Present worth and true discount for a 3-year due amount: What is the present worth of ₹ 3720 due 3 years hence at 8% per annum simple interest? Also find the true discount.

Introduction / Context:
Find present worth PW by discounting a future amount A at simple interest: PW = A / (1 + r * t). The true discount TD is the difference A − PW. This is a direct computation once the period and rate are known.

Given Data / Assumptions:

• A = 3720, t = 3 years.
• r = 8% p.a. simple.

Concept / Approach:
Compute PW; compute TD = A − PW. Confirm using TD formula if desired: TD = A * (r * t) / (1 + r * t).

Step-by-Step Solution:
PW = 3720 / (1 + 0.08 * 3) = 3720 / 1.24 = 3000.TD = 3720 − 3000 = 720.

Verification / Alternative check:
TD via formula: 3720 * 0.24 / 1.24 = 892.8 / 1.24 = 720, consistent with A − PW.

Why Other Options Are Wrong:

• Other pairs do not satisfy both PW and TD identities at 8% for 3 years.

Common Pitfalls:

• Inverting discounting (multiplying instead of dividing).
• Arithmetic errors in 1 + r * t.

Final Answer:
PW = ₹ 3000 and TD = ₹ 720