Find compound interest on Rs. 5000 at 12% p.a. for 1 year, compounded half-yearly.

Appeared in: RRB Staff Nurse Jaipur-6th June 2018

Explanation

For interest compounded half-yearly, the annual rate is halved and the time period is doubled.
The new rate (r) becomes 12% / 2 = 6% per half-year.
The new number of periods (n) becomes 1 year * 2 = 2 half-years.
Using the formula A = P(1 + r/100)ⁿ, the amount is A = 5000 * (1 + 6/100)² = 5000 * 1.1236 = Rs. 5618.
Compound Interest (CI) is the difference between the final amount and the principal: CI = 5618 - 5000 = Rs. 618.

Option A: This value is incorrect. It may result from a miscalculation, such as using an incorrect rate or making an arithmetic error during the multiplication step.
Option C: This value is incorrect. It is close to the simple interest for the period (Rs. 600) but does not accurately account for the compounding effect over two periods.
Option D: This value is incorrect. It might arise from incorrectly applying the formula, for instance, by not squaring the (1 + r/100) term correctly or using an approximated value.

Visual 1: Flowchart: Step-by-step process for calculating compound interest. This would show how to identify P, R, T, adjust for compounding frequency, apply the formula, and find the final interest amount.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of Compound Interest (Compounded Half-Yearly) as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and aptitude, which is a component of many competitive examinations, including those for nursing positions.
While not a direct clinical skill, strong mathematical aptitude is essential for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data charts, where precision is critical for patient safety.
What if the interest was compounded quarterly? The rate would be divided by 4 (12%/4 = 3%) and the time period would be multiplied by 4 (1 year * 4 = 4 quarters). The CI would then be 5000 * (1.03)⁴ - 5000 ≈ Rs. 627.74.

How to Approach the Question

First, identify all the given values from the question: Principal (P = Rs. 5000), annual interest rate (R = 12%), and time period (T = 1 year).
Next, carefully read the compounding condition, which is 'compounded half-yearly'.
Adjust the rate and time based on this condition. For half-yearly, divide the annual rate by 2 and multiply the time in years by 2.
The new rate (r) is 12/2 = 6%. The new number of periods (n) is 1 * 2 = 2.
Apply the compound interest formula to find the total amount: A = P * (1 + r/100)ⁿ.
Calculate the final value: A = 5000 * (1 + 6/100)².

Concept Tested & Keywords

Concept Tested: Calculation of Compound Interest (Compounded Half-Yearly)
Stem keywords: compound interest, Rs. 5000, 12% p.a., 1 year, compounded half-yearly
Lead-in keywords: Find

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