If Rs. 10,000 amounts to Rs. 11,664 when invested at compound interest compounded annually for 2 years, what is the annual rate of compound interest (in percent)?

Introduction:
Here we are given the initial principal, the final amount after 2 years, and the fact that interest is compounded annually. The task is to determine the annual compound interest rate that transforms Rs. 10,000 into Rs. 11,664 in 2 years.

Given Data / Assumptions:

• Principal (P) = Rs. 10,000.
• Amount after 2 years (A) = Rs. 11,664.
• Compounding frequency = once per year (annually).
• Time (t) = 2 years.

Concept / Approach:
The compound amount formula with annual compounding is:
A = P * (1 + r/100)^tWe know A, P, and t, and we must find r. Rearranging gives:
(1 + r/100)^t = A / PTaking the square root for t = 2, we find 1 + r/100, then solve for r.

Step-by-Step Solution:
Step 1: Write the relation: 11,664 = 10,000 * (1 + r/100)^2.Step 2: Divide both sides by 10,000: (1 + r/100)^2 = 11,664 / 10,000 = 1.1664.Step 3: Take the square root of both sides: 1 + r/100 = sqrt(1.1664).Step 4: Compute the square root: sqrt(1.1664) = 1.08.Step 5: Therefore 1 + r/100 = 1.08, which implies r/100 = 0.08.Step 6: Multiply by 100 to get r: r = 8%.So the annual compound interest rate is 8% per annum.

Verification / Alternative check:
Verify by computing the amount at 8% for 2 years: First year amount = 10,000 * 1.08 = 10,800. Second year amount = 10,800 * 1.08 = 11,664. The computed final amount matches the given amount, confirming that 8% is correct.

Why Other Options Are Wrong:
At 6% or 7%, the two year amount would be less than 11,664 because (1.06)^2 and (1.07)^2 are smaller than 1.1664. At 9% or 10%, the amount would exceed 11,664 since (1.09)^2 and (1.10)^2 give larger growth factors. Only 8% gives exactly the required increase from 10,000 to 11,664 over 2 years.

Common Pitfalls:
Students may try to use the simple interest formula or average two years of increase, which does not work with compounding. Others may forget to take the square root when isolating 1 + r/100. Always use the compound interest formula and carefully apply exponents and roots when solving for the rate.

Final Answer:
The annual rate of compound interest that turns Rs. 10,000 into Rs. 11,664 in 2 years is 8% per annum.