Difficulty: Easy
Correct Answer: Rs. 15,000
Explanation:
Introduction / Context:
This is a reverse compound interest problem where the final amount, rate, and time are known, and we need to find the original principal. Such questions are typical when checking whether a given investment amount matches a known maturity value after a certain time at a fixed interest rate.
Given Data / Assumptions:
Concept / Approach:
The compound amount formula for annual compounding is:
A = P * (1 + r / 100)^TGiven A, r, and T, we solve for P:
P = A / (1 + r / 100)^TBecause 10% is a common rate, we can quickly compute (1.1)^3.
Step-by-Step Solution:
Step 1: Compute the growth factor.1 + r / 100 = 1 + 10 / 100 = 1.1(1.1)^3 = 1.331Step 2: Use the formula for principal.P = 19965 / 1.331Step 3: Perform the division.P ≈ Rs. 15,000Indeed, 15000 * 1.331 = 19965
Verification / Alternative check:
We can directly compute the amount produced by a principal of Rs. 15,000 at 10% compound interest for 3 years and verify that it equals Rs. 19,965:
A = 15000 * (1.1)^3 = 15000 * 1.331 = 19965This exactly matches the given amount, confirming that the principal is Rs. 15,000.
Why Other Options Are Wrong:
Rs. 16,000, Rs. 17,000, Rs. 18,000: These would yield amounts higher than Rs. 19,965 when multiplied by 1.331.Rs. 14,000: This would yield an amount less than Rs. 19,965, so it cannot be the correct principal.
Common Pitfalls:
Some learners mistakenly subtract interest or use simple interest formulas. Others forget to divide by the full growth factor (1.1)^3 and divide only by (1.1). Always remember that compound growth over multiple years is exponential, not linear, and that the principal is found by dividing the final amount by the total growth factor.
Final Answer:
The original principal amount invested was Rs. 15,000.
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