Compound Interest — Recover annual growth rate from 3-year population multiplier: A country's population is 100 crore. It is expected to become 133.1 crore in 3 years. What is the annual percentage growth rate (compounded yearly) that leads to this increase?

Introduction / Context:Population growth that “becomes” a larger value after several years is naturally modeled using compound interest (or compound growth). If P0 is today's population and it becomes P after t years at an annual compounding rate r (per year), then P = P0 * (1 + r)^t. This question asks us to recover the annual percentage growth from a known 3-year multiplier.

Given Data / Assumptions:

• Initial population P0 = 100 crore
• Population after 3 years P = 133.1 crore
• Annual compounding; t = 3 years
• Goal: find r as a percent per annum

Concept / Approach:The ratio P / P0 equals (1 + r)^t. Thus r = (P / P0)^(1/t) − 1. Because 133.1 / 100 = 1.331, and 1.331 is a well-known cube (1.1^3), the rate appears to be exactly 10% per year when compounded annually.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 8%, 9%, 12.7%, 15% do not cube to 1.331 when added to 1. Their three-year multipliers are not 1.331.

Common Pitfalls:

• Accidentally using simple interest (linear growth) instead of compound growth.
• Rounding too early; here the cube equality is exact with 10%.

Final Answer:10% per annum (compounded annually).