Recover the principal from two CI snapshots 3 years apart: A sum becomes ₹ 6690 after 3 years and ₹ 10035 after 6 years at compound interest (same annual rate). What is the original principal (sum)?

Introduction / Context:
Knowing amounts at two times that are exactly 3 years apart lets us find (1 + r)^3 from their ratio. Dividing the earlier amount by this factor gives the principal directly, avoiding separate rate computation.

Given Data / Assumptions:

• A(3 years) = ₹ 6690
• A(6 years) = ₹ 10035
• Annual compounding at fixed r

Concept / Approach:
A(6)/A(3) = (1 + r)^3. Therefore (1 + r)^3 = 10035/6690 = 1.5. Hence the principal P = A(3) / (1 + r)^3 = A(3) / 1.5.

Step-by-Step Solution:
(1 + r)^3 = 10035 / 6690 = 1.5P = 6690 / 1.5 = ₹ 4460

Verification / Alternative check:
If P = 4460, then A(3) = 4460 * 1.5 = 6690 (given), and A(6) = 6690 * 1.5 = 10035 (consistent).

Why Other Options Are Wrong:
₹ 4400, ₹ 4445, or ₹ 4520 do not maintain the exact 1.5 growth from year 3 to year 6 when multiplied by (1 + r)^3.

Common Pitfalls:
Trying to compute r via cube root first; while valid, it is unnecessary when the question only asks for the principal.

Final Answer:
₹ 4460