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

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

The question requires finding the principal (P) given the final amount (A), rate (R), and time (n) for compound interest.
The formula for the final amount is A = P(1 + R/100)^n.
Rearranging to solve for P gives P = A / (1 + R/100)^n.
Substituting the values: P = 2916 / (1 + 8/100)^2.
Calculation: P = 2916 / (1.08)^2 = 2916 / 1.1664 = 2500.

Option A: This value is incorrect. It may result from a miscalculation, such as using an incorrect interest rate or time period in the formula.
Option C: This option has the correct numerical value but is a duplicate of option B. In a standard multiple-choice question, there should be only one correct option.
Option D: This value is incorrect. It might be obtained by incorrectly applying the interest calculation, perhaps by confusing simple and compound interest or making an arithmetic error.

Visual 1: Infographic: A chart comparing the growth of an investment with simple interest versus compound interest over time to visually highlight the accelerating nature of compound interest.
Visual 2: Flowchart: A diagram showing the step-by-step process of calculating the principal when the final amount, rate, and time are known for compound interest.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the principal amount using the compound interest formula as background academic context rather than a clinical decision trigger.
Understanding compound interest is a fundamental life skill for financial planning, including saving for retirement, understanding loans, and making investment decisions.
This concept is crucial for managing personal finances, such as calculating returns on fixed deposits, mutual funds, or understanding the total cost of a long-term loan.
What if the interest was simple instead of compound? The formula would be A = P(1 + (R/100)*n). Then, 2916 = P(1 + (8/100)*2) = P(1.16). The principal would be P = 2916 / 1.16 = Rs. 2513.79. This shows that compound interest results in a higher final amount, so the initial principal required is lower for the same outcome.

How to Approach the Question

First, identify all the given variables from the question: Final Amount (A = 2916), Time (n = 2 years), and Rate (R = 8%).
Identify what you need to find: The Principal Sum (P).
Recall the correct formula for compound interest: A = P(1 + R/100)^n.
Rearrange the formula to solve for the unknown variable, P. This gives P = A / (1 + R/100)^n.
Substitute the known values into the rearranged formula.
Perform the calculation step-by-step to avoid errors: first the parenthesis, then the exponent, and finally the division.

Concept Tested & Keywords

Concept Tested: Calculating the principal amount using the compound interest formula.
Stem keywords: sum, 2 years, 8% per annum, compound interest, Rs. 2916
Lead-in keywords: the sum is

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