Simple Interest — Inferring the annual rate from two amounts: A certain principal at simple interest amounts to ₹ 1012 in 2.5 years and to ₹ 1067.20 in 4 years. Find the annual rate of interest (percent per annum).

Introduction / Context:
With simple interest (SI), the amount grows linearly with time. If we know the amounts at two different times for the same principal, we can isolate the interest added between those times to find the rate.

Given Data / Assumptions:

• Amount after 2.5 years, A1 = ₹ 1012
• Amount after 4 years, A2 = ₹ 1067.20
• Time gap Δt = 1.5 years
• Principal = P, annual rate = r% (unknowns)

Concept / Approach:
Amount A = P * (1 + r * t / 100). The extra interest from 2.5 to 4 years equals P * r * Δt / 100 = A2 - A1. Use this with one of the amount equations to solve r.

Step-by-Step Solution:
A2 - A1 = 1067.20 - 1012 = 55.20P * r * (1.5) / 100 = 55.20P * r = (55.20 * 100) / 1.5 = 3680A1 = P * (1 + 2.5r / 100) = 10121012 = P + (P * r * 2.5 / 100) = P + (3680 * 2.5) / 100 = P + 92P = 1012 - 92 = 920r = 3680 / 920 = 4%

Verification / Alternative check:
With P = ₹ 920 and r = 4%, A2 at 4 years: 920 * (1 + 0.04 * 4) = 920 * 1.16 = ₹ 1067.20, matching the data.

Why Other Options Are Wrong:
2.5%, 3%, and 3.5% undercount growth; 5% overshoots the observed difference between A1 and A2.

Common Pitfalls:
Mixing amount with interest, or treating the 1.5 years gap as 15 months without scaling the rate correctly can cause errors.

Final Answer:
4%