Find rate from true discount: The true discount on a sum of ₹ 50,000 for 4 years is ₹ 2,000 at a certain simple-interest rate per annum. Find the annual rate of interest.

Introduction / Context: True discount TD for a future sum S due after t years at rate r (per annum) under simple interest is TD = S * r * t / (1 + r * t). Knowing TD, S, and t allows solving for r. This is a standard algebraic inversion.

Given Data / Assumptions:

• S (future sum) = ₹ 50,000.
• t = 4 years.
• TD = ₹ 2,000.

Concept / Approach: Let u = r * t. Then TD = S * u / (1 + u). Solve u from 2,000 = 50,000 * u / (1 + u), then compute r = u / t.

Step-by-Step Solution:

Verification / Alternative check: Using r ≈ 1.0417% gives TD ≈ 50,000 * (0.010417*4) / (1 + 0.010417*4) ≈ 2,000; rounding to the nearest listed rate is appropriate.

Why Other Options Are Wrong: 1.5%, 2%, and 5% produce TD far from ₹ 2,000 for 4 years; 0.75% underestimates.

Common Pitfalls: Omitting the denominator (1 + r t) and equating TD to S r t, which would overstate the rate.

Final Answer: 1%