Compute growth amount (not final total): A city has population 250000, increasing at 2% per year. What is the increase in population after 2 years (growth amount only)?

Introduction / Context:
We are asked for the increase (difference between the 2-year future population and the original), not the final population itself.

Given Data / Assumptions:

• P0 = 250000.
• Annual rate r = 2%.
• Years n = 2.

Concept / Approach:
Increase = P0 * [(1 + r)^n − 1] = 250000 * (1.02^2 − 1).

Step-by-Step Solution:

Verification / Alternative check:
Year 1 increase: 2% of 250000 = 5000 ⇒ total 255000. Year 2 increase: 2% of 255000 = 5100. Total increase over two years = 5000 + 5100 = 10100.

Why Other Options Are Wrong:

• 2500 and 5000 count only a single year or half.
• 10000 ignores compounding in the second year.
• 252000 is a total population distractor, not the increase.

Common Pitfalls:
Multiplying 2% by 2 without compounding; this underestimates the growth by 100.

Final Answer:
10100