At what annual rate of compound interest, compounded annually, will a sum of Rs 10000 amount to Rs 12321 in 2 years?

Introduction / Context:
In this problem, the principal and the final amount after 2 years are given, and we need to find the annual compound interest rate. This is a standard reverse compound interest question where you use the relation between amount, principal, rate, and time to solve for the rate of interest.

Given Data / Assumptions:

• Principal P = Rs 10000.
• Amount after 2 years A = Rs 12321.
• Interest is compounded annually.
• Time t = 2 years.
• We must determine the annual rate of interest r.

Concept / Approach:
The compound interest amount formula is:
A = P * (1 + r / 100)^t Here t = 2, so:
A = P * (1 + r / 100)^2 We are given A and P, so we can solve for (1 + r / 100) and hence for r.

Step-by-Step Solution:
Substitute the values: 12321 = 10000 * (1 + r / 100)^2. Divide both sides by 10000: 12321 / 10000 = (1 + r / 100)^2. So (1 + r / 100)^2 = 1.2321. Note that 1.2321 is equal to 1.11^2 because 1.11 * 1.11 = 1.2321. Therefore 1 + r / 100 = 1.11. So r / 100 = 0.11, and r = 11% per annum.

Verification / Alternative Check:
Check by forward computation with r = 11%. Amount factor = (1.11)^2 = 1.2321. A = 10000 * 1.2321 = Rs 12321, which matches the given amount. This confirms that 11% is the correct rate.

Why Other Options Are Wrong:
22 percent would produce a much larger amount over 2 years. 7 percent and 15 percent do not give an amount as high as 12321 when applied to 10000 for 2 years.

Common Pitfalls:
Some learners may forget to take the square root when solving for (1 + r / 100). Others might incorrectly assume a simple interest relation, which is not appropriate here.

Final Answer:
The required rate of compound interest is 11 percent per annum.