Future population with annual compounding: A town has 705600 people. If population grows at 5% per annum, what will it be after 2 years?

Introduction / Context:
We compute a 2-year compound increase at 5% per year. This is a direct application of compound growth.

Given Data / Assumptions:

• P0 = 705600.
• Annual rate r = 5% = 0.05.
• Years n = 2.

Concept / Approach:
Population after 2 years: P = P0 * (1 + r)^n = 705600 * 1.05^2 = 705600 * 1.1025.

Step-by-Step Solution:

Verification / Alternative check:
Compute 5% of 705600 = 35280; add to get year 1 (740880). Then 5% of 740880 = 37044; year 2 total = 740880 + 37044 = 777924.

Why Other Options Are Wrong:

• The other numbers are near but not equal to 705600 * 1.1025.

Common Pitfalls:
Multiplying by 1.10 (simple 10% total) instead of 1.1025; compounding matters.

Final Answer:
777924