Find the present worth of ₹2310 due 2½ years hence at 15% per annum (simple interest).

Concept / Approach Under simple interest, present worth (PW) is the discounted value of a future amount A using the time–rate product R = r × t: PW = A / (1 + R) Here, r = 15% per annum and t = 2½ years.

Step-by-step calculation A = ₹2310 r = 15% = 0.15,  t = 2.5 → R = 0.15 × 2.5 = 0.375 PW = 2310 / (1 + 0.375) = 2310 / 1.375 Note: 1.375 = 11/8, so PW = 2310 × (8/11) = ₹1,680

Verification True Discount (TD) = A − PW = 2310 − 1680 = ₹630. Also, interest on PW for R = 0.375 should equal TD: I = PW × R = 1680 × 0.375 = ₹630 Matches perfectly.

Common pitfalls

• Using compound discount instead of simple interest discount.
• Incorrectly converting 2½ years (always use 2.5 in decimals).
• Rounding too early; here it divides cleanly via 8/11.

Final Answer ₹1,680