Back-calculating past population: The current population is 1058400 and grows at 5% per annum. What was the population 2 years ago?

Difficulty: Easy

Correct Answer: 960000

Explanation:


Introduction / Context:
Given the present population and a known annual growth rate, we reverse compound to find the population two years earlier.


Given Data / Assumptions:

  • P_now = 1058400.
  • Annual rate r = 5%.
  • We need P_past such that P_now = P_past * (1.05)^2.

Concept / Approach:
P_past = P_now / (1.05^2) = 1058400 / 1.1025.


Step-by-Step Solution:

Compute 1058400 / 1.1025.Observation: 960000 * 1.1025 = 960000 + 0.1025 * 960000 = 960000 + 98400 = 1058400.Thus P_past = 960000.

Verification / Alternative check:
Exact multiplication confirms the reverse calculation without long division.


Why Other Options Are Wrong:

  • Other figures do not yield 1058400 when multiplied by 1.1025.

Common Pitfalls:
Subtracting 10% once (linear thinking) instead of reversing compound growth.


Final Answer:
960000

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