At 10% per annum compound interest, the amount received after 3 years is Rs. 5,324. What was the principal (in rupees) invested originally?

Introduction / Context:
This question reverses the usual compound interest calculation. Instead of finding the amount from a known principal, we are given the final amount and must work backwards to find the original principal. Such reverse calculations are common in financial planning and loan analysis.

Given Data / Assumptions:

• Amount after 3 years A = Rs. 5,324.
• Annual interest rate r = 10% per annum.
• Time period n = 3 years.
• Interest is compounded annually.
• We need to find the initial principal P.

Concept / Approach:
Under annual compounding, the relationship between principal and amount is A = P * (1 + r)^n. To find P, we rearrange the formula to P = A / (1 + r)^n. Since r and n are known, we can compute the denominator and divide the given amount by it to obtain the original principal.

Step-by-Step Solution:
Step 1: Write the compound interest formula A = P * (1 + r)^n.Step 2: Rearrange to get P = A / (1 + r)^n.Step 3: Substitute values: A = 5,324, r = 0.10, n = 3.Step 4: Compute (1 + r)^n = (1.10)^3 = 1.331.Step 5: Calculate P = 5,324 / 1.331.Step 6: Numerically, 5,324 / 1.331 is approximately 4,000, so the original principal is Rs. 4,000.

Verification / Alternative check:
We can verify by applying 10% compound interest on Rs. 4,000 for 3 years. After 1 year, amount is 4,000 * 1.10 = 4,400. After 2 years, amount is 4,400 * 1.10 = 4,840. After 3 years, amount is 4,840 * 1.10 = 5,324. This matches the given amount exactly, confirming that the original principal was Rs. 4,000.

Why Other Options Are Wrong:

• 4100: At 10% for 3 years, this would grow to 4,100 * 1.331 = 5,457.1, which is larger than 5,324.
• 4200: This would grow to about 4,200 * 1.331 = 5,590.2, also larger than the given amount.
• 4300: This would grow to about 4,300 * 1.331 = 5,756.3, again not equal to 5,324.

Common Pitfalls:
Some students incorrectly treat the given amount as the interest, not the total amount, and subtract or add incorrectly. Others attempt to subtract simple interest instead of using the compound interest formula. It is important to clearly identify that 5,324 is the final amount after compounding, and therefore the principal must be found by dividing by the compound factor, not by subtracting a linear interest estimate.

Final Answer:
The original principal invested was Rs. 4000.