What is the present worth of Rs. 2310 due 2.5 years (2 1/2 years) hence, if the rate of simple interest is 15% per annum?

Introduction / Context:
This problem asks for the present worth of a sum due after a certain time when the rate of simple interest is known. Present worth is the amount which, if invested now at the given rate, will accumulate to the future sum. In true discount terminology, the difference between the future sum and present worth is the true discount.

Given Data / Assumptions:

• Amount due in the future, S = Rs. 2310.
• Time t = 2.5 years = 2 and 1 / 2 years.
• Rate of simple interest r = 15 percent per annum.
• Present worth PW is unknown and must be found.
• Simple interest calculations are used throughout.

Concept / Approach:
If PW is the present worth of S due after time t at rate r, then: S = PW * (1 + r * t / 100). Equivalently: PW = S * 100 / (100 + r * t). We first compute the effective product r * t, then directly compute PW using the second formula. This is standard in discount and present value problems.

Step-by-Step Solution:
Step 1: Compute r * t. r = 15, t = 2.5 years, so r * t = 15 * 2.5 = 37.5. Step 2: Use PW formula: PW = S * 100 / (100 + r * t). PW = 2310 * 100 / (100 + 37.5) = 231000 / 137.5. Step 3: Compute 231000 / 137.5 to get PW = 1680. Thus the present worth is Rs. 1680.

Verification / Alternative check:
Confirm by forward calculation using simple interest. If PW = 1680 is invested at 15 percent for 2.5 years: Interest I = PW * r * t / 100 = 1680 * 15 * 2.5 / 100. First calculate 15 * 2.5 = 37.5. I = 1680 * 37.5 / 100 = 1680 * 0.375 = 630. Amount after 2.5 years = PW + I = 1680 + 630 = 2310. This matches the given future amount, confirming that the present worth is correctly found.

Why Other Options Are Wrong:
Values like Rs. 1440, Rs. 1600, Rs. 1750, or Rs. 1840 either produce too small or too large an amount when accumulated at 15 percent for 2.5 years. Only Rs. 1680 grows exactly to Rs. 2310, so only that satisfies the condition.

Common Pitfalls:
Errors usually arise from miscalculating r * t (for example, treating 2.5 years as 2 years or 25 years) or from mishandling decimal multiplication when computing the interest. Another issue is confusing present worth with the true discount; here we are asked for the present worth directly, not the discount. Always double check by recomputing the amount from the present worth to see if it matches the future sum.

Final Answer:
The present worth of Rs. 2310 due after 2.5 years at 15% per annum is Rs. 1680.