Find the compound interest on Rs 7,500 at 4% per annum for 2 years, if the interest is compounded annually. Give your answer in rupees.

Introduction / Context:
This question is a straightforward computation of compound interest over 2 years with annual compounding. The principal, the rate, and the time are clearly given. We are asked specifically for the compound interest, not the final amount. This type of problem checks basic familiarity with the compound interest formula and the ability to perform simple percentage based calculations accurately.

Given Data / Assumptions:

• Principal (P) = Rs 7,500.
• Rate of interest (R) = 4% per annum.
• Time (T) = 2 years.
• Interest is compounded annually.
• No intermediate deposits or withdrawals are made.

Concept / Approach:
With annual compounding, the amount after T years is:
A = P * (1 + R / 100)^TOnce we find A, the compound interest CI is simply:
CI = A - PFor T = 2 years and R = 4%, the formula becomes:
A = 7500 * (1 + 4 / 100)^2 = 7500 * (1.04)^2

Step-by-Step Solution:
Step 1: Calculate the growth factor per year: 1 + R / 100 = 1 + 4 / 100 = 1.04.Step 2: Because the time is 2 years, square the factor: (1.04)^2 = 1.04 * 1.04 = 1.0816.Step 3: Multiply the principal by this factor to get the amount: A = 7500 * 1.0816.Step 4: Compute 7500 * 1.0816 = 8112.Step 5: The compound interest is CI = A - P = 8112 - 7500.Step 6: Subtract to find CI: 8112 - 7500 = 612.Step 7: Thus, the compound interest earned is Rs 612.

Verification / Alternative check:
We can compute year by year for confirmation. In year 1, interest = 7500 * 4 / 100 = 300, so amount = 7500 + 300 = 7800. In year 2, interest is calculated on 7800: interest = 7800 * 4 / 100 = 312, so final amount = 7800 + 312 = 8112. The total interest over 2 years is 8112 - 7500 = 612, which matches the result derived via the formula.

Why Other Options Are Wrong:
Rs.512, Rs.515, Rs.522, and Rs.600 do not match the total compound interest computed by applying 4% annually for 2 years. For example, Rs.600 would come from approximating 300 each year without updating the principal amount, which is effectively simple interest. The exact compounding adds a little extra interest in the second year, which brings the total to 612. Hence, only Rs.612 is correct.

Common Pitfalls:
A frequent mistake is to calculate simple interest for 2 years as 7500 * 4 * 2 / 100 = 600 and give this as the answer, ignoring that the question mentions compound interest. Some students also miscalculate 1.04^2 or round intermediate values too early. Using the year by year method as a check is a good way to reinforce correct reasoning and arithmetic.

Final Answer:
The compound interest on Rs 7,500 at 4% per annum for 2 years, compounded annually, is Rs.612.