Difficulty: Easy
Correct Answer: Rs. 8000
Explanation:
Introduction / Context:
In this problem we work backwards from a known maturity amount under compound interest to determine the original principal. The interest rate and time are given, and we know that interest is compounded annually at a fixed rate of 10% per annum.
Given Data / Assumptions:
Concept / Approach:
For annual compounding, the relationship between amount and principal is:
A = P * (1 + r/100)^t. Here, r = 10 and t = 3, so:
A = P * (1.10)^3. We rearrange this formula to solve for P by dividing the amount by the growth factor (1.10)^3.
Step-by-Step Solution:
Step 1: Compute the growth factor for 3 years. (1.10)^3 = 1.1 * 1.1 * 1.1 = 1.331. Step 2: Use A = P * 1.331. 10,648 = P * 1.331. Step 3: Solve for P. P = 10,648 / 1.331 = 8000.
Verification / Alternative check:
Check by recomputing the amount from P = Rs. 8000. After 3 years at 10% compounded annually:
A = 8000 * (1.10)^3 = 8000 * 1.331 = 10,648. This matches the given final amount, confirming that the original principal must indeed have been Rs. 8000.
Why Other Options Are Wrong:
If P were Rs. 9000, then A = 9000 * 1.331 = 11,979, which is too high. For Rs. 8500, A would be 11,303.5; for Rs. 7500, A would be 9,982.5, which is too low. Only Rs. 8000 yields exactly the given maturity amount.
Common Pitfalls:
Students sometimes forget that the exponent must match the number of years and may accidentally multiply the rate by time instead of raising the factor to a power, effectively using simple interest instead of compound interest. Another mistake is rounding the growth factor too early, which can slightly distort the final answer. When the numbers are chosen cleanly, as here, the exact factor (1.331) leads to an integer principal.
Final Answer:
The principal originally invested was Rs. 8000.
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