Virat invested ₹83800 at 20% p.a. for 1 year at compound interest, compounded half-yearly. The amount received by him is:

Appeared in: DSSSB 13 August 2024

Explanation

The principal amount (P) is ₹83,800, the annual interest rate (R) is 20%, and the time (T) is 1 year.
Since interest is compounded half-yearly, the rate per period (r) becomes 20%/2 = 10%, and the number of periods (n) becomes 1*2 = 2.
Using the formula Amount = P(1 + r/100)ⁿ, we get Amount = 83800 * (1 + 10/100)².
This simplifies to 83800 * (1.1)² = 83800 * 1.21.
The final calculated amount is ₹101,398.

Option A: This value is a result of an incorrect calculation. It does not match the outcome of applying the correct compound interest formula with the given parameters.
Option C: This is a mathematically incorrect result. It might arise from miscalculation, such as an error in squaring 1.1 or in the final multiplication.
Option D: This value is also an incorrect calculation. It could be the result of calculating simple interest or making a significant error in the compound interest formula.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of amount using compound interest, compounded half-yearly as background academic context rather than a clinical decision trigger.
This question is from the General Intelligence and Reasoning section, which is a common component of nursing recruitment and entrance examinations.
Strong quantitative aptitude skills are necessary for nurses to pass these competitive exams and are also useful in clinical practice for tasks like medication dosage calculations.
What if the interest was compounded quarterly? The rate would be 20%/4 = 5% per quarter, and the number of periods would be 1*4 = 4. The amount would be A = 83800 * (1.05)⁴ ≈ ₹101,855.

How to Approach the Question

First, identify all the given data in the problem: Principal (P), annual rate (R), and time (T).
Next, check the compounding frequency. In this case, it is 'half-yearly'.
Adjust the annual rate (R) and time (T) to match the compounding frequency. Divide the annual rate by the number of compounding periods per year and multiply the time in years by the same number.
For half-yearly, divide the rate by 2 and multiply the time by 2.
Apply the standard compound interest formula: Amount = P * (1 + r/100)ⁿ, where 'r' is the adjusted rate and 'n' is the adjusted number of periods.
Calculate the final value and compare it with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculation of amount using compound interest, compounded half-yearly.
Stem keywords: invested, compound interest, compounded half-yearly, principal, rate, time
Lead-in keywords: amount received

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