The population of a village increases by 5% yearly. If at present the…

Concept

When a quantity grows by a fixed percentage r each year, its present value P relates to its value n years earlier (the past value) by the compound-growth relationship: P = Past × (1 + r/100)n. Rearranging, the past value is recovered by dividing the present value by the same growth factor: Past = P / (1 + r/100)n.

Application

1. Identify the given values: present population P = 4410, yearly growth rate r = 5%, and number of years n = 2.

2. Write the reverse compound-growth formula: Past = P / (1 + r/100)n = 4410 / (1.05)2.

3. Compute the growth factor: (1.05)2 = 1.1025.

4. Divide the present population by this factor: 4410 / 1.1025 = 4000.

Cross-check

Grow 4000 forward by 5% for two successive years: 4000 × 1.05 = 4200 (population after one year); 4200 × 1.05 = 4410 (population after two years) — this exactly matches the present population stated in the question, confirming the result.