Virat invested ₹52500 at 8% p.a. for 1 year at compound interest, compounded half-yearly. The amount received by him is:

Appeared in: DSSSB 14 August 2024

Explanation

The core concept is compound interest calculated semi-annually.
The annual interest rate of 8% must be halved to 4% to reflect the half-yearly period.
The time period of 1 year must be doubled to 2, representing the two half-year compounding periods.
Applying the formula A = P(1 + r/100)ⁿ gives: A = 52500 * (1 + 4/100)².
Solving the equation: 52500 * (1.04)² = 52500 * 1.0816 = 56784.

Option B: This value is incorrect and likely results from a calculation error, such as miscalculating (1.04)² or an error in the final multiplication.
Option C: This value is incorrect. It might be the result of incorrectly applying the interest rate or the number of periods in the compound interest formula.
Option D: This value is incorrect. A possible error could be calculating simple interest for one year (₹4200, total ₹56700) and then making another calculation mistake.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Compound Interest (Half-Yearly Compounding) as background academic context rather than a clinical decision trigger.
This question tests basic mathematical and aptitude skills, which are essential for various non-nursing sections of competitive examinations.
Strong numeracy skills are important for problem-solving in general, a key competency for any professional role.
What if the interest was compounded quarterly? The rate 'r' would be 8%/4 = 2%, and the number of periods 'n' would be 1*4 = 4. The amount would be A = 52500 * (1.02)⁴ ≈ ₹56814.21.

How to Approach the Question

First, identify the key data from the question: Principal (P=₹52500), Annual Rate (R=8%), and Time (T=1 year).
Note the compounding frequency, which is 'half-yearly'. This is the most critical piece of information.
Adjust the rate and time period for the given frequency. For half-yearly: divide the annual rate by 2 and multiply the time in years by 2.
Recall the formula for compound amount: A = P(1 + r/100)ⁿ.
Substitute the adjusted values into the formula and perform the calculation carefully.
Compare the final calculated amount with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Compound Interest (Half-Yearly Compounding)
Stem keywords: invested, ₹52500, 8% p.a., 1 year, compound interest, compounded half-yearly
Lead-in keywords: amount received

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Practise the full DSSSB 14 August 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.