Compound Interest — SBI lends ₹ 1,331 lakh to TATA and receives ₹ 1,728 lakh after 3 years with annual compounding. Find the annual rate of interest.

Introduction / Context:
When both the principal and amount are perfect cubes, recognizing the cube ratio directly yields the growth factor per year.

Given Data / Assumptions:

• P = 1,331 lakh; A (3 years) = 1,728 lakh.
• Annual compounding for 3 years.

Concept / Approach:
(1 + r)^3 = A / P. Note 1,331 = 11^3 and 1,728 = 12^3. Therefore (1 + r)^3 = (12/11)^3 ⇒ 1 + r = 12/11.

Step-by-Step Solution:
1 + r = 12/11 ⇒ r = (12/11) − 1 = 1/11 ≈ 0.0909r ≈ 9.09% per annum

Verification / Alternative check:
Apply 9.09% for 3 years: P*(1 + 1/11)^3 = 11^3*(12/11)^3 = 12^3, matching A.

Why Other Options Are Wrong:
11% and 12% overshoot; 8.33% undershoots; 10% gives 1.1^3 = 1.331, not 1.299... ratio required.

Common Pitfalls:
Using simple interest formula or comparing linear differences instead of cube roots.

Final Answer:
9.09%