both have the same 12% nominal rate—but different compounding. Note that the nominal rate ignores interest earned on interest within the year, which is exactly why it cannot be used to rank the two accounts.
The effective annual rate is the factor by which one year of compounding actually grows a deposit, less one: $i_e = (1+r/m)^{m}-1$, where $r/m$ is the periodic rate already given in the question:
A dollar left for one year grows to $1.1236 at Bank A and to $1.1255 at Bank B—a difference of 0.19 percentage points, worth about $190 a year on a $100,000 balance.
A saver wants the higher effective rate, so Bank B is better (12.55% > 12.36%)—more frequent (quarterly) compounding of the same nominal 12% earns more.
Indifference after one year of saving means the two accounts must multiply a deposit by the same factor over that year, so Bank B's quarterly rate $i$ must satisfy:
Bank B would have to cut its quarterly rate from 3.00% to about 2.9563% (a nominal 11.83% instead of 12%) for the saver to be indifferent; anything above that and the more frequent compounding keeps Bank B ahead.
