A sum becomes ₹ 2916 in 2 years at 8% per annum compound interest. Then sum is

Appeared in: RRB Staff Nurse Ahmedabad-2015

Explanation

The problem requires finding the principal amount (P) using the compound interest formula: A = P(1 + R/100)ⁿ.
Given values are Amount (A) = ₹2916, Rate (R) = 8%, and Time (n) = 2 years.
Substituting the values: 2916 = P(1 + 8/100)², which simplifies to 2916 = P(1.08)² or 2916 = P(1.1664).
Solving for P gives P = 2916 / 1.1664, which equals ₹2500.

Option A: This value is incorrect and likely arises from a miscalculation, such as an error in squaring the term (1 + R/100) or an arithmetic mistake while solving for P.
Option C: This value is very close to the final amount (₹ 2916) and is incorrect. It might be chosen by someone who misunderstands that the principal must be less than the final amount.
Option D: This value is incorrect. It could be the result of a calculation error, perhaps by incorrectly applying the interest rate or making a mistake in the final multiplication/division.

Visual 1: Infographic: A chart illustrating the compound interest formula A = P(1 + R/100)ⁿ with each component (Principal, Rate, Time, Amount) clearly labeled and explained.
Visual 2: Flowchart: A step-by-step visual guide on how to rearrange the compound interest formula to solve for the Principal (P) when the Amount (A) is known.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the Principal in Compound Interest as background academic context rather than a clinical decision trigger.
This question tests fundamental quantitative aptitude skills, which are essential for various competitive exams, including those for nursing positions, to assess analytical and problem-solving abilities.
Understanding financial concepts like compound interest is a useful life skill for personal financial planning, such as managing savings, loans, and investments.
What if the interest was simple instead of compound? The simple interest for 2 years would be P * 8 * 2 / 100 = 0.16P. The amount would be P + 0.16P = 1.16P = 2916. Then P would be 2916 / 1.16 ≈ ₹2513.79, which is not among the options.

How to Approach the Question

First, identify all the given data in the problem: the final amount (A = ₹2916), the time period (n = 2 years), and the rate of interest (R = 8%).
Recognize that the question involves 'compound interest' and requires finding the initial 'sum' or Principal (P).
Recall the standard formula for compound interest: A = P(1 + R/100)ⁿ.
Substitute the known values into the formula: 2916 = P(1 + 8/100)².
Perform the calculation step-by-step to isolate and solve for the unknown variable P.
Compare the calculated result with the given options to find the correct answer.

Concept Tested & Keywords

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