Find the compound interest on Rs 7500 at 4% per annum for 2 years, if the interest is compounded annually.

Introduction:
This question is a direct application of the compound interest formula with annual compounding. It is a standard type of problem in aptitude tests to check whether you can correctly compute the amount and then derive the compound interest from it.

Given Data / Assumptions:

• Principal (P) = Rs 7500.
• Rate of interest (r) = 4% per annum.
• Time (t) = 2 years.
• Interest is compounded annually.
• We must find the compound interest (CI) only.

Concept / Approach:
The standard amount formula for compound interest with annual compounding is A = P * (1 + r/100)^t. The compound interest earned is CI = A − P. We simply substitute the given values of P, r and t into the formula, compute the amount and subtract the principal.

Step-by-Step Solution:
Given P = 7500, r = 4%, t = 2 years.Amount after 2 years: A = 7500 * (1 + 4/100)^2 = 7500 * (1.04)^2(1.04)^2 = 1.0816So A = 7500 * 1.0816 = Rs 8112Compound interest CI = A − P = 8112 − 7500 = Rs 612

Verification / Alternative Check:
You can also compute interest year by year. First year: I1 = 7500 * 4% = 300, amount = 7800. Second year: I2 = 7800 * 4% = 312, amount = 8112. Total interest = 300 + 312 = Rs 612, which confirms the earlier calculation.

Why Other Options Are Wrong:
Rs 512, Rs 515 and Rs 522: These underestimate the interest, possibly coming from arithmetic mistakes or use of simple interest.Rs 620: Slightly higher than the correct value and may result from rounding errors or miscalculations in squaring 1.04.

Common Pitfalls:
Students sometimes miscalculate (1.04)^2 or mistakenly use 1.08 instead of 1.04. Others erroneously apply simple interest by multiplying P * r * t / 100, which would give only Rs 600, not the correct compound interest of Rs 612.

Final Answer:
The compound interest on Rs 7500 at 4% per annum for 2 years is Rs 612.