If the true discount on ₹ 161 due 2.5 years hence is ₹ 21, at what annual simple interest rate is the discount calculated?

Introduction / Context: This repeats the earlier TD-to-rate calculation using the standard formula for true discount under simple interest.

Given Data / Assumptions:

• F = 161
• TD = 21
• t = 2.5 years

Concept / Approach: Use TD = F * (r * t)/(1 + r * t). Let x = r * t and solve for r.

Step-by-Step Solution: 21 = 161 * x/(1 + x) → 21 + 21x = 161x → 21 = 140x → x = 0.15. r = x/t = 0.15/2.5 = 0.06 = 6% p.a.

Verification / Alternative check: Present worth = 161/1.15 = 140; TD = 161 − 140 = 21, consistent.

Why Other Options Are Wrong: Rates other than 6% do not reproduce the given TD for 2.5 years.

Common Pitfalls: Misinterpreting TD as SI on face value; ignoring the denominator; or mishandling time conversion.

Final Answer: 6%