Present worth and true discount (simple interest): A sum of Rs 9300 is due exactly 3 years from now at a simple interest rate of 8% per annum. Compute the present worth (i.e., the amount which, if invested today at 8% simple interest, will grow to Rs 9300 in 3 years). Also find the true discount (difference between the sum due and its present worth). Finally, which of the following values equals the true discount?

Introduction / Context:
This is a standard present worth (PW) and true discount (TD) question under simple interest. PW is the amount today that will accumulate to the future sum at the stated rate and time. TD is the difference between the face value due at maturity and the PW.

Given Data / Assumptions:

• Sum due (face value) S = Rs 9300.
• Simple interest rate r = 8% per annum.
• Time to maturity t = 3 years.

Concept / Approach:
Under simple interest, PW = S / (1 + r * t). True Discount TD = S - PW = S * r * t / (1 + r * t). These formulas follow directly from the linear growth of simple interest with time.

Step-by-Step Solution:

Verification / Alternative check:
Accruing PW for 3 years: 7500 * (1 + 0.08 * 3) = 7500 * 1.24 = 9300 ✔️, confirming the PW/TD values.

Why Other Options Are Wrong:
Rs 1860, 1850, 1890 do not satisfy TD = S - PW with PW computed at the stated rate and time; only Rs 1800 fits exactly.

Common Pitfalls:
Using compound interest (not asked), or mistakenly taking TD = S * r * t (that is the banker’s discount, not the true discount).

Final Answer:
True Discount = Rs 1800; Present Worth = Rs 7500 (correct option for TD is Rs 1,800).