Difficulty: Easy
Correct Answer: Rs 16400
Explanation:
Introduction:
This question focuses on the relationship between simple interest and compound interest for a short period of 2 years. There is a well known shortcut formula for the difference between compound interest and simple interest over 2 years, which makes the calculation much faster than computing each interest separately.
Given Data / Assumptions:
Concept / Approach:
For 2 years at rate r% per annum compounded annually, the difference between compound interest and simple interest is given by the formula: Difference = P * (r/100)^2. This arises from the additional interest earned in the second year on the first year’s interest. Using this compact relation allows us to solve directly for the principal without separately computing CI and SI.
Step-by-Step Solution:
Difference = P * (r/100)^2Here, r = 5%, so r/100 = 0.05Therefore, Difference = P * (0.05)^2 = P * 0.0025We are given: P * 0.0025 = 41So P = 41 / 0.0025P = 41 * 400 = Rs 16400
Verification / Alternative Check:
You can compute SI and CI explicitly. Simple interest for 2 years: SI = P * r * t / 100 = 16400 * 5 * 2 / 100 = Rs 1640. Amount under CI after 2 years: A = 16400 * (1 + 0.05)^2 = 16400 * 1.1025 = Rs 18081. CI = 18081 - 16400 = Rs 1681. Difference = 1681 - 1640 = Rs 41, which confirms the correctness of the principal.
Why Other Options Are Wrong:
Rs 7200, Rs 9600, Rs 8400, and Rs 8800: Each of these values, when substituted into the formula P * (0.05)^2, gives a difference that is not equal to Rs 41. They therefore cannot satisfy the given condition.
Common Pitfalls:
An often seen error is to confuse the formula and use r/100 instead of (r/100)^2. Another mistake is to apply the shortcut even when the period is not exactly 2 years or when compounding is not annual, which can lead to incorrect answers in more complex scenarios.
Final Answer:
The required principal (sum of money) is Rs 16400.
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