Population Growth – Reverse compounding over 3 years: A city’s population grows at 5% per annum. If the present population is 185,220, what was the population 3 years ago?

Introduction / Context:
Population growth under a fixed yearly percentage is a compound process. To find a past population, we divide by the forward growth factor (1 + r)^t.

Given Data / Assumptions:

• Current population = 185,220
• Growth rate r = 5% per annum
• Years back t = 3

Concept / Approach:
Past population = Present / (1 + r)^t.

Step-by-Step Solution:
Growth factor over 3 years = (1.05)^3 = 1.157625Past population = 185220 / 1.157625= 160,000 (exact match)

Verification / Alternative check:
Forward check: 160000 * (1.05)^3 = 160000 * 1.157625 = 185,220 (given).

Why Other Options Are Wrong:
181,500 and 183,433 are too close to the present; 127,783 is far too low.

Common Pitfalls:
Subtracting 5% of the present thrice (a simple, not compound, approach).

Final Answer:
160000