Compound Interest — An amount invested at a compound rate yields totals of ₹ 1,200 after year 1 and ₹ 1,587 after year 3. Find the annual rate of interest.

Introduction / Context:
Knowing the amount after 1 year and after 3 years under the same compound rate allows us to cancel the principal and isolate the growth factor.

Given Data / Assumptions:

• A1 = ₹ 1,200 = P*(1 + r)
• A3 = ₹ 1,587 = P*(1 + r)^3

Concept / Approach:
Divide A3 by A1: (1 + r)^2 = 1,587 / 1,200 = 1.3225. Hence 1 + r = √1.3225.

Step-by-Step Solution:
√1.3225 = 1.15 ⇒ r = 0.15 = 15% p.a.

Verification / Alternative check:
Check: A1 = P*1.15; A3 = P*1.15^3 = P*1.520875; ratio to A1 is 1.15^2 = 1.3225 matching 1,587/1,200.

Why Other Options Are Wrong:
They do not square to 1.3225 when added to 1.

Common Pitfalls:
Attempting to subtract amounts to find r rather than using the ratio method.

Final Answer:
15%