Compound Interest – Amount after half the time: If ₹ 3,000 becomes ₹ 4,329 at compound interest in a certain time, what will ₹ 3,000 amount to in half of that time (same rate, same compounding)?

Introduction / Context:
Compound growth over time is multiplicative. Knowing the full-period amount factor allows us to take the square root to get the half-period factor (for equal subperiods).

Given Data / Assumptions:

• P = ₹ 3,000
• Amount in full time = ₹ 4,329 → growth factor G = 4329/3000 = 1.443
• Half the time → factor = √G

Concept / Approach:
For equal halves of time at the same rate, the mid-time amount is P * √G.

Step-by-Step Solution:
√1.443 ≈ 1.20125Amount at half time ≈ 3000 * 1.20125 = ₹ 3,603.75Closest listed option = ₹ 3,600

Verification / Alternative check:
Squaring 1.20125 gives ≈ 1.443 (returns the full-period factor as required).

Why Other Options Are Wrong:
₹ 3,520 and ₹ 3,400 are too low; ₹ 38,000 is clearly a typo/misfit.

Common Pitfalls:
Halving the rupee interest from the full period instead of taking the square root of the factor.

Final Answer:
₹ 3600