Compound Interest – Find annual rate from 2-year growth: At what annual compound-interest rate will ₹ 1,200 become ₹ 1,348.32 in 2 years?

Introduction / Context:
When the starting principal and ending amount over a set number of years are known, the unknown annual compound rate can be obtained by inverting the compound growth equation and taking a root appropriate to the time period.

Given Data / Assumptions:

• P = 1,200
• A = 1,348.32
• t = 2 years, compounded annually

Concept / Approach:
Use A = P * (1 + r)^t ⇒ (1 + r)^2 = A / P. Then 1 + r = sqrt(A / P). Subtract 1 and convert to percent to get the rate.

Step-by-Step Solution:
A / P = 1,348.32 / 1,200 = 1.12361 + r = sqrt(1.1236) = 1.06Therefore r = 1.06 − 1 = 0.06 = 6%

Verification / Alternative check:
Forward check: 1,200 * (1.06)^2 = 1,200 * 1.1236 = 1,348.32, confirming the rate exactly.

Why Other Options Are Wrong:
Rates 7%, 7.5%, and 6.5% produce larger growth than 1.1236 over 2 years; 5% produces less and does not reach ₹ 1,348.32.

Common Pitfalls:
Using simple interest or averaging methods will not match exponential compounding over more than one year; always use roots for reversing compounded growth.

Final Answer:
6%