Compound Interest with Fractional Year — Find the amount receivable on ₹ 1,750 in 2.5 years at 8% per annum when interest is compounded annually (assume the standard rule for fractional years).

Introduction / Context:
When compounding is specified annually but the total time includes a fractional part (e.g., 0.5 year), the standard treatment is: compound for the full integer years, then add simple interest for the remaining fractional part on the amount after the integer years, computed at the same annual rate pro-rated for the fraction.

Given Data / Assumptions:

• Principal P = ₹ 1,750.
• Annual rate r = 8% = 0.08.
• Total time = 2.5 years: 2 full years + 0.5 year fractional part.

Concept / Approach:
Step 1: Compound for 2 years. Step 2: Apply simple interest for 0.5 year on the amount obtained after 2 years at the same rate, proportionally for 0.5 year.

Step-by-Step Solution:
Amount after 2 years: A2 = 1,750 * (1.08)^2 = 1,750 * 1.1664 = ₹ 2,041.20Interest for remaining 0.5 year: I_half = A2 * r * 0.5 = 2,041.20 * 0.08 * 0.5 = 2,041.20 * 0.04 = ₹ 81.648Total amount: A = A2 + I_half = 2,041.20 + 81.648 = ₹ 2,122.848 ≈ ₹ 2,122.85

Verification / Alternative check:
If we incorrectly compounded for 2.5 years as (1.08)^(2.5), we would implicitly assume sub-annual compounding, which is not stated. The standard textbook rule used here matches the provided options.

Why Other Options Are Wrong:
₹ 2,125 and ₹ 2,118 round or mis-apply the half-year step. ₹ 2,100 and ₹ 2,200 are rough estimates not consistent with precise calculation.

Common Pitfalls:
Treating 0.5 year as another compounding period when only annual compounding is specified; or applying the 8% to the original principal for the last half-year rather than to the amount after 2 years.

Final Answer:
₹ 2,122.85