Find the true discount on ₹ 39.69 due in 2 years when compound interest is reckoned at 5% per annum.

Introduction / Context:
Here, present worth is computed using compound interest, not simple interest. The true discount is the face value minus present worth.

Given Data / Assumptions:

• F = 39.69
• Rate = 5% compounded annually
• Time = 2 years

Concept / Approach:
Present worth with compound interest: P = F / (1 + r)^n. Then TD = F − P.

Step-by-Step Solution:
(1 + r)^n = (1.05)^2 = 1.1025. P = 39.69 / 1.1025 = 36.00. TD = 39.69 − 36.00 = 3.69.

Verification / Alternative check:
Forward check: 36 * 1.1025 = 39.69, confirming the present worth and hence TD.

Why Other Options Are Wrong:
5.00, 5.69, 4.69, 3.00 do not match the exact compound discounting computation.

Common Pitfalls:
Using simple interest discounting for a compound interest question; rounding early; or miscomputing (1.05)^2.

Final Answer:
Rs. 3.69