Recover the amount due from a given true discount: If the true discount on a sum due 2 years hence at 7% per annum (simple) is ₹ 672, find the sum due (future amount).

Introduction / Context:Given true discount TD, time t, and rate r, the due amount A can be found by inverting TD = A * (r * t) / (1 + r * t). This is a standard reverse-calculation task in true discount problems.

Given Data / Assumptions:

• TD = 672.
• t = 2 years.
• r = 7% p.a. simple ⇒ r * t = 0.14.

Concept / Approach:TD = A * 0.14 / 1.14 ⇒ TD = A * (7/50) / (57/50) = A * (7/57). Therefore A = TD * (57/7).

Step-by-Step Solution:A = 672 * 57 / 7 = 96 * 57 = 5472.

Verification / Alternative check:Compute PW = A − TD = 5472 − 672 = 4800. Interest on PW for 2 years at 7% = 4800 * 0.07 * 2 = 672 = TD, confirming correctness.

Why Other Options Are Wrong:

• 5500, 5425, 5300 are not equal to 672 * 57 / 7 and will not produce TD = 672 with the given r and t.

Common Pitfalls:

• Mistaking TD as A * r * t (banker’s discount), which would give A = 672 / 0.14 = 4800 (that is actually the present worth, not the future amount).

Final Answer:₹ 5472