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

Difficulty: Easy

Correct Answer: Rs. 612

Explanation:


Introduction / Context:
This is a straightforward compound interest calculation for a modest rate and time span. It requires application of the standard compound interest formula for annual compounding and careful handling of the arithmetic.


Given Data / Assumptions:

  • Principal P = Rs. 7500.
  • Rate of interest r = 4% per annum.
  • Time period t = 2 years.
  • Interest is compounded annually.


Concept / Approach:

With annual compounding, the amount after t years is A = P * (1 + r / 100)^t. The compound interest CI is given by CI = A - P. Here we substitute P = 7500, r = 4, t = 2, compute the amount, and subtract the principal to get the interest.


Step-by-Step Solution:

Step 1: Write the formula A = P * (1 + r / 100)^t. Step 2: Substitute the values P = 7500, r = 4, t = 2 to get A = 7500 * (1.04)^2. Step 3: Compute (1.04)^2 = 1.04 * 1.04 = 1.0816. Step 4: Therefore A = 7500 * 1.0816 = 8112. Step 5: Compound interest CI = A - P = 8112 - 7500 = 612.


Verification / Alternative check:

Break the process into yearly steps. After 1 year, amount is 7500 * 1.04 = 7800, so interest for the first year is 300. After the second year, interest is 4% of 7800 = 312, giving a new amount of 7800 + 312 = 8112. Total interest over 2 years is 300 + 312 = 612, which matches the previous result.


Why Other Options Are Wrong:

Rs. 712, Rs. 812, and Rs. 912 result from overestimating the interest or from incorrect multiplication of the interest factor. Only Rs. 612 is consistent with a 4% compound rate over 2 years.


Common Pitfalls:

A common mistake is to compute simple interest, namely 7500 * 4 * 2 / 100 = 600, and ignore the small extra interest earned on the first year interest. Others may round the intermediate product too early, slightly distorting the result.


Final Answer:

The compound interest is Rs. 612.

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