Simple vs Compound Interest – Given SI and CI to find the rate: On a certain sum, the simple interest for 2 years is ₹ 120, while the compound interest for the same period is ₹ 129. Find the annual rate of interest.

Introduction / Context:
Relating SI and CI over 2 years allows solving for the rate using two equations: SI = P * r * t / 100, and CI = SI + P * r^2 / 10000.

Given Data / Assumptions:

• SI (2 years) = ₹ 120
• CI (2 years) = ₹ 129
• t = 2 years

Concept / Approach:
Let P be principal and r the rate (% per annum). From SI: 2Pr/100 = 120 → Pr = 6000. From CI − SI: P * r^2 / 10000 = 9.

Step-by-Step Solution:
Pr = 6000 → r = 6000 / PP * r^2 / 10000 = 9 → (P * (6000/P)^2) / 10000 = 936,000,000 / (10000 * P) = 9 → 3600 / P = 9 → P = 400r = 6000 / 400 = 15% per annum

Verification / Alternative check:
At P = 400, SI = 400 * 15% * 2 = 120; CI − SI = 400 * 15^2 / 10000 = 9 → CI = 129 (matches).

Why Other Options Are Wrong:
12% and 14% do not satisfy both SI and CI simultaneously.

Common Pitfalls:
Forgetting the CI − SI relation for 2 years or mixing percent and decimal.

Final Answer:
15%